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+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so uh today we're
+
+ align:start position:0%
+ocw.mit.edu all right so uh today we're
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so uh today we're
+continuing in oxidation reduction and so
+
+ align:start position:0%
+continuing in oxidation reduction and so
+ 
+
+ align:start position:0%
+continuing in oxidation reduction and so
+we started this a little bit last week
+
+ align:start position:0%
+we started this a little bit last week
+ 
+
+ align:start position:0%
+we started this a little bit last week
+and we talked about uh briefly about
+
+ align:start position:0%
+and we talked about uh briefly about
+ 
+
+ align:start position:0%
+and we talked about uh briefly about
+balancing equations which as you recall
+
+ align:start position:0%
+balancing equations which as you recall
+ 
+
+ align:start position:0%
+balancing equations which as you recall
+is really about counting so it's not uh
+
+ align:start position:0%
+is really about counting so it's not uh
+ 
+
+ align:start position:0%
+is really about counting so it's not uh
+an intellectually challenging topic and
+
+ align:start position:0%
+an intellectually challenging topic and
+ 
+
+ align:start position:0%
+an intellectually challenging topic and
+just requires uh you know making sure
+
+ align:start position:0%
+just requires uh you know making sure
+ 
+
+ align:start position:0%
+just requires uh you know making sure
+that you've counted everything
+
+ align:start position:0%
+that you've counted everything
+ 
+
+ align:start position:0%
+that you've counted everything
+appropriately so you have to be a little
+
+ align:start position:0%
+appropriately so you have to be a little
+ 
+
+ align:start position:0%
+appropriately so you have to be a little
+bit careful but doing it but it's really
+
+ align:start position:0%
+bit careful but doing it but it's really
+ 
+
+ align:start position:0%
+bit careful but doing it but it's really
+not too hard so being able to balance
+
+ align:start position:0%
+not too hard so being able to balance
+ 
+
+ align:start position:0%
+not too hard so being able to balance
+oxidation reduction equations then
+
+ align:start position:0%
+oxidation reduction equations then
+ 
+
+ align:start position:0%
+oxidation reduction equations then
+allows you to go on and do the to talk
+
+ align:start position:0%
+allows you to go on and do the to talk
+ 
+
+ align:start position:0%
+allows you to go on and do the to talk
+about the things that we'll be talking
+
+ align:start position:0%
+about the things that we'll be talking
+ 
+
+ align:start position:0%
+about the things that we'll be talking
+about today so today we're going to
+
+ align:start position:0%
+about today so today we're going to
+ 
+
+ align:start position:0%
+about today so today we're going to
+cover electrochemical cells fad law and
+
+ align:start position:0%
+cover electrochemical cells fad law and
+ 
+
+ align:start position:0%
+cover electrochemical cells fad law and
+the relationship between Delta G and uh
+
+ align:start position:0%
+the relationship between Delta G and uh
+ 
+
+ align:start position:0%
+the relationship between Delta G and uh
+cell potential so everyone could quiet
+
+ align:start position:0%
+cell potential so everyone could quiet
+ 
+
+ align:start position:0%
+cell potential so everyone could quiet
+down a little bit I can hear a lot of uh
+
+ align:start position:0%
+down a little bit I can hear a lot of uh
+ 
+
+ align:start position:0%
+down a little bit I can hear a lot of uh
+noise in the background I realize you're
+
+ align:start position:0%
+noise in the background I realize you're
+ 
+
+ align:start position:0%
+noise in the background I realize you're
+still settling down and pulling out your
+
+ align:start position:0%
+still settling down and pulling out your
+ 
+
+ align:start position:0%
+still settling down and pulling out your
+notes um so as as I've mentioned all the
+
+ align:start position:0%
+notes um so as as I've mentioned all the
+ 
+
+ align:start position:0%
+notes um so as as I've mentioned all the
+way through the lectures I've given so
+
+ align:start position:0%
+way through the lectures I've given so
+ 
+
+ align:start position:0%
+way through the lectures I've given so
+far that you have to remember all the
+
+ align:start position:0%
+far that you have to remember all the
+ 
+
+ align:start position:0%
+far that you have to remember all the
+things you've learned because they're
+
+ align:start position:0%
+things you've learned because they're
+ 
+
+ align:start position:0%
+things you've learned because they're
+going to come back again so today we'll
+
+ align:start position:0%
+going to come back again so today we'll
+ 
+
+ align:start position:0%
+going to come back again so today we'll
+be back to thermodynamics and talking
+
+ align:start position:0%
+be back to thermodynamics and talking
+ 
+
+ align:start position:0%
+be back to thermodynamics and talking
+about spontaneous reactions in Delta G
+
+ align:start position:0%
+about spontaneous reactions in Delta G
+ 
+
+ align:start position:0%
+about spontaneous reactions in Delta G
+so this all ties in together this un
+
+ align:start position:0%
+so this all ties in together this un
+ 
+
+ align:start position:0%
+so this all ties in together this un
+these units are really more applications
+
+ align:start position:0%
+these units are really more applications
+ 
+
+ align:start position:0%
+these units are really more applications
+of things that you've already learned in
+
+ align:start position:0%
+of things that you've already learned in
+ 
+
+ align:start position:0%
+of things that you've already learned in
+the first half of the
+
+ align:start position:0%
+the first half of the
+ 
+
+ align:start position:0%
+the first half of the
+course and currently we're in in chapter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+12 so an electrochemical cell what is an
+
+ align:start position:0%
+12 so an electrochemical cell what is an
+ 
+
+ align:start position:0%
+12 so an electrochemical cell what is an
+electric chemical cell uh well it's any
+
+ align:start position:0%
+electric chemical cell uh well it's any
+ 
+
+ align:start position:0%
+electric chemical cell uh well it's any
+device in which you have an electric
+
+ align:start position:0%
+device in which you have an electric
+ 
+
+ align:start position:0%
+device in which you have an electric
+current and electric current is just the
+
+ align:start position:0%
+current and electric current is just the
+ 
+
+ align:start position:0%
+current and electric current is just the
+flow of electrons through a circuit and
+
+ align:start position:0%
+flow of electrons through a circuit and
+ 
+
+ align:start position:0%
+flow of electrons through a circuit and
+it's either the current is either
+
+ align:start position:0%
+it's either the current is either
+ 
+
+ align:start position:0%
+it's either the current is either
+produced by a a spontaneous reaction see
+
+ align:start position:0%
+produced by a a spontaneous reaction see
+ 
+
+ align:start position:0%
+produced by a a spontaneous reaction see
+where Delta G is going to come into this
+
+ align:start position:0%
+where Delta G is going to come into this
+ 
+
+ align:start position:0%
+where Delta G is going to come into this
+it's either produced by spontaneous
+
+ align:start position:0%
+it's either produced by spontaneous
+ 
+
+ align:start position:0%
+it's either produced by spontaneous
+reaction or used to bring about a
+
+ align:start position:0%
+reaction or used to bring about a
+ 
+
+ align:start position:0%
+reaction or used to bring about a
+non-spontaneous reaction so you can use
+
+ align:start position:0%
+non-spontaneous reaction so you can use
+ 
+
+ align:start position:0%
+non-spontaneous reaction so you can use
+uh an electrochemical cell to force a
+
+ align:start position:0%
+uh an electrochemical cell to force a
+ 
+
+ align:start position:0%
+uh an electrochemical cell to force a
+non-spontaneous reaction to go so a
+
+ align:start position:0%
+non-spontaneous reaction to go so a
+ 
+
+ align:start position:0%
+non-spontaneous reaction to go so a
+battery which most of you are are
+
+ align:start position:0%
+battery which most of you are are
+ 
+
+ align:start position:0%
+battery which most of you are are
+familiar with and Ed in many of uh the
+
+ align:start position:0%
+familiar with and Ed in many of uh the
+ 
+
+ align:start position:0%
+familiar with and Ed in many of uh the
+gadgets that you have is really just a
+
+ align:start position:0%
+gadgets that you have is really just a
+ 
+
+ align:start position:0%
+gadgets that you have is really just a
+collection of these uh electrochemical
+
+ align:start position:0%
+collection of these uh electrochemical
+ 
+
+ align:start position:0%
+collection of these uh electrochemical
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+and as we'll see um perhaps at the end
+
+ align:start position:0%
+and as we'll see um perhaps at the end
+ 
+
+ align:start position:0%
+and as we'll see um perhaps at the end
+of today's lecture or next time that all
+
+ align:start position:0%
+of today's lecture or next time that all
+ 
+
+ align:start position:0%
+of today's lecture or next time that all
+these principles that you're learning
+
+ align:start position:0%
+these principles that you're learning
+ 
+
+ align:start position:0%
+these principles that you're learning
+about oxidation reduction apply to
+
+ align:start position:0%
+about oxidation reduction apply to
+ 
+
+ align:start position:0%
+about oxidation reduction apply to
+oxidation reaction reactions that happen
+
+ align:start position:0%
+oxidation reaction reactions that happen
+ 
+
+ align:start position:0%
+oxidation reaction reactions that happen
+in your body so the same same principles
+
+ align:start position:0%
+in your body so the same same principles
+ 
+
+ align:start position:0%
+in your body so the same same principles
+that apply for a battery apply for uh
+
+ align:start position:0%
+that apply for a battery apply for uh
+ 
+
+ align:start position:0%
+that apply for a battery apply for uh
+chemical reactions that are in your body
+
+ align:start position:0%
+chemical reactions that are in your body
+ 
+
+ align:start position:0%
+chemical reactions that are in your body
+that are important for human health so
+
+ align:start position:0%
+that are important for human health so
+ 
+
+ align:start position:0%
+that are important for human health so
+we'll talk about that as
+
+ align:start position:0%
+we'll talk about that as
+ 
+
+ align:start position:0%
+we'll talk about that as
+well so here is a example of an
+
+ align:start position:0%
+well so here is a example of an
+ 
+
+ align:start position:0%
+well so here is a example of an
+electrochemical set this is a pretty
+
+ align:start position:0%
+electrochemical set this is a pretty
+ 
+
+ align:start position:0%
+electrochemical set this is a pretty
+simple electrochemical cell so we have h
+
+ align:start position:0%
+simple electrochemical cell so we have h
+ 
+
+ align:start position:0%
+simple electrochemical cell so we have h
+two two beakers here and uh we have
+
+ align:start position:0%
+two two beakers here and uh we have
+ 
+
+ align:start position:0%
+two two beakers here and uh we have
+electrodes which are connected uh by
+
+ align:start position:0%
+electrodes which are connected uh by
+ 
+
+ align:start position:0%
+electrodes which are connected uh by
+wires and they're connected to something
+
+ align:start position:0%
+wires and they're connected to something
+ 
+
+ align:start position:0%
+wires and they're connected to something
+that can read the uh current that's
+
+ align:start position:0%
+that can read the uh current that's
+ 
+
+ align:start position:0%
+that can read the uh current that's
+coming through the system there's also a
+
+ align:start position:0%
+coming through the system there's also a
+ 
+
+ align:start position:0%
+coming through the system there's also a
+salt bridge which we'll talk about in a
+
+ align:start position:0%
+salt bridge which we'll talk about in a
+ 
+
+ align:start position:0%
+salt bridge which we'll talk about in a
+few minutes so this would be a fairly uh
+
+ align:start position:0%
+few minutes so this would be a fairly uh
+ 
+
+ align:start position:0%
+few minutes so this would be a fairly uh
+simple one that one could construct and
+
+ align:start position:0%
+simple one that one could construct and
+ 
+
+ align:start position:0%
+simple one that one could construct and
+uh I like to joke about you know what
+
+ align:start position:0%
+uh I like to joke about you know what
+ 
+
+ align:start position:0%
+uh I like to joke about you know what
+people would say in the old days when I
+
+ align:start position:0%
+people would say in the old days when I
+ 
+
+ align:start position:0%
+people would say in the old days when I
+go and do uh fundraising stuff for Mi
+
+ align:start position:0%
+go and do uh fundraising stuff for Mi
+ 
+
+ align:start position:0%
+go and do uh fundraising stuff for Mi
+and meet uh alumni that graduated from
+
+ align:start position:0%
+and meet uh alumni that graduated from
+ 
+
+ align:start position:0%
+and meet uh alumni that graduated from
+this place a really long time ago and
+
+ align:start position:0%
+this place a really long time ago and
+ 
+
+ align:start position:0%
+this place a really long time ago and
+they probably say well yeah before we
+
+ align:start position:0%
+they probably say well yeah before we
+ 
+
+ align:start position:0%
+they probably say well yeah before we
+could even do our problem sets you know
+
+ align:start position:0%
+could even do our problem sets you know
+ 
+
+ align:start position:0%
+could even do our problem sets you know
+we had to make our own batteries to be
+
+ align:start position:0%
+we had to make our own batteries to be
+ 
+
+ align:start position:0%
+we had to make our own batteries to be
+able to uh get some electricity to see
+
+ align:start position:0%
+able to uh get some electricity to see
+ 
+
+ align:start position:0%
+able to uh get some electricity to see
+by so uh we don't your your life is a
+
+ align:start position:0%
+by so uh we don't your your life is a
+ 
+
+ align:start position:0%
+by so uh we don't your your life is a
+bit simpler now you should hear some of
+
+ align:start position:0%
+bit simpler now you should hear some of
+ 
+
+ align:start position:0%
+bit simpler now you should hear some of
+the the old stories of what MIT students
+
+ align:start position:0%
+the the old stories of what MIT students
+ 
+
+ align:start position:0%
+the the old stories of what MIT students
+had to go through all right so this is a
+
+ align:start position:0%
+had to go through all right so this is a
+ 
+
+ align:start position:0%
+had to go through all right so this is a
+schematic view of what you just saw and
+
+ align:start position:0%
+schematic view of what you just saw and
+ 
+
+ align:start position:0%
+schematic view of what you just saw and
+we'll walk through and talk about all
+
+ align:start position:0%
+we'll walk through and talk about all
+ 
+
+ align:start position:0%
+we'll walk through and talk about all
+the different parts of the
+
+ align:start position:0%
+the different parts of the
+ 
+
+ align:start position:0%
+the different parts of the
+electrochemical cell
+
+ align:start position:0%
+electrochemical cell
+ 
+
+ align:start position:0%
+electrochemical cell
+so this uh again I drew this this
+
+ align:start position:0%
+so this uh again I drew this this
+ 
+
+ align:start position:0%
+so this uh again I drew this this
+actually myself I think actually I stole
+
+ align:start position:0%
+actually myself I think actually I stole
+ 
+
+ align:start position:0%
+actually myself I think actually I stole
+maybe parts of it or I draw the whole
+
+ align:start position:0%
+maybe parts of it or I draw the whole
+ 
+
+ align:start position:0%
+maybe parts of it or I draw the whole
+thing I can't quite remember but um
+
+ align:start position:0%
+thing I can't quite remember but um
+ 
+
+ align:start position:0%
+thing I can't quite remember but um
+again this is my despic of the beaker as
+
+ align:start position:0%
+again this is my despic of the beaker as
+ 
+
+ align:start position:0%
+again this is my despic of the beaker as
+I've mentioned in the past art was
+
+ align:start position:0%
+I've mentioned in the past art was
+ 
+
+ align:start position:0%
+I've mentioned in the past art was
+really not my strength so this is a
+
+ align:start position:0%
+really not my strength so this is a
+ 
+
+ align:start position:0%
+really not my strength so this is a
+beaker over here filled with liquid in
+
+ align:start position:0%
+beaker over here filled with liquid in
+ 
+
+ align:start position:0%
+beaker over here filled with liquid in
+this case uh we have ions dissolved in
+
+ align:start position:0%
+this case uh we have ions dissolved in
+ 
+
+ align:start position:0%
+this case uh we have ions dissolved in
+uh the solution we have zinc plus two
+
+ align:start position:0%
+uh the solution we have zinc plus two
+ 
+
+ align:start position:0%
+uh the solution we have zinc plus two
+and um and sulfate dissolved another
+
+ align:start position:0%
+and um and sulfate dissolved another
+ 
+
+ align:start position:0%
+and um and sulfate dissolved another
+Beaker over here uh in this in this
+
+ align:start position:0%
+Beaker over here uh in this in this
+ 
+
+ align:start position:0%
+Beaker over here uh in this in this
+Beaker we have a zinc electrode and this
+
+ align:start position:0%
+Beaker we have a zinc electrode and this
+ 
+
+ align:start position:0%
+Beaker we have a zinc electrode and this
+is at the anode and so this is zinc
+
+ align:start position:0%
+is at the anode and so this is zinc
+ 
+
+ align:start position:0%
+is at the anode and so this is zinc
+solid a piece of zinc solid stuck into
+
+ align:start position:0%
+solid a piece of zinc solid stuck into
+ 
+
+ align:start position:0%
+solid a piece of zinc solid stuck into
+this Beaker where you have uh the
+
+ align:start position:0%
+this Beaker where you have uh the
+ 
+
+ align:start position:0%
+this Beaker where you have uh the
+solution there's a wire connecting two
+
+ align:start position:0%
+solution there's a wire connecting two
+ 
+
+ align:start position:0%
+solution there's a wire connecting two
+electrodes on the other side we have the
+
+ align:start position:0%
+electrodes on the other side we have the
+ 
+
+ align:start position:0%
+electrodes on the other side we have the
+cathode and this is made of copper solid
+
+ align:start position:0%
+cathode and this is made of copper solid
+ 
+
+ align:start position:0%
+cathode and this is made of copper solid
+and it's sitting in a beaker that has a
+
+ align:start position:0%
+and it's sitting in a beaker that has a
+ 
+
+ align:start position:0%
+and it's sitting in a beaker that has a
+copper plus two and also sulfate in it
+
+ align:start position:0%
+copper plus two and also sulfate in it
+ 
+
+ align:start position:0%
+copper plus two and also sulfate in it
+and so uh let's look at what would
+
+ align:start position:0%
+and so uh let's look at what would
+ 
+
+ align:start position:0%
+and so uh let's look at what would
+happen if this reaction were to run so
+
+ align:start position:0%
+happen if this reaction were to run so
+ 
+
+ align:start position:0%
+happen if this reaction were to run so
+over here uh at the anode we have zinc
+
+ align:start position:0%
+over here uh at the anode we have zinc
+ 
+
+ align:start position:0%
+over here uh at the anode we have zinc
+solid being oxidized to zinc plus two so
+
+ align:start position:0%
+solid being oxidized to zinc plus two so
+ 
+
+ align:start position:0%
+solid being oxidized to zinc plus two so
+the reaction is is shown down here so
+
+ align:start position:0%
+the reaction is is shown down here so
+ 
+
+ align:start position:0%
+the reaction is is shown down here so
+this electrode actually gets consumed
+
+ align:start position:0%
+this electrode actually gets consumed
+ 
+
+ align:start position:0%
+this electrode actually gets consumed
+during the reaction you actually have
+
+ align:start position:0%
+during the reaction you actually have
+ 
+
+ align:start position:0%
+during the reaction you actually have
+solid being converted to zinc plus two
+
+ align:start position:0%
+solid being converted to zinc plus two
+ 
+
+ align:start position:0%
+solid being converted to zinc plus two
+uh in solution so you have a change in
+
+ align:start position:0%
+uh in solution so you have a change in
+ 
+
+ align:start position:0%
+uh in solution so you have a change in
+phase and as that happens two electr are
+
+ align:start position:0%
+phase and as that happens two electr are
+ 
+
+ align:start position:0%
+phase and as that happens two electr are
+generated from that reaction and the El
+
+ align:start position:0%
+generated from that reaction and the El
+ 
+
+ align:start position:0%
+generated from that reaction and the El
+electrons then will go through the wire
+
+ align:start position:0%
+electrons then will go through the wire
+ 
+
+ align:start position:0%
+electrons then will go through the wire
+and the current will be red they'll go
+
+ align:start position:0%
+and the current will be red they'll go
+ 
+
+ align:start position:0%
+and the current will be red they'll go
+through the wire over to the Copper
+
+ align:start position:0%
+through the wire over to the Copper
+ 
+
+ align:start position:0%
+through the wire over to the Copper
+solid and over here they'll pass into
+
+ align:start position:0%
+solid and over here they'll pass into
+ 
+
+ align:start position:0%
+solid and over here they'll pass into
+this Beaker and the electrons will find
+
+ align:start position:0%
+this Beaker and the electrons will find
+ 
+
+ align:start position:0%
+this Beaker and the electrons will find
+the copper plus two as shown in this
+
+ align:start position:0%
+the copper plus two as shown in this
+ 
+
+ align:start position:0%
+the copper plus two as shown in this
+equation down here and this will form
+
+ align:start position:0%
+equation down here and this will form
+ 
+
+ align:start position:0%
+equation down here and this will form
+copper solid so you're actually going to
+
+ align:start position:0%
+copper solid so you're actually going to
+ 
+
+ align:start position:0%
+copper solid so you're actually going to
+have copper extra copper pleating onto
+
+ align:start position:0%
+have copper extra copper pleating onto
+ 
+
+ align:start position:0%
+have copper extra copper pleating onto
+the electrode so this electrode is going
+
+ align:start position:0%
+the electrode so this electrode is going
+ 
+
+ align:start position:0%
+the electrode so this electrode is going
+to get bigger
+
+ align:start position:0%
+to get bigger
+ 
+
+ align:start position:0%
+to get bigger
+uh and this one will be consumed in the
+
+ align:start position:0%
+uh and this one will be consumed in the
+ 
+
+ align:start position:0%
+uh and this one will be consumed in the
+course of the
+
+ align:start position:0%
+course of the
+ 
+
+ align:start position:0%
+course of the
+reaction and so this is a a little
+
+ align:start position:0%
+reaction and so this is a a little
+ 
+
+ align:start position:0%
+reaction and so this is a a little
+picture over here the electrons coming
+
+ align:start position:0%
+picture over here the electrons coming
+ 
+
+ align:start position:0%
+picture over here the electrons coming
+into the copper solid finding the copper
+
+ align:start position:0%
+into the copper solid finding the copper
+ 
+
+ align:start position:0%
+into the copper solid finding the copper
+plus two and the copper plus two then is
+
+ align:start position:0%
+plus two and the copper plus two then is
+ 
+
+ align:start position:0%
+plus two and the copper plus two then is
+reduced um at the cathode to Copper
+
+ align:start position:0%
+reduced um at the cathode to Copper
+ 
+
+ align:start position:0%
+reduced um at the cathode to Copper
+solid and the blow up on the other side
+
+ align:start position:0%
+solid and the blow up on the other side
+ 
+
+ align:start position:0%
+solid and the blow up on the other side
+shows the copper solid uh once electrons
+
+ align:start position:0%
+shows the copper solid uh once electrons
+ 
+
+ align:start position:0%
+shows the copper solid uh once electrons
+leave uh say the zinc solid electrons
+
+ align:start position:0%
+leave uh say the zinc solid electrons
+ 
+
+ align:start position:0%
+leave uh say the zinc solid electrons
+leave you form Z plus two so these are
+
+ align:start position:0%
+leave you form Z plus two so these are
+ 
+
+ align:start position:0%
+leave you form Z plus two so these are
+sort of blowups of the reactions that
+
+ align:start position:0%
+sort of blowups of the reactions that
+ 
+
+ align:start position:0%
+sort of blowups of the reactions that
+are happening uh at the uh cathode and
+
+ align:start position:0%
+are happening uh at the uh cathode and
+ 
+
+ align:start position:0%
+are happening uh at the uh cathode and
+anode and so as this happens you'll see
+
+ align:start position:0%
+anode and so as this happens you'll see
+ 
+
+ align:start position:0%
+anode and so as this happens you'll see
+there'll be a change in the charge so
+
+ align:start position:0%
+there'll be a change in the charge so
+ 
+
+ align:start position:0%
+there'll be a change in the charge so
+here we have uh zinc solid or zinc zero
+
+ align:start position:0%
+here we have uh zinc solid or zinc zero
+ 
+
+ align:start position:0%
+here we have uh zinc solid or zinc zero
+going to zinc plus two so to balance
+
+ align:start position:0%
+going to zinc plus two so to balance
+ 
+
+ align:start position:0%
+going to zinc plus two so to balance
+that charge there's a salt bridge and
+
+ align:start position:0%
+that charge there's a salt bridge and
+ 
+
+ align:start position:0%
+that charge there's a salt bridge and
+you'll have some kind of ion come in to
+
+ align:start position:0%
+you'll have some kind of ion come in to
+ 
+
+ align:start position:0%
+you'll have some kind of ion come in to
+neutralize the charge and here we have
+
+ align:start position:0%
+neutralize the charge and here we have
+ 
+
+ align:start position:0%
+neutralize the charge and here we have
+chloride minus on the other side we're
+
+ align:start position:0%
+chloride minus on the other side we're
+ 
+
+ align:start position:0%
+chloride minus on the other side we're
+going from copper plus two to Copper
+
+ align:start position:0%
+going from copper plus two to Copper
+ 
+
+ align:start position:0%
+going from copper plus two to Copper
+zero and so you'll have a positively
+
+ align:start position:0%
+zero and so you'll have a positively
+ 
+
+ align:start position:0%
+zero and so you'll have a positively
+charged ion coming in to help neutralize
+
+ align:start position:0%
+charged ion coming in to help neutralize
+ 
+
+ align:start position:0%
+charged ion coming in to help neutralize
+that that change in
+
+ align:start position:0%
+that that change in
+ 
+
+ align:start position:0%
+that that change in
+charge so over here something's being
+
+ align:start position:0%
+charge so over here something's being
+ 
+
+ align:start position:0%
+charge so over here something's being
+oxidized at the anode anode is where you
+
+ align:start position:0%
+oxidized at the anode anode is where you
+ 
+
+ align:start position:0%
+oxidized at the anode anode is where you
+have oxidation and something's being
+
+ align:start position:0%
+have oxidation and something's being
+ 
+
+ align:start position:0%
+have oxidation and something's being
+reduced at the cathode cathode is where
+
+ align:start position:0%
+reduced at the cathode cathode is where
+ 
+
+ align:start position:0%
+reduced at the cathode cathode is where
+you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduction so we could uh write that cell
+
+ align:start position:0%
+reduction so we could uh write that cell
+ 
+
+ align:start position:0%
+reduction so we could uh write that cell
+in a little bit more simple fact instead
+
+ align:start position:0%
+in a little bit more simple fact instead
+ 
+
+ align:start position:0%
+in a little bit more simple fact instead
+of having that picture we can uh convey
+
+ align:start position:0%
+of having that picture we can uh convey
+ 
+
+ align:start position:0%
+of having that picture we can uh convey
+to others what that picture showed us by
+
+ align:start position:0%
+to others what that picture showed us by
+ 
+
+ align:start position:0%
+to others what that picture showed us by
+this equation
+
+ align:start position:0%
+this equation
+ 
+
+ align:start position:0%
+this equation
+here so we have the two reactions going
+
+ align:start position:0%
+here so we have the two reactions going
+ 
+
+ align:start position:0%
+here so we have the two reactions going
+on we have the zinc reaction which is
+
+ align:start position:0%
+on we have the zinc reaction which is
+ 
+
+ align:start position:0%
+on we have the zinc reaction which is
+shown on one side and that reaction was
+
+ align:start position:0%
+shown on one side and that reaction was
+ 
+
+ align:start position:0%
+shown on one side and that reaction was
+the zinc solid going to the zinc plus
+
+ align:start position:0%
+the zinc solid going to the zinc plus
+ 
+
+ align:start position:0%
+the zinc solid going to the zinc plus
+two and this single line here represents
+
+ align:start position:0%
+two and this single line here represents
+ 
+
+ align:start position:0%
+two and this single line here represents
+a change in Phase a phase boundary so
+
+ align:start position:0%
+a change in Phase a phase boundary so
+ 
+
+ align:start position:0%
+a change in Phase a phase boundary so
+solid going to uh an ion dissolved an
+
+ align:start position:0%
+solid going to uh an ion dissolved an
+ 
+
+ align:start position:0%
+solid going to uh an ion dissolved an
+aquous solution the two lines right here
+
+ align:start position:0%
+aquous solution the two lines right here
+ 
+
+ align:start position:0%
+aquous solution the two lines right here
+represent the salt bridge so this uh
+
+ align:start position:0%
+represent the salt bridge so this uh
+ 
+
+ align:start position:0%
+represent the salt bridge so this uh
+equation then is telling you one
+
+ align:start position:0%
+equation then is telling you one
+ 
+
+ align:start position:0%
+equation then is telling you one
+reaction going on in one Beaker
+
+ align:start position:0%
+reaction going on in one Beaker
+ 
+
+ align:start position:0%
+reaction going on in one Beaker
+separated by the salt bridge this would
+
+ align:start position:0%
+separated by the salt bridge this would
+ 
+
+ align:start position:0%
+separated by the salt bridge this would
+be the reaction going on in the other
+
+ align:start position:0%
+be the reaction going on in the other
+ 
+
+ align:start position:0%
+be the reaction going on in the other
+Beaker and so over here we have copper
+
+ align:start position:0%
+Beaker and so over here we have copper
+ 
+
+ align:start position:0%
+Beaker and so over here we have copper
+plus two aquous with a single line for
+
+ align:start position:0%
+plus two aquous with a single line for
+ 
+
+ align:start position:0%
+plus two aquous with a single line for
+the phase boundary going to Copper solid
+
+ align:start position:0%
+the phase boundary going to Copper solid
+ 
+
+ align:start position:0%
+the phase boundary going to Copper solid
+so if you see see this kind of notation
+
+ align:start position:0%
+so if you see see this kind of notation
+ 
+
+ align:start position:0%
+so if you see see this kind of notation
+you can Envision that electrochemical
+
+ align:start position:0%
+you can Envision that electrochemical
+ 
+
+ align:start position:0%
+you can Envision that electrochemical
+cell with the two beakers the wire and
+
+ align:start position:0%
+cell with the two beakers the wire and
+ 
+
+ align:start position:0%
+cell with the two beakers the wire and
+the salt bridge and you uh can this is
+
+ align:start position:0%
+the salt bridge and you uh can this is
+ 
+
+ align:start position:0%
+the salt bridge and you uh can this is
+reaction going on on one side and the
+
+ align:start position:0%
+reaction going on on one side and the
+ 
+
+ align:start position:0%
+reaction going on on one side and the
+reaction going on on the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side so as as I
+
+ align:start position:0%
+side so as as I
+ 
+
+ align:start position:0%
+side so as as I
+mentioned in that particular electric
+
+ align:start position:0%
+mentioned in that particular electric
+ 
+
+ align:start position:0%
+mentioned in that particular electric
+chemical cell zinc is being consumed
+
+ align:start position:0%
+chemical cell zinc is being consumed
+ 
+
+ align:start position:0%
+chemical cell zinc is being consumed
+zinc solid is being consumed it's being
+
+ align:start position:0%
+zinc solid is being consumed it's being
+ 
+
+ align:start position:0%
+zinc solid is being consumed it's being
+converted to zinc plus two whereas
+
+ align:start position:0%
+converted to zinc plus two whereas
+ 
+
+ align:start position:0%
+converted to zinc plus two whereas
+copper solid is being deposited onto the
+
+ align:start position:0%
+copper solid is being deposited onto the
+ 
+
+ align:start position:0%
+copper solid is being deposited onto the
+electrode so in that case you have
+
+ align:start position:0%
+electrode so in that case you have
+ 
+
+ align:start position:0%
+electrode so in that case you have
+copper plus two aquous going to Copper
+
+ align:start position:0%
+copper plus two aquous going to Copper
+ 
+
+ align:start position:0%
+copper plus two aquous going to Copper
+solid so that's being
+
+ align:start position:0%
+solid so that's being
+ 
+
+ align:start position:0%
+solid so that's being
+deposited and the amount of zinc that's
+
+ align:start position:0%
+deposited and the amount of zinc that's
+ 
+
+ align:start position:0%
+deposited and the amount of zinc that's
+consumed and the amount of copper that's
+
+ align:start position:0%
+consumed and the amount of copper that's
+ 
+
+ align:start position:0%
+consumed and the amount of copper that's
+deposited is going to be proportional to
+
+ align:start position:0%
+deposited is going to be proportional to
+ 
+
+ align:start position:0%
+deposited is going to be proportional to
+the charge that passes through the
+
+ align:start position:0%
+the charge that passes through the
+ 
+
+ align:start position:0%
+the charge that passes through the
+system or to the electrons that pass
+
+ align:start position:0%
+system or to the electrons that pass
+ 
+
+ align:start position:0%
+system or to the electrons that pass
+through the system and that makes sense
+
+ align:start position:0%
+through the system and that makes sense
+ 
+
+ align:start position:0%
+through the system and that makes sense
+because if you have uh zinc solid going
+
+ align:start position:0%
+because if you have uh zinc solid going
+ 
+
+ align:start position:0%
+because if you have uh zinc solid going
+to zinc plus two you have two electrons
+
+ align:start position:0%
+to zinc plus two you have two electrons
+ 
+
+ align:start position:0%
+to zinc plus two you have two electrons
+formed which would then go through to
+
+ align:start position:0%
+formed which would then go through to
+ 
+
+ align:start position:0%
+formed which would then go through to
+the other side so the amount of charge
+
+ align:start position:0%
+the other side so the amount of charge
+ 
+
+ align:start position:0%
+the other side so the amount of charge
+that's going to go through has to do
+
+ align:start position:0%
+that's going to go through has to do
+ 
+
+ align:start position:0%
+that's going to go through has to do
+with the amount of zinc that's consumed
+
+ align:start position:0%
+with the amount of zinc that's consumed
+ 
+
+ align:start position:0%
+with the amount of zinc that's consumed
+which would also then have to do with
+
+ align:start position:0%
+which would also then have to do with
+ 
+
+ align:start position:0%
+which would also then have to do with
+the amount of copper that's deposited
+
+ align:start position:0%
+the amount of copper that's deposited
+ 
+
+ align:start position:0%
+the amount of copper that's deposited
+when the electrons get to the other side
+
+ align:start position:0%
+when the electrons get to the other side
+ 
+
+ align:start position:0%
+when the electrons get to the other side
+and so this is a law we don't have very
+
+ align:start position:0%
+and so this is a law we don't have very
+ 
+
+ align:start position:0%
+and so this is a law we don't have very
+many laws in chemistry a lot of times we
+
+ align:start position:0%
+many laws in chemistry a lot of times we
+ 
+
+ align:start position:0%
+many laws in chemistry a lot of times we
+have theories uh that help to explain
+
+ align:start position:0%
+have theories uh that help to explain
+ 
+
+ align:start position:0%
+have theories uh that help to explain
+observed uh information chemistry really
+
+ align:start position:0%
+observed uh information chemistry really
+ 
+
+ align:start position:0%
+observed uh information chemistry really
+is an experimental science so we observe
+
+ align:start position:0%
+is an experimental science so we observe
+ 
+
+ align:start position:0%
+is an experimental science so we observe
+a lot of things and then we try to
+
+ align:start position:0%
+a lot of things and then we try to
+ 
+
+ align:start position:0%
+a lot of things and then we try to
+rationalize why they're true they're not
+
+ align:start position:0%
+rationalize why they're true they're not
+ 
+
+ align:start position:0%
+rationalize why they're true they're not
+a whole lot of laws but this is this is
+
+ align:start position:0%
+a whole lot of laws but this is this is
+ 
+
+ align:start position:0%
+a whole lot of laws but this is this is
+one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them all right so let's just kind of
+
+ align:start position:0%
+them all right so let's just kind of
+ 
+
+ align:start position:0%
+them all right so let's just kind of
+look at little movies of of of this uh
+
+ align:start position:0%
+look at little movies of of of this uh
+ 
+
+ align:start position:0%
+look at little movies of of of this uh
+procedure of what is is happening and
+
+ align:start position:0%
+procedure of what is is happening and
+ 
+
+ align:start position:0%
+procedure of what is is happening and
+here we're going to see
+
+ align:start position:0%
+here we're going to see
+ 
+
+ align:start position:0%
+here we're going to see
+oxidation uh at the anode so we can
+
+ align:start position:0%
+oxidation uh at the anode so we can
+ 
+
+ align:start position:0%
+oxidation uh at the anode so we can
+pretend this is our solid uh electrode
+
+ align:start position:0%
+pretend this is our solid uh electrode
+ 
+
+ align:start position:0%
+pretend this is our solid uh electrode
+here and we have say the zinc and here's
+
+ align:start position:0%
+here and we have say the zinc and here's
+ 
+
+ align:start position:0%
+here and we have say the zinc and here's
+the aquous part so these are water
+
+ align:start position:0%
+the aquous part so these are water
+ 
+
+ align:start position:0%
+the aquous part so these are water
+molecules and you're going to see a
+
+ align:start position:0%
+molecules and you're going to see a
+ 
+
+ align:start position:0%
+molecules and you're going to see a
+electrons leave go up and uh then you're
+
+ align:start position:0%
+electrons leave go up and uh then you're
+ 
+
+ align:start position:0%
+electrons leave go up and uh then you're
+going to have the solid is going to uh
+
+ align:start position:0%
+going to have the solid is going to uh
+ 
+
+ align:start position:0%
+going to have the solid is going to uh
+then be oxidized to in this case zinc
+
+ align:start position:0%
+then be oxidized to in this case zinc
+ 
+
+ align:start position:0%
+then be oxidized to in this case zinc
+plus two and it'll go into solution so
+
+ align:start position:0%
+plus two and it'll go into solution so
+ 
+
+ align:start position:0%
+plus two and it'll go into solution so
+let me just play this for you you can
+
+ align:start position:0%
+let me just play this for you you can
+ 
+
+ align:start position:0%
+let me just play this for you you can
+see you can actually see the electrons
+
+ align:start position:0%
+see you can actually see the electrons
+ 
+
+ align:start position:0%
+see you can actually see the electrons
+leave in this movie which uh is uh
+
+ align:start position:0%
+leave in this movie which uh is uh
+ 
+
+ align:start position:0%
+leave in this movie which uh is uh
+interesting so okay there they go there
+
+ align:start position:0%
+interesting so okay there they go there
+ 
+
+ align:start position:0%
+interesting so okay there they go there
+are the electrons leaving up and you've
+
+ align:start position:0%
+are the electrons leaving up and you've
+ 
+
+ align:start position:0%
+are the electrons leaving up and you've
+you freed up some of the solid and now
+
+ align:start position:0%
+you freed up some of the solid and now
+ 
+
+ align:start position:0%
+you freed up some of the solid and now
+you freed up again so now we have uh
+
+ align:start position:0%
+you freed up again so now we have uh
+ 
+
+ align:start position:0%
+you freed up again so now we have uh
+zinc plus two we had zinc solid but now
+
+ align:start position:0%
+zinc plus two we had zinc solid but now
+ 
+
+ align:start position:0%
+zinc plus two we had zinc solid but now
+uh We've uh consumed some of our
+
+ align:start position:0%
+uh We've uh consumed some of our
+ 
+
+ align:start position:0%
+uh We've uh consumed some of our
+electrode and it's in
+
+ align:start position:0%
+electrode and it's in
+ 
+
+ align:start position:0%
+electrode and it's in
+solution so we can now you know what
+
+ align:start position:0%
+solution so we can now you know what
+ 
+
+ align:start position:0%
+solution so we can now you know what
+you're looking for I'll just play that
+
+ align:start position:0%
+you're looking for I'll just play that
+ 
+
+ align:start position:0%
+you're looking for I'll just play that
+one more time okay the electrons are
+
+ align:start position:0%
+one more time okay the electrons are
+ 
+
+ align:start position:0%
+one more time okay the electrons are
+heading off into the wires and uh you're
+
+ align:start position:0%
+heading off into the wires and uh you're
+ 
+
+ align:start position:0%
+heading off into the wires and uh you're
+consuming your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrode all right so let's go the
+
+ align:start position:0%
+electrode all right so let's go the
+ 
+
+ align:start position:0%
+electrode all right so let's go the
+other direction the electrodes the
+
+ align:start position:0%
+other direction the electrodes the
+ 
+
+ align:start position:0%
+other direction the electrodes the
+electrons that left and passed through
+
+ align:start position:0%
+electrons that left and passed through
+ 
+
+ align:start position:0%
+electrons that left and passed through
+the w
+
+ align:start position:0%
+the w
+ 
+
+ align:start position:0%
+the w
+are now coming down to the cathode and
+
+ align:start position:0%
+are now coming down to the cathode and
+ 
+
+ align:start position:0%
+are now coming down to the cathode and
+so those electrons can come in and uh
+
+ align:start position:0%
+so those electrons can come in and uh
+ 
+
+ align:start position:0%
+so those electrons can come in and uh
+reduce say copper plus two forming
+
+ align:start position:0%
+reduce say copper plus two forming
+ 
+
+ align:start position:0%
+reduce say copper plus two forming
+copper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solid so we have copper plus two here
+
+ align:start position:0%
+solid so we have copper plus two here
+ 
+
+ align:start position:0%
+solid so we have copper plus two here
+come the electrons here come the
+
+ align:start position:0%
+come the electrons here come the
+ 
+
+ align:start position:0%
+come the electrons here come the
+electrons and so now you've plated those
+
+ align:start position:0%
+electrons and so now you've plated those
+ 
+
+ align:start position:0%
+electrons and so now you've plated those
+two copper plus two ions they become
+
+ align:start position:0%
+two copper plus two ions they become
+ 
+
+ align:start position:0%
+two copper plus two ions they become
+copper solid and and now your cathode
+
+ align:start position:0%
+copper solid and and now your cathode
+ 
+
+ align:start position:0%
+copper solid and and now your cathode
+has expanded you've added uh more metal
+
+ align:start position:0%
+has expanded you've added uh more metal
+ 
+
+ align:start position:0%
+has expanded you've added uh more metal
+onto it it's been deposited or plated
+
+ align:start position:0%
+onto it it's been deposited or plated
+ 
+
+ align:start position:0%
+onto it it's been deposited or plated
+onto this uh
+
+ align:start position:0%
+onto this uh
+ 
+
+ align:start position:0%
+onto this uh
+electrod and again the amounts are going
+
+ align:start position:0%
+electrod and again the amounts are going
+ 
+
+ align:start position:0%
+electrod and again the amounts are going
+to be equal so there's Faraday law would
+
+ align:start position:0%
+to be equal so there's Faraday law would
+ 
+
+ align:start position:0%
+to be equal so there's Faraday law would
+tell you that it's all going to be
+
+ align:start position:0%
+tell you that it's all going to be
+ 
+
+ align:start position:0%
+tell you that it's all going to be
+proportional the amount that's consumed
+
+ align:start position:0%
+proportional the amount that's consumed
+ 
+
+ align:start position:0%
+proportional the amount that's consumed
+the amount that's produced is all going
+
+ align:start position:0%
+the amount that's produced is all going
+ 
+
+ align:start position:0%
+the amount that's produced is all going
+to be equal to the number of electrons
+
+ align:start position:0%
+to be equal to the number of electrons
+ 
+
+ align:start position:0%
+to be equal to the number of electrons
+that pass through the
+
+ align:start position:0%
+that pass through the
+ 
+
+ align:start position:0%
+that pass through the
+system so let me just show you uh one
+
+ align:start position:0%
+system so let me just show you uh one
+ 
+
+ align:start position:0%
+system so let me just show you uh one
+more example of why this could be useful
+
+ align:start position:0%
+more example of why this could be useful
+ 
+
+ align:start position:0%
+more example of why this could be useful
+in terms of the plating um so in this uh
+
+ align:start position:0%
+in terms of the plating um so in this uh
+ 
+
+ align:start position:0%
+in terms of the plating um so in this uh
+little experiment we have a steel spoon
+
+ align:start position:0%
+little experiment we have a steel spoon
+ 
+
+ align:start position:0%
+little experiment we have a steel spoon
+and uh it's going to be the steel spoon
+
+ align:start position:0%
+and uh it's going to be the steel spoon
+ 
+
+ align:start position:0%
+and uh it's going to be the steel spoon
+will will act like an electrode and get
+
+ align:start position:0%
+will will act like an electrode and get
+ 
+
+ align:start position:0%
+will will act like an electrode and get
+plated with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+copper so this
+
+ align:start position:0%
+copper so this
+ 
+
+ align:start position:0%
+copper so this
+has this seal spoon will have a thin
+
+ align:start position:0%
+has this seal spoon will have a thin
+ 
+
+ align:start position:0%
+has this seal spoon will have a thin
+coting of copper on there's the copper
+
+ align:start position:0%
+coting of copper on there's the copper
+ 
+
+ align:start position:0%
+coting of copper on there's the copper
+wire cell consists of an copper a
+
+ align:start position:0%
+wire cell consists of an copper a
+ 
+
+ align:start position:0%
+wire cell consists of an copper a
+solution of copper sulfate and as a
+
+ align:start position:0%
+solution of copper sulfate and as a
+ 
+
+ align:start position:0%
+solution of copper sulfate and as a
+cathod a spoon there is no net reaction
+
+ align:start position:0%
+cathod a spoon there is no net reaction
+ 
+
+ align:start position:0%
+cathod a spoon there is no net reaction
+but copper metal is transferred from the
+
+ align:start position:0%
+but copper metal is transferred from the
+ 
+
+ align:start position:0%
+but copper metal is transferred from the
+anod to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cathode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pretty okay so that's pretty simple so
+
+ align:start position:0%
+pretty okay so that's pretty simple so
+ 
+
+ align:start position:0%
+pretty okay so that's pretty simple so
+then you can see how it can get
+
+ align:start position:0%
+then you can see how it can get
+ 
+
+ align:start position:0%
+then you can see how it can get
+deposited uh on top of this which was
+
+ align:start position:0%
+deposited uh on top of this which was
+ 
+
+ align:start position:0%
+deposited uh on top of this which was
+acting as an electrode in this case all
+
+ align:start position:0%
+acting as an electrode in this case all
+ 
+
+ align:start position:0%
+acting as an electrode in this case all
+right so as you probably figured out you
+
+ align:start position:0%
+right so as you probably figured out you
+ 
+
+ align:start position:0%
+right so as you probably figured out you
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's you often will have to figure
+
+ align:start position:0%
+yeah it's you often will have to figure
+ 
+
+ align:start position:0%
+yeah it's you often will have to figure
+that kind of thing out in the example
+
+ align:start position:0%
+that kind of thing out in the example
+ 
+
+ align:start position:0%
+that kind of thing out in the example
+that I showed you it was set up to work
+
+ align:start position:0%
+that I showed you it was set up to work
+ 
+
+ align:start position:0%
+that I showed you it was set up to work
+like that um but as we'll we'll talk
+
+ align:start position:0%
+like that um but as we'll we'll talk
+ 
+
+ align:start position:0%
+like that um but as we'll we'll talk
+about it depends if it's going to be a
+
+ align:start position:0%
+about it depends if it's going to be a
+ 
+
+ align:start position:0%
+about it depends if it's going to be a
+spontaneous reaction or non-spontaneous
+
+ align:start position:0%
+spontaneous reaction or non-spontaneous
+ 
+
+ align:start position:0%
+spontaneous reaction or non-spontaneous
+reaction so if you have a a cell where
+
+ align:start position:0%
+reaction so if you have a a cell where
+ 
+
+ align:start position:0%
+reaction so if you have a a cell where
+it's a spontaneous reaction you can
+
+ align:start position:0%
+it's a spontaneous reaction you can
+ 
+
+ align:start position:0%
+it's a spontaneous reaction you can
+figure out which is going to be it which
+
+ align:start position:0%
+figure out which is going to be it which
+ 
+
+ align:start position:0%
+figure out which is going to be it which
+reaction will occur at the cathode and
+
+ align:start position:0%
+reaction will occur at the cathode and
+ 
+
+ align:start position:0%
+reaction will occur at the cathode and
+which will occur at the anode there's
+
+ align:start position:0%
+which will occur at the anode there's
+ 
+
+ align:start position:0%
+which will occur at the anode there's
+only one one way you can put those thing
+
+ align:start position:0%
+only one one way you can put those thing
+ 
+
+ align:start position:0%
+only one one way you can put those thing
+if you have particular ingredients for
+
+ align:start position:0%
+if you have particular ingredients for
+ 
+
+ align:start position:0%
+if you have particular ingredients for
+it to be spontaneous and so we'll
+
+ align:start position:0%
+it to be spontaneous and so we'll
+ 
+
+ align:start position:0%
+it to be spontaneous and so we'll
+actually talk about that at the end of
+
+ align:start position:0%
+actually talk about that at the end of
+ 
+
+ align:start position:0%
+actually talk about that at the end of
+of the lecture but in that particular
+
+ align:start position:0%
+of the lecture but in that particular
+ 
+
+ align:start position:0%
+of the lecture but in that particular
+case it was just you know stated as you
+
+ align:start position:0%
+case it was just you know stated as you
+ 
+
+ align:start position:0%
+case it was just you know stated as you
+know this is the reaction happening here
+
+ align:start position:0%
+know this is the reaction happening here
+ 
+
+ align:start position:0%
+know this is the reaction happening here
+and here but which will go which place
+
+ align:start position:0%
+and here but which will go which place
+ 
+
+ align:start position:0%
+and here but which will go which place
+will depend on whether you want it to be
+
+ align:start position:0%
+will depend on whether you want it to be
+ 
+
+ align:start position:0%
+will depend on whether you want it to be
+as spontaneous or nonspontaneous I
+
+ align:start position:0%
+as spontaneous or nonspontaneous I
+ 
+
+ align:start position:0%
+as spontaneous or nonspontaneous I
+that's a good question and we'll
+
+ align:start position:0%
+that's a good question and we'll
+ 
+
+ align:start position:0%
+that's a good question and we'll
+definitely come to that so uh in terms
+
+ align:start position:0%
+definitely come to that so uh in terms
+ 
+
+ align:start position:0%
+definitely come to that so uh in terms
+of uh Faraday's law it's proportional
+
+ align:start position:0%
+of uh Faraday's law it's proportional
+ 
+
+ align:start position:0%
+of uh Faraday's law it's proportional
+and that means you can do calculations
+
+ align:start position:0%
+and that means you can do calculations
+ 
+
+ align:start position:0%
+and that means you can do calculations
+so one could figure out how much zinc
+
+ align:start position:0%
+so one could figure out how much zinc
+ 
+
+ align:start position:0%
+so one could figure out how much zinc
+would get consumed or how much copper
+
+ align:start position:0%
+would get consumed or how much copper
+ 
+
+ align:start position:0%
+would get consumed or how much copper
+would get deposited if you had a
+
+ align:start position:0%
+would get deposited if you had a
+ 
+
+ align:start position:0%
+would get deposited if you had a
+particular current flowing for a
+
+ align:start position:0%
+particular current flowing for a
+ 
+
+ align:start position:0%
+particular current flowing for a
+particular amount of time and uh these
+
+ align:start position:0%
+particular amount of time and uh these
+ 
+
+ align:start position:0%
+particular amount of time and uh these
+are actually uh fairly fairly simple
+
+ align:start position:0%
+are actually uh fairly fairly simple
+ 
+
+ align:start position:0%
+are actually uh fairly fairly simple
+calculations to do we'll just go through
+
+ align:start position:0%
+calculations to do we'll just go through
+ 
+
+ align:start position:0%
+calculations to do we'll just go through
+one of
+
+ align:start position:0%
+one of
+ 
+
+ align:start position:0%
+one of
+them so um the first step would be to
+
+ align:start position:0%
+them so um the first step would be to
+ 
+
+ align:start position:0%
+them so um the first step would be to
+figure out how much charge went through
+
+ align:start position:0%
+figure out how much charge went through
+ 
+
+ align:start position:0%
+figure out how much charge went through
+the system so we have q magnitude of of
+
+ align:start position:0%
+the system so we have q magnitude of of
+ 
+
+ align:start position:0%
+the system so we have q magnitude of of
+charge in kums which uh unit is C uh is
+
+ align:start position:0%
+charge in kums which uh unit is C uh is
+ 
+
+ align:start position:0%
+charge in kums which uh unit is C uh is
+going to be equal to the current and
+
+ align:start position:0%
+going to be equal to the current and
+ 
+
+ align:start position:0%
+going to be equal to the current and
+that's in ampers or a and uh here is a
+
+ align:start position:0%
+that's in ampers or a and uh here is a
+ 
+
+ align:start position:0%
+that's in ampers or a and uh here is a
+useful conversion for you to remember
+
+ align:start position:0%
+useful conversion for you to remember
+ 
+
+ align:start position:0%
+useful conversion for you to remember
+and this will be given to you on on a
+
+ align:start position:0%
+and this will be given to you on on a
+ 
+
+ align:start position:0%
+and this will be given to you on on a
+test uh times the amount of time so how
+
+ align:start position:0%
+test uh times the amount of time so how
+ 
+
+ align:start position:0%
+test uh times the amount of time so how
+much current times time will tell you
+
+ align:start position:0%
+much current times time will tell you
+ 
+
+ align:start position:0%
+much current times time will tell you
+the uh the magnitude of the charge so
+
+ align:start position:0%
+the uh the magnitude of the charge so
+ 
+
+ align:start position:0%
+the uh the magnitude of the charge so
+that's that's pretty simple and that
+
+ align:start position:0%
+that's that's pretty simple and that
+ 
+
+ align:start position:0%
+that's that's pretty simple and that
+equation would be given to you as well
+
+ align:start position:0%
+equation would be given to you as well
+ 
+
+ align:start position:0%
+equation would be given to you as well
+so uh we have uh we're told that we had
+
+ align:start position:0%
+so uh we have uh we're told that we had
+ 
+
+ align:start position:0%
+so uh we have uh we're told that we had
+one uh one amp uh for one hour and we've
+
+ align:start position:0%
+one uh one amp uh for one hour and we've
+ 
+
+ align:start position:0%
+one uh one amp uh for one hour and we've
+converted it to seconds so you can get
+
+ align:start position:0%
+converted it to seconds so you can get
+ 
+
+ align:start position:0%
+converted it to seconds so you can get
+the right the right units we can find
+
+ align:start position:0%
+the right the right units we can find
+ 
+
+ align:start position:0%
+the right the right units we can find
+out the magnitude of the charge then in
+
+ align:start position:0%
+out the magnitude of the charge then in
+ 
+
+ align:start position:0%
+out the magnitude of the charge then in
+kums because these units multiplied
+
+ align:start position:0%
+kums because these units multiplied
+ 
+
+ align:start position:0%
+kums because these units multiplied
+together will get you kums
+
+ align:start position:0%
+together will get you kums
+ 
+
+ align:start position:0%
+together will get you kums
+so then uh step two is to figure out how
+
+ align:start position:0%
+so then uh step two is to figure out how
+ 
+
+ align:start position:0%
+so then uh step two is to figure out how
+many moles of electron that charge is
+
+ align:start position:0%
+many moles of electron that charge is
+ 
+
+ align:start position:0%
+many moles of electron that charge is
+equal to and uh we have Faraday constant
+
+ align:start position:0%
+equal to and uh we have Faraday constant
+ 
+
+ align:start position:0%
+equal to and uh we have Faraday constant
+uh which will also be provided to you
+
+ align:start position:0%
+uh which will also be provided to you
+ 
+
+ align:start position:0%
+uh which will also be provided to you
+and its units you can um using the
+
+ align:start position:0%
+and its units you can um using the
+ 
+
+ align:start position:0%
+and its units you can um using the
+conversion Kum per mole and it also is
+
+ align:start position:0%
+conversion Kum per mole and it also is
+ 
+
+ align:start position:0%
+conversion Kum per mole and it also is
+equal to one Faraday which is usually
+
+ align:start position:0%
+equal to one Faraday which is usually
+ 
+
+ align:start position:0%
+equal to one Faraday which is usually
+kind of a squiggly kind of f symbol here
+
+ align:start position:0%
+kind of a squiggly kind of f symbol here
+ 
+
+ align:start position:0%
+kind of a squiggly kind of f symbol here
+and so then if we go through we use
+
+ align:start position:0%
+and so then if we go through we use
+ 
+
+ align:start position:0%
+and so then if we go through we use
+Faraday constant we can figure out that
+
+ align:start position:0%
+Faraday constant we can figure out that
+ 
+
+ align:start position:0%
+Faraday constant we can figure out that
+that number of kums uh convert to moles
+
+ align:start position:0%
+that number of kums uh convert to moles
+ 
+
+ align:start position:0%
+that number of kums uh convert to moles
+and so you would get
+
+ align:start position:0%
+and so you would get
+ 
+
+ align:start position:0%
+and so you would get
+0.373 moles of electrons so this is just
+
+ align:start position:0%
+0.373 moles of electrons so this is just
+ 
+
+ align:start position:0%
+0.373 moles of electrons so this is just
+a conversion using Faraday
+
+ align:start position:0%
+a conversion using Faraday
+ 
+
+ align:start position:0%
+a conversion using Faraday
+constant and then we have to figure out
+
+ align:start position:0%
+constant and then we have to figure out
+ 
+
+ align:start position:0%
+constant and then we have to figure out
+how many moles of the particular element
+
+ align:start position:0%
+how many moles of the particular element
+ 
+
+ align:start position:0%
+how many moles of the particular element
+zinc in this case or copper are
+
+ align:start position:0%
+zinc in this case or copper are
+ 
+
+ align:start position:0%
+zinc in this case or copper are
+deposited and convert to grams so we
+
+ align:start position:0%
+deposited and convert to grams so we
+ 
+
+ align:start position:0%
+deposited and convert to grams so we
+know now how many electrons went through
+
+ align:start position:0%
+know now how many electrons went through
+ 
+
+ align:start position:0%
+know now how many electrons went through
+our our system and so now we just need
+
+ align:start position:0%
+our our system and so now we just need
+ 
+
+ align:start position:0%
+our our system and so now we just need
+to figure out for every one mole of zinc
+
+ align:start position:0%
+to figure out for every one mole of zinc
+ 
+
+ align:start position:0%
+to figure out for every one mole of zinc
+consumed how many moles of electrons
+
+ align:start position:0%
+consumed how many moles of electrons
+ 
+
+ align:start position:0%
+consumed how many moles of electrons
+would have left and in the particular
+
+ align:start position:0%
+would have left and in the particular
+ 
+
+ align:start position:0%
+would have left and in the particular
+example we had what would it be how many
+
+ align:start position:0%
+example we had what would it be how many
+ 
+
+ align:start position:0%
+example we had what would it be how many
+electrons two is we went from zinc to
+
+ align:start position:0%
+electrons two is we went from zinc to
+ 
+
+ align:start position:0%
+electrons two is we went from zinc to
+zinc plus two so we're talking about two
+
+ align:start position:0%
+zinc plus two so we're talking about two
+ 
+
+ align:start position:0%
+zinc plus two so we're talking about two
+electrons for every mole of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zinc and then we can calculate grams of
+
+ align:start position:0%
+zinc and then we can calculate grams of
+ 
+
+ align:start position:0%
+zinc and then we can calculate grams of
+per
+
+ align:start position:0%
+per
+ 
+
+ align:start position:0%
+per
+uh we can CC we can calculate moles and
+
+ align:start position:0%
+uh we can CC we can calculate moles and
+ 
+
+ align:start position:0%
+uh we can CC we can calculate moles and
+convert to grams using the molecular
+
+ align:start position:0%
+convert to grams using the molecular
+ 
+
+ align:start position:0%
+convert to grams using the molecular
+mass of zinc which we can look up so we
+
+ align:start position:0%
+mass of zinc which we can look up so we
+ 
+
+ align:start position:0%
+mass of zinc which we can look up so we
+get 1.2 grams uh are going to be
+
+ align:start position:0%
+get 1.2 grams uh are going to be
+ 
+
+ align:start position:0%
+get 1.2 grams uh are going to be
+consumed at that particular time with
+
+ align:start position:0%
+consumed at that particular time with
+ 
+
+ align:start position:0%
+consumed at that particular time with
+that kind of current passing through the
+
+ align:start position:0%
+that kind of current passing through the
+ 
+
+ align:start position:0%
+that kind of current passing through the
+system we can do the same thing with
+
+ align:start position:0%
+system we can do the same thing with
+ 
+
+ align:start position:0%
+system we can do the same thing with
+copper so we have the same number of
+
+ align:start position:0%
+copper so we have the same number of
+ 
+
+ align:start position:0%
+copper so we have the same number of
+moles of electrons that are going
+
+ align:start position:0%
+moles of electrons that are going
+ 
+
+ align:start position:0%
+moles of electrons that are going
+through our system and now we just need
+
+ align:start position:0%
+through our system and now we just need
+ 
+
+ align:start position:0%
+through our system and now we just need
+to know for every one mole of copper
+
+ align:start position:0%
+to know for every one mole of copper
+ 
+
+ align:start position:0%
+to know for every one mole of copper
+deposited how many electrons are
+
+ align:start position:0%
+deposited how many electrons are
+ 
+
+ align:start position:0%
+deposited how many electrons are
+required and that
+
+ align:start position:0%
+required and that
+ 
+
+ align:start position:0%
+required and that
+is two again because we were taking
+
+ align:start position:0%
+is two again because we were taking
+ 
+
+ align:start position:0%
+is two again because we were taking
+copper plus two to Copper solid so we
+
+ align:start position:0%
+copper plus two to Copper solid so we
+ 
+
+ align:start position:0%
+copper plus two to Copper solid so we
+need two electrons for every one uh mole
+
+ align:start position:0%
+need two electrons for every one uh mole
+ 
+
+ align:start position:0%
+need two electrons for every one uh mole
+of copper that gets
+
+ align:start position:0%
+of copper that gets
+ 
+
+ align:start position:0%
+of copper that gets
+deposited and then we can use uh the
+
+ align:start position:0%
+deposited and then we can use uh the
+ 
+
+ align:start position:0%
+deposited and then we can use uh the
+molecular mass to find out the number of
+
+ align:start position:0%
+molecular mass to find out the number of
+ 
+
+ align:start position:0%
+molecular mass to find out the number of
+grams and since these weigh a very
+
+ align:start position:0%
+grams and since these weigh a very
+ 
+
+ align:start position:0%
+grams and since these weigh a very
+similar amount it's about the same uh
+
+ align:start position:0%
+similar amount it's about the same uh
+ 
+
+ align:start position:0%
+similar amount it's about the same uh
+the same number of grams um if there was
+
+ align:start position:0%
+the same number of grams um if there was
+ 
+
+ align:start position:0%
+the same number of grams um if there was
+a very difference in in molecular mass
+
+ align:start position:0%
+a very difference in in molecular mass
+ 
+
+ align:start position:0%
+a very difference in in molecular mass
+then that wouldn't be true these are not
+
+ align:start position:0%
+then that wouldn't be true these are not
+ 
+
+ align:start position:0%
+then that wouldn't be true these are not
+always near each other all right so
+
+ align:start position:0%
+always near each other all right so
+ 
+
+ align:start position:0%
+always near each other all right so
+that's just how you do one of these
+
+ align:start position:0%
+that's just how you do one of these
+ 
+
+ align:start position:0%
+that's just how you do one of these
+problems they're really pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simple and there are there are some of
+
+ align:start position:0%
+simple and there are there are some of
+ 
+
+ align:start position:0%
+simple and there are there are some of
+those at the end actually of the problem
+
+ align:start position:0%
+those at the end actually of the problem
+ 
+
+ align:start position:0%
+those at the end actually of the problem
+set so the problem set the book has
+
+ align:start position:0%
+set so the problem set the book has
+ 
+
+ align:start position:0%
+set so the problem set the book has
+things in a sort of different order so
+
+ align:start position:0%
+things in a sort of different order so
+ 
+
+ align:start position:0%
+things in a sort of different order so
+uh you'll be able to do the first part
+
+ align:start position:0%
+uh you'll be able to do the first part
+ 
+
+ align:start position:0%
+uh you'll be able to do the first part
+of the problem set and the end of the
+
+ align:start position:0%
+of the problem set and the end of the
+ 
+
+ align:start position:0%
+of the problem set and the end of the
+problem set at this point Point all
+
+ align:start position:0%
+problem set at this point Point all
+ 
+
+ align:start position:0%
+problem set at this point Point all
+right so let me just introduce you to a
+
+ align:start position:0%
+right so let me just introduce you to a
+ 
+
+ align:start position:0%
+right so let me just introduce you to a
+couple of different kinds of
+
+ align:start position:0%
+couple of different kinds of
+ 
+
+ align:start position:0%
+couple of different kinds of
+electrochemical cells so up until this
+
+ align:start position:0%
+electrochemical cells so up until this
+ 
+
+ align:start position:0%
+electrochemical cells so up until this
+point we've only talked about
+
+ align:start position:0%
+point we've only talked about
+ 
+
+ align:start position:0%
+point we've only talked about
+electrochemical cells where something
+
+ align:start position:0%
+electrochemical cells where something
+ 
+
+ align:start position:0%
+electrochemical cells where something
+was deposited or consumed but you can
+
+ align:start position:0%
+was deposited or consumed but you can
+ 
+
+ align:start position:0%
+was deposited or consumed but you can
+use electrodes that are inert I.E they
+
+ align:start position:0%
+use electrodes that are inert I.E they
+ 
+
+ align:start position:0%
+use electrodes that are inert I.E they
+don't get consumed in the reaction or um
+
+ align:start position:0%
+don't get consumed in the reaction or um
+ 
+
+ align:start position:0%
+don't get consumed in the reaction or um
+and an example of that is platinum
+
+ align:start position:0%
+and an example of that is platinum
+ 
+
+ align:start position:0%
+and an example of that is platinum
+electrode so uh as it says they're not
+
+ align:start position:0%
+electrode so uh as it says they're not
+ 
+
+ align:start position:0%
+electrode so uh as it says they're not
+always consumed or produced you can have
+
+ align:start position:0%
+always consumed or produced you can have
+ 
+
+ align:start position:0%
+always consumed or produced you can have
+an inert electrode such as a platinum so
+
+ align:start position:0%
+an inert electrode such as a platinum so
+ 
+
+ align:start position:0%
+an inert electrode such as a platinum so
+in this case we have the Platinum
+
+ align:start position:0%
+in this case we have the Platinum
+ 
+
+ align:start position:0%
+in this case we have the Platinum
+electrode to transfer the electrons
+
+ align:start position:0%
+electrode to transfer the electrons
+ 
+
+ align:start position:0%
+electrode to transfer the electrons
+around but the reaction that's going on
+
+ align:start position:0%
+around but the reaction that's going on
+ 
+
+ align:start position:0%
+around but the reaction that's going on
+is all in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution so this side would be the same
+
+ align:start position:0%
+solution so this side would be the same
+ 
+
+ align:start position:0%
+solution so this side would be the same
+uh this is the the cathode or the
+
+ align:start position:0%
+uh this is the the cathode or the
+ 
+
+ align:start position:0%
+uh this is the the cathode or the
+reduction reaction so we have again the
+
+ align:start position:0%
+reduction reaction so we have again the
+ 
+
+ align:start position:0%
+reduction reaction so we have again the
+copper plus two uh two electrons will
+
+ align:start position:0%
+copper plus two uh two electrons will
+ 
+
+ align:start position:0%
+copper plus two uh two electrons will
+come through the system and plate more
+
+ align:start position:0%
+come through the system and plate more
+ 
+
+ align:start position:0%
+come through the system and plate more
+copper solid on um on to the electrode
+
+ align:start position:0%
+copper solid on um on to the electrode
+ 
+
+ align:start position:0%
+copper solid on um on to the electrode
+here but on the other side the anode
+
+ align:start position:0%
+here but on the other side the anode
+ 
+
+ align:start position:0%
+here but on the other side the anode
+where you have the oxidation the
+
+ align:start position:0%
+where you have the oxidation the
+ 
+
+ align:start position:0%
+where you have the oxidation the
+oxidation reaction is happening all in
+
+ align:start position:0%
+oxidation reaction is happening all in
+ 
+
+ align:start position:0%
+oxidation reaction is happening all in
+solution so the Platinum electrode is
+
+ align:start position:0%
+solution so the Platinum electrode is
+ 
+
+ align:start position:0%
+solution so the Platinum electrode is
+not involved in that so in this case we
+
+ align:start position:0%
+not involved in that so in this case we
+ 
+
+ align:start position:0%
+not involved in that so in this case we
+have chromium plus two going to chromium
+
+ align:start position:0%
+have chromium plus two going to chromium
+ 
+
+ align:start position:0%
+have chromium plus two going to chromium
++ three with one electron so that is
+
+ align:start position:0%
++ three with one electron so that is
+ 
+
+ align:start position:0%
++ three with one electron so that is
+another type of electrochemical cell and
+
+ align:start position:0%
+another type of electrochemical cell and
+ 
+
+ align:start position:0%
+another type of electrochemical cell and
+so we can uh we can write this in look
+
+ align:start position:0%
+so we can uh we can write this in look
+ 
+
+ align:start position:0%
+so we can uh we can write this in look
+at the
+
+ align:start position:0%
+at the
+ 
+
+ align:start position:0%
+at the
+uh look at the notation for this kind of
+
+ align:start position:0%
+uh look at the notation for this kind of
+ 
+
+ align:start position:0%
+uh look at the notation for this kind of
+cell so in in this case you'd put the
+
+ align:start position:0%
+cell so in in this case you'd put the
+ 
+
+ align:start position:0%
+cell so in in this case you'd put the
+Platinum solid in the equation on this
+
+ align:start position:0%
+Platinum solid in the equation on this
+ 
+
+ align:start position:0%
+Platinum solid in the equation on this
+side we have a single line meaning
+
+ align:start position:0%
+side we have a single line meaning
+ 
+
+ align:start position:0%
+side we have a single line meaning
+there's a phase boundary so we're going
+
+ align:start position:0%
+there's a phase boundary so we're going
+ 
+
+ align:start position:0%
+there's a phase boundary so we're going
+from solid uh to to Something in
+
+ align:start position:0%
+from solid uh to to Something in
+ 
+
+ align:start position:0%
+from solid uh to to Something in
+solution and now here is our reaction
+
+ align:start position:0%
+solution and now here is our reaction
+ 
+
+ align:start position:0%
+solution and now here is our reaction
+that happens at the anode and it has a
+
+ align:start position:0%
+that happens at the anode and it has a
+ 
+
+ align:start position:0%
+that happens at the anode and it has a
+comma in between so this indicates that
+
+ align:start position:0%
+comma in between so this indicates that
+ 
+
+ align:start position:0%
+comma in between so this indicates that
+chromium plus two is going to chromium
+
+ align:start position:0%
+chromium plus two is going to chromium
+ 
+
+ align:start position:0%
+chromium plus two is going to chromium
+plus three but there's no phase boundary
+
+ align:start position:0%
+plus three but there's no phase boundary
+ 
+
+ align:start position:0%
+plus three but there's no phase boundary
+between those so there's a comma uh then
+
+ align:start position:0%
+between those so there's a comma uh then
+ 
+
+ align:start position:0%
+between those so there's a comma uh then
+on the other side the two lines
+
+ align:start position:0%
+on the other side the two lines
+ 
+
+ align:start position:0%
+on the other side the two lines
+indicating the salt bridge and then on
+
+ align:start position:0%
+indicating the salt bridge and then on
+ 
+
+ align:start position:0%
+indicating the salt bridge and then on
+the other side we have the copper plus
+
+ align:start position:0%
+the other side we have the copper plus
+ 
+
+ align:start position:0%
+the other side we have the copper plus
+two aquous the line that does indicate
+
+ align:start position:0%
+two aquous the line that does indicate
+ 
+
+ align:start position:0%
+two aquous the line that does indicate
+there's a phase boundary uh going to
+
+ align:start position:0%
+there's a phase boundary uh going to
+ 
+
+ align:start position:0%
+there's a phase boundary uh going to
+Copper so this would be for our anode
+
+ align:start position:0%
+Copper so this would be for our anode
+ 
+
+ align:start position:0%
+Copper so this would be for our anode
+reaction of chromium going to chromium
+
+ align:start position:0%
+reaction of chromium going to chromium
+ 
+
+ align:start position:0%
+reaction of chromium going to chromium
+plus three and one electrode and our
+
+ align:start position:0%
+plus three and one electrode and our
+ 
+
+ align:start position:0%
+plus three and one electrode and our
+cathode reaction copper plus 2 plus two
+
+ align:start position:0%
+cathode reaction copper plus 2 plus two
+ 
+
+ align:start position:0%
+cathode reaction copper plus 2 plus two
+electrons going to Copper solid so
+
+ align:start position:0%
+electrons going to Copper solid so
+ 
+
+ align:start position:0%
+electrons going to Copper solid so
+you'll see this kind of notation in
+
+ align:start position:0%
+you'll see this kind of notation in
+ 
+
+ align:start position:0%
+you'll see this kind of notation in
+these problems as
+
+ align:start position:0%
+these problems as
+ 
+
+ align:start position:0%
+these problems as
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right another example of an inert El
+
+ align:start position:0%
+all right another example of an inert El
+ 
+
+ align:start position:0%
+all right another example of an inert El
+electrode um that sometimes use the
+
+ align:start position:0%
+electrode um that sometimes use the
+ 
+
+ align:start position:0%
+electrode um that sometimes use the
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+electrode
+
+ align:start position:0%
+electrode
+ 
+
+ align:start position:0%
+electrode
+um so often you will see this and
+
+ align:start position:0%
+um so often you will see this and
+ 
+
+ align:start position:0%
+um so often you will see this and
+actually in the back of of your book you
+
+ align:start position:0%
+actually in the back of of your book you
+ 
+
+ align:start position:0%
+actually in the back of of your book you
+will see this as well standard hydrogen
+
+ align:start position:0%
+will see this as well standard hydrogen
+ 
+
+ align:start position:0%
+will see this as well standard hydrogen
+electrode abbreviated she so often
+
+ align:start position:0%
+electrode abbreviated she so often
+ 
+
+ align:start position:0%
+electrode abbreviated she so often
+you'll see in papers or in your book
+
+ align:start position:0%
+you'll see in papers or in your book
+ 
+
+ align:start position:0%
+you'll see in papers or in your book
+that they often need to mention how
+
+ align:start position:0%
+that they often need to mention how
+ 
+
+ align:start position:0%
+that they often need to mention how
+these Redux potentials were measured and
+
+ align:start position:0%
+these Redux potentials were measured and
+ 
+
+ align:start position:0%
+these Redux potentials were measured and
+it's often said it's measured against
+
+ align:start position:0%
+it's often said it's measured against
+ 
+
+ align:start position:0%
+it's often said it's measured against
+she and that's what that stands for the
+
+ align:start position:0%
+she and that's what that stands for the
+ 
+
+ align:start position:0%
+she and that's what that stands for the
+standard hydrogen electrode so you can
+
+ align:start position:0%
+standard hydrogen electrode so you can
+ 
+
+ align:start position:0%
+standard hydrogen electrode so you can
+have the hydrogen electrode on either
+
+ align:start position:0%
+have the hydrogen electrode on either
+ 
+
+ align:start position:0%
+have the hydrogen electrode on either
+side at the anode or at the cathode so
+
+ align:start position:0%
+side at the anode or at the cathode so
+ 
+
+ align:start position:0%
+side at the anode or at the cathode so
+uh over here would be an example when
+
+ align:start position:0%
+uh over here would be an example when
+ 
+
+ align:start position:0%
+uh over here would be an example when
+it's at the at the cathode and in this
+
+ align:start position:0%
+it's at the at the cathode and in this
+ 
+
+ align:start position:0%
+it's at the at the cathode and in this
+case H+ is being reduced and so we have
+
+ align:start position:0%
+case H+ is being reduced and so we have
+ 
+
+ align:start position:0%
+case H+ is being reduced and so we have
+H+ and that's aquous the line for the
+
+ align:start position:0%
+H+ and that's aquous the line for the
+ 
+
+ align:start position:0%
+H+ and that's aquous the line for the
+phase boundary to H2 gas and then you
+
+ align:start position:0%
+phase boundary to H2 gas and then you
+ 
+
+ align:start position:0%
+phase boundary to H2 gas and then you
+have also a phase boundary to the
+
+ align:start position:0%
+have also a phase boundary to the
+ 
+
+ align:start position:0%
+have also a phase boundary to the
+Platinum solid so this is a combining
+
+ align:start position:0%
+Platinum solid so this is a combining
+ 
+
+ align:start position:0%
+Platinum solid so this is a combining
+the platinum and and the
+
+ align:start position:0%
+the platinum and and the
+ 
+
+ align:start position:0%
+the platinum and and the
+hydrogen and uh then on the other side
+
+ align:start position:0%
+hydrogen and uh then on the other side
+ 
+
+ align:start position:0%
+hydrogen and uh then on the other side
+if you had uh it reacting as an anode in
+
+ align:start position:0%
+if you had uh it reacting as an anode in
+ 
+
+ align:start position:0%
+if you had uh it reacting as an anode in
+this case H2 is getting oxidized so you
+
+ align:start position:0%
+this case H2 is getting oxidized so you
+ 
+
+ align:start position:0%
+this case H2 is getting oxidized so you
+have the Platinum solid phase boundary
+
+ align:start position:0%
+have the Platinum solid phase boundary
+ 
+
+ align:start position:0%
+have the Platinum solid phase boundary
+uh hydrogen gas so that would be uh
+
+ align:start position:0%
+uh hydrogen gas so that would be uh
+ 
+
+ align:start position:0%
+uh hydrogen gas so that would be uh
+oxidation state zero phase boundary uh
+
+ align:start position:0%
+oxidation state zero phase boundary uh
+ 
+
+ align:start position:0%
+oxidation state zero phase boundary uh
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+H+ aquous so you can use this sort of
+
+ align:start position:0%
+H+ aquous so you can use this sort of
+ 
+
+ align:start position:0%
+H+ aquous so you can use this sort of
+combination of the platinum and the
+
+ align:start position:0%
+combination of the platinum and the
+ 
+
+ align:start position:0%
+combination of the platinum and the
+hydrogen electrodes as either cathodes
+
+ align:start position:0%
+hydrogen electrodes as either cathodes
+ 
+
+ align:start position:0%
+hydrogen electrodes as either cathodes
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+anodes and so just one example of what
+
+ align:start position:0%
+anodes and so just one example of what
+ 
+
+ align:start position:0%
+anodes and so just one example of what
+this sort of thing would look like so
+
+ align:start position:0%
+this sort of thing would look like so
+ 
+
+ align:start position:0%
+this sort of thing would look like so
+here we have an electrochemical cell now
+
+ align:start position:0%
+here we have an electrochemical cell now
+ 
+
+ align:start position:0%
+here we have an electrochemical cell now
+on this side we just have the the zinc
+
+ align:start position:0%
+on this side we just have the the zinc
+ 
+
+ align:start position:0%
+on this side we just have the the zinc
+electrode which we mentioned in the
+
+ align:start position:0%
+electrode which we mentioned in the
+ 
+
+ align:start position:0%
+electrode which we mentioned in the
+beginning zinc solid and then that would
+
+ align:start position:0%
+beginning zinc solid and then that would
+ 
+
+ align:start position:0%
+beginning zinc solid and then that would
+be zinc plus two in solution we have
+
+ align:start position:0%
+be zinc plus two in solution we have
+ 
+
+ align:start position:0%
+be zinc plus two in solution we have
+wire our salt bridge and in the other
+
+ align:start position:0%
+wire our salt bridge and in the other
+ 
+
+ align:start position:0%
+wire our salt bridge and in the other
+Beaker on the other side we have H some
+
+ align:start position:0%
+Beaker on the other side we have H some
+ 
+
+ align:start position:0%
+Beaker on the other side we have H some
+glass tubing where you would have
+
+ align:start position:0%
+glass tubing where you would have
+ 
+
+ align:start position:0%
+glass tubing where you would have
+hydrogen gas uh in going through into
+
+ align:start position:0%
+hydrogen gas uh in going through into
+ 
+
+ align:start position:0%
+hydrogen gas uh in going through into
+the system um you also have through that
+
+ align:start position:0%
+the system um you also have through that
+ 
+
+ align:start position:0%
+the system um you also have through that
+uh the Platinum uh electrode Platinum
+
+ align:start position:0%
+uh the Platinum uh electrode Platinum
+ 
+
+ align:start position:0%
+uh the Platinum uh electrode Platinum
+solid and you have HCL in your Beaker so
+
+ align:start position:0%
+solid and you have HCL in your Beaker so
+ 
+
+ align:start position:0%
+solid and you have HCL in your Beaker so
+that would be
+
+ align:start position:0%
+that would be
+ 
+
+ align:start position:0%
+that would be
+H+ uh in your
+
+ align:start position:0%
+H+ uh in your
+ 
+
+ align:start position:0%
+H+ uh in your
+Beaker so here is the cathode reaction
+
+ align:start position:0%
+Beaker so here is the cathode reaction
+ 
+
+ align:start position:0%
+Beaker so here is the cathode reaction
+so you would be going from h H+ to h0
+
+ align:start position:0%
+so you would be going from h H+ to h0
+ 
+
+ align:start position:0%
+so you would be going from h H+ to h0
+gas and so as you have the reaction over
+
+ align:start position:0%
+gas and so as you have the reaction over
+ 
+
+ align:start position:0%
+gas and so as you have the reaction over
+here um zinc solid to zinc plus2
+
+ align:start position:0%
+here um zinc solid to zinc plus2
+ 
+
+ align:start position:0%
+here um zinc solid to zinc plus2
+electrons would come along and uh they
+
+ align:start position:0%
+electrons would come along and uh they
+ 
+
+ align:start position:0%
+electrons would come along and uh they
+would convert H+ to H H2 and the
+
+ align:start position:0%
+would convert H+ to H H2 and the
+ 
+
+ align:start position:0%
+would convert H+ to H H2 and the
+electrode here is the inert Platinum
+
+ align:start position:0%
+electrode here is the inert Platinum
+ 
+
+ align:start position:0%
+electrode here is the inert Platinum
+electrode and so here's my attempt to
+
+ align:start position:0%
+electrode and so here's my attempt to
+ 
+
+ align:start position:0%
+electrode and so here's my attempt to
+draw little H2 uh gas bubbles going on
+
+ align:start position:0%
+draw little H2 uh gas bubbles going on
+ 
+
+ align:start position:0%
+draw little H2 uh gas bubbles going on
+so this is another type of electrode
+
+ align:start position:0%
+so this is another type of electrode
+ 
+
+ align:start position:0%
+so this is another type of electrode
+that you should know the the uh notation
+
+ align:start position:0%
+that you should know the the uh notation
+ 
+
+ align:start position:0%
+that you should know the the uh notation
+for it doesn't really change how you do
+
+ align:start position:0%
+for it doesn't really change how you do
+ 
+
+ align:start position:0%
+for it doesn't really change how you do
+problems particularly but it's important
+
+ align:start position:0%
+problems particularly but it's important
+ 
+
+ align:start position:0%
+problems particularly but it's important
+to know what it stands for and again
+
+ align:start position:0%
+to know what it stands for and again
+ 
+
+ align:start position:0%
+to know what it stands for and again
+this is on the other side we've already
+
+ align:start position:0%
+this is on the other side we've already
+ 
+
+ align:start position:0%
+this is on the other side we've already
+talked about about that kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anode all right so this is of course
+
+ align:start position:0%
+anode all right so this is of course
+ 
+
+ align:start position:0%
+anode all right so this is of course
+always things that things that I really
+
+ align:start position:0%
+always things that things that I really
+ 
+
+ align:start position:0%
+always things that things that I really
+like to do because what I like to do is
+
+ align:start position:0%
+like to do because what I like to do is
+ 
+
+ align:start position:0%
+like to do because what I like to do is
+to go back to something you've already
+
+ align:start position:0%
+to go back to something you've already
+ 
+
+ align:start position:0%
+to go back to something you've already
+learned and make connections between
+
+ align:start position:0%
+learned and make connections between
+ 
+
+ align:start position:0%
+learned and make connections between
+different units of fresh freshman
+
+ align:start position:0%
+different units of fresh freshman
+ 
+
+ align:start position:0%
+different units of fresh freshman
+chemistry so we're back to Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G so
+
+ align:start position:0%
+G so
+ 
+
+ align:start position:0%
+G so
+um we're going to now talk about cell
+
+ align:start position:0%
+um we're going to now talk about cell
+ 
+
+ align:start position:0%
+um we're going to now talk about cell
+potential and this is abbreviated Delta
+
+ align:start position:0%
+potential and this is abbreviated Delta
+ 
+
+ align:start position:0%
+potential and this is abbreviated Delta
+e cell potential is often called cell
+
+ align:start position:0%
+e cell potential is often called cell
+ 
+
+ align:start position:0%
+e cell potential is often called cell
+voltage and it's also called the
+
+ align:start position:0%
+voltage and it's also called the
+ 
+
+ align:start position:0%
+voltage and it's also called the
+electron motive force or EMF so you'll
+
+ align:start position:0%
+electron motive force or EMF so you'll
+ 
+
+ align:start position:0%
+electron motive force or EMF so you'll
+see all of those different words and
+
+ align:start position:0%
+see all of those different words and
+ 
+
+ align:start position:0%
+see all of those different words and
+they all sort of stand they stand for
+
+ align:start position:0%
+they all sort of stand they stand for
+ 
+
+ align:start position:0%
+they all sort of stand they stand for
+the same thing this Del Del to e
+
+ align:start position:0%
+the same thing this Del Del to e
+ 
+
+ align:start position:0%
+the same thing this Del Del to e
+term and uh the connection with free
+
+ align:start position:0%
+term and uh the connection with free
+ 
+
+ align:start position:0%
+term and uh the connection with free
+energy so when the electrons
+
+ align:start position:0%
+energy so when the electrons
+ 
+
+ align:start position:0%
+energy so when the electrons
+flow that creates a potential difference
+
+ align:start position:0%
+flow that creates a potential difference
+ 
+
+ align:start position:0%
+flow that creates a potential difference
+a Delta e between the electrodes in the
+
+ align:start position:0%
+a Delta e between the electrodes in the
+ 
+
+ align:start position:0%
+a Delta e between the electrodes in the
+circuit and so the overall free energy
+
+ align:start position:0%
+circuit and so the overall free energy
+ 
+
+ align:start position:0%
+circuit and so the overall free energy
+of the cell is related to this cell
+
+ align:start position:0%
+of the cell is related to this cell
+ 
+
+ align:start position:0%
+of the cell is related to this cell
+potential by the following equation so
+
+ align:start position:0%
+potential by the following equation so
+ 
+
+ align:start position:0%
+potential by the following equation so
+we have Delta G for that particular
+
+ align:start position:0%
+we have Delta G for that particular
+ 
+
+ align:start position:0%
+we have Delta G for that particular
+electrochemical cell is going to be
+
+ align:start position:0%
+electrochemical cell is going to be
+ 
+
+ align:start position:0%
+electrochemical cell is going to be
+equal to to
+
+ align:start position:0%
+equal to to
+ 
+
+ align:start position:0%
+equal to to
+minus n which is the number of electrons
+
+ align:start position:0%
+minus n which is the number of electrons
+ 
+
+ align:start position:0%
+minus n which is the number of electrons
+that are going through the system times
+
+ align:start position:0%
+that are going through the system times
+ 
+
+ align:start position:0%
+that are going through the system times
+Faraday's constant which we talked about
+
+ align:start position:0%
+Faraday's constant which we talked about
+ 
+
+ align:start position:0%
+Faraday's constant which we talked about
+a few minutes ago and Delta e the cell
+
+ align:start position:0%
+a few minutes ago and Delta e the cell
+ 
+
+ align:start position:0%
+a few minutes ago and Delta e the cell
+potential uh for that particular cell so
+
+ align:start position:0%
+potential uh for that particular cell so
+ 
+
+ align:start position:0%
+potential uh for that particular cell so
+there's a nice connection between these
+
+ align:start position:0%
+there's a nice connection between these
+ 
+
+ align:start position:0%
+there's a nice connection between these
+two and that'll be really useful in
+
+ align:start position:0%
+two and that'll be really useful in
+ 
+
+ align:start position:0%
+two and that'll be really useful in
+doing these
+
+ align:start position:0%
+doing these
+ 
+
+ align:start position:0%
+doing these
+problems so um we can also talk about
+
+ align:start position:0%
+problems so um we can also talk about
+ 
+
+ align:start position:0%
+problems so um we can also talk about
+standard States here and the same
+
+ align:start position:0%
+standard States here and the same
+ 
+
+ align:start position:0%
+standard States here and the same
+equation applies whether you're talking
+
+ align:start position:0%
+equation applies whether you're talking
+ 
+
+ align:start position:0%
+equation applies whether you're talking
+about Delta G at any particular time and
+
+ align:start position:0%
+about Delta G at any particular time and
+ 
+
+ align:start position:0%
+about Delta G at any particular time and
+Delta e at any particular time or you're
+
+ align:start position:0%
+Delta e at any particular time or you're
+ 
+
+ align:start position:0%
+Delta e at any particular time or you're
+talking about the Delta G and the Delta
+
+ align:start position:0%
+talking about the Delta G and the Delta
+ 
+
+ align:start position:0%
+talking about the Delta G and the Delta
+e in their standard States so again uh
+
+ align:start position:0%
+e in their standard States so again uh
+ 
+
+ align:start position:0%
+e in their standard States so again uh
+this means the same thing that it has
+
+ align:start position:0%
+this means the same thing that it has
+ 
+
+ align:start position:0%
+this means the same thing that it has
+before uh Delta e KN the knot means that
+
+ align:start position:0%
+before uh Delta e KN the knot means that
+ 
+
+ align:start position:0%
+before uh Delta e KN the knot means that
+you're you're at the standard States and
+
+ align:start position:0%
+you're you're at the standard States and
+ 
+
+ align:start position:0%
+you're you're at the standard States and
+uh Delta G of course a Delta G not is
+
+ align:start position:0%
+uh Delta G of course a Delta G not is
+ 
+
+ align:start position:0%
+uh Delta G of course a Delta G not is
+also Delta G in the standard State and
+
+ align:start position:0%
+also Delta G in the standard State and
+ 
+
+ align:start position:0%
+also Delta G in the standard State and
+uh units of course are important when
+
+ align:start position:0%
+uh units of course are important when
+ 
+
+ align:start position:0%
+uh units of course are important when
+you're talking about without any kind of
+
+ align:start position:0%
+you're talking about without any kind of
+ 
+
+ align:start position:0%
+you're talking about without any kind of
+Delta e or cell potential you're talking
+
+ align:start position:0%
+Delta e or cell potential you're talking
+ 
+
+ align:start position:0%
+Delta e or cell potential you're talking
+about things in volts as the
+
+ align:start position:0%
+about things in volts as the
+ 
+
+ align:start position:0%
+about things in volts as the
+units all right so now what those
+
+ align:start position:0%
+units all right so now what those
+ 
+
+ align:start position:0%
+units all right so now what those
+equations mean is if you calculate a
+
+ align:start position:0%
+equations mean is if you calculate a
+ 
+
+ align:start position:0%
+equations mean is if you calculate a
+Delta e for the cell the cell voltage uh
+
+ align:start position:0%
+Delta e for the cell the cell voltage uh
+ 
+
+ align:start position:0%
+Delta e for the cell the cell voltage uh
+or the cell potential you can figure out
+
+ align:start position:0%
+or the cell potential you can figure out
+ 
+
+ align:start position:0%
+or the cell potential you can figure out
+whether the reaction will be spontaneous
+
+ align:start position:0%
+whether the reaction will be spontaneous
+ 
+
+ align:start position:0%
+whether the reaction will be spontaneous
+or not because you can use that equation
+
+ align:start position:0%
+or not because you can use that equation
+ 
+
+ align:start position:0%
+or not because you can use that equation
+uh and look at with that particular
+
+ align:start position:0%
+uh and look at with that particular
+ 
+
+ align:start position:0%
+uh and look at with that particular
+Delta e will Delta G be negative will be
+
+ align:start position:0%
+Delta e will Delta G be negative will be
+ 
+
+ align:start position:0%
+Delta e will Delta G be negative will be
+a spontaneous reaction so the first
+
+ align:start position:0%
+a spontaneous reaction so the first
+ 
+
+ align:start position:0%
+a spontaneous reaction so the first
+thing we need to learn how to do is how
+
+ align:start position:0%
+thing we need to learn how to do is how
+ 
+
+ align:start position:0%
+thing we need to learn how to do is how
+to calculate the cell potentials or the
+
+ align:start position:0%
+to calculate the cell potentials or the
+ 
+
+ align:start position:0%
+to calculate the cell potentials or the
+electromotive force and then we can we
+
+ align:start position:0%
+electromotive force and then we can we
+ 
+
+ align:start position:0%
+electromotive force and then we can we
+already know how to convert that to
+
+ align:start position:0%
+already know how to convert that to
+ 
+
+ align:start position:0%
+already know how to convert that to
+Delta G so let's let's look at this
+
+ align:start position:0%
+Delta G so let's let's look at this
+ 
+
+ align:start position:0%
+Delta G so let's let's look at this
+equation here and uh calculate what the
+
+ align:start position:0%
+equation here and uh calculate what the
+ 
+
+ align:start position:0%
+equation here and uh calculate what the
+Delta e the cell potential for this
+
+ align:start position:0%
+Delta e the cell potential for this
+ 
+
+ align:start position:0%
+Delta e the cell potential for this
+particular electrochemical cell that
+
+ align:start position:0%
+particular electrochemical cell that
+ 
+
+ align:start position:0%
+particular electrochemical cell that
+we've been talking
+
+ align:start position:0%
+we've been talking
+ 
+
+ align:start position:0%
+we've been talking
+about so the reaction at the anode which
+
+ align:start position:0%
+about so the reaction at the anode which
+ 
+
+ align:start position:0%
+about so the reaction at the anode which
+we mentioned is this zinc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction and this is an
+
+ align:start position:0%
+reaction and this is an
+ 
+
+ align:start position:0%
+reaction and this is an
+oxidation the reaction at the cathode
+
+ align:start position:0%
+oxidation the reaction at the cathode
+ 
+
+ align:start position:0%
+oxidation the reaction at the cathode
+was the reaction with copper copper plus
+
+ align:start position:0%
+was the reaction with copper copper plus
+ 
+
+ align:start position:0%
+was the reaction with copper copper plus
+two and two electrons going to Copper
+
+ align:start position:0%
+two and two electrons going to Copper
+ 
+
+ align:start position:0%
+two and two electrons going to Copper
+solid and that was our reduction
+
+ align:start position:0%
+solid and that was our reduction
+ 
+
+ align:start position:0%
+solid and that was our reduction
+reaction and so now we can just use a
+
+ align:start position:0%
+reaction and so now we can just use a
+ 
+
+ align:start position:0%
+reaction and so now we can just use a
+simple equation to calculate uh Delta e
+
+ align:start position:0%
+simple equation to calculate uh Delta e
+ 
+
+ align:start position:0%
+simple equation to calculate uh Delta e
+KN if we're using the standard reduction
+
+ align:start position:0%
+KN if we're using the standard reduction
+ 
+
+ align:start position:0%
+KN if we're using the standard reduction
+potential for the reaction at the
+
+ align:start position:0%
+potential for the reaction at the
+ 
+
+ align:start position:0%
+potential for the reaction at the
+cathode minus the standard reduction
+
+ align:start position:0%
+cathode minus the standard reduction
+ 
+
+ align:start position:0%
+cathode minus the standard reduction
+potential for the couple at the anode
+
+ align:start position:0%
+potential for the couple at the anode
+ 
+
+ align:start position:0%
+potential for the couple at the anode
+and the point that I want to make here
+
+ align:start position:0%
+and the point that I want to make here
+ 
+
+ align:start position:0%
+and the point that I want to make here
+is that in this fairly simple
+
+ align:start position:0%
+is that in this fairly simple
+ 
+
+ align:start position:0%
+is that in this fairly simple
+equation this term this just e not here
+
+ align:start position:0%
+equation this term this just e not here
+ 
+
+ align:start position:0%
+equation this term this just e not here
+is the standard reduction
+
+ align:start position:0%
+is the standard reduction
+ 
+
+ align:start position:0%
+is the standard reduction
+potential so you don't want to put in
+
+ align:start position:0%
+potential so you don't want to put in
+ 
+
+ align:start position:0%
+potential so you don't want to put in
+something other than that so don't don't
+
+ align:start position:0%
+something other than that so don't don't
+ 
+
+ align:start position:0%
+something other than that so don't don't
+mess around with changing signs of
+
+ align:start position:0%
+mess around with changing signs of
+ 
+
+ align:start position:0%
+mess around with changing signs of
+reactions all you want to do is enter a
+
+ align:start position:0%
+reactions all you want to do is enter a
+ 
+
+ align:start position:0%
+reactions all you want to do is enter a
+reduction potential here and a reduction
+
+ align:start position:0%
+reduction potential here and a reduction
+ 
+
+ align:start position:0%
+reduction potential here and a reduction
+potential here and then this equation
+
+ align:start position:0%
+potential here and then this equation
+ 
+
+ align:start position:0%
+potential here and then this equation
+will always work for you and you'll see
+
+ align:start position:0%
+will always work for you and you'll see
+ 
+
+ align:start position:0%
+will always work for you and you'll see
+what I mean I think a bit more uh when
+
+ align:start position:0%
+what I mean I think a bit more uh when
+ 
+
+ align:start position:0%
+what I mean I think a bit more uh when
+we put that in but if it's the reduction
+
+ align:start position:0%
+we put that in but if it's the reduction
+ 
+
+ align:start position:0%
+we put that in but if it's the reduction
+potential you'd be looking up copper 2
+
+ align:start position:0%
+potential you'd be looking up copper 2
+ 
+
+ align:start position:0%
+potential you'd be looking up copper 2
+plus to Copper solid reduction potential
+
+ align:start position:0%
+plus to Copper solid reduction potential
+ 
+
+ align:start position:0%
+plus to Copper solid reduction potential
+you're looking up zinc plus two to zinc
+
+ align:start position:0%
+you're looking up zinc plus two to zinc
+ 
+
+ align:start position:0%
+you're looking up zinc plus two to zinc
+solid you're you're not caring about
+
+ align:start position:0%
+solid you're you're not caring about
+ 
+
+ align:start position:0%
+solid you're you're not caring about
+which which of these reactions is an
+
+ align:start position:0%
+which which of these reactions is an
+ 
+
+ align:start position:0%
+which which of these reactions is an
+oxidation or which is a reduction at
+
+ align:start position:0%
+oxidation or which is a reduction at
+ 
+
+ align:start position:0%
+oxidation or which is a reduction at
+this point you figured it out by which
+
+ align:start position:0%
+this point you figured it out by which
+ 
+
+ align:start position:0%
+this point you figured it out by which
+is at the cathode if you know what's at
+
+ align:start position:0%
+is at the cathode if you know what's at
+ 
+
+ align:start position:0%
+is at the cathode if you know what's at
+the cathode and you know what's at the
+
+ align:start position:0%
+the cathode and you know what's at the
+ 
+
+ align:start position:0%
+the cathode and you know what's at the
+anode then you enter in the reduction
+
+ align:start position:0%
+anode then you enter in the reduction
+ 
+
+ align:start position:0%
+anode then you enter in the reduction
+potential so let's let's do that and you
+
+ align:start position:0%
+potential so let's let's do that and you
+ 
+
+ align:start position:0%
+potential so let's let's do that and you
+can look up the standard reduction
+
+ align:start position:0%
+can look up the standard reduction
+ 
+
+ align:start position:0%
+can look up the standard reduction
+Potentials in your book there's a table
+
+ align:start position:0%
+Potentials in your book there's a table
+ 
+
+ align:start position:0%
+Potentials in your book there's a table
+in chapter 12 and there's also a table
+
+ align:start position:0%
+in chapter 12 and there's also a table
+ 
+
+ align:start position:0%
+in chapter 12 and there's also a table
+at the end of the book in appendix 2 and
+
+ align:start position:0%
+at the end of the book in appendix 2 and
+ 
+
+ align:start position:0%
+at the end of the book in appendix 2 and
+you can look up the values um and here
+
+ align:start position:0%
+you can look up the values um and here
+ 
+
+ align:start position:0%
+you can look up the values um and here
+they're written as reduction potentials
+
+ align:start position:0%
+they're written as reduction potentials
+ 
+
+ align:start position:0%
+they're written as reduction potentials
+and that's what you'll see in the table
+
+ align:start position:0%
+and that's what you'll see in the table
+ 
+
+ align:start position:0%
+and that's what you'll see in the table
+and uh that's that's what the um
+
+ align:start position:0%
+and uh that's that's what the um
+ 
+
+ align:start position:0%
+and uh that's that's what the um
+information that you can look up and
+
+ align:start position:0%
+information that you can look up and
+ 
+
+ align:start position:0%
+information that you can look up and
+then you have your
+
+ align:start position:0%
+then you have your
+ 
+
+ align:start position:0%
+then you have your
+equation and you will enter in the
+
+ align:start position:0%
+equation and you will enter in the
+ 
+
+ align:start position:0%
+equation and you will enter in the
+reduction potential for the reaction at
+
+ align:start position:0%
+reduction potential for the reaction at
+ 
+
+ align:start position:0%
+reduction potential for the reaction at
+the cathode and enter in the reduction
+
+ align:start position:0%
+the cathode and enter in the reduction
+ 
+
+ align:start position:0%
+the cathode and enter in the reduction
+potential for the reaction at the
+
+ align:start position:0%
+potential for the reaction at the
+ 
+
+ align:start position:0%
+potential for the reaction at the
+anode and here you'll get out a positive
+
+ align:start position:0%
+anode and here you'll get out a positive
+ 
+
+ align:start position:0%
+anode and here you'll get out a positive
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+1.13 volts so again this is the copper
+
+ align:start position:0%
+1.13 volts so again this is the copper
+ 
+
+ align:start position:0%
+1.13 volts so again this is the copper
+reaction this is the zinc reaction so
+
+ align:start position:0%
+reaction this is the zinc reaction so
+ 
+
+ align:start position:0%
+reaction this is the zinc reaction so
+the reason why I want I'm sort of trying
+
+ align:start position:0%
+the reason why I want I'm sort of trying
+ 
+
+ align:start position:0%
+the reason why I want I'm sort of trying
+to jump up and down about the fact that
+
+ align:start position:0%
+to jump up and down about the fact that
+ 
+
+ align:start position:0%
+to jump up and down about the fact that
+you should enter in reduction potentials
+
+ align:start position:0%
+you should enter in reduction potentials
+ 
+
+ align:start position:0%
+you should enter in reduction potentials
+is because if you go if you play around
+
+ align:start position:0%
+is because if you go if you play around
+ 
+
+ align:start position:0%
+is because if you go if you play around
+and all of a sudden switch the signs
+
+ align:start position:0%
+and all of a sudden switch the signs
+ 
+
+ align:start position:0%
+and all of a sudden switch the signs
+then you're going to come out with the
+
+ align:start position:0%
+then you're going to come out with the
+ 
+
+ align:start position:0%
+then you're going to come out with the
+wrong answer and the one of the
+
+ align:start position:0%
+wrong answer and the one of the
+ 
+
+ align:start position:0%
+wrong answer and the one of the
+important points about this answer here
+
+ align:start position:0%
+important points about this answer here
+ 
+
+ align:start position:0%
+important points about this answer here
+is is Delta e positive or negative
+
+ align:start position:0%
+is is Delta e positive or negative
+ 
+
+ align:start position:0%
+is is Delta e positive or negative
+because that's going to tell you if the
+
+ align:start position:0%
+because that's going to tell you if the
+ 
+
+ align:start position:0%
+because that's going to tell you if the
+reaction is spontaneous or not so if you
+
+ align:start position:0%
+reaction is spontaneous or not so if you
+ 
+
+ align:start position:0%
+reaction is spontaneous or not so if you
+do clever things and switch the signs
+
+ align:start position:0%
+do clever things and switch the signs
+ 
+
+ align:start position:0%
+do clever things and switch the signs
+for these around you'll often
+
+ align:start position:0%
+for these around you'll often
+ 
+
+ align:start position:0%
+for these around you'll often
+always come out with the wrong answer
+
+ align:start position:0%
+always come out with the wrong answer
+ 
+
+ align:start position:0%
+always come out with the wrong answer
+there which then affects all the
+
+ align:start position:0%
+there which then affects all the
+ 
+
+ align:start position:0%
+there which then affects all the
+problems that you do after that so as
+
+ align:start position:0%
+problems that you do after that so as
+ 
+
+ align:start position:0%
+problems that you do after that so as
+long as you use this equation and always
+
+ align:start position:0%
+long as you use this equation and always
+ 
+
+ align:start position:0%
+long as you use this equation and always
+enter in a reduction potential you'll be
+
+ align:start position:0%
+enter in a reduction potential you'll be
+ 
+
+ align:start position:0%
+enter in a reduction potential you'll be
+fine and you won't have any of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems all right so is the flow of
+
+ align:start position:0%
+problems all right so is the flow of
+ 
+
+ align:start position:0%
+problems all right so is the flow of
+electrons spontaneous for this
+
+ align:start position:0%
+electrons spontaneous for this
+ 
+
+ align:start position:0%
+electrons spontaneous for this
+particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell so people are saying yes and that's
+
+ align:start position:0%
+cell so people are saying yes and that's
+ 
+
+ align:start position:0%
+cell so people are saying yes and that's
+the right answer and the way that we
+
+ align:start position:0%
+the right answer and the way that we
+ 
+
+ align:start position:0%
+the right answer and the way that we
+know that is because we remember this
+
+ align:start position:0%
+know that is because we remember this
+ 
+
+ align:start position:0%
+know that is because we remember this
+equation con um comparing Delta e and
+
+ align:start position:0%
+equation con um comparing Delta e and
+ 
+
+ align:start position:0%
+equation con um comparing Delta e and
+Delta G so here if this one is is
+
+ align:start position:0%
+Delta G so here if this one is is
+ 
+
+ align:start position:0%
+Delta G so here if this one is is
+positive then this term will be negative
+
+ align:start position:0%
+positive then this term will be negative
+ 
+
+ align:start position:0%
+positive then this term will be negative
+because this is number of moles which is
+
+ align:start position:0%
+because this is number of moles which is
+ 
+
+ align:start position:0%
+because this is number of moles which is
+always positive and Faraday's constant
+
+ align:start position:0%
+always positive and Faraday's constant
+ 
+
+ align:start position:0%
+always positive and Faraday's constant
+is always positive so if we have a
+
+ align:start position:0%
+is always positive so if we have a
+ 
+
+ align:start position:0%
+is always positive so if we have a
+positive value here then the net sum is
+
+ align:start position:0%
+positive value here then the net sum is
+ 
+
+ align:start position:0%
+positive value here then the net sum is
+negative this will be negative and that
+
+ align:start position:0%
+negative this will be negative and that
+ 
+
+ align:start position:0%
+negative this will be negative and that
+will make uh it spont aneous so if Delta
+
+ align:start position:0%
+will make uh it spont aneous so if Delta
+ 
+
+ align:start position:0%
+will make uh it spont aneous so if Delta
+e is positive Delta G will be negative
+
+ align:start position:0%
+e is positive Delta G will be negative
+ 
+
+ align:start position:0%
+e is positive Delta G will be negative
+Delta and this is true again if it's
+
+ align:start position:0%
+Delta and this is true again if it's
+ 
+
+ align:start position:0%
+Delta and this is true again if it's
+Delta e Delta G not uh same equation so
+
+ align:start position:0%
+Delta e Delta G not uh same equation so
+ 
+
+ align:start position:0%
+Delta e Delta G not uh same equation so
+if Delta G is negative will it be
+
+ align:start position:0%
+if Delta G is negative will it be
+ 
+
+ align:start position:0%
+if Delta G is negative will it be
+spontaneous and uh the answer is yes uh
+
+ align:start position:0%
+spontaneous and uh the answer is yes uh
+ 
+
+ align:start position:0%
+spontaneous and uh the answer is yes uh
+back to previous
+
+ align:start position:0%
+back to previous
+ 
+
+ align:start position:0%
+back to previous
+units so um in in some of the problems
+
+ align:start position:0%
+units so um in in some of the problems
+ 
+
+ align:start position:0%
+units so um in in some of the problems
+in your book that you'll work they'll
+
+ align:start position:0%
+in your book that you'll work they'll
+ 
+
+ align:start position:0%
+in your book that you'll work they'll
+tell you that uh this should this is a
+
+ align:start position:0%
+tell you that uh this should this is a
+ 
+
+ align:start position:0%
+tell you that uh this should this is a
+spontaneous it's electrochemical cell
+
+ align:start position:0%
+spontaneous it's electrochemical cell
+ 
+
+ align:start position:0%
+spontaneous it's electrochemical cell
+and then you can figure out which
+
+ align:start position:0%
+and then you can figure out which
+ 
+
+ align:start position:0%
+and then you can figure out which
+reaction had to be at the anode or which
+
+ align:start position:0%
+reaction had to be at the anode or which
+ 
+
+ align:start position:0%
+reaction had to be at the anode or which
+one had to be at the cathode for that uh
+
+ align:start position:0%
+one had to be at the cathode for that uh
+ 
+
+ align:start position:0%
+one had to be at the cathode for that uh
+through looking calculating the Delta e
+
+ align:start position:0%
+through looking calculating the Delta e
+ 
+
+ align:start position:0%
+through looking calculating the Delta e
+and then figuring out if it positive or
+
+ align:start position:0%
+and then figuring out if it positive or
+ 
+
+ align:start position:0%
+and then figuring out if it positive or
+negative therefore Delta G must be uh
+
+ align:start position:0%
+negative therefore Delta G must be uh
+ 
+
+ align:start position:0%
+negative therefore Delta G must be uh
+positive or negative spontaneous or
+
+ align:start position:0%
+positive or negative spontaneous or
+ 
+
+ align:start position:0%
+positive or negative spontaneous or
+non-spontaneous
+
+ align:start position:0%
+non-spontaneous
+ 
+
+ align:start position:0%
+non-spontaneous
+all right so what do you call it if
+
+ align:start position:0%
+all right so what do you call it if
+ 
+
+ align:start position:0%
+all right so what do you call it if
+there is a spontaneous reaction so here
+
+ align:start position:0%
+there is a spontaneous reaction so here
+ 
+
+ align:start position:0%
+there is a spontaneous reaction so here
+are some terms that you should know you
+
+ align:start position:0%
+are some terms that you should know you
+ 
+
+ align:start position:0%
+are some terms that you should know you
+you have a galvanic cell and that's an
+
+ align:start position:0%
+you have a galvanic cell and that's an
+ 
+
+ align:start position:0%
+you have a galvanic cell and that's an
+electrochemical cell in which the
+
+ align:start position:0%
+electrochemical cell in which the
+ 
+
+ align:start position:0%
+electrochemical cell in which the
+reaction is spontaneous so it can
+
+ align:start position:0%
+reaction is spontaneous so it can
+ 
+
+ align:start position:0%
+reaction is spontaneous so it can
+generate an electron electric current
+
+ align:start position:0%
+generate an electron electric current
+ 
+
+ align:start position:0%
+generate an electron electric current
+and your book uses this and will say oh
+
+ align:start position:0%
+and your book uses this and will say oh
+ 
+
+ align:start position:0%
+and your book uses this and will say oh
+this is a galvanic cell and already then
+
+ align:start position:0%
+this is a galvanic cell and already then
+ 
+
+ align:start position:0%
+this is a galvanic cell and already then
+you should know something about that
+
+ align:start position:0%
+you should know something about that
+ 
+
+ align:start position:0%
+you should know something about that
+reaction uh the other option is an
+
+ align:start position:0%
+reaction uh the other option is an
+ 
+
+ align:start position:0%
+reaction uh the other option is an
+electrolytic cell and in this case
+
+ align:start position:0%
+electrolytic cell and in this case
+ 
+
+ align:start position:0%
+electrolytic cell and in this case
+energy has to be um provided to the
+
+ align:start position:0%
+energy has to be um provided to the
+ 
+
+ align:start position:0%
+energy has to be um provided to the
+Circuit to carry out a non-spontaneous
+
+ align:start position:0%
+Circuit to carry out a non-spontaneous
+ 
+
+ align:start position:0%
+Circuit to carry out a non-spontaneous
+reaction so some you might just want
+
+ align:start position:0%
+reaction so some you might just want
+ 
+
+ align:start position:0%
+reaction so some you might just want
+that non-spontaneous reaction to go and
+
+ align:start position:0%
+that non-spontaneous reaction to go and
+ 
+
+ align:start position:0%
+that non-spontaneous reaction to go and
+then you will have to uh Supply some
+
+ align:start position:0%
+then you will have to uh Supply some
+ 
+
+ align:start position:0%
+then you will have to uh Supply some
+form of of energy to get that reaction
+
+ align:start position:0%
+form of of energy to get that reaction
+ 
+
+ align:start position:0%
+form of of energy to get that reaction
+to work and in in the body um there are
+
+ align:start position:0%
+to work and in in the body um there are
+ 
+
+ align:start position:0%
+to work and in in the body um there are
+both of these kinds of reactions
+
+ align:start position:0%
+both of these kinds of reactions
+ 
+
+ align:start position:0%
+both of these kinds of reactions
+sometimes you would have a reaction an
+
+ align:start position:0%
+sometimes you would have a reaction an
+ 
+
+ align:start position:0%
+sometimes you would have a reaction an
+oxidation Rea reduction reaction that's
+
+ align:start position:0%
+oxidation Rea reduction reaction that's
+ 
+
+ align:start position:0%
+oxidation Rea reduction reaction that's
+spontaneous and that could be used to
+
+ align:start position:0%
+spontaneous and that could be used to
+ 
+
+ align:start position:0%
+spontaneous and that could be used to
+produce some kind of energy it would be
+
+ align:start position:0%
+produce some kind of energy it would be
+ 
+
+ align:start position:0%
+produce some kind of energy it would be
+coupled to an energy generating process
+
+ align:start position:0%
+coupled to an energy generating process
+ 
+
+ align:start position:0%
+coupled to an energy generating process
+in the body other times the body needs a
+
+ align:start position:0%
+in the body other times the body needs a
+ 
+
+ align:start position:0%
+in the body other times the body needs a
+reaction that's unfavorable to go and it
+
+ align:start position:0%
+reaction that's unfavorable to go and it
+ 
+
+ align:start position:0%
+reaction that's unfavorable to go and it
+has to also supply energy to get that
+
+ align:start position:0%
+has to also supply energy to get that
+ 
+
+ align:start position:0%
+has to also supply energy to get that
+reaction to go and we'll talk about
+
+ align:start position:0%
+reaction to go and we'll talk about
+ 
+
+ align:start position:0%
+reaction to go and we'll talk about
+biological examples of these as
+
+ align:start position:0%
+biological examples of these as
+ 
+
+ align:start position:0%
+biological examples of these as
+well all right so then just the brief
+
+ align:start position:0%
+well all right so then just the brief
+ 
+
+ align:start position:0%
+well all right so then just the brief
+summary for this part if the cell
+
+ align:start position:0%
+summary for this part if the cell
+ 
+
+ align:start position:0%
+summary for this part if the cell
+operates spontaneously that can be
+
+ align:start position:0%
+operates spontaneously that can be
+ 
+
+ align:start position:0%
+operates spontaneously that can be
+determined by the uh the Delta e a
+
+ align:start position:0%
+determined by the uh the Delta e a
+ 
+
+ align:start position:0%
+determined by the uh the Delta e a
+positive value means a negative value so
+
+ align:start position:0%
+positive value means a negative value so
+ 
+
+ align:start position:0%
+positive value means a negative value so
+that will be spontaneous and you can get
+
+ align:start position:0%
+that will be spontaneous and you can get
+ 
+
+ align:start position:0%
+that will be spontaneous and you can get
+your Delta e uh from standard reduction
+
+ align:start position:0%
+your Delta e uh from standard reduction
+ 
+
+ align:start position:0%
+your Delta e uh from standard reduction
+potentials for the half reactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+involved all
+
+ align:start position:0%
+involved all
+ 
+
+ align:start position:0%
+involved all
+right now we're going to think about
+
+ align:start position:0%
+right now we're going to think about
+ 
+
+ align:start position:0%
+right now we're going to think about
+what it means if we have certain
+
+ align:start position:0%
+what it means if we have certain
+ 
+
+ align:start position:0%
+what it means if we have certain
+standard reduction potentials if you
+
+ align:start position:0%
+standard reduction potentials if you
+ 
+
+ align:start position:0%
+standard reduction potentials if you
+have a standard reduction potential
+
+ align:start position:0%
+have a standard reduction potential
+ 
+
+ align:start position:0%
+have a standard reduction potential
+that's a large positive number or if you
+
+ align:start position:0%
+that's a large positive number or if you
+ 
+
+ align:start position:0%
+that's a large positive number or if you
+have a standard reduction potential
+
+ align:start position:0%
+have a standard reduction potential
+ 
+
+ align:start position:0%
+have a standard reduction potential
+that's a large negative number or if
+
+ align:start position:0%
+that's a large negative number or if
+ 
+
+ align:start position:0%
+that's a large negative number or if
+you're somewhere in between what does
+
+ align:start position:0%
+you're somewhere in between what does
+ 
+
+ align:start position:0%
+you're somewhere in between what does
+that tell you about the properties of
+
+ align:start position:0%
+that tell you about the properties of
+ 
+
+ align:start position:0%
+that tell you about the properties of
+those particular
+
+ align:start position:0%
+those particular
+ 
+
+ align:start position:0%
+those particular
+elements so a large
+
+ align:start position:0%
+elements so a large
+ 
+
+ align:start position:0%
+elements so a large
+positive standard reduction potential
+
+ align:start position:0%
+positive standard reduction potential
+ 
+
+ align:start position:0%
+positive standard reduction potential
+means that the element is easy to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduce so let's look at an example for
+
+ align:start position:0%
+reduce so let's look at an example for
+ 
+
+ align:start position:0%
+reduce so let's look at an example for
+this an example we have uh F2 gas plus
+
+ align:start position:0%
+this an example we have uh F2 gas plus
+ 
+
+ align:start position:0%
+this an example we have uh F2 gas plus
+two electrons going to 2f minus and this
+
+ align:start position:0%
+two electrons going to 2f minus and this
+ 
+
+ align:start position:0%
+two electrons going to 2f minus and this
+has a standard reduction potential of
+
+ align:start position:0%
+has a standard reduction potential of
+ 
+
+ align:start position:0%
+has a standard reduction potential of
+plus 2.87 volts and that is a large
+
+ align:start position:0%
+plus 2.87 volts and that is a large
+ 
+
+ align:start position:0%
+plus 2.87 volts and that is a large
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+number so what that's going to mean is
+
+ align:start position:0%
+number so what that's going to mean is
+ 
+
+ align:start position:0%
+number so what that's going to mean is
+that that this is favorable in the
+
+ align:start position:0%
+that that this is favorable in the
+ 
+
+ align:start position:0%
+that that this is favorable in the
+direction is written and favorable means
+
+ align:start position:0%
+direction is written and favorable means
+ 
+
+ align:start position:0%
+direction is written and favorable means
+it's easy to add electrons this wants to
+
+ align:start position:0%
+it's easy to add electrons this wants to
+ 
+
+ align:start position:0%
+it's easy to add electrons this wants to
+be reduced to F minus it's happy that
+
+ align:start position:0%
+be reduced to F minus it's happy that
+ 
+
+ align:start position:0%
+be reduced to F minus it's happy that
+way if it has a large positive sign for
+
+ align:start position:0%
+way if it has a large positive sign for
+ 
+
+ align:start position:0%
+way if it has a large positive sign for
+for the standard reduction potential
+
+ align:start position:0%
+for the standard reduction potential
+ 
+
+ align:start position:0%
+for the standard reduction potential
+then Delta G will be negative which will
+
+ align:start position:0%
+then Delta G will be negative which will
+ 
+
+ align:start position:0%
+then Delta G will be negative which will
+be SP uh favorable or spontaneous in
+
+ align:start position:0%
+be SP uh favorable or spontaneous in
+ 
+
+ align:start position:0%
+be SP uh favorable or spontaneous in
+that direction so this is a favorable
+
+ align:start position:0%
+that direction so this is a favorable
+ 
+
+ align:start position:0%
+that direction so this is a favorable
+reaction F2 is easy to reduce it wants
+
+ align:start position:0%
+reaction F2 is easy to reduce it wants
+ 
+
+ align:start position:0%
+reaction F2 is easy to reduce it wants
+to be reduced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is it a good oxidating um oxidizing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+agent
+
+ align:start position:0%
+agent
+ 
+
+ align:start position:0%
+agent
+yes so again a good oxidizing agent
+
+ align:start position:0%
+yes so again a good oxidizing agent
+ 
+
+ align:start position:0%
+yes so again a good oxidizing agent
+oxidizes other things and is reduced
+
+ align:start position:0%
+oxidizes other things and is reduced
+ 
+
+ align:start position:0%
+oxidizes other things and is reduced
+itself so it runs around and tries to
+
+ align:start position:0%
+itself so it runs around and tries to
+ 
+
+ align:start position:0%
+itself so it runs around and tries to
+oxidize other stuff which means that it
+
+ align:start position:0%
+oxidize other stuff which means that it
+ 
+
+ align:start position:0%
+oxidize other stuff which means that it
+gets reduced which is what it wants to
+
+ align:start position:0%
+gets reduced which is what it wants to
+ 
+
+ align:start position:0%
+gets reduced which is what it wants to
+be it wants to be reduced so this is a
+
+ align:start position:0%
+be it wants to be reduced so this is a
+ 
+
+ align:start position:0%
+be it wants to be reduced so this is a
+good oxidizing agent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we look at the
+
+ align:start position:0%
+so if we look at the
+ 
+
+ align:start position:0%
+so if we look at the
+couple here
+
+ align:start position:0%
+couple here
+ 
+
+ align:start position:0%
+couple here
+F2 um slf minus this reduction couple
+
+ align:start position:0%
+F2 um slf minus this reduction couple
+ 
+
+ align:start position:0%
+F2 um slf minus this reduction couple
+with the large positive value what we
+
+ align:start position:0%
+with the large positive value what we
+ 
+
+ align:start position:0%
+with the large positive value what we
+can say is that the oxidized
+
+ align:start position:0%
+can say is that the oxidized
+ 
+
+ align:start position:0%
+can say is that the oxidized
+species and that's this one here the F2
+
+ align:start position:0%
+species and that's this one here the F2
+ 
+
+ align:start position:0%
+species and that's this one here the F2
+is very oxidizing it's a good oxidizing
+
+ align:start position:0%
+is very oxidizing it's a good oxidizing
+ 
+
+ align:start position:0%
+is very oxidizing it's a good oxidizing
+agent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a table from your book so
+
+ align:start position:0%
+and this is a table from your book so
+ 
+
+ align:start position:0%
+and this is a table from your book so
+it's not in your handout but you can
+
+ align:start position:0%
+it's not in your handout but you can
+ 
+
+ align:start position:0%
+it's not in your handout but you can
+look it up and uh here's the page number
+
+ align:start position:0%
+look it up and uh here's the page number
+ 
+
+ align:start position:0%
+look it up and uh here's the page number
+and this is the one we just looked at f2
+
+ align:start position:0%
+and this is the one we just looked at f2
+ 
+
+ align:start position:0%
+and this is the one we just looked at f2
+to F minus and it says right on the top
+
+ align:start position:0%
+to F minus and it says right on the top
+ 
+
+ align:start position:0%
+to F minus and it says right on the top
+oxidized form which is F2 is strongly
+
+ align:start position:0%
+oxidized form which is F2 is strongly
+ 
+
+ align:start position:0%
+oxidized form which is F2 is strongly
+oxidizing so it like it has a big
+
+ align:start position:0%
+oxidizing so it like it has a big
+ 
+
+ align:start position:0%
+oxidizing so it like it has a big
+positive number it's at the very top of
+
+ align:start position:0%
+positive number it's at the very top of
+ 
+
+ align:start position:0%
+positive number it's at the very top of
+the table big positive number it likes
+
+ align:start position:0%
+the table big positive number it likes
+ 
+
+ align:start position:0%
+the table big positive number it likes
+to be reduced I.E it likes to oxidize
+
+ align:start position:0%
+to be reduced I.E it likes to oxidize
+ 
+
+ align:start position:0%
+to be reduced I.E it likes to oxidize
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+things so now let's go to the bottom of
+
+ align:start position:0%
+things so now let's go to the bottom of
+ 
+
+ align:start position:0%
+things so now let's go to the bottom of
+the table and see what we can say about
+
+ align:start position:0%
+the table and see what we can say about
+ 
+
+ align:start position:0%
+the table and see what we can say about
+this uh lithium uh plus lithium solid
+
+ align:start position:0%
+this uh lithium uh plus lithium solid
+ 
+
+ align:start position:0%
+this uh lithium uh plus lithium solid
+couple so that had a large negative
+
+ align:start position:0%
+couple so that had a large negative
+ 
+
+ align:start position:0%
+couple so that had a large negative
+value for the standard reduction
+
+ align:start position:0%
+value for the standard reduction
+ 
+
+ align:start position:0%
+value for the standard reduction
+potential and that means it's hard to
+
+ align:start position:0%
+potential and that means it's hard to
+ 
+
+ align:start position:0%
+potential and that means it's hard to
+reduce so let's look at that so we have
+
+ align:start position:0%
+reduce so let's look at that so we have
+ 
+
+ align:start position:0%
+reduce so let's look at that so we have
+lithium plus one plus one electron going
+
+ align:start position:0%
+lithium plus one plus one electron going
+ 
+
+ align:start position:0%
+lithium plus one plus one electron going
+to lithium solid and that reduction is
+
+ align:start position:0%
+to lithium solid and that reduction is
+ 
+
+ align:start position:0%
+to lithium solid and that reduction is
+listed with a standard reduction
+
+ align:start position:0%
+listed with a standard reduction
+ 
+
+ align:start position:0%
+listed with a standard reduction
+potential of minus
+
+ align:start position:0%
+potential of minus
+ 
+
+ align:start position:0%
+potential of minus
+3.45 volts so that's a large negative
+
+ align:start position:0%
+3.45 volts so that's a large negative
+ 
+
+ align:start position:0%
+3.45 volts so that's a large negative
+number so if it's a large negative
+
+ align:start position:0%
+number so if it's a large negative
+ 
+
+ align:start position:0%
+number so if it's a large negative
+number that means it's hard to add
+
+ align:start position:0%
+number that means it's hard to add
+ 
+
+ align:start position:0%
+number that means it's hard to add
+electrons this direction as written is
+
+ align:start position:0%
+electrons this direction as written is
+ 
+
+ align:start position:0%
+electrons this direction as written is
+not particularly favorable lithium plus
+
+ align:start position:0%
+not particularly favorable lithium plus
+ 
+
+ align:start position:0%
+not particularly favorable lithium plus
+one doesn't want to go to lithium solid
+
+ align:start position:0%
+one doesn't want to go to lithium solid
+ 
+
+ align:start position:0%
+one doesn't want to go to lithium solid
+uh it's hard to add that electron that
+
+ align:start position:0%
+uh it's hard to add that electron that
+ 
+
+ align:start position:0%
+uh it's hard to add that electron that
+direction of the reaction the forward
+
+ align:start position:0%
+direction of the reaction the forward
+ 
+
+ align:start position:0%
+direction of the reaction the forward
+direction would not be very favorable
+
+ align:start position:0%
+direction would not be very favorable
+ 
+
+ align:start position:0%
+direction would not be very favorable
+Delta G would be positive it would be a
+
+ align:start position:0%
+Delta G would be positive it would be a
+ 
+
+ align:start position:0%
+Delta G would be positive it would be a
+large positive number so it doesn't want
+
+ align:start position:0%
+large positive number so it doesn't want
+ 
+
+ align:start position:0%
+large positive number so it doesn't want
+to go in that
+
+ align:start position:0%
+to go in that
+ 
+
+ align:start position:0%
+to go in that
+direction so is is lithium plus one a
+
+ align:start position:0%
+direction so is is lithium plus one a
+ 
+
+ align:start position:0%
+direction so is is lithium plus one a
+good oxidizing
+
+ align:start position:0%
+good oxidizing
+ 
+
+ align:start position:0%
+good oxidizing
+agent
+
+ align:start position:0%
+agent
+ 
+
+ align:start position:0%
+agent
+no but it's a good reducing agent or
+
+ align:start position:0%
+no but it's a good reducing agent or
+ 
+
+ align:start position:0%
+no but it's a good reducing agent or
+lithium solid is a good reducing agent
+
+ align:start position:0%
+lithium solid is a good reducing agent
+ 
+
+ align:start position:0%
+lithium solid is a good reducing agent
+so lithium solid reduc likes to reduce
+
+ align:start position:0%
+so lithium solid reduc likes to reduce
+ 
+
+ align:start position:0%
+so lithium solid reduc likes to reduce
+other elements it likes to get oxidized
+
+ align:start position:0%
+other elements it likes to get oxidized
+ 
+
+ align:start position:0%
+other elements it likes to get oxidized
+it w this reaction is favorable in the
+
+ align:start position:0%
+it w this reaction is favorable in the
+ 
+
+ align:start position:0%
+it w this reaction is favorable in the
+reverse Direction so the lithium solid
+
+ align:start position:0%
+reverse Direction so the lithium solid
+ 
+
+ align:start position:0%
+reverse Direction so the lithium solid
+over here would be very happy to be
+
+ align:start position:0%
+over here would be very happy to be
+ 
+
+ align:start position:0%
+over here would be very happy to be
+lithium +
+
+ align:start position:0%
+lithium +
+ 
+
+ align:start position:0%
+lithium +
+one so lithium solid is a good reducing
+
+ align:start position:0%
+one so lithium solid is a good reducing
+ 
+
+ align:start position:0%
+one so lithium solid is a good reducing
+agent so if we look again at this couple
+
+ align:start position:0%
+agent so if we look again at this couple
+ 
+
+ align:start position:0%
+agent so if we look again at this couple
+the lithium plus one lithium couple with
+
+ align:start position:0%
+the lithium plus one lithium couple with
+ 
+
+ align:start position:0%
+the lithium plus one lithium couple with
+a large negative standard reduction
+
+ align:start position:0%
+a large negative standard reduction
+ 
+
+ align:start position:0%
+a large negative standard reduction
+potential we find that the reduced
+
+ align:start position:0%
+potential we find that the reduced
+ 
+
+ align:start position:0%
+potential we find that the reduced
+species the reduced species here is
+
+ align:start position:0%
+species the reduced species here is
+ 
+
+ align:start position:0%
+species the reduced species here is
+lithium solid the reduced species is
+
+ align:start position:0%
+lithium solid the reduced species is
+ 
+
+ align:start position:0%
+lithium solid the reduced species is
+very reducing so it wants to be oxidized
+
+ align:start position:0%
+very reducing so it wants to be oxidized
+ 
+
+ align:start position:0%
+very reducing so it wants to be oxidized
+itself it wants to reduce other things
+
+ align:start position:0%
+itself it wants to reduce other things
+ 
+
+ align:start position:0%
+itself it wants to reduce other things
+it's a good reducing
+
+ align:start position:0%
+it's a good reducing
+ 
+
+ align:start position:0%
+it's a good reducing
+agent so if we go back to our table down
+
+ align:start position:0%
+agent so if we go back to our table down
+ 
+
+ align:start position:0%
+agent so if we go back to our table down
+here it says reduced form is strongly
+
+ align:start position:0%
+here it says reduced form is strongly
+ 
+
+ align:start position:0%
+here it says reduced form is strongly
+reducing so up here on the far corner on
+
+ align:start position:0%
+reducing so up here on the far corner on
+ 
+
+ align:start position:0%
+reducing so up here on the far corner on
+the left hand side
+
+ align:start position:0%
+the left hand side
+ 
+
+ align:start position:0%
+the left hand side
+the oxidized form is strongly oxidizing
+
+ align:start position:0%
+the oxidized form is strongly oxidizing
+ 
+
+ align:start position:0%
+the oxidized form is strongly oxidizing
+down here on the right hand side the
+
+ align:start position:0%
+down here on the right hand side the
+ 
+
+ align:start position:0%
+down here on the right hand side the
+reduced form is strongly reducing so
+
+ align:start position:0%
+reduced form is strongly reducing so
+ 
+
+ align:start position:0%
+reduced form is strongly reducing so
+you'll be asked about various things in
+
+ align:start position:0%
+you'll be asked about various things in
+ 
+
+ align:start position:0%
+you'll be asked about various things in
+between is something a better oxidizing
+
+ align:start position:0%
+between is something a better oxidizing
+ 
+
+ align:start position:0%
+between is something a better oxidizing
+agent than something else is something a
+
+ align:start position:0%
+agent than something else is something a
+ 
+
+ align:start position:0%
+agent than something else is something a
+better reducing agent than something
+
+ align:start position:0%
+better reducing agent than something
+ 
+
+ align:start position:0%
+better reducing agent than something
+else and if you remember uh these parts
+
+ align:start position:0%
+else and if you remember uh these parts
+ 
+
+ align:start position:0%
+else and if you remember uh these parts
+oxidized form up here where where E
+
+ align:start position:0%
+oxidized form up here where where E
+ 
+
+ align:start position:0%
+oxidized form up here where where E
+standard reduction potential e not is
+
+ align:start position:0%
+standard reduction potential e not is
+ 
+
+ align:start position:0%
+standard reduction potential e not is
+positive oxidized form is strongly
+
+ align:start position:0%
+positive oxidized form is strongly
+ 
+
+ align:start position:0%
+positive oxidized form is strongly
+oxidizing down here where you have a
+
+ align:start position:0%
+oxidizing down here where you have a
+ 
+
+ align:start position:0%
+oxidizing down here where you have a
+negative number reduced form is strongly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reducing so this makes sense from what
+
+ align:start position:0%
+reducing so this makes sense from what
+ 
+
+ align:start position:0%
+reducing so this makes sense from what
+you learned before actually and this is
+
+ align:start position:0%
+you learned before actually and this is
+ 
+
+ align:start position:0%
+you learned before actually and this is
+another table from from your book so I
+
+ align:start position:0%
+another table from from your book so I
+ 
+
+ align:start position:0%
+another table from from your book so I
+didn't put it in the handout but we
+
+ align:start position:0%
+didn't put it in the handout but we
+ 
+
+ align:start position:0%
+didn't put it in the handout but we
+talked about uh Florine over here we
+
+ align:start position:0%
+talked about uh Florine over here we
+ 
+
+ align:start position:0%
+talked about uh Florine over here we
+talked about lithium this has a big
+
+ align:start position:0%
+talked about lithium this has a big
+ 
+
+ align:start position:0%
+talked about lithium this has a big
+positive number over here so it's easy
+
+ align:start position:0%
+positive number over here so it's easy
+ 
+
+ align:start position:0%
+positive number over here so it's easy
+it's you have easy to reduce these are
+
+ align:start position:0%
+it's you have easy to reduce these are
+ 
+
+ align:start position:0%
+it's you have easy to reduce these are
+good oxidizing agents and on the other
+
+ align:start position:0%
+good oxidizing agents and on the other
+ 
+
+ align:start position:0%
+good oxidizing agents and on the other
+side these want to be oxidized they're
+
+ align:start position:0%
+side these want to be oxidized they're
+ 
+
+ align:start position:0%
+side these want to be oxidized they're
+good reducing agents Florine minus has a
+
+ align:start position:0%
+good reducing agents Florine minus has a
+ 
+
+ align:start position:0%
+good reducing agents Florine minus has a
+noble gas
+
+ align:start position:0%
+noble gas
+ 
+
+ align:start position:0%
+noble gas
+configuration and lithium plus has a
+
+ align:start position:0%
+configuration and lithium plus has a
+ 
+
+ align:start position:0%
+configuration and lithium plus has a
+noble gas configuration so it makes
+
+ align:start position:0%
+noble gas configuration so it makes
+ 
+
+ align:start position:0%
+noble gas configuration so it makes
+sense from some of the trends you talked
+
+ align:start position:0%
+sense from some of the trends you talked
+ 
+
+ align:start position:0%
+sense from some of the trends you talked
+about earlier in terms of whether
+
+ align:start position:0%
+about earlier in terms of whether
+ 
+
+ align:start position:0%
+about earlier in terms of whether
+something's favorable or not whether it
+
+ align:start position:0%
+something's favorable or not whether it
+ 
+
+ align:start position:0%
+something's favorable or not whether it
+likes to be in the plus one state or
+
+ align:start position:0%
+likes to be in the plus one state or
+ 
+
+ align:start position:0%
+likes to be in the plus one state or
+prefers to be in the minus one state can
+
+ align:start position:0%
+prefers to be in the minus one state can
+ 
+
+ align:start position:0%
+prefers to be in the minus one state can
+all come out of these Ox of these uh
+
+ align:start position:0%
+all come out of these Ox of these uh
+ 
+
+ align:start position:0%
+all come out of these Ox of these uh
+reduction potential numbers and you can
+
+ align:start position:0%
+reduction potential numbers and you can
+ 
+
+ align:start position:0%
+reduction potential numbers and you can
+figure out you know which direction is
+
+ align:start position:0%
+figure out you know which direction is
+ 
+
+ align:start position:0%
+figure out you know which direction is
+favorable the reduction or the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxidation so let's let's take a look at
+
+ align:start position:0%
+oxidation so let's let's take a look at
+ 
+
+ align:start position:0%
+oxidation so let's let's take a look at
+an example here uh of this uh this cell
+
+ align:start position:0%
+an example here uh of this uh this cell
+ 
+
+ align:start position:0%
+an example here uh of this uh this cell
+potential and think about what are good
+
+ align:start position:0%
+potential and think about what are good
+ 
+
+ align:start position:0%
+potential and think about what are good
+oxidizing and reduction uh oxidizing
+
+ align:start position:0%
+oxidizing and reduction uh oxidizing
+ 
+
+ align:start position:0%
+oxidizing and reduction uh oxidizing
+agents and reduction
+
+ align:start position:0%
+agents and reduction
+ 
+
+ align:start position:0%
+agents and reduction
+agents so there uh these two two couples
+
+ align:start position:0%
+agents so there uh these two two couples
+ 
+
+ align:start position:0%
+agents so there uh these two two couples
+over here we're going to look up and
+
+ align:start position:0%
+over here we're going to look up and
+ 
+
+ align:start position:0%
+over here we're going to look up and
+that's hard to see so I'll just go back
+
+ align:start position:0%
+that's hard to see so I'll just go back
+ 
+
+ align:start position:0%
+that's hard to see so I'll just go back
+to this all right so what's happening in
+
+ align:start position:0%
+to this all right so what's happening in
+ 
+
+ align:start position:0%
+to this all right so what's happening in
+this particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction so we have two irons +
+
+ align:start position:0%
+reaction so we have two irons +
+ 
+
+ align:start position:0%
+reaction so we have two irons +
+three and two
+
+ align:start position:0%
+three and two
+ 
+
+ align:start position:0%
+three and two
+electrons going to two
+
+ align:start position:0%
+electrons going to two
+ 
+
+ align:start position:0%
+electrons going to two
+iron +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so is this a a reduction or an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxidation so as written it's a reduction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means it would take place at the
+
+ align:start position:0%
+so that means it would take place at the
+ 
+
+ align:start position:0%
+so that means it would take place at the
+anode or
+
+ align:start position:0%
+anode or
+ 
+
+ align:start position:0%
+anode or
+cathode at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cathode all right the other reaction we
+
+ align:start position:0%
+cathode all right the other reaction we
+ 
+
+ align:start position:0%
+cathode all right the other reaction we
+have is 2 I minus going to I2 solid plus
+
+ align:start position:0%
+have is 2 I minus going to I2 solid plus
+ 
+
+ align:start position:0%
+have is 2 I minus going to I2 solid plus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+electrons as it needs to be balanced so
+
+ align:start position:0%
+electrons as it needs to be balanced so
+ 
+
+ align:start position:0%
+electrons as it needs to be balanced so
+this would be an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxidation and so it should take place at
+
+ align:start position:0%
+oxidation and so it should take place at
+ 
+
+ align:start position:0%
+oxidation and so it should take place at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+anode so now we can calculate the cell
+
+ align:start position:0%
+anode so now we can calculate the cell
+ 
+
+ align:start position:0%
+anode so now we can calculate the cell
+potential for this particular reaction
+
+ align:start position:0%
+potential for this particular reaction
+ 
+
+ align:start position:0%
+potential for this particular reaction
+the Delta e KN for the
+
+ align:start position:0%
+the Delta e KN for the
+ 
+
+ align:start position:0%
+the Delta e KN for the
+cell and that will equal the uh Delta e
+
+ align:start position:0%
+cell and that will equal the uh Delta e
+ 
+
+ align:start position:0%
+cell and that will equal the uh Delta e
+for the cathode
+
+ align:start position:0%
+for the cathode
+ 
+
+ align:start position:0%
+for the cathode
+reaction minus the Delta e for the
+
+ align:start position:0%
+reaction minus the Delta e for the
+ 
+
+ align:start position:0%
+reaction minus the Delta e for the
+anode
+
+ align:start position:0%
+anode
+ 
+
+ align:start position:0%
+anode
+reaction so the Delta e for the cathode
+
+ align:start position:0%
+reaction so the Delta e for the cathode
+ 
+
+ align:start position:0%
+reaction so the Delta e for the cathode
+reaction uh and you were given this in
+
+ align:start position:0%
+reaction uh and you were given this in
+ 
+
+ align:start position:0%
+reaction uh and you were given this in
+in your handouts we have plus we have
+
+ align:start position:0%
+in your handouts we have plus we have
+ 
+
+ align:start position:0%
+in your handouts we have plus we have
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+volts
+
+ align:start position:0%
+volts
+ 
+
+ align:start position:0%
+volts
+minus plus
+
+ align:start position:0%
+minus plus
+ 
+
+ align:start position:0%
+minus plus
+535 Volts for the reaction happening at
+
+ align:start position:0%
+535 Volts for the reaction happening at
+ 
+
+ align:start position:0%
+535 Volts for the reaction happening at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+anode and so that will equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.235
+
+ align:start position:0%
+0.235
+ 
+
+ align:start position:0%
+0.235
+volts and so will that be
+
+ align:start position:0%
+volts and so will that be
+ 
+
+ align:start position:0%
+volts and so will that be
+spontaneous yes so it will be
+
+ align:start position:0%
+spontaneous yes so it will be
+ 
+
+ align:start position:0%
+spontaneous yes so it will be
+spontaneous so Delta e e is positive so
+
+ align:start position:0%
+spontaneous so Delta e e is positive so
+ 
+
+ align:start position:0%
+spontaneous so Delta e e is positive so
+Delta G will be negative so we'll have a
+
+ align:start position:0%
+Delta G will be negative so we'll have a
+ 
+
+ align:start position:0%
+Delta G will be negative so we'll have a
+spontaneous
+
+ align:start position:0%
+spontaneous
+ 
+
+ align:start position:0%
+spontaneous
+reaction now let's consider which are
+
+ align:start position:0%
+reaction now let's consider which are
+ 
+
+ align:start position:0%
+reaction now let's consider which are
+the better oxidizing and reducing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+agents so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better better oxidizing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+agent is it iron + three
+
+ align:start position:0%
+agent is it iron + three
+ 
+
+ align:start position:0%
+agent is it iron + three
+or iodide
+
+ align:start position:0%
+or iodide
+ 
+
+ align:start position:0%
+or iodide
+2 which is a better oxidizing agent and
+
+ align:start position:0%
+2 which is a better oxidizing agent and
+ 
+
+ align:start position:0%
+2 which is a better oxidizing agent and
+we can go back to the Chart here's the
+
+ align:start position:0%
+we can go back to the Chart here's the
+ 
+
+ align:start position:0%
+we can go back to the Chart here's the
+iron and below it is the iodide
+
+ align:start position:0%
+iron and below it is the iodide
+ 
+
+ align:start position:0%
+iron and below it is the iodide
+reaction so which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better so iron I heard I think I heard
+
+ align:start position:0%
+better so iron I heard I think I heard
+ 
+
+ align:start position:0%
+better so iron I heard I think I heard
+some people say
+
+ align:start position:0%
+some people say
+ 
+
+ align:start position:0%
+some people say
+iron +
+
+ align:start position:0%
+iron +
+ 
+
+ align:start position:0%
+iron +
+three so that should be a better
+
+ align:start position:0%
+three so that should be a better
+ 
+
+ align:start position:0%
+three so that should be a better
+oxidizing agent so again and if you look
+
+ align:start position:0%
+oxidizing agent so again and if you look
+ 
+
+ align:start position:0%
+oxidizing agent so again and if you look
+at where they are the things on this
+
+ align:start position:0%
+at where they are the things on this
+ 
+
+ align:start position:0%
+at where they are the things on this
+side at the top are the most oxidizing
+
+ align:start position:0%
+side at the top are the most oxidizing
+ 
+
+ align:start position:0%
+side at the top are the most oxidizing
+or the best oxidizing agent so iron plus
+
+ align:start position:0%
+or the best oxidizing agent so iron plus
+ 
+
+ align:start position:0%
+or the best oxidizing agent so iron plus
+three is there it's going to be uh
+
+ align:start position:0%
+three is there it's going to be uh
+ 
+
+ align:start position:0%
+three is there it's going to be uh
+better and we can also think about this
+
+ align:start position:0%
+better and we can also think about this
+ 
+
+ align:start position:0%
+better and we can also think about this
+in terms of the spontaneous reaction
+
+ align:start position:0%
+in terms of the spontaneous reaction
+ 
+
+ align:start position:0%
+in terms of the spontaneous reaction
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+spontaneous and the iron plus three here
+
+ align:start position:0%
+spontaneous and the iron plus three here
+ 
+
+ align:start position:0%
+spontaneous and the iron plus three here
+is is being is being reduced so it's
+
+ align:start position:0%
+is is being is being reduced so it's
+ 
+
+ align:start position:0%
+is is being is being reduced so it's
+acting as an oxidizing reagent
+
+ align:start position:0%
+acting as an oxidizing reagent
+ 
+
+ align:start position:0%
+acting as an oxidizing reagent
+and that's causing the reaction to be
+
+ align:start position:0%
+and that's causing the reaction to be
+ 
+
+ align:start position:0%
+and that's causing the reaction to be
+spontaneous and if we talk about the
+
+ align:start position:0%
+spontaneous and if we talk about the
+ 
+
+ align:start position:0%
+spontaneous and if we talk about the
+better better reducing agent the
+
+ align:start position:0%
+better better reducing agent the
+ 
+
+ align:start position:0%
+better better reducing agent the
+reducing agent is the thing that wants
+
+ align:start position:0%
+reducing agent is the thing that wants
+ 
+
+ align:start position:0%
+reducing agent is the thing that wants
+to get
+
+ align:start position:0%
+to get
+ 
+
+ align:start position:0%
+to get
+oxidized and if we consider IUS or iron
+
+ align:start position:0%
+oxidized and if we consider IUS or iron
+ 
+
+ align:start position:0%
+oxidized and if we consider IUS or iron
++ 2 which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better I minus is going to be
+
+ align:start position:0%
+better I minus is going to be
+ 
+
+ align:start position:0%
+better I minus is going to be
+better and again it's down here down
+
+ align:start position:0%
+better and again it's down here down
+ 
+
+ align:start position:0%
+better and again it's down here down
+here we have the reduced forms are
+
+ align:start position:0%
+here we have the reduced forms are
+ 
+
+ align:start position:0%
+here we have the reduced forms are
+strongly reducing this is the reduced
+
+ align:start position:0%
+strongly reducing this is the reduced
+ 
+
+ align:start position:0%
+strongly reducing this is the reduced
+form so it's on this end of the table
+
+ align:start position:0%
+form so it's on this end of the table
+ 
+
+ align:start position:0%
+form so it's on this end of the table
+also uh that's the reaction that's
+
+ align:start position:0%
+also uh that's the reaction that's
+ 
+
+ align:start position:0%
+also uh that's the reaction that's
+happening here and it's spontaneous it
+
+ align:start position:0%
+happening here and it's spontaneous it
+ 
+
+ align:start position:0%
+happening here and it's spontaneous it
+has and if you talk about the two
+
+ align:start position:0%
+has and if you talk about the two
+ 
+
+ align:start position:0%
+has and if you talk about the two
+reduction potentials you can figure that
+
+ align:start position:0%
+reduction potentials you can figure that
+ 
+
+ align:start position:0%
+reduction potentials you can figure that
+out okay see you on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Wednesday
\ No newline at end of file
diff --git a/1LEYgS8Wzsk.txt b/1LEYgS8Wzsk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..16e19775e332a6814a85c14193f469d5e1acd63c
--- /dev/null
+++ b/1LEYgS8Wzsk.txt
@@ -0,0 +1,16548 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay good let us
+
+ align:start position:0%
+ocw.mit.edu okay good let us
+ 
+
+ align:start position:0%
+ocw.mit.edu okay good let us
+start so um so last time we talked
+
+ align:start position:0%
+start so um so last time we talked
+ 
+
+ align:start position:0%
+start so um so last time we talked
+about finding the space time
+
+ align:start position:0%
+about finding the space time
+ 
+
+ align:start position:0%
+about finding the space time
+geometry produced by this re
+
+ align:start position:0%
+geometry produced by this re
+ 
+
+ align:start position:0%
+geometry produced by this re
+brain so just by based on
+
+ align:start position:0%
+brain so just by based on
+ 
+
+ align:start position:0%
+brain so just by based on
+symmetry you can write down the matric
+
+ align:start position:0%
+symmetry you can write down the matric
+ 
+
+ align:start position:0%
+symmetry you can write down the matric
+as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following say some
+
+ align:start position:0%
+following say some
+ 
+
+ align:start position:0%
+following say some
+function and then a minkovski
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matric i movy matric
+
+ align:start position:0%
+matric i movy matric
+ 
+
+ align:start position:0%
+matric i movy matric
+for the 3+ One
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction and
+
+ align:start position:0%
+Direction and
+ 
+
+ align:start position:0%
+Direction and
+then the path for the transverse
+
+ align:start position:0%
+then the path for the transverse
+ 
+
+ align:start position:0%
+then the path for the transverse
+Direction which you have AOS which you
+
+ align:start position:0%
+Direction which you have AOS which you
+ 
+
+ align:start position:0%
+Direction which you have AOS which you
+have a rotation
+
+ align:start position:0%
+have a rotation
+ 
+
+ align:start position:0%
+have a rotation
+symmetry so you should think of H the
+
+ align:start position:0%
+symmetry so you should think of H the
+ 
+
+ align:start position:0%
+symmetry so you should think of H the
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+rean as a point in R
+
+ align:start position:0%
+rean as a point in R
+ 
+
+ align:start position:0%
+rean as a point in R
+six then there's a spherical symmetry in
+
+ align:start position:0%
+six then there's a spherical symmetry in
+ 
+
+ align:start position:0%
+six then there's a spherical symmetry in
+R6 around this point and then and then
+
+ align:start position:0%
+R6 around this point and then and then
+ 
+
+ align:start position:0%
+R6 around this point and then and then
+there are other 3 + One Direction which
+
+ align:start position:0%
+there are other 3 + One Direction which
+ 
+
+ align:start position:0%
+there are other 3 + One Direction which
+is this 3 + y direction okay so when you
+
+ align:start position:0%
+is this 3 + y direction okay so when you
+ 
+
+ align:start position:0%
+is this 3 + y direction okay so when you
+solve the Einstein
+
+ align:start position:0%
+solve the Einstein
+ 
+
+ align:start position:0%
+solve the Einstein
+equation when you solve the Einstein
+
+ align:start position:0%
+equation when you solve the Einstein
+ 
+
+ align:start position:0%
+equation when you solve the Einstein
+equation then you find this
+
+ align:start position:0%
+equation then you find this
+ 
+
+ align:start position:0%
+equation then you find this
+FH just replace it can be solved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explicitly by the following form some
+
+ align:start position:0%
+explicitly by the following form some
+ 
+
+ align:start position:0%
+explicitly by the following form some
+other function
+
+ align:start position:0%
+other function
+ 
+
+ align:start position:0%
+other function
+H by the same
+
+ align:start position:0%
+H by the same
+ 
+
+ align:start position:0%
+H by the same
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+with h given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by and R is a
+
+ align:start position:0%
+by and R is a
+ 
+
+ align:start position:0%
+by and R is a
+constant which given by the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form so I essentially have the
+
+ align:start position:0%
+form so I essentially have the
+ 
+
+ align:start position:0%
+form so I essentially have the
+form of some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constants Newton constant and and the
+
+ align:start position:0%
+constants Newton constant and and the
+ 
+
+ align:start position:0%
+constants Newton constant and and the
+times the tension of the this three
+
+ align:start position:0%
+times the tension of the this three
+ 
+
+ align:start position:0%
+times the tension of the this three
+brain and then if have angle of them and
+
+ align:start position:0%
+brain and then if have angle of them and
+ 
+
+ align:start position:0%
+brain and then if have angle of them and
+then this can also be if you written
+
+ align:start position:0%
+then this can also be if you written
+ 
+
+ align:start position:0%
+then this can also be if you written
+everything in terms of alpha Prime uh GS
+
+ align:start position:0%
+everything in terms of alpha Prime uh GS
+ 
+
+ align:start position:0%
+everything in terms of alpha Prime uh GS
+and Alpha Prime can written as 4 Pi GS
+
+ align:start position:0%
+and Alpha Prime can written as 4 Pi GS
+ 
+
+ align:start position:0%
+and Alpha Prime can written as 4 Pi GS
+and Alpha Prime squ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this R so this is just like the
+
+ align:start position:0%
+okay so this R so this is just like the
+ 
+
+ align:start position:0%
+okay so this R so this is just like the
+what you normally see in the SWAT short
+
+ align:start position:0%
+what you normally see in the SWAT short
+ 
+
+ align:start position:0%
+what you normally see in the SWAT short
+matric is like G time the mass except
+
+ align:start position:0%
+matric is like G time the mass except
+ 
+
+ align:start position:0%
+matric is like G time the mass except
+because of the translation symmetry in
+
+ align:start position:0%
+because of the translation symmetry in
+ 
+
+ align:start position:0%
+because of the translation symmetry in
+this re + One Direction so we have the
+
+ align:start position:0%
+this re + One Direction so we have the
+ 
+
+ align:start position:0%
+this re + One Direction so we have the
+tension appear here so GN is
+
+ align:start position:0%
+tension appear here so GN is
+ 
+
+ align:start position:0%
+tension appear here so GN is
+proportional to solution Conant is
+
+ align:start position:0%
+proportional to solution Conant is
+ 
+
+ align:start position:0%
+proportional to solution Conant is
+proportional to GS squ and T3 is propor
+
+ align:start position:0%
+proportional to GS squ and T3 is propor
+ 
+
+ align:start position:0%
+proportional to GS squ and T3 is propor
+to one over GS so this product be
+
+ align:start position:0%
+to one over GS so this product be
+ 
+
+ align:start position:0%
+to one over GS so this product be
+proportion to
+
+ align:start position:0%
+proportion to
+ 
+
+ align:start position:0%
+proportion to
+GS okay and there's n of them so there's
+
+ align:start position:0%
+GS okay and there's n of them so there's
+ 
+
+ align:start position:0%
+GS okay and there's n of them so there's
+n here and on dimensional
+
+ align:start position:0%
+n here and on dimensional
+ 
+
+ align:start position:0%
+n here and on dimensional
+ground this is dimension four so you
+
+ align:start position:0%
+ground this is dimension four so you
+ 
+
+ align:start position:0%
+ground this is dimension four so you
+have Alpha Prime Square here okay so
+
+ align:start position:0%
+have Alpha Prime Square here okay so
+ 
+
+ align:start position:0%
+have Alpha Prime Square here okay so
+again you can write down everything on
+
+ align:start position:0%
+again you can write down everything on
+ 
+
+ align:start position:0%
+again you can write down everything on
+dimensional ground and the only thing is
+
+ align:start position:0%
+dimensional ground and the only thing is
+ 
+
+ align:start position:0%
+dimensional ground and the only thing is
+just this four Pi you have to be careful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so this is the full this rebrin
+
+ align:start position:0%
+okay so so this is the full this rebrin
+ 
+
+ align:start position:0%
+okay so so this is the full this rebrin
+matric so this is the full this rebrin
+
+ align:start position:0%
+matric so this is the full this rebrin
+ 
+
+ align:start position:0%
+matric so this is the full this rebrin
+matric so now now let's understand a
+
+ align:start position:0%
+matric so now now let's understand a
+ 
+
+ align:start position:0%
+matric so now now let's understand a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+bit physics of this matric so try to
+
+ align:start position:0%
+bit physics of this matric so try to
+ 
+
+ align:start position:0%
+bit physics of this matric so try to
+which give us a deeper understanding of
+
+ align:start position:0%
+which give us a deeper understanding of
+ 
+
+ align:start position:0%
+which give us a deeper understanding of
+the physics of this repr
+
+ align:start position:0%
+the physics of this repr
+ 
+
+ align:start position:0%
+the physics of this repr
+brains so
+
+ align:start position:0%
+brains so
+ 
+
+ align:start position:0%
+brains so
+first let's consider whyus regime
+
+ align:start position:0%
+first let's consider whyus regime
+ 
+
+ align:start position:0%
+first let's consider whyus regime
+of R okay so let's consider say R first
+
+ align:start position:0%
+of R okay so let's consider say R first
+ 
+
+ align:start position:0%
+of R okay so let's consider say R first
+consider R go to
+
+ align:start position:0%
+consider R go to
+ 
+
+ align:start position:0%
+consider R go to
+Infinity so in AR go to Infinity HR just
+
+ align:start position:0%
+Infinity so in AR go to Infinity HR just
+ 
+
+ align:start position:0%
+Infinity so in AR go to Infinity HR just
+become
+
+ align:start position:0%
+become
+ 
+
+ align:start position:0%
+become
+one H just become
+
+ align:start position:0%
+one H just become
+ 
+
+ align:start position:0%
+one H just become
+one okay and then you just recover U
+
+ align:start position:0%
+one okay and then you just recover U
+ 
+
+ align:start position:0%
+one okay and then you just recover U
+um 10 dimensional minkovski
+
+ align:start position:0%
+um 10 dimensional minkovski
+ 
+
+ align:start position:0%
+um 10 dimensional minkovski
+matric okay so this is very easy to
+
+ align:start position:0%
+matric okay so this is very easy to
+ 
+
+ align:start position:0%
+matric okay so this is very easy to
+understand you're infinite away from the
+
+ align:start position:0%
+understand you're infinite away from the
+ 
+
+ align:start position:0%
+understand you're infinite away from the
+this Rebrand of course you don't feel
+
+ align:start position:0%
+this Rebrand of course you don't feel
+ 
+
+ align:start position:0%
+this Rebrand of course you don't feel
+anything and so you just recover the uh
+
+ align:start position:0%
+anything and so you just recover the uh
+ 
+
+ align:start position:0%
+anything and so you just recover the uh
+uh 10 dimensional movi space time so
+
+ align:start position:0%
+uh 10 dimensional movi space time so
+ 
+
+ align:start position:0%
+uh 10 dimensional movi space time so
+here is one here is one uh this is a
+
+ align:start position:0%
+here is one here is one uh this is a
+ 
+
+ align:start position:0%
+here is one here is one uh this is a
+funny way to write down 10 dimensional
+
+ align:start position:0%
+funny way to write down 10 dimensional
+ 
+
+ align:start position:0%
+funny way to write down 10 dimensional
+movi space time so this is just a flat
+
+ align:start position:0%
+movi space time so this is just a flat
+ 
+
+ align:start position:0%
+movi space time so this is just a flat
+R6 metric
+
+ align:start position:0%
+R6 metric
+ 
+
+ align:start position:0%
+R6 metric
+okay and now let's not consider R go to
+
+ align:start position:0%
+okay and now let's not consider R go to
+ 
+
+ align:start position:0%
+okay and now let's not consider R go to
+Infinity just only R much much smaller
+
+ align:start position:0%
+Infinity just only R much much smaller
+ 
+
+ align:start position:0%
+Infinity just only R much much smaller
+than R than this capital r
+
+ align:start position:0%
+than R than this capital r
+ 
+
+ align:start position:0%
+than R than this capital r
+then then this
+
+ align:start position:0%
+then then this
+ 
+
+ align:start position:0%
+then then this
+function so so so again let me call this
+
+ align:start position:0%
+function so so so again let me call this
+ 
+
+ align:start position:0%
+function so so so again let me call this
+F let me call this
+
+ align:start position:0%
+F let me call this
+ 
+
+ align:start position:0%
+F let me call this
+H so for example the the uh did I call
+
+ align:start position:0%
+H so for example the the uh did I call
+ 
+
+ align:start position:0%
+H so for example the the uh did I call
+them H or G yeah uh H yeah yeah so for
+
+ align:start position:0%
+them H or G yeah uh H yeah yeah so for
+ 
+
+ align:start position:0%
+them H or G yeah uh H yeah yeah so for
+example the F the is similar thing with
+
+ align:start position:0%
+example the F the is similar thing with
+ 
+
+ align:start position:0%
+example the F the is similar thing with
+G with h so the F will be one
+
+ align:start position:0%
+G with h so the F will be one
+ 
+
+ align:start position:0%
+G with h so the F will be one
+plus say something of order R to ^ 4 / R
+
+ align:start position:0%
+plus say something of order R to ^ 4 / R
+ 
+
+ align:start position:0%
+plus say something of order R to ^ 4 / R
+to the^ 4 similar
+
+ align:start position:0%
+to the^ 4 similar
+ 
+
+ align:start position:0%
+to the^ 4 similar
+uh with the uh uh
+
+ align:start position:0%
+uh with the uh uh
+ 
+
+ align:start position:0%
+uh with the uh uh
+H so now you
+
+ align:start position:0%
+H so now you
+ 
+
+ align:start position:0%
+H so now you
+recognize that this one /
+
+ align:start position:0%
+recognize that this one /
+ 
+
+ align:start position:0%
+recognize that this one /
+R4 is precisely long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+range coolant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential in in six
+
+ align:start position:0%
+potential in in six
+ 
+
+ align:start position:0%
+potential in in six
+Dimension okay in R six
+
+ align:start position:0%
+Dimension okay in R six
+ 
+
+ align:start position:0%
+Dimension okay in R six
+because the because only transverse
+
+ align:start position:0%
+because the because only transverse
+ 
+
+ align:start position:0%
+because the because only transverse
+Direction
+
+ align:start position:0%
+Direction
+ 
+
+ align:start position:0%
+Direction
+matters and in three spatial Dimension
+
+ align:start position:0%
+matters and in three spatial Dimension
+ 
+
+ align:start position:0%
+matters and in three spatial Dimension
+if you have a point then you have one of
+
+ align:start position:0%
+if you have a point then you have one of
+ 
+
+ align:start position:0%
+if you have a point then you have one of
+R and in six Dimension then you again J
+
+ align:start position:0%
+R and in six Dimension then you again J
+ 
+
+ align:start position:0%
+R and in six Dimension then you again J
+uh you go down two Powers then you get
+
+ align:start position:0%
+uh you go down two Powers then you get
+ 
+
+ align:start position:0%
+uh you go down two Powers then you get
+one over
+
+ align:start position:0%
+one over
+ 
+
+ align:start position:0%
+one over
+R4 so so this Behavior can simply be
+
+ align:start position:0%
+R4 so so this Behavior can simply be
+ 
+
+ align:start position:0%
+R4 so so this Behavior can simply be
+understood say essentially say as you
+
+ align:start position:0%
+understood say essentially say as you
+ 
+
+ align:start position:0%
+understood say essentially say as you
+have some kind of colum
+
+ align:start position:0%
+have some kind of colum
+ 
+
+ align:start position:0%
+have some kind of colum
+potential uh
+
+ align:start position:0%
+potential uh
+ 
+
+ align:start position:0%
+potential uh
+um I both due to the say the conserved
+
+ align:start position:0%
+um I both due to the say the conserved
+ 
+
+ align:start position:0%
+um I both due to the say the conserved
+both due to the uh uh the charge of this
+
+ align:start position:0%
+both due to the uh uh the charge of this
+ 
+
+ align:start position:0%
+both due to the uh uh the charge of this
+part charge of the brain and also due to
+
+ align:start position:0%
+part charge of the brain and also due to
+ 
+
+ align:start position:0%
+part charge of the brain and also due to
+the gravity okay just you have some long
+
+ align:start position:0%
+the gravity okay just you have some long
+ 
+
+ align:start position:0%
+the gravity okay just you have some long
+range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential so now the interesting
+
+ align:start position:0%
+potential so now the interesting
+ 
+
+ align:start position:0%
+potential so now the interesting
+thing things become more interesting is
+
+ align:start position:0%
+thing things become more interesting is
+ 
+
+ align:start position:0%
+thing things become more interesting is
+when R become of order
+
+ align:start position:0%
+when R become of order
+ 
+
+ align:start position:0%
+when R become of order
+R when R become all R then this
+
+ align:start position:0%
+R when R become all R then this
+ 
+
+ align:start position:0%
+R when R become all R then this
+HR start to be sign different from one
+
+ align:start position:0%
+HR start to be sign different from one
+ 
+
+ align:start position:0%
+HR start to be sign different from one
+okay and then then tells you
+
+ align:start position:0%
+okay and then then tells you
+ 
+
+ align:start position:0%
+okay and then then tells you
+so so this is the uh
+
+ align:start position:0%
+so so this is the uh
+ 
+
+ align:start position:0%
+so so this is the uh
+um when all the what the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentation Yeah at this range
+
+ align:start position:0%
+differentation Yeah at this range
+ 
+
+ align:start position:0%
+differentation Yeah at this range
+information of SpaceTime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Magic
+
+ align:start position:0%
+Magic
+ 
+
+ align:start position:0%
+Magic
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+this three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brains become
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+significant okay so in other words this
+
+ align:start position:0%
+significant okay so in other words this
+ 
+
+ align:start position:0%
+significant okay so in other words this
+this capital r this constant essentially
+
+ align:start position:0%
+this capital r this constant essentially
+ 
+
+ align:start position:0%
+this capital r this constant essentially
+signals the distance from the brain
+
+ align:start position:0%
+signals the distance from the brain
+ 
+
+ align:start position:0%
+signals the distance from the brain
+where the uh the gravitational effect or
+
+ align:start position:0%
+where the uh the gravitational effect or
+ 
+
+ align:start position:0%
+where the uh the gravitational effect or
+the become strong okay
+
+ align:start position:0%
+the become strong okay
+ 
+
+ align:start position:0%
+the become strong okay
+the gravitation effect of the deep brain
+
+ align:start position:0%
+the gravitation effect of the deep brain
+ 
+
+ align:start position:0%
+the gravitation effect of the deep brain
+becomes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J and in particular you can check
+
+ align:start position:0%
+J and in particular you can check
+ 
+
+ align:start position:0%
+J and in particular you can check
+yourself you can calculate yourself the
+
+ align:start position:0%
+yourself you can calculate yourself the
+ 
+
+ align:start position:0%
+yourself you can calculate yourself the
+curvature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radius now become of order r or the
+
+ align:start position:0%
+radius now become of order r or the
+ 
+
+ align:start position:0%
+radius now become of order r or the
+curvature itself yeah let me just say
+
+ align:start position:0%
+curvature itself yeah let me just say
+ 
+
+ align:start position:0%
+curvature itself yeah let me just say
+the curvature uh curvature C become R to
+
+ align:start position:0%
+the curvature uh curvature C become R to
+ 
+
+ align:start position:0%
+the curvature uh curvature C become R to
+Theus 4 uh R to Theus
+
+ align:start position:0%
+Theus 4 uh R to Theus
+ 
+
+ align:start position:0%
+Theus 4 uh R to Theus
+2 okay
+
+ align:start position:0%
+2 okay
+ 
+
+ align:start position:0%
+2 okay
+so so essentially the r give you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the say a measure of when the gravity
+
+ align:start position:0%
+the say a measure of when the gravity
+ 
+
+ align:start position:0%
+the say a measure of when the gravity
+becom strong or or or or or or the scale
+
+ align:start position:0%
+becom strong or or or or or or the scale
+ 
+
+ align:start position:0%
+becom strong or or or or or or the scale
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curvature so so we are we solved this
+
+ align:start position:0%
+curvature so so we are we solved this
+ 
+
+ align:start position:0%
+curvature so so we are we solved this
+metric in the context of the superg
+
+ align:start position:0%
+metric in the context of the superg
+ 
+
+ align:start position:0%
+metric in the context of the superg
+gravity in the context of lower
+
+ align:start position:0%
+gravity in the context of lower
+ 
+
+ align:start position:0%
+gravity in the context of lower
+effective the super gravity so so in
+
+ align:start position:0%
+effective the super gravity so so in
+ 
+
+ align:start position:0%
+effective the super gravity so so in
+order for the approximation to works we
+
+ align:start position:0%
+order for the approximation to works we
+ 
+
+ align:start position:0%
+order for the approximation to works we
+said before we wanted the alpha Prime
+
+ align:start position:0%
+said before we wanted the alpha Prime
+ 
+
+ align:start position:0%
+said before we wanted the alpha Prime
+Times the curvature to be much much
+
+ align:start position:0%
+Times the curvature to be much much
+ 
+
+ align:start position:0%
+Times the curvature to be much much
+smaller than one so we said last time so
+
+ align:start position:0%
+smaller than one so we said last time so
+ 
+
+ align:start position:0%
+smaller than one so we said last time so
+so that means we want this to be much
+
+ align:start position:0%
+so that means we want this to be much
+ 
+
+ align:start position:0%
+so that means we want this to be much
+much smaller than
+
+ align:start position:0%
+much smaller than
+ 
+
+ align:start position:0%
+much smaller than
+one so that the super gravity
+
+ align:start position:0%
+one so that the super gravity
+ 
+
+ align:start position:0%
+one so that the super gravity
+approximation can be valed so now if you
+
+ align:start position:0%
+approximation can be valed so now if you
+ 
+
+ align:start position:0%
+approximation can be valed so now if you
+look at the expression of the
+
+ align:start position:0%
+look at the expression of the
+ 
+
+ align:start position:0%
+look at the expression of the
+R so this tells you that the GSM must be
+
+ align:start position:0%
+R so this tells you that the GSM must be
+ 
+
+ align:start position:0%
+R so this tells you that the GSM must be
+much much greater than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yes and must much greater than
+
+ align:start position:0%
+okay yes and must much greater than
+ 
+
+ align:start position:0%
+okay yes and must much greater than
+one and uh and also in order to have the
+
+ align:start position:0%
+one and uh and also in order to have the
+ 
+
+ align:start position:0%
+one and uh and also in order to have the
+string Loop correction to be small we
+
+ align:start position:0%
+string Loop correction to be small we
+ 
+
+ align:start position:0%
+string Loop correction to be small we
+also need GS to be much much smaller
+
+ align:start position:0%
+also need GS to be much much smaller
+ 
+
+ align:start position:0%
+also need GS to be much much smaller
+than one so believe GSN to be much much
+
+ align:start position:0%
+than one so believe GSN to be much much
+ 
+
+ align:start position:0%
+than one so believe GSN to be much much
+greater than one but also GS to much
+
+ align:start position:0%
+greater than one but also GS to much
+ 
+
+ align:start position:0%
+greater than one but also GS to much
+much smaller than one so in order for
+
+ align:start position:0%
+much smaller than one so in order for
+ 
+
+ align:start position:0%
+much smaller than one so in order for
+the um so gravity uh uh
+
+ align:start position:0%
+the um so gravity uh uh
+ 
+
+ align:start position:0%
+the um so gravity uh uh
+um approximation to work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's
+
+ align:start position:0%
+okay so now let's
+ 
+
+ align:start position:0%
+okay so now let's
+consider so we set up the the problem so
+
+ align:start position:0%
+consider so we set up the the problem so
+ 
+
+ align:start position:0%
+consider so we set up the the problem so
+this matric is written that I equal to
+
+ align:start position:0%
+this matric is written that I equal to
+ 
+
+ align:start position:0%
+this matric is written that I equal to
+zero is the location of the brain okay I
+
+ align:start position:0%
+zero is the location of the brain okay I
+ 
+
+ align:start position:0%
+zero is the location of the brain okay I
+to Z is location of brain that we uh
+
+ align:start position:0%
+to Z is location of brain that we uh
+ 
+
+ align:start position:0%
+to Z is location of brain that we uh
+when we solve this problem you uh I to Z
+
+ align:start position:0%
+when we solve this problem you uh I to Z
+ 
+
+ align:start position:0%
+when we solve this problem you uh I to Z
+is the presume the location of the brain
+
+ align:start position:0%
+is the presume the location of the brain
+ 
+
+ align:start position:0%
+is the presume the location of the brain
+so now what happens let's see what
+
+ align:start position:0%
+so now what happens let's see what
+ 
+
+ align:start position:0%
+so now what happens let's see what
+happens when we
+
+ align:start position:0%
+happens when we
+ 
+
+ align:start position:0%
+happens when we
+um yeah that's where you put the source
+
+ align:start position:0%
+um yeah that's where you put the source
+ 
+
+ align:start position:0%
+um yeah that's where you put the source
+okay that's where you put the source so
+
+ align:start position:0%
+okay that's where you put the source so
+ 
+
+ align:start position:0%
+okay that's where you put the source so
+now let's consider
+
+ align:start position:0%
+now let's consider
+ 
+
+ align:start position:0%
+now let's consider
+now let's ask the question what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens to the
+
+ align:start position:0%
+happens to the
+ 
+
+ align:start position:0%
+happens to the
+matric if R goes zero if we try to
+
+ align:start position:0%
+matric if R goes zero if we try to
+ 
+
+ align:start position:0%
+matric if R goes zero if we try to
+approach the brain okay okay if we try
+
+ align:start position:0%
+approach the brain okay okay if we try
+ 
+
+ align:start position:0%
+approach the brain okay okay if we try
+to approach
+
+ align:start position:0%
+to approach
+ 
+
+ align:start position:0%
+to approach
+brain so so this this is very easy to do
+
+ align:start position:0%
+brain so so this this is very easy to do
+ 
+
+ align:start position:0%
+brain so so this this is very easy to do
+so when R become much smaller than R to
+
+ align:start position:0%
+so when R become much smaller than R to
+ 
+
+ align:start position:0%
+so when R become much smaller than R to
+the capital r when R goes to
+
+ align:start position:0%
+the capital r when R goes to
+ 
+
+ align:start position:0%
+the capital r when R goes to
+zero then in this expression this term
+
+ align:start position:0%
+zero then in this expression this term
+ 
+
+ align:start position:0%
+zero then in this expression this term
+will dominate
+
+ align:start position:0%
+will dominate
+ 
+
+ align:start position:0%
+will dominate
+okay we can forget about one this term
+
+ align:start position:0%
+okay we can forget about one this term
+ 
+
+ align:start position:0%
+okay we can forget about one this term
+will dominate so so in this case the H
+
+ align:start position:0%
+will dominate so so in this case the H
+ 
+
+ align:start position:0%
+will dominate so so in this case the H
+will be will be given by R to the 4
+
+ align:start position:0%
+will be will be given by R to the 4
+ 
+
+ align:start position:0%
+will be will be given by R to the 4
+R4 okay then you just plug this into the
+
+ align:start position:0%
+R4 okay then you just plug this into the
+ 
+
+ align:start position:0%
+R4 okay then you just plug this into the
+your original
+
+ align:start position:0%
+your original
+ 
+
+ align:start position:0%
+your original
+matric okay so you plug this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back so when you plug this
+
+ align:start position:0%
+back so when you plug this
+ 
+
+ align:start position:0%
+back so when you plug this
+back so so H is equal to so H minus 12
+
+ align:start position:0%
+back so so H is equal to so H minus 12
+ 
+
+ align:start position:0%
+back so so H is equal to so H minus 12
+then just become r s / r s then we still
+
+ align:start position:0%
+then just become r s / r s then we still
+ 
+
+ align:start position:0%
+then just become r s / r s then we still
+have DT s + DX
+
+ align:start position:0%
+have DT s + DX
+ 
+
+ align:start position:0%
+have DT s + DX
+s then plus
+
+ align:start position:0%
+s then plus
+ 
+
+ align:start position:0%
+s then plus
+r² r s so that's is positive
+
+ align:start position:0%
+r² r s so that's is positive
+ 
+
+ align:start position:0%
+r² r s so that's is positive
+12 then the r² + r² the OM 5
+
+ align:start position:0%
+12 then the r² + r² the OM 5
+ 
+
+ align:start position:0%
+12 then the r² + r² the OM 5
+S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but now something miraculous
+
+ align:start position:0%
+okay but now something miraculous
+ 
+
+ align:start position:0%
+okay but now something miraculous
+happened something miraculous happened
+
+ align:start position:0%
+happened something miraculous happened
+ 
+
+ align:start position:0%
+happened something miraculous happened
+so let me slightly write this matric in
+
+ align:start position:0%
+so let me slightly write this matric in
+ 
+
+ align:start position:0%
+so let me slightly write this matric in
+the slightly more explicit way and I
+
+ align:start position:0%
+the slightly more explicit way and I
+ 
+
+ align:start position:0%
+the slightly more explicit way and I
+write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so let me just separate these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+okay so there two important thing
+
+ align:start position:0%
+okay so there two important thing
+ 
+
+ align:start position:0%
+okay so there two important thing
+happens the two important thing happens
+
+ align:start position:0%
+happens the two important thing happens
+ 
+
+ align:start position:0%
+happens the two important thing happens
+just to give you a
+
+ align:start position:0%
+just to give you a
+ 
+
+ align:start position:0%
+just to give you a
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um uh um yeah let me just do it
+
+ align:start position:0%
+um uh um yeah let me just do it
+ 
+
+ align:start position:0%
+um uh um yeah let me just do it
+here yeah let me do it here maybe it's
+
+ align:start position:0%
+here yeah let me do it here maybe it's
+ 
+
+ align:start position:0%
+here yeah let me do it here maybe it's
+good enough maybe be good just safe so
+
+ align:start position:0%
+good enough maybe be good just safe so
+ 
+
+ align:start position:0%
+good enough maybe be good just safe so
+previously let's just draw the plot like
+
+ align:start position:0%
+previously let's just draw the plot like
+ 
+
+ align:start position:0%
+previously let's just draw the plot like
+this so let's call this R six okay just
+
+ align:start position:0%
+this so let's call this R six okay just
+ 
+
+ align:start position:0%
+this so let's call this R six okay just
+for my
+
+ align:start position:0%
+for my
+ 
+
+ align:start position:0%
+for my
+purpose yeah let's consider uh uh this
+
+ align:start position:0%
+purpose yeah let's consider uh uh this
+ 
+
+ align:start position:0%
+purpose yeah let's consider uh uh this
+is the r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six and uh yeah forget about what's
+
+ align:start position:0%
+six and uh yeah forget about what's
+ 
+
+ align:start position:0%
+six and uh yeah forget about what's
+outside it just imagine the
+
+ align:start position:0%
+outside it just imagine the
+ 
+
+ align:start position:0%
+outside it just imagine the
+yeah there's no outside just the whole
+
+ align:start position:0%
+yeah there's no outside just the whole
+ 
+
+ align:start position:0%
+yeah there's no outside just the whole
+thing is R six okay and when we start
+
+ align:start position:0%
+thing is R six okay and when we start
+ 
+
+ align:start position:0%
+thing is R six okay and when we start
+solving this problem that this rein this
+
+ align:start position:0%
+solving this problem that this rein this
+ 
+
+ align:start position:0%
+solving this problem that this rein this
+rein are point in this R six and then
+
+ align:start position:0%
+rein are point in this R six and then
+ 
+
+ align:start position:0%
+rein are point in this R six and then
+there's some flux coming out of
+
+ align:start position:0%
+there's some flux coming out of
+ 
+
+ align:start position:0%
+there's some flux coming out of
+it okay there's some F5 flux coming out
+
+ align:start position:0%
+it okay there's some F5 flux coming out
+ 
+
+ align:start position:0%
+it okay there's some F5 flux coming out
+of it uh so this is the picture the flux
+
+ align:start position:0%
+of it uh so this is the picture the flux
+ 
+
+ align:start position:0%
+of it uh so this is the picture the flux
+is normal to the F6 H the flux is normal
+
+ align:start position:0%
+is normal to the F6 H the flux is normal
+ 
+
+ align:start position:0%
+is normal to the F6 H the flux is normal
+to F to R6 or no the flux is normal to
+
+ align:start position:0%
+to F to R6 or no the flux is normal to
+ 
+
+ align:start position:0%
+to F to R6 or no the flux is normal to
+the S5 surrounding the
+
+ align:start position:0%
+the S5 surrounding the
+ 
+
+ align:start position:0%
+the S5 surrounding the
+point and just like that I'm just saying
+
+ align:start position:0%
+point and just like that I'm just saying
+ 
+
+ align:start position:0%
+point and just like that I'm just saying
+think about the plane is a whole R six
+
+ align:start position:0%
+think about the plane is a whole R six
+ 
+
+ align:start position:0%
+think about the plane is a whole R six
+uhhuh uh uh uh there's nothing outside
+
+ align:start position:0%
+uhhuh uh uh uh there's nothing outside
+ 
+
+ align:start position:0%
+uhhuh uh uh uh there's nothing outside
+the plane okay okay I want to reserve
+
+ align:start position:0%
+the plane okay okay I want to reserve
+ 
+
+ align:start position:0%
+the plane okay okay I want to reserve
+the things outside plane for other
+
+ align:start position:0%
+the things outside plane for other
+ 
+
+ align:start position:0%
+the things outside plane for other
+purpose I just now think about R is the
+
+ align:start position:0%
+purpose I just now think about R is the
+ 
+
+ align:start position:0%
+purpose I just now think about R is the
+whole thing this is your whole
+
+ align:start position:0%
+whole thing this is your whole
+ 
+
+ align:start position:0%
+whole thing this is your whole
+Space okay so so if you look at this
+
+ align:start position:0%
+Space okay so so if you look at this
+ 
+
+ align:start position:0%
+Space okay so so if you look at this
+situation there are two in there two
+
+ align:start position:0%
+situation there are two in there two
+ 
+
+ align:start position:0%
+situation there are two in there two
+things first there's a source at I equal
+
+ align:start position:0%
+things first there's a source at I equal
+ 
+
+ align:start position:0%
+things first there's a source at I equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+zero you should see you see see a data
+
+ align:start position:0%
+zero you should see you see see a data
+ 
+
+ align:start position:0%
+zero you should see you see see a data
+function which is the source of the flux
+
+ align:start position:0%
+function which is the source of the flux
+ 
+
+ align:start position:0%
+function which is the source of the flux
+and this the source of the mass okay
+
+ align:start position:0%
+and this the source of the mass okay
+ 
+
+ align:start position:0%
+and this the source of the mass okay
+there's some tension there and another
+
+ align:start position:0%
+there's some tension there and another
+ 
+
+ align:start position:0%
+there's some tension there and another
+thing is that if you look at
+
+ align:start position:0%
+thing is that if you look at
+ 
+
+ align:start position:0%
+thing is that if you look at
+S5 around this point and this five when
+
+ align:start position:0%
+S5 around this point and this five when
+ 
+
+ align:start position:0%
+S5 around this point and this five when
+you go to the point then S5 will become
+
+ align:start position:0%
+you go to the point then S5 will become
+ 
+
+ align:start position:0%
+you go to the point then S5 will become
+zero sides okay so around this
+
+ align:start position:0%
+zero sides okay so around this
+ 
+
+ align:start position:0%
+zero sides okay so around this
+point yeah just in flat space around the
+
+ align:start position:0%
+point yeah just in flat space around the
+ 
+
+ align:start position:0%
+point yeah just in flat space around the
+uh uh you have if you write in the polar
+
+ align:start position:0%
+uh uh you have if you write in the polar
+ 
+
+ align:start position:0%
+uh uh you have if you write in the polar
+coordinate so the Sid of this S5
+
+ align:start position:0%
+coordinate so the Sid of this S5
+ 
+
+ align:start position:0%
+coordinate so the Sid of this S5
+surrounding this point become zero sides
+
+ align:start position:0%
+surrounding this point become zero sides
+ 
+
+ align:start position:0%
+surrounding this point become zero sides
+when you go to that point okay
+
+ align:start position:0%
+when you go to that point okay
+ 
+
+ align:start position:0%
+when you go to that point okay
+uh uh uh uh uh
+
+ align:start position:0%
+uh uh uh uh uh
+ 
+
+ align:start position:0%
+uh uh uh uh uh
+yeah but now if you look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matric now if you look at this
+
+ align:start position:0%
+matric now if you look at this
+ 
+
+ align:start position:0%
+matric now if you look at this
+metric now actually when you go to the
+
+ align:start position:0%
+metric now actually when you go to the
+ 
+
+ align:start position:0%
+metric now actually when you go to the
+when you go to the brain location of the
+
+ align:start position:0%
+when you go to the brain location of the
+ 
+
+ align:start position:0%
+when you go to the brain location of the
+brain actually level reach I equal to
+
+ align:start position:0%
+brain actually level reach I equal to
+ 
+
+ align:start position:0%
+brain actually level reach I equal to
+zero actually this S5 now become a
+
+ align:start position:0%
+zero actually this S5 now become a
+ 
+
+ align:start position:0%
+zero actually this S5 now become a
+constant sides okay and also now if you
+
+ align:start position:0%
+constant sides okay and also now if you
+ 
+
+ align:start position:0%
+constant sides okay and also now if you
+can look at this so there are two things
+
+ align:start position:0%
+can look at this so there are two things
+ 
+
+ align:start position:0%
+can look at this so there are two things
+is happening so first this is one this
+
+ align:start position:0%
+is happening so first this is one this
+ 
+
+ align:start position:0%
+is happening so first this is one this
+is two so the first
+
+ align:start position:0%
+is two so the first
+ 
+
+ align:start position:0%
+is two so the first
+thing is said S5
+
+ align:start position:0%
+thing is said S5
+ 
+
+ align:start position:0%
+thing is said S5
+direction S5 let me call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S5 now has a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radius given by this R so this is first
+
+ align:start position:0%
+radius given by this R so this is first
+ 
+
+ align:start position:0%
+radius given by this R so this is first
+thing and the second
+
+ align:start position:0%
+thing and the second
+ 
+
+ align:start position:0%
+thing and the second
+thing is that because of this Dr R
+
+ align:start position:0%
+thing is that because of this Dr R
+ 
+
+ align:start position:0%
+thing is that because of this Dr R
+square over R square
+
+ align:start position:0%
+square over R square
+ 
+
+ align:start position:0%
+square over R square
+structure so if you write as a proper
+
+ align:start position:0%
+structure so if you write as a proper
+ 
+
+ align:start position:0%
+structure so if you write as a proper
+distance write it as DL squ so DL will
+
+ align:start position:0%
+distance write it as DL squ so DL will
+ 
+
+ align:start position:0%
+distance write it as DL squ so DL will
+be the proper
+
+ align:start position:0%
+be the proper
+ 
+
+ align:start position:0%
+be the proper
+distance then you when you solve this
+
+ align:start position:0%
+distance then you when you solve this
+ 
+
+ align:start position:0%
+distance then you when you solve this
+then you find L is essentially log R say
+
+ align:start position:0%
+then you find L is essentially log R say
+ 
+
+ align:start position:0%
+then you find L is essentially log R say
+plus some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant then as R goes to zero the L
+
+ align:start position:0%
+constant then as R goes to zero the L
+ 
+
+ align:start position:0%
+constant then as R goes to zero the L
+goes to when R goes to zero the L goes
+
+ align:start position:0%
+goes to when R goes to zero the L goes
+ 
+
+ align:start position:0%
+goes to when R goes to zero the L goes
+to minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity that means that I equal to
+
+ align:start position:0%
+Infinity that means that I equal to
+ 
+
+ align:start position:0%
+Infinity that means that I equal to
+zero yeah let me just write it here this
+
+ align:start position:0%
+zero yeah let me just write it here this
+ 
+
+ align:start position:0%
+zero yeah let me just write it here this
+means IAL to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+sit at infinite proper distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for all practical purpose the
+
+ align:start position:0%
+okay so for all practical purpose the
+ 
+
+ align:start position:0%
+okay so for all practical purpose the
+brain has
+
+ align:start position:0%
+brain has
+ 
+
+ align:start position:0%
+brain has
+disappeared okay so so the geometric
+
+ align:start position:0%
+disappeared okay so so the geometric
+ 
+
+ align:start position:0%
+disappeared okay so so the geometric
+picture is that when you include this uh
+
+ align:start position:0%
+picture is that when you include this uh
+ 
+
+ align:start position:0%
+picture is that when you include this uh
+the uh when you include the gravity of
+
+ align:start position:0%
+the uh when you include the gravity of
+ 
+
+ align:start position:0%
+the uh when you include the gravity of
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+source so now I have to draw something
+
+ align:start position:0%
+source so now I have to draw something
+ 
+
+ align:start position:0%
+source so now I have to draw something
+called the embedding diagram just use
+
+ align:start position:0%
+called the embedding diagram just use
+ 
+
+ align:start position:0%
+called the embedding diagram just use
+the this actual direction to show the
+
+ align:start position:0%
+the this actual direction to show the
+ 
+
+ align:start position:0%
+the this actual direction to show the
+curvature okay so so when you go when
+
+ align:start position:0%
+curvature okay so so when you go when
+ 
+
+ align:start position:0%
+curvature okay so so when you go when
+you approach this point what do you find
+
+ align:start position:0%
+you approach this point what do you find
+ 
+
+ align:start position:0%
+you approach this point what do you find
+you don't find the point actually you
+
+ align:start position:0%
+you don't find the point actually you
+ 
+
+ align:start position:0%
+you don't find the point actually you
+find this infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+throat and so when you try to go
+
+ align:start position:0%
+throat and so when you try to go
+ 
+
+ align:start position:0%
+throat and so when you try to go
+approach this point and this is this is
+
+ align:start position:0%
+approach this point and this is this is
+ 
+
+ align:start position:0%
+approach this point and this is this is
+the cross-section of this
+
+ align:start position:0%
+the cross-section of this
+ 
+
+ align:start position:0%
+the cross-section of this
+throat which I can not draw is
+
+ align:start position:0%
+throat which I can not draw is
+ 
+
+ align:start position:0%
+throat which I can not draw is
+S5 with a constant
+
+ align:start position:0%
+S5 with a constant
+ 
+
+ align:start position:0%
+S5 with a constant
+radius and uh and then this SLO has
+
+ align:start position:0%
+radius and uh and then this SLO has
+ 
+
+ align:start position:0%
+radius and uh and then this SLO has
+infinite non distance
+
+ align:start position:0%
+infinite non distance
+ 
+
+ align:start position:0%
+infinite non distance
+okay so it's l and and and here and and
+
+ align:start position:0%
+okay so it's l and and and here and and
+ 
+
+ align:start position:0%
+okay so it's l and and and here and and
+and have a infinite
+
+ align:start position:0%
+and have a infinite
+ 
+
+ align:start position:0%
+and have a infinite
+distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh uh so that's what's happening
+
+ align:start position:0%
+okay so uh uh so that's what's happening
+ 
+
+ align:start position:0%
+okay so uh uh so that's what's happening
+here and yeah the size of this sphere of
+
+ align:start position:0%
+here and yeah the size of this sphere of
+ 
+
+ align:start position:0%
+here and yeah the size of this sphere of
+course is R of radius
+
+ align:start position:0%
+course is R of radius
+ 
+
+ align:start position:0%
+course is R of radius
+R of radius
+
+ align:start position:0%
+R of radius
+ 
+
+ align:start position:0%
+R of radius
+r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this
+
+ align:start position:0%
+so in this
+ 
+
+ align:start position:0%
+so in this
+picture so when you include the uh the
+
+ align:start position:0%
+picture so when you include the uh the
+ 
+
+ align:start position:0%
+picture so when you include the uh the
+say what we say the back reaction of the
+
+ align:start position:0%
+say what we say the back reaction of the
+ 
+
+ align:start position:0%
+say what we say the back reaction of the
+dis rant essentially the dis rant
+
+ align:start position:0%
+dis rant essentially the dis rant
+ 
+
+ align:start position:0%
+dis rant essentially the dis rant
+themselves have disappeared the only
+
+ align:start position:0%
+themselves have disappeared the only
+ 
+
+ align:start position:0%
+themselves have disappeared the only
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+left uh are this curved geometry and the
+
+ align:start position:0%
+left uh are this curved geometry and the
+ 
+
+ align:start position:0%
+left uh are this curved geometry and the
+fluxes yeah they still uh uh the fluxes
+
+ align:start position:0%
+fluxes yeah they still uh uh the fluxes
+ 
+
+ align:start position:0%
+fluxes yeah they still uh uh the fluxes
+won't go away so you will still see the
+
+ align:start position:0%
+won't go away so you will still see the
+ 
+
+ align:start position:0%
+won't go away so you will still see the
+the S5 flux the F5 the F5 flock through
+
+ align:start position:0%
+the S5 flux the F5 the F5 flock through
+ 
+
+ align:start position:0%
+the S5 flux the F5 the F5 flock through
+this S5 okay so there still flock
+
+ align:start position:0%
+this S5 okay so there still flock
+ 
+
+ align:start position:0%
+this S5 okay so there still flock
+through this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S5
+
+ align:start position:0%
+S5
+ 
+
+ align:start position:0%
+S5
+okay and this matric so this is S5 which
+
+ align:start position:0%
+okay and this matric so this is S5 which
+ 
+
+ align:start position:0%
+okay and this matric so this is S5 which
+completely decoupled from the rest part
+
+ align:start position:0%
+completely decoupled from the rest part
+ 
+
+ align:start position:0%
+completely decoupled from the rest part
+so this have a constant radius so this
+
+ align:start position:0%
+so this have a constant radius so this
+ 
+
+ align:start position:0%
+so this have a constant radius so this
+S5 have decoupled from the rest part so
+
+ align:start position:0%
+S5 have decoupled from the rest part so
+ 
+
+ align:start position:0%
+S5 have decoupled from the rest part so
+it's natur just look at this part and
+
+ align:start position:0%
+it's natur just look at this part and
+ 
+
+ align:start position:0%
+it's natur just look at this part and
+this is actually
+
+ align:start position:0%
+this is actually
+ 
+
+ align:start position:0%
+this is actually
+ads5 so so so uh so let me call one so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is just a this is the matric of five
+
+ align:start position:0%
+one is just a this is the matric of five
+ 
+
+ align:start position:0%
+one is just a this is the matric of five
+dimensional and space time and times
+
+ align:start position:0%
+dimensional and space time and times
+ 
+
+ align:start position:0%
+dimensional and space time and times
+S5 okay and at S5 uh have the
+
+ align:start position:0%
+S5 okay and at S5 uh have the
+ 
+
+ align:start position:0%
+S5 okay and at S5 uh have the
+matric so let me just copy here
+
+ align:start position:0%
+matric so let me just copy here
+ 
+
+ align:start position:0%
+matric so let me just copy here
+essentially just this part r² Rus DT s+
+
+ align:start position:0%
+essentially just this part r² Rus DT s+
+ 
+
+ align:start position:0%
+essentially just this part r² Rus DT s+
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+x²
+
+ align:start position:0%
+x²
+ 
+
+ align:start position:0%
+x²
+plus r² r² r s okay so this is ADS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+so Something Magic has
+
+ align:start position:0%
+so Something Magic has
+ 
+
+ align:start position:0%
+so Something Magic has
+happened when you try to reach the brain
+
+ align:start position:0%
+happened when you try to reach the brain
+ 
+
+ align:start position:0%
+happened when you try to reach the brain
+then you find the brain is no longer
+
+ align:start position:0%
+then you find the brain is no longer
+ 
+
+ align:start position:0%
+then you find the brain is no longer
+there and actually develop a infinite
+
+ align:start position:0%
+there and actually develop a infinite
+ 
+
+ align:start position:0%
+there and actually develop a infinite
+throat and this Thro the Matrix given by
+
+ align:start position:0%
+throat and this Thro the Matrix given by
+ 
+
+ align:start position:0%
+throat and this Thro the Matrix given by
+S5 * S5 okay of course at Infinity you
+
+ align:start position:0%
+S5 * S5 okay of course at Infinity you
+ 
+
+ align:start position:0%
+S5 * S5 okay of course at Infinity you
+still see a flat space
+
+ align:start position:0%
+still see a flat space
+ 
+
+ align:start position:0%
+still see a flat space
+SP and infinity still see FL movy
+
+ align:start position:0%
+SP and infinity still see FL movy
+ 
+
+ align:start position:0%
+SP and infinity still see FL movy
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we have to take a little bit
+
+ align:start position:0%
+okay so now we have to take a little bit
+ 
+
+ align:start position:0%
+okay so now we have to take a little bit
+conceptual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deap so now we have to take a little bit
+
+ align:start position:0%
+deap so now we have to take a little bit
+ 
+
+ align:start position:0%
+deap so now we have to take a little bit
+conceptual deap yes so we just basically
+
+ align:start position:0%
+conceptual deap yes so we just basically
+ 
+
+ align:start position:0%
+conceptual deap yes so we just basically
+found the most General uh solution of gr
+
+ align:start position:0%
+found the most General uh solution of gr
+ 
+
+ align:start position:0%
+found the most General uh solution of gr
+with the given symmetries given by the r
+
+ align:start position:0%
+with the given symmetries given by the r
+ 
+
+ align:start position:0%
+with the given symmetries given by the r
+yeah with uh what do we mean by most
+
+ align:start position:0%
+yeah with uh what do we mean by most
+ 
+
+ align:start position:0%
+yeah with uh what do we mean by most
+General we have a specific D3 brains
+
+ align:start position:0%
+General we have a specific D3 brains
+ 
+
+ align:start position:0%
+General we have a specific D3 brains
+well so we we fixed the Symmetry given
+
+ align:start position:0%
+well so we we fixed the Symmetry given
+ 
+
+ align:start position:0%
+well so we we fixed the Symmetry given
+by the D3 brain and then no you also fix
+
+ align:start position:0%
+by the D3 brain and then no you also fix
+ 
+
+ align:start position:0%
+by the D3 brain and then no you also fix
+the this rant charge and this rent
+
+ align:start position:0%
+the this rant charge and this rent
+ 
+
+ align:start position:0%
+the this rant charge and this rent
+tension okay no that you Lally fix
+
+ align:start position:0%
+tension okay no that you Lally fix
+ 
+
+ align:start position:0%
+tension okay no that you Lally fix
+everything okay yeah yes so what is the
+
+ align:start position:0%
+everything okay yeah yes so what is the
+ 
+
+ align:start position:0%
+everything okay yeah yes so what is the
+nature of the source originally in this
+
+ align:start position:0%
+nature of the source originally in this
+ 
+
+ align:start position:0%
+nature of the source originally in this
+is like a
+
+ align:start position:0%
+is like a
+ 
+
+ align:start position:0%
+is like a
+electromagnetic but now it's like a
+
+ align:start position:0%
+electromagnetic but now it's like a
+ 
+
+ align:start position:0%
+electromagnetic but now it's like a
+mass no not the mass even the mass is
+
+ align:start position:0%
+mass no not the mass even the mass is
+ 
+
+ align:start position:0%
+mass no not the mass even the mass is
+gone you only see a curved space time uh
+
+ align:start position:0%
+gone you only see a curved space time uh
+ 
+
+ align:start position:0%
+gone you only see a curved space time uh
+uh curved space time and with some
+
+ align:start position:0%
+uh curved space time and with some
+ 
+
+ align:start position:0%
+uh curved space time and with some
+fluxes I mean
+
+ align:start position:0%
+fluxes I mean
+ 
+
+ align:start position:0%
+fluxes I mean
+that c
+
+ align:start position:0%
+that c
+ 
+
+ align:start position:0%
+that c
+c re for the mass yeah but the mass now
+
+ align:start position:0%
+c re for the mass yeah but the mass now
+ 
+
+ align:start position:0%
+c re for the mass yeah but the mass now
+is completely gone it's sitting it's in
+
+ align:start position:0%
+is completely gone it's sitting it's in
+ 
+
+ align:start position:0%
+is completely gone it's sitting it's in
+some sense sitting at infinite distance
+
+ align:start position:0%
+some sense sitting at infinite distance
+ 
+
+ align:start position:0%
+some sense sitting at infinite distance
+away you can never reach it and uh and
+
+ align:start position:0%
+away you can never reach it and uh and
+ 
+
+ align:start position:0%
+away you can never reach it and uh and
+for all practical purpose if you leave
+
+ align:start position:0%
+for all practical purpose if you leave
+ 
+
+ align:start position:0%
+for all practical purpose if you leave
+this space time you will never see the
+
+ align:start position:0%
+this space time you will never see the
+ 
+
+ align:start position:0%
+this space time you will never see the
+source what you will see what you will
+
+ align:start position:0%
+source what you will see what you will
+ 
+
+ align:start position:0%
+source what you will see what you will
+observe is just a curve space time with
+
+ align:start position:0%
+observe is just a curve space time with
+ 
+
+ align:start position:0%
+observe is just a curve space time with
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+fluxes and uh and these are also perfect
+
+ align:start position:0%
+fluxes and uh and these are also perfect
+ 
+
+ align:start position:0%
+fluxes and uh and these are also perfect
+solution of the Einstein equation yeah
+
+ align:start position:0%
+solution of the Einstein equation yeah
+ 
+
+ align:start position:0%
+solution of the Einstein equation yeah
+because away from the source it's also
+
+ align:start position:0%
+because away from the source it's also
+ 
+
+ align:start position:0%
+because away from the source it's also
+perfect solution of Einstein equations
+
+ align:start position:0%
+perfect solution of Einstein equations
+ 
+
+ align:start position:0%
+perfect solution of Einstein equations
+yeah yeah you have first yeah yeah so I
+
+ align:start position:0%
+yeah yeah you have first yeah yeah so I
+ 
+
+ align:start position:0%
+yeah yeah you have first yeah yeah so I
+was just so I was just trying to
+
+ align:start position:0%
+was just so I was just trying to
+ 
+
+ align:start position:0%
+was just so I was just trying to
+understand so the point is that so is
+
+ align:start position:0%
+understand so the point is that so is
+ 
+
+ align:start position:0%
+understand so the point is that so is
+this somehow like protecting us from
+
+ align:start position:0%
+this somehow like protecting us from
+ 
+
+ align:start position:0%
+this somehow like protecting us from
+these issues that I mean even
+
+ align:start position:0%
+these issues that I mean even
+ 
+
+ align:start position:0%
+these issues that I mean even
+electromagnetism or even Quantum these
+
+ align:start position:0%
+electromagnetism or even Quantum these
+ 
+
+ align:start position:0%
+electromagnetism or even Quantum these
+issues of like the Divergence of kind of
+
+ align:start position:0%
+issues of like the Divergence of kind of
+ 
+
+ align:start position:0%
+issues of like the Divergence of kind of
+going towards a point charge so this is
+
+ align:start position:0%
+going towards a point charge so this is
+ 
+
+ align:start position:0%
+going towards a point charge so this is
+this somehow like getting around that by
+
+ align:start position:0%
+this somehow like getting around that by
+ 
+
+ align:start position:0%
+this somehow like getting around that by
+like making it you know go far away or
+
+ align:start position:0%
+like making it you know go far away or
+ 
+
+ align:start position:0%
+like making it you know go far away or
+not really yeah no this is not getting
+
+ align:start position:0%
+not really yeah no this is not getting
+ 
+
+ align:start position:0%
+not really yeah no this is not getting
+around that this is
+
+ align:start position:0%
+around that this is
+ 
+
+ align:start position:0%
+around that this is
+the solution present
+
+ align:start position:0%
+the solution present
+ 
+
+ align:start position:0%
+the solution present
+itself no we did not dictate this
+
+ align:start position:0%
+itself no we did not dictate this
+ 
+
+ align:start position:0%
+itself no we did not dictate this
+solution this is a pure
+
+ align:start position:0%
+solution this is a pure
+ 
+
+ align:start position:0%
+solution this is a pure
+mathematics and we just trying to
+
+ align:start position:0%
+mathematics and we just trying to
+ 
+
+ align:start position:0%
+mathematics and we just trying to
+interpret this uh mathematics right but
+
+ align:start position:0%
+interpret this uh mathematics right but
+ 
+
+ align:start position:0%
+interpret this uh mathematics right but
+I'm saying but but it does achieve that
+
+ align:start position:0%
+I'm saying but but it does achieve that
+ 
+
+ align:start position:0%
+I'm saying but but it does achieve that
+I mean we for right right yeah just the
+
+ align:start position:0%
+I mean we for right right yeah just the
+ 
+
+ align:start position:0%
+I mean we for right right yeah just the
+solution present itself that's crazy
+
+ align:start position:0%
+solution present itself that's crazy
+ 
+
+ align:start position:0%
+solution present itself that's crazy
+okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+wouldn't space like this but D well what
+
+ align:start position:0%
+wouldn't space like this but D well what
+ 
+
+ align:start position:0%
+wouldn't space like this but D well what
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+other like yeah yeah that's something
+
+ align:start position:0%
+other like yeah yeah that's something
+ 
+
+ align:start position:0%
+other like yeah yeah that's something
+similar will happen but the story is
+
+ align:start position:0%
+similar will happen but the story is
+ 
+
+ align:start position:0%
+similar will happen but the story is
+even more complicated yeah so the this
+
+ align:start position:0%
+even more complicated yeah so the this
+ 
+
+ align:start position:0%
+even more complicated yeah so the this
+re brain the matric is
+
+ align:start position:0%
+re brain the matric is
+ 
+
+ align:start position:0%
+re brain the matric is
+simplest yeah for reasons I will mention
+
+ align:start position:0%
+simplest yeah for reasons I will mention
+ 
+
+ align:start position:0%
+simplest yeah for reasons I will mention
+later yeah yeah so the reason I choose
+
+ align:start position:0%
+later yeah yeah so the reason I choose
+ 
+
+ align:start position:0%
+later yeah yeah so the reason I choose
+this Reb brain just because the the
+
+ align:start position:0%
+this Reb brain just because the the
+ 
+
+ align:start position:0%
+this Reb brain just because the the
+matric is a simp is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one other
+
+ align:start position:0%
+one other
+ 
+
+ align:start position:0%
+one other
+questions so the longterm long range
+
+ align:start position:0%
+questions so the longterm long range
+ 
+
+ align:start position:0%
+questions so the longterm long range
+cooling potential that's from the charge
+
+ align:start position:0%
+cooling potential that's from the charge
+ 
+
+ align:start position:0%
+cooling potential that's from the charge
+of the brain both okay you can't really
+
+ align:start position:0%
+of the brain both okay you can't really
+ 
+
+ align:start position:0%
+of the brain both okay you can't really
+separate yeah in principle you can
+
+ align:start position:0%
+separate yeah in principle you can
+ 
+
+ align:start position:0%
+separate yeah in principle you can
+separate depend on your probe yeah but
+
+ align:start position:0%
+separate depend on your probe yeah but
+ 
+
+ align:start position:0%
+separate depend on your probe yeah but
+from the metric from the metric from the
+
+ align:start position:0%
+from the metric from the metric from the
+ 
+
+ align:start position:0%
+from the metric from the metric from the
+metric actually from the matric it just
+
+ align:start position:0%
+metric actually from the matric it just
+ 
+
+ align:start position:0%
+metric actually from the matric it just
+from the in some sense it come from the
+
+ align:start position:0%
+from the in some sense it come from the
+ 
+
+ align:start position:0%
+from the in some sense it come from the
+um uh uh
+
+ align:start position:0%
+um uh uh
+ 
+
+ align:start position:0%
+um uh uh
+it's from matric of course you should
+
+ align:start position:0%
+it's from matric of course you should
+ 
+
+ align:start position:0%
+it's from matric of course you should
+just interpret as a gravitational part
+
+ align:start position:0%
+just interpret as a gravitational part
+ 
+
+ align:start position:0%
+just interpret as a gravitational part
+yeah this is just gravitational part
+
+ align:start position:0%
+yeah this is just gravitational part
+ 
+
+ align:start position:0%
+yeah this is just gravitational part
+question so there you draw the flu
+
+ align:start position:0%
+question so there you draw the flu
+ 
+
+ align:start position:0%
+question so there you draw the flu
+flowing out of the cylinder or alone the
+
+ align:start position:0%
+flowing out of the cylinder or alone the
+ 
+
+ align:start position:0%
+flowing out of the cylinder or alone the
+cylinder I guess it's alone Cinder no no
+
+ align:start position:0%
+cylinder I guess it's alone Cinder no no
+ 
+
+ align:start position:0%
+cylinder I guess it's alone Cinder no no
+no not alone the cylinder alone the
+
+ align:start position:0%
+no not alone the cylinder alone the
+ 
+
+ align:start position:0%
+no not alone the cylinder alone the
+cinder is the R Direction yeah the flux
+
+ align:start position:0%
+cinder is the R Direction yeah the flux
+ 
+
+ align:start position:0%
+cinder is the R Direction yeah the flux
+is the flux is in the S5 it's just think
+
+ align:start position:0%
+is the flux is in the S5 it's just think
+ 
+
+ align:start position:0%
+is the flux is in the S5 it's just think
+of a hollow
+
+ align:start position:0%
+of a hollow
+ 
+
+ align:start position:0%
+of a hollow
+S2 think of a h Square think of a h S2
+
+ align:start position:0%
+S2 think of a h Square think of a h S2
+ 
+
+ align:start position:0%
+S2 think of a h Square think of a h S2
+then on S2 you can have magnetic flux
+
+ align:start position:0%
+then on S2 you can have magnetic flux
+ 
+
+ align:start position:0%
+then on S2 you can have magnetic flux
+and flex is along the radial Direction
+
+ align:start position:0%
+and flex is along the radial Direction
+ 
+
+ align:start position:0%
+and flex is along the radial Direction
+no no there's no radial direction if you
+
+ align:start position:0%
+no no there's no radial direction if you
+ 
+
+ align:start position:0%
+no no there's no radial direction if you
+only have S2 then there's no radial
+
+ align:start position:0%
+only have S2 then there's no radial
+ 
+
+ align:start position:0%
+only have S2 then there's no radial
+Direction just only have S2 okay and
+
+ align:start position:0%
+Direction just only have S2 okay and
+ 
+
+ align:start position:0%
+Direction just only have S2 okay and
+then you can have a flux on that S2 yes
+
+ align:start position:0%
+then you can have a flux on that S2 yes
+ 
+
+ align:start position:0%
+then you can have a flux on that S2 yes
+yeah something proportional to F Theta 5
+
+ align:start position:0%
+yeah something proportional to F Theta 5
+ 
+
+ align:start position:0%
+yeah something proportional to F Theta 5
+say in electromagnetism yeah so this
+
+ align:start position:0%
+say in electromagnetism yeah so this
+ 
+
+ align:start position:0%
+say in electromagnetism yeah so this
+would be a magnetic flux in the yeah yes
+
+ align:start position:0%
+would be a magnetic flux in the yeah yes
+ 
+
+ align:start position:0%
+would be a magnetic flux in the yeah yes
+so write in s uh oh oh yes but but you
+
+ align:start position:0%
+so write in s uh oh oh yes but but you
+ 
+
+ align:start position:0%
+so write in s uh oh oh yes but but you
+write it like in R six if you're writing
+
+ align:start position:0%
+write it like in R six if you're writing
+ 
+
+ align:start position:0%
+write it like in R six if you're writing
+in R six it is along the radius
+
+ align:start position:0%
+in R six it is along the radius
+ 
+
+ align:start position:0%
+in R six it is along the radius
+Direction uh yeah just forget about the
+
+ align:start position:0%
+Direction uh yeah just forget about the
+ 
+
+ align:start position:0%
+Direction uh yeah just forget about the
+uh in this
+
+ align:start position:0%
+uh in this
+ 
+
+ align:start position:0%
+uh in this
+picture is like in the uh in the in the
+
+ align:start position:0%
+picture is like in the uh in the in the
+ 
+
+ align:start position:0%
+picture is like in the uh in the in the
+radio Direction
+
+ align:start position:0%
+radio Direction
+ 
+
+ align:start position:0%
+radio Direction
+but once in this picture and then this
+
+ align:start position:0%
+but once in this picture and then this
+ 
+
+ align:start position:0%
+but once in this picture and then this
+become completely decoupled and and then
+
+ align:start position:0%
+become completely decoupled and and then
+ 
+
+ align:start position:0%
+become completely decoupled and and then
+just you just have separate S5
+
+ align:start position:0%
+just you just have separate S5
+ 
+
+ align:start position:0%
+just you just have separate S5
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+yeah okay so now we have to do a little
+
+ align:start position:0%
+yeah okay so now we have to do a little
+ 
+
+ align:start position:0%
+yeah okay so now we have to do a little
+bit conceptual deap it's not too big is
+
+ align:start position:0%
+bit conceptual deap it's not too big is
+ 
+
+ align:start position:0%
+bit conceptual deap it's not too big is
+said now we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brains okay so in the description
+
+ align:start position:0%
+brains okay so in the description
+ 
+
+ align:start position:0%
+brains okay so in the description
+one you just have a deep brain you
+
+ align:start position:0%
+one you just have a deep brain you
+ 
+
+ align:start position:0%
+one you just have a deep brain you
+really just have some dly boundary
+
+ align:start position:0%
+really just have some dly boundary
+ 
+
+ align:start position:0%
+really just have some dly boundary
+conditions in
+
+ align:start position:0%
+conditions in
+ 
+
+ align:start position:0%
+conditions in
+flat same in corsky 10 dimensional space
+
+ align:start position:0%
+flat same in corsky 10 dimensional space
+ 
+
+ align:start position:0%
+flat same in corsky 10 dimensional space
+time and where open strings can end
+
+ align:start position:0%
+time and where open strings can end
+ 
+
+ align:start position:0%
+time and where open strings can end
+where open strings leave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say so in this picture you just you
+
+ align:start position:0%
+say so in this picture you just you
+ 
+
+ align:start position:0%
+say so in this picture you just you
+specify some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane some some some surface in the
+
+ align:start position:0%
+plane some some some surface in the
+ 
+
+ align:start position:0%
+plane some some some surface in the
+minkovski 10
+
+ align:start position:0%
+minkovski 10
+ 
+
+ align:start position:0%
+minkovski 10
+Dimension and uh and so this is R1 R3
+
+ align:start position:0%
+Dimension and uh and so this is R1 R3
+ 
+
+ align:start position:0%
+Dimension and uh and so this is R1 R3
+say or1 comma 3 if you include the time
+
+ align:start position:0%
+say or1 comma 3 if you include the time
+ 
+
+ align:start position:0%
+say or1 comma 3 if you include the time
+Direction so include so you just specify
+
+ align:start position:0%
+Direction so include so you just specify
+ 
+
+ align:start position:0%
+Direction so include so you just specify
+some plane in the space time in the 10
+
+ align:start position:0%
+some plane in the space time in the 10
+ 
+
+ align:start position:0%
+some plane in the space time in the 10
+SP time where on this plane you can have
+
+ align:start position:0%
+SP time where on this plane you can have
+ 
+
+ align:start position:0%
+SP time where on this plane you can have
+open string
+
+ align:start position:0%
+open string
+ 
+
+ align:start position:0%
+open string
+excitations
+
+ align:start position:0%
+excitations
+ 
+
+ align:start position:0%
+excitations
+okay and then this the system of course
+
+ align:start position:0%
+okay and then this the system of course
+ 
+
+ align:start position:0%
+okay and then this the system of course
+can also have close
+
+ align:start position:0%
+can also have close
+ 
+
+ align:start position:0%
+can also have close
+strings then this close string can
+
+ align:start position:0%
+strings then this close string can
+ 
+
+ align:start position:0%
+strings then this close string can
+interact with the brain can interact
+
+ align:start position:0%
+interact with the brain can interact
+ 
+
+ align:start position:0%
+interact with the brain can interact
+with the open strings Etc and uh and uh
+
+ align:start position:0%
+with the open strings Etc and uh and uh
+ 
+
+ align:start position:0%
+with the open strings Etc and uh and uh
+uh uh the
+
+ align:start position:0%
+uh uh the
+ 
+
+ align:start position:0%
+uh uh the
+only so everything is in the flat space
+
+ align:start position:0%
+only so everything is in the flat space
+ 
+
+ align:start position:0%
+only so everything is in the flat space
+everything is in the flat space and uh
+
+ align:start position:0%
+everything is in the flat space and uh
+ 
+
+ align:start position:0%
+everything is in the flat space and uh
+and uh uh uh uh you have open string you
+
+ align:start position:0%
+and uh uh uh uh you have open string you
+ 
+
+ align:start position:0%
+and uh uh uh uh you have open string you
+have closed string open string leave on
+
+ align:start position:0%
+have closed string open string leave on
+ 
+
+ align:start position:0%
+have closed string open string leave on
+the brain the Clos string can attct with
+
+ align:start position:0%
+the brain the Clos string can attct with
+ 
+
+ align:start position:0%
+the brain the Clos string can attct with
+the brain the Clos string can attct with
+
+ align:start position:0%
+the brain the Clos string can attct with
+ 
+
+ align:start position:0%
+the brain the Clos string can attct with
+open string in particular for example
+
+ align:start position:0%
+open string in particular for example
+ 
+
+ align:start position:0%
+open string in particular for example
+you can send the close string and
+
+ align:start position:0%
+you can send the close string and
+ 
+
+ align:start position:0%
+you can send the close string and
+absorbed by the brain and then Decay
+
+ align:start position:0%
+absorbed by the brain and then Decay
+ 
+
+ align:start position:0%
+absorbed by the brain and then Decay
+into open string is possible uh so this
+
+ align:start position:0%
+into open string is possible uh so this
+ 
+
+ align:start position:0%
+into open string is possible uh so this
+just corresponding to say yeah or or you
+
+ align:start position:0%
+just corresponding to say yeah or or you
+ 
+
+ align:start position:0%
+just corresponding to say yeah or or you
+can have two open string Collide then
+
+ align:start position:0%
+can have two open string Collide then
+ 
+
+ align:start position:0%
+can have two open string Collide then
+become a Clos string and then jump out
+
+ align:start position:0%
+become a Clos string and then jump out
+ 
+
+ align:start position:0%
+become a Clos string and then jump out
+of the brain yeah you can have all kind
+
+ align:start position:0%
+of the brain yeah you can have all kind
+ 
+
+ align:start position:0%
+of the brain yeah you can have all kind
+of this kind of interactions uh the key
+
+ align:start position:0%
+of this kind of interactions uh the key
+ 
+
+ align:start position:0%
+of this kind of interactions uh the key
+point is that in this
+
+ align:start position:0%
+point is that in this
+ 
+
+ align:start position:0%
+point is that in this
+description the only thing you need
+
+ align:start position:0%
+description the only thing you need
+ 
+
+ align:start position:0%
+description the only thing you need
+is the only thing you need is the derly
+
+ align:start position:0%
+is the only thing you need is the derly
+ 
+
+ align:start position:0%
+is the only thing you need is the derly
+boundary conditions specified on the um
+
+ align:start position:0%
+boundary conditions specified on the um
+ 
+
+ align:start position:0%
+boundary conditions specified on the um
+on your on some component of your um W
+
+ align:start position:0%
+on your on some component of your um W
+ 
+
+ align:start position:0%
+on your on some component of your um W
+sheet field for the screen
+
+ align:start position:0%
+sheet field for the screen
+ 
+
+ align:start position:0%
+sheet field for the screen
+okay so this is but now from here we
+
+ align:start position:0%
+okay so this is but now from here we
+ 
+
+ align:start position:0%
+okay so this is but now from here we
+have also found a different a second
+
+ align:start position:0%
+have also found a different a second
+ 
+
+ align:start position:0%
+have also found a different a second
+description is that we have SpaceTime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one which is some curve space time then
+
+ align:start position:0%
+one which is some curve space time then
+ 
+
+ align:start position:0%
+one which is some curve space time then
+plus F5
+
+ align:start position:0%
+plus F5
+ 
+
+ align:start position:0%
+plus F5
+FL on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F5 okay so here there's no de brains
+
+ align:start position:0%
+F5 okay so here there's no de brains
+ 
+
+ align:start position:0%
+F5 okay so here there's no de brains
+anymore we just have some curve space
+
+ align:start position:0%
+anymore we just have some curve space
+ 
+
+ align:start position:0%
+anymore we just have some curve space
+time with some fluxes so here the the
+
+ align:start position:0%
+time with some fluxes so here the the
+ 
+
+ align:start position:0%
+time with some fluxes so here the the
+only thing needs is a close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Str so
+
+ align:start position:0%
+Str so
+ 
+
+ align:start position:0%
+Str so
+only close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strs but but those close string see a
+
+ align:start position:0%
+strs but but those close string see a
+ 
+
+ align:start position:0%
+strs but but those close string see a
+curves
+
+ align:start position:0%
+curves
+ 
+
+ align:start position:0%
+curves
+geometry okay so now I can include all
+
+ align:start position:0%
+geometry okay so now I can include all
+ 
+
+ align:start position:0%
+geometry okay so now I can include all
+Dimensions let me just draw the just to
+
+ align:start position:0%
+Dimensions let me just draw the just to
+ 
+
+ align:start position:0%
+Dimensions let me just draw the just to
+contrast this two let me draw this
+
+ align:start position:0%
+contrast this two let me draw this
+ 
+
+ align:start position:0%
+contrast this two let me draw this
+picture again now let's draw a 10
+
+ align:start position:0%
+picture again now let's draw a 10
+ 
+
+ align:start position:0%
+picture again now let's draw a 10
+dimensional picture so this is R
+
+ align:start position:0%
+dimensional picture so this is R
+ 
+
+ align:start position:0%
+dimensional picture so this is R
+minkovski
+
+ align:start position:0%
+minkovski
+ 
+
+ align:start position:0%
+minkovski
+10 yeah so this is movy
+
+ align:start position:0%
+10 yeah so this is movy
+ 
+
+ align:start position:0%
+10 yeah so this is movy
+10 so when you know go to smaller radius
+
+ align:start position:0%
+10 so when you know go to smaller radius
+ 
+
+ align:start position:0%
+10 so when you know go to smaller radius
+R and then you develop infinite throat
+
+ align:start position:0%
+R and then you develop infinite throat
+ 
+
+ align:start position:0%
+R and then you develop infinite throat
+so this become Aus five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times5
+
+ align:start position:0%
+times5
+ 
+
+ align:start position:0%
+times5
+okay down the
+
+ align:start position:0%
+okay down the
+ 
+
+ align:start position:0%
+okay down the
+thir and here only Co string
+
+ align:start position:0%
+thir and here only Co string
+ 
+
+ align:start position:0%
+thir and here only Co string
+can can
+
+ align:start position:0%
+can can
+ 
+
+ align:start position:0%
+can can
+propagate there's no de brain but the co
+
+ align:start position:0%
+propagate there's no de brain but the co
+ 
+
+ align:start position:0%
+propagate there's no de brain but the co
+string can can add infinity can in ad is
+
+ align:start position:0%
+string can can add infinity can in ad is
+ 
+
+ align:start position:0%
+string can can add infinity can in ad is
+five so you can have Co strs okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is this clear why we have close
+
+ align:start position:0%
+so is this clear why we have close
+ 
+
+ align:start position:0%
+so is this clear why we have close
+strings because in low energy cases it's
+
+ align:start position:0%
+strings because in low energy cases it's
+ 
+
+ align:start position:0%
+strings because in low energy cases it's
+no strings we only have a effective
+
+ align:start position:0%
+no strings we only have a effective
+ 
+
+ align:start position:0%
+no strings we only have a effective
+field but you can have yeah uh but this
+
+ align:start position:0%
+field but you can have yeah uh but this
+ 
+
+ align:start position:0%
+field but you can have yeah uh but this
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+geometry this provide the geometry in
+
+ align:start position:0%
+geometry this provide the geometry in
+ 
+
+ align:start position:0%
+geometry this provide the geometry in
+principle close the excitations will be
+
+ align:start position:0%
+principle close the excitations will be
+ 
+
+ align:start position:0%
+principle close the excitations will be
+close Str so if you now you can do Str
+
+ align:start position:0%
+close Str so if you now you can do Str
+ 
+
+ align:start position:0%
+close Str so if you now you can do Str
+in this geometry oh oh I see yeah so now
+
+ align:start position:0%
+in this geometry oh oh I see yeah so now
+ 
+
+ align:start position:0%
+in this geometry oh oh I see yeah so now
+essentially treated as a targets new
+
+ align:start position:0%
+essentially treated as a targets new
+ 
+
+ align:start position:0%
+essentially treated as a targets new
+Target space and exactly oh and the do
+
+ align:start position:0%
+Target space and exactly oh and the do
+ 
+
+ align:start position:0%
+Target space and exactly oh and the do
+new stre exactly so so we start with a
+
+ align:start position:0%
+new stre exactly so so we start with a
+ 
+
+ align:start position:0%
+new stre exactly so so we start with a
+de brain and then we solve the geometry
+
+ align:start position:0%
+de brain and then we solve the geometry
+ 
+
+ align:start position:0%
+de brain and then we solve the geometry
+due to that de
+
+ align:start position:0%
+due to that de
+ 
+
+ align:start position:0%
+due to that de
+brain geometry due to that de brain and
+
+ align:start position:0%
+brain geometry due to that de brain and
+ 
+
+ align:start position:0%
+brain geometry due to that de brain and
+then now you can quantize the screen
+
+ align:start position:0%
+then now you can quantize the screen
+ 
+
+ align:start position:0%
+then now you can quantize the screen
+theory in that little geometry then that
+
+ align:start position:0%
+theory in that little geometry then that
+ 
+
+ align:start position:0%
+theory in that little geometry then that
+will describe how things intact with de
+
+ align:start position:0%
+will describe how things intact with de
+ 
+
+ align:start position:0%
+will describe how things intact with de
+brain okay yeah but in this picture
+
+ align:start position:0%
+brain okay yeah but in this picture
+ 
+
+ align:start position:0%
+brain okay yeah but in this picture
+there's no de anymore there only close
+
+ align:start position:0%
+there's no de anymore there only close
+ 
+
+ align:start position:0%
+there's no de anymore there only close
+JS Okay so so we just have uh
+
+ align:start position:0%
+JS Okay so so we just have uh
+ 
+
+ align:start position:0%
+JS Okay so so we just have uh
+yeah good
+
+ align:start position:0%
+yeah good
+ 
+
+ align:start position:0%
+yeah good
+yes H what was F5 F5 is the is the is
+
+ align:start position:0%
+yes H what was F5 F5 is the is the is
+ 
+
+ align:start position:0%
+yes H what was F5 F5 is the is the is
+the this F5 form of the tpe Tob stren
+
+ align:start position:0%
+the this F5 form of the tpe Tob stren
+ 
+
+ align:start position:0%
+the this F5 form of the tpe Tob stren
+which this this Rebrand carry the charge
+
+ align:start position:0%
+which this this Rebrand carry the charge
+ 
+
+ align:start position:0%
+which this this Rebrand carry the charge
+so this generalized charge I discussed
+
+ align:start position:0%
+so this generalized charge I discussed
+ 
+
+ align:start position:0%
+so this generalized charge I discussed
+last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions in last class that we know the
+
+ align:start position:0%
+questions in last class that we know the
+ 
+
+ align:start position:0%
+questions in last class that we know the
+F5 is from the effective
+
+ align:start position:0%
+F5 is from the effective
+ 
+
+ align:start position:0%
+F5 is from the effective
+Theory uh yeah and the effective theory
+
+ align:start position:0%
+Theory uh yeah and the effective theory
+ 
+
+ align:start position:0%
+Theory uh yeah and the effective theory
+is from the open string Spectrum no no
+
+ align:start position:0%
+is from the open string Spectrum no no
+ 
+
+ align:start position:0%
+is from the open string Spectrum no no
+no no F5 is close to Spectrum oh it's
+
+ align:start position:0%
+no no F5 is close to Spectrum oh it's
+ 
+
+ align:start position:0%
+no no F5 is close to Spectrum oh it's
+close toing Spectrum so why can you we
+
+ align:start position:0%
+close toing Spectrum so why can you we
+ 
+
+ align:start position:0%
+close toing Spectrum so why can you we
+why why can we apply string series twice
+
+ align:start position:0%
+why why can we apply string series twice
+ 
+
+ align:start position:0%
+why why can we apply string series twice
+I mean the first time we get a flx and
+
+ align:start position:0%
+I mean the first time we get a flx and
+ 
+
+ align:start position:0%
+I mean the first time we get a flx and
+then we get a modified Target space then
+
+ align:start position:0%
+then we get a modified Target space then
+ 
+
+ align:start position:0%
+then we get a modified Target space then
+we apply again yeah yeah you can yeah uh
+
+ align:start position:0%
+we apply again yeah yeah you can yeah uh
+ 
+
+ align:start position:0%
+we apply again yeah yeah you can yeah uh
+um streen Ser you can work with any c
+
+ align:start position:0%
+um streen Ser you can work with any c
+ 
+
+ align:start position:0%
+um streen Ser you can work with any c
+space time you can you can think about
+
+ align:start position:0%
+space time you can you can think about
+ 
+
+ align:start position:0%
+space time you can you can think about
+propagating a string in a generic c
+
+ align:start position:0%
+propagating a string in a generic c
+ 
+
+ align:start position:0%
+propagating a string in a generic c
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay because it's it seems like uh
+
+ align:start position:0%
+okay okay because it's it seems like uh
+ 
+
+ align:start position:0%
+okay okay because it's it seems like uh
+the second application of string theory
+
+ align:start position:0%
+the second application of string theory
+ 
+
+ align:start position:0%
+the second application of string theory
+is like a higher correction no seems
+
+ align:start position:0%
+is like a higher correction no seems
+ 
+
+ align:start position:0%
+is like a higher correction no seems
+like no this picture this picture I'm
+
+ align:start position:0%
+like no this picture this picture I'm
+ 
+
+ align:start position:0%
+like no this picture this picture I'm
+just look at forget about deep brain I
+
+ align:start position:0%
+just look at forget about deep brain I
+ 
+
+ align:start position:0%
+just look at forget about deep brain I
+just look at some charged object I can
+
+ align:start position:0%
+just look at some charged object I can
+ 
+
+ align:start position:0%
+just look at some charged object I can
+look at some charged object in string
+
+ align:start position:0%
+look at some charged object in string
+ 
+
+ align:start position:0%
+look at some charged object in string
+ser and that object have some charge
+
+ align:start position:0%
+ser and that object have some charge
+ 
+
+ align:start position:0%
+ser and that object have some charge
+have some Mass then I will call this
+
+ align:start position:0%
+have some Mass then I will call this
+ 
+
+ align:start position:0%
+have some Mass then I will call this
+matric I will call this matric and the
+
+ align:start position:0%
+matric I will call this matric and the
+ 
+
+ align:start position:0%
+matric I will call this matric and the
+string must be able to live in that uh
+
+ align:start position:0%
+string must be able to live in that uh
+ 
+
+ align:start position:0%
+string must be able to live in that uh
+uh uh must be able to live in that
+
+ align:start position:0%
+uh uh must be able to live in that
+ 
+
+ align:start position:0%
+uh uh must be able to live in that
+matric and if we if I want to work out
+
+ align:start position:0%
+matric and if we if I want to work out
+ 
+
+ align:start position:0%
+matric and if we if I want to work out
+the property of the string then matri I
+
+ align:start position:0%
+the property of the string then matri I
+ 
+
+ align:start position:0%
+the property of the string then matri I
+Quant the string in this uh in this
+
+ align:start position:0%
+Quant the string in this uh in this
+ 
+
+ align:start position:0%
+Quant the string in this uh in this
+geometry qu stren so this point of view
+
+ align:start position:0%
+geometry qu stren so this point of view
+ 
+
+ align:start position:0%
+geometry qu stren so this point of view
+just purely to view the this brain as
+
+ align:start position:0%
+just purely to view the this brain as
+ 
+
+ align:start position:0%
+just purely to view the this brain as
+some charged object in the in the scen
+
+ align:start position:0%
+some charged object in the in the scen
+ 
+
+ align:start position:0%
+some charged object in the in the scen
+theory you you you just solve this
+
+ align:start position:0%
+theory you you you just solve this
+ 
+
+ align:start position:0%
+theory you you you just solve this
+your okay any other questions so this is
+
+ align:start position:0%
+your okay any other questions so this is
+ 
+
+ align:start position:0%
+your okay any other questions so this is
+a very important point this very
+
+ align:start position:0%
+a very important point this very
+ 
+
+ align:start position:0%
+a very important point this very
+important point so now the
+
+ align:start position:0%
+important point so now the
+ 
+
+ align:start position:0%
+important point so now the
+key the now the
+
+ align:start position:0%
+key the now the
+ 
+
+ align:start position:0%
+key the now the
+key is by consistency a must equal to
+
+ align:start position:0%
+key is by consistency a must equal to
+ 
+
+ align:start position:0%
+key is by consistency a must equal to
+B so these two distribution must be
+
+ align:start position:0%
+B so these two distribution must be
+ 
+
+ align:start position:0%
+B so these two distribution must be
+equivalent okay so this can be
+
+ align:start position:0%
+equivalent okay so this can be
+ 
+
+ align:start position:0%
+equivalent okay so this can be
+generalization as the simple exercise we
+
+ align:start position:0%
+generalization as the simple exercise we
+ 
+
+ align:start position:0%
+generalization as the simple exercise we
+described
+
+ align:start position:0%
+described
+ 
+
+ align:start position:0%
+described
+earlier that if you want to describe the
+
+ align:start position:0%
+earlier that if you want to describe the
+ 
+
+ align:start position:0%
+earlier that if you want to describe the
+the interaction between the two de
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brains you can use in two equivalent way
+
+ align:start position:0%
+brains you can use in two equivalent way
+ 
+
+ align:start position:0%
+brains you can use in two equivalent way
+why is to consider Some Loops of open
+
+ align:start position:0%
+why is to consider Some Loops of open
+ 
+
+ align:start position:0%
+why is to consider Some Loops of open
+strings which only need to consider the
+
+ align:start position:0%
+strings which only need to consider the
+ 
+
+ align:start position:0%
+strings which only need to consider the
+flat space just consider Loops of open
+
+ align:start position:0%
+flat space just consider Loops of open
+ 
+
+ align:start position:0%
+flat space just consider Loops of open
+strings or you can the gravit
+
+ align:start position:0%
+strings or you can the gravit
+ 
+
+ align:start position:0%
+strings or you can the gravit
+exchange between the two de BRS and
+
+ align:start position:0%
+exchange between the two de BRS and
+ 
+
+ align:start position:0%
+exchange between the two de BRS and
+gravit exchange between the two de BR is
+
+ align:start position:0%
+gravit exchange between the two de BR is
+ 
+
+ align:start position:0%
+gravit exchange between the two de BR is
+to view that the other de BR have
+
+ align:start position:0%
+to view that the other de BR have
+ 
+
+ align:start position:0%
+to view that the other de BR have
+already curved your space time and the
+
+ align:start position:0%
+already curved your space time and the
+ 
+
+ align:start position:0%
+already curved your space time and the
+the other de living in that curve space
+
+ align:start position:0%
+the other de living in that curve space
+ 
+
+ align:start position:0%
+the other de living in that curve space
+time so so so these are precise the
+
+ align:start position:0%
+time so so so these are precise the
+ 
+
+ align:start position:0%
+time so so so these are precise the
+generalization of that equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we have two object two description
+
+ align:start position:0%
+now we have two object two description
+ 
+
+ align:start position:0%
+now we have two object two description
+of De Brands which are completely
+
+ align:start position:0%
+of De Brands which are completely
+ 
+
+ align:start position:0%
+of De Brands which are completely
+different this one involving flash space
+
+ align:start position:0%
+different this one involving flash space
+ 
+
+ align:start position:0%
+different this one involving flash space
+and open and Clos string and this one
+
+ align:start position:0%
+and open and Clos string and this one
+ 
+
+ align:start position:0%
+and open and Clos string and this one
+only involing Clos but in some curve
+
+ align:start position:0%
+only involing Clos but in some curve
+ 
+
+ align:start position:0%
+only involing Clos but in some curve
+space time
+
+ align:start position:0%
+space time
+ 
+
+ align:start position:0%
+space time
+okay and in principle both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+descriptions can in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+valid for all value of alpha
+
+ align:start position:0%
+valid for all value of alpha
+ 
+
+ align:start position:0%
+valid for all value of alpha
+Prime and G
+
+ align:start position:0%
+Prime and G
+ 
+
+ align:start position:0%
+Prime and G
+stren okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the two parameters in the stren
+
+ align:start position:0%
+so the two parameters in the stren
+ 
+
+ align:start position:0%
+so the two parameters in the stren
+theory Alpha Prime and and but all Alpha
+
+ align:start position:0%
+theory Alpha Prime and and but all Alpha
+ 
+
+ align:start position:0%
+theory Alpha Prime and and but all Alpha
+Prime just consider for all energies uh
+
+ align:start position:0%
+Prime just consider for all energies uh
+ 
+
+ align:start position:0%
+Prime just consider for all energies uh
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay why it seems like they're con
+
+ align:start position:0%
+okay why it seems like they're con
+ 
+
+ align:start position:0%
+okay why it seems like they're con
+strain yeah yeah uh so so first in this
+
+ align:start position:0%
+strain yeah yeah uh so so first in this
+ 
+
+ align:start position:0%
+strain yeah yeah uh so so first in this
+picture there's no
+
+ align:start position:0%
+picture there's no
+ 
+
+ align:start position:0%
+picture there's no
+restriction on what is the alpha prime
+
+ align:start position:0%
+restriction on what is the alpha prime
+ 
+
+ align:start position:0%
+restriction on what is the alpha prime
+or G string and and you just impose D
+
+ align:start position:0%
+or G string and and you just impose D
+ 
+
+ align:start position:0%
+or G string and and you just impose D
+boundary condition and when you have a g
+
+ align:start position:0%
+boundary condition and when you have a g
+ 
+
+ align:start position:0%
+boundary condition and when you have a g
+string you just need to include the
+
+ align:start position:0%
+string you just need to include the
+ 
+
+ align:start position:0%
+string you just need to include the
+higher Loop diagrams
+
+ align:start position:0%
+higher Loop diagrams
+ 
+
+ align:start position:0%
+higher Loop diagrams
+Etc so so when we work out this
+
+ align:start position:0%
+Etc so so when we work out this
+ 
+
+ align:start position:0%
+Etc so so when we work out this
+geometry
+
+ align:start position:0%
+geometry
+ 
+
+ align:start position:0%
+geometry
+so so this statement is more try to
+
+ align:start position:0%
+so so this statement is more try to
+ 
+
+ align:start position:0%
+so so this statement is more try to
+apply to B in B when we apply when we
+
+ align:start position:0%
+apply to B in B when we apply when we
+ 
+
+ align:start position:0%
+apply to B in B when we apply when we
+work out this geometry and also uh uh
+
+ align:start position:0%
+work out this geometry and also uh uh
+ 
+
+ align:start position:0%
+work out this geometry and also uh uh
+this uh uh that a and S5 we were working
+
+ align:start position:0%
+this uh uh that a and S5 we were working
+ 
+
+ align:start position:0%
+this uh uh that a and S5 we were working
+using the approximation that the the
+
+ align:start position:0%
+using the approximation that the the
+ 
+
+ align:start position:0%
+using the approximation that the the
+alpha Prime should be small and the g
+
+ align:start position:0%
+alpha Prime should be small and the g
+ 
+
+ align:start position:0%
+alpha Prime should be small and the g
+string should be small
+
+ align:start position:0%
+string should be small
+ 
+
+ align:start position:0%
+string should be small
+yes but once you have worked out that
+
+ align:start position:0%
+yes but once you have worked out that
+ 
+
+ align:start position:0%
+yes but once you have worked out that
+solution in this regime in principle if
+
+ align:start position:0%
+solution in this regime in principle if
+ 
+
+ align:start position:0%
+solution in this regime in principle if
+you're technically powerful enough you
+
+ align:start position:0%
+you're technically powerful enough you
+ 
+
+ align:start position:0%
+you're technically powerful enough you
+should be able to extend this to to to
+
+ align:start position:0%
+should be able to extend this to to to
+ 
+
+ align:start position:0%
+should be able to extend this to to to
+General values of g string and Alpha
+
+ align:start position:0%
+General values of g string and Alpha
+ 
+
+ align:start position:0%
+General values of g string and Alpha
+prime it may not be precisely this
+
+ align:start position:0%
+prime it may not be precisely this
+ 
+
+ align:start position:0%
+prime it may not be precisely this
+matric but with some kind of deformation
+
+ align:start position:0%
+matric but with some kind of deformation
+ 
+
+ align:start position:0%
+matric but with some kind of deformation
+of that from alpha Prime Corrections and
+
+ align:start position:0%
+of that from alpha Prime Corrections and
+ 
+
+ align:start position:0%
+of that from alpha Prime Corrections and
+G string corrections but you should be
+
+ align:start position:0%
+G string corrections but you should be
+ 
+
+ align:start position:0%
+G string corrections but you should be
+able to do
+
+ align:start position:0%
+able to do
+ 
+
+ align:start position:0%
+able to do
+that yeah yeah I'm just say so that's
+
+ align:start position:0%
+that yeah yeah I'm just say so that's
+ 
+
+ align:start position:0%
+that yeah yeah I'm just say so that's
+why I say in
+
+ align:start position:0%
+why I say in
+ 
+
+ align:start position:0%
+why I say in
+principle okay
+
+ align:start position:0%
+principle okay
+ 
+
+ align:start position:0%
+principle okay
+so so we must have this two description
+
+ align:start position:0%
+so so we must have this two description
+ 
+
+ align:start position:0%
+so so we must have this two description
+and this two PR value for all range of
+
+ align:start position:0%
+and this two PR value for all range of
+ 
+
+ align:start position:0%
+and this two PR value for all range of
+the parameters you can you can be
+
+ align:start position:0%
+the parameters you can you can be
+ 
+
+ align:start position:0%
+the parameters you can you can be
+interested in
+
+ align:start position:0%
+interested in
+ 
+
+ align:start position:0%
+interested in
+okay and so this is a a very surprising
+
+ align:start position:0%
+okay and so this is a a very surprising
+ 
+
+ align:start position:0%
+okay and so this is a a very surprising
+statement this a equal to B but there's
+
+ align:start position:0%
+statement this a equal to B but there's
+ 
+
+ align:start position:0%
+statement this a equal to B but there's
+not much to to do about it because this
+
+ align:start position:0%
+not much to to do about it because this
+ 
+
+ align:start position:0%
+not much to to do about it because this
+is a complicated
+
+ align:start position:0%
+is a complicated
+ 
+
+ align:start position:0%
+is a complicated
+thing and this is also complicated thing
+
+ align:start position:0%
+thing and this is also complicated thing
+ 
+
+ align:start position:0%
+thing and this is also complicated thing
+this is even more complicated doing
+
+ align:start position:0%
+this is even more complicated doing
+ 
+
+ align:start position:0%
+this is even more complicated doing
+stren some curve space time in
+
+ align:start position:0%
+stren some curve space time in
+ 
+
+ align:start position:0%
+stren some curve space time in
+particular say if you consider string is
+
+ align:start position:0%
+particular say if you consider string is
+ 
+
+ align:start position:0%
+particular say if you consider string is
+very small Etc then maybe you can do
+
+ align:start position:0%
+very small Etc then maybe you can do
+ 
+
+ align:start position:0%
+very small Etc then maybe you can do
+something but then it's not that
+
+ align:start position:0%
+something but then it's not that
+ 
+
+ align:start position:0%
+something but then it's not that
+interesting because on both side you do
+
+ align:start position:0%
+interesting because on both side you do
+ 
+
+ align:start position:0%
+interesting because on both side you do
+some peration Theory Etc anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but the remarkable thing which M
+
+ align:start position:0%
+so but the remarkable thing which M
+ 
+
+ align:start position:0%
+so but the remarkable thing which M
+realized in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1997 in
+
+ align:start position:0%
+1997 in
+ 
+
+ align:start position:0%
+1997 in
+1997 is said you can actually take a
+
+ align:start position:0%
+1997 is said you can actually take a
+ 
+
+ align:start position:0%
+1997 is said you can actually take a
+limit of this statement
+
+ align:start position:0%
+limit of this statement
+ 
+
+ align:start position:0%
+limit of this statement
+and when you take a limit of this
+
+ align:start position:0%
+and when you take a limit of this
+ 
+
+ align:start position:0%
+and when you take a limit of this
+statement then the statement become very
+
+ align:start position:0%
+statement then the statement become very
+ 
+
+ align:start position:0%
+statement then the statement become very
+interesting then you can actually do a
+
+ align:start position:0%
+interesting then you can actually do a
+ 
+
+ align:start position:0%
+interesting then you can actually do a
+lot okay and uh and uh and the limit is
+
+ align:start position:0%
+lot okay and uh and uh and the limit is
+ 
+
+ align:start position:0%
+lot okay and uh and uh and the limit is
+the Lage
+
+ align:start position:0%
+the Lage
+ 
+
+ align:start position:0%
+the Lage
+limit so if you consider the Lage
+
+ align:start position:0%
+limit so if you consider the Lage
+ 
+
+ align:start position:0%
+limit so if you consider the Lage
+limit then then you derive what is now
+
+ align:start position:0%
+limit then then you derive what is now
+ 
+
+ align:start position:0%
+limit then then you derive what is now
+called ads C of
+
+ align:start position:0%
+called ads C of
+ 
+
+ align:start position:0%
+called ads C of
+Correspondence we will now explain how
+
+ align:start position:0%
+Correspondence we will now explain how
+ 
+
+ align:start position:0%
+Correspondence we will now explain how
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+that yes it seems like this
+
+ align:start position:0%
+that yes it seems like this
+ 
+
+ align:start position:0%
+that yes it seems like this
+correspondence between A and B only
+
+ align:start position:0%
+correspondence between A and B only
+ 
+
+ align:start position:0%
+correspondence between A and B only
+exists in the low energy limit because
+
+ align:start position:0%
+exists in the low energy limit because
+ 
+
+ align:start position:0%
+exists in the low energy limit because
+here the the the Clos strings traveling
+
+ align:start position:0%
+here the the the Clos strings traveling
+ 
+
+ align:start position:0%
+here the the the Clos strings traveling
+in the b space time that space time is
+
+ align:start position:0%
+in the b space time that space time is
+ 
+
+ align:start position:0%
+in the b space time that space time is
+only the low energy Corrections from the
+
+ align:start position:0%
+only the low energy Corrections from the
+ 
+
+ align:start position:0%
+only the low energy Corrections from the
+deep brain not the higher
+
+ align:start position:0%
+deep brain not the higher
+ 
+
+ align:start position:0%
+deep brain not the higher
+expectation um CU we only solved the low
+
+ align:start position:0%
+expectation um CU we only solved the low
+ 
+
+ align:start position:0%
+expectation um CU we only solved the low
+energy effective
+
+ align:start position:0%
+energy effective
+ 
+
+ align:start position:0%
+energy effective
+Theory no
+
+ align:start position:0%
+Theory no
+ 
+
+ align:start position:0%
+Theory no
+that's this is a good question but
+
+ align:start position:0%
+that's this is a good question but
+ 
+
+ align:start position:0%
+that's this is a good question but
+that's what I was trying to uh say
+
+ align:start position:0%
+that's what I was trying to uh say
+ 
+
+ align:start position:0%
+that's what I was trying to uh say
+earlier so we find this
+
+ align:start position:0%
+earlier so we find this
+ 
+
+ align:start position:0%
+earlier so we find this
+matric by working in this regime
+
+ align:start position:0%
+matric by working in this regime
+ 
+
+ align:start position:0%
+matric by working in this regime
+but now if I want to go away from this
+
+ align:start position:0%
+but now if I want to go away from this
+ 
+
+ align:start position:0%
+but now if I want to go away from this
+regime if I want to go away from this
+
+ align:start position:0%
+regime if I want to go away from this
+ 
+
+ align:start position:0%
+regime if I want to go away from this
+regime then
+
+ align:start position:0%
+regime then
+ 
+
+ align:start position:0%
+regime then
+um if I want to go away from this regime
+
+ align:start position:0%
+um if I want to go away from this regime
+ 
+
+ align:start position:0%
+um if I want to go away from this regime
+then I have to take into account other
+
+ align:start position:0%
+then I have to take into account other
+ 
+
+ align:start position:0%
+then I have to take into account other
+Prime crash EXC and this is a
+
+ align:start position:0%
+Prime crash EXC and this is a
+ 
+
+ align:start position:0%
+Prime crash EXC and this is a
+complicated process but in principle I
+
+ align:start position:0%
+complicated process but in principle I
+ 
+
+ align:start position:0%
+complicated process but in principle I
+can do that yeah in principle I can do
+
+ align:start position:0%
+can do that yeah in principle I can do
+ 
+
+ align:start position:0%
+can do that yeah in principle I can do
+that so so so so that geometry may get
+
+ align:start position:0%
+that so so so so that geometry may get
+ 
+
+ align:start position:0%
+that so so so so that geometry may get
+modified sketch but in PR something in
+
+ align:start position:0%
+modified sketch but in PR something in
+ 
+
+ align:start position:0%
+modified sketch but in PR something in
+principle I can
+
+ align:start position:0%
+principle I can
+ 
+
+ align:start position:0%
+principle I can
+do and
+
+ align:start position:0%
+do and
+ 
+
+ align:start position:0%
+do and
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um so now it turns out if you consider
+
+ align:start position:0%
+um so now it turns out if you consider
+ 
+
+ align:start position:0%
+um so now it turns out if you consider
+low limit of this a equal to B then you
+
+ align:start position:0%
+low limit of this a equal to B then you
+ 
+
+ align:start position:0%
+low limit of this a equal to B then you
+can actually derive a very powerful
+
+ align:start position:0%
+can actually derive a very powerful
+ 
+
+ align:start position:0%
+can actually derive a very powerful
+statement okay is this actually is a ler
+
+ align:start position:0%
+statement okay is this actually is a ler
+ 
+
+ align:start position:0%
+statement okay is this actually is a ler
+limit no this is no this itself is not
+
+ align:start position:0%
+limit no this is no this itself is not
+ 
+
+ align:start position:0%
+limit no this is no this itself is not
+lower limit this is a classical gravity
+
+ align:start position:0%
+lower limit this is a classical gravity
+ 
+
+ align:start position:0%
+lower limit this is a classical gravity
+limit what's the difference H what's the
+
+ align:start position:0%
+limit what's the difference H what's the
+ 
+
+ align:start position:0%
+limit what's the difference H what's the
+difference I will explain that no this
+
+ align:start position:0%
+difference I will explain that no this
+ 
+
+ align:start position:0%
+difference I will explain that no this
+is the classical gravity limit okay and
+
+ align:start position:0%
+is the classical gravity limit okay and
+ 
+
+ align:start position:0%
+is the classical gravity limit okay and
+and at least the Lage limit does not
+
+ align:start position:0%
+and at least the Lage limit does not
+ 
+
+ align:start position:0%
+and at least the Lage limit does not
+involve this
+
+ align:start position:0%
+involve this
+ 
+
+ align:start position:0%
+involve this
+does not invol yeah I will explain what
+
+ align:start position:0%
+does not invol yeah I will explain what
+ 
+
+ align:start position:0%
+does not invol yeah I will explain what
+this No Limit yeah any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions good okay so now let's look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit in
+
+ align:start position:0%
+limit in
+ 
+
+ align:start position:0%
+limit in
+particular here I don't do any
+
+ align:start position:0%
+particular here I don't do any
+ 
+
+ align:start position:0%
+particular here I don't do any
+restriction on the G string so G string
+
+ align:start position:0%
+restriction on the G string so G string
+ 
+
+ align:start position:0%
+restriction on the G string so G string
+can in principle be strong here I don't
+
+ align:start position:0%
+can in principle be strong here I don't
+ 
+
+ align:start position:0%
+can in principle be strong here I don't
+impose any constraint on the string
+
+ align:start position:0%
+impose any constraint on the string
+ 
+
+ align:start position:0%
+impose any constraint on the string
+coupling now I only consider the energy
+
+ align:start position:0%
+coupling now I only consider the energy
+ 
+
+ align:start position:0%
+coupling now I only consider the energy
+okay so the low energy limit
+
+ align:start position:0%
+okay so the low energy limit
+ 
+
+ align:start position:0%
+okay so the low energy limit
+corresponding to I fix the energy e some
+
+ align:start position:0%
+corresponding to I fix the energy e some
+ 
+
+ align:start position:0%
+corresponding to I fix the energy e some
+energy some
+
+ align:start position:0%
+energy some
+ 
+
+ align:start position:0%
+energy some
+process I'm interested in some typical
+
+ align:start position:0%
+process I'm interested in some typical
+ 
+
+ align:start position:0%
+process I'm interested in some typical
+energy I'm interested
+
+ align:start position:0%
+energy I'm interested
+ 
+
+ align:start position:0%
+energy I'm interested
+in then then I want to take the the
+
+ align:start position:0%
+in then then I want to take the the
+ 
+
+ align:start position:0%
+in then then I want to take the the
+alpha Prime go to zero
+
+ align:start position:0%
+alpha Prime go to zero
+ 
+
+ align:start position:0%
+alpha Prime go to zero
+limit okay or or you fix
+
+ align:start position:0%
+limit okay or or you fix
+ 
+
+ align:start position:0%
+limit okay or or you fix
+the equivalent you can fix Alpha Prime
+
+ align:start position:0%
+the equivalent you can fix Alpha Prime
+ 
+
+ align:start position:0%
+the equivalent you can fix Alpha Prime
+then you take equal to zero okay because
+
+ align:start position:0%
+then you take equal to zero okay because
+ 
+
+ align:start position:0%
+then you take equal to zero okay because
+only the dimension is product of the
+
+ align:start position:0%
+only the dimension is product of the
+ 
+
+ align:start position:0%
+only the dimension is product of the
+matters and I can describe either way
+
+ align:start position:0%
+matters and I can describe either way
+ 
+
+ align:start position:0%
+matters and I can describe either way
+okay so so physically uh what is more
+
+ align:start position:0%
+okay so so physically uh what is more
+ 
+
+ align:start position:0%
+okay so so physically uh what is more
+convenient normally mathematically
+
+ align:start position:0%
+convenient normally mathematically
+ 
+
+ align:start position:0%
+convenient normally mathematically
+normally what is more convenient is that
+
+ align:start position:0%
+normally what is more convenient is that
+ 
+
+ align:start position:0%
+normally what is more convenient is that
+we think we fix e and then take Al Prim
+
+ align:start position:0%
+we think we fix e and then take Al Prim
+ 
+
+ align:start position:0%
+we think we fix e and then take Al Prim
+go zero but you can think either way
+
+ align:start position:0%
+go zero but you can think either way
+ 
+
+ align:start position:0%
+go zero but you can think either way
+okay so the low energ limit essentially
+
+ align:start position:0%
+okay so the low energ limit essentially
+ 
+
+ align:start position:0%
+okay so the low energ limit essentially
+just the the limit Alpha Prime Time e s
+
+ align:start position:0%
+just the the limit Alpha Prime Time e s
+ 
+
+ align:start position:0%
+just the the limit Alpha Prime Time e s
+goes zero uh uh uh uh that's the
+
+ align:start position:0%
+goes zero uh uh uh uh that's the
+ 
+
+ align:start position:0%
+goes zero uh uh uh uh that's the
+dimensional statement okay so this is
+
+ align:start position:0%
+dimensional statement okay so this is
+ 
+
+ align:start position:0%
+dimensional statement okay so this is
+the low limit I only consider those
+
+ align:start position:0%
+the low limit I only consider those
+ 
+
+ align:start position:0%
+the low limit I only consider those
+physical process with E that would
+
+ align:start position:0%
+physical process with E that would
+ 
+
+ align:start position:0%
+physical process with E that would
+satisfy this
+
+ align:start position:0%
+satisfy this
+ 
+
+ align:start position:0%
+satisfy this
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good and uh I'm do doing no restriction
+
+ align:start position:0%
+good and uh I'm do doing no restriction
+ 
+
+ align:start position:0%
+good and uh I'm do doing no restriction
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+GS so now let's consider a what is the L
+
+ align:start position:0%
+GS so now let's consider a what is the L
+ 
+
+ align:start position:0%
+GS so now let's consider a what is the L
+limit for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a for a we
+
+ align:start position:0%
+a for a we
+ 
+
+ align:start position:0%
+a for a we
+know so a we have two sectors we have
+
+ align:start position:0%
+know so a we have two sectors we have
+ 
+
+ align:start position:0%
+know so a we have two sectors we have
+open string sector which is leave on the
+
+ align:start position:0%
+open string sector which is leave on the
+ 
+
+ align:start position:0%
+open string sector which is leave on the
+deep brain then we also have closed
+
+ align:start position:0%
+deep brain then we also have closed
+ 
+
+ align:start position:0%
+deep brain then we also have closed
+string sector
+
+ align:start position:0%
+string sector
+ 
+
+ align:start position:0%
+string sector
+okay uh which leave outside the brain
+
+ align:start position:0%
+okay uh which leave outside the brain
+ 
+
+ align:start position:0%
+okay uh which leave outside the brain
+for the open string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sector we just recover so we discussed
+
+ align:start position:0%
+sector we just recover so we discussed
+ 
+
+ align:start position:0%
+sector we just recover so we discussed
+before when in on the Deep bre when you
+
+ align:start position:0%
+before when in on the Deep bre when you
+ 
+
+ align:start position:0%
+before when in on the Deep bre when you
+go to low
+
+ align:start position:0%
+go to low
+ 
+
+ align:start position:0%
+go to low
+energy what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get super yes you just recover y series
+
+ align:start position:0%
+get super yes you just recover y series
+ 
+
+ align:start position:0%
+get super yes you just recover y series
+just recover super M ser and in this
+
+ align:start position:0%
+just recover super M ser and in this
+ 
+
+ align:start position:0%
+just recover super M ser and in this
+case let me give you a special name for
+
+ align:start position:0%
+case let me give you a special name for
+ 
+
+ align:start position:0%
+case let me give you a special name for
+the this three brain it turn out you you
+
+ align:start position:0%
+the this three brain it turn out you you
+ 
+
+ align:start position:0%
+the this three brain it turn out you you
+get the inity for super Yos just a
+
+ align:start position:0%
+get the inity for super Yos just a
+ 
+
+ align:start position:0%
+get the inity for super Yos just a
+specific Super Y Ser in four dimension
+
+ align:start position:0%
+specific Super Y Ser in four dimension
+ 
+
+ align:start position:0%
+specific Super Y Ser in four dimension
+and we skage
+
+ align:start position:0%
+and we skage
+ 
+
+ align:start position:0%
+and we skage
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+un okay because we have consider deep
+
+ align:start position:0%
+un okay because we have consider deep
+ 
+
+ align:start position:0%
+un okay because we have consider deep
+brains and deep
+
+ align:start position:0%
+brains and deep
+ 
+
+ align:start position:0%
+brains and deep
+brains and uh and in particular as we
+
+ align:start position:0%
+brains and uh and in particular as we
+ 
+
+ align:start position:0%
+brains and uh and in particular as we
+said before the yam
+
+ align:start position:0%
+said before the yam
+ 
+
+ align:start position:0%
+said before the yam
+coupling is
+
+ align:start position:0%
+coupling is
+ 
+
+ align:start position:0%
+coupling is
+related to the G
+
+ align:start position:0%
+related to the G
+ 
+
+ align:start position:0%
+related to the G
+GS okay it's propon to the
+
+ align:start position:0%
+GS okay it's propon to the
+ 
+
+ align:start position:0%
+GS okay it's propon to the
+GS and uh so so this re brain give rise
+
+ align:start position:0%
+GS and uh so so this re brain give rise
+ 
+
+ align:start position:0%
+GS and uh so so this re brain give rise
+to a three plus one dimensional fi Ser
+
+ align:start position:0%
+to a three plus one dimensional fi Ser
+ 
+
+ align:start position:0%
+to a three plus one dimensional fi Ser
+in the three plus one dimensional fi
+
+ align:start position:0%
+in the three plus one dimensional fi
+ 
+
+ align:start position:0%
+in the three plus one dimensional fi
+series the Y's comping is dimensionless
+
+ align:start position:0%
+series the Y's comping is dimensionless
+ 
+
+ align:start position:0%
+series the Y's comping is dimensionless
+so there's no other dimensional
+
+ align:start position:0%
+so there's no other dimensional
+ 
+
+ align:start position:0%
+so there's no other dimensional
+parameter here so there's only so so
+
+ align:start position:0%
+parameter here so there's only so so
+ 
+
+ align:start position:0%
+parameter here so there's only so so
+there's only numerical fact be 4 Pi
+
+ align:start position:0%
+there's only numerical fact be 4 Pi
+ 
+
+ align:start position:0%
+there's only numerical fact be 4 Pi
+which you can work out by expit
+
+ align:start position:0%
+which you can work out by expit
+ 
+
+ align:start position:0%
+which you can work out by expit
+calculations so this is key because if
+
+ align:start position:0%
+calculations so this is key because if
+ 
+
+ align:start position:0%
+calculations so this is key because if
+there's a a scale here then the story is
+
+ align:start position:0%
+there's a a scale here then the story is
+ 
+
+ align:start position:0%
+there's a a scale here then the story is
+more complicated because the because you
+
+ align:start position:0%
+more complicated because the because you
+ 
+
+ align:start position:0%
+more complicated because the because you
+have to take Alpha goes zero Etc okay so
+
+ align:start position:0%
+have to take Alpha goes zero Etc okay so
+ 
+
+ align:start position:0%
+have to take Alpha goes zero Etc okay so
+the key is that this is a dimension is
+
+ align:start position:0%
+the key is that this is a dimension is
+ 
+
+ align:start position:0%
+the key is that this is a dimension is
+coupling they have see simple
+
+ align:start position:0%
+coupling they have see simple
+ 
+
+ align:start position:0%
+coupling they have see simple
+relation so in open string when you take
+
+ align:start position:0%
+relation so in open string when you take
+ 
+
+ align:start position:0%
+relation so in open string when you take
+the L limit you just get a y the as some
+
+ align:start position:0%
+the L limit you just get a y the as some
+ 
+
+ align:start position:0%
+the L limit you just get a y the as some
+F at coupling okay which is determined
+
+ align:start position:0%
+F at coupling okay which is determined
+ 
+
+ align:start position:0%
+F at coupling okay which is determined
+by the string coupling
+
+ align:start position:0%
+by the string coupling
+ 
+
+ align:start position:0%
+by the string coupling
+Conant but in this series there's also a
+
+ align:start position:0%
+Conant but in this series there's also a
+ 
+
+ align:start position:0%
+Conant but in this series there's also a
+close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sector in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sector again when you take low limit you
+
+ align:start position:0%
+sector again when you take low limit you
+ 
+
+ align:start position:0%
+sector again when you take low limit you
+get the mless modes you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graviton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Daton Etc but only mes modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but now there's a very important
+
+ align:start position:0%
+okay but now there's a very important
+ 
+
+ align:start position:0%
+okay but now there's a very important
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the coupling between the closed and open
+
+ align:start position:0%
+the coupling between the closed and open
+ 
+
+ align:start position:0%
+the coupling between the closed and open
+string are mediated through
+
+ align:start position:0%
+string are mediated through
+ 
+
+ align:start position:0%
+string are mediated through
+gravitational effect okay so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comping between the mass so only Mass
+
+ align:start position:0%
+comping between the mass so only Mass
+ 
+
+ align:start position:0%
+comping between the mass so only Mass
+mod left so the cing between the
+
+ align:start position:0%
+mod left so the cing between the
+ 
+
+ align:start position:0%
+mod left so the cing between the
+Mist
+
+ align:start position:0%
+Mist
+ 
+
+ align:start position:0%
+Mist
+closed and open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string
+
+ align:start position:0%
+string
+ 
+
+ align:start position:0%
+string
+all closeing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+themselves all closing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+themselves those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interactions just it's always controlled
+
+ align:start position:0%
+interactions just it's always controlled
+ 
+
+ align:start position:0%
+interactions just it's always controlled
+by G Newton this weow because this is
+
+ align:start position:0%
+by G Newton this weow because this is
+ 
+
+ align:start position:0%
+by G Newton this weow because this is
+the low energy limit you have grav contr
+
+ align:start position:0%
+the low energy limit you have grav contr
+ 
+
+ align:start position:0%
+the low energy limit you have grav contr
+by G Newton
+
+ align:start position:0%
+by G Newton
+ 
+
+ align:start position:0%
+by G Newton
+it's gravitational by gravitational
+
+ align:start position:0%
+it's gravitational by gravitational
+ 
+
+ align:start position:0%
+it's gravitational by gravitational
+interactions but now the key the key is
+
+ align:start position:0%
+interactions but now the key the key is
+ 
+
+ align:start position:0%
+interactions but now the key the key is
+that J Newton in contrast to this yam
+
+ align:start position:0%
+that J Newton in contrast to this yam
+ 
+
+ align:start position:0%
+that J Newton in contrast to this yam
+cing which is dimension this G Newton is
+
+ align:start position:0%
+cing which is dimension this G Newton is
+ 
+
+ align:start position:0%
+cing which is dimension this G Newton is
+dimensional and G Newton is proportional
+
+ align:start position:0%
+dimensional and G Newton is proportional
+ 
+
+ align:start position:0%
+dimensional and G Newton is proportional
+to G s² Alpha Prime to the power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 so that means in the low energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit then the dimension is
+
+ align:start position:0%
+limit then the dimension is
+ 
+
+ align:start position:0%
+limit then the dimension is
+cing then the dimension is parameter is
+
+ align:start position:0%
+cing then the dimension is parameter is
+ 
+
+ align:start position:0%
+cing then the dimension is parameter is
+g to the power say 8 because this have
+
+ align:start position:0%
+g to the power say 8 because this have
+ 
+
+ align:start position:0%
+g to the power say 8 because this have
+Dimension eight so this a dimension this
+
+ align:start position:0%
+Dimension eight so this a dimension this
+ 
+
+ align:start position:0%
+Dimension eight so this a dimension this
+will go
+
+ align:start position:0%
+will go
+ 
+
+ align:start position:0%
+will go
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay so that actually tells you in the
+
+ align:start position:0%
+okay so that actually tells you in the
+ 
+
+ align:start position:0%
+okay so that actually tells you in the
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+limit the the the interaction between
+
+ align:start position:0%
+limit the the the interaction between
+ 
+
+ align:start position:0%
+limit the the the interaction between
+open and closing with decouple okay this
+
+ align:start position:0%
+open and closing with decouple okay this
+ 
+
+ align:start position:0%
+open and closing with decouple okay this
+is our familiar
+
+ align:start position:0%
+is our familiar
+ 
+
+ align:start position:0%
+is our familiar
+fact that electron when we talk about
+
+ align:start position:0%
+fact that electron when we talk about
+ 
+
+ align:start position:0%
+fact that electron when we talk about
+electron you don't have to talk about
+
+ align:start position:0%
+electron you don't have to talk about
+ 
+
+ align:start position:0%
+electron you don't have to talk about
+gravity because the energy Sol low the
+
+ align:start position:0%
+gravity because the energy Sol low the
+ 
+
+ align:start position:0%
+gravity because the energy Sol low the
+gravity is so weak okay and the gravity
+
+ align:start position:0%
+gravity is so weak okay and the gravity
+ 
+
+ align:start position:0%
+gravity is so weak okay and the gravity
+only become strong if the energy become
+
+ align:start position:0%
+only become strong if the energy become
+ 
+
+ align:start position:0%
+only become strong if the energy become
+big
+
+ align:start position:0%
+big
+ 
+
+ align:start position:0%
+big
+okay just because of this in 3 + one we
+
+ align:start position:0%
+okay just because of this in 3 + one we
+ 
+
+ align:start position:0%
+okay just because of this in 3 + one we
+just GN * e s but here we in 10
+
+ align:start position:0%
+just GN * e s but here we in 10
+ 
+
+ align:start position:0%
+just GN * e s but here we in 10
+Dimensions e to the^ a doesn't
+
+ align:start position:0%
+Dimensions e to the^ a doesn't
+ 
+
+ align:start position:0%
+Dimensions e to the^ a doesn't
+matter so so now that
+
+ align:start position:0%
+matter so so now that
+ 
+
+ align:start position:0%
+matter so so now that
+means in the equal to zero
+
+ align:start position:0%
+means in the equal to zero
+ 
+
+ align:start position:0%
+means in the equal to zero
+limit what we find is we find the
+
+ align:start position:0%
+limit what we find is we find the
+ 
+
+ align:start position:0%
+limit what we find is we find the
+interacting in for super Y3
+
+ align:start position:0%
+interacting in for super Y3
+ 
+
+ align:start position:0%
+interacting in for super Y3
+plus three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravitons plus other Methodist modes but
+
+ align:start position:0%
+gravitons plus other Methodist modes but
+ 
+
+ align:start position:0%
+gravitons plus other Methodist modes but
+they all become free because the the
+
+ align:start position:0%
+they all become free because the the
+ 
+
+ align:start position:0%
+they all become free because the the
+interaction essentially switch off any
+
+ align:start position:0%
+interaction essentially switch off any
+ 
+
+ align:start position:0%
+interaction essentially switch off any
+interaction this sector this reach off
+
+ align:start position:0%
+interaction this sector this reach off
+ 
+
+ align:start position:0%
+interaction this sector this reach off
+in particular there's no interaction
+
+ align:start position:0%
+in particular there's no interaction
+ 
+
+ align:start position:0%
+in particular there's no interaction
+between these two
+
+ align:start position:0%
+between these two
+ 
+
+ align:start position:0%
+between these two
+sector
+
+ align:start position:0%
+sector
+ 
+
+ align:start position:0%
+sector
+okay so so this what we get on the uh a
+
+ align:start position:0%
+okay so so this what we get on the uh a
+ 
+
+ align:start position:0%
+okay so so this what we get on the uh a
+picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+e e I'm just saying this is the
+
+ align:start position:0%
+e e I'm just saying this is the
+ 
+
+ align:start position:0%
+e e I'm just saying this is the
+dimension is combination of
+
+ align:start position:0%
+dimension is combination of
+ 
+
+ align:start position:0%
+dimension is combination of
+them it's the actual C no the actual C
+
+ align:start position:0%
+them it's the actual C no the actual C
+ 
+
+ align:start position:0%
+them it's the actual C no the actual C
+can be2 can be square root of the contr
+
+ align:start position:0%
+can be2 can be square root of the contr
+ 
+
+ align:start position:0%
+can be2 can be square root of the contr
+by the Jon the key thing is contr by Jon
+
+ align:start position:0%
+by the Jon the key thing is contr by Jon
+ 
+
+ align:start position:0%
+by the Jon the key thing is contr by Jon
+and Jon is a
+
+ align:start position:0%
+and Jon is a
+ 
+
+ align:start position:0%
+and Jon is a
+dimension is a dimensional
+
+ align:start position:0%
+dimension is a dimensional
+ 
+
+ align:start position:0%
+dimension is a dimensional
+parameter that's just the key yes why
+
+ align:start position:0%
+parameter that's just the key yes why
+ 
+
+ align:start position:0%
+parameter that's just the key yes why
+can't they through G
+
+ align:start position:0%
+can't they through G
+ 
+
+ align:start position:0%
+can't they through G
+or no the g b interact with themselves
+
+ align:start position:0%
+or no the g b interact with themselves
+ 
+
+ align:start position:0%
+or no the g b interact with themselves
+the interaction of the guge Bon with
+
+ align:start position:0%
+the interaction of the guge Bon with
+ 
+
+ align:start position:0%
+the interaction of the guge Bon with
+graviton is gravitational have to go
+
+ align:start position:0%
+graviton is gravitational have to go
+ 
+
+ align:start position:0%
+graviton is gravitational have to go
+through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gon the gaug bottom inag with themselves
+
+ align:start position:0%
+gon the gaug bottom inag with themselves
+ 
+
+ align:start position:0%
+gon the gaug bottom inag with themselves
+is captured by
+
+ align:start position:0%
+is captured by
+ 
+
+ align:start position:0%
+is captured by
+here so anything involving gravity
+
+ align:start position:0%
+here so anything involving gravity
+ 
+
+ align:start position:0%
+here so anything involving gravity
+involve dimensional cing then they will
+
+ align:start position:0%
+involve dimensional cing then they will
+ 
+
+ align:start position:0%
+involve dimensional cing then they will
+switch off in the low energy limit just
+
+ align:start position:0%
+switch off in the low energy limit just
+ 
+
+ align:start position:0%
+switch off in the low energy limit just
+like we don't have to worry about the uh
+
+ align:start position:0%
+like we don't have to worry about the uh
+ 
+
+ align:start position:0%
+like we don't have to worry about the uh
+uh uh the gravitational
+
+ align:start position:0%
+uh uh the gravitational
+ 
+
+ align:start position:0%
+uh uh the gravitational
+inaction of electron when we talk about
+
+ align:start position:0%
+inaction of electron when we talk about
+ 
+
+ align:start position:0%
+inaction of electron when we talk about
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+atom no but we know that from qft course
+
+ align:start position:0%
+atom no but we know that from qft course
+ 
+
+ align:start position:0%
+atom no but we know that from qft course
+but how do we see from here that no no
+
+ align:start position:0%
+but how do we see from here that no no
+ 
+
+ align:start position:0%
+but how do we see from here that no no
+no no you just from
+
+ align:start position:0%
+no no you just from
+ 
+
+ align:start position:0%
+no no you just from
+here no no no this is just the
+
+ align:start position:0%
+here no no no this is just the
+ 
+
+ align:start position:0%
+here no no no this is just the
+thing you can calculate the C you can
+
+ align:start position:0%
+thing you can calculate the C you can
+ 
+
+ align:start position:0%
+thing you can calculate the C you can
+calculate you can calculate precisely
+
+ align:start position:0%
+calculate you can calculate precisely
+ 
+
+ align:start position:0%
+calculate you can calculate precisely
+work out the uh the scattering amplitude
+
+ align:start position:0%
+work out the uh the scattering amplitude
+ 
+
+ align:start position:0%
+work out the uh the scattering amplitude
+between the photon and graviton take the
+
+ align:start position:0%
+between the photon and graviton take the
+ 
+
+ align:start position:0%
+between the photon and graviton take the
+L you find that scattering goes to zero
+
+ align:start position:0%
+L you find that scattering goes to zero
+ 
+
+ align:start position:0%
+L you find that scattering goes to zero
+uh you will you can do that calculation
+
+ align:start position:0%
+uh you will you can do that calculation
+ 
+
+ align:start position:0%
+uh you will you can do that calculation
+expc and take the limit but this
+
+ align:start position:0%
+expc and take the limit but this
+ 
+
+ align:start position:0%
+expc and take the limit but this
+argument tells you that you don't have
+
+ align:start position:0%
+argument tells you that you don't have
+ 
+
+ align:start position:0%
+argument tells you that you don't have
+to do the calculation you will always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work okay so now let's look at picture
+
+ align:start position:0%
+work okay so now let's look at picture
+ 
+
+ align:start position:0%
+work okay so now let's look at picture
+B when we take the low limit and now
+
+ align:start position:0%
+B when we take the low limit and now
+ 
+
+ align:start position:0%
+B when we take the low limit and now
+let's go back to this
+
+ align:start position:0%
+let's go back to this
+ 
+
+ align:start position:0%
+let's go back to this
+matric now let's go back to this matric
+
+ align:start position:0%
+matric now let's go back to this matric
+ 
+
+ align:start position:0%
+matric now let's go back to this matric
+so actually it's
+
+ align:start position:0%
+so actually it's
+ 
+
+ align:start position:0%
+so actually it's
+handy so now let's look at picture B the
+
+ align:start position:0%
+handy so now let's look at picture B the
+ 
+
+ align:start position:0%
+handy so now let's look at picture B the
+L limit let's look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+magic so this is a curve space
+
+ align:start position:0%
+magic so this is a curve space
+ 
+
+ align:start position:0%
+magic so this is a curve space
+time so when we take low energ limit we
+
+ align:start position:0%
+time so when we take low energ limit we
+ 
+
+ align:start position:0%
+time so when we take low energ limit we
+have to be
+
+ align:start position:0%
+have to be
+ 
+
+ align:start position:0%
+have to be
+careful because one repeated one
+
+ align:start position:0%
+careful because one repeated one
+ 
+
+ align:start position:0%
+careful because one repeated one
+important thing you always keep in mind
+
+ align:start position:0%
+important thing you always keep in mind
+ 
+
+ align:start position:0%
+important thing you always keep in mind
+when you have a curple space time the
+
+ align:start position:0%
+when you have a curple space time the
+ 
+
+ align:start position:0%
+when you have a curple space time the
+time depend on where you sit you have to
+
+ align:start position:0%
+time depend on where you sit you have to
+ 
+
+ align:start position:0%
+time depend on where you sit you have to
+always specify a reference time because
+
+ align:start position:0%
+always specify a reference time because
+ 
+
+ align:start position:0%
+always specify a reference time because
+time is no longer the absolute thing
+
+ align:start position:0%
+time is no longer the absolute thing
+ 
+
+ align:start position:0%
+time is no longer the absolute thing
+okay because the the local time EXA you
+
+ align:start position:0%
+okay because the the local time EXA you
+ 
+
+ align:start position:0%
+okay because the the local time EXA you
+have to specify your time frame
+
+ align:start position:0%
+have to specify your time frame
+ 
+
+ align:start position:0%
+have to specify your time frame
+okay and so so we have to ask what is
+
+ align:start position:0%
+okay and so so we have to ask what is
+ 
+
+ align:start position:0%
+okay and so so we have to ask what is
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e in picture a translate into this
+
+ align:start position:0%
+e in picture a translate into this
+ 
+
+ align:start position:0%
+e in picture a translate into this
+picture in picture a everything is in
+
+ align:start position:0%
+picture in picture a everything is in
+ 
+
+ align:start position:0%
+picture in picture a everything is in
+movi space
+
+ align:start position:0%
+movi space
+ 
+
+ align:start position:0%
+movi space
+time and that e is essentially
+
+ align:start position:0%
+time and that e is essentially
+ 
+
+ align:start position:0%
+time and that e is essentially
+e of the for the for the m case time at
+
+ align:start position:0%
+e of the for the for the m case time at
+ 
+
+ align:start position:0%
+e of the for the for the m case time at
+Infinity in the picture B okay so in
+
+ align:start position:0%
+Infinity in the picture B okay so in
+ 
+
+ align:start position:0%
+Infinity in the picture B okay so in
+other words the
+
+ align:start position:0%
+other words the
+ 
+
+ align:start position:0%
+other words the
+e in other was so here yeah let me just
+
+ align:start position:0%
+e in other was so here yeah let me just
+ 
+
+ align:start position:0%
+e in other was so here yeah let me just
+say the curve space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time must be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+careful to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specify what energy we interested in
+
+ align:start position:0%
+specify what energy we interested in
+ 
+
+ align:start position:0%
+specify what energy we interested in
+what energy we talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the energy depend on the your
+
+ align:start position:0%
+okay so the energy depend on the your
+ 
+
+ align:start position:0%
+okay so the energy depend on the your
+your choice of time or depend on your
+
+ align:start position:0%
+your choice of time or depend on your
+ 
+
+ align:start position:0%
+your choice of time or depend on your
+Observer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so but we have to but in order
+
+ align:start position:0%
+okay so so but we have to but in order
+ 
+
+ align:start position:0%
+okay so so but we have to but in order
+to compare a with B we have to translate
+
+ align:start position:0%
+to compare a with B we have to translate
+ 
+
+ align:start position:0%
+to compare a with B we have to translate
+what is e in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is translate into B is
+
+ align:start position:0%
+this is translate into B is
+ 
+
+ align:start position:0%
+this is translate into B is
+defined respect
+
+ align:start position:0%
+defined respect
+ 
+
+ align:start position:0%
+defined respect
+to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T this T there okay uh in other words is
+
+ align:start position:0%
+T this T there okay uh in other words is
+ 
+
+ align:start position:0%
+T this T there okay uh in other words is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+time at I equal to
+
+ align:start position:0%
+time at I equal to
+ 
+
+ align:start position:0%
+time at I equal to
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+okay so that energy scale is defined
+
+ align:start position:0%
+okay so that energy scale is defined
+ 
+
+ align:start position:0%
+okay so that energy scale is defined
+with that to to that specific uh a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time but now when we talk about the
+
+ align:start position:0%
+time but now when we talk about the
+ 
+
+ align:start position:0%
+time but now when we talk about the
+physics happening in this space time for
+
+ align:start position:0%
+physics happening in this space time for
+ 
+
+ align:start position:0%
+physics happening in this space time for
+example we talking about string series
+
+ align:start position:0%
+example we talking about string series
+ 
+
+ align:start position:0%
+example we talking about string series
+string excitations or the mass of the
+
+ align:start position:0%
+string excitations or the mass of the
+ 
+
+ align:start position:0%
+string excitations or the mass of the
+string or excit you have to refer to the
+
+ align:start position:0%
+string or excit you have to refer to the
+ 
+
+ align:start position:0%
+string or excit you have to refer to the
+local proper time at whatever Place uh
+
+ align:start position:0%
+local proper time at whatever Place uh
+ 
+
+ align:start position:0%
+local proper time at whatever Place uh
+other uh at whatever Place uh you are
+
+ align:start position:0%
+other uh at whatever Place uh you are
+ 
+
+ align:start position:0%
+other uh at whatever Place uh you are
+talking about uh uh your physical
+
+ align:start position:0%
+talking about uh uh your physical
+ 
+
+ align:start position:0%
+talking about uh uh your physical
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+okay so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means oh actually today we are
+
+ align:start position:0%
+means oh actually today we are
+ 
+
+ align:start position:0%
+means oh actually today we are
+going um to
+
+ align:start position:0%
+going um to
+ 
+
+ align:start position:0%
+going um to
+6:30 oh yeah right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so suppose you are at some location r
+
+ align:start position:0%
+um so suppose you are at some location r
+ 
+
+ align:start position:0%
+um so suppose you are at some location r
+then the local prop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time which have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qu local prop time the to then it's
+
+ align:start position:0%
+qu local prop time the to then it's
+ 
+
+ align:start position:0%
+qu local prop time the to then it's
+related to the time at Infinity by this
+
+ align:start position:0%
+related to the time at Infinity by this
+ 
+
+ align:start position:0%
+related to the time at Infinity by this
+Factor okay by this Factor just this the
+
+ align:start position:0%
+Factor okay by this Factor just this the
+ 
+
+ align:start position:0%
+Factor okay by this Factor just this the
+local Observer equ call this your D
+
+ align:start position:0%
+local Observer equ call this your D
+ 
+
+ align:start position:0%
+local Observer equ call this your D
+Square so uh so so they relate to this
+
+ align:start position:0%
+Square so uh so so they relate to this
+ 
+
+ align:start position:0%
+Square so uh so so they relate to this
+by by this
+
+ align:start position:0%
+by by this
+ 
+
+ align:start position:0%
+by by this
+Factor so now you can reasing convert
+
+ align:start position:0%
+Factor so now you can reasing convert
+ 
+
+ align:start position:0%
+Factor so now you can reasing convert
+then the local proper energy is related
+
+ align:start position:0%
+then the local proper energy is related
+ 
+
+ align:start position:0%
+then the local proper energy is related
+to the energy we are talking about here
+
+ align:start position:0%
+to the energy we are talking about here
+ 
+
+ align:start position:0%
+to the energy we are talking about here
+by h to^
+
+ align:start position:0%
+by h to^
+ 
+
+ align:start position:0%
+by h to^
+one4 e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so now tonight it's very
+
+ align:start position:0%
+okay okay so now tonight it's very
+ 
+
+ align:start position:0%
+okay okay so now tonight it's very
+important when we take the L limit we
+
+ align:start position:0%
+important when we take the L limit we
+ 
+
+ align:start position:0%
+important when we take the L limit we
+take this e
+
+ align:start position:0%
+take this e
+ 
+
+ align:start position:0%
+take this e
+small but due to the gravitational red
+
+ align:start position:0%
+small but due to the gravitational red
+ 
+
+ align:start position:0%
+small but due to the gravitational red
+shift effect this e does not have to be
+
+ align:start position:0%
+shift effect this e does not have to be
+ 
+
+ align:start position:0%
+shift effect this e does not have to be
+small okay and so this is the thing will
+
+ align:start position:0%
+small okay and so this is the thing will
+ 
+
+ align:start position:0%
+small okay and so this is the thing will
+be important
+
+ align:start position:0%
+be important
+ 
+
+ align:start position:0%
+be important
+here so
+
+ align:start position:0%
+here so
+ 
+
+ align:start position:0%
+here so
+when when R is much much greater than R
+
+ align:start position:0%
+when when R is much much greater than R
+ 
+
+ align:start position:0%
+when when R is much much greater than R
+so when we are sitting around
+
+ align:start position:0%
+so when we are sitting around
+ 
+
+ align:start position:0%
+so when we are sitting around
+here when we are sitting around
+
+ align:start position:0%
+here when we are sitting around
+ 
+
+ align:start position:0%
+here when we are sitting around
+here then H is
+
+ align:start position:0%
+here then H is
+ 
+
+ align:start position:0%
+here then H is
+one okay then then the limit e s here
+
+ align:start position:0%
+one okay then then the limit e s here
+ 
+
+ align:start position:0%
+one okay then then the limit e s here
+Alpha Prime goes
+
+ align:start position:0%
+Alpha Prime goes
+ 
+
+ align:start position:0%
+Alpha Prime goes
+zero really just tells you that all
+
+ align:start position:0%
+zero really just tells you that all
+ 
+
+ align:start position:0%
+zero really just tells you that all
+massive close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+couple
+
+ align:start position:0%
+couple
+ 
+
+ align:start position:0%
+couple
+okay in
+
+ align:start position:0%
+okay in
+ 
+
+ align:start position:0%
+okay in
+particular in particular the the
+
+ align:start position:0%
+particular in particular the the
+ 
+
+ align:start position:0%
+particular in particular the the
+inaction more closing themselves by the
+
+ align:start position:0%
+inaction more closing themselves by the
+ 
+
+ align:start position:0%
+inaction more closing themselves by the
+same argument they also become weaker
+
+ align:start position:0%
+same argument they also become weaker
+ 
+
+ align:start position:0%
+same argument they also become weaker
+and weaker when you go to low limit so
+
+ align:start position:0%
+and weaker when you go to low limit so
+ 
+
+ align:start position:0%
+and weaker when you go to low limit so
+essentially again they become free
+
+ align:start position:0%
+essentially again they become free
+ 
+
+ align:start position:0%
+essentially again they become free
+gravitons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but now let's look
+
+ align:start position:0%
+okay but now let's look
+ 
+
+ align:start position:0%
+okay but now let's look
+at but now let's look at the other
+
+ align:start position:0%
+at but now let's look at the other
+ 
+
+ align:start position:0%
+at but now let's look at the other
+regime and R around here
+
+ align:start position:0%
+regime and R around here
+ 
+
+ align:start position:0%
+regime and R around here
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+now so this is for that so for but now
+
+ align:start position:0%
+now so this is for that so for but now
+ 
+
+ align:start position:0%
+now so this is for that so for but now
+for let's consider R smaller than r
+
+ align:start position:0%
+for let's consider R smaller than r
+ 
+
+ align:start position:0%
+for let's consider R smaller than r
+capital r and then in this regime we go
+
+ align:start position:0%
+capital r and then in this regime we go
+ 
+
+ align:start position:0%
+capital r and then in this regime we go
+to this ad S5 * S5 then H become R to
+
+ align:start position:0%
+to this ad S5 * S5 then H become R to
+ 
+
+ align:start position:0%
+to this ad S5 * S5 then H become R to
+the^ 4
+
+ align:start position:0%
+the^ 4
+ 
+
+ align:start position:0%
+the^ 4
+R4 and now this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement and the E Square Alpha Prime
+
+ align:start position:0%
+statement and the E Square Alpha Prime
+ 
+
+ align:start position:0%
+statement and the E Square Alpha Prime
+go to zero translate now you have red
+
+ align:start position:0%
+go to zero translate now you have red
+ 
+
+ align:start position:0%
+go to zero translate now you have red
+shift Factor eal square if I translate
+
+ align:start position:0%
+shift Factor eal square if I translate
+ 
+
+ align:start position:0%
+shift Factor eal square if I translate
+inal the local energy scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in particular now let's remember
+
+ align:start position:0%
+okay in particular now let's remember
+ 
+
+ align:start position:0%
+okay in particular now let's remember
+this R square is R4 is given by that so
+
+ align:start position:0%
+this R square is R4 is given by that so
+ 
+
+ align:start position:0%
+this R square is R4 is given by that so
+this can be
+
+ align:start position:0%
+this can be
+ 
+
+ align:start position:0%
+this can be
+written e t Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r² 4 Pi
+
+ align:start position:0%
+r² 4 Pi
+ 
+
+ align:start position:0%
+r² 4 Pi
+GSN goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so now important thing
+
+ align:start position:0%
+zero so now important thing
+ 
+
+ align:start position:0%
+zero so now important thing
+happened important thing just happened
+
+ align:start position:0%
+happened important thing just happened
+ 
+
+ align:start position:0%
+happened important thing just happened
+then you find this Alpha Prime actually
+
+ align:start position:0%
+then you find this Alpha Prime actually
+ 
+
+ align:start position:0%
+then you find this Alpha Prime actually
+cancel with each other Alpha Prime here
+
+ align:start position:0%
+cancel with each other Alpha Prime here
+ 
+
+ align:start position:0%
+cancel with each other Alpha Prime here
+and Alpha Prime there they cancel each
+
+ align:start position:0%
+and Alpha Prime there they cancel each
+ 
+
+ align:start position:0%
+and Alpha Prime there they cancel each
+other and here there's nothing off Prime
+
+ align:start position:0%
+other and here there's nothing off Prime
+ 
+
+ align:start position:0%
+other and here there's nothing off Prime
+left okay so when you take this limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you take this limit and uh it's so
+
+ align:start position:0%
+when you take this limit and uh it's so
+ 
+
+ align:start position:0%
+when you take this limit and uh it's so
+then this become this quantity goes to
+
+ align:start position:0%
+then this become this quantity goes to
+ 
+
+ align:start position:0%
+then this become this quantity goes to
+zero and now
+
+ align:start position:0%
+zero and now
+ 
+
+ align:start position:0%
+zero and now
+eow can actually be
+
+ align:start position:0%
+eow can actually be
+ 
+
+ align:start position:0%
+eow can actually be
+anything as far as R sufficiently small
+
+ align:start position:0%
+anything as far as R sufficiently small
+ 
+
+ align:start position:0%
+anything as far as R sufficiently small
+okay so that means for any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eal you can even have huge energy noal
+
+ align:start position:0%
+eal you can even have huge energy noal
+ 
+
+ align:start position:0%
+eal you can even have huge energy noal
+proper energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can satisfy the L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit if those modes leave at R very
+
+ align:start position:0%
+limit if those modes leave at R very
+ 
+
+ align:start position:0%
+limit if those modes leave at R very
+close to
+
+ align:start position:0%
+close to
+ 
+
+ align:start position:0%
+close to
+zero means that they they leave on this
+
+ align:start position:0%
+zero means that they they leave on this
+ 
+
+ align:start position:0%
+zero means that they they leave on this
+throat deep
+
+ align:start position:0%
+throat deep
+ 
+
+ align:start position:0%
+throat deep
+enough so this is very
+
+ align:start position:0%
+enough so this is very
+ 
+
+ align:start position:0%
+enough so this is very
+simple physically this is very
+
+ align:start position:0%
+simple physically this is very
+ 
+
+ align:start position:0%
+simple physically this is very
+simple because of this curved space
+
+ align:start position:0%
+simple because of this curved space
+ 
+
+ align:start position:0%
+simple because of this curved space
+effect because of H this curve space
+
+ align:start position:0%
+effect because of H this curve space
+ 
+
+ align:start position:0%
+effect because of H this curve space
+effect there's a huge amount of red
+
+ align:start position:0%
+effect there's a huge amount of red
+ 
+
+ align:start position:0%
+effect there's a huge amount of red
+shift between here and there between the
+
+ align:start position:0%
+shift between here and there between the
+ 
+
+ align:start position:0%
+shift between here and there between the
+local prob time here and there very big
+
+ align:start position:0%
+local prob time here and there very big
+ 
+
+ align:start position:0%
+local prob time here and there very big
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+here build from here can become very
+
+ align:start position:0%
+here build from here can become very
+ 
+
+ align:start position:0%
+here build from here can become very
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+small in particular you go deeper into
+
+ align:start position:0%
+small in particular you go deeper into
+ 
+
+ align:start position:0%
+small in particular you go deeper into
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+throat the red shift factor is bigger so
+
+ align:start position:0%
+throat the red shift factor is bigger so
+ 
+
+ align:start position:0%
+throat the red shift factor is bigger so
+no matter how large the
+
+ align:start position:0%
+no matter how large the
+ 
+
+ align:start position:0%
+no matter how large the
+energy if you go deeper enough deep
+
+ align:start position:0%
+energy if you go deeper enough deep
+ 
+
+ align:start position:0%
+energy if you go deeper enough deep
+enough we always appear within a Lage
+
+ align:start position:0%
+enough we always appear within a Lage
+ 
+
+ align:start position:0%
+enough we always appear within a Lage
+limit here
+
+ align:start position:0%
+limit here
+ 
+
+ align:start position:0%
+limit here
+okay okay so that means when you sit
+
+ align:start position:0%
+okay okay so that means when you sit
+ 
+
+ align:start position:0%
+okay okay so that means when you sit
+deep
+
+ align:start position:0%
+deep
+ 
+
+ align:start position:0%
+deep
+enough then actually anything is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a including a massive stream mode
+
+ align:start position:0%
+a including a massive stream mode
+ 
+
+ align:start position:0%
+a including a massive stream mode
+okay including massive stream mode so
+
+ align:start position:0%
+okay including massive stream mode so
+ 
+
+ align:start position:0%
+okay including massive stream mode so
+now we remember when you go I go to Z
+
+ align:start position:0%
+now we remember when you go I go to Z
+ 
+
+ align:start position:0%
+now we remember when you go I go to Z
+essentially you get this ads 5 time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S5 so in I equal to Z we just get this
+
+ align:start position:0%
+S5 so in I equal to Z we just get this
+ 
+
+ align:start position:0%
+S5 so in I equal to Z we just get this
+geometry which is a is five times so
+
+ align:start position:0%
+geometry which is a is five times so
+ 
+
+ align:start position:0%
+geometry which is a is five times so
+it's five so now what we find is that in
+
+ align:start position:0%
+it's five so now what we find is that in
+ 
+
+ align:start position:0%
+it's five so now what we find is that in
+the ler m in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B we get three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravitons and I to
+
+ align:start position:0%
+gravitons and I to
+ 
+
+ align:start position:0%
+gravitons and I to
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+plus full string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theory in is five times is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay F so so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and again the two SE is decouple
+
+ align:start position:0%
+yeah and again the two SE is decouple
+ 
+
+ align:start position:0%
+yeah and again the two SE is decouple
+because when you take the L limit then
+
+ align:start position:0%
+because when you take the L limit then
+ 
+
+ align:start position:0%
+because when you take the L limit then
+those then those string mode have to
+
+ align:start position:0%
+those then those string mode have to
+ 
+
+ align:start position:0%
+those then those string mode have to
+leave very far
+
+ align:start position:0%
+leave very far
+ 
+
+ align:start position:0%
+leave very far
+down in this throat and then they have
+
+ align:start position:0%
+down in this throat and then they have
+ 
+
+ align:start position:0%
+down in this throat and then they have
+low overlap with the graviton and leave
+
+ align:start position:0%
+low overlap with the graviton and leave
+ 
+
+ align:start position:0%
+low overlap with the graviton and leave
+at Infinity okay and have over with gra
+
+ align:start position:0%
+at Infinity okay and have over with gra
+ 
+
+ align:start position:0%
+at Infinity okay and have over with gra
+yes so I'm confused about the way that
+
+ align:start position:0%
+yes so I'm confused about the way that
+ 
+
+ align:start position:0%
+yes so I'm confused about the way that
+you wrot that so you say three so
+
+ align:start position:0%
+you wrot that so you say three so
+ 
+
+ align:start position:0%
+you wrot that so you say three so
+there's three gravitons that are
+
+ align:start position:0%
+there's three gravitons that are
+ 
+
+ align:start position:0%
+there's three gravitons that are
+Infinity but also full string theory in
+
+ align:start position:0%
+Infinity but also full string theory in
+ 
+
+ align:start position:0%
+Infinity but also full string theory in
+the last but doesn't full String Theory
+
+ align:start position:0%
+the last but doesn't full String Theory
+ 
+
+ align:start position:0%
+the last but doesn't full String Theory
+include gravitons no no no yeah yeah
+
+ align:start position:0%
+include gravitons no no no yeah yeah
+ 
+
+ align:start position:0%
+include gravitons no no no yeah yeah
+this is the uh uh this is a full there's
+
+ align:start position:0%
+this is the uh uh this is a full there's
+ 
+
+ align:start position:0%
+this is the uh uh this is a full there's
+some different graviton in ads 5 *
+
+ align:start position:0%
+some different graviton in ads 5 *
+ 
+
+ align:start position:0%
+some different graviton in ads 5 *
+S5 I'm say full stren Ser in ads 5 * S5
+
+ align:start position:0%
+S5 I'm say full stren Ser in ads 5 * S5
+ 
+
+ align:start position:0%
+S5 I'm say full stren Ser in ads 5 * S5
+those those are not fre minkovski space
+
+ align:start position:0%
+those those are not fre minkovski space
+ 
+
+ align:start position:0%
+those those are not fre minkovski space
+graviton this is minkovski space
+
+ align:start position:0%
+graviton this is minkovski space
+ 
+
+ align:start position:0%
+graviton this is minkovski space
+graviton so this is minkovsky space
+
+ align:start position:0%
+graviton so this is minkovsky space
+ 
+
+ align:start position:0%
+graviton so this is minkovsky space
+gra and things which live
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here the nature are very
+
+ align:start position:0%
+here the nature are very
+ 
+
+ align:start position:0%
+here the nature are very
+different yeah okay yes full String
+
+ align:start position:0%
+different yeah okay yes full String
+ 
+
+ align:start position:0%
+different yeah okay yes full String
+Theory only for closed strings only
+
+ align:start position:0%
+Theory only for closed strings only
+ 
+
+ align:start position:0%
+Theory only for closed strings only
+closed string there's no open string in
+
+ align:start position:0%
+closed string there's no open string in
+ 
+
+ align:start position:0%
+closed string there's no open string in
+this picture there only closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry no no there's no AR that's what I
+
+ align:start position:0%
+sorry no no there's no AR that's what I
+ 
+
+ align:start position:0%
+sorry no no there's no AR that's what I
+just explained those free gra leave here
+
+ align:start position:0%
+just explained those free gra leave here
+ 
+
+ align:start position:0%
+just explained those free gra leave here
+and string leave infinite down the
+
+ align:start position:0%
+and string leave infinite down the
+ 
+
+ align:start position:0%
+and string leave infinite down the
+throat throat in the low limit they they
+
+ align:start position:0%
+throat throat in the low limit they they
+ 
+
+ align:start position:0%
+throat throat in the low limit they they
+infinite they INF they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially as not proper distance you
+
+ align:start position:0%
+essentially as not proper distance you
+ 
+
+ align:start position:0%
+essentially as not proper distance you
+want to separate them depend on how low
+
+ align:start position:0%
+want to separate them depend on how low
+ 
+
+ align:start position:0%
+want to separate them depend on how low
+energy you want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go yeah I'm just saying when you take
+
+ align:start position:0%
+go yeah I'm just saying when you take
+ 
+
+ align:start position:0%
+go yeah I'm just saying when you take
+the low
+
+ align:start position:0%
+the low
+ 
+
+ align:start position:0%
+the low
+limit when you take the lower limit then
+
+ align:start position:0%
+limit when you take the lower limit then
+ 
+
+ align:start position:0%
+limit when you take the lower limit then
+the separation separation then become
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinite no they have nothing to do with
+
+ align:start position:0%
+infinite no they have nothing to do with
+ 
+
+ align:start position:0%
+infinite no they have nothing to do with
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+other geographically they live one is in
+
+ align:start position:0%
+other geographically they live one is in
+ 
+
+ align:start position:0%
+other geographically they live one is in
+the this side of the Galaxy the other is
+
+ align:start position:0%
+the this side of the Galaxy the other is
+ 
+
+ align:start position:0%
+the this side of the Galaxy the other is
+living on the other side the C they have
+
+ align:start position:0%
+living on the other side the C they have
+ 
+
+ align:start position:0%
+living on the other side the C they have
+low the wave function have low overlap
+
+ align:start position:0%
+low the wave function have low overlap
+ 
+
+ align:start position:0%
+low the wave function have low overlap
+with each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+something yeah I'm just saying when you
+
+ align:start position:0%
+something yeah I'm just saying when you
+ 
+
+ align:start position:0%
+something yeah I'm just saying when you
+take the L
+
+ align:start position:0%
+take the L
+ 
+
+ align:start position:0%
+take the L
+limit then the only mode which can
+
+ align:start position:0%
+limit then the only mode which can
+ 
+
+ align:start position:0%
+limit then the only mode which can
+survive other than the masses mode which
+
+ align:start position:0%
+survive other than the masses mode which
+ 
+
+ align:start position:0%
+survive other than the masses mode which
+live around here just fin energy mode
+
+ align:start position:0%
+live around here just fin energy mode
+ 
+
+ align:start position:0%
+live around here just fin energy mode
+they cannot leave in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place yeah do the string theory on ad I
+
+ align:start position:0%
+place yeah do the string theory on ad I
+ 
+
+ align:start position:0%
+place yeah do the string theory on ad I
+see the flock as well yeah yeah yeah
+
+ align:start position:0%
+see the flock as well yeah yeah yeah
+ 
+
+ align:start position:0%
+see the flock as well yeah yeah yeah
+yeah flock yeah yeah with the flux yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then this two sectors should de
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+couple so now we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derived so from this a equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B then we take the L energy
+
+ align:start position:0%
+B then we take the L energy
+ 
+
+ align:start position:0%
+B then we take the L energy
+limit so here we we have in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graviton and here you have tpe Tob
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string S5 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S5 plus three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gra
+
+ align:start position:0%
+gra
+ 
+
+ align:start position:0%
+gra
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the free gravit part is the
+
+ align:start position:0%
+and the free gravit part is the
+ 
+
+ align:start position:0%
+and the free gravit part is the
+same then you conclude and they they're
+
+ align:start position:0%
+same then you conclude and they they're
+ 
+
+ align:start position:0%
+same then you conclude and they they're
+just free and the inac in part of both
+
+ align:start position:0%
+just free and the inac in part of both
+ 
+
+ align:start position:0%
+just free and the inac in part of both
+sides then then you just equate them you
+
+ align:start position:0%
+sides then then you just equate them you
+ 
+
+ align:start position:0%
+sides then then you just equate them you
+find force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M with un
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n then is equal to type to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string this five just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F so this was a surprising statement
+
+ align:start position:0%
+F so this was a surprising statement
+ 
+
+ align:start position:0%
+F so this was a surprising statement
+saying a equal to
+
+ align:start position:0%
+saying a equal to
+ 
+
+ align:start position:0%
+saying a equal to
+B But A and B are both say complicated
+
+ align:start position:0%
+B But A and B are both say complicated
+ 
+
+ align:start position:0%
+B But A and B are both say complicated
+object both are complicated object but
+
+ align:start position:0%
+object both are complicated object but
+ 
+
+ align:start position:0%
+object both are complicated object but
+now when we take the L range limit and
+
+ align:start position:0%
+now when we take the L range limit and
+ 
+
+ align:start position:0%
+now when we take the L range limit and
+then one side then you reach something
+
+ align:start position:0%
+then one side then you reach something
+ 
+
+ align:start position:0%
+then one side then you reach something
+very surprising because on this side
+
+ align:start position:0%
+very surprising because on this side
+ 
+
+ align:start position:0%
+very surprising because on this side
+there's no
+
+ align:start position:0%
+there's no
+ 
+
+ align:start position:0%
+there's no
+gravity on this side there's no gravity
+
+ align:start position:0%
+gravity on this side there's no gravity
+ 
+
+ align:start position:0%
+gravity on this side there's no gravity
+but this side is a full String Theory so
+
+ align:start position:0%
+but this side is a full String Theory so
+ 
+
+ align:start position:0%
+but this side is a full String Theory so
+now you equate some field Theory with a
+
+ align:start position:0%
+now you equate some field Theory with a
+ 
+
+ align:start position:0%
+now you equate some field Theory with a
+full String
+
+ align:start position:0%
+full String
+ 
+
+ align:start position:0%
+full String
+Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yes so the the super Yang Mills is
+
+ align:start position:0%
+okay yes so the the super Yang Mills is
+ 
+
+ align:start position:0%
+okay yes so the the super Yang Mills is
+living just on the D3 brain yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions regarding
+
+ align:start position:0%
+any questions regarding
+ 
+
+ align:start position:0%
+any questions regarding
+this so for example when
+
+ align:start position:0%
+this so for example when
+ 
+
+ align:start position:0%
+this so for example when
+Ral R is
+
+ align:start position:0%
+Ral R is
+ 
+
+ align:start position:0%
+Ral R is
+also yeah this yeah yeah but that's
+
+ align:start position:0%
+also yeah this yeah yeah but that's
+ 
+
+ align:start position:0%
+also yeah this yeah yeah but that's
+always F at proper distance away they
+
+ align:start position:0%
+always F at proper distance away they
+ 
+
+ align:start position:0%
+always F at proper distance away they
+always file at the proper distance so
+
+ align:start position:0%
+always file at the proper distance so
+ 
+
+ align:start position:0%
+always file at the proper distance so
+the key is that when you talk about the
+
+ align:start position:0%
+the key is that when you talk about the
+ 
+
+ align:start position:0%
+the key is that when you talk about the
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+mode uh uh uh you can anything you talk
+
+ align:start position:0%
+mode uh uh uh you can anything you talk
+ 
+
+ align:start position:0%
+mode uh uh uh you can anything you talk
+about is f distance way we taking a
+
+ align:start position:0%
+about is f distance way we taking a
+ 
+
+ align:start position:0%
+about is f distance way we taking a
+limit here this is going to Infinity
+
+ align:start position:0%
+limit here this is going to Infinity
+ 
+
+ align:start position:0%
+limit here this is going to Infinity
+you're leaving infinite down the throat
+
+ align:start position:0%
+you're leaving infinite down the throat
+ 
+
+ align:start position:0%
+you're leaving infinite down the throat
+anything fin is free H yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything when you talk about the finite
+
+ align:start position:0%
+anything when you talk about the finite
+ 
+
+ align:start position:0%
+anything when you talk about the finite
+energy then the story is always
+
+ align:start position:0%
+energy then the story is always
+ 
+
+ align:start position:0%
+energy then the story is always
+complicated and uh then all this
+
+ align:start position:0%
+complicated and uh then all this
+ 
+
+ align:start position:0%
+complicated and uh then all this
+geometry will matter and and the thing
+
+ align:start position:0%
+geometry will matter and and the thing
+ 
+
+ align:start position:0%
+geometry will matter and and the thing
+only become simple you really take the E
+
+ align:start position:0%
+only become simple you really take the E
+ 
+
+ align:start position:0%
+only become simple you really take the E
+go to zero limit and it's the same thing
+
+ align:start position:0%
+go to zero limit and it's the same thing
+ 
+
+ align:start position:0%
+go to zero limit and it's the same thing
+here same thing in this picture when we
+
+ align:start position:0%
+here same thing in this picture when we
+ 
+
+ align:start position:0%
+here same thing in this picture when we
+say you go to the in for Super Y
+
+ align:start position:0%
+say you go to the in for Super Y
+ 
+
+ align:start position:0%
+say you go to the in for Super Y
+you always have to take that limit e
+
+ align:start position:0%
+you always have to take that limit e
+ 
+
+ align:start position:0%
+you always have to take that limit e
+goes to zero limit then you completely
+
+ align:start position:0%
+goes to zero limit then you completely
+ 
+
+ align:start position:0%
+goes to zero limit then you completely
+decouple the other things because any
+
+ align:start position:0%
+decouple the other things because any
+ 
+
+ align:start position:0%
+decouple the other things because any
+tiny tiny long z e there's always some
+
+ align:start position:0%
+tiny tiny long z e there's always some
+ 
+
+ align:start position:0%
+tiny tiny long z e there's always some
+gravity left so you really really have
+
+ align:start position:0%
+gravity left so you really really have
+ 
+
+ align:start position:0%
+gravity left so you really really have
+to take that energy go to zero limit and
+
+ align:start position:0%
+to take that energy go to zero limit and
+ 
+
+ align:start position:0%
+to take that energy go to zero limit and
+then you rescale the energy to be finite
+
+ align:start position:0%
+then you rescale the energy to be finite
+ 
+
+ align:start position:0%
+then you rescale the energy to be finite
+you understand what I mean you always
+
+ align:start position:0%
+you understand what I mean you always
+ 
+
+ align:start position:0%
+you understand what I mean you always
+have to take that singular limit it's
+
+ align:start position:0%
+have to take that singular limit it's
+ 
+
+ align:start position:0%
+have to take that singular limit it's
+just like when you take the in the C you
+
+ align:start position:0%
+just like when you take the in the C you
+ 
+
+ align:start position:0%
+just like when you take the in the C you
+have to take the infinite volume limit
+
+ align:start position:0%
+have to take the infinite volume limit
+ 
+
+ align:start position:0%
+have to take the infinite volume limit
+and then Things become simple and and
+
+ align:start position:0%
+and then Things become simple and and
+ 
+
+ align:start position:0%
+and then Things become simple and and
+here it's the same thing
+
+ align:start position:0%
+here it's the same thing
+ 
+
+ align:start position:0%
+here it's the same thing
+yeah whenever you have some finite
+
+ align:start position:0%
+yeah whenever you have some finite
+ 
+
+ align:start position:0%
+yeah whenever you have some finite
+energy they always some call some
+
+ align:start position:0%
+energy they always some call some
+ 
+
+ align:start position:0%
+energy they always some call some
+component between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them good so do you want to have a break
+
+ align:start position:0%
+them good so do you want to have a break
+ 
+
+ align:start position:0%
+them good so do you want to have a break
+this is like a FIS guas that some how
+
+ align:start position:0%
+this is like a FIS guas that some how
+ 
+
+ align:start position:0%
+this is like a FIS guas that some how
+these two must be the same
+
+ align:start position:0%
+these two must be the same
+ 
+
+ align:start position:0%
+these two must be the same
+okay these two must be the same so so
+
+ align:start position:0%
+okay these two must be the same so so
+ 
+
+ align:start position:0%
+okay these two must be the same so so
+this is a surprising statement because
+
+ align:start position:0%
+this is a surprising statement because
+ 
+
+ align:start position:0%
+this is a surprising statement because
+the uh because on the one side it's a
+
+ align:start position:0%
+the uh because on the one side it's a
+ 
+
+ align:start position:0%
+the uh because on the one side it's a
+field Theory and and the other side is
+
+ align:start position:0%
+field Theory and and the other side is
+ 
+
+ align:start position:0%
+field Theory and and the other side is
+full gravity
+
+ align:start position:0%
+full gravity
+ 
+
+ align:start position:0%
+full gravity
+Ser so so you said that in principle you
+
+ align:start position:0%
+Ser so so you said that in principle you
+ 
+
+ align:start position:0%
+Ser so so you said that in principle you
+can generalize this distribution for any
+
+ align:start position:0%
+can generalize this distribution for any
+ 
+
+ align:start position:0%
+can generalize this distribution for any
+matric in the full Str the for any reg
+
+ align:start position:0%
+matric in the full Str the for any reg
+ 
+
+ align:start position:0%
+matric in the full Str the for any reg
+yeah but in that case maybe you will not
+
+ align:start position:0%
+yeah but in that case maybe you will not
+ 
+
+ align:start position:0%
+yeah but in that case maybe you will not
+probably not get Geometry as same as
+
+ align:start position:0%
+probably not get Geometry as same as
+ 
+
+ align:start position:0%
+probably not get Geometry as same as
+adh5 oh yeah that's a very good question
+
+ align:start position:0%
+adh5 oh yeah that's a very good question
+ 
+
+ align:start position:0%
+adh5 oh yeah that's a very good question
+uh uh that's a very good question it it
+
+ align:start position:0%
+uh uh that's a very good question it it
+ 
+
+ align:start position:0%
+uh uh that's a very good question it it
+turns out in indeed logically you you
+
+ align:start position:0%
+turns out in indeed logically you you
+ 
+
+ align:start position:0%
+turns out in indeed logically you you
+may not but the uh uh but actually S5 *
+
+ align:start position:0%
+may not but the uh uh but actually S5 *
+ 
+
+ align:start position:0%
+may not but the uh uh but actually S5 *
+S5 is a highly I as I will explain it's
+
+ align:start position:0%
+S5 is a highly I as I will explain it's
+ 
+
+ align:start position:0%
+S5 is a highly I as I will explain it's
+a very highly symmetric space it turns
+
+ align:start position:0%
+a very highly symmetric space it turns
+ 
+
+ align:start position:0%
+a very highly symmetric space it turns
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+actually it is exact stre the at least
+
+ align:start position:0%
+actually it is exact stre the at least
+ 
+
+ align:start position:0%
+actually it is exact stre the at least
+we believe is exact stren series
+
+ align:start position:0%
+we believe is exact stren series
+ 
+
+ align:start position:0%
+we believe is exact stren series
+geometry and when you include all those
+
+ align:start position:0%
+geometry and when you include all those
+ 
+
+ align:start position:0%
+geometry and when you include all those
+corre this will not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change yes so so with this in mind that
+
+ align:start position:0%
+change yes so so with this in mind that
+ 
+
+ align:start position:0%
+change yes so so with this in mind that
+means that people don't they only know
+
+ align:start position:0%
+means that people don't they only know
+ 
+
+ align:start position:0%
+means that people don't they only know
+this juristically yeah so there's no
+
+ align:start position:0%
+this juristically yeah so there's no
+ 
+
+ align:start position:0%
+this juristically yeah so there's no
+actual like proof of this besides the
+
+ align:start position:0%
+actual like proof of this besides the
+ 
+
+ align:start position:0%
+actual like proof of this besides the
+fact that everyone believes it works
+
+ align:start position:0%
+fact that everyone believes it works
+ 
+
+ align:start position:0%
+fact that everyone believes it works
+yeah depend on what you the level what
+
+ align:start position:0%
+yeah depend on what you the level what
+ 
+
+ align:start position:0%
+yeah depend on what you the level what
+do you mean it
+
+ align:start position:0%
+do you mean it
+ 
+
+ align:start position:0%
+do you mean it
+works so uh so the physicist way it
+
+ align:start position:0%
+works so uh so the physicist way it
+ 
+
+ align:start position:0%
+works so uh so the physicist way it
+works is that one works two works yeah
+
+ align:start position:0%
+works is that one works two works yeah
+ 
+
+ align:start position:0%
+works is that one works two works yeah
+inity one works in two Works in three
+
+ align:start position:0%
+inity one works in two Works in three
+ 
+
+ align:start position:0%
+inity one works in two Works in three
+Works in four works then we say it works
+
+ align:start position:0%
+Works in four works then we say it works
+ 
+
+ align:start position:0%
+Works in four works then we say it works
+and uh and this have way past that so
+
+ align:start position:0%
+and uh and this have way past that so
+ 
+
+ align:start position:0%
+and uh and this have way past that so
+maybe this worked to until the 10,000
+
+ align:start position:0%
+maybe this worked to until the 10,000
+ 
+
+ align:start position:0%
+maybe this worked to until the 10,000
+something like that but it's not the
+
+ align:start position:0%
+something like that but it's not the
+ 
+
+ align:start position:0%
+something like that but it's not the
+proof sure yeah but worked until the
+
+ align:start position:0%
+proof sure yeah but worked until the
+ 
+
+ align:start position:0%
+proof sure yeah but worked until the
+10,000 something like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay good so uh so now let's talk
+
+ align:start position:0%
+yeah okay good so uh so now let's talk
+ 
+
+ align:start position:0%
+yeah okay good so uh so now let's talk
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+Duality so this is normally called adsf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Duality
+
+ align:start position:0%
+Duality
+ 
+
+ align:start position:0%
+Duality
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+um so so to understand this D let's
+
+ align:start position:0%
+um so so to understand this D let's
+ 
+
+ align:start position:0%
+um so so to understand this D let's
+first uh understand the object in this
+
+ align:start position:0%
+first uh understand the object in this
+ 
+
+ align:start position:0%
+first uh understand the object in this
+relation okay so let me just say a
+
+ align:start position:0%
+relation okay so let me just say a
+ 
+
+ align:start position:0%
+relation okay so let me just say a
+little bit about the object in this
+
+ align:start position:0%
+little bit about the object in this
+ 
+
+ align:start position:0%
+little bit about the object in this
+relation first let me say a little bit
+
+ align:start position:0%
+relation first let me say a little bit
+ 
+
+ align:start position:0%
+relation first let me say a little bit
+about anti space since the um uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um since that may not be something
+
+ align:start position:0%
+um since that may not be something
+ 
+
+ align:start position:0%
+um since that may not be something
+something you have worked
+
+ align:start position:0%
+something you have worked
+ 
+
+ align:start position:0%
+something you have worked
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+um okay so so one way to write the
+
+ align:start position:0%
+um okay so so one way to write the
+ 
+
+ align:start position:0%
+um okay so so one way to write the
+Matrix is this Matrix so this is ads5
+
+ align:start position:0%
+Matrix is this Matrix so this is ads5
+ 
+
+ align:start position:0%
+Matrix is this Matrix so this is ads5
+so this is ADS 5 okay so this is ADS 5
+
+ align:start position:0%
+so this is ADS 5 okay so this is ADS 5
+ 
+
+ align:start position:0%
+so this is ADS 5 okay so this is ADS 5
+magic uh uh so so the yeah you can
+
+ align:start position:0%
+magic uh uh so so the yeah you can
+ 
+
+ align:start position:0%
+magic uh uh so so the yeah you can
+actually write it as ads yeah let me
+
+ align:start position:0%
+actually write it as ads yeah let me
+ 
+
+ align:start position:0%
+actually write it as ads yeah let me
+just copy it down so you can generalize
+
+ align:start position:0%
+just copy it down so you can generalize
+ 
+
+ align:start position:0%
+just copy it down so you can generalize
+to any number of
+
+ align:start position:0%
+to any number of
+ 
+
+ align:start position:0%
+to any number of
+Dimensions you can generate number any
+
+ align:start position:0%
+Dimensions you can generate number any
+ 
+
+ align:start position:0%
+Dimensions you can generate number any
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+Dimensions if we make if you make this
+
+ align:start position:0%
+Dimensions if we make if you make this
+ 
+
+ align:start position:0%
+Dimensions if we make if you make this
+part into a d dimensional minkovsky
+
+ align:start position:0%
+part into a d dimensional minkovsky
+ 
+
+ align:start position:0%
+part into a d dimensional minkovsky
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then then this would be the matric of
+
+ align:start position:0%
+then then this would be the matric of
+ 
+
+ align:start position:0%
+then then this would be the matric of
+ads say d+1 Dimension so this is a d d
+
+ align:start position:0%
+ads say d+1 Dimension so this is a d d
+ 
+
+ align:start position:0%
+ads say d+1 Dimension so this is a d d
+plus y Dimension movi then you have a
+
+ align:start position:0%
+plus y Dimension movi then you have a
+ 
+
+ align:start position:0%
+plus y Dimension movi then you have a
+lot R Direction so uh so let me call
+
+ align:start position:0%
+lot R Direction so uh so let me call
+ 
+
+ align:start position:0%
+lot R Direction so uh so let me call
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+my my uh so now let me relabel this to
+
+ align:start position:0%
+my my uh so now let me relabel this to
+ 
+
+ align:start position:0%
+my my uh so now let me relabel this to
+be one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so R can be as a curvature radius of
+
+ align:start position:0%
+so so R can be as a curvature radius of
+ 
+
+ align:start position:0%
+so so R can be as a curvature radius of
+this space time so this I is a constant
+
+ align:start position:0%
+this space time so this I is a constant
+ 
+
+ align:start position:0%
+this space time so this I is a constant
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this this radius R goes from zero to
+
+ align:start position:0%
+this this radius R goes from zero to
+ 
+
+ align:start position:0%
+this this radius R goes from zero to
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+okay R goes Zero from Infinity so
+
+ align:start position:0%
+okay R goes Zero from Infinity so
+ 
+
+ align:start position:0%
+okay R goes Zero from Infinity so
+roughly a geometric picture here is that
+
+ align:start position:0%
+roughly a geometric picture here is that
+ 
+
+ align:start position:0%
+roughly a geometric picture here is that
+so you can see that you have half
+
+ align:start position:0%
+so you can see that you have half
+ 
+
+ align:start position:0%
+so you can see that you have half
+space okay you have a half space r from
+
+ align:start position:0%
+space okay you have a half space r from
+ 
+
+ align:start position:0%
+space okay you have a half space r from
+zero to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity and uh and at each value of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r at each value of R there's movi space
+
+ align:start position:0%
+r at each value of R there's movi space
+ 
+
+ align:start position:0%
+r at each value of R there's movi space
+time there D dimensional movy space time
+
+ align:start position:0%
+time there D dimensional movy space time
+ 
+
+ align:start position:0%
+time there D dimensional movy space time
+so if you fix R then you just get some D
+
+ align:start position:0%
+so if you fix R then you just get some D
+ 
+
+ align:start position:0%
+so if you fix R then you just get some D
+dimensional movi space time and uh and
+
+ align:start position:0%
+dimensional movi space time and uh and
+ 
+
+ align:start position:0%
+dimensional movi space time and uh and
+with some prefactor to define the scale
+
+ align:start position:0%
+with some prefactor to define the scale
+ 
+
+ align:start position:0%
+with some prefactor to define the scale
+of the movi space time okay so so just
+
+ align:start position:0%
+of the movi space time okay so so just
+ 
+
+ align:start position:0%
+of the movi space time okay so so just
+like this it's a it's a you have half
+
+ align:start position:0%
+like this it's a it's a you have half
+ 
+
+ align:start position:0%
+like this it's a it's a you have half
+line are from zero to Infinity then at
+
+ align:start position:0%
+line are from zero to Infinity then at
+ 
+
+ align:start position:0%
+line are from zero to Infinity then at
+each point of this half line exfoliated
+
+ align:start position:0%
+each point of this half line exfoliated
+ 
+
+ align:start position:0%
+each point of this half line exfoliated
+by the dimensional movi space time so
+
+ align:start position:0%
+by the dimensional movi space time so
+ 
+
+ align:start position:0%
+by the dimensional movi space time so
+that essentially what this does so the
+
+ align:start position:0%
+that essentially what this does so the
+ 
+
+ align:start position:0%
+that essentially what this does so the
+key thing is that the movi time is what
+
+ align:start position:0%
+key thing is that the movi time is what
+ 
+
+ align:start position:0%
+key thing is that the movi time is what
+we normally call warped is that the the
+
+ align:start position:0%
+we normally call warped is that the the
+ 
+
+ align:start position:0%
+we normally call warped is that the the
+the the scale factor of this minkovski
+
+ align:start position:0%
+the the scale factor of this minkovski
+ 
+
+ align:start position:0%
+the the scale factor of this minkovski
+space time depend on where you
+
+ align:start position:0%
+space time depend on where you
+ 
+
+ align:start position:0%
+space time depend on where you
+sit in the in the in the radar Direction
+
+ align:start position:0%
+sit in the in the in the radar Direction
+ 
+
+ align:start position:0%
+sit in the in the in the radar Direction
+okay so this R we l call radar Direction
+
+ align:start position:0%
+okay so this R we l call radar Direction
+ 
+
+ align:start position:0%
+okay so this R we l call radar Direction
+it depend on where you see in the radio
+
+ align:start position:0%
+it depend on where you see in the radio
+ 
+
+ align:start position:0%
+it depend on where you see in the radio
+Direction so when you R go to Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at R go to
+
+ align:start position:0%
+at R go to
+ 
+
+ align:start position:0%
+at R go to
+Infinity the scale size become infinite
+
+ align:start position:0%
+Infinity the scale size become infinite
+ 
+
+ align:start position:0%
+Infinity the scale size become infinite
+so this would normally call it to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary so this we call to be the
+
+ align:start position:0%
+boundary so this we call to be the
+ 
+
+ align:start position:0%
+boundary so this we call to be the
+boundary say say IAL Infinity we call to
+
+ align:start position:0%
+boundary say say IAL Infinity we call to
+ 
+
+ align:start position:0%
+boundary say say IAL Infinity we call to
+be the
+
+ align:start position:0%
+be the
+ 
+
+ align:start position:0%
+be the
+boundary of the space
+
+ align:start position:0%
+boundary of the space
+ 
+
+ align:start position:0%
+boundary of the space
+time so this is a similar to say when we
+
+ align:start position:0%
+time so this is a similar to say when we
+ 
+
+ align:start position:0%
+time so this is a similar to say when we
+say when we write them in uh you create
+
+ align:start position:0%
+say when we write them in uh you create
+ 
+
+ align:start position:0%
+say when we write them in uh you create
+a matric in this
+
+ align:start position:0%
+a matric in this
+ 
+
+ align:start position:0%
+a matric in this
+form when R goes to Infinity the sphere
+
+ align:start position:0%
+form when R goes to Infinity the sphere
+ 
+
+ align:start position:0%
+form when R goes to Infinity the sphere
+size become infinite and then this is
+
+ align:start position:0%
+size become infinite and then this is
+ 
+
+ align:start position:0%
+size become infinite and then this is
+essentially the SpaceTime boundary
+
+ align:start position:0%
+essentially the SpaceTime boundary
+ 
+
+ align:start position:0%
+essentially the SpaceTime boundary
+roughly and so this can be similarly
+
+ align:start position:0%
+roughly and so this can be similarly
+ 
+
+ align:start position:0%
+roughly and so this can be similarly
+understand that way
+
+ align:start position:0%
+understand that way
+ 
+
+ align:start position:0%
+understand that way
+okay so this ads is the space
+
+ align:start position:0%
+okay so this ads is the space
+ 
+
+ align:start position:0%
+okay so this ads is the space
+time ads is a space
+
+ align:start position:0%
+time ads is a space
+ 
+
+ align:start position:0%
+time ads is a space
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+of constant curvature constant negative
+
+ align:start position:0%
+of constant curvature constant negative
+ 
+
+ align:start position:0%
+of constant curvature constant negative
+curvature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in fact this is the most symmetric
+
+ align:start position:0%
+okay in fact this is the most symmetric
+ 
+
+ align:start position:0%
+okay in fact this is the most symmetric
+SpaceTime of lective constant
+
+ align:start position:0%
+SpaceTime of lective constant
+ 
+
+ align:start position:0%
+SpaceTime of lective constant
+curvature so so uh you can easily
+
+ align:start position:0%
+curvature so so uh you can easily
+ 
+
+ align:start position:0%
+curvature so so uh you can easily
+check can easily check this satisfi the
+
+ align:start position:0%
+check can easily check this satisfi the
+ 
+
+ align:start position:0%
+check can easily check this satisfi the
+Einstein
+
+ align:start position:0%
+Einstein
+ 
+
+ align:start position:0%
+Einstein
+equation with the lative c modu constant
+
+ align:start position:0%
+equation with the lative c modu constant
+ 
+
+ align:start position:0%
+equation with the lative c modu constant
+so so you can easily check you satisfy
+
+ align:start position:0%
+so so you can easily check you satisfy
+ 
+
+ align:start position:0%
+so so you can easily check you satisfy
+the Einstein equation so now because now
+
+ align:start position:0%
+the Einstein equation so now because now
+ 
+
+ align:start position:0%
+the Einstein equation so now because now
+using this R you load this radius this
+
+ align:start position:0%
+using this R you load this radius this
+ 
+
+ align:start position:0%
+using this R you load this radius this
+curvature radius so now I will call my
+
+ align:start position:0%
+curvature radius so now I will call my
+ 
+
+ align:start position:0%
+curvature radius so now I will call my
+curvature tensor always using the script
+
+ align:start position:0%
+curvature tensor always using the script
+ 
+
+ align:start position:0%
+curvature tensor always using the script
+now now so also MN now refers to all
+
+ align:start position:0%
+now now so also MN now refers to all
+ 
+
+ align:start position:0%
+now now so also MN now refers to all
+directions in this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ads so you can easily check and satisfy
+
+ align:start position:0%
+ads so you can easily check and satisfy
+ 
+
+ align:start position:0%
+ads so you can easily check and satisfy
+this Einstein equation with some Co modu
+
+ align:start position:0%
+this Einstein equation with some Co modu
+ 
+
+ align:start position:0%
+this Einstein equation with some Co modu
+constant and uh you you can just compute
+
+ align:start position:0%
+constant and uh you you can just compute
+ 
+
+ align:start position:0%
+constant and uh you you can just compute
+the uh it's easy to compute the curv of
+
+ align:start position:0%
+the uh it's easy to compute the curv of
+ 
+
+ align:start position:0%
+the uh it's easy to compute the curv of
+this guy so let me just write down the
+
+ align:start position:0%
+this guy so let me just write down the
+ 
+
+ align:start position:0%
+this guy so let me just write down the
+answer so yeah yeah first you can uh
+
+ align:start position:0%
+answer so yeah yeah first you can uh
+ 
+
+ align:start position:0%
+answer so yeah yeah first you can uh
+yeah you can compute the curvature of
+
+ align:start position:0%
+yeah you can compute the curvature of
+ 
+
+ align:start position:0%
+yeah you can compute the curvature of
+this guy you can just find the answer so
+
+ align:start position:0%
+this guy you can just find the answer so
+ 
+
+ align:start position:0%
+this guy you can just find the answer so
+you find
+
+ align:start position:0%
+you find
+ 
+
+ align:start position:0%
+you find
+the the curvature the rich scaler is
+
+ align:start position:0%
+the the curvature the rich scaler is
+ 
+
+ align:start position:0%
+the the curvature the rich scaler is
+given by minus D * D + 1 R
+
+ align:start position:0%
+given by minus D * D + 1 R
+ 
+
+ align:start position:0%
+given by minus D * D + 1 R
+square okay so so this is a rich scaler
+
+ align:start position:0%
+square okay so so this is a rich scaler
+ 
+
+ align:start position:0%
+square okay so so this is a rich scaler
+this R is the same as this is
+
+ align:start position:0%
+this R is the same as this is
+ 
+
+ align:start position:0%
+this R is the same as this is
+r and similarly you find the co modu
+
+ align:start position:0%
+r and similarly you find the co modu
+ 
+
+ align:start position:0%
+r and similarly you find the co modu
+constant then you can find here from is
+
+ align:start position:0%
+constant then you can find here from is
+ 
+
+ align:start position:0%
+constant then you can find here from is
+given by minus
+
+ align:start position:0%
+given by minus
+ 
+
+ align:start position:0%
+given by minus
+one2 D D minus one /
+
+ align:start position:0%
+one2 D D minus one /
+ 
+
+ align:start position:0%
+one2 D D minus one /
+r² sorry here should be minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and I I said that this is the most
+
+ align:start position:0%
+okay and I I said that this is the most
+ 
+
+ align:start position:0%
+okay and I I said that this is the most
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+homogeneous negative curvature space
+
+ align:start position:0%
+homogeneous negative curvature space
+ 
+
+ align:start position:0%
+homogeneous negative curvature space
+time so this is reflect it in that
+
+ align:start position:0%
+time so this is reflect it in that
+ 
+
+ align:start position:0%
+time so this is reflect it in that
+actually you can
+
+ align:start position:0%
+actually you can
+ 
+
+ align:start position:0%
+actually you can
+write the REM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tensor the REM tensor of this space
+
+ align:start position:0%
+tensor the REM tensor of this space
+ 
+
+ align:start position:0%
+tensor the REM tensor of this space
+time purely in terms of this metric
+
+ align:start position:0%
+time purely in terms of this metric
+ 
+
+ align:start position:0%
+time purely in terms of this metric
+itself without using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is essentially definition
+
+ align:start position:0%
+okay so this is essentially definition
+ 
+
+ align:start position:0%
+okay so this is essentially definition
+of the uh the the most
+
+ align:start position:0%
+of the uh the the most
+ 
+
+ align:start position:0%
+of the uh the the most
+symmetric retive curvature space time is
+
+ align:start position:0%
+symmetric retive curvature space time is
+ 
+
+ align:start position:0%
+symmetric retive curvature space time is
+that the remman tensor can be written
+
+ align:start position:0%
+that the remman tensor can be written
+ 
+
+ align:start position:0%
+that the remman tensor can be written
+solely in terms of metric itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these are just some fact of this
+
+ align:start position:0%
+okay so these are just some fact of this
+ 
+
+ align:start position:0%
+okay so these are just some fact of this
+uh uh um uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space so so we often we use a lot of
+
+ align:start position:0%
+space so so we often we use a lot of
+ 
+
+ align:start position:0%
+space so so we often we use a lot of
+coordinates sometimes it's often
+
+ align:start position:0%
+coordinates sometimes it's often
+ 
+
+ align:start position:0%
+coordinates sometimes it's often
+convenient to
+
+ align:start position:0%
+convenient to
+ 
+
+ align:start position:0%
+convenient to
+use instead of using this
+
+ align:start position:0%
+use instead of using this
+ 
+
+ align:start position:0%
+use instead of using this
+R of using this R we will introduce
+
+ align:start position:0%
+R of using this R we will introduce
+ 
+
+ align:start position:0%
+R of using this R we will introduce
+another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinate is introduce a z equal to r²
+
+ align:start position:0%
+coordinate is introduce a z equal to r²
+ 
+
+ align:start position:0%
+coordinate is introduce a z equal to r²
+divided by capital r squ divided by
+
+ align:start position:0%
+divided by capital r squ divided by
+ 
+
+ align:start position:0%
+divided by capital r squ divided by
+small R essentially just the 1 /
+
+ align:start position:0%
+small R essentially just the 1 /
+ 
+
+ align:start position:0%
+small R essentially just the 1 /
+R and because the capital r goes from
+
+ align:start position:0%
+R and because the capital r goes from
+ 
+
+ align:start position:0%
+R and because the capital r goes from
+zero to
+
+ align:start position:0%
+zero to
+ 
+
+ align:start position:0%
+zero to
+Infinity then small Z also going from
+
+ align:start position:0%
+Infinity then small Z also going from
+ 
+
+ align:start position:0%
+Infinity then small Z also going from
+zero to
+
+ align:start position:0%
+zero to
+ 
+
+ align:start position:0%
+zero to
+Infinity but now the
+
+ align:start position:0%
+Infinity but now the
+ 
+
+ align:start position:0%
+Infinity but now the
+boundary but now is equal to zero is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary rather than the equal to
+
+ align:start position:0%
+boundary rather than the equal to
+ 
+
+ align:start position:0%
+boundary rather than the equal to
+infinity and then the
+
+ align:start position:0%
+infinity and then the
+ 
+
+ align:start position:0%
+infinity and then the
+Matrix can be written in a slightly
+
+ align:start position:0%
+Matrix can be written in a slightly
+ 
+
+ align:start position:0%
+Matrix can be written in a slightly
+different way
+
+ align:start position:0%
+different way
+ 
+
+ align:start position:0%
+different way
+in terms of this Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates you can read in this form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the you can see the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easyd so so again here you just change
+
+ align:start position:0%
+easyd so so again here you just change
+ 
+
+ align:start position:0%
+easyd so so again here you just change
+the label R by Z and Z equal to Z is the
+
+ align:start position:0%
+the label R by Z and Z equal to Z is the
+ 
+
+ align:start position:0%
+the label R by Z and Z equal to Z is the
+boundary and and going to Interior
+
+ align:start position:0%
+boundary and and going to Interior
+ 
+
+ align:start position:0%
+boundary and and going to Interior
+correspond to increase Z so Z
+
+ align:start position:0%
+correspond to increase Z so Z
+ 
+
+ align:start position:0%
+correspond to increase Z so Z
+corresponding to in the different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+okay previously in order to this
+
+ align:start position:0%
+okay previously in order to this
+ 
+
+ align:start position:0%
+okay previously in order to this
+HS we already assume the small R
+
+ align:start position:0%
+HS we already assume the small R
+ 
+
+ align:start position:0%
+HS we already assume the small R
+approach to Z yeah but here it
+
+ align:start position:0%
+approach to Z yeah but here it
+ 
+
+ align:start position:0%
+approach to Z yeah but here it
+can yeah that's a very good question uh
+
+ align:start position:0%
+can yeah that's a very good question uh
+ 
+
+ align:start position:0%
+can yeah that's a very good question uh
+I'm waiting for for for some of you to
+
+ align:start position:0%
+I'm waiting for for for some of you to
+ 
+
+ align:start position:0%
+I'm waiting for for for some of you to
+ask so so this is the
+
+ align:start position:0%
+ask so so this is the
+ 
+
+ align:start position:0%
+ask so so this is the
+uh so this is the uh uh the fysic is
+
+ align:start position:0%
+uh so this is the uh uh the fysic is
+ 
+
+ align:start position:0%
+uh so this is the uh uh the fysic is
+Magic which we um uh uh described yeah
+
+ align:start position:0%
+Magic which we um uh uh described yeah
+ 
+
+ align:start position:0%
+Magic which we um uh uh described yeah
+this is the fysic is magic so
+
+ align:start position:0%
+this is the fysic is magic so
+ 
+
+ align:start position:0%
+this is the fysic is magic so
+um yeah let me just say this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so you have infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ro so we uh going to learn you should
+
+ align:start position:0%
+Ro so we uh going to learn you should
+ 
+
+ align:start position:0%
+Ro so we uh going to learn you should
+just go very much down in the throat
+
+ align:start position:0%
+just go very much down in the throat
+ 
+
+ align:start position:0%
+just go very much down in the throat
+okay but once you go down very once you
+
+ align:start position:0%
+okay but once you go down very once you
+ 
+
+ align:start position:0%
+okay but once you go down very once you
+decouple those descrip Freedom then you
+
+ align:start position:0%
+decouple those descrip Freedom then you
+ 
+
+ align:start position:0%
+decouple those descrip Freedom then you
+can just rescale your energy scale uh
+
+ align:start position:0%
+can just rescale your energy scale uh
+ 
+
+ align:start position:0%
+can just rescale your energy scale uh
+whatever you want uh whatever you want
+
+ align:start position:0%
+whatever you want uh whatever you want
+ 
+
+ align:start position:0%
+whatever you want uh whatever you want
+you go to go to find energy EXC and as
+
+ align:start position:0%
+you go to go to find energy EXC and as
+ 
+
+ align:start position:0%
+you go to go to find energy EXC and as
+far as you in the ads
+
+ align:start position:0%
+far as you in the ads
+ 
+
+ align:start position:0%
+far as you in the ads
+5 as far yeah once you decou those
+
+ align:start position:0%
+5 as far yeah once you decou those
+ 
+
+ align:start position:0%
+5 as far yeah once you decou those
+things then you are living in
+
+ align:start position:0%
+things then you are living in
+ 
+
+ align:start position:0%
+things then you are living in
+ads then you are living in the ads and
+
+ align:start position:0%
+ads then you are living in the ads and
+ 
+
+ align:start position:0%
+ads then you are living in the ads and
+then you can talk about the energy scale
+
+ align:start position:0%
+then you can talk about the energy scale
+ 
+
+ align:start position:0%
+then you can talk about the energy scale
+or or any radius as you want just become
+
+ align:start position:0%
+or or any radius as you want just become
+ 
+
+ align:start position:0%
+or or any radius as you want just become
+relative to
+
+ align:start position:0%
+relative to
+ 
+
+ align:start position:0%
+relative to
+itself you see what I mean is that kind
+
+ align:start position:0%
+itself you see what I mean is that kind
+ 
+
+ align:start position:0%
+itself you see what I mean is that kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+normalization no no this is not
+
+ align:start position:0%
+normalization no no this is not
+ 
+
+ align:start position:0%
+normalization no no this is not
+normalization this is this is just say
+
+ align:start position:0%
+normalization this is this is just say
+ 
+
+ align:start position:0%
+normalization this is this is just say
+when you normally when we say when we
+
+ align:start position:0%
+when you normally when we say when we
+ 
+
+ align:start position:0%
+when you normally when we say when we
+take the Lage
+
+ align:start position:0%
+take the Lage
+ 
+
+ align:start position:0%
+take the Lage
+limit the reason we take the Lage limit
+
+ align:start position:0%
+limit the reason we take the Lage limit
+ 
+
+ align:start position:0%
+limit the reason we take the Lage limit
+is we want to decou those massive modes
+
+ align:start position:0%
+is we want to decou those massive modes
+ 
+
+ align:start position:0%
+is we want to decou those massive modes
+and once we decover those massive modes
+
+ align:start position:0%
+and once we decover those massive modes
+ 
+
+ align:start position:0%
+and once we decover those massive modes
+and then we consider the finite energy
+
+ align:start position:0%
+and then we consider the finite energy
+ 
+
+ align:start position:0%
+and then we consider the finite energy
+and and when fight energy because we
+
+ align:start position:0%
+and and when fight energy because we
+ 
+
+ align:start position:0%
+and and when fight energy because we
+consider fight energy relative to
+
+ align:start position:0%
+consider fight energy relative to
+ 
+
+ align:start position:0%
+consider fight energy relative to
+L we still consider a fight range of
+
+ align:start position:0%
+L we still consider a fight range of
+ 
+
+ align:start position:0%
+L we still consider a fight range of
+energy it's the same thing as
+
+ align:start position:0%
+energy it's the same thing as
+ 
+
+ align:start position:0%
+energy it's the same thing as
+that is this clear to everybody this is
+
+ align:start position:0%
+that is this clear to everybody this is
+ 
+
+ align:start position:0%
+that is this clear to everybody this is
+a very important
+
+ align:start position:0%
+a very important
+ 
+
+ align:start position:0%
+a very important
+Point
+
+ align:start position:0%
+Point
+ 
+
+ align:start position:0%
+Point
+yeah good
+
+ align:start position:0%
+yeah good
+ 
+
+ align:start position:0%
+yeah good
+yeah the
+
+ align:start position:0%
+yeah the
+ 
+
+ align:start position:0%
+yeah the
+question is that previously in order to
+
+ align:start position:0%
+question is that previously in order to
+ 
+
+ align:start position:0%
+question is that previously in order to
+decouple those high energy modes when we
+
+ align:start position:0%
+decouple those high energy modes when we
+ 
+
+ align:start position:0%
+decouple those high energy modes when we
+take a lower limit we have to take I
+
+ align:start position:0%
+take a lower limit we have to take I
+ 
+
+ align:start position:0%
+take a lower limit we have to take I
+equal to zero so why here we worri about
+
+ align:start position:0%
+equal to zero so why here we worri about
+ 
+
+ align:start position:0%
+equal to zero so why here we worri about
+I go to Infinity IAL Infinity here okay
+
+ align:start position:0%
+I go to Infinity IAL Infinity here okay
+ 
+
+ align:start position:0%
+I go to Infinity IAL Infinity here okay
+why are we worry about IAL Infinity
+
+ align:start position:0%
+why are we worry about IAL Infinity
+ 
+
+ align:start position:0%
+why are we worry about IAL Infinity
+seems like this is uh going outside our
+
+ align:start position:0%
+seems like this is uh going outside our
+ 
+
+ align:start position:0%
+seems like this is uh going outside our
+previous regime uh uh but the answer is
+
+ align:start position:0%
+previous regime uh uh but the answer is
+ 
+
+ align:start position:0%
+previous regime uh uh but the answer is
+that once we decouple those uh high
+
+ align:start position:0%
+that once we decouple those uh high
+ 
+
+ align:start position:0%
+that once we decouple those uh high
+energy mode then you can just extend the
+
+ align:start position:0%
+energy mode then you can just extend the
+ 
+
+ align:start position:0%
+energy mode then you can just extend the
+energy whatever to to whatever energy
+
+ align:start position:0%
+energy whatever to to whatever energy
+ 
+
+ align:start position:0%
+energy whatever to to whatever energy
+range you want because you you have
+
+ align:start position:0%
+range you want because you you have
+ 
+
+ align:start position:0%
+range you want because you you have
+served the purpose of discover decou
+
+ align:start position:0%
+served the purpose of discover decou
+ 
+
+ align:start position:0%
+served the purpose of discover decou
+those uh uh yeah because those thing
+
+ align:start position:0%
+those uh uh yeah because those thing
+ 
+
+ align:start position:0%
+those uh uh yeah because those thing
+already go went to Infinity don't have
+
+ align:start position:0%
+already go went to Infinity don't have
+ 
+
+ align:start position:0%
+already go went to Infinity don't have
+to worry about
+
+ align:start position:0%
+to worry about
+ 
+
+ align:start position:0%
+to worry about
+them yeah is it clear yeah just like in
+
+ align:start position:0%
+them yeah is it clear yeah just like in
+ 
+
+ align:start position:0%
+them yeah is it clear yeah just like in
+the Y Theory we say we take the eny to
+
+ align:start position:0%
+the Y Theory we say we take the eny to
+ 
+
+ align:start position:0%
+the Y Theory we say we take the eny to
+to cover those massive modes but
+
+ align:start position:0%
+to cover those massive modes but
+ 
+
+ align:start position:0%
+to cover those massive modes but
+eventually in the yam we will consider
+
+ align:start position:0%
+eventually in the yam we will consider
+ 
+
+ align:start position:0%
+eventually in the yam we will consider
+very high energy process in the yam
+
+ align:start position:0%
+very high energy process in the yam
+ 
+
+ align:start position:0%
+very high energy process in the yam
+the okay and but but those since we
+
+ align:start position:0%
+the okay and but but those since we
+ 
+
+ align:start position:0%
+the okay and but but those since we
+cover have even even higher energy scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good good
+
+ align:start position:0%
+okay good good
+ 
+
+ align:start position:0%
+okay good good
+good so we call this is so this is one
+
+ align:start position:0%
+good so we call this is so this is one
+ 
+
+ align:start position:0%
+good so we call this is so this is one
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+two so in fact actually one and two they
+
+ align:start position:0%
+two so in fact actually one and two they
+ 
+
+ align:start position:0%
+two so in fact actually one and two they
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+not covering the full anti- de space
+
+ align:start position:0%
+not covering the full anti- de space
+ 
+
+ align:start position:0%
+not covering the full anti- de space
+time so actually they only cover a part
+
+ align:start position:0%
+time so actually they only cover a part
+ 
+
+ align:start position:0%
+time so actually they only cover a part
+of an deal space time so so they they
+
+ align:start position:0%
+of an deal space time so so they they
+ 
+
+ align:start position:0%
+of an deal space time so so they they
+only cover say what is so-call a p a
+
+ align:start position:0%
+only cover say what is so-call a p a
+ 
+
+ align:start position:0%
+only cover say what is so-call a p a
+patch a patch of deed space time anti
+
+ align:start position:0%
+patch a patch of deed space time anti
+ 
+
+ align:start position:0%
+patch a patch of deed space time anti
+deed space time so now let me just
+
+ align:start position:0%
+deed space time so now let me just
+ 
+
+ align:start position:0%
+deed space time so now let me just
+mention a little bit what is normally
+
+ align:start position:0%
+mention a little bit what is normally
+ 
+
+ align:start position:0%
+mention a little bit what is normally
+called the global ads okay so so the ads
+
+ align:start position:0%
+called the global ads okay so so the ads
+ 
+
+ align:start position:0%
+called the global ads okay so so the ads
+or or Global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ads so yeah so let me first write down
+
+ align:start position:0%
+ads so yeah so let me first write down
+ 
+
+ align:start position:0%
+ads so yeah so let me first write down
+the sentence so one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two one
+
+ align:start position:0%
+two one
+ 
+
+ align:start position:0%
+two one
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only cover
+
+ align:start position:0%
+only cover
+ 
+
+ align:start position:0%
+only cover
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part of four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+okay so the the global ads the so-called
+
+ align:start position:0%
+okay so the the global ads the so-called
+ 
+
+ align:start position:0%
+okay so the the global ads the so-called
+Global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ads can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defined can be
+
+ align:start position:0%
+defined can be
+ 
+
+ align:start position:0%
+defined can be
+described
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a A hyperboloid in the lent space
+
+ align:start position:0%
+as a A hyperboloid in the lent space
+ 
+
+ align:start position:0%
+as a A hyperboloid in the lent space
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+holoid in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minkovski D plus two minkovski spe time
+
+ align:start position:0%
+minkovski D plus two minkovski spe time
+ 
+
+ align:start position:0%
+minkovski D plus two minkovski spe time
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Signature 2 comma D okay so to make this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+precise say for example if you go to the
+
+ align:start position:0%
+precise say for example if you go to the
+ 
+
+ align:start position:0%
+precise say for example if you go to the
+gr book for example the cing Hat the
+
+ align:start position:0%
+gr book for example the cing Hat the
+ 
+
+ align:start position:0%
+gr book for example the cing Hat the
+book by Hawking and alies called the
+
+ align:start position:0%
+book by Hawking and alies called the
+ 
+
+ align:start position:0%
+book by Hawking and alies called the
+large scale SP large scale structure of
+
+ align:start position:0%
+large scale SP large scale structure of
+ 
+
+ align:start position:0%
+large scale SP large scale structure of
+space time the way they Define the the
+
+ align:start position:0%
+space time the way they Define the the
+ 
+
+ align:start position:0%
+space time the way they Define the the
+anti deaser is as
+
+ align:start position:0%
+anti deaser is as
+ 
+
+ align:start position:0%
+anti deaser is as
+follows so you
+
+ align:start position:0%
+follows so you
+ 
+
+ align:start position:0%
+follows so you
+consider a d plus 2 Dimension movi space
+
+ align:start position:0%
+consider a d plus 2 Dimension movi space
+ 
+
+ align:start position:0%
+consider a d plus 2 Dimension movi space
+time with Signature 2 comma d
+
+ align:start position:0%
+time with Signature 2 comma d
+ 
+
+ align:start position:0%
+time with Signature 2 comma d
+so you
+
+ align:start position:0%
+so you
+ 
+
+ align:start position:0%
+so you
+consider om minkovski space time like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay so now you uh uh uh you have D
+
+ align:start position:0%
+this okay so now you uh uh uh you have D
+ 
+
+ align:start position:0%
+this okay so now you uh uh uh you have D
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+signature and the two negative signature
+
+ align:start position:0%
+signature and the two negative signature
+ 
+
+ align:start position:0%
+signature and the two negative signature
+so X start from minus one index zero
+
+ align:start position:0%
+so X start from minus one index zero
+ 
+
+ align:start position:0%
+so X start from minus one index zero
+which give you the lative uh signature
+
+ align:start position:0%
+which give you the lative uh signature
+ 
+
+ align:start position:0%
+which give you the lative uh signature
+and then you have yeah so this is the
+
+ align:start position:0%
+and then you have yeah so this is the
+ 
+
+ align:start position:0%
+and then you have yeah so this is the
+minkovski space time of the 2 comma D
+
+ align:start position:0%
+minkovski space time of the 2 comma D
+ 
+
+ align:start position:0%
+minkovski space time of the 2 comma D
+signature so now you consider the
+
+ align:start position:0%
+signature so now you consider the
+ 
+
+ align:start position:0%
+signature so now you consider the
+following hypersurface in that space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so this is
+
+ align:start position:0%
+okay so this is
+ 
+
+ align:start position:0%
+okay so this is
+hypoid in that space time and this this
+
+ align:start position:0%
+hypoid in that space time and this this
+ 
+
+ align:start position:0%
+hypoid in that space time and this this
+defines your ads okay so this
+
+ align:start position:0%
+defines your ads okay so this
+ 
+
+ align:start position:0%
+defines your ads okay so this
+surface defines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ads this is
+
+ align:start position:0%
+ads this is
+ 
+
+ align:start position:0%
+ads this is
+Def
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ads so of course this is a very
+
+ align:start position:0%
+ads so of course this is a very
+ 
+
+ align:start position:0%
+ads so of course this is a very
+different way to parameterize uh uh to
+
+ align:start position:0%
+different way to parameterize uh uh to
+ 
+
+ align:start position:0%
+different way to parameterize uh uh to
+uh to um parameterize a this then either
+
+ align:start position:0%
+uh to um parameterize a this then either
+ 
+
+ align:start position:0%
+uh to um parameterize a this then either
+this Matrix or that
+
+ align:start position:0%
+this Matrix or that
+ 
+
+ align:start position:0%
+this Matrix or that
+Matrix and you can actually pariz ads in
+
+ align:start position:0%
+Matrix and you can actually pariz ads in
+ 
+
+ align:start position:0%
+Matrix and you can actually pariz ads in
+many many different ways so now let me
+
+ align:start position:0%
+many many different ways so now let me
+ 
+
+ align:start position:0%
+many many different ways so now let me
+just mention a few ways to a few choice
+
+ align:start position:0%
+just mention a few ways to a few choice
+ 
+
+ align:start position:0%
+just mention a few ways to a few choice
+of different coordinates to parameterize
+
+ align:start position:0%
+of different coordinates to parameterize
+ 
+
+ align:start position:0%
+of different coordinates to parameterize
+this hyperboloids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the first is what we one is
+
+ align:start position:0%
+okay so the first is what we one is
+ 
+
+ align:start position:0%
+okay so the first is what we one is
+called the P coordinates is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so first we want we call pcre
+
+ align:start position:0%
+one so first we want we call pcre
+ 
+
+ align:start position:0%
+one so first we want we call pcre
+coordinates so in this P coordinates you
+
+ align:start position:0%
+coordinates so in this P coordinates you
+ 
+
+ align:start position:0%
+coordinates so in this P coordinates you
+introduce r r there is given by x -
+
+ align:start position:0%
+introduce r r there is given by x -
+ 
+
+ align:start position:0%
+introduce r r there is given by x -
+one plus
+
+ align:start position:0%
+one plus
+ 
+
+ align:start position:0%
+one plus
+XD so you take the one of the netive
+
+ align:start position:0%
+XD so you take the one of the netive
+ 
+
+ align:start position:0%
+XD so you take the one of the netive
+signature and the one of the positive
+
+ align:start position:0%
+signature and the one of the positive
+ 
+
+ align:start position:0%
+signature and the one of the positive
+signature you take xus One X add them
+
+ align:start position:0%
+signature you take xus One X add them
+ 
+
+ align:start position:0%
+signature you take xus One X add them
+together so this is like some kind of
+
+ align:start position:0%
+together so this is like some kind of
+ 
+
+ align:start position:0%
+together so this is like some kind of
+nightc and uh and then you write X
+
+ align:start position:0%
+nightc and uh and then you write X
+ 
+
+ align:start position:0%
+nightc and uh and then you write X
+mu so there we always always write X
+
+ align:start position:0%
+mu so there we always always write X
+ 
+
+ align:start position:0%
+mu so there we always always write X
+mu equal to
+
+ align:start position:0%
+mu equal to
+ 
+
+ align:start position:0%
+mu equal to
+TX okay so this is a d dimensional movi
+
+ align:start position:0%
+TX okay so this is a d dimensional movi
+ 
+
+ align:start position:0%
+TX okay so this is a d dimensional movi
+coordinates add X mu equal to R *
+
+ align:start position:0%
+coordinates add X mu equal to R *
+ 
+
+ align:start position:0%
+coordinates add X mu equal to R *
+Capital
+
+ align:start position:0%
+Capital
+ 
+
+ align:start position:0%
+Capital
+mu / by
+
+ align:start position:0%
+mu / by
+ 
+
+ align:start position:0%
+mu / by
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um in this
+
+ align:start position:0%
+um in this
+ 
+
+ align:start position:0%
+um in this
+hyperboloid you make this St
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you restrict to the region of R
+
+ align:start position:0%
+and then you restrict to the region of R
+ 
+
+ align:start position:0%
+and then you restrict to the region of R
+greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero then you recover so
+
+ align:start position:0%
+zero then you recover so
+ 
+
+ align:start position:0%
+zero then you recover so
+one correspond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to are greater than zero part of this
+
+ align:start position:0%
+to are greater than zero part of this
+ 
+
+ align:start position:0%
+to are greater than zero part of this
+magic
+
+ align:start position:0%
+magic
+ 
+
+ align:start position:0%
+magic
+okay of this space time and you can
+
+ align:start position:0%
+okay of this space time and you can
+ 
+
+ align:start position:0%
+okay of this space time and you can
+easily check yourself just make this
+
+ align:start position:0%
+easily check yourself just make this
+ 
+
+ align:start position:0%
+easily check yourself just make this
+definition uh this is exercise you
+
+ align:start position:0%
+definition uh this is exercise you
+ 
+
+ align:start position:0%
+definition uh this is exercise you
+should do which I don't have time to do
+
+ align:start position:0%
+should do which I don't have time to do
+ 
+
+ align:start position:0%
+should do which I don't have time to do
+here just plug this in plug this into
+
+ align:start position:0%
+here just plug this in plug this into
+ 
+
+ align:start position:0%
+here just plug this in plug this into
+that Matrix plug this parameterization
+
+ align:start position:0%
+that Matrix plug this parameterization
+ 
+
+ align:start position:0%
+that Matrix plug this parameterization
+into that Matrix and then you find you
+
+ align:start position:0%
+into that Matrix and then you find you
+ 
+
+ align:start position:0%
+into that Matrix and then you find you
+will recover one and one will
+
+ align:start position:0%
+will recover one and one will
+ 
+
+ align:start position:0%
+will recover one and one will
+corresponding one is only restricted to
+
+ align:start position:0%
+corresponding one is only restricted to
+ 
+
+ align:start position:0%
+corresponding one is only restricted to
+r equal to Z to Infinity so you only
+
+ align:start position:0%
+r equal to Z to Infinity so you only
+ 
+
+ align:start position:0%
+r equal to Z to Infinity so you only
+restrict to R greater than zero part of
+
+ align:start position:0%
+restrict to R greater than zero part of
+ 
+
+ align:start position:0%
+restrict to R greater than zero part of
+this and if you just introduce this in
+
+ align:start position:0%
+this and if you just introduce this in
+ 
+
+ align:start position:0%
+this and if you just introduce this in
+pcle of course R can be smaller than
+
+ align:start position:0%
+pcle of course R can be smaller than
+ 
+
+ align:start position:0%
+pcle of course R can be smaller than
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay so so this are P coordinates so
+
+ align:start position:0%
+okay so so this are P coordinates so
+ 
+
+ align:start position:0%
+okay so so this are P coordinates so
+once you go to to that matric then go to
+
+ align:start position:0%
+once you go to to that matric then go to
+ 
+
+ align:start position:0%
+once you go to to that matric then go to
+this matric just it's the
+
+ align:start position:0%
+this matric just it's the
+ 
+
+ align:start position:0%
+this matric just it's the
+same also let me describe something
+
+ align:start position:0%
+same also let me describe something
+ 
+
+ align:start position:0%
+same also let me describe something
+called the global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates so this is BYO is the
+
+ align:start position:0%
+coordinates so this is BYO is the
+ 
+
+ align:start position:0%
+coordinates so this is BYO is the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+structure so this is have the form of
+
+ align:start position:0%
+structure so this is have the form of
+ 
+
+ align:start position:0%
+structure so this is have the form of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+two the the difference of two
+
+ align:start position:0%
+two the the difference of two
+ 
+
+ align:start position:0%
+two the the difference of two
+squares so I can write
+
+ align:start position:0%
+squares so I can write
+ 
+
+ align:start position:0%
+squares so I can write
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's write
+
+ align:start position:0%
+let's write
+ 
+
+ align:start position:0%
+let's write
+x i to one to d x i s to be some some
+
+ align:start position:0%
+x i to one to d x i s to be some some
+ 
+
+ align:start position:0%
+x i to one to d x i s to be some some
+function R square and R square time R
+
+ align:start position:0%
+function R square and R square time R
+ 
+
+ align:start position:0%
+function R square and R square time R
+square so this R have nothing to do with
+
+ align:start position:0%
+square so this R have nothing to do with
+ 
+
+ align:start position:0%
+square so this R have nothing to do with
+that RW now we are doing a different set
+
+ align:start position:0%
+that RW now we are doing a different set
+ 
+
+ align:start position:0%
+that RW now we are doing a different set
+of coordinates uh I'm just using the the
+
+ align:start position:0%
+of coordinates uh I'm just using the the
+ 
+
+ align:start position:0%
+of coordinates uh I'm just using the the
+same notation for
+
+ align:start position:0%
+same notation for
+ 
+
+ align:start position:0%
+same notation for
+convenience so so so let's introduce a
+
+ align:start position:0%
+convenience so so so let's introduce a
+ 
+
+ align:start position:0%
+convenience so so so let's introduce a
+new coordinate r which is just the sum
+
+ align:start position:0%
+new coordinate r which is just the sum
+ 
+
+ align:start position:0%
+new coordinate r which is just the sum
+of all these
+
+ align:start position:0%
+of all these
+ 
+
+ align:start position:0%
+of all these
+square and then I
+
+ align:start position:0%
+square and then I
+ 
+
+ align:start position:0%
+square and then I
+introduce then then from this equation
+
+ align:start position:0%
+introduce then then from this equation
+ 
+
+ align:start position:0%
+introduce then then from this equation
+the X1 minus x0 s should be equal to r²
+
+ align:start position:0%
+the X1 minus x0 s should be equal to r²
+ 
+
+ align:start position:0%
+the X1 minus x0 s should be equal to r²
++ 1 * R
+
+ align:start position:0%
++ 1 * R
+ 
+
+ align:start position:0%
++ 1 * R
+square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now I can so this is a this is a
+
+ align:start position:0%
+okay so now I can so this is a this is a
+ 
+
+ align:start position:0%
+okay so now I can so this is a this is a
+circle so for fixed R this is a
+
+ align:start position:0%
+circle so for fixed R this is a
+ 
+
+ align:start position:0%
+circle so for fixed R this is a
+circle for fixed R this is a D minus one
+
+ align:start position:0%
+circle for fixed R this is a D minus one
+ 
+
+ align:start position:0%
+circle for fixed R this is a D minus one
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+sphere
+
+ align:start position:0%
+sphere
+ 
+
+ align:start position:0%
+sphere
+okay so I can introduce this D minus one
+
+ align:start position:0%
+okay so I can introduce this D minus one
+ 
+
+ align:start position:0%
+okay so I can introduce this D minus one
+spical coordinates on this and introduce
+
+ align:start position:0%
+spical coordinates on this and introduce
+ 
+
+ align:start position:0%
+spical coordinates on this and introduce
+a circular circular coordinate on this
+
+ align:start position:0%
+a circular circular coordinate on this
+ 
+
+ align:start position:0%
+a circular circular coordinate on this
+okay so if I do that so let me just call
+
+ align:start position:0%
+okay so if I do that so let me just call
+ 
+
+ align:start position:0%
+okay so if I do that so let me just call
+the circular coordinate on here
+
+ align:start position:0%
+the circular coordinate on here
+ 
+
+ align:start position:0%
+the circular coordinate on here
+to uh the polar coordinate in the in the
+
+ align:start position:0%
+to uh the polar coordinate in the in the
+ 
+
+ align:start position:0%
+to uh the polar coordinate in the in the
+in the xus Y uh
+
+ align:start position:0%
+in the xus Y uh
+ 
+
+ align:start position:0%
+in the xus Y uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+polar coordinates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the xus one and x0 plane so let me
+
+ align:start position:0%
+in the xus one and x0 plane so let me
+ 
+
+ align:start position:0%
+in the xus one and x0 plane so let me
+call this tle and let me call the sple
+
+ align:start position:0%
+call this tle and let me call the sple
+ 
+
+ align:start position:0%
+call this tle and let me call the sple
+coordinate here Omega minus one Omega D
+
+ align:start position:0%
+coordinate here Omega minus one Omega D
+ 
+
+ align:start position:0%
+coordinate here Omega minus one Omega D
+minus one okay then you plug this into
+
+ align:start position:0%
+minus one okay then you plug this into
+ 
+
+ align:start position:0%
+minus one okay then you plug this into
+here then you find you find the
+
+ align:start position:0%
+here then you find you find the
+ 
+
+ align:start position:0%
+here then you find you find the
+following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you find the following
+
+ align:start position:0%
+so you find the following
+ 
+
+ align:start position:0%
+so you find the following
+magic you
+
+ align:start position:0%
+magic you
+ 
+
+ align:start position:0%
+magic you
+find D
+
+ align:start position:0%
+find D
+ 
+
+ align:start position:0%
+find D
+s² equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r² minus 1 + r² d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+square plus d r² + 1 +
+
+ align:start position:0%
+square plus d r² + 1 +
+ 
+
+ align:start position:0%
+square plus d r² + 1 +
+r² + r sare d Omega D minus 1
+
+ align:start position:0%
+r² + r sare d Omega D minus 1
+ 
+
+ align:start position:0%
+r² + r sare d Omega D minus 1
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so remember T is the polar
+
+ align:start position:0%
+okay so so remember T is the polar
+ 
+
+ align:start position:0%
+okay so so remember T is the polar
+coordinate in this xus one and x0 plane
+
+ align:start position:0%
+coordinate in this xus one and x0 plane
+ 
+
+ align:start position:0%
+coordinate in this xus one and x0 plane
+and Omega D minus one is the polar
+
+ align:start position:0%
+and Omega D minus one is the polar
+ 
+
+ align:start position:0%
+and Omega D minus one is the polar
+coordinate in the X1 to
+
+ align:start position:0%
+coordinate in the X1 to
+ 
+
+ align:start position:0%
+coordinate in the X1 to
+XT
+
+ align:start position:0%
+XT
+ 
+
+ align:start position:0%
+XT
+okay and then you get
+
+ align:start position:0%
+okay and then you get
+ 
+
+ align:start position:0%
+okay and then you get
+this again it's an exercise you should
+
+ align:start position:0%
+this again it's an exercise you should
+ 
+
+ align:start position:0%
+this again it's an exercise you should
+go through yourself yes so question so
+
+ align:start position:0%
+go through yourself yes so question so
+ 
+
+ align:start position:0%
+go through yourself yes so question so
+I'm just trying to visualize this so
+
+ align:start position:0%
+I'm just trying to visualize this so
+ 
+
+ align:start position:0%
+I'm just trying to visualize this so
+there's these I mean at least the way
+
+ align:start position:0%
+there's these I mean at least the way
+ 
+
+ align:start position:0%
+there's these I mean at least the way
+works in RM imagine so you have these
+
+ align:start position:0%
+works in RM imagine so you have these
+ 
+
+ align:start position:0%
+works in RM imagine so you have these
+two sheets which are like disjoint from
+
+ align:start position:0%
+two sheets which are like disjoint from
+ 
+
+ align:start position:0%
+two sheets which are like disjoint from
+each other so how is it that this
+
+ align:start position:0%
+each other so how is it that this
+ 
+
+ align:start position:0%
+each other so how is it that this
+enables us to go smoothly between them
+
+ align:start position:0%
+enables us to go smoothly between them
+ 
+
+ align:start position:0%
+enables us to go smoothly between them
+like it seems that there's so maybe I'm
+
+ align:start position:0%
+like it seems that there's so maybe I'm
+ 
+
+ align:start position:0%
+like it seems that there's so maybe I'm
+confused about what you did okay what do
+
+ align:start position:0%
+confused about what you did okay what do
+ 
+
+ align:start position:0%
+confused about what you did okay what do
+you mean so we're trying to describe
+
+ align:start position:0%
+you mean so we're trying to describe
+ 
+
+ align:start position:0%
+you mean so we're trying to describe
+this object which has two disjoint
+
+ align:start position:0%
+this object which has two disjoint
+ 
+
+ align:start position:0%
+this object which has two disjoint
+components we only look at one component
+
+ align:start position:0%
+components we only look at one component
+ 
+
+ align:start position:0%
+components we only look at one component
+so what's the point of global
+
+ align:start position:0%
+so what's the point of global
+ 
+
+ align:start position:0%
+so what's the point of global
+coordinates is it just a
+
+ align:start position:0%
+coordinates is it just a
+ 
+
+ align:start position:0%
+coordinates is it just a
+different no no no no that only covers
+
+ align:start position:0%
+different no no no no that only covers
+ 
+
+ align:start position:0%
+different no no no no that only covers
+part of the one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+component oh I see okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay yeah okay good so you look at
+
+ align:start position:0%
+yes okay yeah okay good so you look at
+ 
+
+ align:start position:0%
+yes okay yeah okay good so you look at
+here um yeah so uh so so that's the M
+
+ align:start position:0%
+here um yeah so uh so so that's the M
+ 
+
+ align:start position:0%
+here um yeah so uh so so that's the M
+again R where goes from zero to Infinity
+
+ align:start position:0%
+again R where goes from zero to Infinity
+ 
+
+ align:start position:0%
+again R where goes from zero to Infinity
+but this R is very different from this R
+
+ align:start position:0%
+but this R is very different from this R
+ 
+
+ align:start position:0%
+but this R is very different from this R
+law
+
+ align:start position:0%
+law
+ 
+
+ align:start position:0%
+law
+okay uh so in this
+
+ align:start position:0%
+okay uh so in this
+ 
+
+ align:start position:0%
+okay uh so in this
+definition t is a polar coordinate so in
+
+ align:start position:0%
+definition t is a polar coordinate so in
+ 
+
+ align:start position:0%
+definition t is a polar coordinate so in
+this definition t will go from 0 to 2 pi
+
+ align:start position:0%
+this definition t will go from 0 to 2 pi
+ 
+
+ align:start position:0%
+this definition t will go from 0 to 2 pi
+okay but once you write it in this
+
+ align:start position:0%
+okay but once you write it in this
+ 
+
+ align:start position:0%
+okay but once you write it in this
+form nothing depends on T so you can
+
+ align:start position:0%
+form nothing depends on T so you can
+ 
+
+ align:start position:0%
+form nothing depends on T so you can
+extend T to any range you want so once
+
+ align:start position:0%
+extend T to any range you want so once
+ 
+
+ align:start position:0%
+extend T to any range you want so once
+we write this form we take
+
+ align:start position:0%
+we write this form we take
+ 
+
+ align:start position:0%
+we write this form we take
+to goes to minus infinity to plus
+
+ align:start position:0%
+to goes to minus infinity to plus
+ 
+
+ align:start position:0%
+to goes to minus infinity to plus
+infinity so this is our gening time
+
+ align:start position:0%
+infinity so this is our gening time
+ 
+
+ align:start position:0%
+infinity so this is our gening time
+rather than from 0 to from PI 0 to 0 to
+
+ align:start position:0%
+rather than from 0 to from PI 0 to 0 to
+ 
+
+ align:start position:0%
+rather than from 0 to from PI 0 to 0 to
+2 pi we take to from minus infinity to
+
+ align:start position:0%
+2 pi we take to from minus infinity to
+ 
+
+ align:start position:0%
+2 pi we take to from minus infinity to
+plus infinity so sometimes this is also
+
+ align:start position:0%
+plus infinity so sometimes this is also
+ 
+
+ align:start position:0%
+plus infinity so sometimes this is also
+called extended
+
+ align:start position:0%
+called extended
+ 
+
+ align:start position:0%
+called extended
+ads sometime people don't just bother to
+
+ align:start position:0%
+ads sometime people don't just bother to
+ 
+
+ align:start position:0%
+ads sometime people don't just bother to
+do that you just extend it automatically
+
+ align:start position:0%
+do that you just extend it automatically
+ 
+
+ align:start position:0%
+do that you just extend it automatically
+okay so strictly
+
+ align:start position:0%
+okay so strictly
+ 
+
+ align:start position:0%
+okay so strictly
+speaking
+
+ align:start position:0%
+speaking
+ 
+
+ align:start position:0%
+speaking
+this as a definition of ads only
+
+ align:start position:0%
+this as a definition of ads only
+ 
+
+ align:start position:0%
+this as a definition of ads only
+corresponding to the part of to from 0
+
+ align:start position:0%
+corresponding to the part of to from 0
+ 
+
+ align:start position:0%
+corresponding to the part of to from 0
+to 2 pi okay and and when you when you
+
+ align:start position:0%
+to 2 pi okay and and when you when you
+ 
+
+ align:start position:0%
+to 2 pi okay and and when you when you
+extend to from minus infinity to minus
+
+ align:start position:0%
+extend to from minus infinity to minus
+ 
+
+ align:start position:0%
+extend to from minus infinity to minus
+infinity you actually have infinite copy
+
+ align:start position:0%
+infinity you actually have infinite copy
+ 
+
+ align:start position:0%
+infinity you actually have infinite copy
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay so now with one more thing we
+
+ align:start position:0%
+this okay so now with one more thing we
+ 
+
+ align:start position:0%
+this okay so now with one more thing we
+can so this coordinate is
+
+ align:start position:0%
+can so this coordinate is
+ 
+
+ align:start position:0%
+can so this coordinate is
+nice now it covers
+
+ align:start position:0%
+nice now it covers
+ 
+
+ align:start position:0%
+nice now it covers
+everything covers everything but even
+
+ align:start position:0%
+everything covers everything but even
+ 
+
+ align:start position:0%
+everything covers everything but even
+actually a little bit more because you
+
+ align:start position:0%
+actually a little bit more because you
+ 
+
+ align:start position:0%
+actually a little bit more because you
+have now you extend the tower to minus
+
+ align:start position:0%
+have now you extend the tower to minus
+ 
+
+ align:start position:0%
+have now you extend the tower to minus
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+infinity we can visualize this matric a
+
+ align:start position:0%
+infinity we can visualize this matric a
+ 
+
+ align:start position:0%
+infinity we can visualize this matric a
+little bit better by doing the the
+
+ align:start position:0%
+little bit better by doing the the
+ 
+
+ align:start position:0%
+little bit better by doing the the
+following a lot of transformation so now
+
+ align:start position:0%
+following a lot of transformation so now
+ 
+
+ align:start position:0%
+following a lot of transformation so now
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+take yeah before so that let me say a
+
+ align:start position:0%
+take yeah before so that let me say a
+ 
+
+ align:start position:0%
+take yeah before so that let me say a
+few words about yeah let me just uh uh
+
+ align:start position:0%
+few words about yeah let me just uh uh
+ 
+
+ align:start position:0%
+few words about yeah let me just uh uh
+do this first let's take to again take
+
+ align:start position:0%
+do this first let's take to again take
+ 
+
+ align:start position:0%
+do this first let's take to again take
+Ral to tangent row row some other
+
+ align:start position:0%
+Ral to tangent row row some other
+ 
+
+ align:start position:0%
+Ral to tangent row row some other
+coordinates and R from Z to Infinity
+
+ align:start position:0%
+coordinates and R from Z to Infinity
+ 
+
+ align:start position:0%
+coordinates and R from Z to Infinity
+then row will be from0 to 2 Pi Pi /
+
+ align:start position:0%
+then row will be from0 to 2 Pi Pi /
+ 
+
+ align:start position:0%
+then row will be from0 to 2 Pi Pi /
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay Z pi
+
+ align:start position:0%
+okay Z pi
+ 
+
+ align:start position:0%
+okay Z pi
+two and you plug this into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is a little bit
+
+ align:start position:0%
+here is a little bit
+ 
+
+ align:start position:0%
+here is a little bit
+tiny so after 2 seconds you find the
+
+ align:start position:0%
+tiny so after 2 seconds you find the
+ 
+
+ align:start position:0%
+tiny so after 2 seconds you find the
+following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is easy to see because 1 plus T
+
+ align:start position:0%
+so this is easy to see because 1 plus T
+ 
+
+ align:start position:0%
+so this is easy to see because 1 plus T
+row square is just one over cosine
+
+ align:start position:0%
+row square is just one over cosine
+ 
+
+ align:start position:0%
+row square is just one over cosine
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+and ex true so the reason this matric is
+
+ align:start position:0%
+and ex true so the reason this matric is
+ 
+
+ align:start position:0%
+and ex true so the reason this matric is
+nice because other than this conformal
+
+ align:start position:0%
+nice because other than this conformal
+ 
+
+ align:start position:0%
+nice because other than this conformal
+Factor this thing we can easily
+
+ align:start position:0%
+Factor this thing we can easily
+ 
+
+ align:start position:0%
+Factor this thing we can easily
+recognize so this is just a
+
+ align:start position:0%
+recognize so this is just a
+ 
+
+ align:start position:0%
+recognize so this is just a
+cylinder so this is just a
+
+ align:start position:0%
+cylinder so this is just a
+ 
+
+ align:start position:0%
+cylinder so this is just a
+cylinder and let me draw it here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cylinder
+
+ align:start position:0%
+cylinder
+ 
+
+ align:start position:0%
+cylinder
+okay so this direction can be consider
+
+ align:start position:0%
+okay so this direction can be consider
+ 
+
+ align:start position:0%
+okay so this direction can be consider
+the the radial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction is the row Direction
+
+ align:start position:0%
+direction is the row Direction
+ 
+
+ align:start position:0%
+direction is the row Direction
+Direction and the circular dire and this
+
+ align:start position:0%
+Direction and the circular dire and this
+ 
+
+ align:start position:0%
+Direction and the circular dire and this
+direction is the T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction and this direction is the uh
+
+ align:start position:0%
+Direction and this direction is the uh
+ 
+
+ align:start position:0%
+Direction and this direction is the uh
+the the Omega D minus one or or the
+
+ align:start position:0%
+the the Omega D minus one or or the
+ 
+
+ align:start position:0%
+the the Omega D minus one or or the
+polar coordinate Direction I'm only
+
+ align:start position:0%
+polar coordinate Direction I'm only
+ 
+
+ align:start position:0%
+polar coordinate Direction I'm only
+drawing one of
+
+ align:start position:0%
+drawing one of
+ 
+
+ align:start position:0%
+drawing one of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+okay so essentially this have a
+
+ align:start position:0%
+okay so essentially this have a
+ 
+
+ align:start position:0%
+okay so essentially this have a
+structure of a
+
+ align:start position:0%
+structure of a
+ 
+
+ align:start position:0%
+structure of a
+cylinder and at the center here I have
+
+ align:start position:0%
+cylinder and at the center here I have
+ 
+
+ align:start position:0%
+cylinder and at the center here I have
+row equal to zero
+
+ align:start position:0%
+row equal to zero
+ 
+
+ align:start position:0%
+row equal to zero
+and here I have row equal to pi/
+
+ align:start position:0%
+and here I have row equal to pi/
+ 
+
+ align:start position:0%
+and here I have row equal to pi/
+2 okay Row from 0 to pi/
+
+ align:start position:0%
+2 okay Row from 0 to pi/
+ 
+
+ align:start position:0%
+2 okay Row from 0 to pi/
+2 okay and uh and when you go to pi/ two
+
+ align:start position:0%
+2 okay and uh and when you go to pi/ two
+ 
+
+ align:start position:0%
+2 okay and uh and when you go to pi/ two
+this Quant Factor goes zero so so the
+
+ align:start position:0%
+this Quant Factor goes zero so so the
+ 
+
+ align:start position:0%
+this Quant Factor goes zero so so the
+overall scale blows up so so here is
+
+ align:start position:0%
+overall scale blows up so so here is
+ 
+
+ align:start position:0%
+overall scale blows up so so here is
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+boundary so so the uh um so pi over
+
+ align:start position:0%
+boundary so so the uh um so pi over
+ 
+
+ align:start position:0%
+boundary so so the uh um so pi over
+two yeah so so
+
+ align:start position:0%
+two yeah so so
+ 
+
+ align:start position:0%
+two yeah so so
+the so pi/ two is the boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay is this
+
+ align:start position:0%
+okay is this
+ 
+
+ align:start position:0%
+okay is this
+clear the pi/ two is the boundary now
+
+ align:start position:0%
+clear the pi/ two is the boundary now
+ 
+
+ align:start position:0%
+clear the pi/ two is the boundary now
+the boundary map so so so the boundary
+
+ align:start position:0%
+the boundary map so so so the boundary
+ 
+
+ align:start position:0%
+the boundary map so so so the boundary
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+cylinder so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary now is at sitting atal to pi/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 has the
+
+ align:start position:0%
+2 has the
+ 
+
+ align:start position:0%
+2 has the
+topology of r
+
+ align:start position:0%
+topology of r
+ 
+
+ align:start position:0%
+topology of r
+time sdus
+
+ align:start position:0%
+time sdus
+ 
+
+ align:start position:0%
+time sdus
+one okay so the boundary itself is a so
+
+ align:start position:0%
+one okay so the boundary itself is a so
+ 
+
+ align:start position:0%
+one okay so the boundary itself is a so
+the boundary itself is the cinder the
+
+ align:start position:0%
+the boundary itself is the cinder the
+ 
+
+ align:start position:0%
+the boundary itself is the cinder the
+whole Space is is a solid cylinder it's
+
+ align:start position:0%
+whole Space is is a solid cylinder it's
+ 
+
+ align:start position:0%
+whole Space is is a solid cylinder it's
+a fied cylinder
+
+ align:start position:0%
+a fied cylinder
+ 
+
+ align:start position:0%
+a fied cylinder
+okay and but the scale factor blows up
+
+ align:start position:0%
+okay and but the scale factor blows up
+ 
+
+ align:start position:0%
+okay and but the scale factor blows up
+when you approach the boundary because
+
+ align:start position:0%
+when you approach the boundary because
+ 
+
+ align:start position:0%
+when you approach the boundary because
+of this pre
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factor and the r is the time and the
+
+ align:start position:0%
+factor and the r is the time and the
+ 
+
+ align:start position:0%
+factor and the r is the time and the
+sdus one is
+
+ align:start position:0%
+sdus one is
+ 
+
+ align:start position:0%
+sdus one is
+the so so let's now to visualize this
+
+ align:start position:0%
+the so so let's now to visualize this
+ 
+
+ align:start position:0%
+the so so let's now to visualize this
+space a little bit more better let's
+
+ align:start position:0%
+space a little bit more better let's
+ 
+
+ align:start position:0%
+space a little bit more better let's
+look at the
+
+ align:start position:0%
+look at the
+ 
+
+ align:start position:0%
+look at the
+cross-section so imagine you put a
+
+ align:start position:0%
+cross-section so imagine you put a
+ 
+
+ align:start position:0%
+cross-section so imagine you put a
+plane in this space okay so now imagine
+
+ align:start position:0%
+plane in this space okay so now imagine
+ 
+
+ align:start position:0%
+plane in this space okay so now imagine
+and now let me call this U this circular
+
+ align:start position:0%
+and now let me call this U this circular
+ 
+
+ align:start position:0%
+and now let me call this U this circular
+Direction let's call it Theta and then
+
+ align:start position:0%
+Direction let's call it Theta and then
+ 
+
+ align:start position:0%
+Direction let's call it Theta and then
+now let's consider the cross-section
+
+ align:start position:0%
+now let's consider the cross-section
+ 
+
+ align:start position:0%
+now let's consider the cross-section
+across this solid cylinder so then we
+
+ align:start position:0%
+across this solid cylinder so then we
+ 
+
+ align:start position:0%
+across this solid cylinder so then we
+just have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane okay have a plane I should not
+
+ align:start position:0%
+plane okay have a plane I should not
+ 
+
+ align:start position:0%
+plane okay have a plane I should not
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's consider this cross-section okay
+
+ align:start position:0%
+let's consider this cross-section okay
+ 
+
+ align:start position:0%
+let's consider this cross-section okay
+uh in the center of this
+
+ align:start position:0%
+uh in the center of this
+ 
+
+ align:start position:0%
+uh in the center of this
+cylinder I cut half cylinder cut it in
+
+ align:start position:0%
+cylinder I cut half cylinder cut it in
+ 
+
+ align:start position:0%
+cylinder I cut half cylinder cut it in
+half so so um so for example in this
+
+ align:start position:0%
+half so so um so for example in this
+ 
+
+ align:start position:0%
+half so so um so for example in this
+notation so this will be row equal to
+
+ align:start position:0%
+notation so this will be row equal to
+ 
+
+ align:start position:0%
+notation so this will be row equal to
+Zer so here is rowal to Pi /
+
+ align:start position:0%
+Zer so here is rowal to Pi /
+ 
+
+ align:start position:0%
+Zer so here is rowal to Pi /
+2 and I introduce this angular
+
+ align:start position:0%
+2 and I introduce this angular
+ 
+
+ align:start position:0%
+2 and I introduce this angular
+coordinate that corresponding to Theta
+
+ align:start position:0%
+coordinate that corresponding to Theta
+ 
+
+ align:start position:0%
+coordinate that corresponding to Theta
+equal to zero and here will be again row
+
+ align:start position:0%
+equal to zero and here will be again row
+ 
+
+ align:start position:0%
+equal to zero and here will be again row
+= to Pi / 2 but Theta equal to
+
+ align:start position:0%
+= to Pi / 2 but Theta equal to
+ 
+
+ align:start position:0%
+= to Pi / 2 but Theta equal to
+Pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and again this is the TP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction is they clear what I'm doing I
+
+ align:start position:0%
+direction is they clear what I'm doing I
+ 
+
+ align:start position:0%
+direction is they clear what I'm doing I
+cut s in half and that's that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross-section
+
+ align:start position:0%
+cross-section
+ 
+
+ align:start position:0%
+cross-section
+so now because of this T because of
+
+ align:start position:0%
+so now because of this T because of
+ 
+
+ align:start position:0%
+so now because of this T because of
+this structure of this times or
+
+ align:start position:0%
+this structure of this times or
+ 
+
+ align:start position:0%
+this structure of this times or
+conformal factor of all scale
+
+ align:start position:0%
+conformal factor of all scale
+ 
+
+ align:start position:0%
+conformal factor of all scale
+factor so the propagation of a light
+
+ align:start position:0%
+factor so the propagation of a light
+ 
+
+ align:start position:0%
+factor so the propagation of a light
+Ray does not depend on this overall
+
+ align:start position:0%
+Ray does not depend on this overall
+ 
+
+ align:start position:0%
+Ray does not depend on this overall
+Factor the propagation of that Ray can
+
+ align:start position:0%
+Factor the propagation of that Ray can
+ 
+
+ align:start position:0%
+Factor the propagation of that Ray can
+be seen from here okay so now let's
+
+ align:start position:0%
+be seen from here okay so now let's
+ 
+
+ align:start position:0%
+be seen from here okay so now let's
+consider the radial that Ray which only
+
+ align:start position:0%
+consider the radial that Ray which only
+ 
+
+ align:start position:0%
+consider the radial that Ray which only
+goes into the row Direction say so
+
+ align:start position:0%
+goes into the row Direction say so
+ 
+
+ align:start position:0%
+goes into the row Direction say so
+there's no in the in this angle
+
+ align:start position:0%
+there's no in the in this angle
+ 
+
+ align:start position:0%
+there's no in the in this angle
+Direction Let's can the radial light
+
+ align:start position:0%
+Direction Let's can the radial light
+ 
+
+ align:start position:0%
+Direction Let's can the radial light
+Ray then then from that picture it's
+
+ align:start position:0%
+Ray then then from that picture it's
+ 
+
+ align:start position:0%
+Ray then then from that picture it's
+very clear so let's say this is to equal
+
+ align:start position:0%
+very clear so let's say this is to equal
+ 
+
+ align:start position:0%
+very clear so let's say this is to equal
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero then actually takes only Pi /
+
+ align:start position:0%
+zero then actually takes only Pi /
+ 
+
+ align:start position:0%
+zero then actually takes only Pi /
+2 for light rate to reach the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary okay because the row only goes
+
+ align:start position:0%
+boundary okay because the row only goes
+ 
+
+ align:start position:0%
+boundary okay because the row only goes
+from PI pi/ two and that rate only TR
+
+ align:start position:0%
+from PI pi/ two and that rate only TR
+ 
+
+ align:start position:0%
+from PI pi/ two and that rate only TR
+always traveling 45° so this is just
+
+ align:start position:0%
+always traveling 45° so this is just
+ 
+
+ align:start position:0%
+always traveling 45° so this is just
+like if you look at the to Plus Square
+
+ align:start position:0%
+like if you look at the to Plus Square
+ 
+
+ align:start position:0%
+like if you look at the to Plus Square
+this just
+
+ align:start position:0%
+this just
+ 
+
+ align:start position:0%
+this just
+minkovski and so lat travel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+45° and and then you reach the boundary
+
+ align:start position:0%
+45° and and then you reach the boundary
+ 
+
+ align:start position:0%
+45° and and then you reach the boundary
+and then take lot pi over two yeah so
+
+ align:start position:0%
+and then take lot pi over two yeah so
+ 
+
+ align:start position:0%
+and then take lot pi over two yeah so
+this is pi/ two so this is toal to zero
+
+ align:start position:0%
+this is pi/ two so this is toal to zero
+ 
+
+ align:start position:0%
+this is pi/ two so this is toal to zero
+and then this then this will be tall
+
+ align:start position:0%
+and then this then this will be tall
+ 
+
+ align:start position:0%
+and then this then this will be tall
+equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to pi/
+
+ align:start position:0%
+to pi/
+ 
+
+ align:start position:0%
+to pi/
+2 then then suppose you put some
+
+ align:start position:0%
+2 then then suppose you put some
+ 
+
+ align:start position:0%
+2 then then suppose you put some
+reflecting wall here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then by the time tal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi it it has bounced
+
+ align:start position:0%
+Pi it it has bounced
+ 
+
+ align:start position:0%
+Pi it it has bounced
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+okay and now if you go lot around then
+
+ align:start position:0%
+okay and now if you go lot around then
+ 
+
+ align:start position:0%
+okay and now if you go lot around then
+after that toal 2 pi then precisely go
+
+ align:start position:0%
+after that toal 2 pi then precisely go
+ 
+
+ align:start position:0%
+after that toal 2 pi then precisely go
+back to the
+
+ align:start position:0%
+back to the
+ 
+
+ align:start position:0%
+back to the
+origin then you go through a period okay
+
+ align:start position:0%
+origin then you go through a period okay
+ 
+
+ align:start position:0%
+origin then you go through a period okay
+and that actually precisely is that tal
+
+ align:start position:0%
+and that actually precisely is that tal
+ 
+
+ align:start position:0%
+and that actually precisely is that tal
+to 2 pi which you define the angular
+
+ align:start position:0%
+to 2 pi which you define the angular
+ 
+
+ align:start position:0%
+to 2 pi which you define the angular
+coordinates yeah if you follow follow
+
+ align:start position:0%
+coordinates yeah if you follow follow
+ 
+
+ align:start position:0%
+coordinates yeah if you follow follow
+that if you follow that then that
+
+ align:start position:0%
+that if you follow that then that
+ 
+
+ align:start position:0%
+that if you follow that then that
+corresponding to precisely one period of
+
+ align:start position:0%
+corresponding to precisely one period of
+ 
+
+ align:start position:0%
+corresponding to precisely one period of
+the light rate traveling in this okay
+
+ align:start position:0%
+the light rate traveling in this okay
+ 
+
+ align:start position:0%
+the light rate traveling in this okay
+but but the key thing is that the light
+
+ align:start position:0%
+but but the key thing is that the light
+ 
+
+ align:start position:0%
+but but the key thing is that the light
+rate will travel pi/ two to the
+
+ align:start position:0%
+rate will travel pi/ two to the
+ 
+
+ align:start position:0%
+rate will travel pi/ two to the
+boundary and now you can check if you
+
+ align:start position:0%
+boundary and now you can check if you
+ 
+
+ align:start position:0%
+boundary and now you can check if you
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+the not the light Ray so light Ray
+
+ align:start position:0%
+the not the light Ray so light Ray
+ 
+
+ align:start position:0%
+the not the light Ray so light Ray
+travels along the light nastics but if
+
+ align:start position:0%
+travels along the light nastics but if
+ 
+
+ align:start position:0%
+travels along the light nastics but if
+you look at the time neasc which is
+
+ align:start position:0%
+you look at the time neasc which is
+ 
+
+ align:start position:0%
+you look at the time neasc which is
+traveled by by Massive particle then you
+
+ align:start position:0%
+traveled by by Massive particle then you
+ 
+
+ align:start position:0%
+traveled by by Massive particle then you
+can show that the massive particle level
+
+ align:start position:0%
+can show that the massive particle level
+ 
+
+ align:start position:0%
+can show that the massive particle level
+reach the boundary it will go into a
+
+ align:start position:0%
+reach the boundary it will go into a
+ 
+
+ align:start position:0%
+reach the boundary it will go into a
+motion like
+
+ align:start position:0%
+motion like
+ 
+
+ align:start position:0%
+motion like
+this okay so this is a massive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle uh so the massive particle will
+
+ align:start position:0%
+particle uh so the massive particle will
+ 
+
+ align:start position:0%
+particle uh so the massive particle will
+never reach the boundary we always uh be
+
+ align:start position:0%
+never reach the boundary we always uh be
+ 
+
+ align:start position:0%
+never reach the boundary we always uh be
+reflected
+
+ align:start position:0%
+reflected
+ 
+
+ align:start position:0%
+reflected
+back uh uh intuitively from the gravity
+
+ align:start position:0%
+back uh uh intuitively from the gravity
+ 
+
+ align:start position:0%
+back uh uh intuitively from the gravity
+potential okay so you will show this
+
+ align:start position:0%
+potential okay so you will show this
+ 
+
+ align:start position:0%
+potential okay so you will show this
+fact yourself in your pet to show that
+
+ align:start position:0%
+fact yourself in your pet to show that
+ 
+
+ align:start position:0%
+fact yourself in your pet to show that
+actually the massive particle will never
+
+ align:start position:0%
+actually the massive particle will never
+ 
+
+ align:start position:0%
+actually the massive particle will never
+reach the
+
+ align:start position:0%
+reach the
+ 
+
+ align:start position:0%
+reach the
+boundary so in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense so if you look at this Matrix at
+
+ align:start position:0%
+sense so if you look at this Matrix at
+ 
+
+ align:start position:0%
+sense so if you look at this Matrix at
+row equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero at row to Z this is essentially
+
+ align:start position:0%
+zero at row to Z this is essentially
+ 
+
+ align:start position:0%
+zero at row to Z this is essentially
+like a flat Matrix because like to Z
+
+ align:start position:0%
+like a flat Matrix because like to Z
+ 
+
+ align:start position:0%
+like a flat Matrix because like to Z
+this is just a sphere so this become
+
+ align:start position:0%
+this is just a sphere so this become
+ 
+
+ align:start position:0%
+this is just a sphere so this become
+what this is a
+
+ align:start position:0%
+what this is a
+ 
+
+ align:start position:0%
+what this is a
+sphere
+
+ align:start position:0%
+sphere
+ 
+
+ align:start position:0%
+sphere
+yeah yeah yeah rowal to zero this is
+
+ align:start position:0%
+yeah yeah yeah rowal to zero this is
+ 
+
+ align:start position:0%
+yeah yeah yeah rowal to zero this is
+just like Ting space because this sign
+
+ align:start position:0%
+just like Ting space because this sign
+ 
+
+ align:start position:0%
+just like Ting space because this sign
+row Square become row Square okay so
+
+ align:start position:0%
+row Square become row Square okay so
+ 
+
+ align:start position:0%
+row Square become row Square okay so
+this just become like cre in space in
+
+ align:start position:0%
+this just become like cre in space in
+ 
+
+ align:start position:0%
+this just become like cre in space in
+poate and then you have a time and then
+
+ align:start position:0%
+poate and then you have a time and then
+ 
+
+ align:start position:0%
+poate and then you have a time and then
+this scale factor become one so zal to
+
+ align:start position:0%
+this scale factor become one so zal to
+ 
+
+ align:start position:0%
+this scale factor become one so zal to
+zero just like you have ordinary movi
+
+ align:start position:0%
+zero just like you have ordinary movi
+ 
+
+ align:start position:0%
+zero just like you have ordinary movi
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+time and uh and then and then uh then
+
+ align:start position:0%
+time and uh and then and then uh then
+ 
+
+ align:start position:0%
+time and uh and then and then uh then
+the curvature comes in when you go to
+
+ align:start position:0%
+the curvature comes in when you go to
+ 
+
+ align:start position:0%
+the curvature comes in when you go to
+fight row and then those Factor become
+
+ align:start position:0%
+fight row and then those Factor become
+ 
+
+ align:start position:0%
+fight row and then those Factor become
+important and then you can show yeah
+
+ align:start position:0%
+important and then you can show yeah
+ 
+
+ align:start position:0%
+important and then you can show yeah
+just because of that you can show that
+
+ align:start position:0%
+just because of that you can show that
+ 
+
+ align:start position:0%
+just because of that you can show that
+the massive particle will never actually
+
+ align:start position:0%
+the massive particle will never actually
+ 
+
+ align:start position:0%
+the massive particle will never actually
+travel to the boundary okay always
+
+ align:start position:0%
+travel to the boundary okay always
+ 
+
+ align:start position:0%
+travel to the boundary okay always
+reflected back in some sense you can
+
+ align:start position:0%
+reflected back in some sense you can
+ 
+
+ align:start position:0%
+reflected back in some sense you can
+think of that the massive particle is
+
+ align:start position:0%
+think of that the massive particle is
+ 
+
+ align:start position:0%
+think of that the massive particle is
+always pulled back by the gravitational
+
+ align:start position:0%
+always pulled back by the gravitational
+ 
+
+ align:start position:0%
+always pulled back by the gravitational
+potential okay pull back by gravity poal
+
+ align:start position:0%
+potential okay pull back by gravity poal
+ 
+
+ align:start position:0%
+potential okay pull back by gravity poal
+so so from a from a different point of
+
+ align:start position:0%
+so so from a from a different point of
+ 
+
+ align:start position:0%
+so so from a from a different point of
+view is that another way to say
+
+ align:start position:0%
+view is that another way to say
+ 
+
+ align:start position:0%
+view is that another way to say
+it is a familiar statement which people
+
+ align:start position:0%
+it is a familiar statement which people
+ 
+
+ align:start position:0%
+it is a familiar statement which people
+often
+
+ align:start position:0%
+often
+ 
+
+ align:start position:0%
+often
+make and uh and often can give you great
+
+ align:start position:0%
+make and uh and often can give you great
+ 
+
+ align:start position:0%
+make and uh and often can give you great
+intuition physical
+
+ align:start position:0%
+intuition physical
+ 
+
+ align:start position:0%
+intuition physical
+intuition in in many physical
+
+ align:start position:0%
+intuition in in many physical
+ 
+
+ align:start position:0%
+intuition in in many physical
+problems is that
+
+ align:start position:0%
+problems is that
+ 
+
+ align:start position:0%
+problems is that
+ads is like a confining
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+box just like a box so things cannot
+
+ align:start position:0%
+box just like a box so things cannot
+ 
+
+ align:start position:0%
+box just like a box so things cannot
+escape from it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay and in in in particular
+
+ align:start position:0%
+okay okay and in in in particular
+ 
+
+ align:start position:0%
+okay okay and in in in particular
+particular the typical curvature radius
+
+ align:start position:0%
+particular the typical curvature radius
+ 
+
+ align:start position:0%
+particular the typical curvature radius
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+R so you can roughly imagine this and
+
+ align:start position:0%
+R so you can roughly imagine this and
+ 
+
+ align:start position:0%
+R so you can roughly imagine this and
+because in the center it's like a flat
+
+ align:start position:0%
+because in the center it's like a flat
+ 
+
+ align:start position:0%
+because in the center it's like a flat
+space so it's more like a box of sides R
+
+ align:start position:0%
+space so it's more like a box of sides R
+ 
+
+ align:start position:0%
+space so it's more like a box of sides R
+okay it's roughly you can horis think of
+
+ align:start position:0%
+okay it's roughly you can horis think of
+ 
+
+ align:start position:0%
+okay it's roughly you can horis think of
+it as a box of sides R yes does it have
+
+ align:start position:0%
+it as a box of sides R yes does it have
+ 
+
+ align:start position:0%
+it as a box of sides R yes does it have
+finite INF volume H this a finite
+
+ align:start position:0%
+finite INF volume H this a finite
+ 
+
+ align:start position:0%
+finite INF volume H this a finite
+infinite volume yeah infinite volume
+
+ align:start position:0%
+infinite volume yeah infinite volume
+ 
+
+ align:start position:0%
+infinite volume yeah infinite volume
+volume yeah but because it's confining
+
+ align:start position:0%
+volume yeah but because it's confining
+ 
+
+ align:start position:0%
+volume yeah but because it's confining
+it most of the particles we only see the
+
+ align:start position:0%
+it most of the particles we only see the
+ 
+
+ align:start position:0%
+it most of the particles we only see the
+sides off so so one question so can we
+
+ align:start position:0%
+sides off so so one question so can we
+ 
+
+ align:start position:0%
+sides off so so one question so can we
+is it correct to say that it's like an
+
+ align:start position:0%
+is it correct to say that it's like an
+ 
+
+ align:start position:0%
+is it correct to say that it's like an
+anti-h harmonic
+
+ align:start position:0%
+anti-h harmonic
+ 
+
+ align:start position:0%
+anti-h harmonic
+tra um like I mean so like I throw if
+
+ align:start position:0%
+tra um like I mean so like I throw if
+ 
+
+ align:start position:0%
+tra um like I mean so like I throw if
+I'm in space and I throw a ball out it's
+
+ align:start position:0%
+I'm in space and I throw a ball out it's
+ 
+
+ align:start position:0%
+I'm in space and I throw a ball out it's
+going to come and hit me back in the
+
+ align:start position:0%
+going to come and hit me back in the
+ 
+
+ align:start position:0%
+going to come and hit me back in the
+head or something like that like it
+
+ align:start position:0%
+head or something like that like it
+ 
+
+ align:start position:0%
+head or something like that like it
+seems like yeah right right yeah we
+
+ align:start position:0%
+seems like yeah right right yeah we
+ 
+
+ align:start position:0%
+seems like yeah right right yeah we
+bounce back yeah um yeah actually our
+
+ align:start position:0%
+bounce back yeah um yeah actually our
+ 
+
+ align:start position:0%
+bounce back yeah um yeah actually our
+own friend Frank whech in the 80s have
+
+ align:start position:0%
+own friend Frank whech in the 80s have
+ 
+
+ align:start position:0%
+own friend Frank whech in the 80s have
+tried to use this ideas this feature to
+
+ align:start position:0%
+tried to use this ideas this feature to
+ 
+
+ align:start position:0%
+tried to use this ideas this feature to
+say maybe this actually
+
+ align:start position:0%
+say maybe this actually
+ 
+
+ align:start position:0%
+say maybe this actually
+it describes
+
+ align:start position:0%
+it describes
+ 
+
+ align:start position:0%
+it describes
+confinement because of if you put a
+
+ align:start position:0%
+confinement because of if you put a
+ 
+
+ align:start position:0%
+confinement because of if you put a
+quock there and they're confined anyway
+
+ align:start position:0%
+quock there and they're confined anyway
+ 
+
+ align:start position:0%
+quock there and they're confined anyway
+um yeah but but but keep this fistic
+
+ align:start position:0%
+um yeah but but but keep this fistic
+ 
+
+ align:start position:0%
+um yeah but but but keep this fistic
+picture in mind because many physical
+
+ align:start position:0%
+picture in mind because many physical
+ 
+
+ align:start position:0%
+picture in mind because many physical
+problems actually if you think of in
+
+ align:start position:0%
+problems actually if you think of in
+ 
+
+ align:start position:0%
+problems actually if you think of in
+terms of this picture become very
+
+ align:start position:0%
+terms of this picture become very
+ 
+
+ align:start position:0%
+terms of this picture become very
+intuitive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay um and
+
+ align:start position:0%
+okay okay um and
+ 
+
+ align:start position:0%
+okay okay um and
+often so you say this is a you say this
+
+ align:start position:0%
+often so you say this is a you say this
+ 
+
+ align:start position:0%
+often so you say this is a you say this
+is the exception for the light Ray but
+
+ align:start position:0%
+is the exception for the light Ray but
+ 
+
+ align:start position:0%
+is the exception for the light Ray but
+often we we impose the reflecting
+
+ align:start position:0%
+often we we impose the reflecting
+ 
+
+ align:start position:0%
+often we we impose the reflecting
+boundary condition on the light Ray and
+
+ align:start position:0%
+boundary condition on the light Ray and
+ 
+
+ align:start position:0%
+boundary condition on the light Ray and
+for the light Ray this is also like a
+
+ align:start position:0%
+for the light Ray this is also like a
+ 
+
+ align:start position:0%
+for the light Ray this is also like a
+box and and you go to the boundary and
+
+ align:start position:0%
+box and and you go to the boundary and
+ 
+
+ align:start position:0%
+box and and you go to the boundary and
+you bounce back Etc
+
+ align:start position:0%
+you bounce back Etc
+ 
+
+ align:start position:0%
+you bounce back Etc
+okay so now let me again just say it but
+
+ align:start position:0%
+okay so now let me again just say it but
+ 
+
+ align:start position:0%
+okay so now let me again just say it but
+you should go back to check
+
+ align:start position:0%
+you should go back to check
+ 
+
+ align:start position:0%
+you should go back to check
+yourself now by looking at the relation
+
+ align:start position:0%
+yourself now by looking at the relation
+ 
+
+ align:start position:0%
+yourself now by looking at the relation
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+here so here is a specific relation
+
+ align:start position:0%
+here so here is a specific relation
+ 
+
+ align:start position:0%
+here so here is a specific relation
+between R and
+
+ align:start position:0%
+between R and
+ 
+
+ align:start position:0%
+between R and
+x and here is a specific relation
+
+ align:start position:0%
+x and here is a specific relation
+ 
+
+ align:start position:0%
+x and here is a specific relation
+between the between this X and this Tow
+
+ align:start position:0%
+between the between this X and this Tow
+ 
+
+ align:start position:0%
+between the between this X and this Tow
+and the this R you can find the relation
+
+ align:start position:0%
+and the this R you can find the relation
+ 
+
+ align:start position:0%
+and the this R you can find the relation
+between the this P coordinate and this
+
+ align:start position:0%
+between the this P coordinate and this
+ 
+
+ align:start position:0%
+between the this P coordinate and this
+global
+
+ align:start position:0%
+global
+ 
+
+ align:start position:0%
+global
+coordinates okay I use a little bit
+
+ align:start position:0%
+coordinates okay I use a little bit
+ 
+
+ align:start position:0%
+coordinates okay I use a little bit
+effort and then you can show
+
+ align:start position:0%
+effort and then you can show
+ 
+
+ align:start position:0%
+effort and then you can show
+yourself then you can show yourself let
+
+ align:start position:0%
+yourself then you can show yourself let
+ 
+
+ align:start position:0%
+yourself then you can show yourself let
+me just draw the
+
+ align:start position:0%
+me just draw the
+ 
+
+ align:start position:0%
+me just draw the
+picture again let me using the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture you can show that the p pth
+
+ align:start position:0%
+picture you can show that the p pth
+ 
+
+ align:start position:0%
+picture you can show that the p pth
+cover a wedge say at Le in this
+
+ align:start position:0%
+cover a wedge say at Le in this
+ 
+
+ align:start position:0%
+cover a wedge say at Le in this
+cross-section the P patch cover a
+
+ align:start position:0%
+cross-section the P patch cover a
+ 
+
+ align:start position:0%
+cross-section the P patch cover a
+cross-section uh uh of This Global ideas
+
+ align:start position:0%
+cross-section uh uh of This Global ideas
+ 
+
+ align:start position:0%
+cross-section uh uh of This Global ideas
+okay so so here it's
+
+ align:start position:0%
+okay so so here it's
+ 
+
+ align:start position:0%
+okay so so here it's
+tall equal to minus pi and here is t
+
+ align:start position:0%
+tall equal to minus pi and here is t
+ 
+
+ align:start position:0%
+tall equal to minus pi and here is t
+equal to plus pi and here say tal to
+
+ align:start position:0%
+equal to plus pi and here say tal to
+ 
+
+ align:start position:0%
+equal to plus pi and here say tal to
+zero and uh and in the in this P patch
+
+ align:start position:0%
+zero and uh and in the in this P patch
+ 
+
+ align:start position:0%
+zero and uh and in the in this P patch
+and then this n become IAL to zero and
+
+ align:start position:0%
+and then this n become IAL to zero and
+ 
+
+ align:start position:0%
+and then this n become IAL to zero and
+tal to minus
+
+ align:start position:0%
+tal to minus
+ 
+
+ align:start position:0%
+tal to minus
+infinity and this nine become I equal to
+
+ align:start position:0%
+infinity and this nine become I equal to
+ 
+
+ align:start position:0%
+infinity and this nine become I equal to
+Z and t plus
+
+ align:start position:0%
+Z and t plus
+ 
+
+ align:start position:0%
+Z and t plus
+infinity okay plus
+
+ align:start position:0%
+infinity okay plus
+ 
+
+ align:start position:0%
+infinity okay plus
+infinity and uh so so the time
+
+ align:start position:0%
+infinity and uh so so the time
+ 
+
+ align:start position:0%
+infinity and uh so so the time
+essentially goes around like
+
+ align:start position:0%
+essentially goes around like
+ 
+
+ align:start position:0%
+essentially goes around like
+this time go around like this and and
+
+ align:start position:0%
+this time go around like this and and
+ 
+
+ align:start position:0%
+this time go around like this and and
+and this line corresponding to t equal
+
+ align:start position:0%
+and this line corresponding to t equal
+ 
+
+ align:start position:0%
+and this line corresponding to t equal
+to Z okay so tal Z and tal to Z
+
+ align:start position:0%
+to Z okay so tal Z and tal to Z
+ 
+
+ align:start position:0%
+to Z okay so tal Z and tal to Z
+coincides and then you go to minus
+
+ align:start position:0%
+coincides and then you go to minus
+ 
+
+ align:start position:0%
+coincides and then you go to minus
+infinity Rota to that
+
+ align:start position:0%
+infinity Rota to that
+ 
+
+ align:start position:0%
+infinity Rota to that
+so so and the constant R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface so this is the constant R
+
+ align:start position:0%
+surface so this is the constant R
+ 
+
+ align:start position:0%
+surface so this is the constant R
+surface in the P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinate goes like this so the time
+
+ align:start position:0%
+coordinate goes like this so the time
+ 
+
+ align:start position:0%
+coordinate goes like this so the time
+goes up okay and you can check yourself
+
+ align:start position:0%
+goes up okay and you can check yourself
+ 
+
+ align:start position:0%
+goes up okay and you can check yourself
+uh just by working out the relation
+
+ align:start position:0%
+uh just by working out the relation
+ 
+
+ align:start position:0%
+uh just by working out the relation
+between those coordinates through the
+
+ align:start position:0%
+between those coordinates through the
+ 
+
+ align:start position:0%
+between those coordinates through the
+a uh you mean this is uh WRA on the CER
+
+ align:start position:0%
+a uh you mean this is uh WRA on the CER
+ 
+
+ align:start position:0%
+a uh you mean this is uh WRA on the CER
+no no no no I'm just saying uh which
+
+ align:start position:0%
+no no no no I'm just saying uh which
+ 
+
+ align:start position:0%
+no no no no I'm just saying uh which
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+picture just within this crosssection I
+
+ align:start position:0%
+picture just within this crosssection I
+ 
+
+ align:start position:0%
+picture just within this crosssection I
+can look at this crosssection I see how
+
+ align:start position:0%
+can look at this crosssection I see how
+ 
+
+ align:start position:0%
+can look at this crosssection I see how
+this translate into P coordinates and
+
+ align:start position:0%
+this translate into P coordinates and
+ 
+
+ align:start position:0%
+this translate into P coordinates and
+that's what's happening a p coordinate
+
+ align:start position:0%
+that's what's happening a p coordinate
+ 
+
+ align:start position:0%
+that's what's happening a p coordinate
+cover this part
+
+ align:start position:0%
+cover this part
+ 
+
+ align:start position:0%
+cover this part
+okay okay cover this part I can also
+
+ align:start position:0%
+okay okay cover this part I can also
+ 
+
+ align:start position:0%
+okay okay cover this part I can also
+draw a more fancy picture
+
+ align:start position:0%
+draw a more fancy picture
+ 
+
+ align:start position:0%
+draw a more fancy picture
+here then then roughly uh what you can
+
+ align:start position:0%
+here then then roughly uh what you can
+ 
+
+ align:start position:0%
+here then then roughly uh what you can
+show is that the in this General
+
+ align:start position:0%
+show is that the in this General
+ 
+
+ align:start position:0%
+show is that the in this General
+picture is said the P patch cover
+
+ align:start position:0%
+picture is said the P patch cover
+ 
+
+ align:start position:0%
+picture is said the P patch cover
+something like this
+
+ align:start position:0%
+something like this
+ 
+
+ align:start position:0%
+something like this
+okay and the region between these two
+
+ align:start position:0%
+okay and the region between these two
+ 
+
+ align:start position:0%
+okay and the region between these two
+lines so so this is a spatial Infinity
+
+ align:start position:0%
+lines so so this is a spatial Infinity
+ 
+
+ align:start position:0%
+lines so so this is a spatial Infinity
+of the in in the in this P
+
+ align:start position:0%
+of the in in the in this P
+ 
+
+ align:start position:0%
+of the in in the in this P
+patch the boundary is minkovski space
+
+ align:start position:0%
+patch the boundary is minkovski space
+ 
+
+ align:start position:0%
+patch the boundary is minkovski space
+time so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so you see so the p p cover like that
+
+ align:start position:0%
+so so you see so the p p cover like that
+ 
+
+ align:start position:0%
+so so you see so the p p cover like that
+and and then and then this is a spal
+
+ align:start position:0%
+and and then and then this is a spal
+ 
+
+ align:start position:0%
+and and then and then this is a spal
+Infinity of the movi space time this is
+
+ align:start position:0%
+Infinity of the movi space time this is
+ 
+
+ align:start position:0%
+Infinity of the movi space time this is
+the time infinity and time P movi space
+
+ align:start position:0%
+the time infinity and time P movi space
+ 
+
+ align:start position:0%
+the time infinity and time P movi space
+time okay so so you I urge you to do it
+
+ align:start position:0%
+time okay so so you I urge you to do it
+ 
+
+ align:start position:0%
+time okay so so you I urge you to do it
+yourself because this kind of thing uh
+
+ align:start position:0%
+yourself because this kind of thing uh
+ 
+
+ align:start position:0%
+yourself because this kind of thing uh
+you really have to work through yourself
+
+ align:start position:0%
+you really have to work through yourself
+ 
+
+ align:start position:0%
+you really have to work through yourself
+to to have intuitive feeling for it but
+
+ align:start position:0%
+to to have intuitive feeling for it but
+ 
+
+ align:start position:0%
+to to have intuitive feeling for it but
+this is a
+
+ align:start position:0%
+this is a
+ 
+
+ align:start position:0%
+this is a
+picture once you work out yourself you
+
+ align:start position:0%
+picture once you work out yourself you
+ 
+
+ align:start position:0%
+picture once you work out yourself you
+compare with my picture and then you
+
+ align:start position:0%
+compare with my picture and then you
+ 
+
+ align:start position:0%
+compare with my picture and then you
+will understand
+
+ align:start position:0%
+will understand
+ 
+
+ align:start position:0%
+will understand
+okay so I we stop here
+
+ align:start position:0%
+okay so I we stop here
+ 
+
+ align:start position:0%
+okay so I we stop here
+today so so in some sense yeah let me
+
+ align:start position:0%
+today so so in some sense yeah let me
+ 
+
+ align:start position:0%
+today so so in some sense yeah let me
+just say one one more sentence this
+
+ align:start position:0%
+just say one one more sentence this
+ 
+
+ align:start position:0%
+just say one one more sentence this
+extended ideas contain infinite copies
+
+ align:start position:0%
+extended ideas contain infinite copies
+ 
+
+ align:start position:0%
+extended ideas contain infinite copies
+of this P patch
+
+ align:start position:0%
+of this P patch
+ 
+
+ align:start position:0%
+of this P patch
+okay
\ No newline at end of file
diff --git a/466icY9MQp4.txt b/466icY9MQp4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..52800aaed7c19fc8b9efee688908b1766ee490e5
--- /dev/null
+++ b/466icY9MQp4.txt
@@ -0,0 +1,8139 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu I wanted to say a few things
+
+ align:start position:0%
+ocw.mit.edu I wanted to say a few things
+ 
+
+ align:start position:0%
+ocw.mit.edu I wanted to say a few things
+about the end
+
+ align:start position:0%
+about the end
+ 
+
+ align:start position:0%
+about the end
+of what was meant to be the the end of
+
+ align:start position:0%
+of what was meant to be the the end of
+ 
+
+ align:start position:0%
+of what was meant to be the the end of
+class 6
+
+ align:start position:0%
+class 6
+ 
+
+ align:start position:0%
+class 6
+uh it's chapter 7 in the book
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but we
+
+ align:start position:0%
+uh but we
+ 
+
+ align:start position:0%
+uh but we
+were it was meant to be a overview of
+
+ align:start position:0%
+were it was meant to be a overview of
+ 
+
+ align:start position:0%
+were it was meant to be a overview of
+the forbrain and I
+
+ align:start position:0%
+the forbrain and I
+ 
+
+ align:start position:0%
+the forbrain and I
+was at the end here I was talking about
+
+ align:start position:0%
+was at the end here I was talking about
+ 
+
+ align:start position:0%
+was at the end here I was talking about
+the well we got to through the limic
+
+ align:start position:0%
+the well we got to through the limic
+ 
+
+ align:start position:0%
+the well we got to through the limic
+system and then I wanted to say a little
+
+ align:start position:0%
+system and then I wanted to say a little
+ 
+
+ align:start position:0%
+system and then I wanted to say a little
+bit about the neocortex
+
+ align:start position:0%
+bit about the neocortex
+ 
+
+ align:start position:0%
+bit about the neocortex
+so this picture here just gives a little
+
+ align:start position:0%
+so this picture here just gives a little
+ 
+
+ align:start position:0%
+so this picture here just gives a little
+outline of meant to show the addition of
+
+ align:start position:0%
+outline of meant to show the addition of
+ 
+
+ align:start position:0%
+outline of meant to show the addition of
+neocortex
+
+ align:start position:0%
+neocortex
+ 
+
+ align:start position:0%
+neocortex
+and it was a slide where I'm showing
+
+ align:start position:0%
+and it was a slide where I'm showing
+ 
+
+ align:start position:0%
+and it was a slide where I'm showing
+that the lyic system is one way to
+
+ align:start position:0%
+that the lyic system is one way to
+ 
+
+ align:start position:0%
+that the lyic system is one way to
+define It Is by connections to the
+
+ align:start position:0%
+define It Is by connections to the
+ 
+
+ align:start position:0%
+define It Is by connections to the
+hypothalamus but now when we get to
+
+ align:start position:0%
+hypothalamus but now when we get to
+ 
+
+ align:start position:0%
+hypothalamus but now when we get to
+neocortex the first topic that we always
+
+ align:start position:0%
+neocortex the first topic that we always
+ 
+
+ align:start position:0%
+neocortex the first topic that we always
+think of neocortex is so important in
+
+ align:start position:0%
+think of neocortex is so important in
+ 
+
+ align:start position:0%
+think of neocortex is so important in
+learning and I want to point out that it
+
+ align:start position:0%
+learning and I want to point out that it
+ 
+
+ align:start position:0%
+learning and I want to point out that it
+was in the early olda factory system
+
+ align:start position:0%
+was in the early olda factory system
+ 
+
+ align:start position:0%
+was in the early olda factory system
+long before there was any
+
+ align:start position:0%
+long before there was any
+ 
+
+ align:start position:0%
+long before there was any
+neocortex there evolved these two types
+
+ align:start position:0%
+neocortex there evolved these two types
+ 
+
+ align:start position:0%
+neocortex there evolved these two types
+two types of learning that have renamed
+
+ align:start position:0%
+two types of learning that have renamed
+ 
+
+ align:start position:0%
+two types of learning that have renamed
+the two major types of learning that do
+
+ align:start position:0%
+the two major types of learning that do
+ 
+
+ align:start position:0%
+the two major types of learning that do
+involve neocortex in uh in
+
+ align:start position:0%
+involve neocortex in uh in
+ 
+
+ align:start position:0%
+involve neocortex in uh in
+mammals including human beings two
+
+ align:start position:0%
+mammals including human beings two
+ 
+
+ align:start position:0%
+mammals including human beings two
+different kinds of learning so what are
+
+ align:start position:0%
+different kinds of learning so what are
+ 
+
+ align:start position:0%
+different kinds of learning so what are
+these two different kinds of learning
+
+ align:start position:0%
+these two different kinds of learning
+ 
+
+ align:start position:0%
+these two different kinds of learning
+and I'm talking
+
+ align:start position:0%
+and I'm talking
+ 
+
+ align:start position:0%
+and I'm talking
+about you can think of them in terms of
+
+ align:start position:0%
+about you can think of them in terms of
+ 
+
+ align:start position:0%
+about you can think of them in terms of
+the structures that are involved or you
+
+ align:start position:0%
+the structures that are involved or you
+ 
+
+ align:start position:0%
+the structures that are involved or you
+can give them a name the types of
+
+ align:start position:0%
+can give them a name the types of
+ 
+
+ align:start position:0%
+can give them a name the types of
+learning you know what I'm talking about
+
+ align:start position:0%
+learning you know what I'm talking about
+ 
+
+ align:start position:0%
+learning you know what I'm talking about
+any of
+
+ align:start position:0%
+any of
+ 
+
+ align:start position:0%
+any of
+you remember I talked about the early
+
+ align:start position:0%
+you remember I talked about the early
+ 
+
+ align:start position:0%
+you remember I talked about the early
+evolution of old faction and how the
+
+ align:start position:0%
+evolution of old faction and how the
+ 
+
+ align:start position:0%
+evolution of old faction and how the
+connections were with this ventral most
+
+ align:start position:0%
+connections were with this ventral most
+ 
+
+ align:start position:0%
+connections were with this ventral most
+part of the striatum Corpus striatum and
+
+ align:start position:0%
+part of the striatum Corpus striatum and
+ 
+
+ align:start position:0%
+part of the striatum Corpus striatum and
+I said that the important thing about
+
+ align:start position:0%
+I said that the important thing about
+ 
+
+ align:start position:0%
+I said that the important thing about
+those connections was that they were
+
+ align:start position:0%
+those connections was that they were
+ 
+
+ align:start position:0%
+those connections was that they were
+plastic they could change that's how
+
+ align:start position:0%
+plastic they could change that's how
+ 
+
+ align:start position:0%
+plastic they could change that's how
+animals learn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to to like certain uh smells and not
+
+ align:start position:0%
+to to like certain uh smells and not
+ 
+
+ align:start position:0%
+to to like certain uh smells and not
+like others they identified objects that
+
+ align:start position:0%
+like others they identified objects that
+ 
+
+ align:start position:0%
+like others they identified objects that
+way but they did all another thing too
+
+ align:start position:0%
+way but they did all another thing too
+ 
+
+ align:start position:0%
+way but they did all another thing too
+uh different regions they went to
+
+ align:start position:0%
+uh different regions they went to
+ 
+
+ align:start position:0%
+uh different regions they went to
+smelled
+
+ align:start position:0%
+smelled
+ 
+
+ align:start position:0%
+smelled
+different so without any Vision there
+
+ align:start position:0%
+different so without any Vision there
+ 
+
+ align:start position:0%
+different so without any Vision there
+were two kinds of learning that were
+
+ align:start position:0%
+were two kinds of learning that were
+ 
+
+ align:start position:0%
+were two kinds of learning that were
+possible places
+
+ align:start position:0%
+possible places
+ 
+
+ align:start position:0%
+possible places
+that were good or bad for them according
+
+ align:start position:0%
+that were good or bad for them according
+ 
+
+ align:start position:0%
+that were good or bad for them according
+to the feedback they get and the objects
+
+ align:start position:0%
+to the feedback they get and the objects
+ 
+
+ align:start position:0%
+to the feedback they get and the objects
+in those places that could be good or
+
+ align:start position:0%
+in those places that could be good or
+ 
+
+ align:start position:0%
+in those places that could be good or
+bad to eat for example they also of
+
+ align:start position:0%
+bad to eat for example they also of
+ 
+
+ align:start position:0%
+bad to eat for example they also of
+course could smell predators and that's
+
+ align:start position:0%
+course could smell predators and that's
+ 
+
+ align:start position:0%
+course could smell predators and that's
+still true in many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mammals okay so this is the way I
+
+ align:start position:0%
+mammals okay so this is the way I
+ 
+
+ align:start position:0%
+mammals okay so this is the way I
+summarized it learned object preferences
+
+ align:start position:0%
+summarized it learned object preferences
+ 
+
+ align:start position:0%
+summarized it learned object preferences
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+identification of objects according to
+
+ align:start position:0%
+identification of objects according to
+ 
+
+ align:start position:0%
+identification of objects according to
+whether they're good or bad and Place
+
+ align:start position:0%
+whether they're good or bad and Place
+ 
+
+ align:start position:0%
+whether they're good or bad and Place
+Learning identification and memory of
+
+ align:start position:0%
+Learning identification and memory of
+ 
+
+ align:start position:0%
+Learning identification and memory of
+good places and bad
+
+ align:start position:0%
+good places and bad
+ 
+
+ align:start position:0%
+good places and bad
+places the first one is stodal dependent
+
+ align:start position:0%
+places the first one is stodal dependent
+ 
+
+ align:start position:0%
+places the first one is stodal dependent
+and that remains true even though the
+
+ align:start position:0%
+and that remains true even though the
+ 
+
+ align:start position:0%
+and that remains true even though the
+habits formed aren't dependent on so
+
+ align:start position:0%
+habits formed aren't dependent on so
+ 
+
+ align:start position:0%
+habits formed aren't dependent on so
+much on Al faction in in primates
+
+ align:start position:0%
+much on Al faction in in primates
+ 
+
+ align:start position:0%
+much on Al faction in in primates
+they're mostly dependent on the other
+
+ align:start position:0%
+they're mostly dependent on the other
+ 
+
+ align:start position:0%
+they're mostly dependent on the other
+senses but Al faction is still important
+
+ align:start position:0%
+senses but Al faction is still important
+ 
+
+ align:start position:0%
+senses but Al faction is still important
+the other is Place Learning and that has
+
+ align:start position:0%
+the other is Place Learning and that has
+ 
+
+ align:start position:0%
+the other is Place Learning and that has
+become critical for what humans usually
+
+ align:start position:0%
+become critical for what humans usually
+ 
+
+ align:start position:0%
+become critical for what humans usually
+think of when we think of memory
+
+ align:start position:0%
+think of when we think of memory
+ 
+
+ align:start position:0%
+think of when we think of memory
+long-term memory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formation okay and that will be a theme
+
+ align:start position:0%
+formation okay and that will be a theme
+ 
+
+ align:start position:0%
+formation okay and that will be a theme
+uh that will recur in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class and what is the part of the brain
+
+ align:start position:0%
+class and what is the part of the brain
+ 
+
+ align:start position:0%
+class and what is the part of the brain
+involved here we always think of
+
+ align:start position:0%
+involved here we always think of
+ 
+
+ align:start position:0%
+involved here we always think of
+hippocampus but in many animals long
+
+ align:start position:0%
+hippocampus but in many animals long
+ 
+
+ align:start position:0%
+hippocampus but in many animals long
+before you could really identify
+
+ align:start position:0%
+before you could really identify
+ 
+
+ align:start position:0%
+before you could really identify
+something that looked like a a seahorse
+
+ align:start position:0%
+something that looked like a a seahorse
+ 
+
+ align:start position:0%
+something that looked like a a seahorse
+a HP campus it was part of the P it was
+
+ align:start position:0%
+a HP campus it was part of the P it was
+ 
+
+ align:start position:0%
+a HP campus it was part of the P it was
+the medial p okay and in a in a picture
+
+ align:start position:0%
+the medial p okay and in a in a picture
+ 
+
+ align:start position:0%
+the medial p okay and in a in a picture
+like this it's this part
+
+ align:start position:0%
+like this it's this part
+ 
+
+ align:start position:0%
+like this it's this part
+here that's meant to be medial it's a
+
+ align:start position:0%
+here that's meant to be medial it's a
+ 
+
+ align:start position:0%
+here that's meant to be medial it's a
+little hard to show medial and lateral
+
+ align:start position:0%
+little hard to show medial and lateral
+ 
+
+ align:start position:0%
+little hard to show medial and lateral
+in a picture like this but it's part of
+
+ align:start position:0%
+in a picture like this but it's part of
+ 
+
+ align:start position:0%
+in a picture like this but it's part of
+the lyic system connected to
+
+ align:start position:0%
+the lyic system connected to
+ 
+
+ align:start position:0%
+the lyic system connected to
+hypothalamus and we're going to discuss
+
+ align:start position:0%
+hypothalamus and we're going to discuss
+ 
+
+ align:start position:0%
+hypothalamus and we're going to discuss
+later why that came to be true how that
+
+ align:start position:0%
+later why that came to be true how that
+ 
+
+ align:start position:0%
+later why that came to be true how that
+evolved there are good reasons why we
+
+ align:start position:0%
+evolved there are good reasons why we
+ 
+
+ align:start position:0%
+evolved there are good reasons why we
+became so dependent on parts of the
+
+ align:start position:0%
+became so dependent on parts of the
+ 
+
+ align:start position:0%
+became so dependent on parts of the
+limic system for our
+
+ align:start position:0%
+limic system for our
+ 
+
+ align:start position:0%
+limic system for our
+memories
+
+ align:start position:0%
+memories
+ 
+
+ align:start position:0%
+memories
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so now with neoc cortic
+
+ align:start position:0%
+right so now with neoc cortic
+ 
+
+ align:start position:0%
+right so now with neoc cortic
+expansion there were new sensory
+
+ align:start position:0%
+expansion there were new sensory
+ 
+
+ align:start position:0%
+expansion there were new sensory
+Pathways that became prominent they were
+
+ align:start position:0%
+Pathways that became prominent they were
+ 
+
+ align:start position:0%
+Pathways that became prominent they were
+rapid more rapidly conducting than the
+
+ align:start position:0%
+rapid more rapidly conducting than the
+ 
+
+ align:start position:0%
+rapid more rapidly conducting than the
+spinal reticular Pathways and the
+
+ align:start position:0%
+spinal reticular Pathways and the
+ 
+
+ align:start position:0%
+spinal reticular Pathways and the
+spinothalamic pathways and sending
+
+ align:start position:0%
+spinothalamic pathways and sending
+ 
+
+ align:start position:0%
+spinothalamic pathways and sending
+information to the to the
+
+ align:start position:0%
+information to the to the
+ 
+
+ align:start position:0%
+information to the to the
+Forin now we're talking mainly about
+
+ align:start position:0%
+Forin now we're talking mainly about
+ 
+
+ align:start position:0%
+Forin now we're talking mainly about
+Pathways to
+
+ align:start position:0%
+Pathways to
+ 
+
+ align:start position:0%
+Pathways to
+neocortex okay
+
+ align:start position:0%
+neocortex okay
+ 
+
+ align:start position:0%
+neocortex okay
+and here I'm just showing the addition
+
+ align:start position:0%
+and here I'm just showing the addition
+ 
+
+ align:start position:0%
+and here I'm just showing the addition
+of Cortex and then here's I've altered
+
+ align:start position:0%
+of Cortex and then here's I've altered
+ 
+
+ align:start position:0%
+of Cortex and then here's I've altered
+this diagram here to show neocortex up
+
+ align:start position:0%
+this diagram here to show neocortex up
+ 
+
+ align:start position:0%
+this diagram here to show neocortex up
+here there's the medial pallum so I made
+
+ align:start position:0%
+here there's the medial pallum so I made
+ 
+
+ align:start position:0%
+here there's the medial pallum so I made
+it look like a
+
+ align:start position:0%
+it look like a
+ 
+
+ align:start position:0%
+it look like a
+hippocampus okay so that's part of the
+
+ align:start position:0%
+hippocampus okay so that's part of the
+ 
+
+ align:start position:0%
+hippocampus okay so that's part of the
+limic system which is all of this in the
+
+ align:start position:0%
+limic system which is all of this in the
+ 
+
+ align:start position:0%
+limic system which is all of this in the
+diagram and this is really also lyic but
+
+ align:start position:0%
+diagram and this is really also lyic but
+ 
+
+ align:start position:0%
+diagram and this is really also lyic but
+it's old factory the factory parts of
+
+ align:start position:0%
+it's old factory the factory parts of
+ 
+
+ align:start position:0%
+it's old factory the factory parts of
+the lyic system they're lyic because
+
+ align:start position:0%
+the lyic system they're lyic because
+ 
+
+ align:start position:0%
+the lyic system they're lyic because
+they're closely connected with
+
+ align:start position:0%
+they're closely connected with
+ 
+
+ align:start position:0%
+they're closely connected with
+hypothalamus in fact many animals
+
+ align:start position:0%
+hypothalamus in fact many animals
+ 
+
+ align:start position:0%
+hypothalamus in fact many animals
+actually have direct ol factory
+
+ align:start position:0%
+actually have direct ol factory
+ 
+
+ align:start position:0%
+actually have direct ol factory
+connections to the
+
+ align:start position:0%
+connections to the
+ 
+
+ align:start position:0%
+connections to the
+hypothalamus all right so now the two
+
+ align:start position:0%
+hypothalamus all right so now the two
+ 
+
+ align:start position:0%
+hypothalamus all right so now the two
+Pathways I don't know why but students
+
+ align:start position:0%
+Pathways I don't know why but students
+ 
+
+ align:start position:0%
+Pathways I don't know why but students
+always find it difficult to to memorize
+
+ align:start position:0%
+always find it difficult to to memorize
+ 
+
+ align:start position:0%
+always find it difficult to to memorize
+this we talked about spinal reticular we
+
+ align:start position:0%
+this we talked about spinal reticular we
+ 
+
+ align:start position:0%
+this we talked about spinal reticular we
+talked about spinal tham now here is
+
+ align:start position:0%
+talked about spinal tham now here is
+ 
+
+ align:start position:0%
+talked about spinal tham now here is
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+system that has a number of branches but
+
+ align:start position:0%
+system that has a number of branches but
+ 
+
+ align:start position:0%
+system that has a number of branches but
+it's it many more of its axons go all
+
+ align:start position:0%
+it's it many more of its axons go all
+ 
+
+ align:start position:0%
+it's it many more of its axons go all
+the way to the phons so it's a pathway
+
+ align:start position:0%
+the way to the phons so it's a pathway
+ 
+
+ align:start position:0%
+the way to the phons so it's a pathway
+to the neocortex by way of the felons
+
+ align:start position:0%
+to the neocortex by way of the felons
+ 
+
+ align:start position:0%
+to the neocortex by way of the felons
+and I've shown here that the first part
+
+ align:start position:0%
+and I've shown here that the first part
+ 
+
+ align:start position:0%
+and I've shown here that the first part
+of it is the dorsal
+
+ align:start position:0%
+of it is the dorsal
+ 
+
+ align:start position:0%
+of it is the dorsal
+columns they are actually axons of
+
+ align:start position:0%
+columns they are actually axons of
+ 
+
+ align:start position:0%
+columns they are actually axons of
+primary Sensory neurons so here they
+
+ align:start position:0%
+primary Sensory neurons so here they
+ 
+
+ align:start position:0%
+primary Sensory neurons so here they
+start out in the skin specialized in
+
+ align:start position:0%
+start out in the skin specialized in
+ 
+
+ align:start position:0%
+start out in the skin specialized in
+organs
+
+ align:start position:0%
+organs
+ 
+
+ align:start position:0%
+organs
+like Pini and cor pusle sensitive Define
+
+ align:start position:0%
+like Pini and cor pusle sensitive Define
+ 
+
+ align:start position:0%
+like Pini and cor pusle sensitive Define
+touch and things like that in the skin
+
+ align:start position:0%
+touch and things like that in the skin
+ 
+
+ align:start position:0%
+touch and things like that in the skin
+okay and there's its axon it does Branch
+
+ align:start position:0%
+okay and there's its axon it does Branch
+ 
+
+ align:start position:0%
+okay and there's its axon it does Branch
+it connects in the spinal cord too but
+
+ align:start position:0%
+it connects in the spinal cord too but
+ 
+
+ align:start position:0%
+it connects in the spinal cord too but
+it ascends all the way to the top of the
+
+ align:start position:0%
+it ascends all the way to the top of the
+ 
+
+ align:start position:0%
+it ascends all the way to the top of the
+spinal cord and some Anatomy texts say
+
+ align:start position:0%
+spinal cord and some Anatomy texts say
+ 
+
+ align:start position:0%
+spinal cord and some Anatomy texts say
+coddle end of the hbr it's a little bit
+
+ align:start position:0%
+coddle end of the hbr it's a little bit
+ 
+
+ align:start position:0%
+coddle end of the hbr it's a little bit
+arbitrary where you mark that Division I
+
+ align:start position:0%
+arbitrary where you mark that Division I
+ 
+
+ align:start position:0%
+arbitrary where you mark that Division I
+follow NAA he puts it at the very top of
+
+ align:start position:0%
+follow NAA he puts it at the very top of
+ 
+
+ align:start position:0%
+follow NAA he puts it at the very top of
+the spinal cord that's the dorsal column
+
+ align:start position:0%
+the spinal cord that's the dorsal column
+ 
+
+ align:start position:0%
+the spinal cord that's the dorsal column
+nuclei as you go we we'll see I'll we'll
+
+ align:start position:0%
+nuclei as you go we we'll see I'll we'll
+ 
+
+ align:start position:0%
+nuclei as you go we we'll see I'll we'll
+be talking about that very soon you'll
+
+ align:start position:0%
+be talking about that very soon you'll
+ 
+
+ align:start position:0%
+be talking about that very soon you'll
+see the call
+
+ align:start position:0%
+see the call
+ 
+
+ align:start position:0%
+see the call
+nuclea okay representing all different
+
+ align:start position:0%
+nuclea okay representing all different
+ 
+
+ align:start position:0%
+nuclea okay representing all different
+parts of the body except the face but in
+
+ align:start position:0%
+parts of the body except the face but in
+ 
+
+ align:start position:0%
+parts of the body except the face but in
+fact the face is represented there too
+
+ align:start position:0%
+fact the face is represented there too
+ 
+
+ align:start position:0%
+fact the face is represented there too
+and I will show you how okay but that is
+
+ align:start position:0%
+and I will show you how okay but that is
+ 
+
+ align:start position:0%
+and I will show you how okay but that is
+the first synaps in the pathway so it's
+
+ align:start position:0%
+the first synaps in the pathway so it's
+ 
+
+ align:start position:0%
+the first synaps in the pathway so it's
+it it conducts rapidly they tend to be
+
+ align:start position:0%
+it it conducts rapidly they tend to be
+ 
+
+ align:start position:0%
+it it conducts rapidly they tend to be
+all mated fairly large
+
+ align:start position:0%
+all mated fairly large
+ 
+
+ align:start position:0%
+all mated fairly large
+accs so this pathway now from the dorsal
+
+ align:start position:0%
+accs so this pathway now from the dorsal
+ 
+
+ align:start position:0%
+accs so this pathway now from the dorsal
+column nuclei Decat right here
+
+ align:start position:0%
+column nuclei Decat right here
+ 
+
+ align:start position:0%
+column nuclei Decat right here
+here and ascends in a pathway through
+
+ align:start position:0%
+here and ascends in a pathway through
+ 
+
+ align:start position:0%
+here and ascends in a pathway through
+the hindbrain and midbrain that we call
+
+ align:start position:0%
+the hindbrain and midbrain that we call
+ 
+
+ align:start position:0%
+the hindbrain and midbrain that we call
+the medial liscus the medial ribbon okay
+
+ align:start position:0%
+the medial liscus the medial ribbon okay
+ 
+
+ align:start position:0%
+the medial liscus the medial ribbon okay
+that goes directly to the
+
+ align:start position:0%
+that goes directly to the
+ 
+
+ align:start position:0%
+that goes directly to the
+fals there are a
+
+ align:start position:0%
+fals there are a
+ 
+
+ align:start position:0%
+fals there are a
+few branches that go into reticular
+
+ align:start position:0%
+few branches that go into reticular
+ 
+
+ align:start position:0%
+few branches that go into reticular
+formation but the main pathway goes
+
+ align:start position:0%
+formation but the main pathway goes
+ 
+
+ align:start position:0%
+formation but the main pathway goes
+right to the fs and those thalamic cells
+
+ align:start position:0%
+right to the fs and those thalamic cells
+ 
+
+ align:start position:0%
+right to the fs and those thalamic cells
+connect to cicin Tre neocortex that's
+
+ align:start position:0%
+connect to cicin Tre neocortex that's
+ 
+
+ align:start position:0%
+connect to cicin Tre neocortex that's
+how our sensory cortex gets its major
+
+ align:start position:0%
+how our sensory cortex gets its major
+ 
+
+ align:start position:0%
+how our sensory cortex gets its major
+input it does get input through the
+
+ align:start position:0%
+input it does get input through the
+ 
+
+ align:start position:0%
+input it does get input through the
+spinal thalamic pathway and even a
+
+ align:start position:0%
+spinal thalamic pathway and even a
+ 
+
+ align:start position:0%
+spinal thalamic pathway and even a
+little bit spinal reticular also but
+
+ align:start position:0%
+little bit spinal reticular also but
+ 
+
+ align:start position:0%
+little bit spinal reticular also but
+this at least for fine touch very
+
+ align:start position:0%
+this at least for fine touch very
+ 
+
+ align:start position:0%
+this at least for fine touch very
+discriminative
+
+ align:start position:0%
+discriminative
+ 
+
+ align:start position:0%
+discriminative
+touch especially the touch that we use
+
+ align:start position:0%
+touch especially the touch that we use
+ 
+
+ align:start position:0%
+touch especially the touch that we use
+when we're moving our fingers over
+
+ align:start position:0%
+when we're moving our fingers over
+ 
+
+ align:start position:0%
+when we're moving our fingers over
+something very dependent on this pathway
+
+ align:start position:0%
+something very dependent on this pathway
+ 
+
+ align:start position:0%
+something very dependent on this pathway
+all right so here is the top view it
+
+ align:start position:0%
+all right so here is the top view it
+ 
+
+ align:start position:0%
+all right so here is the top view it
+shows the same thing the primary sensory
+
+ align:start position:0%
+shows the same thing the primary sensory
+ 
+
+ align:start position:0%
+shows the same thing the primary sensory
+neuron and it's axon terminating if this
+
+ align:start position:0%
+neuron and it's axon terminating if this
+ 
+
+ align:start position:0%
+neuron and it's axon terminating if this
+is in the lumbar enlargement so let's
+
+ align:start position:0%
+is in the lumbar enlargement so let's
+ 
+
+ align:start position:0%
+is in the lumbar enlargement so let's
+say it's coming from the foot it would
+
+ align:start position:0%
+say it's coming from the foot it would
+ 
+
+ align:start position:0%
+say it's coming from the foot it would
+go to the
+
+ align:start position:0%
+go to the
+ 
+
+ align:start position:0%
+go to the
+medial dorsal column nucleus there's two
+
+ align:start position:0%
+medial dorsal column nucleus there's two
+ 
+
+ align:start position:0%
+medial dorsal column nucleus there's two
+nuclei there the medial one represents
+
+ align:start position:0%
+nuclei there the medial one represents
+ 
+
+ align:start position:0%
+nuclei there the medial one represents
+the lower body and the upper one
+
+ align:start position:0%
+the lower body and the upper one
+ 
+
+ align:start position:0%
+the lower body and the upper one
+represents the arms and chest okay and
+
+ align:start position:0%
+represents the arms and chest okay and
+ 
+
+ align:start position:0%
+represents the arms and chest okay and
+there's the axon that Decat the axon of
+
+ align:start position:0%
+there's the axon that Decat the axon of
+ 
+
+ align:start position:0%
+there's the axon that Decat the axon of
+the medial oniscus starts in the dorsal
+
+ align:start position:0%
+the medial oniscus starts in the dorsal
+ 
+
+ align:start position:0%
+the medial oniscus starts in the dorsal
+column nuclei crosses over goes of the
+
+ align:start position:0%
+column nuclei crosses over goes of the
+ 
+
+ align:start position:0%
+column nuclei crosses over goes of the
+thalamus so it's a cross
+
+ align:start position:0%
+thalamus so it's a cross
+ 
+
+ align:start position:0%
+thalamus so it's a cross
+pathway so that all evolved after the
+
+ align:start position:0%
+pathway so that all evolved after the
+ 
+
+ align:start position:0%
+pathway so that all evolved after the
+crossing
+
+ align:start position:0%
+crossing
+ 
+
+ align:start position:0%
+crossing
+evolved which was admittedly very early
+
+ align:start position:0%
+evolved which was admittedly very early
+ 
+
+ align:start position:0%
+evolved which was admittedly very early
+okay very early
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cordat but if we look at the most
+
+ align:start position:0%
+cordat but if we look at the most
+ 
+
+ align:start position:0%
+cordat but if we look at the most
+ancient ones we look at hagfish we look
+
+ align:start position:0%
+ancient ones we look at hagfish we look
+ 
+
+ align:start position:0%
+ancient ones we look at hagfish we look
+at Sea lrey they don't have any pathway
+
+ align:start position:0%
+at Sea lrey they don't have any pathway
+ 
+
+ align:start position:0%
+at Sea lrey they don't have any pathway
+resembling this in fact most mammals
+
+ align:start position:0%
+resembling this in fact most mammals
+ 
+
+ align:start position:0%
+resembling this in fact most mammals
+don't have much of a pathway that's like
+
+ align:start position:0%
+don't have much of a pathway that's like
+ 
+
+ align:start position:0%
+don't have much of a pathway that's like
+this one it's the mammals this becomes
+
+ align:start position:0%
+this one it's the mammals this becomes
+ 
+
+ align:start position:0%
+this one it's the mammals this becomes
+prominent and other Advanced vertebrates
+
+ align:start position:0%
+prominent and other Advanced vertebrates
+ 
+
+ align:start position:0%
+prominent and other Advanced vertebrates
+like birds
+
+ align:start position:0%
+like birds
+ 
+
+ align:start position:0%
+like birds
+okay and now along with that you get
+
+ align:start position:0%
+okay and now along with that you get
+ 
+
+ align:start position:0%
+okay and now along with that you get
+descending Pathways coming down from
+
+ align:start position:0%
+descending Pathways coming down from
+ 
+
+ align:start position:0%
+descending Pathways coming down from
+those ca regions and one of the C
+
+ align:start position:0%
+those ca regions and one of the C
+ 
+
+ align:start position:0%
+those ca regions and one of the C
+sensory CA sensory regions became more
+
+ align:start position:0%
+sensory CA sensory regions became more
+ 
+
+ align:start position:0%
+sensory CA sensory regions became more
+specialized for controlling fine
+
+ align:start position:0%
+specialized for controlling fine
+ 
+
+ align:start position:0%
+specialized for controlling fine
+movement that was the motor
+
+ align:start position:0%
+movement that was the motor
+ 
+
+ align:start position:0%
+movement that was the motor
+CeX okay so I'm showing it here the side
+
+ align:start position:0%
+CeX okay so I'm showing it here the side
+ 
+
+ align:start position:0%
+CeX okay so I'm showing it here the side
+view and I'm depi two neurons for a good
+
+ align:start position:0%
+view and I'm depi two neurons for a good
+ 
+
+ align:start position:0%
+view and I'm depi two neurons for a good
+reason because I want to point out that
+
+ align:start position:0%
+reason because I want to point out that
+ 
+
+ align:start position:0%
+reason because I want to point out that
+the SM sensory what we call sensory
+
+ align:start position:0%
+the SM sensory what we call sensory
+ 
+
+ align:start position:0%
+the SM sensory what we call sensory
+cortex and motor cortex both have
+
+ align:start position:0%
+cortex and motor cortex both have
+ 
+
+ align:start position:0%
+cortex and motor cortex both have
+Pathways to the spinal
+
+ align:start position:0%
+Pathways to the spinal
+ 
+
+ align:start position:0%
+Pathways to the spinal
+cord here's the one you're probably most
+
+ align:start position:0%
+cord here's the one you're probably most
+ 
+
+ align:start position:0%
+cord here's the one you're probably most
+familiar with comes from motor cortex it
+
+ align:start position:0%
+familiar with comes from motor cortex it
+ 
+
+ align:start position:0%
+familiar with comes from motor cortex it
+does have some not note that there is
+
+ align:start position:0%
+does have some not note that there is
+ 
+
+ align:start position:0%
+does have some not note that there is
+branches to the striatum to the thalamus
+
+ align:start position:0%
+branches to the striatum to the thalamus
+ 
+
+ align:start position:0%
+branches to the striatum to the thalamus
+to the midbrain to the hindbrain
+
+ align:start position:0%
+to the midbrain to the hindbrain
+ 
+
+ align:start position:0%
+to the midbrain to the hindbrain
+especially to The Ponds but it goes all
+
+ align:start position:0%
+especially to The Ponds but it goes all
+ 
+
+ align:start position:0%
+especially to The Ponds but it goes all
+the way down to the spinal cord where
+
+ align:start position:0%
+the way down to the spinal cord where
+ 
+
+ align:start position:0%
+the way down to the spinal cord where
+most of the axons in on interneurons in
+
+ align:start position:0%
+most of the axons in on interneurons in
+ 
+
+ align:start position:0%
+most of the axons in on interneurons in
+the ventral horn okay a few of them as I
+
+ align:start position:0%
+the ventral horn okay a few of them as I
+ 
+
+ align:start position:0%
+the ventral horn okay a few of them as I
+show here go directly the motor neurons
+
+ align:start position:0%
+show here go directly the motor neurons
+ 
+
+ align:start position:0%
+show here go directly the motor neurons
+now this The Meta sensory cortex has
+
+ align:start position:0%
+now this The Meta sensory cortex has
+ 
+
+ align:start position:0%
+now this The Meta sensory cortex has
+similarly descending Pathways all the
+
+ align:start position:0%
+similarly descending Pathways all the
+ 
+
+ align:start position:0%
+similarly descending Pathways all the
+way to the spinal cord but these
+
+ align:start position:0%
+way to the spinal cord but these
+ 
+
+ align:start position:0%
+way to the spinal cord but these
+terminate in the dorsal horn okay part
+
+ align:start position:0%
+terminate in the dorsal horn okay part
+ 
+
+ align:start position:0%
+terminate in the dorsal horn okay part
+of the spinal cord that gets sensory
+
+ align:start position:0%
+of the spinal cord that gets sensory
+ 
+
+ align:start position:0%
+of the spinal cord that gets sensory
+input from the dorsal Roots we'll show
+
+ align:start position:0%
+input from the dorsal Roots we'll show
+ 
+
+ align:start position:0%
+input from the dorsal Roots we'll show
+the adult we'll be talking a little more
+
+ align:start position:0%
+the adult we'll be talking a little more
+ 
+
+ align:start position:0%
+the adult we'll be talking a little more
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+that very soon okay so and here's shows
+
+ align:start position:0%
+that very soon okay so and here's shows
+ 
+
+ align:start position:0%
+that very soon okay so and here's shows
+that that of course has to be a
+
+ align:start position:0%
+that that of course has to be a
+ 
+
+ align:start position:0%
+that that of course has to be a
+decoating pathway too because we know
+
+ align:start position:0%
+decoating pathway too because we know
+ 
+
+ align:start position:0%
+decoating pathway too because we know
+that the opposite side of the body is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+represented this is the left side it's
+
+ align:start position:0%
+represented this is the left side it's
+ 
+
+ align:start position:0%
+represented this is the left side it's
+representing the right side of the brain
+
+ align:start position:0%
+representing the right side of the brain
+ 
+
+ align:start position:0%
+representing the right side of the brain
+so that pathway Decat too at about the
+
+ align:start position:0%
+so that pathway Decat too at about the
+ 
+
+ align:start position:0%
+so that pathway Decat too at about the
+same place the medal oniscus deat okay
+
+ align:start position:0%
+same place the medal oniscus deat okay
+ 
+
+ align:start position:0%
+same place the medal oniscus deat okay
+at the CLE that's a very dramatic place
+
+ align:start position:0%
+at the CLE that's a very dramatic place
+ 
+
+ align:start position:0%
+at the CLE that's a very dramatic place
+in the brain between hind brain and
+
+ align:start position:0%
+in the brain between hind brain and
+ 
+
+ align:start position:0%
+in the brain between hind brain and
+spinal cord because of the major
+
+ align:start position:0%
+spinal cord because of the major
+ 
+
+ align:start position:0%
+spinal cord because of the major
+decussations that occur there just above
+
+ align:start position:0%
+decussations that occur there just above
+ 
+
+ align:start position:0%
+decussations that occur there just above
+the dorsal column that
+
+ align:start position:0%
+the dorsal column that
+ 
+
+ align:start position:0%
+the dorsal column that
+the all right and I mentioned birds have
+
+ align:start position:0%
+the all right and I mentioned birds have
+ 
+
+ align:start position:0%
+the all right and I mentioned birds have
+this too uh you have a structure in
+
+ align:start position:0%
+this too uh you have a structure in
+ 
+
+ align:start position:0%
+this too uh you have a structure in
+Birds particularly prominent in the more
+
+ align:start position:0%
+Birds particularly prominent in the more
+ 
+
+ align:start position:0%
+Birds particularly prominent in the more
+advanced
+
+ align:start position:0%
+advanced
+ 
+
+ align:start position:0%
+advanced
+Birds
+
+ align:start position:0%
+Birds
+ 
+
+ align:start position:0%
+Birds
+uh like owls and other Raptors uh but
+
+ align:start position:0%
+uh like owls and other Raptors uh but
+ 
+
+ align:start position:0%
+uh like owls and other Raptors uh but
+many birds have this it's a the word
+
+ align:start position:0%
+many birds have this it's a the word
+ 
+
+ align:start position:0%
+many birds have this it's a the word
+word Vol in German means a bulge and it
+
+ align:start position:0%
+word Vol in German means a bulge and it
+ 
+
+ align:start position:0%
+word Vol in German means a bulge and it
+does form a bulge in the hemispheres of
+
+ align:start position:0%
+does form a bulge in the hemispheres of
+ 
+
+ align:start position:0%
+does form a bulge in the hemispheres of
+these animals and they have a motor
+
+ align:start position:0%
+these animals and they have a motor
+ 
+
+ align:start position:0%
+these animals and they have a motor
+wolst just like our motor cortex IT
+
+ align:start position:0%
+wolst just like our motor cortex IT
+ 
+
+ align:start position:0%
+wolst just like our motor cortex IT
+projects directly to the spinal cord
+
+ align:start position:0%
+projects directly to the spinal cord
+ 
+
+ align:start position:0%
+projects directly to the spinal cord
+they do have some met sensory wolst and
+
+ align:start position:0%
+they do have some met sensory wolst and
+ 
+
+ align:start position:0%
+they do have some met sensory wolst and
+visual wolst as
+
+ align:start position:0%
+visual wolst as
+ 
+
+ align:start position:0%
+visual wolst as
+well they also have a very large
+
+ align:start position:0%
+well they also have a very large
+ 
+
+ align:start position:0%
+well they also have a very large
+subcortical region that has connections
+
+ align:start position:0%
+subcortical region that has connections
+ 
+
+ align:start position:0%
+subcortical region that has connections
+also like neocortex Just Like the Wolf
+
+ align:start position:0%
+also like neocortex Just Like the Wolf
+ 
+
+ align:start position:0%
+also like neocortex Just Like the Wolf
+does but it doesn't look like CeX at all
+
+ align:start position:0%
+does but it doesn't look like CeX at all
+ 
+
+ align:start position:0%
+does but it doesn't look like CeX at all
+it's actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subcortical okay it's called the nested
+
+ align:start position:0%
+subcortical okay it's called the nested
+ 
+
+ align:start position:0%
+subcortical okay it's called the nested
+pallum or the Nido pallion
+
+ align:start position:0%
+pallum or the Nido pallion
+ 
+
+ align:start position:0%
+pallum or the Nido pallion
+we'll mention that a few times just so
+
+ align:start position:0%
+we'll mention that a few times just so
+ 
+
+ align:start position:0%
+we'll mention that a few times just so
+you know something about our
+
+ align:start position:0%
+you know something about our
+ 
+
+ align:start position:0%
+you know something about our
+other companions it's Advanced
+
+ align:start position:0%
+other companions it's Advanced
+ 
+
+ align:start position:0%
+other companions it's Advanced
+vertebrates all
+
+ align:start position:0%
+vertebrates all
+ 
+
+ align:start position:0%
+vertebrates all
+right now let's just mention very brief
+
+ align:start position:0%
+right now let's just mention very brief
+ 
+
+ align:start position:0%
+right now let's just mention very brief
+briefly what characterizes the sensory
+
+ align:start position:0%
+briefly what characterizes the sensory
+ 
+
+ align:start position:0%
+briefly what characterizes the sensory
+and motor functions of the
+
+ align:start position:0%
+and motor functions of the
+ 
+
+ align:start position:0%
+and motor functions of the
+neocortex and what other types of
+
+ align:start position:0%
+neocortex and what other types of
+ 
+
+ align:start position:0%
+neocortex and what other types of
+functions depend on
+
+ align:start position:0%
+functions depend on
+ 
+
+ align:start position:0%
+functions depend on
+neocortex think of neocortex as adding
+
+ align:start position:0%
+neocortex think of neocortex as adding
+ 
+
+ align:start position:0%
+neocortex think of neocortex as adding
+to S sensory
+
+ align:start position:0%
+to S sensory
+ 
+
+ align:start position:0%
+to S sensory
+processes
+
+ align:start position:0%
+processes
+ 
+
+ align:start position:0%
+processes
+Acuity both sensory and motor fine
+
+ align:start position:0%
+Acuity both sensory and motor fine
+ 
+
+ align:start position:0%
+Acuity both sensory and motor fine
+movement
+
+ align:start position:0%
+movement
+ 
+
+ align:start position:0%
+movement
+control fine discrimination of objects
+
+ align:start position:0%
+control fine discrimination of objects
+ 
+
+ align:start position:0%
+control fine discrimination of objects
+that also made better object P objects
+
+ align:start position:0%
+that also made better object P objects
+ 
+
+ align:start position:0%
+that also made better object P objects
+could be separated from the background
+
+ align:start position:0%
+could be separated from the background
+ 
+
+ align:start position:0%
+could be separated from the background
+more easily so it's not just a m mish
+
+ align:start position:0%
+more easily so it's not just a m mish
+ 
+
+ align:start position:0%
+more easily so it's not just a m mish
+mash of stimuli they're responding to
+
+ align:start position:0%
+mash of stimuli they're responding to
+ 
+
+ align:start position:0%
+mash of stimuli they're responding to
+but they respond to specific objects so
+
+ align:start position:0%
+but they respond to specific objects so
+ 
+
+ align:start position:0%
+but they respond to specific objects so
+that means they have to form images of
+
+ align:start position:0%
+that means they have to form images of
+ 
+
+ align:start position:0%
+that means they have to form images of
+those objects and that's something NE
+
+ align:start position:0%
+those objects and that's something NE
+ 
+
+ align:start position:0%
+those objects and that's something NE
+cortex
+
+ align:start position:0%
+cortex
+ 
+
+ align:start position:0%
+cortex
+does and I think the most unique thing
+
+ align:start position:0%
+does and I think the most unique thing
+ 
+
+ align:start position:0%
+does and I think the most unique thing
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+neocortex you know just that fine
+
+ align:start position:0%
+neocortex you know just that fine
+ 
+
+ align:start position:0%
+neocortex you know just that fine
+control the Acuity sensory and motor
+
+ align:start position:0%
+control the Acuity sensory and motor
+ 
+
+ align:start position:0%
+control the Acuity sensory and motor
+that's just sort of a quantitative
+
+ align:start position:0%
+that's just sort of a quantitative
+ 
+
+ align:start position:0%
+that's just sort of a quantitative
+improvement over what lower structures
+
+ align:start position:0%
+improvement over what lower structures
+ 
+
+ align:start position:0%
+improvement over what lower structures
+did but this is something really unique
+
+ align:start position:0%
+did but this is something really unique
+ 
+
+ align:start position:0%
+did but this is something really unique
+it in it adds the ability to anticipate
+
+ align:start position:0%
+it in it adds the ability to anticipate
+ 
+
+ align:start position:0%
+it in it adds the ability to anticipate
+and plan anticipate stimuli we do that
+
+ align:start position:0%
+and plan anticipate stimuli we do that
+ 
+
+ align:start position:0%
+and plan anticipate stimuli we do that
+through image
+
+ align:start position:0%
+through image
+ 
+
+ align:start position:0%
+through image
+formation Imaging depends on the
+
+ align:start position:0%
+formation Imaging depends on the
+ 
+
+ align:start position:0%
+formation Imaging depends on the
+posterior parts of the ne cortex and
+
+ align:start position:0%
+posterior parts of the ne cortex and
+ 
+
+ align:start position:0%
+posterior parts of the ne cortex and
+also we plan movements we don't just
+
+ align:start position:0%
+also we plan movements we don't just
+ 
+
+ align:start position:0%
+also we plan movements we don't just
+react uh that uses an internal model a
+
+ align:start position:0%
+react uh that uses an internal model a
+ 
+
+ align:start position:0%
+react uh that uses an internal model a
+kind of simulation of the world depends
+
+ align:start position:0%
+kind of simulation of the world depends
+ 
+
+ align:start position:0%
+kind of simulation of the world depends
+on those images as well so those are
+
+ align:start position:0%
+on those images as well so those are
+ 
+
+ align:start position:0%
+on those images as well so those are
+really the unique parts and I put review
+
+ align:start position:0%
+really the unique parts and I put review
+ 
+
+ align:start position:0%
+really the unique parts and I put review
+slides at the end of this chapter that
+
+ align:start position:0%
+slides at the end of this chapter that
+ 
+
+ align:start position:0%
+slides at the end of this chapter that
+you should look
+
+ align:start position:0%
+you should look
+ 
+
+ align:start position:0%
+you should look
+at because I want to get on here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the main topic of the day formation
+
+ align:start position:0%
+with the main topic of the day formation
+ 
+
+ align:start position:0%
+with the main topic of the day formation
+the neural tube in the embryo how
+
+ align:start position:0%
+the neural tube in the embryo how
+ 
+
+ align:start position:0%
+the neural tube in the embryo how
+central nervous system develop be
+
+ align:start position:0%
+central nervous system develop be
+ 
+
+ align:start position:0%
+central nervous system develop be
+development begins and we'll focus on
+
+ align:start position:0%
+development begins and we'll focus on
+ 
+
+ align:start position:0%
+development begins and we'll focus on
+the spinal level but that is where the
+
+ align:start position:0%
+the spinal level but that is where the
+ 
+
+ align:start position:0%
+the spinal level but that is where the
+neural tube first fully forms but the
+
+ align:start position:0%
+neural tube first fully forms but the
+ 
+
+ align:start position:0%
+neural tube first fully forms but the
+entire central nervous system begins as
+
+ align:start position:0%
+entire central nervous system begins as
+ 
+
+ align:start position:0%
+entire central nervous system begins as
+a tube all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember it all evolves actually
+
+ align:start position:0%
+remember it all evolves actually
+ 
+
+ align:start position:0%
+remember it all evolves actually
+together we
+
+ align:start position:0%
+together we
+ 
+
+ align:start position:0%
+together we
+saw so we're going to do the embryology
+
+ align:start position:0%
+saw so we're going to do the embryology
+ 
+
+ align:start position:0%
+saw so we're going to do the embryology
+today and then next time we'll be able
+
+ align:start position:0%
+today and then next time we'll be able
+ 
+
+ align:start position:0%
+today and then next time we'll be able
+to get to the adult spinal cord and also
+
+ align:start position:0%
+to get to the adult spinal cord and also
+ 
+
+ align:start position:0%
+to get to the adult spinal cord and also
+the autonomic nervous
+
+ align:start position:0%
+the autonomic nervous
+ 
+
+ align:start position:0%
+the autonomic nervous
+system these are the stages of
+
+ align:start position:0%
+system these are the stages of
+ 
+
+ align:start position:0%
+system these are the stages of
+development of a nervous system after
+
+ align:start position:0%
+development of a nervous system after
+ 
+
+ align:start position:0%
+development of a nervous system after
+the egg is
+
+ align:start position:0%
+the egg is
+ 
+
+ align:start position:0%
+the egg is
+fertilized you get the formation of a
+
+ align:start position:0%
+fertilized you get the formation of a
+ 
+
+ align:start position:0%
+fertilized you get the formation of a
+mora a clump of cells that becomes a
+
+ align:start position:0%
+mora a clump of cells that becomes a
+ 
+
+ align:start position:0%
+mora a clump of cells that becomes a
+blastula which is a hollow ball of cells
+
+ align:start position:0%
+blastula which is a hollow ball of cells
+ 
+
+ align:start position:0%
+blastula which is a hollow ball of cells
+but now it's got fluid in the middle
+
+ align:start position:0%
+but now it's got fluid in the middle
+ 
+
+ align:start position:0%
+but now it's got fluid in the middle
+then a major step
+
+ align:start position:0%
+then a major step
+ 
+
+ align:start position:0%
+then a major step
+gastrulation where the organism instead
+
+ align:start position:0%
+gastrulation where the organism instead
+ 
+
+ align:start position:0%
+gastrulation where the organism instead
+of just this hollow ball of cells the
+
+ align:start position:0%
+of just this hollow ball of cells the
+ 
+
+ align:start position:0%
+of just this hollow ball of cells the
+fluid in the middle becomes shaped like
+
+ align:start position:0%
+fluid in the middle becomes shaped like
+ 
+
+ align:start position:0%
+fluid in the middle becomes shaped like
+a dut formation of the elementary Canal
+
+ align:start position:0%
+a dut formation of the elementary Canal
+ 
+
+ align:start position:0%
+a dut formation of the elementary Canal
+mouth at one and anus at the other that
+
+ align:start position:0%
+mouth at one and anus at the other that
+ 
+
+ align:start position:0%
+mouth at one and anus at the other that
+forms very early you'll see pictures of
+
+ align:start position:0%
+forms very early you'll see pictures of
+ 
+
+ align:start position:0%
+forms very early you'll see pictures of
+that and then finally neurulation
+
+ align:start position:0%
+that and then finally neurulation
+ 
+
+ align:start position:0%
+that and then finally neurulation
+formation of a nervous system the major
+
+ align:start position:0%
+formation of a nervous system the major
+ 
+
+ align:start position:0%
+formation of a nervous system the major
+thing we want to talk
+
+ align:start position:0%
+thing we want to talk
+ 
+
+ align:start position:0%
+thing we want to talk
+about now LS walper in this very
+
+ align:start position:0%
+about now LS walper in this very
+ 
+
+ align:start position:0%
+about now LS walper in this very
+interesting little book Triumph of the
+
+ align:start position:0%
+interesting little book Triumph of the
+ 
+
+ align:start position:0%
+interesting little book Triumph of the
+embryo when he revised it other authors
+
+ align:start position:0%
+embryo when he revised it other authors
+ 
+
+ align:start position:0%
+embryo when he revised it other authors
+join other authors joined him and it
+
+ align:start position:0%
+join other authors joined him and it
+ 
+
+ align:start position:0%
+join other authors joined him and it
+became a more standard embryology
+
+ align:start position:0%
+became a more standard embryology
+ 
+
+ align:start position:0%
+became a more standard embryology
+book uh which is also very interesting
+
+ align:start position:0%
+book uh which is also very interesting
+ 
+
+ align:start position:0%
+book uh which is also very interesting
+all the things that I found in Triumph
+
+ align:start position:0%
+all the things that I found in Triumph
+ 
+
+ align:start position:0%
+all the things that I found in Triumph
+of the embryo is still there but he
+
+ align:start position:0%
+of the embryo is still there but he
+ 
+
+ align:start position:0%
+of the embryo is still there but he
+really simplified it and talked about
+
+ align:start position:0%
+really simplified it and talked about
+ 
+
+ align:start position:0%
+really simplified it and talked about
+the major principles and one of the
+
+ align:start position:0%
+the major principles and one of the
+ 
+
+ align:start position:0%
+the major principles and one of the
+things he laid out was the cellular
+
+ align:start position:0%
+things he laid out was the cellular
+ 
+
+ align:start position:0%
+things he laid out was the cellular
+events what are the cellular events that
+
+ align:start position:0%
+events what are the cellular events that
+ 
+
+ align:start position:0%
+events what are the cellular events that
+characterize development of the nervous
+
+ align:start position:0%
+characterize development of the nervous
+ 
+
+ align:start position:0%
+characterize development of the nervous
+system what are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they well contraction parts of the cell
+
+ align:start position:0%
+they well contraction parts of the cell
+ 
+
+ align:start position:0%
+they well contraction parts of the cell
+could contract what does that involve it
+
+ align:start position:0%
+could contract what does that involve it
+ 
+
+ align:start position:0%
+could contract what does that involve it
+involves contractable proteins just like
+
+ align:start position:0%
+involves contractable proteins just like
+ 
+
+ align:start position:0%
+involves contractable proteins just like
+we have in muscle okay but cells have
+
+ align:start position:0%
+we have in muscle okay but cells have
+ 
+
+ align:start position:0%
+we have in muscle okay but cells have
+that all cells have that to some degree
+
+ align:start position:0%
+that all cells have that to some degree
+ 
+
+ align:start position:0%
+that all cells have that to some degree
+in development okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contraction well cells have to in order
+
+ align:start position:0%
+contraction well cells have to in order
+ 
+
+ align:start position:0%
+contraction well cells have to in order
+to be to form organized tissue cells
+
+ align:start position:0%
+to be to form organized tissue cells
+ 
+
+ align:start position:0%
+to be to form organized tissue cells
+have to be able to stick to things stick
+
+ align:start position:0%
+have to be able to stick to things stick
+ 
+
+ align:start position:0%
+have to be able to stick to things stick
+to each other uh they form these little
+
+ align:start position:0%
+to each other uh they form these little
+ 
+
+ align:start position:0%
+to each other uh they form these little
+processes that can adhere to something
+
+ align:start position:0%
+processes that can adhere to something
+ 
+
+ align:start position:0%
+processes that can adhere to something
+so they show adhesion and that adhes the
+
+ align:start position:0%
+so they show adhesion and that adhes the
+ 
+
+ align:start position:0%
+so they show adhesion and that adhes the
+adhesive properties through cell
+
+ align:start position:0%
+adhesive properties through cell
+ 
+
+ align:start position:0%
+adhesive properties through cell
+adhesion molecules in the membrane which
+
+ align:start position:0%
+adhesion molecules in the membrane which
+ 
+
+ align:start position:0%
+adhesion molecules in the membrane which
+can change during the course of
+
+ align:start position:0%
+can change during the course of
+ 
+
+ align:start position:0%
+can change during the course of
+development uh that's a a big part of
+
+ align:start position:0%
+development uh that's a a big part of
+ 
+
+ align:start position:0%
+development uh that's a a big part of
+development selective adhesion and
+
+ align:start position:0%
+development selective adhesion and
+ 
+
+ align:start position:0%
+development selective adhesion and
+changes in
+
+ align:start position:0%
+changes in
+ 
+
+ align:start position:0%
+changes in
+adhesion okay and then cells can move
+
+ align:start position:0%
+adhesion okay and then cells can move
+ 
+
+ align:start position:0%
+adhesion okay and then cells can move
+how do they move so we'll be talking
+
+ align:start position:0%
+how do they move so we'll be talking
+ 
+
+ align:start position:0%
+how do they move so we'll be talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that and uh finally of course growth and
+
+ align:start position:0%
+that and uh finally of course growth and
+ 
+
+ align:start position:0%
+that and uh finally of course growth and
+by growth often an embryologist is
+
+ align:start position:0%
+by growth often an embryologist is
+ 
+
+ align:start position:0%
+by growth often an embryologist is
+talking about growth by proliferation of
+
+ align:start position:0%
+talking about growth by proliferation of
+ 
+
+ align:start position:0%
+talking about growth by proliferation of
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+mitosis it also means growth increased
+
+ align:start position:0%
+mitosis it also means growth increased
+ 
+
+ align:start position:0%
+mitosis it also means growth increased
+size of cells but the main factor is
+
+ align:start position:0%
+size of cells but the main factor is
+ 
+
+ align:start position:0%
+size of cells but the main factor is
+increased numbers of cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's the pictures that walper
+
+ align:start position:0%
+okay so here's the pictures that walper
+ 
+
+ align:start position:0%
+okay so here's the pictures that walper
+uses from a single fertilized
+
+ align:start position:0%
+uses from a single fertilized
+ 
+
+ align:start position:0%
+uses from a single fertilized
+egg here to the Mora a clump of it looks
+
+ align:start position:0%
+egg here to the Mora a clump of it looks
+ 
+
+ align:start position:0%
+egg here to the Mora a clump of it looks
+like a raspberry and here it becomes the
+
+ align:start position:0%
+like a raspberry and here it becomes the
+ 
+
+ align:start position:0%
+like a raspberry and here it becomes the
+blastula fluid in the middle and then
+
+ align:start position:0%
+blastula fluid in the middle and then
+ 
+
+ align:start position:0%
+blastula fluid in the middle and then
+note some cells have moved to the
+
+ align:start position:0%
+note some cells have moved to the
+ 
+
+ align:start position:0%
+note some cells have moved to the
+interior and there's more contraction at
+
+ align:start position:0%
+interior and there's more contraction at
+ 
+
+ align:start position:0%
+interior and there's more contraction at
+one side
+
+ align:start position:0%
+one side
+ 
+
+ align:start position:0%
+one side
+the out the the outside of the cell then
+
+ align:start position:0%
+the out the the outside of the cell then
+ 
+
+ align:start position:0%
+the out the the outside of the cell then
+on the inside and that leads to an
+
+ align:start position:0%
+on the inside and that leads to an
+ 
+
+ align:start position:0%
+on the inside and that leads to an
+invagination as you see beginning here
+
+ align:start position:0%
+invagination as you see beginning here
+ 
+
+ align:start position:0%
+invagination as you see beginning here
+and then look what
+
+ align:start position:0%
+and then look what
+ 
+
+ align:start position:0%
+and then look what
+happens these little processes extend
+
+ align:start position:0%
+happens these little processes extend
+ 
+
+ align:start position:0%
+happens these little processes extend
+out those little filaments are called
+
+ align:start position:0%
+out those little filaments are called
+ 
+
+ align:start position:0%
+out those little filaments are called
+filopodia okay filamentous feet okay
+
+ align:start position:0%
+filopodia okay filamentous feet okay
+ 
+
+ align:start position:0%
+filopodia okay filamentous feet okay
+they extend out and they actually reach
+
+ align:start position:0%
+they extend out and they actually reach
+ 
+
+ align:start position:0%
+they extend out and they actually reach
+the other side where they adhere so now
+
+ align:start position:0%
+the other side where they adhere so now
+ 
+
+ align:start position:0%
+the other side where they adhere so now
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+adhesion you have most of these
+
+ align:start position:0%
+adhesion you have most of these
+ 
+
+ align:start position:0%
+adhesion you have most of these
+processes we just talked about are
+
+ align:start position:0%
+processes we just talked about are
+ 
+
+ align:start position:0%
+processes we just talked about are
+happening
+
+ align:start position:0%
+happening
+ 
+
+ align:start position:0%
+happening
+contraction
+
+ align:start position:0%
+contraction
+ 
+
+ align:start position:0%
+contraction
+adhesion
+
+ align:start position:0%
+adhesion
+ 
+
+ align:start position:0%
+adhesion
+movement notice the movement that's
+
+ align:start position:0%
+movement notice the movement that's
+ 
+
+ align:start position:0%
+movement notice the movement that's
+being caused by the contraction
+
+ align:start position:0%
+being caused by the contraction
+ 
+
+ align:start position:0%
+being caused by the contraction
+contractable proteins in those filipodia
+
+ align:start position:0%
+contractable proteins in those filipodia
+ 
+
+ align:start position:0%
+contractable proteins in those filipodia
+so it
+
+ align:start position:0%
+so it
+ 
+
+ align:start position:0%
+so it
+pulls this side of the embryo right
+
+ align:start position:0%
+pulls this side of the embryo right
+ 
+
+ align:start position:0%
+pulls this side of the embryo right
+across and that causes changes that
+
+ align:start position:0%
+across and that causes changes that
+ 
+
+ align:start position:0%
+across and that causes changes that
+cause an opening to
+
+ align:start position:0%
+cause an opening to
+ 
+
+ align:start position:0%
+cause an opening to
+form between here and here the cells
+
+ align:start position:0%
+form between here and here the cells
+ 
+
+ align:start position:0%
+form between here and here the cells
+continue to move to the in inside but
+
+ align:start position:0%
+continue to move to the in inside but
+ 
+
+ align:start position:0%
+continue to move to the in inside but
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+process from here to here or actually
+
+ align:start position:0%
+process from here to here or actually
+ 
+
+ align:start position:0%
+process from here to here or actually
+all along the bottom is called
+
+ align:start position:0%
+all along the bottom is called
+ 
+
+ align:start position:0%
+all along the bottom is called
+gastrulation it's just seen in the
+
+ align:start position:0%
+gastrulation it's just seen in the
+ 
+
+ align:start position:0%
+gastrulation it's just seen in the
+sections okay this just shows us one of
+
+ align:start position:0%
+sections okay this just shows us one of
+ 
+
+ align:start position:0%
+sections okay this just shows us one of
+the cells that how complicated they can
+
+ align:start position:0%
+the cells that how complicated they can
+ 
+
+ align:start position:0%
+the cells that how complicated they can
+be with their various extensions and
+
+ align:start position:0%
+be with their various extensions and
+ 
+
+ align:start position:0%
+be with their various extensions and
+movement
+
+ align:start position:0%
+movement
+ 
+
+ align:start position:0%
+movement
+because if this was all there is we'd
+
+ align:start position:0%
+because if this was all there is we'd
+ 
+
+ align:start position:0%
+because if this was all there is we'd
+have one
+
+ align:start position:0%
+have one
+ 
+
+ align:start position:0%
+have one
+layer that outer layer is the ectoderm
+
+ align:start position:0%
+layer that outer layer is the ectoderm
+ 
+
+ align:start position:0%
+layer that outer layer is the ectoderm
+but cells move inward they move to the
+
+ align:start position:0%
+but cells move inward they move to the
+ 
+
+ align:start position:0%
+but cells move inward they move to the
+interior and that becomes the mism and
+
+ align:start position:0%
+interior and that becomes the mism and
+ 
+
+ align:start position:0%
+interior and that becomes the mism and
+the endoderm mism forming muscle and
+
+ align:start position:0%
+the endoderm mism forming muscle and
+ 
+
+ align:start position:0%
+the endoderm mism forming muscle and
+skeleton and the endoderm forming the
+
+ align:start position:0%
+skeleton and the endoderm forming the
+ 
+
+ align:start position:0%
+skeleton and the endoderm forming the
+internal organs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then we want to talk
+
+ align:start position:0%
+okay so then we want to talk
+ 
+
+ align:start position:0%
+okay so then we want to talk
+about that still doesn't none of this
+
+ align:start position:0%
+about that still doesn't none of this
+ 
+
+ align:start position:0%
+about that still doesn't none of this
+gives you a central nervous system okay
+
+ align:start position:0%
+gives you a central nervous system okay
+ 
+
+ align:start position:0%
+gives you a central nervous system okay
+how do we get a central nervous system
+
+ align:start position:0%
+how do we get a central nervous system
+ 
+
+ align:start position:0%
+how do we get a central nervous system
+out of
+
+ align:start position:0%
+out of
+ 
+
+ align:start position:0%
+out of
+that so we need to talk about neural
+
+ align:start position:0%
+that so we need to talk about neural
+ 
+
+ align:start position:0%
+that so we need to talk about neural
+with the formation of the neural tube
+
+ align:start position:0%
+with the formation of the neural tube
+ 
+
+ align:start position:0%
+with the formation of the neural tube
+and then proliferation of the cells
+
+ align:start position:0%
+and then proliferation of the cells
+ 
+
+ align:start position:0%
+and then proliferation of the cells
+migration of cells and differentiation
+
+ align:start position:0%
+migration of cells and differentiation
+ 
+
+ align:start position:0%
+migration of cells and differentiation
+of cells by differentiation we mean the
+
+ align:start position:0%
+of cells by differentiation we mean the
+ 
+
+ align:start position:0%
+of cells by differentiation we mean the
+cell changes so the cells look different
+
+ align:start position:0%
+cell changes so the cells look different
+ 
+
+ align:start position:0%
+cell changes so the cells look different
+from each other they differentiate from
+
+ align:start position:0%
+from each other they differentiate from
+ 
+
+ align:start position:0%
+from each other they differentiate from
+each other they form dendrites they form
+
+ align:start position:0%
+each other they form dendrites they form
+ 
+
+ align:start position:0%
+each other they form dendrites they form
+axons if they're
+
+ align:start position:0%
+axons if they're
+ 
+
+ align:start position:0%
+axons if they're
+neurons if they're gal cells they also
+
+ align:start position:0%
+neurons if they're gal cells they also
+ 
+
+ align:start position:0%
+neurons if they're gal cells they also
+form processes depending on what kind of
+
+ align:start position:0%
+form processes depending on what kind of
+ 
+
+ align:start position:0%
+form processes depending on what kind of
+Gia they are all
+
+ align:start position:0%
+Gia they are all
+ 
+
+ align:start position:0%
+Gia they are all
+right so these are the questions I'm
+
+ align:start position:0%
+right so these are the questions I'm
+ 
+
+ align:start position:0%
+right so these are the questions I'm
+asking first of all what is the not
+
+ align:start position:0%
+asking first of all what is the not
+ 
+
+ align:start position:0%
+asking first of all what is the not
+chord we heard that term used before you
+
+ align:start position:0%
+chord we heard that term used before you
+ 
+
+ align:start position:0%
+chord we heard that term used before you
+should remember what it
+
+ align:start position:0%
+should remember what it
+ 
+
+ align:start position:0%
+should remember what it
+is some of you might what is the not
+
+ align:start position:0%
+is some of you might what is the not
+ 
+
+ align:start position:0%
+is some of you might what is the not
+cord it's not in all
+
+ align:start position:0%
+cord it's not in all
+ 
+
+ align:start position:0%
+cord it's not in all
+animals it's just in all animals that we
+
+ align:start position:0%
+animals it's just in all animals that we
+ 
+
+ align:start position:0%
+animals it's just in all animals that we
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+cordat so what is it the
+
+ align:start position:0%
+cordat so what is it the
+ 
+
+ align:start position:0%
+cordat so what is it the
+Nord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's it tube may not be the most
+
+ align:start position:0%
+yeah it's it tube may not be the most
+ 
+
+ align:start position:0%
+yeah it's it tube may not be the most
+accurate it's cartilaginous for sure uh
+
+ align:start position:0%
+accurate it's cartilaginous for sure uh
+ 
+
+ align:start position:0%
+accurate it's cartilaginous for sure uh
+where is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it but wait it precedes the neural
+
+ align:start position:0%
+it but wait it precedes the neural
+ 
+
+ align:start position:0%
+it but wait it precedes the neural
+tool but it is a but where in the
+
+ align:start position:0%
+tool but it is a but where in the
+ 
+
+ align:start position:0%
+tool but it is a but where in the
+organism the what at least what does it
+
+ align:start position:0%
+organism the what at least what does it
+ 
+
+ align:start position:0%
+organism the what at least what does it
+become in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organism the back exactly it's always
+
+ align:start position:0%
+organism the back exactly it's always
+ 
+
+ align:start position:0%
+organism the back exactly it's always
+along the back okay or at least what's
+
+ align:start position:0%
+along the back okay or at least what's
+ 
+
+ align:start position:0%
+along the back okay or at least what's
+going to become the back it maybe that's
+
+ align:start position:0%
+going to become the back it maybe that's
+ 
+
+ align:start position:0%
+going to become the back it maybe that's
+how it becomes a back okay the not
+
+ align:start position:0%
+how it becomes a back okay the not
+ 
+
+ align:start position:0%
+how it becomes a back okay the not
+cordant is at the surface one side that
+
+ align:start position:0%
+cordant is at the surface one side that
+ 
+
+ align:start position:0%
+cordant is at the surface one side that
+becomes the back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it doesn't become the backbone but
+
+ align:start position:0%
+okay it doesn't become the backbone but
+ 
+
+ align:start position:0%
+okay it doesn't become the backbone but
+the back the skeletal elements form
+
+ align:start position:0%
+the back the skeletal elements form
+ 
+
+ align:start position:0%
+the back the skeletal elements form
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+it okay there are induction processes
+
+ align:start position:0%
+it okay there are induction processes
+ 
+
+ align:start position:0%
+it okay there are induction processes
+molecules coming from the noord exert
+
+ align:start position:0%
+molecules coming from the noord exert
+ 
+
+ align:start position:0%
+molecules coming from the noord exert
+really powerful changes first of all in
+
+ align:start position:0%
+really powerful changes first of all in
+ 
+
+ align:start position:0%
+really powerful changes first of all in
+the formation of the nervous system then
+
+ align:start position:0%
+the formation of the nervous system then
+ 
+
+ align:start position:0%
+the formation of the nervous system then
+the formation of the skeleton as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay who
+
+ align:start position:0%
+okay who
+ 
+
+ align:start position:0%
+okay who
+discovered this phenomenon of induction
+
+ align:start position:0%
+discovered this phenomenon of induction
+ 
+
+ align:start position:0%
+discovered this phenomenon of induction
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+CNS now it we know now that the
+
+ align:start position:0%
+CNS now it we know now that the
+ 
+
+ align:start position:0%
+CNS now it we know now that the
+inductive process the not cord induces
+
+ align:start position:0%
+inductive process the not cord induces
+ 
+
+ align:start position:0%
+inductive process the not cord induces
+the formation of a nervous system but
+
+ align:start position:0%
+the formation of a nervous system but
+ 
+
+ align:start position:0%
+the formation of a nervous system but
+how did we how is it discovered who
+
+ align:start position:0%
+how did we how is it discovered who
+ 
+
+ align:start position:0%
+how did we how is it discovered who
+discovered it that that there's some
+
+ align:start position:0%
+discovered it that that there's some
+ 
+
+ align:start position:0%
+discovered it that that there's some
+kind of induction that's happening
+
+ align:start position:0%
+kind of induction that's happening
+ 
+
+ align:start position:0%
+kind of induction that's happening
+because if you move things around you
+
+ align:start position:0%
+because if you move things around you
+ 
+
+ align:start position:0%
+because if you move things around you
+can get nervous system farming
+
+ align:start position:0%
+can get nervous system farming
+ 
+
+ align:start position:0%
+can get nervous system farming
+differently or in different
+
+ align:start position:0%
+differently or in different
+ 
+
+ align:start position:0%
+differently or in different
+places you remember the names there were
+
+ align:start position:0%
+places you remember the names there were
+ 
+
+ align:start position:0%
+places you remember the names there were
+actually two people but only one of them
+
+ align:start position:0%
+actually two people but only one of them
+ 
+
+ align:start position:0%
+actually two people but only one of them
+got the Nobel Prize for
+
+ align:start position:0%
+got the Nobel Prize for
+ 
+
+ align:start position:0%
+got the Nobel Prize for
+it he's name was
+
+ align:start position:0%
+it he's name was
+ 
+
+ align:start position:0%
+it he's name was
+Hunan okay Shaman got the prize but the
+
+ align:start position:0%
+Hunan okay Shaman got the prize but the
+ 
+
+ align:start position:0%
+Hunan okay Shaman got the prize but the
+discovery was made made in his lab by a
+
+ align:start position:0%
+discovery was made made in his lab by a
+ 
+
+ align:start position:0%
+discovery was made made in his lab by a
+student young woman named Hilda
+
+ align:start position:0%
+student young woman named Hilda
+ 
+
+ align:start position:0%
+student young woman named Hilda
+Mangold
+
+ align:start position:0%
+Mangold
+ 
+
+ align:start position:0%
+Mangold
+okay why didn't she get The Nobel
+
+ align:start position:0%
+okay why didn't she get The Nobel
+ 
+
+ align:start position:0%
+okay why didn't she get The Nobel
+Prize Unfortunately they don't give
+
+ align:start position:0%
+Prize Unfortunately they don't give
+ 
+
+ align:start position:0%
+Prize Unfortunately they don't give
+Nobel prizes to someone who has
+
+ align:start position:0%
+Nobel prizes to someone who has
+ 
+
+ align:start position:0%
+Nobel prizes to someone who has
+died she died in the kitchen accident
+
+ align:start position:0%
+died she died in the kitchen accident
+ 
+
+ align:start position:0%
+died she died in the kitchen accident
+when she was only 26 years
+
+ align:start position:0%
+when she was only 26 years
+ 
+
+ align:start position:0%
+when she was only 26 years
+old but she should be remembered just as
+
+ align:start position:0%
+old but she should be remembered just as
+ 
+
+ align:start position:0%
+old but she should be remembered just as
+famon is for the discovery of induction
+
+ align:start position:0%
+famon is for the discovery of induction
+ 
+
+ align:start position:0%
+famon is for the discovery of induction
+of the nervous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system and then we want to know what
+
+ align:start position:0%
+system and then we want to know what
+ 
+
+ align:start position:0%
+system and then we want to know what
+neuroc crest cells are You' got to know
+
+ align:start position:0%
+neuroc crest cells are You' got to know
+ 
+
+ align:start position:0%
+neuroc crest cells are You' got to know
+something about the neural tube
+
+ align:start position:0%
+something about the neural tube
+ 
+
+ align:start position:0%
+something about the neural tube
+formation to be able to answer that you
+
+ align:start position:0%
+formation to be able to answer that you
+ 
+
+ align:start position:0%
+formation to be able to answer that you
+can I should have a piece of paper here
+
+ align:start position:0%
+can I should have a piece of paper here
+ 
+
+ align:start position:0%
+can I should have a piece of paper here
+I didn't bring my piece of paper you
+
+ align:start position:0%
+I didn't bring my piece of paper you
+ 
+
+ align:start position:0%
+I didn't bring my piece of paper you
+just take a piece of paper and push it
+
+ align:start position:0%
+just take a piece of paper and push it
+ 
+
+ align:start position:0%
+just take a piece of paper and push it
+to two ends what happens it will indent
+
+ align:start position:0%
+to two ends what happens it will indent
+ 
+
+ align:start position:0%
+to two ends what happens it will indent
+right and you can get it to indent in
+
+ align:start position:0%
+right and you can get it to indent in
+ 
+
+ align:start position:0%
+right and you can get it to indent in
+one place that's what happens to the
+
+ align:start position:0%
+one place that's what happens to the
+ 
+
+ align:start position:0%
+one place that's what happens to the
+nervous system system here okay here
+
+ align:start position:0%
+nervous system system here okay here
+ 
+
+ align:start position:0%
+nervous system system here okay here
+here's the sheet of paper it's one cell
+
+ align:start position:0%
+here's the sheet of paper it's one cell
+ 
+
+ align:start position:0%
+here's the sheet of paper it's one cell
+thick uh
+
+ align:start position:0%
+thick uh
+ 
+
+ align:start position:0%
+thick uh
+ectoderm and that is the not
+
+ align:start position:0%
+ectoderm and that is the not
+ 
+
+ align:start position:0%
+ectoderm and that is the not
+cord this is just part of the ectoderm
+
+ align:start position:0%
+cord this is just part of the ectoderm
+ 
+
+ align:start position:0%
+cord this is just part of the ectoderm
+the part that will become the back of
+
+ align:start position:0%
+the part that will become the back of
+ 
+
+ align:start position:0%
+the part that will become the back of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+organism okay there's the not cord then
+
+ align:start position:0%
+organism okay there's the not cord then
+ 
+
+ align:start position:0%
+organism okay there's the not cord then
+there's an influence from the not cord
+
+ align:start position:0%
+there's an influence from the not cord
+ 
+
+ align:start position:0%
+there's an influence from the not cord
+note here I show cells getting thicker
+
+ align:start position:0%
+note here I show cells getting thicker
+ 
+
+ align:start position:0%
+note here I show cells getting thicker
+in this region that's we call a neural
+
+ align:start position:0%
+in this region that's we call a neural
+ 
+
+ align:start position:0%
+in this region that's we call a neural
+plate
+
+ align:start position:0%
+plate
+ 
+
+ align:start position:0%
+plate
+the cells are already determined now
+
+ align:start position:0%
+the cells are already determined now
+ 
+
+ align:start position:0%
+the cells are already determined now
+which ones are going to become nervous
+
+ align:start position:0%
+which ones are going to become nervous
+ 
+
+ align:start position:0%
+which ones are going to become nervous
+system and which will
+
+ align:start position:0%
+system and which will
+ 
+
+ align:start position:0%
+system and which will
+remain other parts of the ectoderm like
+
+ align:start position:0%
+remain other parts of the ectoderm like
+ 
+
+ align:start position:0%
+remain other parts of the ectoderm like
+the skin primarily
+
+ align:start position:0%
+the skin primarily
+ 
+
+ align:start position:0%
+the skin primarily
+okay and then because of differences in
+
+ align:start position:0%
+okay and then because of differences in
+ 
+
+ align:start position:0%
+okay and then because of differences in
+contraction just like during
+
+ align:start position:0%
+contraction just like during
+ 
+
+ align:start position:0%
+contraction just like during
+gastrulation earlier you get an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invagination so it doesn't really happen
+
+ align:start position:0%
+invagination so it doesn't really happen
+ 
+
+ align:start position:0%
+invagination so it doesn't really happen
+because somebody pushed the Sid
+
+ align:start position:0%
+because somebody pushed the Sid
+ 
+
+ align:start position:0%
+because somebody pushed the Sid
+like a piece of paper but the Dynamics
+
+ align:start position:0%
+like a piece of paper but the Dynamics
+ 
+
+ align:start position:0%
+like a piece of paper but the Dynamics
+are very similar so it starts to form a
+
+ align:start position:0%
+are very similar so it starts to form a
+ 
+
+ align:start position:0%
+are very similar so it starts to form a
+Groove along the back of the organism so
+
+ align:start position:0%
+Groove along the back of the organism so
+ 
+
+ align:start position:0%
+Groove along the back of the organism so
+think of it in three dimensions that's
+
+ align:start position:0%
+think of it in three dimensions that's
+ 
+
+ align:start position:0%
+think of it in three dimensions that's
+why I like you to think of a piece of
+
+ align:start position:0%
+why I like you to think of a piece of
+ 
+
+ align:start position:0%
+why I like you to think of a piece of
+paper if we push in it's going to form a
+
+ align:start position:0%
+paper if we push in it's going to form a
+ 
+
+ align:start position:0%
+paper if we push in it's going to form a
+big Groove all along the back of the
+
+ align:start position:0%
+big Groove all along the back of the
+ 
+
+ align:start position:0%
+big Groove all along the back of the
+organism there's the
+
+ align:start position:0%
+organism there's the
+ 
+
+ align:start position:0%
+organism there's the
+nort where molecules emanating from that
+
+ align:start position:0%
+nort where molecules emanating from that
+ 
+
+ align:start position:0%
+nort where molecules emanating from that
+noord are what's causing these changes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the ectoderm above it okay and North
+
+ align:start position:0%
+in the ectoderm above it okay and North
+ 
+
+ align:start position:0%
+in the ectoderm above it okay and North
+I hear I show two little bulges on the
+
+ align:start position:0%
+I hear I show two little bulges on the
+ 
+
+ align:start position:0%
+I hear I show two little bulges on the
+sides that is called the neural crest
+
+ align:start position:0%
+sides that is called the neural crest
+ 
+
+ align:start position:0%
+sides that is called the neural crest
+and it's very different because as these
+
+ align:start position:0%
+and it's very different because as these
+ 
+
+ align:start position:0%
+and it's very different because as these
+two edges come together so you end up
+
+ align:start position:0%
+two edges come together so you end up
+ 
+
+ align:start position:0%
+two edges come together so you end up
+with a tube these cells don't become
+
+ align:start position:0%
+with a tube these cells don't become
+ 
+
+ align:start position:0%
+with a tube these cells don't become
+part of the tube they stay on the
+
+ align:start position:0%
+part of the tube they stay on the
+ 
+
+ align:start position:0%
+part of the tube they stay on the
+outside it's those neural crust cells
+
+ align:start position:0%
+outside it's those neural crust cells
+ 
+
+ align:start position:0%
+outside it's those neural crust cells
+that form the peripheral nervous system
+
+ align:start position:0%
+that form the peripheral nervous system
+ 
+
+ align:start position:0%
+that form the peripheral nervous system
+all the cells of the peripheral nervous
+
+ align:start position:0%
+all the cells of the peripheral nervous
+ 
+
+ align:start position:0%
+all the cells of the peripheral nervous
+nous
+
+ align:start position:0%
+nous
+ 
+
+ align:start position:0%
+nous
+system come from the neural
+
+ align:start position:0%
+system come from the neural
+ 
+
+ align:start position:0%
+system come from the neural
+crest at this level of the nervous
+
+ align:start position:0%
+crest at this level of the nervous
+ 
+
+ align:start position:0%
+crest at this level of the nervous
+system now there are cells that don't
+
+ align:start position:0%
+system now there are cells that don't
+ 
+
+ align:start position:0%
+system now there are cells that don't
+come from neural crest in the head
+
+ align:start position:0%
+come from neural crest in the head
+ 
+
+ align:start position:0%
+come from neural crest in the head
+region there they come from both neural
+
+ align:start position:0%
+region there they come from both neural
+ 
+
+ align:start position:0%
+region there they come from both neural
+crest and from what we call plot just
+
+ align:start position:0%
+crest and from what we call plot just
+ 
+
+ align:start position:0%
+crest and from what we call plot just
+thickening of the ectoderm that happens
+
+ align:start position:0%
+thickening of the ectoderm that happens
+ 
+
+ align:start position:0%
+thickening of the ectoderm that happens
+due to other inductive
+
+ align:start position:0%
+due to other inductive
+ 
+
+ align:start position:0%
+due to other inductive
+influences okay not the noord now they
+
+ align:start position:0%
+influences okay not the noord now they
+ 
+
+ align:start position:0%
+influences okay not the noord now they
+can also for form periphal nervous
+
+ align:start position:0%
+can also for form periphal nervous
+ 
+
+ align:start position:0%
+can also for form periphal nervous
+system but here in the spinal cord
+
+ align:start position:0%
+system but here in the spinal cord
+ 
+
+ align:start position:0%
+system but here in the spinal cord
+all comes from the neural crest okay and
+
+ align:start position:0%
+all comes from the neural crest okay and
+ 
+
+ align:start position:0%
+all comes from the neural crest okay and
+then there's a few names you should
+
+ align:start position:0%
+then there's a few names you should
+ 
+
+ align:start position:0%
+then there's a few names you should
+learn when this tube
+
+ align:start position:0%
+learn when this tube
+ 
+
+ align:start position:0%
+learn when this tube
+forms note I show here the tube is
+
+ align:start position:0%
+forms note I show here the tube is
+ 
+
+ align:start position:0%
+forms note I show here the tube is
+already getting a little thicker
+
+ align:start position:0%
+already getting a little thicker
+ 
+
+ align:start position:0%
+already getting a little thicker
+there're cell proliferating there they
+
+ align:start position:0%
+there're cell proliferating there they
+ 
+
+ align:start position:0%
+there're cell proliferating there they
+proliferate in the sides of the tube not
+
+ align:start position:0%
+proliferate in the sides of the tube not
+ 
+
+ align:start position:0%
+proliferate in the sides of the tube not
+at the very top and the very bottom the
+
+ align:start position:0%
+at the very top and the very bottom the
+ 
+
+ align:start position:0%
+at the very top and the very bottom the
+very top is called the roof plate it
+
+ align:start position:0%
+very top is called the roof plate it
+ 
+
+ align:start position:0%
+very top is called the roof plate it
+remains one C thic and the bottom is the
+
+ align:start position:0%
+remains one C thic and the bottom is the
+ 
+
+ align:start position:0%
+remains one C thic and the bottom is the
+floor plate it also remains one cell
+
+ align:start position:0%
+floor plate it also remains one cell
+ 
+
+ align:start position:0%
+floor plate it also remains one cell
+thick right to the adult okay but the
+
+ align:start position:0%
+thick right to the adult okay but the
+ 
+
+ align:start position:0%
+thick right to the adult okay but the
+walls get thicker and thicker and in
+
+ align:start position:0%
+walls get thicker and thicker and in
+ 
+
+ align:start position:0%
+walls get thicker and thicker and in
+development the ventral part closest to
+
+ align:start position:0%
+development the ventral part closest to
+ 
+
+ align:start position:0%
+development the ventral part closest to
+the Nord tends to proliferate a little
+
+ align:start position:0%
+the Nord tends to proliferate a little
+ 
+
+ align:start position:0%
+the Nord tends to proliferate a little
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+faster okay that's where all the motor
+
+ align:start position:0%
+faster okay that's where all the motor
+ 
+
+ align:start position:0%
+faster okay that's where all the motor
+neurons will form so we call the upper
+
+ align:start position:0%
+neurons will form so we call the upper
+ 
+
+ align:start position:0%
+neurons will form so we call the upper
+part here the AER plate and the lower
+
+ align:start position:0%
+part here the AER plate and the lower
+ 
+
+ align:start position:0%
+part here the AER plate and the lower
+part the basil plate and the little
+
+ align:start position:0%
+part the basil plate and the little
+ 
+
+ align:start position:0%
+part the basil plate and the little
+Groove separating the two
+
+ align:start position:0%
+Groove separating the two
+ 
+
+ align:start position:0%
+Groove separating the two
+it's called the sulcus limitans the
+
+ align:start position:0%
+it's called the sulcus limitans the
+ 
+
+ align:start position:0%
+it's called the sulcus limitans the
+limiting sulcus you'll see pictures of
+
+ align:start position:0%
+limiting sulcus you'll see pictures of
+ 
+
+ align:start position:0%
+limiting sulcus you'll see pictures of
+that as we go
+
+ align:start position:0%
+that as we go
+ 
+
+ align:start position:0%
+that as we go
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+okay so let's
+
+ align:start position:0%
+okay so let's
+ 
+
+ align:start position:0%
+okay so let's
+take let's see do I have well we'll get
+
+ align:start position:0%
+take let's see do I have well we'll get
+ 
+
+ align:start position:0%
+take let's see do I have well we'll get
+to that I'm going to show you some
+
+ align:start position:0%
+to that I'm going to show you some
+ 
+
+ align:start position:0%
+to that I'm going to show you some
+pictures of it uh we mentioned this
+
+ align:start position:0%
+pictures of it uh we mentioned this
+ 
+
+ align:start position:0%
+pictures of it uh we mentioned this
+story already the discovery of induction
+
+ align:start position:0%
+story already the discovery of induction
+ 
+
+ align:start position:0%
+story already the discovery of induction
+where does that closure begin remember
+
+ align:start position:0%
+where does that closure begin remember
+ 
+
+ align:start position:0%
+where does that closure begin remember
+it's a group it's a neural group all
+
+ align:start position:0%
+it's a group it's a neural group all
+ 
+
+ align:start position:0%
+it's a group it's a neural group all
+along the back of the organism and then
+
+ align:start position:0%
+along the back of the organism and then
+ 
+
+ align:start position:0%
+along the back of the organism and then
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+uh it forms a tube in as you see in this
+
+ align:start position:0%
+uh it forms a tube in as you see in this
+ 
+
+ align:start position:0%
+uh it forms a tube in as you see in this
+picture okay well where does that where
+
+ align:start position:0%
+picture okay well where does that where
+ 
+
+ align:start position:0%
+picture okay well where does that where
+does this first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+begin here so I show you this
+
+ align:start position:0%
+begin here so I show you this
+ 
+
+ align:start position:0%
+begin here so I show you this
+picture it begins sort of in the middle
+
+ align:start position:0%
+picture it begins sort of in the middle
+ 
+
+ align:start position:0%
+picture it begins sort of in the middle
+so this is the head this is rostral this
+
+ align:start position:0%
+so this is the head this is rostral this
+ 
+
+ align:start position:0%
+so this is the head this is rostral this
+is the CLE end here that's where the
+
+ align:start position:0%
+is the CLE end here that's where the
+ 
+
+ align:start position:0%
+is the CLE end here that's where the
+neural tube is first closing so if we go
+
+ align:start position:0%
+neural tube is first closing so if we go
+ 
+
+ align:start position:0%
+neural tube is first closing so if we go
+further back or further forward it would
+
+ align:start position:0%
+further back or further forward it would
+ 
+
+ align:start position:0%
+further back or further forward it would
+look like this it would be a neural
+
+ align:start position:0%
+look like this it would be a neural
+ 
+
+ align:start position:0%
+look like this it would be a neural
+group still okay so it starts to close
+
+ align:start position:0%
+group still okay so it starts to close
+ 
+
+ align:start position:0%
+group still okay so it starts to close
+that region corresponds to the cervical
+
+ align:start position:0%
+that region corresponds to the cervical
+ 
+
+ align:start position:0%
+that region corresponds to the cervical
+region of the spinal cord the upper part
+
+ align:start position:0%
+region of the spinal cord the upper part
+ 
+
+ align:start position:0%
+region of the spinal cord the upper part
+or the most rostal part of the spinal
+
+ align:start position:0%
+or the most rostal part of the spinal
+ 
+
+ align:start position:0%
+or the most rostal part of the spinal
+cord that's where development is a
+
+ align:start position:0%
+cord that's where development is a
+ 
+
+ align:start position:0%
+cord that's where development is a
+little more advanced that's where the
+
+ align:start position:0%
+little more advanced that's where the
+ 
+
+ align:start position:0%
+little more advanced that's where the
+neural treat first
+
+ align:start position:0%
+neural treat first
+ 
+
+ align:start position:0%
+neural treat first
+closes
+
+ align:start position:0%
+closes
+ 
+
+ align:start position:0%
+closes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the last regions to close as you can
+
+ align:start position:0%
+so the last regions to close as you can
+ 
+
+ align:start position:0%
+so the last regions to close as you can
+guess it sort of zips up this way and
+
+ align:start position:0%
+guess it sort of zips up this way and
+ 
+
+ align:start position:0%
+guess it sort of zips up this way and
+zips up cloudly very tail region here
+
+ align:start position:0%
+zips up cloudly very tail region here
+ 
+
+ align:start position:0%
+zips up cloudly very tail region here
+the last part to close and
+
+ align:start position:0%
+the last part to close and
+ 
+
+ align:start position:0%
+the last part to close and
+similarly the furthest the most Ral part
+
+ align:start position:0%
+similarly the furthest the most Ral part
+ 
+
+ align:start position:0%
+similarly the furthest the most Ral part
+of the CNS the last part to close so if
+
+ align:start position:0%
+of the CNS the last part to close so if
+ 
+
+ align:start position:0%
+of the CNS the last part to close so if
+some abnormality occurs during early
+
+ align:start position:0%
+some abnormality occurs during early
+ 
+
+ align:start position:0%
+some abnormality occurs during early
+development and it does happen you can
+
+ align:start position:0%
+development and it does happen you can
+ 
+
+ align:start position:0%
+development and it does happen you can
+get a failure to completely close when
+
+ align:start position:0%
+get a failure to completely close when
+ 
+
+ align:start position:0%
+get a failure to completely close when
+it doesn't close
+
+ align:start position:0%
+it doesn't close
+ 
+
+ align:start position:0%
+it doesn't close
+codly here you get a condition known as
+
+ align:start position:0%
+codly here you get a condition known as
+ 
+
+ align:start position:0%
+codly here you get a condition known as
+spinabifida
+
+ align:start position:0%
+spinabifida
+ 
+
+ align:start position:0%
+spinabifida
+okay that can be corrected
+
+ align:start position:0%
+okay that can be corrected
+ 
+
+ align:start position:0%
+okay that can be corrected
+surgically but when it fails to close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rostrally the there's a failure of the
+
+ align:start position:0%
+rostrally the there's a failure of the
+ 
+
+ align:start position:0%
+rostrally the there's a failure of the
+of the forbrain to
+
+ align:start position:0%
+of the forbrain to
+ 
+
+ align:start position:0%
+of the forbrain to
+develop you call it anany basically it
+
+ align:start position:0%
+develop you call it anany basically it
+ 
+
+ align:start position:0%
+develop you call it anany basically it
+means without a
+
+ align:start position:0%
+means without a
+ 
+
+ align:start position:0%
+means without a
+brain they do have some brain they have
+
+ align:start position:0%
+brain they do have some brain they have
+ 
+
+ align:start position:0%
+brain they do have some brain they have
+a brain stem
+
+ align:start position:0%
+a brain stem
+ 
+
+ align:start position:0%
+a brain stem
+and babies that are born that way don't
+
+ align:start position:0%
+and babies that are born that way don't
+ 
+
+ align:start position:0%
+and babies that are born that way don't
+live very long it's impossible to repair
+
+ align:start position:0%
+live very long it's impossible to repair
+ 
+
+ align:start position:0%
+live very long it's impossible to repair
+that uh they've been studied a little
+
+ align:start position:0%
+that uh they've been studied a little
+ 
+
+ align:start position:0%
+that uh they've been studied a little
+bit uh in their brief very brief lives
+
+ align:start position:0%
+bit uh in their brief very brief lives
+ 
+
+ align:start position:0%
+bit uh in their brief very brief lives
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's take a look at that
+
+ align:start position:0%
+so let's take a look at that
+ 
+
+ align:start position:0%
+so let's take a look at that
+happening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are interesting animations that
+
+ align:start position:0%
+these are interesting animations that
+ 
+
+ align:start position:0%
+these are interesting animations that
+you can actually find on the web if you
+
+ align:start position:0%
+you can actually find on the web if you
+ 
+
+ align:start position:0%
+you can actually find on the web if you
+look at the cross-section up here don't
+
+ align:start position:0%
+look at the cross-section up here don't
+ 
+
+ align:start position:0%
+look at the cross-section up here don't
+take notes Now look up here look up
+
+ align:start position:0%
+take notes Now look up here look up
+ 
+
+ align:start position:0%
+take notes Now look up here look up
+here look at the screen are you're
+
+ align:start position:0%
+here look at the screen are you're
+ 
+
+ align:start position:0%
+here look at the screen are you're
+missing the main
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+show you see the neural tube in the 3D
+
+ align:start position:0%
+show you see the neural tube in the 3D
+ 
+
+ align:start position:0%
+show you see the neural tube in the 3D
+picture there closing and you see what's
+
+ align:start position:0%
+picture there closing and you see what's
+ 
+
+ align:start position:0%
+picture there closing and you see what's
+happening up there
+
+ align:start position:0%
+happening up there
+ 
+
+ align:start position:0%
+happening up there
+the black dots are the neural crest
+
+ align:start position:0%
+the black dots are the neural crest
+ 
+
+ align:start position:0%
+the black dots are the neural crest
+cells that are staying in the outside
+
+ align:start position:0%
+cells that are staying in the outside
+ 
+
+ align:start position:0%
+cells that are staying in the outside
+they don't get
+
+ align:start position:0%
+they don't get
+ 
+
+ align:start position:0%
+they don't get
+Incorporated the tube closes without
+
+ align:start position:0%
+Incorporated the tube closes without
+ 
+
+ align:start position:0%
+Incorporated the tube closes without
+them the red is the mism okay mostly
+
+ align:start position:0%
+them the red is the mism okay mostly
+ 
+
+ align:start position:0%
+them the red is the mism okay mostly
+muscle tissue there and the vertebrae
+
+ align:start position:0%
+muscle tissue there and the vertebrae
+ 
+
+ align:start position:0%
+muscle tissue there and the vertebrae
+are farming around the around the neural
+
+ align:start position:0%
+are farming around the around the neural
+ 
+
+ align:start position:0%
+are farming around the around the neural
+tube okay so now what are there that's
+
+ align:start position:0%
+tube okay so now what are there that's
+ 
+
+ align:start position:0%
+tube okay so now what are there that's
+where you find the pereral ganglia of
+
+ align:start position:0%
+where you find the pereral ganglia of
+ 
+
+ align:start position:0%
+where you find the pereral ganglia of
+the sympathetic nervous system and
+
+ align:start position:0%
+the sympathetic nervous system and
+ 
+
+ align:start position:0%
+the sympathetic nervous system and
+there's the dorsal root ganglia okay
+
+ align:start position:0%
+there's the dorsal root ganglia okay
+ 
+
+ align:start position:0%
+there's the dorsal root ganglia okay
+what are these out here there other
+
+ align:start position:0%
+what are these out here there other
+ 
+
+ align:start position:0%
+what are these out here there other
+neural crust cells I didn't mention
+
+ align:start position:0%
+neural crust cells I didn't mention
+ 
+
+ align:start position:0%
+neural crust cells I didn't mention
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+before they're migrating into the skin
+
+ align:start position:0%
+before they're migrating into the skin
+ 
+
+ align:start position:0%
+before they're migrating into the skin
+mostly
+
+ align:start position:0%
+mostly
+ 
+
+ align:start position:0%
+mostly
+melanoides the pigmented cells in the
+
+ align:start position:0%
+melanoides the pigmented cells in the
+ 
+
+ align:start position:0%
+melanoides the pigmented cells in the
+skin all
+
+ align:start position:0%
+skin all
+ 
+
+ align:start position:0%
+skin all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and rather than look at that again I
+
+ align:start position:0%
+and rather than look at that again I
+ 
+
+ align:start position:0%
+and rather than look at that again I
+want to show you an actual ual
+
+ align:start position:0%
+want to show you an actual ual
+ 
+
+ align:start position:0%
+want to show you an actual ual
+photograph of neurulation in the quad
+
+ align:start position:0%
+photograph of neurulation in the quad
+ 
+
+ align:start position:0%
+photograph of neurulation in the quad
+crog the
+
+ align:start position:0%
+crog the
+ 
+
+ align:start position:0%
+crog the
+zenopus okay it happens very fast here
+
+ align:start position:0%
+zenopus okay it happens very fast here
+ 
+
+ align:start position:0%
+zenopus okay it happens very fast here
+so we'll look at it several times if you
+
+ align:start position:0%
+so we'll look at it several times if you
+ 
+
+ align:start position:0%
+so we'll look at it several times if you
+just focus on one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these you see the whole thing because
+
+ align:start position:0%
+these you see the whole thing because
+ 
+
+ align:start position:0%
+these you see the whole thing because
+they've speeded it up so much with the
+
+ align:start position:0%
+they've speeded it up so much with the
+ 
+
+ align:start position:0%
+they've speeded it up so much with the
+formation you don't really see the
+
+ align:start position:0%
+formation you don't really see the
+ 
+
+ align:start position:0%
+formation you don't really see the
+neural plate but you see the neural
+
+ align:start position:0%
+neural plate but you see the neural
+ 
+
+ align:start position:0%
+neural plate but you see the neural
+Groove for me and you see it close uh
+
+ align:start position:0%
+Groove for me and you see it close uh
+ 
+
+ align:start position:0%
+Groove for me and you see it close uh
+zips
+
+ align:start position:0%
+zips
+ 
+
+ align:start position:0%
+zips
+up rostrally and codly and then the
+
+ align:start position:0%
+up rostrally and codly and then the
+ 
+
+ align:start position:0%
+up rostrally and codly and then the
+embryo turns a little bit so it looks
+
+ align:start position:0%
+embryo turns a little bit so it looks
+ 
+
+ align:start position:0%
+embryo turns a little bit so it looks
+more like the end of this
+
+ align:start position:0%
+more like the end of this
+ 
+
+ align:start position:0%
+more like the end of this
+one all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you can find those if you do some
+
+ align:start position:0%
+right you can find those if you do some
+ 
+
+ align:start position:0%
+right you can find those if you do some
+searching you can find them
+
+ align:start position:0%
+searching you can find them
+ 
+
+ align:start position:0%
+searching you can find them
+online this is just a picture of that
+
+ align:start position:0%
+online this is just a picture of that
+ 
+
+ align:start position:0%
+online this is just a picture of that
+early stage done with taken with the
+
+ align:start position:0%
+early stage done with taken with the
+ 
+
+ align:start position:0%
+early stage done with taken with the
+electron microscope when they've used a
+
+ align:start position:0%
+electron microscope when they've used a
+ 
+
+ align:start position:0%
+electron microscope when they've used a
+a method called Freeze fracture they
+
+ align:start position:0%
+a method called Freeze fracture they
+ 
+
+ align:start position:0%
+a method called Freeze fracture they
+freeze it solid then if they could get
+
+ align:start position:0%
+freeze it solid then if they could get
+ 
+
+ align:start position:0%
+freeze it solid then if they could get
+it to break along this line they will
+
+ align:start position:0%
+it to break along this line they will
+ 
+
+ align:start position:0%
+it to break along this line they will
+you can see individual
+
+ align:start position:0%
+you can see individual
+ 
+
+ align:start position:0%
+you can see individual
+cells uh in both the CNS there in the
+
+ align:start position:0%
+cells uh in both the CNS there in the
+ 
+
+ align:start position:0%
+cells uh in both the CNS there in the
+neural tube and the mism and the
+
+ align:start position:0%
+neural tube and the mism and the
+ 
+
+ align:start position:0%
+neural tube and the mism and the
+ectoderm and then you see the endoderm
+
+ align:start position:0%
+ectoderm and then you see the endoderm
+ 
+
+ align:start position:0%
+ectoderm and then you see the endoderm
+down here okay and this just shows what
+
+ align:start position:0%
+down here okay and this just shows what
+ 
+
+ align:start position:0%
+down here okay and this just shows what
+it's like in humans at particular stages
+
+ align:start position:0%
+it's like in humans at particular stages
+ 
+
+ align:start position:0%
+it's like in humans at particular stages
+22 and 24
+
+ align:start position:0%
+22 and 24
+ 
+
+ align:start position:0%
+22 and 24
+days after
+
+ align:start position:0%
+days after
+ 
+
+ align:start position:0%
+days after
+conception uh
+
+ align:start position:0%
+conception uh
+ 
+
+ align:start position:0%
+conception uh
+this is I pick this because it's right
+
+ align:start position:0%
+this is I pick this because it's right
+ 
+
+ align:start position:0%
+this is I pick this because it's right
+after the neural tube starts to close in
+
+ align:start position:0%
+after the neural tube starts to close in
+ 
+
+ align:start position:0%
+after the neural tube starts to close in
+a hamster that I've used this it's it
+
+ align:start position:0%
+a hamster that I've used this it's it
+ 
+
+ align:start position:0%
+a hamster that I've used this it's it
+closes on the eighth day after
+
+ align:start position:0%
+closes on the eighth day after
+ 
+
+ align:start position:0%
+closes on the eighth day after
+conception so it can happen in some
+
+ align:start position:0%
+conception so it can happen in some
+ 
+
+ align:start position:0%
+conception so it can happen in some
+species very very fast of course they're
+
+ align:start position:0%
+species very very fast of course they're
+ 
+
+ align:start position:0%
+species very very fast of course they're
+much smaller Too
+
+ align:start position:0%
+much smaller Too
+ 
+
+ align:start position:0%
+much smaller Too
+Human tends to be slower in the larger
+
+ align:start position:0%
+Human tends to be slower in the larger
+ 
+
+ align:start position:0%
+Human tends to be slower in the larger
+animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what is this term Sonic Hedgehog
+
+ align:start position:0%
+okay so what is this term Sonic Hedgehog
+ 
+
+ align:start position:0%
+okay so what is this term Sonic Hedgehog
+we're not going back to comparative
+
+ align:start position:0%
+we're not going back to comparative
+ 
+
+ align:start position:0%
+we're not going back to comparative
+neurology here it's the name for
+
+ align:start position:0%
+neurology here it's the name for
+ 
+
+ align:start position:0%
+neurology here it's the name for
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry it's a it's a
+
+ align:start position:0%
+sorry it's a it's a
+ 
+
+ align:start position:0%
+sorry it's a it's a
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+molecule Sonic Hedgehog it's just the
+
+ align:start position:0%
+molecule Sonic Hedgehog it's just the
+ 
+
+ align:start position:0%
+molecule Sonic Hedgehog it's just the
+name for a
+
+ align:start position:0%
+name for a
+ 
+
+ align:start position:0%
+name for a
+protein okay a molecule but where do
+
+ align:start position:0%
+protein okay a molecule but where do
+ 
+
+ align:start position:0%
+protein okay a molecule but where do
+Sonic Hedgehog it actually has a number
+
+ align:start position:0%
+Sonic Hedgehog it actually has a number
+ 
+
+ align:start position:0%
+Sonic Hedgehog it actually has a number
+of roles in the formation of nervous
+
+ align:start position:0%
+of roles in the formation of nervous
+ 
+
+ align:start position:0%
+of roles in the formation of nervous
+system where does it come from
+
+ align:start position:0%
+system where does it come from
+ 
+
+ align:start position:0%
+system where does it come from
+in this process we're studying right
+
+ align:start position:0%
+in this process we're studying right
+ 
+
+ align:start position:0%
+in this process we're studying right
+now I told you before where the
+
+ align:start position:0%
+now I told you before where the
+ 
+
+ align:start position:0%
+now I told you before where the
+induction comes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the notor Sonic Hedgehog is
+
+ align:start position:0%
+from the notor Sonic Hedgehog is
+ 
+
+ align:start position:0%
+from the notor Sonic Hedgehog is
+generated by the
+
+ align:start position:0%
+generated by the
+ 
+
+ align:start position:0%
+generated by the
+notocord it's induces the formation of
+
+ align:start position:0%
+notocord it's induces the formation of
+ 
+
+ align:start position:0%
+notocord it's induces the formation of
+the nervous system and does other things
+
+ align:start position:0%
+the nervous system and does other things
+ 
+
+ align:start position:0%
+the nervous system and does other things
+too and uh if we look at this
+
+ align:start position:0%
+too and uh if we look at this
+ 
+
+ align:start position:0%
+too and uh if we look at this
+picture they're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coming these would be where the
+
+ align:start position:0%
+coming these would be where the
+ 
+
+ align:start position:0%
+coming these would be where the
+molecules are of course they're probably
+
+ align:start position:0%
+molecules are of course they're probably
+ 
+
+ align:start position:0%
+molecules are of course they're probably
+going all around I'm showing the ones
+
+ align:start position:0%
+going all around I'm showing the ones
+ 
+
+ align:start position:0%
+going all around I'm showing the ones
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+are are in a concentrated way are
+
+ align:start position:0%
+are are in a concentrated way are
+ 
+
+ align:start position:0%
+are are in a concentrated way are
+affecting these cells above it it's
+
+ align:start position:0%
+affecting these cells above it it's
+ 
+
+ align:start position:0%
+affecting these cells above it it's
+still coming there and it's affecting
+
+ align:start position:0%
+still coming there and it's affecting
+ 
+
+ align:start position:0%
+still coming there and it's affecting
+this lower part of the cord it serves as
+
+ align:start position:0%
+this lower part of the cord it serves as
+ 
+
+ align:start position:0%
+this lower part of the cord it serves as
+a ventralizing influence it makes that
+
+ align:start position:0%
+a ventralizing influence it makes that
+ 
+
+ align:start position:0%
+a ventralizing influence it makes that
+ventral part
+
+ align:start position:0%
+ventral part
+ 
+
+ align:start position:0%
+ventral part
+of the neural tube see they're still
+
+ align:start position:0%
+of the neural tube see they're still
+ 
+
+ align:start position:0%
+of the neural tube see they're still
+here it makes the cells here form
+
+ align:start position:0%
+here it makes the cells here form
+ 
+
+ align:start position:0%
+here it makes the cells here form
+differently than the cells up
+
+ align:start position:0%
+differently than the cells up
+ 
+
+ align:start position:0%
+differently than the cells up
+here without Sonic Hedgehog and its
+
+ align:start position:0%
+here without Sonic Hedgehog and its
+ 
+
+ align:start position:0%
+here without Sonic Hedgehog and its
+ventralizing influence you wouldn't get
+
+ align:start position:0%
+ventralizing influence you wouldn't get
+ 
+
+ align:start position:0%
+ventralizing influence you wouldn't get
+the form early differentiation of motor
+
+ align:start position:0%
+the form early differentiation of motor
+ 
+
+ align:start position:0%
+the form early differentiation of motor
+neurons okay what about the dorsal
+
+ align:start position:0%
+neurons okay what about the dorsal
+ 
+
+ align:start position:0%
+neurons okay what about the dorsal
+part there are induction inductive
+
+ align:start position:0%
+part there are induction inductive
+ 
+
+ align:start position:0%
+part there are induction inductive
+influences on this part the part that
+
+ align:start position:0%
+influences on this part the part that
+ 
+
+ align:start position:0%
+influences on this part the part that
+came from way out here forms the dorsal
+
+ align:start position:0%
+came from way out here forms the dorsal
+ 
+
+ align:start position:0%
+came from way out here forms the dorsal
+part of the
+
+ align:start position:0%
+part of the
+ 
+
+ align:start position:0%
+part of the
+cord those inductive influences came
+
+ align:start position:0%
+cord those inductive influences came
+ 
+
+ align:start position:0%
+cord those inductive influences came
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+ectoderm okay and I mention it here the
+
+ align:start position:0%
+ectoderm okay and I mention it here the
+ 
+
+ align:start position:0%
+ectoderm okay and I mention it here the
+dorsalizing factors are secreted by the
+
+ align:start position:0%
+dorsalizing factors are secreted by the
+ 
+
+ align:start position:0%
+dorsalizing factors are secreted by the
+ectoderm Adent adjacent to the neural
+
+ align:start position:0%
+ectoderm Adent adjacent to the neural
+ 
+
+ align:start position:0%
+ectoderm Adent adjacent to the neural
+tube the main ones are this uh BMP four
+
+ align:start position:0%
+tube the main ones are this uh BMP four
+ 
+
+ align:start position:0%
+tube the main ones are this uh BMP four
+and seven BMP actually means bone
+
+ align:start position:0%
+and seven BMP actually means bone
+ 
+
+ align:start position:0%
+and seven BMP actually means bone
+morphogenetic protein because it has a
+
+ align:start position:0%
+morphogenetic protein because it has a
+ 
+
+ align:start position:0%
+morphogenetic protein because it has a
+role in B bone formation as well but now
+
+ align:start position:0%
+role in B bone formation as well but now
+ 
+
+ align:start position:0%
+role in B bone formation as well but now
+we're talking about its influence on the
+
+ align:start position:0%
+we're talking about its influence on the
+ 
+
+ align:start position:0%
+we're talking about its influence on the
+nervous system so it induces changes in
+
+ align:start position:0%
+nervous system so it induces changes in
+ 
+
+ align:start position:0%
+nervous system so it induces changes in
+the dorsal part of the
+
+ align:start position:0%
+the dorsal part of the
+ 
+
+ align:start position:0%
+the dorsal part of the
+cord okay that has causes those cells to
+
+ align:start position:0%
+cord okay that has causes those cells to
+ 
+
+ align:start position:0%
+cord okay that has causes those cells to
+develop differently than the ones
+
+ align:start position:0%
+develop differently than the ones
+ 
+
+ align:start position:0%
+develop differently than the ones
+eventually that leaves a lot of things
+
+ align:start position:0%
+eventually that leaves a lot of things
+ 
+
+ align:start position:0%
+eventually that leaves a lot of things
+unexplained but at least it was a start
+
+ align:start position:0%
+unexplained but at least it was a start
+ 
+
+ align:start position:0%
+unexplained but at least it was a start
+in looking at how the nervous system
+
+ align:start position:0%
+in looking at how the nervous system
+ 
+
+ align:start position:0%
+in looking at how the nervous system
+develops so now I want to talk about
+
+ align:start position:0%
+develops so now I want to talk about
+ 
+
+ align:start position:0%
+develops so now I want to talk about
+cell division what are the two main
+
+ align:start position:0%
+cell division what are the two main
+ 
+
+ align:start position:0%
+cell division what are the two main
+types of cell division that I describe
+
+ align:start position:0%
+types of cell division that I describe
+ 
+
+ align:start position:0%
+types of cell division that I describe
+in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chapter there are differences in cell
+
+ align:start position:0%
+chapter there are differences in cell
+ 
+
+ align:start position:0%
+chapter there are differences in cell
+division that make a huge difference in
+
+ align:start position:0%
+division that make a huge difference in
+ 
+
+ align:start position:0%
+division that make a huge difference in
+how the nervous system
+
+ align:start position:0%
+how the nervous system
+ 
+
+ align:start position:0%
+how the nervous system
+forms symmetric and asymmetric and for
+
+ align:start position:0%
+forms symmetric and asymmetric and for
+ 
+
+ align:start position:0%
+forms symmetric and asymmetric and for
+that we need to look at a picture like
+
+ align:start position:0%
+that we need to look at a picture like
+ 
+
+ align:start position:0%
+that we need to look at a picture like
+this this is the cell
+
+ align:start position:0%
+this this is the cell
+ 
+
+ align:start position:0%
+this this is the cell
+cycle
+
+ align:start position:0%
+cycle
+ 
+
+ align:start position:0%
+cycle
+uh the cell here moves away from The
+
+ align:start position:0%
+uh the cell here moves away from The
+ 
+
+ align:start position:0%
+uh the cell here moves away from The
+ventricle but when I say the cell I
+
+ align:start position:0%
+ventricle but when I say the cell I
+ 
+
+ align:start position:0%
+ventricle but when I say the cell I
+really mean the nucleus cell because
+
+ align:start position:0%
+really mean the nucleus cell because
+ 
+
+ align:start position:0%
+really mean the nucleus cell because
+it's ATT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attached to the P out here to The
+
+ align:start position:0%
+attached to the P out here to The
+ 
+
+ align:start position:0%
+attached to the P out here to The
+ventricle
+
+ align:start position:0%
+ventricle
+ 
+
+ align:start position:0%
+ventricle
+here but it moves away from The
+
+ align:start position:0%
+here but it moves away from The
+ 
+
+ align:start position:0%
+here but it moves away from The
+ventricle in order to synthesize its DNA
+
+ align:start position:0%
+ventricle in order to synthesize its DNA
+ 
+
+ align:start position:0%
+ventricle in order to synthesize its DNA
+moves towards the ventricle in order to
+
+ align:start position:0%
+moves towards the ventricle in order to
+ 
+
+ align:start position:0%
+moves towards the ventricle in order to
+undergo
+
+ align:start position:0%
+undergo
+ 
+
+ align:start position:0%
+undergo
+mitosis and it can undergo
+
+ align:start position:0%
+mitosis and it can undergo
+ 
+
+ align:start position:0%
+mitosis and it can undergo
+mitosis with a symmetric split or an
+
+ align:start position:0%
+mitosis with a symmetric split or an
+ 
+
+ align:start position:0%
+mitosis with a symmetric split or an
+asymmetric
+
+ align:start position:0%
+asymmetric
+ 
+
+ align:start position:0%
+asymmetric
+split when it spits split symmetrically
+
+ align:start position:0%
+split when it spits split symmetrically
+ 
+
+ align:start position:0%
+split when it spits split symmetrically
+it tends to submit uh to split at a
+
+ align:start position:0%
+it tends to submit uh to split at a
+ 
+
+ align:start position:0%
+it tends to submit uh to split at a
+along a line that's at right angles to
+
+ align:start position:0%
+along a line that's at right angles to
+ 
+
+ align:start position:0%
+along a line that's at right angles to
+the ventricular
+
+ align:start position:0%
+the ventricular
+ 
+
+ align:start position:0%
+the ventricular
+surface and when it does that the
+
+ align:start position:0%
+surface and when it does that the
+ 
+
+ align:start position:0%
+surface and when it does that the
+distribution of proteins in the
+
+ align:start position:0%
+distribution of proteins in the
+ 
+
+ align:start position:0%
+distribution of proteins in the
+cell there's two proteins in particular
+
+ align:start position:0%
+cell there's two proteins in particular
+ 
+
+ align:start position:0%
+cell there's two proteins in particular
+uh tends to be pretty even in the two
+
+ align:start position:0%
+uh tends to be pretty even in the two
+ 
+
+ align:start position:0%
+uh tends to be pretty even in the two
+daughter cells so the two uh daughter
+
+ align:start position:0%
+daughter cells so the two uh daughter
+ 
+
+ align:start position:0%
+daughter cells so the two uh daughter
+cells will behave pretty similarly
+
+ align:start position:0%
+cells will behave pretty similarly
+ 
+
+ align:start position:0%
+cells will behave pretty similarly
+basically they became they remain stem
+
+ align:start position:0%
+basically they became they remain stem
+ 
+
+ align:start position:0%
+basically they became they remain stem
+cells they keep dividing okay
+
+ align:start position:0%
+cells they keep dividing okay
+ 
+
+ align:start position:0%
+cells they keep dividing okay
+but when it splits
+
+ align:start position:0%
+but when it splits
+ 
+
+ align:start position:0%
+but when it splits
+asymmetrically you end up with a very
+
+ align:start position:0%
+asymmetrically you end up with a very
+ 
+
+ align:start position:0%
+asymmetrically you end up with a very
+uneven distribution of those proteins
+
+ align:start position:0%
+uneven distribution of those proteins
+ 
+
+ align:start position:0%
+uneven distribution of those proteins
+Notch and numb they're
+
+ align:start position:0%
+Notch and numb they're
+ 
+
+ align:start position:0%
+Notch and numb they're
+called uh and now you get the two cells
+
+ align:start position:0%
+called uh and now you get the two cells
+ 
+
+ align:start position:0%
+called uh and now you get the two cells
+behave differently one remains a stem
+
+ align:start position:0%
+behave differently one remains a stem
+ 
+
+ align:start position:0%
+behave differently one remains a stem
+cell it keeps dividing the other one
+
+ align:start position:0%
+cell it keeps dividing the other one
+ 
+
+ align:start position:0%
+cell it keeps dividing the other one
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+postotic and does something very
+
+ align:start position:0%
+postotic and does something very
+ 
+
+ align:start position:0%
+postotic and does something very
+differently it migrates
+
+ align:start position:0%
+differently it migrates
+ 
+
+ align:start position:0%
+differently it migrates
+away and in many cases the migration is
+
+ align:start position:0%
+away and in many cases the migration is
+ 
+
+ align:start position:0%
+away and in many cases the migration is
+simply
+
+ align:start position:0%
+simply
+ 
+
+ align:start position:0%
+simply
+like over here in the cell cycle the
+
+ align:start position:0%
+like over here in the cell cycle the
+ 
+
+ align:start position:0%
+like over here in the cell cycle the
+nucleus just moves away from The
+
+ align:start position:0%
+nucleus just moves away from The
+ 
+
+ align:start position:0%
+nucleus just moves away from The
+ventricle it can be doing that the
+
+ align:start position:0%
+ventricle it can be doing that the
+ 
+
+ align:start position:0%
+ventricle it can be doing that the
+attachments can remain and kahal saw
+
+ align:start position:0%
+attachments can remain and kahal saw
+ 
+
+ align:start position:0%
+attachments can remain and kahal saw
+things like this
+
+ align:start position:0%
+things like this
+ 
+
+ align:start position:0%
+things like this
+um these are the way they look in GOI in
+
+ align:start position:0%
+um these are the way they look in GOI in
+ 
+
+ align:start position:0%
+um these are the way they look in GOI in
+many cases he might have been looking at
+
+ align:start position:0%
+many cases he might have been looking at
+ 
+
+ align:start position:0%
+many cases he might have been looking at
+two cells here but in some cases they
+
+ align:start position:0%
+two cells here but in some cases they
+ 
+
+ align:start position:0%
+two cells here but in some cases they
+might might be cells with two
+
+ align:start position:0%
+might might be cells with two
+ 
+
+ align:start position:0%
+might might be cells with two
+nuclei here's a cell that's lost it's
+
+ align:start position:0%
+nuclei here's a cell that's lost it's
+ 
+
+ align:start position:0%
+nuclei here's a cell that's lost it's
+external process okay all of these and
+
+ align:start position:0%
+external process okay all of these and
+ 
+
+ align:start position:0%
+external process okay all of these and
+here they've regained the attachment to
+
+ align:start position:0%
+here they've regained the attachment to
+ 
+
+ align:start position:0%
+here they've regained the attachment to
+the Pia and when the nucleus just moves
+
+ align:start position:0%
+the Pia and when the nucleus just moves
+ 
+
+ align:start position:0%
+the Pia and when the nucleus just moves
+further and further from The ventricle
+
+ align:start position:0%
+further and further from The ventricle
+ 
+
+ align:start position:0%
+further and further from The ventricle
+and never returns it's we say it's
+
+ align:start position:0%
+and never returns it's we say it's
+ 
+
+ align:start position:0%
+and never returns it's we say it's
+migrating we say it's migrating by
+
+ align:start position:0%
+migrating we say it's migrating by
+ 
+
+ align:start position:0%
+migrating we say it's migrating by
+nuclear
+
+ align:start position:0%
+nuclear
+ 
+
+ align:start position:0%
+nuclear
+translocation first type of migration
+
+ align:start position:0%
+translocation first type of migration
+ 
+
+ align:start position:0%
+translocation first type of migration
+okay here's his picture of the chick's
+
+ align:start position:0%
+okay here's his picture of the chick's
+ 
+
+ align:start position:0%
+okay here's his picture of the chick's
+spinal cord and the third day of
+
+ align:start position:0%
+spinal cord and the third day of
+ 
+
+ align:start position:0%
+spinal cord and the third day of
+incubation chicks grow up very fast
+
+ align:start position:0%
+incubation chicks grow up very fast
+ 
+
+ align:start position:0%
+incubation chicks grow up very fast
+they're favorite in know embryologist
+
+ align:start position:0%
+they're favorite in know embryologist
+ 
+
+ align:start position:0%
+they're favorite in know embryologist
+because you can cut a little window in
+
+ align:start position:0%
+because you can cut a little window in
+ 
+
+ align:start position:0%
+because you can cut a little window in
+the egg and you can look at these things
+
+ align:start position:0%
+the egg and you can look at these things
+ 
+
+ align:start position:0%
+the egg and you can look at these things
+happening okay and note that some of the
+
+ align:start position:0%
+happening okay and note that some of the
+ 
+
+ align:start position:0%
+happening okay and note that some of the
+cells are right near the ventricle but
+
+ align:start position:0%
+cells are right near the ventricle but
+ 
+
+ align:start position:0%
+cells are right near the ventricle but
+all of them that he shows in this
+
+ align:start position:0%
+all of them that he shows in this
+ 
+
+ align:start position:0%
+all of them that he shows in this
+particular picture are attached to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pia so it's really similar to the roof
+
+ align:start position:0%
+Pia so it's really similar to the roof
+ 
+
+ align:start position:0%
+Pia so it's really similar to the roof
+plate and floor plate there it's just
+
+ align:start position:0%
+plate and floor plate there it's just
+ 
+
+ align:start position:0%
+plate and floor plate there it's just
+that this s a lot longer here and
+
+ align:start position:0%
+that this s a lot longer here and
+ 
+
+ align:start position:0%
+that this s a lot longer here and
+there's more of
+
+ align:start position:0%
+there's more of
+ 
+
+ align:start position:0%
+there's more of
+them all right well if you look at other
+
+ align:start position:0%
+them all right well if you look at other
+ 
+
+ align:start position:0%
+them all right well if you look at other
+day three
+
+ align:start position:0%
+day three
+ 
+
+ align:start position:0%
+day three
+pictures
+
+ align:start position:0%
+pictures
+ 
+
+ align:start position:0%
+pictures
+uh you'll let's just look at that right
+
+ align:start position:0%
+uh you'll let's just look at that right
+ 
+
+ align:start position:0%
+uh you'll let's just look at that right
+now here's another dayree
+
+ align:start position:0%
+now here's another dayree
+ 
+
+ align:start position:0%
+now here's another dayree
+picture GOI is
+
+ align:start position:0%
+picture GOI is
+ 
+
+ align:start position:0%
+picture GOI is
+selected sometimes you're getting more
+
+ align:start position:0%
+selected sometimes you're getting more
+ 
+
+ align:start position:0%
+selected sometimes you're getting more
+advanced cells when you're looking at
+
+ align:start position:0%
+advanced cells when you're looking at
+ 
+
+ align:start position:0%
+advanced cells when you're looking at
+developing animals sometimes you're
+
+ align:start position:0%
+developing animals sometimes you're
+ 
+
+ align:start position:0%
+developing animals sometimes you're
+getting uh the more the early developing
+
+ align:start position:0%
+getting uh the more the early developing
+ 
+
+ align:start position:0%
+getting uh the more the early developing
+cells but you see on that same day
+
+ align:start position:0%
+cells but you see on that same day
+ 
+
+ align:start position:0%
+cells but you see on that same day
+perhaps later in the day
+
+ align:start position:0%
+perhaps later in the day
+ 
+
+ align:start position:0%
+perhaps later in the day
+he was able to
+
+ align:start position:0%
+he was able to
+ 
+
+ align:start position:0%
+he was able to
+identify ventral and dorsal Roots foring
+
+ align:start position:0%
+identify ventral and dorsal Roots foring
+ 
+
+ align:start position:0%
+identify ventral and dorsal Roots foring
+how did he do
+
+ align:start position:0%
+how did he do
+ 
+
+ align:start position:0%
+how did he do
+that by recognizing
+
+ align:start position:0%
+that by recognizing
+ 
+
+ align:start position:0%
+that by recognizing
+something that he was probably the first
+
+ align:start position:0%
+something that he was probably the first
+ 
+
+ align:start position:0%
+something that he was probably the first
+to recognize and he named
+
+ align:start position:0%
+to recognize and he named
+ 
+
+ align:start position:0%
+to recognize and he named
+them the active growing tips that we
+
+ align:start position:0%
+them the active growing tips that we
+ 
+
+ align:start position:0%
+them the active growing tips that we
+call a growth cone processes extending
+
+ align:start position:0%
+call a growth cone processes extending
+ 
+
+ align:start position:0%
+call a growth cone processes extending
+out and when he saw that happening here
+
+ align:start position:0%
+out and when he saw that happening here
+ 
+
+ align:start position:0%
+out and when he saw that happening here
+he looked at them a little older he
+
+ align:start position:0%
+he looked at them a little older he
+ 
+
+ align:start position:0%
+he looked at them a little older he
+would see the growth cone further away
+
+ align:start position:0%
+would see the growth cone further away
+ 
+
+ align:start position:0%
+would see the growth cone further away
+he could see that an ax an axon was
+
+ align:start position:0%
+he could see that an ax an axon was
+ 
+
+ align:start position:0%
+he could see that an ax an axon was
+growing forming a vental root so he
+
+ align:start position:0%
+growing forming a vental root so he
+ 
+
+ align:start position:0%
+growing forming a vental root so he
+started seeing
+
+ align:start position:0%
+started seeing
+ 
+
+ align:start position:0%
+started seeing
+that uh in day three of the
+
+ align:start position:0%
+that uh in day three of the
+ 
+
+ align:start position:0%
+that uh in day three of the
+chick he also grow saw growth cones
+
+ align:start position:0%
+chick he also grow saw growth cones
+ 
+
+ align:start position:0%
+chick he also grow saw growth cones
+within the spinal developing spinal cord
+
+ align:start position:0%
+within the spinal developing spinal cord
+ 
+
+ align:start position:0%
+within the spinal developing spinal cord
+and here he saw some of those cells of
+
+ align:start position:0%
+and here he saw some of those cells of
+ 
+
+ align:start position:0%
+and here he saw some of those cells of
+the neural crest that weren't in the CNS
+
+ align:start position:0%
+the neural crest that weren't in the CNS
+ 
+
+ align:start position:0%
+the neural crest that weren't in the CNS
+he saw saw them with two growth cones
+
+ align:start position:0%
+he saw saw them with two growth cones
+ 
+
+ align:start position:0%
+he saw saw them with two growth cones
+one growing out towards the periphery
+
+ align:start position:0%
+one growing out towards the periphery
+ 
+
+ align:start position:0%
+one growing out towards the periphery
+another one
+
+ align:start position:0%
+another one
+ 
+
+ align:start position:0%
+another one
+growing in towards the in and right into
+
+ align:start position:0%
+growing in towards the in and right into
+ 
+
+ align:start position:0%
+growing in towards the in and right into
+the neural
+
+ align:start position:0%
+the neural
+ 
+
+ align:start position:0%
+the neural
+tool okay that was Cal's work so
+
+ align:start position:0%
+tool okay that was Cal's work so
+ 
+
+ align:start position:0%
+tool okay that was Cal's work so
+here I'm asking how did neuroscientists
+
+ align:start position:0%
+here I'm asking how did neuroscientists
+ 
+
+ align:start position:0%
+here I'm asking how did neuroscientists
+come to know that there are at least two
+
+ align:start position:0%
+come to know that there are at least two
+ 
+
+ align:start position:0%
+come to know that there are at least two
+major modes of cell migration in the
+
+ align:start position:0%
+major modes of cell migration in the
+ 
+
+ align:start position:0%
+major modes of cell migration in the
+embryonic central nervous system here's
+
+ align:start position:0%
+embryonic central nervous system here's
+ 
+
+ align:start position:0%
+embryonic central nervous system here's
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+happened I just describe nuclear
+
+ align:start position:0%
+happened I just describe nuclear
+ 
+
+ align:start position:0%
+happened I just describe nuclear
+translocation as a type of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+migration like this picture here when
+
+ align:start position:0%
+migration like this picture here when
+ 
+
+ align:start position:0%
+migration like this picture here when
+these cells are moving like this one
+
+ align:start position:0%
+these cells are moving like this one
+ 
+
+ align:start position:0%
+these cells are moving like this one
+it's moved very far it's moved way out
+
+ align:start position:0%
+it's moved very far it's moved way out
+ 
+
+ align:start position:0%
+it's moved very far it's moved way out
+towards the peel surface if it never
+
+ align:start position:0%
+towards the peel surface if it never
+ 
+
+ align:start position:0%
+towards the peel surface if it never
+comes back because it's not in the cell
+
+ align:start position:0%
+comes back because it's not in the cell
+ 
+
+ align:start position:0%
+comes back because it's not in the cell
+cycle anymore it we say it's migrated
+
+ align:start position:0%
+cycle anymore it we say it's migrated
+ 
+
+ align:start position:0%
+cycle anymore it we say it's migrated
+okay and eventually it loses its
+
+ align:start position:0%
+okay and eventually it loses its
+ 
+
+ align:start position:0%
+okay and eventually it loses its
+process and usually loses both of its
+
+ align:start position:0%
+process and usually loses both of its
+ 
+
+ align:start position:0%
+process and usually loses both of its
+attachments to the piia on the one side
+
+ align:start position:0%
+attachments to the piia on the one side
+ 
+
+ align:start position:0%
+attachments to the piia on the one side
+and to The ventricle on the other
+
+ align:start position:0%
+and to The ventricle on the other
+ 
+
+ align:start position:0%
+and to The ventricle on the other
+okay that had been
+
+ align:start position:0%
+okay that had been
+ 
+
+ align:start position:0%
+okay that had been
+described had been seen by kahal it was
+
+ align:start position:0%
+described had been seen by kahal it was
+ 
+
+ align:start position:0%
+described had been seen by kahal it was
+described by Kent morest who was at
+
+ align:start position:0%
+described by Kent morest who was at
+ 
+
+ align:start position:0%
+described by Kent morest who was at
+Harvard and then moved to University of
+
+ align:start position:0%
+Harvard and then moved to University of
+ 
+
+ align:start position:0%
+Harvard and then moved to University of
+Connecticut and then a man named POS
+
+ align:start position:0%
+Connecticut and then a man named POS
+ 
+
+ align:start position:0%
+Connecticut and then a man named POS
+gorak also at Harvard but then he moved
+
+ align:start position:0%
+gorak also at Harvard but then he moved
+ 
+
+ align:start position:0%
+gorak also at Harvard but then he moved
+to Yale he discovered he worked on a
+
+ align:start position:0%
+to Yale he discovered he worked on a
+ 
+
+ align:start position:0%
+to Yale he discovered he worked on a
+different part of the brain and he
+
+ align:start position:0%
+different part of the brain and he
+ 
+
+ align:start position:0%
+different part of the brain and he
+worked on primates he discovered
+
+ align:start position:0%
+worked on primates he discovered
+ 
+
+ align:start position:0%
+worked on primates he discovered
+evidence that in
+
+ align:start position:0%
+evidence that in
+ 
+
+ align:start position:0%
+evidence that in
+primates that is not house cells
+
+ align:start position:0%
+primates that is not house cells
+ 
+
+ align:start position:0%
+primates that is not house cells
+migrated they attached to a G cell that
+
+ align:start position:0%
+migrated they attached to a G cell that
+ 
+
+ align:start position:0%
+migrated they attached to a G cell that
+was elongated and they used the G cell
+
+ align:start position:0%
+was elongated and they used the G cell
+ 
+
+ align:start position:0%
+was elongated and they used the G cell
+sort of as a lad and they moved along it
+
+ align:start position:0%
+sort of as a lad and they moved along it
+ 
+
+ align:start position:0%
+sort of as a lad and they moved along it
+so he said that's the way cells in the
+
+ align:start position:0%
+so he said that's the way cells in the
+ 
+
+ align:start position:0%
+so he said that's the way cells in the
+central nervous system migrate and there
+
+ align:start position:0%
+central nervous system migrate and there
+ 
+
+ align:start position:0%
+central nervous system migrate and there
+actually became a sort of a conflict
+
+ align:start position:0%
+actually became a sort of a conflict
+ 
+
+ align:start position:0%
+actually became a sort of a conflict
+between these two views which was really
+
+ align:start position:0%
+between these two views which was really
+ 
+
+ align:start position:0%
+between these two views which was really
+silly because as you might expect both
+
+ align:start position:0%
+silly because as you might expect both
+ 
+
+ align:start position:0%
+silly because as you might expect both
+occur
+
+ align:start position:0%
+occur
+ 
+
+ align:start position:0%
+occur
+okay and I want you to know how that
+
+ align:start position:0%
+okay and I want you to know how that
+ 
+
+ align:start position:0%
+okay and I want you to know how that
+argument was
+
+ align:start position:0%
+argument was
+ 
+
+ align:start position:0%
+argument was
+settled
+
+ align:start position:0%
+settled
+ 
+
+ align:start position:0%
+settled
+by proof that nuclear
+
+ align:start position:0%
+by proof that nuclear
+ 
+
+ align:start position:0%
+by proof that nuclear
+translocation is not just in the spinal
+
+ align:start position:0%
+translocation is not just in the spinal
+ 
+
+ align:start position:0%
+translocation is not just in the spinal
+cord but right in the brain can be the
+
+ align:start position:0%
+cord but right in the brain can be the
+ 
+
+ align:start position:0%
+cord but right in the brain can be the
+major mode of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+movement now we know there's other kinds
+
+ align:start position:0%
+movement now we know there's other kinds
+ 
+
+ align:start position:0%
+movement now we know there's other kinds
+of cell movement too along other
+
+ align:start position:0%
+of cell movement too along other
+ 
+
+ align:start position:0%
+of cell movement too along other
+substrate factors but we're just going
+
+ align:start position:0%
+substrate factors but we're just going
+ 
+
+ align:start position:0%
+substrate factors but we're just going
+to talk about this and we'll talk more
+
+ align:start position:0%
+to talk about this and we'll talk more
+ 
+
+ align:start position:0%
+to talk about this and we'll talk more
+about guidance by radial real cells much
+
+ align:start position:0%
+about guidance by radial real cells much
+ 
+
+ align:start position:0%
+about guidance by radial real cells much
+later when we talk about development of
+
+ align:start position:0%
+later when we talk about development of
+ 
+
+ align:start position:0%
+later when we talk about development of
+Cortex but let's talk about a study
+
+ align:start position:0%
+Cortex but let's talk about a study
+ 
+
+ align:start position:0%
+Cortex but let's talk about a study
+using it was by these two people morest
+
+ align:start position:0%
+using it was by these two people morest
+ 
+
+ align:start position:0%
+using it was by these two people morest
+and Valerie domask who was a student of
+
+ align:start position:0%
+and Valerie domask who was a student of
+ 
+
+ align:start position:0%
+and Valerie domask who was a student of
+Naas here at MIT that went to work with
+
+ align:start position:0%
+Naas here at MIT that went to work with
+ 
+
+ align:start position:0%
+Naas here at MIT that went to work with
+mores this will be the just briefly the
+
+ align:start position:0%
+mores this will be the just briefly the
+ 
+
+ align:start position:0%
+mores this will be the just briefly the
+last topic they used they were studying
+
+ align:start position:0%
+last topic they used they were studying
+ 
+
+ align:start position:0%
+last topic they used they were studying
+a cell in the
+
+ align:start position:0%
+a cell in the
+ 
+
+ align:start position:0%
+a cell in the
+tectum that was very interesting because
+
+ align:start position:0%
+tectum that was very interesting because
+ 
+
+ align:start position:0%
+tectum that was very interesting because
+it always if you look at the at the
+
+ align:start position:0%
+it always if you look at the at the
+ 
+
+ align:start position:0%
+it always if you look at the at the
+adult you would see the cell and its
+
+ align:start position:0%
+adult you would see the cell and its
+ 
+
+ align:start position:0%
+adult you would see the cell and its
+dendrites here near the surface of the
+
+ align:start position:0%
+dendrites here near the surface of the
+ 
+
+ align:start position:0%
+dendrites here near the surface of the
+tectum it always the initial part of its
+
+ align:start position:0%
+tectum it always the initial part of its
+ 
+
+ align:start position:0%
+tectum it always the initial part of its
+axon had this peculiar bend it looks
+
+ align:start position:0%
+axon had this peculiar bend it looks
+ 
+
+ align:start position:0%
+axon had this peculiar bend it looks
+like looks like a the crook in a
+
+ align:start position:0%
+like looks like a the crook in a
+ 
+
+ align:start position:0%
+like looks like a the crook in a
+shepherd's staff so it was called The
+
+ align:start position:0%
+shepherd's staff so it was called The
+ 
+
+ align:start position:0%
+shepherd's staff so it was called The
+Shepherd's crook
+
+ align:start position:0%
+Shepherd's crook
+ 
+
+ align:start position:0%
+Shepherd's crook
+cell that was the name it had they look
+
+ align:start position:0%
+cell that was the name it had they look
+ 
+
+ align:start position:0%
+cell that was the name it had they look
+at earlier and earlier periods they kept
+
+ align:start position:0%
+at earlier and earlier periods they kept
+ 
+
+ align:start position:0%
+at earlier and earlier periods they kept
+seeing the crook but it they found a
+
+ align:start position:0%
+seeing the crook but it they found a
+ 
+
+ align:start position:0%
+seeing the crook but it they found a
+period where the axon was just beginning
+
+ align:start position:0%
+period where the axon was just beginning
+ 
+
+ align:start position:0%
+period where the axon was just beginning
+to form it had the peculiar Bend there's
+
+ align:start position:0%
+to form it had the peculiar Bend there's
+ 
+
+ align:start position:0%
+to form it had the peculiar Bend there's
+the growth cone and then they saw that
+
+ align:start position:0%
+the growth cone and then they saw that
+ 
+
+ align:start position:0%
+the growth cone and then they saw that
+well at that stage the cell body was way
+
+ align:start position:0%
+well at that stage the cell body was way
+ 
+
+ align:start position:0%
+well at that stage the cell body was way
+down here near The ventricle the cell
+
+ align:start position:0%
+down here near The ventricle the cell
+ 
+
+ align:start position:0%
+down here near The ventricle the cell
+body hadn't moved yet it hadn't migrated
+
+ align:start position:0%
+body hadn't moved yet it hadn't migrated
+ 
+
+ align:start position:0%
+body hadn't moved yet it hadn't migrated
+and yet the axon was already forming so
+
+ align:start position:0%
+and yet the axon was already forming so
+ 
+
+ align:start position:0%
+and yet the axon was already forming so
+you have to think of the realize that
+
+ align:start position:0%
+you have to think of the realize that
+ 
+
+ align:start position:0%
+you have to think of the realize that
+the cell extends all the way from
+
+ align:start position:0%
+the cell extends all the way from
+ 
+
+ align:start position:0%
+the cell extends all the way from
+ventricle to the midbrain surface here
+
+ align:start position:0%
+ventricle to the midbrain surface here
+ 
+
+ align:start position:0%
+ventricle to the midbrain surface here
+the axon is forming here long before the
+
+ align:start position:0%
+the axon is forming here long before the
+ 
+
+ align:start position:0%
+the axon is forming here long before the
+cell body is there and then the cell
+
+ align:start position:0%
+cell body is there and then the cell
+ 
+
+ align:start position:0%
+cell body is there and then the cell
+body is moving as you see here
+
+ align:start position:0%
+body is moving as you see here
+ 
+
+ align:start position:0%
+body is moving as you see here
+and finally gets to the point where the
+
+ align:start position:0%
+and finally gets to the point where the
+ 
+
+ align:start position:0%
+and finally gets to the point where the
+axone
+
+ align:start position:0%
+axone
+ 
+
+ align:start position:0%
+axone
+originates they looked at many closely
+
+ align:start position:0%
+originates they looked at many closely
+ 
+
+ align:start position:0%
+originates they looked at many closely
+embryos closely spaced in age and they
+
+ align:start position:0%
+embryos closely spaced in age and they
+ 
+
+ align:start position:0%
+embryos closely spaced in age and they
+saw all these
+
+ align:start position:0%
+saw all these
+ 
+
+ align:start position:0%
+saw all these
+stages and they reported it at the
+
+ align:start position:0%
+stages and they reported it at the
+ 
+
+ align:start position:0%
+stages and they reported it at the
+American Association of anatomists
+
+ align:start position:0%
+American Association of anatomists
+ 
+
+ align:start position:0%
+American Association of anatomists
+meeting where a group called The the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the kahal club met uh was a favorite
+
+ align:start position:0%
+uh the kahal club met uh was a favorite
+ 
+
+ align:start position:0%
+uh the kahal club met uh was a favorite
+meeting of neuroanatomists at that time
+
+ align:start position:0%
+meeting of neuroanatomists at that time
+ 
+
+ align:start position:0%
+meeting of neuroanatomists at that time
+it before there was a society for
+
+ align:start position:0%
+it before there was a society for
+ 
+
+ align:start position:0%
+it before there was a society for
+Neuroscience but their talk was so
+
+ align:start position:0%
+Neuroscience but their talk was so
+ 
+
+ align:start position:0%
+Neuroscience but their talk was so
+convincing and rockich was there he
+
+ align:start position:0%
+convincing and rockich was there he
+ 
+
+ align:start position:0%
+convincing and rockich was there he
+agreed afterwards okay there's got to be
+
+ align:start position:0%
+agreed afterwards okay there's got to be
+ 
+
+ align:start position:0%
+agreed afterwards okay there's got to be
+at least two kinds of migration because
+
+ align:start position:0%
+at least two kinds of migration because
+ 
+
+ align:start position:0%
+at least two kinds of migration because
+I know that that's not how it happens in
+
+ align:start position:0%
+I know that that's not how it happens in
+ 
+
+ align:start position:0%
+I know that that's not how it happens in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+neocortex so that's the story of how
+
+ align:start position:0%
+neocortex so that's the story of how
+ 
+
+ align:start position:0%
+neocortex so that's the story of how
+we're we became more certain that there
+
+ align:start position:0%
+we're we became more certain that there
+ 
+
+ align:start position:0%
+we're we became more certain that there
+were two different kinds of migration
+
+ align:start position:0%
+were two different kinds of migration
+ 
+
+ align:start position:0%
+were two different kinds of migration
+okay so that's where we're going to stop
+
+ align:start position:0%
+okay so that's where we're going to stop
+ 
+
+ align:start position:0%
+okay so that's where we're going to stop
+today uh we've already talked about
+
+ align:start position:0%
+today uh we've already talked about
+ 
+
+ align:start position:0%
+today uh we've already talked about
+this so I guess we finished except for a
+
+ align:start position:0%
+this so I guess we finished except for a
+ 
+
+ align:start position:0%
+this so I guess we finished except for a
+review so I'll post these slides you can
+
+ align:start position:0%
+review so I'll post these slides you can
+ 
+
+ align:start position:0%
+review so I'll post these slides you can
+go over them and we'll be able to talk
+
+ align:start position:0%
+go over them and we'll be able to talk
+ 
+
+ align:start position:0%
+go over them and we'll be able to talk
+about the the next chapter the adults
+
+ align:start position:0%
+about the the next chapter the adults
+ 
+
+ align:start position:0%
+about the the next chapter the adults
+final court on
+
+ align:start position:0%
+final court on
+ 
+
+ align:start position:0%
+final court on
+Friday
\ No newline at end of file
diff --git a/4N68XQDT38c.txt b/4N68XQDT38c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f8f3248fe301fdb7315fd64703384ec47d08047b
--- /dev/null
+++ b/4N68XQDT38c.txt
@@ -0,0 +1,14179 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+should be the most interesting class of
+
+ align:start position:0%
+should be the most interesting class of
+ 
+
+ align:start position:0%
+should be the most interesting class of
+the semester
+
+ align:start position:0%
+the semester
+ 
+
+ align:start position:0%
+the semester
+possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what y'all think of possible
+
+ align:start position:0%
+what y'all think of possible
+ 
+
+ align:start position:0%
+what y'all think of possible
+oh this robert we were discussing
+
+ align:start position:0%
+oh this robert we were discussing
+ 
+
+ align:start position:0%
+oh this robert we were discussing
+earlier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+well let's go let's do the facts first
+
+ align:start position:0%
+well let's go let's do the facts first
+ 
+
+ align:start position:0%
+well let's go let's do the facts first
+let's tell the story
+
+ align:start position:0%
+let's tell the story
+ 
+
+ align:start position:0%
+let's tell the story
+let's start uh let's just go back and
+
+ align:start position:0%
+let's start uh let's just go back and
+ 
+
+ align:start position:0%
+let's start uh let's just go back and
+forth round around until we get it done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i think what the author is doing
+
+ align:start position:0%
+well i think what the author is doing
+ 
+
+ align:start position:0%
+well i think what the author is doing
+there uh is emphasizing
+
+ align:start position:0%
+there uh is emphasizing
+ 
+
+ align:start position:0%
+there uh is emphasizing
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh the first principle of moral behavior
+
+ align:start position:0%
+uh the first principle of moral behavior
+ 
+
+ align:start position:0%
+uh the first principle of moral behavior
+is family
+
+ align:start position:0%
+is family
+ 
+
+ align:start position:0%
+is family
+kinship
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh we have to know his lineage
+
+ align:start position:0%
+that uh we have to know his lineage
+ 
+
+ align:start position:0%
+that uh we have to know his lineage
+before we can know him
+
+ align:start position:0%
+before we can know him
+ 
+
+ align:start position:0%
+before we can know him
+and whatever he does i think there's
+
+ align:start position:0%
+and whatever he does i think there's
+ 
+
+ align:start position:0%
+and whatever he does i think there's
+another and that and um
+
+ align:start position:0%
+another and that and um
+ 
+
+ align:start position:0%
+another and that and um
+that's a big difference
+
+ align:start position:0%
+that's a big difference
+ 
+
+ align:start position:0%
+that's a big difference
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mallory
+
+ align:start position:0%
+mallory
+ 
+
+ align:start position:0%
+mallory
+this is your this is your
+
+ align:start position:0%
+this is your this is your
+ 
+
+ align:start position:0%
+this is your this is your
+king office legend
+
+ align:start position:0%
+king office legend
+ 
+
+ align:start position:0%
+king office legend
+in the first form
+
+ align:start position:0%
+in the first form
+ 
+
+ align:start position:0%
+in the first form
+okay this one here
+
+ align:start position:0%
+okay this one here
+ 
+
+ align:start position:0%
+okay this one here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that is that there's a lot of attention
+
+ align:start position:0%
+that is that there's a lot of attention
+ 
+
+ align:start position:0%
+that is that there's a lot of attention
+given to um
+
+ align:start position:0%
+given to um
+ 
+
+ align:start position:0%
+given to um
+the morality of being a knight
+
+ align:start position:0%
+the morality of being a knight
+ 
+
+ align:start position:0%
+the morality of being a knight
+uh but the first principle is uh first
+
+ align:start position:0%
+uh but the first principle is uh first
+ 
+
+ align:start position:0%
+uh but the first principle is uh first
+principle i think is kinship
+
+ align:start position:0%
+principle i think is kinship
+ 
+
+ align:start position:0%
+principle i think is kinship
+and an interesting principle is
+
+ align:start position:0%
+and an interesting principle is
+ 
+
+ align:start position:0%
+and an interesting principle is
+that it's immoral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to do to mistreat a kinship a relative
+
+ align:start position:0%
+to do to mistreat a kinship a relative
+ 
+
+ align:start position:0%
+to do to mistreat a kinship a relative
+even if you don't know that this direct
+
+ align:start position:0%
+even if you don't know that this direct
+ 
+
+ align:start position:0%
+even if you don't know that this direct
+person is a relative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember that you're not supposed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to respond that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and and there's there's this big to
+
+ align:start position:0%
+so and and there's there's this big to
+ 
+
+ align:start position:0%
+so and and there's there's this big to
+do about all of these relationships
+
+ align:start position:0%
+do about all of these relationships
+ 
+
+ align:start position:0%
+do about all of these relationships
+and you don't discover them immediately
+
+ align:start position:0%
+and you don't discover them immediately
+ 
+
+ align:start position:0%
+and you don't discover them immediately
+you find them out later
+
+ align:start position:0%
+you find them out later
+ 
+
+ align:start position:0%
+you find them out later
+okay so uh
+
+ align:start position:0%
+okay so uh
+ 
+
+ align:start position:0%
+okay so uh
+parzival's father
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goes out
+
+ align:start position:0%
+goes out
+ 
+
+ align:start position:0%
+goes out
+gets married
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh to a no doesn't does a heroic deed
+
+ align:start position:0%
+uh to a no doesn't does a heroic deed
+ 
+
+ align:start position:0%
+uh to a no doesn't does a heroic deed
+marry is a queen as a result of it
+
+ align:start position:0%
+marry is a queen as a result of it
+ 
+
+ align:start position:0%
+marry is a queen as a result of it
+thanks
+
+ align:start position:0%
+thanks
+ 
+
+ align:start position:0%
+thanks
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+gets tired of being a king and goes back
+
+ align:start position:0%
+gets tired of being a king and goes back
+ 
+
+ align:start position:0%
+gets tired of being a king and goes back
+out on the road so to speak
+
+ align:start position:0%
+out on the road so to speak
+ 
+
+ align:start position:0%
+out on the road so to speak
+mary's again
+
+ align:start position:0%
+mary's again
+ 
+
+ align:start position:0%
+mary's again
+finds no legal or moral problem in doing
+
+ align:start position:0%
+finds no legal or moral problem in doing
+ 
+
+ align:start position:0%
+finds no legal or moral problem in doing
+that because
+
+ align:start position:0%
+that because
+ 
+
+ align:start position:0%
+that because
+one uh wife was a pagan and the other
+
+ align:start position:0%
+one uh wife was a pagan and the other
+ 
+
+ align:start position:0%
+one uh wife was a pagan and the other
+one was a christian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well keep going keep y'all getting i
+
+ align:start position:0%
+well keep going keep y'all getting i
+ 
+
+ align:start position:0%
+well keep going keep y'all getting i
+want to hear more about these stories
+
+ align:start position:0%
+want to hear more about these stories
+ 
+
+ align:start position:0%
+want to hear more about these stories
+you can and you can do it bullet wise
+
+ align:start position:0%
+you can and you can do it bullet wise
+ 
+
+ align:start position:0%
+you can and you can do it bullet wise
+just you don't have to go from the
+
+ align:start position:0%
+just you don't have to go from the
+ 
+
+ align:start position:0%
+just you don't have to go from the
+beginning to the end what what were some
+
+ align:start position:0%
+beginning to the end what what were some
+ 
+
+ align:start position:0%
+beginning to the end what what were some
+of the things that struck you about this
+
+ align:start position:0%
+of the things that struck you about this
+ 
+
+ align:start position:0%
+of the things that struck you about this
+and then we're going to tie it all in
+
+ align:start position:0%
+and then we're going to tie it all in
+ 
+
+ align:start position:0%
+and then we're going to tie it all in
+at the end
+
+ align:start position:0%
+at the end
+ 
+
+ align:start position:0%
+at the end
+make sure we get the facts straight
+
+ align:start position:0%
+make sure we get the facts straight
+ 
+
+ align:start position:0%
+make sure we get the facts straight
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember some of the things he did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's a loyalty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah they are afraid that some other
+
+ align:start position:0%
+yeah they are afraid that some other
+ 
+
+ align:start position:0%
+yeah they are afraid that some other
+person
+
+ align:start position:0%
+person
+ 
+
+ align:start position:0%
+person
+might
+
+ align:start position:0%
+might
+ 
+
+ align:start position:0%
+might
+take over his property and do
+
+ align:start position:0%
+take over his property and do
+ 
+
+ align:start position:0%
+take over his property and do
+her and her child some harm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+she doesn't want him to be like his
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all father
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+say that's for me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+i don't i didn't remember that but i uh
+
+ align:start position:0%
+i don't i didn't remember that but i uh
+ 
+
+ align:start position:0%
+i don't i didn't remember that but i uh
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the fisher king
+
+ align:start position:0%
+the fisher king
+ 
+
+ align:start position:0%
+the fisher king
+now let's talk about the fisher king
+
+ align:start position:0%
+now let's talk about the fisher king
+ 
+
+ align:start position:0%
+now let's talk about the fisher king
+let's go into the fisher king in some
+
+ align:start position:0%
+let's go into the fisher king in some
+ 
+
+ align:start position:0%
+let's go into the fisher king in some
+detail
+
+ align:start position:0%
+detail
+ 
+
+ align:start position:0%
+detail
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+when does he encounter the fisher king
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the grail
+
+ align:start position:0%
+this is the grail
+ 
+
+ align:start position:0%
+this is the grail
+grail king
+
+ align:start position:0%
+grail king
+ 
+
+ align:start position:0%
+grail king
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and he doesn't know he's the grill king
+
+ align:start position:0%
+and he doesn't know he's the grill king
+ 
+
+ align:start position:0%
+and he doesn't know he's the grill king
+at first all he sees is a man out in a
+
+ align:start position:0%
+at first all he sees is a man out in a
+ 
+
+ align:start position:0%
+at first all he sees is a man out in a
+boat
+
+ align:start position:0%
+boat
+ 
+
+ align:start position:0%
+boat
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you can read uh quick portions of
+
+ align:start position:0%
+right you can read uh quick portions of
+ 
+
+ align:start position:0%
+right you can read uh quick portions of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+that's legitimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and he didn't know he was the king at
+
+ align:start position:0%
+and he didn't know he was the king at
+ 
+
+ align:start position:0%
+and he didn't know he was the king at
+the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes that's the point i'm getting it
+
+ align:start position:0%
+yes that's the point i'm getting it
+ 
+
+ align:start position:0%
+yes that's the point i'm getting it
+seems like everybody
+
+ align:start position:0%
+seems like everybody
+ 
+
+ align:start position:0%
+seems like everybody
+knows about this right
+
+ align:start position:0%
+knows about this right
+ 
+
+ align:start position:0%
+knows about this right
+but the other thing is that
+
+ align:start position:0%
+but the other thing is that
+ 
+
+ align:start position:0%
+but the other thing is that
+people come what they fault him for
+
+ align:start position:0%
+people come what they fault him for
+ 
+
+ align:start position:0%
+people come what they fault him for
+and i think in today's society
+
+ align:start position:0%
+and i think in today's society
+ 
+
+ align:start position:0%
+and i think in today's society
+would claim innocence because i didn't
+
+ align:start position:0%
+would claim innocence because i didn't
+ 
+
+ align:start position:0%
+would claim innocence because i didn't
+know i didn't know why you liked me but
+
+ align:start position:0%
+know i didn't know why you liked me but
+ 
+
+ align:start position:0%
+know i didn't know why you liked me but
+there he sort of feels like
+
+ align:start position:0%
+there he sort of feels like
+ 
+
+ align:start position:0%
+there he sort of feels like
+he feels guilty
+
+ align:start position:0%
+he feels guilty
+ 
+
+ align:start position:0%
+he feels guilty
+i should have asked the questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the second uh the way i look at it the
+
+ align:start position:0%
+the second uh the way i look at it the
+ 
+
+ align:start position:0%
+the second uh the way i look at it the
+first principles of morality for him are
+
+ align:start position:0%
+first principles of morality for him are
+ 
+
+ align:start position:0%
+first principles of morality for him are
+kinship and the second set of principles
+
+ align:start position:0%
+kinship and the second set of principles
+ 
+
+ align:start position:0%
+kinship and the second set of principles
+are chivalrous
+
+ align:start position:0%
+are chivalrous
+ 
+
+ align:start position:0%
+are chivalrous
+which are connected too
+
+ align:start position:0%
+which are connected too
+ 
+
+ align:start position:0%
+which are connected too
+in some way
+
+ align:start position:0%
+in some way
+ 
+
+ align:start position:0%
+in some way
+uh but yeah let's let's i want to delve
+
+ align:start position:0%
+uh but yeah let's let's i want to delve
+ 
+
+ align:start position:0%
+uh but yeah let's let's i want to delve
+into this question
+
+ align:start position:0%
+into this question
+ 
+
+ align:start position:0%
+into this question
+yeah the the notion of admitting
+
+ align:start position:0%
+yeah the the notion of admitting
+ 
+
+ align:start position:0%
+yeah the the notion of admitting
+wrongdoing and wanting
+
+ align:start position:0%
+wrongdoing and wanting
+ 
+
+ align:start position:0%
+wrongdoing and wanting
+to atone for it atonement is sort of a
+
+ align:start position:0%
+to atone for it atonement is sort of a
+ 
+
+ align:start position:0%
+to atone for it atonement is sort of a
+major theme in this
+
+ align:start position:0%
+major theme in this
+ 
+
+ align:start position:0%
+major theme in this
+book
+
+ align:start position:0%
+book
+ 
+
+ align:start position:0%
+book
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that to me the mistake or the sin seems
+
+ align:start position:0%
+that to me the mistake or the sin seems
+ 
+
+ align:start position:0%
+that to me the mistake or the sin seems
+sort of trivial like not
+
+ align:start position:0%
+sort of trivial like not
+ 
+
+ align:start position:0%
+sort of trivial like not
+not asking you a question out of
+
+ align:start position:0%
+not asking you a question out of
+ 
+
+ align:start position:0%
+not asking you a question out of
+politeness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not a compelling sin to me or
+
+ align:start position:0%
+is not a compelling sin to me or
+ 
+
+ align:start position:0%
+is not a compelling sin to me or
+compelling wrongdoing but
+
+ align:start position:0%
+compelling wrongdoing but
+ 
+
+ align:start position:0%
+compelling wrongdoing but
+it's what's used in the story and
+
+ align:start position:0%
+it's what's used in the story and
+ 
+
+ align:start position:0%
+it's what's used in the story and
+first of all right feels very guilty
+
+ align:start position:0%
+first of all right feels very guilty
+ 
+
+ align:start position:0%
+first of all right feels very guilty
+about it and wants to return for it like
+
+ align:start position:0%
+about it and wants to return for it like
+ 
+
+ align:start position:0%
+about it and wants to return for it like
+makes it his mission
+
+ align:start position:0%
+makes it his mission
+ 
+
+ align:start position:0%
+makes it his mission
+right that was my first make his way
+
+ align:start position:0%
+right that was my first make his way
+ 
+
+ align:start position:0%
+right that was my first make his way
+back to different yeah
+
+ align:start position:0%
+back to different yeah
+ 
+
+ align:start position:0%
+back to different yeah
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+i don't know if you all read joseph
+
+ align:start position:0%
+i don't know if you all read joseph
+ 
+
+ align:start position:0%
+i don't know if you all read joseph
+campbell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+the only reason i haven't assigned
+
+ align:start position:0%
+the only reason i haven't assigned
+ 
+
+ align:start position:0%
+the only reason i haven't assigned
+joseph campbell yet is that i can't
+
+ align:start position:0%
+joseph campbell yet is that i can't
+ 
+
+ align:start position:0%
+joseph campbell yet is that i can't
+figure out which one to assign
+
+ align:start position:0%
+figure out which one to assign
+ 
+
+ align:start position:0%
+figure out which one to assign
+because uh uh i'd have been reading four
+
+ align:start position:0%
+because uh uh i'd have been reading four
+ 
+
+ align:start position:0%
+because uh uh i'd have been reading four
+or five of them and watching
+
+ align:start position:0%
+or five of them and watching
+ 
+
+ align:start position:0%
+or five of them and watching
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this tv program
+
+ align:start position:0%
+this tv program
+ 
+
+ align:start position:0%
+this tv program
+where you know bill moyers
+
+ align:start position:0%
+where you know bill moyers
+ 
+
+ align:start position:0%
+where you know bill moyers
+he does one with bill moyers uh called
+
+ align:start position:0%
+he does one with bill moyers uh called
+ 
+
+ align:start position:0%
+he does one with bill moyers uh called
+the power of it
+
+ align:start position:0%
+the power of it
+ 
+
+ align:start position:0%
+the power of it
+and he's a spectacular lecturer and he's
+
+ align:start position:0%
+and he's a spectacular lecturer and he's
+ 
+
+ align:start position:0%
+and he's a spectacular lecturer and he's
+got some um i've got some video
+
+ align:start position:0%
+got some um i've got some video
+ 
+
+ align:start position:0%
+got some um i've got some video
+videotapes of his in his classes
+
+ align:start position:0%
+videotapes of his in his classes
+ 
+
+ align:start position:0%
+videotapes of his in his classes
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so i think that uh well for me
+
+ align:start position:0%
+so i think that uh well for me
+ 
+
+ align:start position:0%
+so i think that uh well for me
+uh joe joseph campbell is one of my
+
+ align:start position:0%
+uh joe joseph campbell is one of my
+ 
+
+ align:start position:0%
+uh joe joseph campbell is one of my
+maybe top five if you want to put it
+
+ align:start position:0%
+maybe top five if you want to put it
+ 
+
+ align:start position:0%
+maybe top five if you want to put it
+that way scholars
+
+ align:start position:0%
+that way scholars
+ 
+
+ align:start position:0%
+that way scholars
+now here's the big issue that joseph
+
+ align:start position:0%
+now here's the big issue that joseph
+ 
+
+ align:start position:0%
+now here's the big issue that joseph
+campbell makes out of the question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+campbell starts off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+poet by the name of t.s eliot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got a nobel prize for literature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of
+
+ align:start position:0%
+and one of
+ 
+
+ align:start position:0%
+and one of
+one of elliot's pieces
+
+ align:start position:0%
+one of elliot's pieces
+ 
+
+ align:start position:0%
+one of elliot's pieces
+is called the waste land
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in the wasteland
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the wasteland is a place
+
+ align:start position:0%
+the wasteland is a place
+ 
+
+ align:start position:0%
+the wasteland is a place
+where everybody does what everybody else
+
+ align:start position:0%
+where everybody does what everybody else
+ 
+
+ align:start position:0%
+where everybody does what everybody else
+expects you to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you never break out and find your
+
+ align:start position:0%
+so you never break out and find your
+ 
+
+ align:start position:0%
+so you never break out and find your
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+what he calls bliss
+
+ align:start position:0%
+what he calls bliss
+ 
+
+ align:start position:0%
+what he calls bliss
+what i call destiny
+
+ align:start position:0%
+what i call destiny
+ 
+
+ align:start position:0%
+what i call destiny
+you never break out of that you're
+
+ align:start position:0%
+you never break out of that you're
+ 
+
+ align:start position:0%
+you never break out of that you're
+always you come in you learn the rules
+
+ align:start position:0%
+always you come in you learn the rules
+ 
+
+ align:start position:0%
+always you come in you learn the rules
+and you follow them
+
+ align:start position:0%
+and you follow them
+ 
+
+ align:start position:0%
+and you follow them
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh which is good 99 of the time
+
+ align:start position:0%
+uh which is good 99 of the time
+ 
+
+ align:start position:0%
+uh which is good 99 of the time
+the question is when you break out
+
+ align:start position:0%
+the question is when you break out
+ 
+
+ align:start position:0%
+the question is when you break out
+and by what reason do you break out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle really wants to be a good night
+
+ align:start position:0%
+particle really wants to be a good night
+ 
+
+ align:start position:0%
+particle really wants to be a good night
+i'm sorry
+
+ align:start position:0%
+i'm sorry
+ 
+
+ align:start position:0%
+i'm sorry
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+competent night
+
+ align:start position:0%
+competent night
+ 
+
+ align:start position:0%
+competent night
+just playing with words good night okay
+
+ align:start position:0%
+just playing with words good night okay
+ 
+
+ align:start position:0%
+just playing with words good night okay
+uh and he's been taught very well
+
+ align:start position:0%
+uh and he's been taught very well
+ 
+
+ align:start position:0%
+uh and he's been taught very well
+remember his teacher
+
+ align:start position:0%
+remember his teacher
+ 
+
+ align:start position:0%
+remember his teacher
+and the teacher said told him
+
+ align:start position:0%
+and the teacher said told him
+ 
+
+ align:start position:0%
+and the teacher said told him
+virtually when you go to somebody's
+
+ align:start position:0%
+virtually when you go to somebody's
+ 
+
+ align:start position:0%
+virtually when you go to somebody's
+house you don't start a quiz you're
+
+ align:start position:0%
+house you don't start a quiz you're
+ 
+
+ align:start position:0%
+house you don't start a quiz you're
+asking uh questions
+
+ align:start position:0%
+asking uh questions
+ 
+
+ align:start position:0%
+asking uh questions
+that's one of the rules of sugar
+
+ align:start position:0%
+that's one of the rules of sugar
+ 
+
+ align:start position:0%
+that's one of the rules of sugar
+and parcel wants to be
+
+ align:start position:0%
+and parcel wants to be
+ 
+
+ align:start position:0%
+and parcel wants to be
+uh true to all the rules of shiva
+
+ align:start position:0%
+uh true to all the rules of shiva
+ 
+
+ align:start position:0%
+uh true to all the rules of shiva
+but he's sitting there
+
+ align:start position:0%
+but he's sitting there
+ 
+
+ align:start position:0%
+but he's sitting there
+talking to his host
+
+ align:start position:0%
+talking to his host
+ 
+
+ align:start position:0%
+talking to his host
+and his host is in pain
+
+ align:start position:0%
+and his host is in pain
+ 
+
+ align:start position:0%
+and his host is in pain
+and the authors have made it clear that
+
+ align:start position:0%
+and the authors have made it clear that
+ 
+
+ align:start position:0%
+and the authors have made it clear that
+this is the worst kind of pain that a
+
+ align:start position:0%
+this is the worst kind of pain that a
+ 
+
+ align:start position:0%
+this is the worst kind of pain that a
+man can endure
+
+ align:start position:0%
+man can endure
+ 
+
+ align:start position:0%
+man can endure
+okay now actually the worst kind of pain
+
+ align:start position:0%
+okay now actually the worst kind of pain
+ 
+
+ align:start position:0%
+okay now actually the worst kind of pain
+i've heard i've had six physicians tell
+
+ align:start position:0%
+i've heard i've had six physicians tell
+ 
+
+ align:start position:0%
+i've heard i've had six physicians tell
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+that kidney stones the worst kind of
+
+ align:start position:0%
+that kidney stones the worst kind of
+ 
+
+ align:start position:0%
+that kidney stones the worst kind of
+pain a man can endure it's man's
+
+ align:start position:0%
+pain a man can endure it's man's
+ 
+
+ align:start position:0%
+pain a man can endure it's man's
+equivalent
+
+ align:start position:0%
+equivalent
+ 
+
+ align:start position:0%
+equivalent
+of a woman's childbirth
+
+ align:start position:0%
+of a woman's childbirth
+ 
+
+ align:start position:0%
+of a woman's childbirth
+natural childhood
+
+ align:start position:0%
+natural childhood
+ 
+
+ align:start position:0%
+natural childhood
+worse than pains in their army
+
+ align:start position:0%
+worse than pains in their army
+ 
+
+ align:start position:0%
+worse than pains in their army
+and i've had them i know
+
+ align:start position:0%
+and i've had them i know
+ 
+
+ align:start position:0%
+and i've had them i know
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+there is nothing
+
+ align:start position:0%
+there is nothing
+ 
+
+ align:start position:0%
+there is nothing
+fearful attached
+
+ align:start position:0%
+fearful attached
+ 
+
+ align:start position:0%
+fearful attached
+to kidney stones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have not lost my manhood
+
+ align:start position:0%
+i have not lost my manhood
+ 
+
+ align:start position:0%
+i have not lost my manhood
+when i pass a kidney stone this man lost
+
+ align:start position:0%
+when i pass a kidney stone this man lost
+ 
+
+ align:start position:0%
+when i pass a kidney stone this man lost
+his mouth
+
+ align:start position:0%
+his mouth
+ 
+
+ align:start position:0%
+his mouth
+not only that but the tip of that thing
+
+ align:start position:0%
+not only that but the tip of that thing
+ 
+
+ align:start position:0%
+not only that but the tip of that thing
+is still stuck in it
+
+ align:start position:0%
+is still stuck in it
+ 
+
+ align:start position:0%
+is still stuck in it
+so then you ask yourself if if possible
+
+ align:start position:0%
+so then you ask yourself if if possible
+ 
+
+ align:start position:0%
+so then you ask yourself if if possible
+is going to
+
+ align:start position:0%
+is going to
+ 
+
+ align:start position:0%
+is going to
+lift himself up above the rules
+
+ align:start position:0%
+lift himself up above the rules
+ 
+
+ align:start position:0%
+lift himself up above the rules
+now is the time to do it okay you got a
+
+ align:start position:0%
+now is the time to do it okay you got a
+ 
+
+ align:start position:0%
+now is the time to do it okay you got a
+colleague sitting there suffering the
+
+ align:start position:0%
+colleague sitting there suffering the
+ 
+
+ align:start position:0%
+colleague sitting there suffering the
+worst pain they could ever suffer and
+
+ align:start position:0%
+worst pain they could ever suffer and
+ 
+
+ align:start position:0%
+worst pain they could ever suffer and
+it's going to die of it
+
+ align:start position:0%
+it's going to die of it
+ 
+
+ align:start position:0%
+it's going to die of it
+least you could do is say oh my god i
+
+ align:start position:0%
+least you could do is say oh my god i
+ 
+
+ align:start position:0%
+least you could do is say oh my god i
+feel sorry for you
+
+ align:start position:0%
+feel sorry for you
+ 
+
+ align:start position:0%
+feel sorry for you
+possibly didn't do it
+
+ align:start position:0%
+possibly didn't do it
+ 
+
+ align:start position:0%
+possibly didn't do it
+now there's another game that everybody
+
+ align:start position:0%
+now there's another game that everybody
+ 
+
+ align:start position:0%
+now there's another game that everybody
+plays particularly parents
+
+ align:start position:0%
+plays particularly parents
+ 
+
+ align:start position:0%
+plays particularly parents
+there's some lessons you cannot teach a
+
+ align:start position:0%
+there's some lessons you cannot teach a
+ 
+
+ align:start position:0%
+there's some lessons you cannot teach a
+child
+
+ align:start position:0%
+child
+ 
+
+ align:start position:0%
+child
+by giving them the answer first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you got to say you got to put the child
+
+ align:start position:0%
+you got to say you got to put the child
+ 
+
+ align:start position:0%
+you got to say you got to put the child
+in this situation you got everybody does
+
+ align:start position:0%
+in this situation you got everybody does
+ 
+
+ align:start position:0%
+in this situation you got everybody does
+it there are certain situations you get
+
+ align:start position:0%
+it there are certain situations you get
+ 
+
+ align:start position:0%
+it there are certain situations you get
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you just can't tell if you're going to
+
+ align:start position:0%
+you just can't tell if you're going to
+ 
+
+ align:start position:0%
+you just can't tell if you're going to
+give a person some kind of a test you
+
+ align:start position:0%
+give a person some kind of a test you
+ 
+
+ align:start position:0%
+give a person some kind of a test you
+can't tell them
+
+ align:start position:0%
+can't tell them
+ 
+
+ align:start position:0%
+can't tell them
+uh you know uh certain things like for
+
+ align:start position:0%
+uh you know uh certain things like for
+ 
+
+ align:start position:0%
+uh you know uh certain things like for
+example when i had my first test on the
+
+ align:start position:0%
+example when i had my first test on the
+ 
+
+ align:start position:0%
+example when i had my first test on the
+job they couldn't tell me or we got that
+
+ align:start position:0%
+job they couldn't tell me or we got that
+ 
+
+ align:start position:0%
+job they couldn't tell me or we got that
+covered in case you mess up
+
+ align:start position:0%
+covered in case you mess up
+ 
+
+ align:start position:0%
+covered in case you mess up
+i had to believe that this was it
+
+ align:start position:0%
+i had to believe that this was it
+ 
+
+ align:start position:0%
+i had to believe that this was it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so they couldn't tell him
+
+ align:start position:0%
+all right so they couldn't tell him
+ 
+
+ align:start position:0%
+all right so they couldn't tell him
+to ask that question
+
+ align:start position:0%
+to ask that question
+ 
+
+ align:start position:0%
+to ask that question
+and that the result would be that he
+
+ align:start position:0%
+and that the result would be that he
+ 
+
+ align:start position:0%
+and that the result would be that he
+would become the grail king
+
+ align:start position:0%
+would become the grail king
+ 
+
+ align:start position:0%
+would become the grail king
+he had to break out of the rule
+
+ align:start position:0%
+he had to break out of the rule
+ 
+
+ align:start position:0%
+he had to break out of the rule
+and show that he was worth it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's that big issue now with the
+
+ align:start position:0%
+so there's that big issue now with the
+ 
+
+ align:start position:0%
+so there's that big issue now with the
+grail king
+
+ align:start position:0%
+grail king
+ 
+
+ align:start position:0%
+grail king
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible uh felt bad and
+
+ align:start position:0%
+possible uh felt bad and
+ 
+
+ align:start position:0%
+possible uh felt bad and
+that he missed the chance he felt bad
+
+ align:start position:0%
+that he missed the chance he felt bad
+ 
+
+ align:start position:0%
+that he missed the chance he felt bad
+that he should have
+
+ align:start position:0%
+that he should have
+ 
+
+ align:start position:0%
+that he should have
+shown some compassion at least verbally
+
+ align:start position:0%
+shown some compassion at least verbally
+ 
+
+ align:start position:0%
+shown some compassion at least verbally
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh but the real issue is
+
+ align:start position:0%
+uh but the real issue is
+ 
+
+ align:start position:0%
+uh but the real issue is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this test
+
+ align:start position:0%
+this test
+ 
+
+ align:start position:0%
+this test
+was one of his fitness to be the grilled
+
+ align:start position:0%
+was one of his fitness to be the grilled
+ 
+
+ align:start position:0%
+was one of his fitness to be the grilled
+king
+
+ align:start position:0%
+king
+ 
+
+ align:start position:0%
+king
+and the fitness was not measured in
+
+ align:start position:0%
+and the fitness was not measured in
+ 
+
+ align:start position:0%
+and the fitness was not measured in
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+of obedience to the rules the fitness
+
+ align:start position:0%
+of obedience to the rules the fitness
+ 
+
+ align:start position:0%
+of obedience to the rules the fitness
+was measured in terms of leaping quote
+
+ align:start position:0%
+was measured in terms of leaping quote
+ 
+
+ align:start position:0%
+was measured in terms of leaping quote
+important above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there's a film called uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the cincinnati kid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the same theme as uh the hustler
+
+ align:start position:0%
+it's the same theme as uh the hustler
+ 
+
+ align:start position:0%
+it's the same theme as uh the hustler
+except that the hustler was about pooled
+
+ align:start position:0%
+except that the hustler was about pooled
+ 
+
+ align:start position:0%
+except that the hustler was about pooled
+professional food players
+
+ align:start position:0%
+professional food players
+ 
+
+ align:start position:0%
+professional food players
+and uh cincinnati kid was about
+
+ align:start position:0%
+and uh cincinnati kid was about
+ 
+
+ align:start position:0%
+and uh cincinnati kid was about
+professional uh carplay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the the film ends i'm assuming that
+
+ align:start position:0%
+and the the film ends i'm assuming that
+ 
+
+ align:start position:0%
+and the the film ends i'm assuming that
+y'all are not going to watch the film
+
+ align:start position:0%
+y'all are not going to watch the film
+ 
+
+ align:start position:0%
+y'all are not going to watch the film
+won't be disappointed by me telling you
+
+ align:start position:0%
+won't be disappointed by me telling you
+ 
+
+ align:start position:0%
+won't be disappointed by me telling you
+the ending
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no y'all won't watch it because it's in
+
+ align:start position:0%
+no y'all won't watch it because it's in
+ 
+
+ align:start position:0%
+no y'all won't watch it because it's in
+black and white
+
+ align:start position:0%
+black and white
+ 
+
+ align:start position:0%
+black and white
+i think it's a black one maybe
+
+ align:start position:0%
+i think it's a black one maybe
+ 
+
+ align:start position:0%
+i think it's a black one maybe
+maybe color but anyway the film ends
+
+ align:start position:0%
+maybe color but anyway the film ends
+ 
+
+ align:start position:0%
+maybe color but anyway the film ends
+where the main character
+
+ align:start position:0%
+where the main character
+ 
+
+ align:start position:0%
+where the main character
+loses this card game
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he loses it to the old master you
+
+ align:start position:0%
+and he loses it to the old master you
+ 
+
+ align:start position:0%
+and he loses it to the old master you
+beat him up until the very end and he
+
+ align:start position:0%
+beat him up until the very end and he
+ 
+
+ align:start position:0%
+beat him up until the very end and he
+loses all his money and he comes up to
+
+ align:start position:0%
+loses all his money and he comes up to
+ 
+
+ align:start position:0%
+loses all his money and he comes up to
+the master at the end and he says to him
+
+ align:start position:0%
+the master at the end and he says to him
+ 
+
+ align:start position:0%
+the master at the end and he says to him
+says uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why didn't
+
+ align:start position:0%
+why didn't
+ 
+
+ align:start position:0%
+why didn't
+why did you give up that king
+
+ align:start position:0%
+why did you give up that king
+ 
+
+ align:start position:0%
+why did you give up that king
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+well he said that was uh
+
+ align:start position:0%
+well he said that was uh
+ 
+
+ align:start position:0%
+well he said that was uh
+against all of the rules
+
+ align:start position:0%
+against all of the rules
+ 
+
+ align:start position:0%
+against all of the rules
+of uh probability
+
+ align:start position:0%
+of uh probability
+ 
+
+ align:start position:0%
+of uh probability
+everybody knows it
+
+ align:start position:0%
+everybody knows it
+ 
+
+ align:start position:0%
+everybody knows it
+and the old man said
+
+ align:start position:0%
+and the old man said
+ 
+
+ align:start position:0%
+and the old man said
+the proud the question is not about
+
+ align:start position:0%
+the proud the question is not about
+ 
+
+ align:start position:0%
+the proud the question is not about
+making mistakes the question is about
+
+ align:start position:0%
+making mistakes the question is about
+ 
+
+ align:start position:0%
+making mistakes the question is about
+when to make it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words he threw the guy off
+
+ align:start position:0%
+in other words he threw the guy off
+ 
+
+ align:start position:0%
+in other words he threw the guy off
+by throwing away that kid
+
+ align:start position:0%
+by throwing away that kid
+ 
+
+ align:start position:0%
+by throwing away that kid
+uh so um
+
+ align:start position:0%
+uh so um
+ 
+
+ align:start position:0%
+uh so um
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+when the time comes for you to break the
+
+ align:start position:0%
+when the time comes for you to break the
+ 
+
+ align:start position:0%
+when the time comes for you to break the
+rule
+
+ align:start position:0%
+rule
+ 
+
+ align:start position:0%
+rule
+you got to know that the time that this
+
+ align:start position:0%
+you got to know that the time that this
+ 
+
+ align:start position:0%
+you got to know that the time that this
+is the time
+
+ align:start position:0%
+is the time
+ 
+
+ align:start position:0%
+is the time
+and to be prepared to sell the concept
+
+ align:start position:0%
+and to be prepared to sell the concept
+ 
+
+ align:start position:0%
+and to be prepared to sell the concept
+and muscle wasn't willing to do that and
+
+ align:start position:0%
+and muscle wasn't willing to do that and
+ 
+
+ align:start position:0%
+and muscle wasn't willing to do that and
+possible had to mature how long was how
+
+ align:start position:0%
+possible had to mature how long was how
+ 
+
+ align:start position:0%
+possible had to mature how long was how
+many years passed between
+
+ align:start position:0%
+many years passed between
+ 
+
+ align:start position:0%
+many years passed between
+the time that he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+missed his chance at the time that he
+
+ align:start position:0%
+missed his chance at the time that he
+ 
+
+ align:start position:0%
+missed his chance at the time that he
+came back and became grail king
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he's looking for this thing all
+
+ align:start position:0%
+and he's looking for this thing all
+ 
+
+ align:start position:0%
+and he's looking for this thing all
+along
+
+ align:start position:0%
+along
+ 
+
+ align:start position:0%
+along
+the castle disappears remember he gets
+
+ align:start position:0%
+the castle disappears remember he gets
+ 
+
+ align:start position:0%
+the castle disappears remember he gets
+up the next morning
+
+ align:start position:0%
+up the next morning
+ 
+
+ align:start position:0%
+up the next morning
+and he hears uh the knights thundering
+
+ align:start position:0%
+and he hears uh the knights thundering
+ 
+
+ align:start position:0%
+and he hears uh the knights thundering
+out of the castle on his way their way
+
+ align:start position:0%
+out of the castle on his way their way
+ 
+
+ align:start position:0%
+out of the castle on his way their way
+someplace and he gets all dressed up and
+
+ align:start position:0%
+someplace and he gets all dressed up and
+ 
+
+ align:start position:0%
+someplace and he gets all dressed up and
+goes out to follow them
+
+ align:start position:0%
+goes out to follow them
+ 
+
+ align:start position:0%
+goes out to follow them
+he can't find them he turns around to go
+
+ align:start position:0%
+he can't find them he turns around to go
+ 
+
+ align:start position:0%
+he can't find them he turns around to go
+back and the castle is gone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he spends the next x amount of time
+
+ align:start position:0%
+and he spends the next x amount of time
+ 
+
+ align:start position:0%
+and he spends the next x amount of time
+to find go back and find the castle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh my calculation was 20 years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh i want you to take some time
+
+ align:start position:0%
+uh i want you to take some time
+ 
+
+ align:start position:0%
+uh i want you to take some time
+if you dispute that
+
+ align:start position:0%
+if you dispute that
+ 
+
+ align:start position:0%
+if you dispute that
+ready
+
+ align:start position:0%
+ready
+ 
+
+ align:start position:0%
+ready
+to give that some thought maybe look
+
+ align:start position:0%
+to give that some thought maybe look
+ 
+
+ align:start position:0%
+to give that some thought maybe look
+through the book a little bit more
+
+ align:start position:0%
+through the book a little bit more
+ 
+
+ align:start position:0%
+through the book a little bit more
+he was out there for quite a while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and after he has all of these exploits
+
+ align:start position:0%
+and after he has all of these exploits
+ 
+
+ align:start position:0%
+and after he has all of these exploits
+then he has proved himself worthy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they never say exactly
+
+ align:start position:0%
+they never say exactly
+ 
+
+ align:start position:0%
+they never say exactly
+and i didn't want to go get one of the
+
+ align:start position:0%
+and i didn't want to go get one of the
+ 
+
+ align:start position:0%
+and i didn't want to go get one of the
+cliff notes or anything like that to
+
+ align:start position:0%
+cliff notes or anything like that to
+ 
+
+ align:start position:0%
+cliff notes or anything like that to
+look it up i just did not want to do
+
+ align:start position:0%
+look it up i just did not want to do
+ 
+
+ align:start position:0%
+look it up i just did not want to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and so i went back and started reading
+
+ align:start position:0%
+and so i went back and started reading
+ 
+
+ align:start position:0%
+and so i went back and started reading
+and taking little pieces
+
+ align:start position:0%
+and taking little pieces
+ 
+
+ align:start position:0%
+and taking little pieces
+and my account like i said
+
+ align:start position:0%
+and my account like i said
+ 
+
+ align:start position:0%
+and my account like i said
+there is a good answer to that if you go
+
+ align:start position:0%
+there is a good answer to that if you go
+ 
+
+ align:start position:0%
+there is a good answer to that if you go
+to the humanities
+
+ align:start position:0%
+to the humanities
+ 
+
+ align:start position:0%
+to the humanities
+department they'll all know the number
+
+ align:start position:0%
+department they'll all know the number
+ 
+
+ align:start position:0%
+department they'll all know the number
+all right but i didn't want to do it i
+
+ align:start position:0%
+all right but i didn't want to do it i
+ 
+
+ align:start position:0%
+all right but i didn't want to do it i
+wanted to have fun doing it on my own
+
+ align:start position:0%
+wanted to have fun doing it on my own
+ 
+
+ align:start position:0%
+wanted to have fun doing it on my own
+and i want to leave that to you all
+
+ align:start position:0%
+and i want to leave that to you all
+ 
+
+ align:start position:0%
+and i want to leave that to you all
+but my calculation was 20 years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh i should have
+
+ align:start position:0%
+oh i should have
+ 
+
+ align:start position:0%
+oh i should have
+i feel so awful i should have asked him
+
+ align:start position:0%
+i feel so awful i should have asked him
+ 
+
+ align:start position:0%
+i feel so awful i should have asked him
+about his illness i feel that i need to
+
+ align:start position:0%
+about his illness i feel that i need to
+ 
+
+ align:start position:0%
+about his illness i feel that i need to
+go back like other people told him that
+
+ align:start position:0%
+go back like other people told him that
+ 
+
+ align:start position:0%
+go back like other people told him that
+he messed up
+
+ align:start position:0%
+he messed up
+ 
+
+ align:start position:0%
+he messed up
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+an interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take on sort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh now this is another uh trait
+
+ align:start position:0%
+yeah uh now this is another uh trait
+ 
+
+ align:start position:0%
+yeah uh now this is another uh trait
+of uh many uh mythic heroes
+
+ align:start position:0%
+of uh many uh mythic heroes
+ 
+
+ align:start position:0%
+of uh many uh mythic heroes
+uh and that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they all have at least one
+
+ align:start position:0%
+they all have at least one
+ 
+
+ align:start position:0%
+they all have at least one
+fatal
+
+ align:start position:0%
+fatal
+ 
+
+ align:start position:0%
+fatal
+character flaw
+
+ align:start position:0%
+character flaw
+ 
+
+ align:start position:0%
+character flaw
+fatal
+
+ align:start position:0%
+fatal
+ 
+
+ align:start position:0%
+fatal
+if you read oedipus
+
+ align:start position:0%
+if you read oedipus
+ 
+
+ align:start position:0%
+if you read oedipus
+you go back to the trojan wars
+
+ align:start position:0%
+you go back to the trojan wars
+ 
+
+ align:start position:0%
+you go back to the trojan wars
+no matter who they are they all have
+
+ align:start position:0%
+no matter who they are they all have
+ 
+
+ align:start position:0%
+no matter who they are they all have
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+bad
+
+ align:start position:0%
+bad
+ 
+
+ align:start position:0%
+bad
+bad is not the word fatal is the word
+
+ align:start position:0%
+bad is not the word fatal is the word
+ 
+
+ align:start position:0%
+bad is not the word fatal is the word
+uh even if it doesn't kill them it kills
+
+ align:start position:0%
+uh even if it doesn't kill them it kills
+ 
+
+ align:start position:0%
+uh even if it doesn't kill them it kills
+their careers it does all of these
+
+ align:start position:0%
+their careers it does all of these
+ 
+
+ align:start position:0%
+their careers it does all of these
+terrible things
+
+ align:start position:0%
+terrible things
+ 
+
+ align:start position:0%
+terrible things
+uh and and
+
+ align:start position:0%
+uh and and
+ 
+
+ align:start position:0%
+uh and and
+does that is there a lesson in all of
+
+ align:start position:0%
+does that is there a lesson in all of
+ 
+
+ align:start position:0%
+does that is there a lesson in all of
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i think one lesson is that if
+
+ align:start position:0%
+well i think one lesson is that if
+ 
+
+ align:start position:0%
+well i think one lesson is that if
+you're going to look for somebody to
+
+ align:start position:0%
+you're going to look for somebody to
+ 
+
+ align:start position:0%
+you're going to look for somebody to
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+your life after in any way
+
+ align:start position:0%
+your life after in any way
+ 
+
+ align:start position:0%
+your life after in any way
+in any particular way or if you're going
+
+ align:start position:0%
+in any particular way or if you're going
+ 
+
+ align:start position:0%
+in any particular way or if you're going
+to advise your children
+
+ align:start position:0%
+to advise your children
+ 
+
+ align:start position:0%
+to advise your children
+to be like somebody else
+
+ align:start position:0%
+to be like somebody else
+ 
+
+ align:start position:0%
+to be like somebody else
+you're not going to find anybody that's
+
+ align:start position:0%
+you're not going to find anybody that's
+ 
+
+ align:start position:0%
+you're not going to find anybody that's
+perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unless you've got a religious bent but
+
+ align:start position:0%
+unless you've got a religious bent but
+ 
+
+ align:start position:0%
+unless you've got a religious bent but
+uh you know you're gonna find people who
+
+ align:start position:0%
+uh you know you're gonna find people who
+ 
+
+ align:start position:0%
+uh you know you're gonna find people who
+make mistakes
+
+ align:start position:0%
+make mistakes
+ 
+
+ align:start position:0%
+make mistakes
+and the heroes at least all of the ones
+
+ align:start position:0%
+and the heroes at least all of the ones
+ 
+
+ align:start position:0%
+and the heroes at least all of the ones
+that i have read
+
+ align:start position:0%
+that i have read
+ 
+
+ align:start position:0%
+that i have read
+are the ones who not only do great deeds
+
+ align:start position:0%
+are the ones who not only do great deeds
+ 
+
+ align:start position:0%
+are the ones who not only do great deeds
+but make big mistakes i mean when they
+
+ align:start position:0%
+but make big mistakes i mean when they
+ 
+
+ align:start position:0%
+but make big mistakes i mean when they
+make a mistake
+
+ align:start position:0%
+make a mistake
+ 
+
+ align:start position:0%
+make a mistake
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+big
+
+ align:start position:0%
+big
+ 
+
+ align:start position:0%
+big
+terrible to them terrible to everybody
+
+ align:start position:0%
+terrible to them terrible to everybody
+ 
+
+ align:start position:0%
+terrible to them terrible to everybody
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and i think that's the way it is if you
+
+ align:start position:0%
+and i think that's the way it is if you
+ 
+
+ align:start position:0%
+and i think that's the way it is if you
+play in the if you play in the big game
+
+ align:start position:0%
+play in the if you play in the big game
+ 
+
+ align:start position:0%
+play in the if you play in the big game
+you make big mistakes you make big gains
+
+ align:start position:0%
+you make big mistakes you make big gains
+ 
+
+ align:start position:0%
+you make big mistakes you make big gains
+when you make them but you make big
+
+ align:start position:0%
+when you make them but you make big
+ 
+
+ align:start position:0%
+when you make them but you make big
+mistakes too
+
+ align:start position:0%
+mistakes too
+ 
+
+ align:start position:0%
+mistakes too
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let's talk about his character some
+
+ align:start position:0%
+yeah let's talk about his character some
+ 
+
+ align:start position:0%
+yeah let's talk about his character some
+more what about was did he did his
+
+ align:start position:0%
+more what about was did he did his
+ 
+
+ align:start position:0%
+more what about was did he did his
+character change as he got older
+
+ align:start position:0%
+character change as he got older
+ 
+
+ align:start position:0%
+character change as he got older
+yeah i think he did
+
+ align:start position:0%
+yeah i think he did
+ 
+
+ align:start position:0%
+yeah i think he did
+i mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frustrates me the way he became a knight
+
+ align:start position:0%
+frustrates me the way he became a knight
+ 
+
+ align:start position:0%
+frustrates me the way he became a knight
+was by killing another knight in order
+
+ align:start position:0%
+was by killing another knight in order
+ 
+
+ align:start position:0%
+was by killing another knight in order
+to get his clothing yeah
+
+ align:start position:0%
+to get his clothing yeah
+ 
+
+ align:start position:0%
+to get his clothing yeah
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i know that
+
+ align:start position:0%
+i know that
+ 
+
+ align:start position:0%
+i know that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+trajectory in the book is that he is
+
+ align:start position:0%
+trajectory in the book is that he is
+ 
+
+ align:start position:0%
+trajectory in the book is that he is
+he's foolish he's young he doesn't know
+
+ align:start position:0%
+he's foolish he's young he doesn't know
+ 
+
+ align:start position:0%
+he's foolish he's young he doesn't know
+about knighthood
+
+ align:start position:0%
+about knighthood
+ 
+
+ align:start position:0%
+about knighthood
+he thinks he needs all the night to get
+
+ align:start position:0%
+he thinks he needs all the night to get
+ 
+
+ align:start position:0%
+he thinks he needs all the night to get
+close and then he matures
+
+ align:start position:0%
+close and then he matures
+ 
+
+ align:start position:0%
+close and then he matures
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the author doesn't like that
+
+ align:start position:0%
+but the author doesn't like that
+ 
+
+ align:start position:0%
+but the author doesn't like that
+murder ought to be
+
+ align:start position:0%
+murder ought to be
+ 
+
+ align:start position:0%
+murder ought to be
+the major flaw
+
+ align:start position:0%
+the major flaw
+ 
+
+ align:start position:0%
+the major flaw
+no the major
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it wasn't a heroic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+i wouldn't call that heroic uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because there was nobody nobody else no
+
+ align:start position:0%
+because there was nobody nobody else no
+ 
+
+ align:start position:0%
+because there was nobody nobody else no
+one else's interest at stake
+
+ align:start position:0%
+one else's interest at stake
+ 
+
+ align:start position:0%
+one else's interest at stake
+that he was protecting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there's a scene i'm trying to think of
+
+ align:start position:0%
+there's a scene i'm trying to think of
+ 
+
+ align:start position:0%
+there's a scene i'm trying to think of
+it uh in the film is one of my one of my
+
+ align:start position:0%
+it uh in the film is one of my one of my
+ 
+
+ align:start position:0%
+it uh in the film is one of my one of my
+favorite films um
+
+ align:start position:0%
+favorite films um
+ 
+
+ align:start position:0%
+favorite films um
+trying to think of what i think it was
+
+ align:start position:0%
+trying to think of what i think it was
+ 
+
+ align:start position:0%
+trying to think of what i think it was
+robert
+
+ align:start position:0%
+robert
+ 
+
+ align:start position:0%
+robert
+one of robin one of the robin hood
+
+ align:start position:0%
+one of robin one of the robin hood
+ 
+
+ align:start position:0%
+one of robin one of the robin hood
+movies
+
+ align:start position:0%
+movies
+ 
+
+ align:start position:0%
+movies
+where robin hood gets into the sword
+
+ align:start position:0%
+where robin hood gets into the sword
+ 
+
+ align:start position:0%
+where robin hood gets into the sword
+fight
+
+ align:start position:0%
+fight
+ 
+
+ align:start position:0%
+fight
+with his knight and he doesn't know it's
+
+ align:start position:0%
+with his knight and he doesn't know it's
+ 
+
+ align:start position:0%
+with his knight and he doesn't know it's
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+it's uh
+
+ align:start position:0%
+it's uh
+ 
+
+ align:start position:0%
+it's uh
+richard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they're fighting
+
+ align:start position:0%
+and they're fighting
+ 
+
+ align:start position:0%
+and they're fighting
+and richard goes with a lunge
+
+ align:start position:0%
+and richard goes with a lunge
+ 
+
+ align:start position:0%
+and richard goes with a lunge
+and robin hood steps out of the way and
+
+ align:start position:0%
+and robin hood steps out of the way and
+ 
+
+ align:start position:0%
+and robin hood steps out of the way and
+richard gets his
+
+ align:start position:0%
+richard gets his
+ 
+
+ align:start position:0%
+richard gets his
+sword
+
+ align:start position:0%
+sword
+ 
+
+ align:start position:0%
+sword
+stuck into a tree
+
+ align:start position:0%
+stuck into a tree
+ 
+
+ align:start position:0%
+stuck into a tree
+now they're fighting to the death this
+
+ align:start position:0%
+now they're fighting to the death this
+ 
+
+ align:start position:0%
+now they're fighting to the death this
+is serious
+
+ align:start position:0%
+is serious
+ 
+
+ align:start position:0%
+is serious
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+robin hood i think it is puts down his
+
+ align:start position:0%
+robin hood i think it is puts down his
+ 
+
+ align:start position:0%
+robin hood i think it is puts down his
+sword and goes helps him pull it out of
+
+ align:start position:0%
+sword and goes helps him pull it out of
+ 
+
+ align:start position:0%
+sword and goes helps him pull it out of
+the tree
+
+ align:start position:0%
+the tree
+ 
+
+ align:start position:0%
+the tree
+he got an opportunity to stab the man in
+
+ align:start position:0%
+he got an opportunity to stab the man in
+ 
+
+ align:start position:0%
+he got an opportunity to stab the man in
+the back but chivalry says
+
+ align:start position:0%
+the back but chivalry says
+ 
+
+ align:start position:0%
+the back but chivalry says
+you don't do that all right
+
+ align:start position:0%
+you don't do that all right
+ 
+
+ align:start position:0%
+you don't do that all right
+so uh they got this these rules of
+
+ align:start position:0%
+so uh they got this these rules of
+ 
+
+ align:start position:0%
+so uh they got this these rules of
+chivalry
+
+ align:start position:0%
+chivalry
+ 
+
+ align:start position:0%
+chivalry
+will i think they i think if you follow
+
+ align:start position:0%
+will i think they i think if you follow
+ 
+
+ align:start position:0%
+will i think they i think if you follow
+the rules of chivalry there's something
+
+ align:start position:0%
+the rules of chivalry there's something
+ 
+
+ align:start position:0%
+the rules of chivalry there's something
+about it that's
+
+ align:start position:0%
+about it that's
+ 
+
+ align:start position:0%
+about it that's
+that is hero making in it
+
+ align:start position:0%
+that is hero making in it
+ 
+
+ align:start position:0%
+that is hero making in it
+it helps you get there
+
+ align:start position:0%
+it helps you get there
+ 
+
+ align:start position:0%
+it helps you get there
+uh i don't think those are heroic deeds
+
+ align:start position:0%
+uh i don't think those are heroic deeds
+ 
+
+ align:start position:0%
+uh i don't think those are heroic deeds
+but it sort of gets you into a mindset
+
+ align:start position:0%
+but it sort of gets you into a mindset
+ 
+
+ align:start position:0%
+but it sort of gets you into a mindset
+that there's something that's higher
+
+ align:start position:0%
+that there's something that's higher
+ 
+
+ align:start position:0%
+that there's something that's higher
+than you
+
+ align:start position:0%
+than you
+ 
+
+ align:start position:0%
+than you
+and uh that you i mean if a man
+
+ align:start position:0%
+and uh that you i mean if a man
+ 
+
+ align:start position:0%
+and uh that you i mean if a man
+if you're gonna kill a man you don't
+
+ align:start position:0%
+if you're gonna kill a man you don't
+ 
+
+ align:start position:0%
+if you're gonna kill a man you don't
+kill him by stabbing him in the back or
+
+ align:start position:0%
+kill him by stabbing him in the back or
+ 
+
+ align:start position:0%
+kill him by stabbing him in the back or
+certain kind of things you just don't do
+
+ align:start position:0%
+certain kind of things you just don't do
+ 
+
+ align:start position:0%
+certain kind of things you just don't do
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about his half brother
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see any point to
+
+ align:start position:0%
+you see any point to
+ 
+
+ align:start position:0%
+you see any point to
+the story of him and his half brother
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fear fees that's the best pronunciation
+
+ align:start position:0%
+fear fees that's the best pronunciation
+ 
+
+ align:start position:0%
+fear fees that's the best pronunciation
+i can get out of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well he
+
+ align:start position:0%
+well he
+ 
+
+ align:start position:0%
+well he
+certainly
+
+ align:start position:0%
+certainly
+ 
+
+ align:start position:0%
+certainly
+seems essential
+
+ align:start position:0%
+seems essential
+ 
+
+ align:start position:0%
+seems essential
+to parcel
+
+ align:start position:0%
+to parcel
+ 
+
+ align:start position:0%
+to parcel
+eventual saving of the
+
+ align:start position:0%
+eventual saving of the
+ 
+
+ align:start position:0%
+eventual saving of the
+castle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you could probably argue that if he
+
+ align:start position:0%
+and you could probably argue that if he
+ 
+
+ align:start position:0%
+and you could probably argue that if he
+hadn't met up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why do you think the author
+
+ align:start position:0%
+why do you think the author
+ 
+
+ align:start position:0%
+why do you think the author
+made this bizarre
+
+ align:start position:0%
+made this bizarre
+ 
+
+ align:start position:0%
+made this bizarre
+uh characterization of fear fears
+
+ align:start position:0%
+uh characterization of fear fears
+ 
+
+ align:start position:0%
+uh characterization of fear fears
+as being
+
+ align:start position:0%
+as being
+ 
+
+ align:start position:0%
+as being
+patched black like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like a like like a pinto horse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why would an author just
+
+ align:start position:0%
+why would an author just
+ 
+
+ align:start position:0%
+why would an author just
+do that uh is there is there any connect
+
+ align:start position:0%
+do that uh is there is there any connect
+ 
+
+ align:start position:0%
+do that uh is there is there any connect
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+why would an author do that that was not
+
+ align:start position:0%
+why would an author do that that was not
+ 
+
+ align:start position:0%
+why would an author do that that was not
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the ligo i think why would author do
+
+ align:start position:0%
+the ligo i think why would author do
+ 
+
+ align:start position:0%
+the ligo i think why would author do
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i tell you what i think well i'll
+
+ align:start position:0%
+well i tell you what i think well i'll
+ 
+
+ align:start position:0%
+well i tell you what i think well i'll
+tell you what joseph campbell says
+
+ align:start position:0%
+tell you what joseph campbell says
+ 
+
+ align:start position:0%
+tell you what joseph campbell says
+and then i'll tell you what i think
+
+ align:start position:0%
+and then i'll tell you what i think
+ 
+
+ align:start position:0%
+and then i'll tell you what i think
+which is almost the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this author
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wants to reconcile
+
+ align:start position:0%
+wants to reconcile
+ 
+
+ align:start position:0%
+wants to reconcile
+the humans pagans
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the only thing that's going to
+
+ align:start position:0%
+and the only thing that's going to
+ 
+
+ align:start position:0%
+and the only thing that's going to
+impress possible in terms of
+
+ align:start position:0%
+impress possible in terms of
+ 
+
+ align:start position:0%
+impress possible in terms of
+reconciliation is kinship
+
+ align:start position:0%
+reconciliation is kinship
+ 
+
+ align:start position:0%
+reconciliation is kinship
+so i think what he's trying to say is
+
+ align:start position:0%
+so i think what he's trying to say is
+ 
+
+ align:start position:0%
+so i think what he's trying to say is
+that fearful fear fees is half black
+
+ align:start position:0%
+that fearful fear fees is half black
+ 
+
+ align:start position:0%
+that fearful fear fees is half black
+half white
+
+ align:start position:0%
+half white
+ 
+
+ align:start position:0%
+half white
+she was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the key issue was
+
+ align:start position:0%
+but the key issue was
+ 
+
+ align:start position:0%
+but the key issue was
+pagan versus christian
+
+ align:start position:0%
+pagan versus christian
+ 
+
+ align:start position:0%
+pagan versus christian
+and that the two of them became the best
+
+ align:start position:0%
+and that the two of them became the best
+ 
+
+ align:start position:0%
+and that the two of them became the best
+of friends at the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i think the author was trying to say
+
+ align:start position:0%
+so i think the author was trying to say
+ 
+
+ align:start position:0%
+so i think the author was trying to say
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+this these are the uh
+
+ align:start position:0%
+this these are the uh
+ 
+
+ align:start position:0%
+this these are the uh
+early middle ages and the dark ages
+
+ align:start position:0%
+early middle ages and the dark ages
+ 
+
+ align:start position:0%
+early middle ages and the dark ages
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+all of this all of this hatred
+
+ align:start position:0%
+all of this all of this hatred
+ 
+
+ align:start position:0%
+all of this all of this hatred
+between christians pagans gotta go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he tries to do it in the most
+
+ align:start position:0%
+and he tries to do it in the most
+ 
+
+ align:start position:0%
+and he tries to do it in the most
+compelling way to somebody like possible
+
+ align:start position:0%
+compelling way to somebody like possible
+ 
+
+ align:start position:0%
+compelling way to somebody like possible
+make it part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's interesting that
+
+ align:start position:0%
+but it's interesting that
+ 
+
+ align:start position:0%
+but it's interesting that
+oh yeah so carsonville accepted fear of
+
+ align:start position:0%
+oh yeah so carsonville accepted fear of
+ 
+
+ align:start position:0%
+oh yeah so carsonville accepted fear of
+views as he was black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll have the wife that he wanted
+
+ align:start position:0%
+we'll have the wife that he wanted
+ 
+
+ align:start position:0%
+we'll have the wife that he wanted
+to leave the life that he wanted he had
+
+ align:start position:0%
+to leave the life that he wanted he had
+ 
+
+ align:start position:0%
+to leave the life that he wanted he had
+to be baptized
+
+ align:start position:0%
+to be baptized
+ 
+
+ align:start position:0%
+to be baptized
+that's right he still had to be baptized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well uh let's uh
+
+ align:start position:0%
+well uh let's uh
+ 
+
+ align:start position:0%
+well uh let's uh
+dig into that one um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the time
+
+ align:start position:0%
+at the time
+ 
+
+ align:start position:0%
+at the time
+civilizations were created around the
+
+ align:start position:0%
+civilizations were created around the
+ 
+
+ align:start position:0%
+civilizations were created around the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+uh independently of one another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it was motivated by two things number
+
+ align:start position:0%
+it was motivated by two things number
+ 
+
+ align:start position:0%
+it was motivated by two things number
+one what was motivated by the weather
+
+ align:start position:0%
+one what was motivated by the weather
+ 
+
+ align:start position:0%
+one what was motivated by the weather
+yeah i mean it was a time when
+
+ align:start position:0%
+yeah i mean it was a time when
+ 
+
+ align:start position:0%
+yeah i mean it was a time when
+there were these grasses
+
+ align:start position:0%
+there were these grasses
+ 
+
+ align:start position:0%
+there were these grasses
+in that could that could sustain hip a
+
+ align:start position:0%
+in that could that could sustain hip a
+ 
+
+ align:start position:0%
+in that could that could sustain hip a
+large populations
+
+ align:start position:0%
+large populations
+ 
+
+ align:start position:0%
+large populations
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we have the uh wheat
+
+ align:start position:0%
+we have the uh wheat
+ 
+
+ align:start position:0%
+we have the uh wheat
+cultures in the middle east the rice
+
+ align:start position:0%
+cultures in the middle east the rice
+ 
+
+ align:start position:0%
+cultures in the middle east the rice
+cultures in the east the corn
+
+ align:start position:0%
+cultures in the east the corn
+ 
+
+ align:start position:0%
+cultures in the east the corn
+cultures in the uh
+
+ align:start position:0%
+cultures in the uh
+ 
+
+ align:start position:0%
+cultures in the uh
+western uh
+
+ align:start position:0%
+western uh
+ 
+
+ align:start position:0%
+western uh
+in the americas the western americas
+
+ align:start position:0%
+in the americas the western americas
+ 
+
+ align:start position:0%
+in the americas the western americas
+they could sustain large cultures and
+
+ align:start position:0%
+they could sustain large cultures and
+ 
+
+ align:start position:0%
+they could sustain large cultures and
+the cultures did not have to be nomadic
+
+ align:start position:0%
+the cultures did not have to be nomadic
+ 
+
+ align:start position:0%
+the cultures did not have to be nomadic
+or semi-nomadic they could stay in one
+
+ align:start position:0%
+or semi-nomadic they could stay in one
+ 
+
+ align:start position:0%
+or semi-nomadic they could stay in one
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+the other thing was around that time was
+
+ align:start position:0%
+the other thing was around that time was
+ 
+
+ align:start position:0%
+the other thing was around that time was
+that human beings
+
+ align:start position:0%
+that human beings
+ 
+
+ align:start position:0%
+that human beings
+had figured out
+
+ align:start position:0%
+had figured out
+ 
+
+ align:start position:0%
+had figured out
+how to herd animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so instead of going out hoping you see
+
+ align:start position:0%
+so instead of going out hoping you see
+ 
+
+ align:start position:0%
+so instead of going out hoping you see
+one one day and
+
+ align:start position:0%
+one one day and
+ 
+
+ align:start position:0%
+one one day and
+killing it and hoping it doesn't kill
+
+ align:start position:0%
+killing it and hoping it doesn't kill
+ 
+
+ align:start position:0%
+killing it and hoping it doesn't kill
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+you can just
+
+ align:start position:0%
+you can just
+ 
+
+ align:start position:0%
+you can just
+herd the animals right along and take
+
+ align:start position:0%
+herd the animals right along and take
+ 
+
+ align:start position:0%
+herd the animals right along and take
+one whenever you get ready
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have two kinds of cultures you
+
+ align:start position:0%
+so you have two kinds of cultures you
+ 
+
+ align:start position:0%
+so you have two kinds of cultures you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+the herding culture and you have
+
+ align:start position:0%
+the herding culture and you have
+ 
+
+ align:start position:0%
+the herding culture and you have
+the agrarian culture
+
+ align:start position:0%
+the agrarian culture
+ 
+
+ align:start position:0%
+the agrarian culture
+the herding is still moving around the
+
+ align:start position:0%
+the herding is still moving around the
+ 
+
+ align:start position:0%
+the herding is still moving around the
+agrarian is sept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+herding cultures
+
+ align:start position:0%
+herding cultures
+ 
+
+ align:start position:0%
+herding cultures
+are kinship societies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+civilization was made up by different
+
+ align:start position:0%
+civilization was made up by different
+ 
+
+ align:start position:0%
+civilization was made up by different
+kinship groups it was a multicultural
+
+ align:start position:0%
+kinship groups it was a multicultural
+ 
+
+ align:start position:0%
+kinship groups it was a multicultural
+society
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the rules of social order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a uh for civilization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+were more strict or stricter
+
+ align:start position:0%
+were more strict or stricter
+ 
+
+ align:start position:0%
+were more strict or stricter
+or more or
+
+ align:start position:0%
+or more or
+ 
+
+ align:start position:0%
+or more or
+social order was more problematic for
+
+ align:start position:0%
+social order was more problematic for
+ 
+
+ align:start position:0%
+social order was more problematic for
+cultures
+
+ align:start position:0%
+cultures
+ 
+
+ align:start position:0%
+cultures
+for for for civilized cultures than it
+
+ align:start position:0%
+for for for civilized cultures than it
+ 
+
+ align:start position:0%
+for for for civilized cultures than it
+was for
+
+ align:start position:0%
+was for
+ 
+
+ align:start position:0%
+was for
+nomadic
+
+ align:start position:0%
+nomadic
+ 
+
+ align:start position:0%
+nomadic
+hurting cultures because all you did was
+
+ align:start position:0%
+hurting cultures because all you did was
+ 
+
+ align:start position:0%
+hurting cultures because all you did was
+obey your father and your father obeyed
+
+ align:start position:0%
+obey your father and your father obeyed
+ 
+
+ align:start position:0%
+obey your father and your father obeyed
+his grant your grandfather
+
+ align:start position:0%
+his grant your grandfather
+ 
+
+ align:start position:0%
+his grant your grandfather
+you obeyed your mother
+
+ align:start position:0%
+you obeyed your mother
+ 
+
+ align:start position:0%
+you obeyed your mother
+your mother obeyed her grandmother
+
+ align:start position:0%
+your mother obeyed her grandmother
+ 
+
+ align:start position:0%
+your mother obeyed her grandmother
+but when you've got different families
+
+ align:start position:0%
+but when you've got different families
+ 
+
+ align:start position:0%
+but when you've got different families
+in living in the same place how do you
+
+ align:start position:0%
+in living in the same place how do you
+ 
+
+ align:start position:0%
+in living in the same place how do you
+keep them in order
+
+ align:start position:0%
+keep them in order
+ 
+
+ align:start position:0%
+keep them in order
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and uh here's how they did it
+
+ align:start position:0%
+and uh here's how they did it
+ 
+
+ align:start position:0%
+and uh here's how they did it
+religion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so they they invented great priesthoods
+
+ align:start position:0%
+so they they invented great priesthoods
+ 
+
+ align:start position:0%
+so they they invented great priesthoods
+and the great priesthoods
+
+ align:start position:0%
+and the great priesthoods
+ 
+
+ align:start position:0%
+and the great priesthoods
+uh found it increasingly difficult to
+
+ align:start position:0%
+uh found it increasingly difficult to
+ 
+
+ align:start position:0%
+uh found it increasingly difficult to
+keep the social order
+
+ align:start position:0%
+keep the social order
+ 
+
+ align:start position:0%
+keep the social order
+so what they did was they had to find
+
+ align:start position:0%
+so what they did was they had to find
+ 
+
+ align:start position:0%
+so what they did was they had to find
+ways of keeping people anchored
+
+ align:start position:0%
+ways of keeping people anchored
+ 
+
+ align:start position:0%
+ways of keeping people anchored
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+to an idea
+
+ align:start position:0%
+to an idea
+ 
+
+ align:start position:0%
+to an idea
+that was compelling on them
+
+ align:start position:0%
+that was compelling on them
+ 
+
+ align:start position:0%
+that was compelling on them
+and the shaman
+
+ align:start position:0%
+and the shaman
+ 
+
+ align:start position:0%
+and the shaman
+with talk with with uh his um
+
+ align:start position:0%
+with talk with with uh his um
+ 
+
+ align:start position:0%
+with talk with with uh his um
+insights in the unconscious
+
+ align:start position:0%
+insights in the unconscious
+ 
+
+ align:start position:0%
+insights in the unconscious
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+just became
+
+ align:start position:0%
+just became
+ 
+
+ align:start position:0%
+just became
+not very compelling any longer
+
+ align:start position:0%
+not very compelling any longer
+ 
+
+ align:start position:0%
+not very compelling any longer
+because people did not share the same
+
+ align:start position:0%
+because people did not share the same
+ 
+
+ align:start position:0%
+because people did not share the same
+unconscious
+
+ align:start position:0%
+unconscious
+ 
+
+ align:start position:0%
+unconscious
+they were different from different
+
+ align:start position:0%
+they were different from different
+ 
+
+ align:start position:0%
+they were different from different
+groups different families
+
+ align:start position:0%
+groups different families
+ 
+
+ align:start position:0%
+groups different families
+so what happened in the end was
+
+ align:start position:0%
+so what happened in the end was
+ 
+
+ align:start position:0%
+so what happened in the end was
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+priesthood developed
+
+ align:start position:0%
+priesthood developed
+ 
+
+ align:start position:0%
+priesthood developed
+probably not out of the shamans
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because a shaman has a personality
+
+ align:start position:0%
+because a shaman has a personality
+ 
+
+ align:start position:0%
+because a shaman has a personality
+that requires a discussion
+
+ align:start position:0%
+that requires a discussion
+ 
+
+ align:start position:0%
+that requires a discussion
+so i don't see
+
+ align:start position:0%
+so i don't see
+ 
+
+ align:start position:0%
+so i don't see
+three or four shaman getting down and
+
+ align:start position:0%
+three or four shaman getting down and
+ 
+
+ align:start position:0%
+three or four shaman getting down and
+saying let's start a priest
+
+ align:start position:0%
+saying let's start a priest
+ 
+
+ align:start position:0%
+saying let's start a priest
+uh and work together and in a hierarchy
+
+ align:start position:0%
+uh and work together and in a hierarchy
+ 
+
+ align:start position:0%
+uh and work together and in a hierarchy
+i don't see that
+
+ align:start position:0%
+i don't see that
+ 
+
+ align:start position:0%
+i don't see that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a shaman becomes a shaman by way of
+
+ align:start position:0%
+a shaman becomes a shaman by way of
+ 
+
+ align:start position:0%
+a shaman becomes a shaman by way of
+having
+
+ align:start position:0%
+having
+ 
+
+ align:start position:0%
+having
+i hope you all can tolerate some of
+
+ align:start position:0%
+i hope you all can tolerate some of
+ 
+
+ align:start position:0%
+i hope you all can tolerate some of
+these diversions because it's just too
+
+ align:start position:0%
+these diversions because it's just too
+ 
+
+ align:start position:0%
+these diversions because it's just too
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+a shaman becomes a shaman by virtue of
+
+ align:start position:0%
+a shaman becomes a shaman by virtue of
+ 
+
+ align:start position:0%
+a shaman becomes a shaman by virtue of
+having had
+
+ align:start position:0%
+having had
+ 
+
+ align:start position:0%
+having had
+a traumatic experience in childhood
+
+ align:start position:0%
+a traumatic experience in childhood
+ 
+
+ align:start position:0%
+a traumatic experience in childhood
+i'm sorry
+
+ align:start position:0%
+i'm sorry
+ 
+
+ align:start position:0%
+i'm sorry
+the word
+
+ align:start position:0%
+the word
+ 
+
+ align:start position:0%
+the word
+describes a witch duck okay
+
+ align:start position:0%
+describes a witch duck okay
+ 
+
+ align:start position:0%
+describes a witch duck okay
+in very early prehistorics yes
+
+ align:start position:0%
+in very early prehistorics yes
+ 
+
+ align:start position:0%
+in very early prehistorics yes
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but you can find people who do not have
+
+ align:start position:0%
+but you can find people who do not have
+ 
+
+ align:start position:0%
+but you can find people who do not have
+the function of ashaming
+
+ align:start position:0%
+the function of ashaming
+ 
+
+ align:start position:0%
+the function of ashaming
+in society today
+
+ align:start position:0%
+in society today
+ 
+
+ align:start position:0%
+in society today
+uh one one
+
+ align:start position:0%
+uh one one
+ 
+
+ align:start position:0%
+uh one one
+a very good example of a of a person who
+
+ align:start position:0%
+a very good example of a of a person who
+ 
+
+ align:start position:0%
+a very good example of a of a person who
+has the same personality
+
+ align:start position:0%
+has the same personality
+ 
+
+ align:start position:0%
+has the same personality
+uh as a shaman uh is this mathematician
+
+ align:start position:0%
+uh as a shaman uh is this mathematician
+ 
+
+ align:start position:0%
+uh as a shaman uh is this mathematician
+named ramanujan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he's an indian
+
+ align:start position:0%
+he's an indian
+ 
+
+ align:start position:0%
+he's an indian
+and the story is that
+
+ align:start position:0%
+and the story is that
+ 
+
+ align:start position:0%
+and the story is that
+when he was a child his parents would
+
+ align:start position:0%
+when he was a child his parents would
+ 
+
+ align:start position:0%
+when he was a child his parents would
+get into these
+
+ align:start position:0%
+get into these
+ 
+
+ align:start position:0%
+get into these
+violent arguments
+
+ align:start position:0%
+violent arguments
+ 
+
+ align:start position:0%
+violent arguments
+and he would crawl under the bed
+
+ align:start position:0%
+and he would crawl under the bed
+ 
+
+ align:start position:0%
+and he would crawl under the bed
+with a pencil and paper and try to do
+
+ align:start position:0%
+with a pencil and paper and try to do
+ 
+
+ align:start position:0%
+with a pencil and paper and try to do
+math problems to keep it out of his head
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what happened in the end was that he
+
+ align:start position:0%
+uh what happened in the end was that he
+ 
+
+ align:start position:0%
+uh what happened in the end was that he
+became a very great
+
+ align:start position:0%
+became a very great
+ 
+
+ align:start position:0%
+became a very great
+mathematician but they called him an
+
+ align:start position:0%
+mathematician but they called him an
+ 
+
+ align:start position:0%
+mathematician but they called him an
+intuitive mathematician he could not
+
+ align:start position:0%
+intuitive mathematician he could not
+ 
+
+ align:start position:0%
+intuitive mathematician he could not
+prove to you any of his
+
+ align:start position:0%
+prove to you any of his
+ 
+
+ align:start position:0%
+prove to you any of his
+results but his results worked one of
+
+ align:start position:0%
+results but his results worked one of
+ 
+
+ align:start position:0%
+results but his results worked one of
+the things he did was uh
+
+ align:start position:0%
+the things he did was uh
+ 
+
+ align:start position:0%
+the things he did was uh
+now here's something for you to look up
+
+ align:start position:0%
+now here's something for you to look up
+ 
+
+ align:start position:0%
+now here's something for you to look up
+in the details i'm just i'm going to
+
+ align:start position:0%
+in the details i'm just i'm going to
+ 
+
+ align:start position:0%
+in the details i'm just i'm going to
+recite from memory
+
+ align:start position:0%
+recite from memory
+ 
+
+ align:start position:0%
+recite from memory
+ramanujan
+
+ align:start position:0%
+ramanujan
+ 
+
+ align:start position:0%
+ramanujan
+found a way
+
+ align:start position:0%
+found a way
+ 
+
+ align:start position:0%
+found a way
+to discern
+
+ align:start position:0%
+to discern
+ 
+
+ align:start position:0%
+to discern
+whether
+
+ align:start position:0%
+whether
+ 
+
+ align:start position:0%
+whether
+a 20-digit number
+
+ align:start position:0%
+a 20-digit number
+ 
+
+ align:start position:0%
+a 20-digit number
+was a prime number or not
+
+ align:start position:0%
+was a prime number or not
+ 
+
+ align:start position:0%
+was a prime number or not
+and he figured it out
+
+ align:start position:0%
+and he figured it out
+ 
+
+ align:start position:0%
+and he figured it out
+by hand i mean there's a hand method
+
+ align:start position:0%
+by hand i mean there's a hand method
+ 
+
+ align:start position:0%
+by hand i mean there's a hand method
+where you could figure out
+
+ align:start position:0%
+where you could figure out
+ 
+
+ align:start position:0%
+where you could figure out
+uh whether it's prime or not
+
+ align:start position:0%
+uh whether it's prime or not
+ 
+
+ align:start position:0%
+uh whether it's prime or not
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+um somebody
+
+ align:start position:0%
+um somebody
+ 
+
+ align:start position:0%
+um somebody
+use that method
+
+ align:start position:0%
+use that method
+ 
+
+ align:start position:0%
+use that method
+uh to to um
+
+ align:start position:0%
+uh to to um
+ 
+
+ align:start position:0%
+uh to to um
+frustrate the us military
+
+ align:start position:0%
+frustrate the us military
+ 
+
+ align:start position:0%
+frustrate the us military
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the military uh
+
+ align:start position:0%
+uh the military uh
+ 
+
+ align:start position:0%
+uh the military uh
+had its
+
+ align:start position:0%
+had its
+ 
+
+ align:start position:0%
+had its
+um icbms is intercontinental with this
+
+ align:start position:0%
+um icbms is intercontinental with this
+ 
+
+ align:start position:0%
+um icbms is intercontinental with this
+ballistic missiles
+
+ align:start position:0%
+ballistic missiles
+ 
+
+ align:start position:0%
+ballistic missiles
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+their orders were coded in prime numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can break the code by at hand the
+
+ align:start position:0%
+you can break the code by at hand the
+ 
+
+ align:start position:0%
+you can break the code by at hand the
+idea is you could still break the code
+
+ align:start position:0%
+idea is you could still break the code
+ 
+
+ align:start position:0%
+idea is you could still break the code
+by a computer but you'd have to run a
+
+ align:start position:0%
+by a computer but you'd have to run a
+ 
+
+ align:start position:0%
+by a computer but you'd have to run a
+computer
+
+ align:start position:0%
+computer
+ 
+
+ align:start position:0%
+computer
+for a month
+
+ align:start position:0%
+for a month
+ 
+
+ align:start position:0%
+for a month
+by that time they would change
+
+ align:start position:0%
+by that time they would change
+ 
+
+ align:start position:0%
+by that time they would change
+the codes
+
+ align:start position:0%
+the codes
+ 
+
+ align:start position:0%
+the codes
+well if you could come in and do it by
+
+ align:start position:0%
+well if you could come in and do it by
+ 
+
+ align:start position:0%
+well if you could come in and do it by
+hand you could knock it down they said
+
+ align:start position:0%
+hand you could knock it down they said
+ 
+
+ align:start position:0%
+hand you could knock it down they said
+the story is that they had to
+
+ align:start position:0%
+the story is that they had to
+ 
+
+ align:start position:0%
+the story is that they had to
+reconfigure the whole thing raman new
+
+ align:start position:0%
+reconfigure the whole thing raman new
+ 
+
+ align:start position:0%
+reconfigure the whole thing raman new
+jersey
+
+ align:start position:0%
+jersey
+ 
+
+ align:start position:0%
+jersey
+so with we're talking about a person who
+
+ align:start position:0%
+so with we're talking about a person who
+ 
+
+ align:start position:0%
+so with we're talking about a person who
+really is an outsider
+
+ align:start position:0%
+really is an outsider
+ 
+
+ align:start position:0%
+really is an outsider
+a person who really lives
+
+ align:start position:0%
+a person who really lives
+ 
+
+ align:start position:0%
+a person who really lives
+in another
+
+ align:start position:0%
+in another
+ 
+
+ align:start position:0%
+in another
+minds a state of mind
+
+ align:start position:0%
+minds a state of mind
+ 
+
+ align:start position:0%
+minds a state of mind
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i saw some people who had that state of
+
+ align:start position:0%
+i saw some people who had that state of
+ 
+
+ align:start position:0%
+i saw some people who had that state of
+mind i saw a program on television
+
+ align:start position:0%
+mind i saw a program on television
+ 
+
+ align:start position:0%
+mind i saw a program on television
+a documentary
+
+ align:start position:0%
+a documentary
+ 
+
+ align:start position:0%
+a documentary
+we talked about savants and other types
+
+ align:start position:0%
+we talked about savants and other types
+ 
+
+ align:start position:0%
+we talked about savants and other types
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+people that have the shame of
+
+ align:start position:0%
+people that have the shame of
+ 
+
+ align:start position:0%
+people that have the shame of
+shamanistic personality they always had
+
+ align:start position:0%
+shamanistic personality they always had
+ 
+
+ align:start position:0%
+shamanistic personality they always had
+these traumatic childhood experiences
+
+ align:start position:0%
+these traumatic childhood experiences
+ 
+
+ align:start position:0%
+these traumatic childhood experiences
+where they tried to get away from the
+
+ align:start position:0%
+where they tried to get away from the
+ 
+
+ align:start position:0%
+where they tried to get away from the
+world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh they showed this one guy
+
+ align:start position:0%
+and uh they showed this one guy
+ 
+
+ align:start position:0%
+and uh they showed this one guy
+now this is what i'm telling you now is
+
+ align:start position:0%
+now this is what i'm telling you now is
+ 
+
+ align:start position:0%
+now this is what i'm telling you now is
+good scientific stuff we're not talking
+
+ align:start position:0%
+good scientific stuff we're not talking
+ 
+
+ align:start position:0%
+good scientific stuff we're not talking
+about alien visitations
+
+ align:start position:0%
+about alien visitations
+ 
+
+ align:start position:0%
+about alien visitations
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+this is very well documented these
+
+ align:start position:0%
+this is very well documented these
+ 
+
+ align:start position:0%
+this is very well documented these
+people that have been studied in college
+
+ align:start position:0%
+people that have been studied in college
+ 
+
+ align:start position:0%
+people that have been studied in college
+by researchers
+
+ align:start position:0%
+by researchers
+ 
+
+ align:start position:0%
+by researchers
+they had this one man who was about when
+
+ align:start position:0%
+they had this one man who was about when
+ 
+
+ align:start position:0%
+they had this one man who was about when
+he was 50 years old
+
+ align:start position:0%
+he was 50 years old
+ 
+
+ align:start position:0%
+he was 50 years old
+he could tell you the weather of every
+
+ align:start position:0%
+he could tell you the weather of every
+ 
+
+ align:start position:0%
+he could tell you the weather of every
+day of his life
+
+ align:start position:0%
+day of his life
+ 
+
+ align:start position:0%
+day of his life
+well after three or four
+
+ align:start position:0%
+well after three or four
+ 
+
+ align:start position:0%
+well after three or four
+you say well what was the weather like
+
+ align:start position:0%
+you say well what was the weather like
+ 
+
+ align:start position:0%
+you say well what was the weather like
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+november 6 1942 i ran that day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they go back and check and sure
+
+ align:start position:0%
+and they go back and check and sure
+ 
+
+ align:start position:0%
+and they go back and check and sure
+enough it was
+
+ align:start position:0%
+enough it was
+ 
+
+ align:start position:0%
+enough it was
+now how do you explain that well it
+
+ align:start position:0%
+now how do you explain that well it
+ 
+
+ align:start position:0%
+now how do you explain that well it
+turns out
+
+ align:start position:0%
+turns out
+ 
+
+ align:start position:0%
+turns out
+basically he knew nothing else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but he memorized those things to keep
+
+ align:start position:0%
+but he memorized those things to keep
+ 
+
+ align:start position:0%
+but he memorized those things to keep
+whatever problem he had as a child out
+
+ align:start position:0%
+whatever problem he had as a child out
+ 
+
+ align:start position:0%
+whatever problem he had as a child out
+of his mind
+
+ align:start position:0%
+of his mind
+ 
+
+ align:start position:0%
+of his mind
+uh and so they tried to rehabilitate him
+
+ align:start position:0%
+uh and so they tried to rehabilitate him
+ 
+
+ align:start position:0%
+uh and so they tried to rehabilitate him
+and they showed a scene where
+
+ align:start position:0%
+and they showed a scene where
+ 
+
+ align:start position:0%
+and they showed a scene where
+he goes to the street to cross the
+
+ align:start position:0%
+he goes to the street to cross the
+ 
+
+ align:start position:0%
+he goes to the street to cross the
+street
+
+ align:start position:0%
+street
+ 
+
+ align:start position:0%
+street
+and the sign is saying
+
+ align:start position:0%
+and the sign is saying
+ 
+
+ align:start position:0%
+and the sign is saying
+go and he gets out in the middle of the
+
+ align:start position:0%
+go and he gets out in the middle of the
+ 
+
+ align:start position:0%
+go and he gets out in the middle of the
+street and the sign says stop and he
+
+ align:start position:0%
+street and the sign says stop and he
+ 
+
+ align:start position:0%
+street and the sign says stop and he
+stops
+
+ align:start position:0%
+stops
+ 
+
+ align:start position:0%
+stops
+you know he can he just doesn't
+
+ align:start position:0%
+you know he can he just doesn't
+ 
+
+ align:start position:0%
+you know he can he just doesn't
+no he i think his mother kept him close
+
+ align:start position:0%
+no he i think his mother kept him close
+ 
+
+ align:start position:0%
+no he i think his mother kept him close
+to her all his life he just didn't know
+
+ align:start position:0%
+to her all his life he just didn't know
+ 
+
+ align:start position:0%
+to her all his life he just didn't know
+those things the more he got
+
+ align:start position:0%
+those things the more he got
+ 
+
+ align:start position:0%
+those things the more he got
+into society got a job
+
+ align:start position:0%
+into society got a job
+ 
+
+ align:start position:0%
+into society got a job
+he could only hold a job for something
+
+ align:start position:0%
+he could only hold a job for something
+ 
+
+ align:start position:0%
+he could only hold a job for something
+like one hour a day
+
+ align:start position:0%
+like one hour a day
+ 
+
+ align:start position:0%
+like one hour a day
+at first
+
+ align:start position:0%
+at first
+ 
+
+ align:start position:0%
+at first
+cleaning the busing tables
+
+ align:start position:0%
+cleaning the busing tables
+ 
+
+ align:start position:0%
+cleaning the busing tables
+the more he got
+
+ align:start position:0%
+the more he got
+ 
+
+ align:start position:0%
+the more he got
+socialized
+
+ align:start position:0%
+socialized
+ 
+
+ align:start position:0%
+socialized
+the more he began to lose that skill
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+they say uh that the um
+
+ align:start position:0%
+they say uh that the um
+ 
+
+ align:start position:0%
+they say uh that the um
+the bards that uh
+
+ align:start position:0%
+the bards that uh
+ 
+
+ align:start position:0%
+the bards that uh
+back in um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+400 bc
+
+ align:start position:0%
+400 bc
+ 
+
+ align:start position:0%
+400 bc
+once we were going around talking
+
+ align:start position:0%
+once we were going around talking
+ 
+
+ align:start position:0%
+once we were going around talking
+about former and all of it
+
+ align:start position:0%
+about former and all of it
+ 
+
+ align:start position:0%
+about former and all of it
+they said that they could tell they had
+
+ align:start position:0%
+they said that they could tell they had
+ 
+
+ align:start position:0%
+they said that they could tell they had
+memorized i read some place where they
+
+ align:start position:0%
+memorized i read some place where they
+ 
+
+ align:start position:0%
+memorized i read some place where they
+where these people had memorized
+
+ align:start position:0%
+where these people had memorized
+ 
+
+ align:start position:0%
+where these people had memorized
+something like a million lines of verse
+
+ align:start position:0%
+something like a million lines of verse
+ 
+
+ align:start position:0%
+something like a million lines of verse
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+now a million lines of verse
+
+ align:start position:0%
+now a million lines of verse
+ 
+
+ align:start position:0%
+now a million lines of verse
+so i sat down one day and i did a
+
+ align:start position:0%
+so i sat down one day and i did a
+ 
+
+ align:start position:0%
+so i sat down one day and i did a
+calculation i know how long the lines
+
+ align:start position:0%
+calculation i know how long the lines
+ 
+
+ align:start position:0%
+calculation i know how long the lines
+are about the same length of a line in
+
+ align:start position:0%
+are about the same length of a line in
+ 
+
+ align:start position:0%
+are about the same length of a line in
+shakespeare
+
+ align:start position:0%
+shakespeare
+ 
+
+ align:start position:0%
+shakespeare
+so i did you know back of the hand kind
+
+ align:start position:0%
+so i did you know back of the hand kind
+ 
+
+ align:start position:0%
+so i did you know back of the hand kind
+of a calculation
+
+ align:start position:0%
+of a calculation
+ 
+
+ align:start position:0%
+of a calculation
+10 volumes of shakespeare
+
+ align:start position:0%
+10 volumes of shakespeare
+ 
+
+ align:start position:0%
+10 volumes of shakespeare
+now i concluded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from that television
+
+ align:start position:0%
+from that television
+ 
+
+ align:start position:0%
+from that television
+program i saw
+
+ align:start position:0%
+program i saw
+ 
+
+ align:start position:0%
+program i saw
+that these pr people probably didn't
+
+ align:start position:0%
+that these pr people probably didn't
+ 
+
+ align:start position:0%
+that these pr people probably didn't
+know a whole lot of anything else
+
+ align:start position:0%
+know a whole lot of anything else
+ 
+
+ align:start position:0%
+know a whole lot of anything else
+uh one other program that i saw uh
+
+ align:start position:0%
+uh one other program that i saw uh
+ 
+
+ align:start position:0%
+uh one other program that i saw uh
+was one where they were talking about
+
+ align:start position:0%
+was one where they were talking about
+ 
+
+ align:start position:0%
+was one where they were talking about
+about um
+
+ align:start position:0%
+about um
+ 
+
+ align:start position:0%
+about um
+these professional scrabble players
+
+ align:start position:0%
+these professional scrabble players
+ 
+
+ align:start position:0%
+these professional scrabble players
+actually i think yeah they play for
+
+ align:start position:0%
+actually i think yeah they play for
+ 
+
+ align:start position:0%
+actually i think yeah they play for
+money
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they talked about how many words
+
+ align:start position:0%
+and they talked about how many words
+ 
+
+ align:start position:0%
+and they talked about how many words
+these people
+
+ align:start position:0%
+these people
+ 
+
+ align:start position:0%
+these people
+had memorized and not only that but they
+
+ align:start position:0%
+had memorized and not only that but they
+ 
+
+ align:start position:0%
+had memorized and not only that but they
+had a skill
+
+ align:start position:0%
+had a skill
+ 
+
+ align:start position:0%
+had a skill
+to um
+
+ align:start position:0%
+to um
+ 
+
+ align:start position:0%
+to um
+to take the words on their uh
+
+ align:start position:0%
+to take the words on their uh
+ 
+
+ align:start position:0%
+to take the words on their uh
+palette
+
+ align:start position:0%
+palette
+ 
+
+ align:start position:0%
+palette
+i mean the letters
+
+ align:start position:0%
+i mean the letters
+ 
+
+ align:start position:0%
+i mean the letters
+and be able to turn them around in their
+
+ align:start position:0%
+and be able to turn them around in their
+ 
+
+ align:start position:0%
+and be able to turn them around in their
+minds
+
+ align:start position:0%
+minds
+ 
+
+ align:start position:0%
+minds
+to see the patterns before they put them
+
+ align:start position:0%
+to see the patterns before they put them
+ 
+
+ align:start position:0%
+to see the patterns before they put them
+down we try to do i try to do that if
+
+ align:start position:0%
+down we try to do i try to do that if
+ 
+
+ align:start position:0%
+down we try to do i try to do that if
+it's obvious i can do it i can do it
+
+ align:start position:0%
+it's obvious i can do it i can do it
+ 
+
+ align:start position:0%
+it's obvious i can do it i can do it
+with three letters if there's one but
+
+ align:start position:0%
+with three letters if there's one but
+ 
+
+ align:start position:0%
+with three letters if there's one but
+seven yeah it takes an effort these
+
+ align:start position:0%
+seven yeah it takes an effort these
+ 
+
+ align:start position:0%
+seven yeah it takes an effort these
+people just do it like that
+
+ align:start position:0%
+people just do it like that
+ 
+
+ align:start position:0%
+people just do it like that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then they and they had all these
+
+ align:start position:0%
+then they and they had all these
+ 
+
+ align:start position:0%
+then they and they had all these
+interviews with the the winners
+
+ align:start position:0%
+interviews with the the winners
+ 
+
+ align:start position:0%
+interviews with the the winners
+it turns out in the end
+
+ align:start position:0%
+it turns out in the end
+ 
+
+ align:start position:0%
+it turns out in the end
+that the winners
+
+ align:start position:0%
+that the winners
+ 
+
+ align:start position:0%
+that the winners
+know the meanings of very few words
+
+ align:start position:0%
+know the meanings of very few words
+ 
+
+ align:start position:0%
+know the meanings of very few words
+but they know a word from a non-word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they interviewed some of them at
+
+ align:start position:0%
+and they interviewed some of them at
+ 
+
+ align:start position:0%
+and they interviewed some of them at
+home and and these people had shamanic
+
+ align:start position:0%
+home and and these people had shamanic
+ 
+
+ align:start position:0%
+home and and these people had shamanic
+personalities i mean um
+
+ align:start position:0%
+personalities i mean um
+ 
+
+ align:start position:0%
+personalities i mean um
+uh you just don't see two of them
+
+ align:start position:0%
+uh you just don't see two of them
+ 
+
+ align:start position:0%
+uh you just don't see two of them
+sitting down for long organizing
+
+ align:start position:0%
+sitting down for long organizing
+ 
+
+ align:start position:0%
+sitting down for long organizing
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+okay so in my mind i don't see shane
+
+ align:start position:0%
+okay so in my mind i don't see shane
+ 
+
+ align:start position:0%
+okay so in my mind i don't see shane
+uh oh i tell you where else you find
+
+ align:start position:0%
+uh oh i tell you where else you find
+ 
+
+ align:start position:0%
+uh oh i tell you where else you find
+shane
+
+ align:start position:0%
+shane
+ 
+
+ align:start position:0%
+shane
+a shaman
+
+ align:start position:0%
+a shaman
+ 
+
+ align:start position:0%
+a shaman
+i knew a person who was not ashamed but
+
+ align:start position:0%
+i knew a person who was not ashamed but
+ 
+
+ align:start position:0%
+i knew a person who was not ashamed but
+she said she was taught by shane and so
+
+ align:start position:0%
+she said she was taught by shane and so
+ 
+
+ align:start position:0%
+she said she was taught by shane and so
+she knows some of the shame and skills
+
+ align:start position:0%
+she knows some of the shame and skills
+ 
+
+ align:start position:0%
+she knows some of the shame and skills
+native
+
+ align:start position:0%
+native
+ 
+
+ align:start position:0%
+native
+americans still have you can still find
+
+ align:start position:0%
+americans still have you can still find
+ 
+
+ align:start position:0%
+americans still have you can still find
+a shape
+
+ align:start position:0%
+a shape
+ 
+
+ align:start position:0%
+a shape
+out there
+
+ align:start position:0%
+out there
+ 
+
+ align:start position:0%
+out there
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so what happened was but going back to
+
+ align:start position:0%
+so what happened was but going back to
+ 
+
+ align:start position:0%
+so what happened was but going back to
+civilization
+
+ align:start position:0%
+civilization
+ 
+
+ align:start position:0%
+civilization
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the priests were able to
+
+ align:start position:0%
+the priests were able to
+ 
+
+ align:start position:0%
+the priests were able to
+find cycles
+
+ align:start position:0%
+find cycles
+ 
+
+ align:start position:0%
+find cycles
+that were connected first with the moon
+
+ align:start position:0%
+that were connected first with the moon
+ 
+
+ align:start position:0%
+that were connected first with the moon
+than with the sun
+
+ align:start position:0%
+than with the sun
+ 
+
+ align:start position:0%
+than with the sun
+by which they were able to organize
+
+ align:start position:0%
+by which they were able to organize
+ 
+
+ align:start position:0%
+by which they were able to organize
+everybody to plant
+
+ align:start position:0%
+everybody to plant
+ 
+
+ align:start position:0%
+everybody to plant
+and to read
+
+ align:start position:0%
+and to read
+ 
+
+ align:start position:0%
+and to read
+and that kit and so therefore
+
+ align:start position:0%
+and that kit and so therefore
+ 
+
+ align:start position:0%
+and that kit and so therefore
+it's very easy to understand from that
+
+ align:start position:0%
+it's very easy to understand from that
+ 
+
+ align:start position:0%
+it's very easy to understand from that
+who invented mathematics
+
+ align:start position:0%
+who invented mathematics
+ 
+
+ align:start position:0%
+who invented mathematics
+and astronomy
+
+ align:start position:0%
+and astronomy
+ 
+
+ align:start position:0%
+and astronomy
+okay these priests
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh now i'm getting to my point now i'm
+
+ align:start position:0%
+uh now i'm getting to my point now i'm
+ 
+
+ align:start position:0%
+uh now i'm getting to my point now i'm
+getting to my point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joseph campbell
+
+ align:start position:0%
+joseph campbell
+ 
+
+ align:start position:0%
+joseph campbell
+makes the big point
+
+ align:start position:0%
+makes the big point
+ 
+
+ align:start position:0%
+makes the big point
+that in primitive society
+
+ align:start position:0%
+that in primitive society
+ 
+
+ align:start position:0%
+that in primitive society
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+in the transition from
+
+ align:start position:0%
+in the transition from
+ 
+
+ align:start position:0%
+in the transition from
+small primitive societies to big ones
+
+ align:start position:0%
+small primitive societies to big ones
+ 
+
+ align:start position:0%
+small primitive societies to big ones
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+instead of having
+
+ align:start position:0%
+instead of having
+ 
+
+ align:start position:0%
+instead of having
+six or seven people in a family group
+
+ align:start position:0%
+six or seven people in a family group
+ 
+
+ align:start position:0%
+six or seven people in a family group
+now you're talking about hundreds
+
+ align:start position:0%
+now you're talking about hundreds
+ 
+
+ align:start position:0%
+now you're talking about hundreds
+and they're eating and they're and
+
+ align:start position:0%
+and they're eating and they're and
+ 
+
+ align:start position:0%
+and they're eating and they're and
+they're um
+
+ align:start position:0%
+they're um
+ 
+
+ align:start position:0%
+they're um
+are hurting these the the the these uh
+
+ align:start position:0%
+are hurting these the the the these uh
+ 
+
+ align:start position:0%
+are hurting these the the the these uh
+reindeer or cattle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's what happens now joseph campbell
+
+ align:start position:0%
+here's what happens now joseph campbell
+ 
+
+ align:start position:0%
+here's what happens now joseph campbell
+i think is right about this
+
+ align:start position:0%
+i think is right about this
+ 
+
+ align:start position:0%
+i think is right about this
+he does a lot of anthropocultural
+
+ align:start position:0%
+he does a lot of anthropocultural
+ 
+
+ align:start position:0%
+he does a lot of anthropocultural
+anthropology
+
+ align:start position:0%
+anthropology
+ 
+
+ align:start position:0%
+anthropology
+this is germane to all of this and i'll
+
+ align:start position:0%
+this is germane to all of this and i'll
+ 
+
+ align:start position:0%
+this is germane to all of this and i'll
+make all of this make sense before the
+
+ align:start position:0%
+make all of this make sense before the
+ 
+
+ align:start position:0%
+make all of this make sense before the
+class is out
+
+ align:start position:0%
+class is out
+ 
+
+ align:start position:0%
+class is out
+i don't ask you to trust me but that's a
+
+ align:start position:0%
+i don't ask you to trust me but that's a
+ 
+
+ align:start position:0%
+i don't ask you to trust me but that's a
+promise
+
+ align:start position:0%
+promise
+ 
+
+ align:start position:0%
+promise
+joseph campbell says
+
+ align:start position:0%
+joseph campbell says
+ 
+
+ align:start position:0%
+joseph campbell says
+that once you have a successful society
+
+ align:start position:0%
+that once you have a successful society
+ 
+
+ align:start position:0%
+that once you have a successful society
+successful in terms of holding people
+
+ align:start position:0%
+successful in terms of holding people
+ 
+
+ align:start position:0%
+successful in terms of holding people
+together and feeding everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you will find that your biggest problem
+
+ align:start position:0%
+you will find that your biggest problem
+ 
+
+ align:start position:0%
+you will find that your biggest problem
+is not family
+
+ align:start position:0%
+is not family
+ 
+
+ align:start position:0%
+is not family
+the biggest problem is not disease
+
+ align:start position:0%
+the biggest problem is not disease
+ 
+
+ align:start position:0%
+the biggest problem is not disease
+he says you want to guess what he says
+
+ align:start position:0%
+he says you want to guess what he says
+ 
+
+ align:start position:0%
+he says you want to guess what he says
+your biggest problem is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+men with free time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you get a bad combination the
+
+ align:start position:0%
+because you get a bad combination the
+ 
+
+ align:start position:0%
+because you get a bad combination the
+women don't have free time
+
+ align:start position:0%
+women don't have free time
+ 
+
+ align:start position:0%
+women don't have free time
+you got kids
+
+ align:start position:0%
+you got kids
+ 
+
+ align:start position:0%
+you got kids
+that's a that's 24 hours a day
+
+ align:start position:0%
+that's a that's 24 hours a day
+ 
+
+ align:start position:0%
+that's a that's 24 hours a day
+men with free time
+
+ align:start position:0%
+men with free time
+ 
+
+ align:start position:0%
+men with free time
+here's the bad combination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because everybody's what they do they
+
+ align:start position:0%
+because everybody's what they do they
+ 
+
+ align:start position:0%
+because everybody's what they do they
+if they if they want to shoot they just
+
+ align:start position:0%
+if they if they want to shoot they just
+ 
+
+ align:start position:0%
+if they if they want to shoot they just
+go out get one
+
+ align:start position:0%
+go out get one
+ 
+
+ align:start position:0%
+go out get one
+they got free time men with free time
+
+ align:start position:0%
+they got free time men with free time
+ 
+
+ align:start position:0%
+they got free time men with free time
+here's the bad combination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free time
+
+ align:start position:0%
+free time
+ 
+
+ align:start position:0%
+free time
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+inclination to organizing hierarchical
+
+ align:start position:0%
+inclination to organizing hierarchical
+ 
+
+ align:start position:0%
+inclination to organizing hierarchical
+groups
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and guess what the last piece of the
+
+ align:start position:0%
+and guess what the last piece of the
+ 
+
+ align:start position:0%
+and guess what the last piece of the
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+high levels of testosterone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+high levels of testosterone
+
+ align:start position:0%
+high levels of testosterone
+ 
+
+ align:start position:0%
+high levels of testosterone
+that's a bad combination
+
+ align:start position:0%
+that's a bad combination
+ 
+
+ align:start position:0%
+that's a bad combination
+free time
+
+ align:start position:0%
+free time
+ 
+
+ align:start position:0%
+free time
+men men with free time
+
+ align:start position:0%
+men men with free time
+ 
+
+ align:start position:0%
+men men with free time
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what happens is
+
+ align:start position:0%
+so what happens is
+ 
+
+ align:start position:0%
+so what happens is
+that to let out that energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the things that been learned to
+
+ align:start position:0%
+one of the things that been learned to
+ 
+
+ align:start position:0%
+one of the things that been learned to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+was to hunt other men
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is the root of the heroic story
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what and these ancient or hurting
+
+ align:start position:0%
+and what and these ancient or hurting
+ 
+
+ align:start position:0%
+and what and these ancient or hurting
+societies
+
+ align:start position:0%
+societies
+ 
+
+ align:start position:0%
+societies
+anthropologists call warrior warrior
+
+ align:start position:0%
+anthropologists call warrior warrior
+ 
+
+ align:start position:0%
+anthropologists call warrior warrior
+herding societies they were warriors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+civilization was priests
+
+ align:start position:0%
+civilization was priests
+ 
+
+ align:start position:0%
+civilization was priests
+and farmers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now here's the last piece of this puzzle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as civilization got more complicated you
+
+ align:start position:0%
+as civilization got more complicated you
+ 
+
+ align:start position:0%
+as civilization got more complicated you
+get more people
+
+ align:start position:0%
+get more people
+ 
+
+ align:start position:0%
+get more people
+got bigger problems
+
+ align:start position:0%
+got bigger problems
+ 
+
+ align:start position:0%
+got bigger problems
+uh the priest can't handle keep
+
+ align:start position:0%
+uh the priest can't handle keep
+ 
+
+ align:start position:0%
+uh the priest can't handle keep
+everybody together just on holidays
+
+ align:start position:0%
+everybody together just on holidays
+ 
+
+ align:start position:0%
+everybody together just on holidays
+and you know and
+
+ align:start position:0%
+and you know and
+ 
+
+ align:start position:0%
+and you know and
+and and sundays if you want to put it
+
+ align:start position:0%
+and and sundays if you want to put it
+ 
+
+ align:start position:0%
+and and sundays if you want to put it
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+you have to have a principle of force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what happened was
+
+ align:start position:0%
+so what happened was
+ 
+
+ align:start position:0%
+so what happened was
+that the the warrior herders the young
+
+ align:start position:0%
+that the the warrior herders the young
+ 
+
+ align:start position:0%
+that the the warrior herders the young
+men would get out and say well look we
+
+ align:start position:0%
+men would get out and say well look we
+ 
+
+ align:start position:0%
+men would get out and say well look we
+got to prove our manhood
+
+ align:start position:0%
+got to prove our manhood
+ 
+
+ align:start position:0%
+got to prove our manhood
+so they run out to uh or
+
+ align:start position:0%
+so they run out to uh or
+ 
+
+ align:start position:0%
+so they run out to uh or
+run out over to some civilization kill
+
+ align:start position:0%
+run out over to some civilization kill
+ 
+
+ align:start position:0%
+run out over to some civilization kill
+someone
+
+ align:start position:0%
+someone
+ 
+
+ align:start position:0%
+someone
+still steal some women
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh then the civilization started
+
+ align:start position:0%
+uh then the civilization started
+ 
+
+ align:start position:0%
+uh then the civilization started
+building walls to keep them out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then what happened was the priests
+
+ align:start position:0%
+and then what happened was the priests
+ 
+
+ align:start position:0%
+and then what happened was the priests
+started hiring them as mercenaries
+
+ align:start position:0%
+started hiring them as mercenaries
+ 
+
+ align:start position:0%
+started hiring them as mercenaries
+the priests started hiring them as first
+
+ align:start position:0%
+the priests started hiring them as first
+ 
+
+ align:start position:0%
+the priests started hiring them as first
+of all mercenaries
+
+ align:start position:0%
+of all mercenaries
+ 
+
+ align:start position:0%
+of all mercenaries
+whenever they uh whenever one civilized
+
+ align:start position:0%
+whenever they uh whenever one civilized
+ 
+
+ align:start position:0%
+whenever they uh whenever one civilized
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+thought that they needed something from
+
+ align:start position:0%
+thought that they needed something from
+ 
+
+ align:start position:0%
+thought that they needed something from
+another civilian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay some bugs got in and ate all of the
+
+ align:start position:0%
+okay some bugs got in and ate all of the
+ 
+
+ align:start position:0%
+okay some bugs got in and ate all of the
+wheat
+
+ align:start position:0%
+wheat
+ 
+
+ align:start position:0%
+wheat
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+these people got wheat over there
+
+ align:start position:0%
+these people got wheat over there
+ 
+
+ align:start position:0%
+these people got wheat over there
+they're not going to give you any wheat
+
+ align:start position:0%
+they're not going to give you any wheat
+ 
+
+ align:start position:0%
+they're not going to give you any wheat
+over here so you hire some of these
+
+ align:start position:0%
+over here so you hire some of these
+ 
+
+ align:start position:0%
+over here so you hire some of these
+mercenaries go beat up on a couple of
+
+ align:start position:0%
+mercenaries go beat up on a couple of
+ 
+
+ align:start position:0%
+mercenaries go beat up on a couple of
+them and bring some feedback
+
+ align:start position:0%
+them and bring some feedback
+ 
+
+ align:start position:0%
+them and bring some feedback
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then you have all of these problems
+
+ align:start position:0%
+then you have all of these problems
+ 
+
+ align:start position:0%
+then you have all of these problems
+within the culture
+
+ align:start position:0%
+within the culture
+ 
+
+ align:start position:0%
+within the culture
+people are fighting
+
+ align:start position:0%
+people are fighting
+ 
+
+ align:start position:0%
+people are fighting
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so then you have these people not as
+
+ align:start position:0%
+so then you have these people not as
+ 
+
+ align:start position:0%
+so then you have these people not as
+mercenaries but you're hired as police
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see it the invention of the king
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you already got the high priest the king
+
+ align:start position:0%
+you already got the high priest the king
+ 
+
+ align:start position:0%
+you already got the high priest the king
+is really an outsider
+
+ align:start position:0%
+is really an outsider
+ 
+
+ align:start position:0%
+is really an outsider
+that's what happened the roman empire
+
+ align:start position:0%
+that's what happened the roman empire
+ 
+
+ align:start position:0%
+that's what happened the roman empire
+the romans came in they just didn't
+
+ align:start position:0%
+the romans came in they just didn't
+ 
+
+ align:start position:0%
+the romans came in they just didn't
+subdue everybody and beat everybody out
+
+ align:start position:0%
+subdue everybody and beat everybody out
+ 
+
+ align:start position:0%
+subdue everybody and beat everybody out
+they just came in and became
+
+ align:start position:0%
+they just came in and became
+ 
+
+ align:start position:0%
+they just came in and became
+the police
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they left a lot of the high priest in
+
+ align:start position:0%
+they left a lot of the high priest in
+ 
+
+ align:start position:0%
+they left a lot of the high priest in
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+so what i'm saying now is
+
+ align:start position:0%
+so what i'm saying now is
+ 
+
+ align:start position:0%
+so what i'm saying now is
+that the religion in religion in warrior
+
+ align:start position:0%
+that the religion in religion in warrior
+ 
+
+ align:start position:0%
+that the religion in religion in warrior
+societies is based on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kinship and they are they
+
+ align:start position:0%
+kinship and they are they
+ 
+
+ align:start position:0%
+kinship and they are they
+they don't believe
+
+ align:start position:0%
+they don't believe
+ 
+
+ align:start position:0%
+they don't believe
+that they lose anything by
+
+ align:start position:0%
+that they lose anything by
+ 
+
+ align:start position:0%
+that they lose anything by
+adopting your religion
+
+ align:start position:0%
+adopting your religion
+ 
+
+ align:start position:0%
+adopting your religion
+you can't adopt theirs because you're
+
+ align:start position:0%
+you can't adopt theirs because you're
+ 
+
+ align:start position:0%
+you can't adopt theirs because you're
+not a member of the family
+
+ align:start position:0%
+not a member of the family
+ 
+
+ align:start position:0%
+not a member of the family
+so warrior hurting societies are not
+
+ align:start position:0%
+so warrior hurting societies are not
+ 
+
+ align:start position:0%
+so warrior hurting societies are not
+like civilized society civilized
+
+ align:start position:0%
+like civilized society civilized
+ 
+
+ align:start position:0%
+like civilized society civilized
+societies compete
+
+ align:start position:0%
+societies compete
+ 
+
+ align:start position:0%
+societies compete
+to debt to the debt over religion
+
+ align:start position:0%
+to debt to the debt over religion
+ 
+
+ align:start position:0%
+to debt to the debt over religion
+warrior hurting society doesn't matter
+
+ align:start position:0%
+warrior hurting society doesn't matter
+ 
+
+ align:start position:0%
+warrior hurting society doesn't matter
+that much to them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the pagans that we're talking about
+
+ align:start position:0%
+the pagans that we're talking about
+ 
+
+ align:start position:0%
+the pagans that we're talking about
+impossible
+
+ align:start position:0%
+impossible
+ 
+
+ align:start position:0%
+impossible
+were warrior hurting arabs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so so fearfully really wasn't giving
+
+ align:start position:0%
+so so so fearfully really wasn't giving
+ 
+
+ align:start position:0%
+so so so fearfully really wasn't giving
+up a whole lot to become
+
+ align:start position:0%
+up a whole lot to become
+ 
+
+ align:start position:0%
+up a whole lot to become
+a christian
+
+ align:start position:0%
+a christian
+ 
+
+ align:start position:0%
+a christian
+not a whole lot
+
+ align:start position:0%
+not a whole lot
+ 
+
+ align:start position:0%
+not a whole lot
+i mean uh even even um
+
+ align:start position:0%
+i mean uh even even um
+ 
+
+ align:start position:0%
+i mean uh even even um
+when muhammad
+
+ align:start position:0%
+when muhammad
+ 
+
+ align:start position:0%
+when muhammad
+invented islam
+
+ align:start position:0%
+invented islam
+ 
+
+ align:start position:0%
+invented islam
+he did it as an attempt
+
+ align:start position:0%
+he did it as an attempt
+ 
+
+ align:start position:0%
+he did it as an attempt
+to synthesize
+
+ align:start position:0%
+to synthesize
+ 
+
+ align:start position:0%
+to synthesize
+their own religions
+
+ align:start position:0%
+their own religions
+ 
+
+ align:start position:0%
+their own religions
+with christianity and judaism
+
+ align:start position:0%
+with christianity and judaism
+ 
+
+ align:start position:0%
+with christianity and judaism
+and one other one um
+
+ align:start position:0%
+and one other one um
+ 
+
+ align:start position:0%
+and one other one um
+zoroastrianism
+
+ align:start position:0%
+zoroastrianism
+ 
+
+ align:start position:0%
+zoroastrianism
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh any person who comes in here who says
+
+ align:start position:0%
+uh any person who comes in here who says
+ 
+
+ align:start position:0%
+uh any person who comes in here who says
+that i am a muslim
+
+ align:start position:0%
+that i am a muslim
+ 
+
+ align:start position:0%
+that i am a muslim
+will say that i have very few arguments
+
+ align:start position:0%
+will say that i have very few arguments
+ 
+
+ align:start position:0%
+will say that i have very few arguments
+with you about religion
+
+ align:start position:0%
+with you about religion
+ 
+
+ align:start position:0%
+with you about religion
+you will say i have a lot of arguments
+
+ align:start position:0%
+you will say i have a lot of arguments
+ 
+
+ align:start position:0%
+you will say i have a lot of arguments
+with you about religion but they will
+
+ align:start position:0%
+with you about religion but they will
+ 
+
+ align:start position:0%
+with you about religion but they will
+say i don't have a whole lot of
+
+ align:start position:0%
+say i don't have a whole lot of
+ 
+
+ align:start position:0%
+say i don't have a whole lot of
+arguments with you about it because part
+
+ align:start position:0%
+arguments with you about it because part
+ 
+
+ align:start position:0%
+arguments with you about it because part
+of my religion is already built in
+
+ align:start position:0%
+of my religion is already built in
+ 
+
+ align:start position:0%
+of my religion is already built in
+christianity
+
+ align:start position:0%
+christianity
+ 
+
+ align:start position:0%
+christianity
+so fear fears wasn't given up a whole
+
+ align:start position:0%
+so fear fears wasn't given up a whole
+ 
+
+ align:start position:0%
+so fear fears wasn't given up a whole
+lot by doing it
+
+ align:start position:0%
+lot by doing it
+ 
+
+ align:start position:0%
+lot by doing it
+it meant almost everything to possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh so i thought i'd go through that long
+
+ align:start position:0%
+uh so i thought i'd go through that long
+ 
+
+ align:start position:0%
+uh so i thought i'd go through that long
+spiel
+
+ align:start position:0%
+spiel
+ 
+
+ align:start position:0%
+spiel
+because we have because it's built into
+
+ align:start position:0%
+because we have because it's built into
+ 
+
+ align:start position:0%
+because we have because it's built into
+the story here
+
+ align:start position:0%
+the story here
+ 
+
+ align:start position:0%
+the story here
+these things are built into the story
+
+ align:start position:0%
+these things are built into the story
+ 
+
+ align:start position:0%
+these things are built into the story
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what had just happened was
+
+ align:start position:0%
+what had just happened was
+ 
+
+ align:start position:0%
+what had just happened was
+what created the knights and what made
+
+ align:start position:0%
+what created the knights and what made
+ 
+
+ align:start position:0%
+what created the knights and what made
+them who they were
+
+ align:start position:0%
+them who they were
+ 
+
+ align:start position:0%
+them who they were
+was that there was this big void
+
+ align:start position:0%
+was that there was this big void
+ 
+
+ align:start position:0%
+was that there was this big void
+in the western world after the roman
+
+ align:start position:0%
+in the western world after the roman
+ 
+
+ align:start position:0%
+in the western world after the roman
+empire collapse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when any time some big power
+
+ align:start position:0%
+and when any time some big power
+ 
+
+ align:start position:0%
+and when any time some big power
+collapse collapses
+
+ align:start position:0%
+collapse collapses
+ 
+
+ align:start position:0%
+collapse collapses
+a whole lot of people rushing in to fill
+
+ align:start position:0%
+a whole lot of people rushing in to fill
+ 
+
+ align:start position:0%
+a whole lot of people rushing in to fill
+the void and get the piece of the action
+
+ align:start position:0%
+the void and get the piece of the action
+ 
+
+ align:start position:0%
+the void and get the piece of the action
+okay then came islam
+
+ align:start position:0%
+okay then came islam
+ 
+
+ align:start position:0%
+okay then came islam
+that lasted for a while went back and
+
+ align:start position:0%
+that lasted for a while went back and
+ 
+
+ align:start position:0%
+that lasted for a while went back and
+now you have the dark ages
+
+ align:start position:0%
+now you have the dark ages
+ 
+
+ align:start position:0%
+now you have the dark ages
+and then when everything comes back
+
+ align:start position:0%
+and then when everything comes back
+ 
+
+ align:start position:0%
+and then when everything comes back
+together you start having the middle
+
+ align:start position:0%
+together you start having the middle
+ 
+
+ align:start position:0%
+together you start having the middle
+ages
+
+ align:start position:0%
+ages
+ 
+
+ align:start position:0%
+ages
+and when did you start having the middle
+
+ align:start position:0%
+and when did you start having the middle
+ 
+
+ align:start position:0%
+and when did you start having the middle
+ages
+
+ align:start position:0%
+ages
+ 
+
+ align:start position:0%
+ages
+when charlemagne
+
+ align:start position:0%
+when charlemagne
+ 
+
+ align:start position:0%
+when charlemagne
+uh started organizing all of these dukes
+
+ align:start position:0%
+uh started organizing all of these dukes
+ 
+
+ align:start position:0%
+uh started organizing all of these dukes
+under one king
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some people would say it was otto first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who came after charlemagne but
+
+ align:start position:0%
+who came after charlemagne but
+ 
+
+ align:start position:0%
+who came after charlemagne but
+nevertheless
+
+ align:start position:0%
+nevertheless
+ 
+
+ align:start position:0%
+nevertheless
+okay so we're talking about a time now
+
+ align:start position:0%
+okay so we're talking about a time now
+ 
+
+ align:start position:0%
+okay so we're talking about a time now
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+uh the the west was ruled by arabs who
+
+ align:start position:0%
+uh the the west was ruled by arabs who
+ 
+
+ align:start position:0%
+uh the the west was ruled by arabs who
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+and you got this big void and you have
+
+ align:start position:0%
+and you got this big void and you have
+ 
+
+ align:start position:0%
+and you got this big void and you have
+these a feudal system
+
+ align:start position:0%
+these a feudal system
+ 
+
+ align:start position:0%
+these a feudal system
+and the knights
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+serve a feudal lord
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there is there's something about
+
+ align:start position:0%
+and there is there's something about
+ 
+
+ align:start position:0%
+and there is there's something about
+some of these knights that say
+
+ align:start position:0%
+some of these knights that say
+ 
+
+ align:start position:0%
+some of these knights that say
+well look uh yeah we're ravaging the
+
+ align:start position:0%
+well look uh yeah we're ravaging the
+ 
+
+ align:start position:0%
+well look uh yeah we're ravaging the
+land and all of that
+
+ align:start position:0%
+land and all of that
+ 
+
+ align:start position:0%
+land and all of that
+but there's got to be some principles on
+
+ align:start position:0%
+but there's got to be some principles on
+ 
+
+ align:start position:0%
+but there's got to be some principles on
+all of this
+
+ align:start position:0%
+all of this
+ 
+
+ align:start position:0%
+all of this
+and some of these nights really did
+
+ align:start position:0%
+and some of these nights really did
+ 
+
+ align:start position:0%
+and some of these nights really did
+bring chivalry
+
+ align:start position:0%
+bring chivalry
+ 
+
+ align:start position:0%
+bring chivalry
+to a high peak level
+
+ align:start position:0%
+to a high peak level
+ 
+
+ align:start position:0%
+to a high peak level
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+some of them even call themselves
+
+ align:start position:0%
+some of them even call themselves
+ 
+
+ align:start position:0%
+some of them even call themselves
+priests like the knights templar
+
+ align:start position:0%
+priests like the knights templar
+ 
+
+ align:start position:0%
+priests like the knights templar
+they thought of themselves
+
+ align:start position:0%
+they thought of themselves
+ 
+
+ align:start position:0%
+they thought of themselves
+so that's that's that's where we are
+
+ align:start position:0%
+so that's that's that's where we are
+ 
+
+ align:start position:0%
+so that's that's that's where we are
+with all of this and that
+
+ align:start position:0%
+with all of this and that
+ 
+
+ align:start position:0%
+with all of this and that
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+one of one thing that isn't
+
+ align:start position:0%
+one of one thing that isn't
+ 
+
+ align:start position:0%
+one of one thing that isn't
+emphasized in here
+
+ align:start position:0%
+emphasized in here
+ 
+
+ align:start position:0%
+emphasized in here
+uh like it is other places the killing
+
+ align:start position:0%
+uh like it is other places the killing
+ 
+
+ align:start position:0%
+uh like it is other places the killing
+of the dragon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that the purpose of mythology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hold a society together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of his functions is
+
+ align:start position:0%
+and one of his functions is
+ 
+
+ align:start position:0%
+and one of his functions is
+is to organize the men with the free
+
+ align:start position:0%
+is to organize the men with the free
+ 
+
+ align:start position:0%
+is to organize the men with the free
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and say now if you're going to kill
+
+ align:start position:0%
+and say now if you're going to kill
+ 
+
+ align:start position:0%
+and say now if you're going to kill
+somebody they got to be smooth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh and why have these things lasted
+
+ align:start position:0%
+uh and why have these things lasted
+ 
+
+ align:start position:0%
+uh and why have these things lasted
+so long well what we find out is that
+
+ align:start position:0%
+so long well what we find out is that
+ 
+
+ align:start position:0%
+so long well what we find out is that
+they've lasted a long time
+
+ align:start position:0%
+they've lasted a long time
+ 
+
+ align:start position:0%
+they've lasted a long time
+because they become metaphors for
+
+ align:start position:0%
+because they become metaphors for
+ 
+
+ align:start position:0%
+because they become metaphors for
+everybody's problem
+
+ align:start position:0%
+everybody's problem
+ 
+
+ align:start position:0%
+everybody's problem
+big with your big problems in your life
+
+ align:start position:0%
+big with your big problems in your life
+ 
+
+ align:start position:0%
+big with your big problems in your life
+and one that i like to talk about
+
+ align:start position:0%
+and one that i like to talk about
+ 
+
+ align:start position:0%
+and one that i like to talk about
+make mention here
+
+ align:start position:0%
+make mention here
+ 
+
+ align:start position:0%
+make mention here
+is uh let's let's entertain a problem
+
+ align:start position:0%
+is uh let's let's entertain a problem
+ 
+
+ align:start position:0%
+is uh let's let's entertain a problem
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh you've just graduated
+
+ align:start position:0%
+uh you've just graduated
+ 
+
+ align:start position:0%
+uh you've just graduated
+no you're not haven't just graduated
+
+ align:start position:0%
+no you're not haven't just graduated
+ 
+
+ align:start position:0%
+no you're not haven't just graduated
+you've graduated and you're working and
+
+ align:start position:0%
+you've graduated and you're working and
+ 
+
+ align:start position:0%
+you've graduated and you're working and
+you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sacrificed a lot
+
+ align:start position:0%
+sacrificed a lot
+ 
+
+ align:start position:0%
+sacrificed a lot
+and you've progressed
+
+ align:start position:0%
+and you've progressed
+ 
+
+ align:start position:0%
+and you've progressed
+in your company
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+your company
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is about ready to
+
+ align:start position:0%
+is about ready to
+ 
+
+ align:start position:0%
+is about ready to
+is competing for a contract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's say with the germans
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're going to make the company's gonna
+
+ align:start position:0%
+you're going to make the company's gonna
+ 
+
+ align:start position:0%
+you're going to make the company's gonna
+make his pitch
+
+ align:start position:0%
+make his pitch
+ 
+
+ align:start position:0%
+make his pitch
+monday morning
+
+ align:start position:0%
+monday morning
+ 
+
+ align:start position:0%
+monday morning
+and you have to leave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sunday night you get a call
+
+ align:start position:0%
+sunday night you get a call
+ 
+
+ align:start position:0%
+sunday night you get a call
+from your husband's
+
+ align:start position:0%
+from your husband's
+ 
+
+ align:start position:0%
+from your husband's
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mother
+
+ align:start position:0%
+mother
+ 
+
+ align:start position:0%
+mother
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+arizona
+
+ align:start position:0%
+arizona
+ 
+
+ align:start position:0%
+arizona
+the kids are out visiting
+
+ align:start position:0%
+the kids are out visiting
+ 
+
+ align:start position:0%
+the kids are out visiting
+she's your husband says
+
+ align:start position:0%
+she's your husband says
+ 
+
+ align:start position:0%
+she's your husband says
+one of the kids got hit by a car
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the doctor says
+
+ align:start position:0%
+uh the doctor says
+ 
+
+ align:start position:0%
+uh the doctor says
+we don't know if the kid's gonna last
+
+ align:start position:0%
+we don't know if the kid's gonna last
+ 
+
+ align:start position:0%
+we don't know if the kid's gonna last
+another two days
+
+ align:start position:0%
+another two days
+ 
+
+ align:start position:0%
+another two days
+now do you go to that meeting on monday
+
+ align:start position:0%
+now do you go to that meeting on monday
+ 
+
+ align:start position:0%
+now do you go to that meeting on monday
+or do you go to arizona
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right well let me tell you what this
+
+ align:start position:0%
+right well let me tell you what this
+ 
+
+ align:start position:0%
+right well let me tell you what this
+heroic story is gonna
+
+ align:start position:0%
+heroic story is gonna
+ 
+
+ align:start position:0%
+heroic story is gonna
+how this heroic story is gonna help you
+
+ align:start position:0%
+how this heroic story is gonna help you
+ 
+
+ align:start position:0%
+how this heroic story is gonna help you
+with that decision
+
+ align:start position:0%
+with that decision
+ 
+
+ align:start position:0%
+with that decision
+the heroic story says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that your conscious mind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh possesses
+
+ align:start position:0%
+uh possesses
+ 
+
+ align:start position:0%
+uh possesses
+does not possess all of the knowledge
+
+ align:start position:0%
+does not possess all of the knowledge
+ 
+
+ align:start position:0%
+does not possess all of the knowledge
+that your mind possesses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your unconscious mind and i'm not
+
+ align:start position:0%
+your unconscious mind and i'm not
+ 
+
+ align:start position:0%
+your unconscious mind and i'm not
+talking about memories right now
+
+ align:start position:0%
+talking about memories right now
+ 
+
+ align:start position:0%
+talking about memories right now
+about parts of your conscious mind that
+
+ align:start position:0%
+about parts of your conscious mind that
+ 
+
+ align:start position:0%
+about parts of your conscious mind that
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+virtually permanent
+
+ align:start position:0%
+virtually permanent
+ 
+
+ align:start position:0%
+virtually permanent
+there are some truths that are hidden
+
+ align:start position:0%
+there are some truths that are hidden
+ 
+
+ align:start position:0%
+there are some truths that are hidden
+down in your unconscious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you are able to get into a mythic
+
+ align:start position:0%
+and if you are able to get into a mythic
+ 
+
+ align:start position:0%
+and if you are able to get into a mythic
+state of mind
+
+ align:start position:0%
+state of mind
+ 
+
+ align:start position:0%
+state of mind
+then what you will be able to do
+
+ align:start position:0%
+then what you will be able to do
+ 
+
+ align:start position:0%
+then what you will be able to do
+is to go down in your unconscious and
+
+ align:start position:0%
+is to go down in your unconscious and
+ 
+
+ align:start position:0%
+is to go down in your unconscious and
+find out if one of those monsters down
+
+ align:start position:0%
+find out if one of those monsters down
+ 
+
+ align:start position:0%
+find out if one of those monsters down
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+needs to be killed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what kind of monster would be down
+
+ align:start position:0%
+now what kind of monster would be down
+ 
+
+ align:start position:0%
+now what kind of monster would be down
+there well i'll tell you one kind that
+
+ align:start position:0%
+there well i'll tell you one kind that
+ 
+
+ align:start position:0%
+there well i'll tell you one kind that
+would be down there your ambition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because that your ambition is competing
+
+ align:start position:0%
+because that your ambition is competing
+ 
+
+ align:start position:0%
+because that your ambition is competing
+with that child
+
+ align:start position:0%
+with that child
+ 
+
+ align:start position:0%
+with that child
+now i was unfair because i made you all
+
+ align:start position:0%
+now i was unfair because i made you all
+ 
+
+ align:start position:0%
+now i was unfair because i made you all
+mothers
+
+ align:start position:0%
+mothers
+ 
+
+ align:start position:0%
+mothers
+but suppose
+
+ align:start position:0%
+but suppose
+ 
+
+ align:start position:0%
+but suppose
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it was some people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that are gonna die if you don't go help
+
+ align:start position:0%
+that are gonna die if you don't go help
+ 
+
+ align:start position:0%
+that are gonna die if you don't go help
+them as opposed to going all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh then you gotta then you gotta
+
+ align:start position:0%
+okay uh then you gotta then you gotta
+ 
+
+ align:start position:0%
+okay uh then you gotta then you gotta
+face that that demon down there that's
+
+ align:start position:0%
+face that that demon down there that's
+ 
+
+ align:start position:0%
+face that that demon down there that's
+your ambition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what you have got to do
+
+ align:start position:0%
+and what you have got to do
+ 
+
+ align:start position:0%
+and what you have got to do
+is to say
+
+ align:start position:0%
+is to say
+ 
+
+ align:start position:0%
+is to say
+that i would rather be dead to continue
+
+ align:start position:0%
+that i would rather be dead to continue
+ 
+
+ align:start position:0%
+that i would rather be dead to continue
+to live a life
+
+ align:start position:0%
+to live a life
+ 
+
+ align:start position:0%
+to live a life
+of not being able to deal with these
+
+ align:start position:0%
+of not being able to deal with these
+ 
+
+ align:start position:0%
+of not being able to deal with these
+decisions
+
+ align:start position:0%
+decisions
+ 
+
+ align:start position:0%
+decisions
+i got to deal with this maybe my
+
+ align:start position:0%
+i got to deal with this maybe my
+ 
+
+ align:start position:0%
+i got to deal with this maybe my
+ambition is good
+
+ align:start position:0%
+ambition is good
+ 
+
+ align:start position:0%
+ambition is good
+for me
+
+ align:start position:0%
+for me
+ 
+
+ align:start position:0%
+for me
+or maybe it's got to be killed but
+
+ align:start position:0%
+or maybe it's got to be killed but
+ 
+
+ align:start position:0%
+or maybe it's got to be killed but
+whatever it is i've got to face the
+
+ align:start position:0%
+whatever it is i've got to face the
+ 
+
+ align:start position:0%
+whatever it is i've got to face the
+devil
+
+ align:start position:0%
+devil
+ 
+
+ align:start position:0%
+devil
+and i am ready to die
+
+ align:start position:0%
+and i am ready to die
+ 
+
+ align:start position:0%
+and i am ready to die
+because that unconscious demon is lethal
+
+ align:start position:0%
+because that unconscious demon is lethal
+ 
+
+ align:start position:0%
+because that unconscious demon is lethal
+in the real world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you decide that on somebody else's
+
+ align:start position:0%
+so if you decide that on somebody else's
+ 
+
+ align:start position:0%
+so if you decide that on somebody else's
+behalf
+
+ align:start position:0%
+behalf
+ 
+
+ align:start position:0%
+behalf
+you are willing to kill the demon and to
+
+ align:start position:0%
+you are willing to kill the demon and to
+ 
+
+ align:start position:0%
+you are willing to kill the demon and to
+bring the truth back
+
+ align:start position:0%
+bring the truth back
+ 
+
+ align:start position:0%
+bring the truth back
+to your conscious mind
+
+ align:start position:0%
+to your conscious mind
+ 
+
+ align:start position:0%
+to your conscious mind
+that's the best way to handle the
+
+ align:start position:0%
+that's the best way to handle the
+ 
+
+ align:start position:0%
+that's the best way to handle the
+problem whatever decision you come up
+
+ align:start position:0%
+problem whatever decision you come up
+ 
+
+ align:start position:0%
+problem whatever decision you come up
+with after that is the best you can do
+
+ align:start position:0%
+with after that is the best you can do
+ 
+
+ align:start position:0%
+with after that is the best you can do
+and the metaphor
+
+ align:start position:0%
+and the metaphor
+ 
+
+ align:start position:0%
+and the metaphor
+is in the heroic story
+
+ align:start position:0%
+is in the heroic story
+ 
+
+ align:start position:0%
+is in the heroic story
+so if you can get into the story to the
+
+ align:start position:0%
+so if you can get into the story to the
+ 
+
+ align:start position:0%
+so if you can get into the story to the
+point where you can get into possible's
+
+ align:start position:0%
+point where you can get into possible's
+ 
+
+ align:start position:0%
+point where you can get into possible's
+place and actually feel
+
+ align:start position:0%
+place and actually feel
+ 
+
+ align:start position:0%
+place and actually feel
+the possible feels and then get into
+
+ align:start position:0%
+the possible feels and then get into
+ 
+
+ align:start position:0%
+the possible feels and then get into
+some of these other stories where
+
+ align:start position:0%
+some of these other stories where
+ 
+
+ align:start position:0%
+some of these other stories where
+they're really killing dragons
+
+ align:start position:0%
+they're really killing dragons
+ 
+
+ align:start position:0%
+they're really killing dragons
+uh then what it does
+
+ align:start position:0%
+uh then what it does
+ 
+
+ align:start position:0%
+uh then what it does
+what what we know now
+
+ align:start position:0%
+what what we know now
+ 
+
+ align:start position:0%
+what what we know now
+um a thousand years later is that if you
+
+ align:start position:0%
+um a thousand years later is that if you
+ 
+
+ align:start position:0%
+um a thousand years later is that if you
+embrace those things seriously and if
+
+ align:start position:0%
+embrace those things seriously and if
+ 
+
+ align:start position:0%
+embrace those things seriously and if
+you really feel that you are possible
+
+ align:start position:0%
+you really feel that you are possible
+ 
+
+ align:start position:0%
+you really feel that you are possible
+in there
+
+ align:start position:0%
+in there
+ 
+
+ align:start position:0%
+in there
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the wiring in your brain will change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+your 12 year old will start looking like
+
+ align:start position:0%
+your 12 year old will start looking like
+ 
+
+ align:start position:0%
+your 12 year old will start looking like
+a 14 year old
+
+ align:start position:0%
+a 14 year old
+ 
+
+ align:start position:0%
+a 14 year old
+not somebody who's going to be 18 year
+
+ align:start position:0%
+not somebody who's going to be 18 year
+ 
+
+ align:start position:0%
+not somebody who's going to be 18 year
+old still looking like 12
+
+ align:start position:0%
+old still looking like 12
+ 
+
+ align:start position:0%
+old still looking like 12
+that your physiology if you're young
+
+ align:start position:0%
+that your physiology if you're young
+ 
+
+ align:start position:0%
+that your physiology if you're young
+enough will change
+
+ align:start position:0%
+enough will change
+ 
+
+ align:start position:0%
+enough will change
+you will grow up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+ancient people
+
+ align:start position:0%
+ancient people
+ 
+
+ align:start position:0%
+ancient people
+uh and medieval people
+
+ align:start position:0%
+uh and medieval people
+ 
+
+ align:start position:0%
+uh and medieval people
+and early modern people do all of this
+
+ align:start position:0%
+and early modern people do all of this
+ 
+
+ align:start position:0%
+and early modern people do all of this
+before the science could prove any of it
+
+ align:start position:0%
+before the science could prove any of it
+ 
+
+ align:start position:0%
+before the science could prove any of it
+uh better stated
+
+ align:start position:0%
+uh better stated
+ 
+
+ align:start position:0%
+uh better stated
+better stated
+
+ align:start position:0%
+better stated
+ 
+
+ align:start position:0%
+better stated
+they were willing to commit to it
+
+ align:start position:0%
+they were willing to commit to it
+ 
+
+ align:start position:0%
+they were willing to commit to it
+regardless
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when they had their young
+
+ align:start position:0%
+so when they had their young
+ 
+
+ align:start position:0%
+so when they had their young
+kids coming along
+
+ align:start position:0%
+kids coming along
+ 
+
+ align:start position:0%
+kids coming along
+particularly if they were afraid that
+
+ align:start position:0%
+particularly if they were afraid that
+ 
+
+ align:start position:0%
+particularly if they were afraid that
+the boys
+
+ align:start position:0%
+the boys
+ 
+
+ align:start position:0%
+the boys
+were going to have some free time
+
+ align:start position:0%
+were going to have some free time
+ 
+
+ align:start position:0%
+were going to have some free time
+oh i mean it's a nightmare if you got a
+
+ align:start position:0%
+oh i mean it's a nightmare if you got a
+ 
+
+ align:start position:0%
+oh i mean it's a nightmare if you got a
+16 year old
+
+ align:start position:0%
+16 year old
+ 
+
+ align:start position:0%
+16 year old
+on a saturday night
+
+ align:start position:0%
+on a saturday night
+ 
+
+ align:start position:0%
+on a saturday night
+i don't care how much you put into it
+
+ align:start position:0%
+i don't care how much you put into it
+ 
+
+ align:start position:0%
+i don't care how much you put into it
+that can be a bad night for you okay
+
+ align:start position:0%
+that can be a bad night for you okay
+ 
+
+ align:start position:0%
+that can be a bad night for you okay
+i know i was 16 years old
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if you read these stories to them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if they can embrace them
+
+ align:start position:0%
+and if they can embrace them
+ 
+
+ align:start position:0%
+and if they can embrace them
+then that's a big help
+
+ align:start position:0%
+then that's a big help
+ 
+
+ align:start position:0%
+then that's a big help
+it's a big help
+
+ align:start position:0%
+it's a big help
+ 
+
+ align:start position:0%
+it's a big help
+uh some people have said that freud no
+
+ align:start position:0%
+uh some people have said that freud no
+ 
+
+ align:start position:0%
+uh some people have said that freud no
+matter what they what what others say
+
+ align:start position:0%
+matter what they what what others say
+ 
+
+ align:start position:0%
+matter what they what what others say
+that he brought
+
+ align:start position:0%
+that he brought
+ 
+
+ align:start position:0%
+that he brought
+the scientific method to the study of
+
+ align:start position:0%
+the scientific method to the study of
+ 
+
+ align:start position:0%
+the scientific method to the study of
+the mind what they really say is that
+
+ align:start position:0%
+the mind what they really say is that
+ 
+
+ align:start position:0%
+the mind what they really say is that
+freud was actually a
+
+ align:start position:0%
+freud was actually a
+ 
+
+ align:start position:0%
+freud was actually a
+pathologist
+
+ align:start position:0%
+pathologist
+ 
+
+ align:start position:0%
+pathologist
+because what he said was that that's the
+
+ align:start position:0%
+because what he said was that that's the
+ 
+
+ align:start position:0%
+because what he said was that that's the
+solution to your problem
+
+ align:start position:0%
+solution to your problem
+ 
+
+ align:start position:0%
+solution to your problem
+freud went one other step
+
+ align:start position:0%
+freud went one other step
+ 
+
+ align:start position:0%
+freud went one other step
+this is very significant and see if you
+
+ align:start position:0%
+this is very significant and see if you
+ 
+
+ align:start position:0%
+this is very significant and see if you
+can find it in any of these stories
+
+ align:start position:0%
+can find it in any of these stories
+ 
+
+ align:start position:0%
+can find it in any of these stories
+freud said that
+
+ align:start position:0%
+freud said that
+ 
+
+ align:start position:0%
+freud said that
+if you are an amateur fooling around
+
+ align:start position:0%
+if you are an amateur fooling around
+ 
+
+ align:start position:0%
+if you are an amateur fooling around
+with the unconscious
+
+ align:start position:0%
+with the unconscious
+ 
+
+ align:start position:0%
+with the unconscious
+you're unconscious or anybody else's
+
+ align:start position:0%
+you're unconscious or anybody else's
+ 
+
+ align:start position:0%
+you're unconscious or anybody else's
+you may release the demon
+
+ align:start position:0%
+you may release the demon
+ 
+
+ align:start position:0%
+you may release the demon
+but unless you make
+
+ align:start position:0%
+but unless you make
+ 
+
+ align:start position:0%
+but unless you make
+the demon morally acceptable to your
+
+ align:start position:0%
+the demon morally acceptable to your
+ 
+
+ align:start position:0%
+the demon morally acceptable to your
+conscious mind
+
+ align:start position:0%
+conscious mind
+ 
+
+ align:start position:0%
+conscious mind
+the demon will get up there and run you
+
+ align:start position:0%
+the demon will get up there and run you
+ 
+
+ align:start position:0%
+the demon will get up there and run you
+to the insane side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and freud talked about that in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+competition
+
+ align:start position:0%
+competition
+ 
+
+ align:start position:0%
+competition
+the boys have with the father
+
+ align:start position:0%
+the boys have with the father
+ 
+
+ align:start position:0%
+the boys have with the father
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+wanting to kill the father and take the
+
+ align:start position:0%
+wanting to kill the father and take the
+ 
+
+ align:start position:0%
+wanting to kill the father and take the
+father's place with the mother
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+mary shelley made a big deal out of it
+
+ align:start position:0%
+mary shelley made a big deal out of it
+ 
+
+ align:start position:0%
+mary shelley made a big deal out of it
+with frankenstein
+
+ align:start position:0%
+with frankenstein
+ 
+
+ align:start position:0%
+with frankenstein
+because what did frankenstein want to do
+
+ align:start position:0%
+because what did frankenstein want to do
+ 
+
+ align:start position:0%
+because what did frankenstein want to do
+to kill his maker
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know down his wire down in the brain
+
+ align:start position:0%
+you know down his wire down in the brain
+ 
+
+ align:start position:0%
+you know down his wire down in the brain
+freud said if that's the truth
+
+ align:start position:0%
+freud said if that's the truth
+ 
+
+ align:start position:0%
+freud said if that's the truth
+then that's a hard thing to justify
+
+ align:start position:0%
+then that's a hard thing to justify
+ 
+
+ align:start position:0%
+then that's a hard thing to justify
+morally
+
+ align:start position:0%
+morally
+ 
+
+ align:start position:0%
+morally
+so it's best left down there unless you
+
+ align:start position:0%
+so it's best left down there unless you
+ 
+
+ align:start position:0%
+so it's best left down there unless you
+can find a way to bring it up moral
+
+ align:start position:0%
+can find a way to bring it up moral
+ 
+
+ align:start position:0%
+can find a way to bring it up moral
+so mythology is supposed to do all that
+
+ align:start position:0%
+so mythology is supposed to do all that
+ 
+
+ align:start position:0%
+so mythology is supposed to do all that
+now let's talk about how
+
+ align:start position:0%
+now let's talk about how
+ 
+
+ align:start position:0%
+now let's talk about how
+this thing fits into this class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you want to solve an ethical problem
+
+ align:start position:0%
+if you want to solve an ethical problem
+ 
+
+ align:start position:0%
+if you want to solve an ethical problem
+and you want to solve it by using
+
+ align:start position:0%
+and you want to solve it by using
+ 
+
+ align:start position:0%
+and you want to solve it by using
+the method of virtues
+
+ align:start position:0%
+the method of virtues
+ 
+
+ align:start position:0%
+the method of virtues
+but you don't want to deal you don't
+
+ align:start position:0%
+but you don't want to deal you don't
+ 
+
+ align:start position:0%
+but you don't want to deal you don't
+want the virtue the list of virtues that
+
+ align:start position:0%
+want the virtue the list of virtues that
+ 
+
+ align:start position:0%
+want the virtue the list of virtues that
+plague or any of those people have
+
+ align:start position:0%
+plague or any of those people have
+ 
+
+ align:start position:0%
+plague or any of those people have
+but you want to find a character like i
+
+ align:start position:0%
+but you want to find a character like i
+ 
+
+ align:start position:0%
+but you want to find a character like i
+did
+
+ align:start position:0%
+did
+ 
+
+ align:start position:0%
+did
+with my first day on an engineering job
+
+ align:start position:0%
+with my first day on an engineering job
+ 
+
+ align:start position:0%
+with my first day on an engineering job
+put that character in your place work
+
+ align:start position:0%
+put that character in your place work
+ 
+
+ align:start position:0%
+put that character in your place work
+the character through it and then
+
+ align:start position:0%
+the character through it and then
+ 
+
+ align:start position:0%
+the character through it and then
+imitate to some extent that character
+
+ align:start position:0%
+imitate to some extent that character
+ 
+
+ align:start position:0%
+imitate to some extent that character
+the question is what character to choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not simply a matter of choosing a
+
+ align:start position:0%
+it's not simply a matter of choosing a
+ 
+
+ align:start position:0%
+it's not simply a matter of choosing a
+good person
+
+ align:start position:0%
+good person
+ 
+
+ align:start position:0%
+good person
+because in the end what you want
+
+ align:start position:0%
+because in the end what you want
+ 
+
+ align:start position:0%
+because in the end what you want
+is to still have your job
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+you might not you have to be prepared to
+
+ align:start position:0%
+you might not you have to be prepared to
+ 
+
+ align:start position:0%
+you might not you have to be prepared to
+lose it
+
+ align:start position:0%
+lose it
+ 
+
+ align:start position:0%
+lose it
+but what you want in the end
+
+ align:start position:0%
+but what you want in the end
+ 
+
+ align:start position:0%
+but what you want in the end
+is to have somebody on your side
+
+ align:start position:0%
+is to have somebody on your side
+ 
+
+ align:start position:0%
+is to have somebody on your side
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now what what the at the idea of the
+
+ align:start position:0%
+now what what the at the idea of the
+ 
+
+ align:start position:0%
+now what what the at the idea of the
+mythic story is that the mythic story
+
+ align:start position:0%
+mythic story is that the mythic story
+ 
+
+ align:start position:0%
+mythic story is that the mythic story
+provides a hero
+
+ align:start position:0%
+provides a hero
+ 
+
+ align:start position:0%
+provides a hero
+that is uh not only a hero to you but as
+
+ align:start position:0%
+that is uh not only a hero to you but as
+ 
+
+ align:start position:0%
+that is uh not only a hero to you but as
+a hero of people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and why is that because of the long
+
+ align:start position:0%
+and why is that because of the long
+ 
+
+ align:start position:0%
+and why is that because of the long
+story i just gave it it it
+
+ align:start position:0%
+story i just gave it it it
+ 
+
+ align:start position:0%
+story i just gave it it it
+it it's another thing that sort of wired
+
+ align:start position:0%
+it it's another thing that sort of wired
+ 
+
+ align:start position:0%
+it it's another thing that sort of wired
+into the brain that after a while
+
+ align:start position:0%
+into the brain that after a while
+ 
+
+ align:start position:0%
+into the brain that after a while
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+people began to see from these stories
+
+ align:start position:0%
+people began to see from these stories
+ 
+
+ align:start position:0%
+people began to see from these stories
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh you know there's there's something of
+
+ align:start position:0%
+uh you know there's there's something of
+ 
+
+ align:start position:0%
+uh you know there's there's something of
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+in these heroes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why is that all right
+
+ align:start position:0%
+why is that all right
+ 
+
+ align:start position:0%
+why is that all right
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right this is where gestalt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's take the neck or cube again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your brain actually sees is a
+
+ align:start position:0%
+your brain actually sees is a
+ 
+
+ align:start position:0%
+your brain actually sees is a
+three-dimensional figure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's up there's
+
+ align:start position:0%
+what's up there's
+ 
+
+ align:start position:0%
+what's up there's
+12 lines on a flat
+
+ align:start position:0%
+12 lines on a flat
+ 
+
+ align:start position:0%
+12 lines on a flat
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+when you're sitting around with your
+
+ align:start position:0%
+when you're sitting around with your
+ 
+
+ align:start position:0%
+when you're sitting around with your
+family
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh is the one person that gets up to
+
+ align:start position:0%
+uh is the one person that gets up to
+ 
+
+ align:start position:0%
+uh is the one person that gets up to
+sort of like
+
+ align:start position:0%
+sort of like
+ 
+
+ align:start position:0%
+sort of like
+represents
+
+ align:start position:0%
+represents
+ 
+
+ align:start position:0%
+represents
+you know your family you know
+
+ align:start position:0%
+you know your family you know
+ 
+
+ align:start position:0%
+you know your family you know
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+is there such a thing as an mit person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you go to the airport
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and say well there are 400 students out
+
+ align:start position:0%
+and say well there are 400 students out
+ 
+
+ align:start position:0%
+and say well there are 400 students out
+here but
+
+ align:start position:0%
+here but
+ 
+
+ align:start position:0%
+here but
+that one is probably for them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doesn't matter if you're right or wrong
+
+ align:start position:0%
+doesn't matter if you're right or wrong
+ 
+
+ align:start position:0%
+doesn't matter if you're right or wrong
+the point is you got a picture in your
+
+ align:start position:0%
+the point is you got a picture in your
+ 
+
+ align:start position:0%
+the point is you got a picture in your
+mind
+
+ align:start position:0%
+mind
+ 
+
+ align:start position:0%
+mind
+did i ever tell you a story about the
+
+ align:start position:0%
+did i ever tell you a story about the
+ 
+
+ align:start position:0%
+did i ever tell you a story about the
+old uh about the old blues that yale
+
+ align:start position:0%
+old uh about the old blues that yale
+ 
+
+ align:start position:0%
+old uh about the old blues that yale
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+i was chair of faculty senate we were we
+
+ align:start position:0%
+i was chair of faculty senate we were we
+ 
+
+ align:start position:0%
+i was chair of faculty senate we were we
+had just gotten the constitution
+
+ align:start position:0%
+had just gotten the constitution
+ 
+
+ align:start position:0%
+had just gotten the constitution
+approved where we could get faculty
+
+ align:start position:0%
+approved where we could get faculty
+ 
+
+ align:start position:0%
+approved where we could get faculty
+members on the board of trustees the
+
+ align:start position:0%
+members on the board of trustees the
+ 
+
+ align:start position:0%
+members on the board of trustees the
+question was what kind of faculty member
+
+ align:start position:0%
+question was what kind of faculty member
+ 
+
+ align:start position:0%
+question was what kind of faculty member
+we want
+
+ align:start position:0%
+we want
+ 
+
+ align:start position:0%
+we want
+you get somebody that's quote unquote
+
+ align:start position:0%
+you get somebody that's quote unquote
+ 
+
+ align:start position:0%
+you get somebody that's quote unquote
+too scholarly the trust the board won't
+
+ align:start position:0%
+too scholarly the trust the board won't
+ 
+
+ align:start position:0%
+too scholarly the trust the board won't
+understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you get somebody who's too
+
+ align:start position:0%
+uh you get somebody who's too
+ 
+
+ align:start position:0%
+uh you get somebody who's too
+business-like and he won't reflect the
+
+ align:start position:0%
+business-like and he won't reflect the
+ 
+
+ align:start position:0%
+business-like and he won't reflect the
+rest or she won't reflect the rest of
+
+ align:start position:0%
+rest or she won't reflect the rest of
+ 
+
+ align:start position:0%
+rest or she won't reflect the rest of
+so what do you do how do you deal with
+
+ align:start position:0%
+so what do you do how do you deal with
+ 
+
+ align:start position:0%
+so what do you do how do you deal with
+that problem there was one faculty
+
+ align:start position:0%
+that problem there was one faculty
+ 
+
+ align:start position:0%
+that problem there was one faculty
+member there who
+
+ align:start position:0%
+member there who
+ 
+
+ align:start position:0%
+member there who
+got his law degree from jail and he said
+
+ align:start position:0%
+got his law degree from jail and he said
+ 
+
+ align:start position:0%
+got his law degree from jail and he said
+well look why don't you call up to the
+
+ align:start position:0%
+well look why don't you call up to the
+ 
+
+ align:start position:0%
+well look why don't you call up to the
+call up to the president's office and uh
+
+ align:start position:0%
+call up to the president's office and uh
+ 
+
+ align:start position:0%
+call up to the president's office and uh
+ask for the person who staffs the uh
+
+ align:start position:0%
+ask for the person who staffs the uh
+ 
+
+ align:start position:0%
+ask for the person who staffs the uh
+trustee
+
+ align:start position:0%
+trustee
+ 
+
+ align:start position:0%
+trustee
+and when you get the person on the phone
+
+ align:start position:0%
+and when you get the person on the phone
+ 
+
+ align:start position:0%
+and when you get the person on the phone
+asking what an old blue is i said what's
+
+ align:start position:0%
+asking what an old blue is i said what's
+ 
+
+ align:start position:0%
+asking what an old blue is i said what's
+an it's a drastic person okay so i call
+
+ align:start position:0%
+an it's a drastic person okay so i call
+ 
+
+ align:start position:0%
+an it's a drastic person okay so i call
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+they gave me the staff person for the
+
+ align:start position:0%
+they gave me the staff person for the
+ 
+
+ align:start position:0%
+they gave me the staff person for the
+board and i said what's an old blue
+
+ align:start position:0%
+board and i said what's an old blue
+ 
+
+ align:start position:0%
+board and i said what's an old blue
+and she said an old blue is a member of
+
+ align:start position:0%
+and she said an old blue is a member of
+ 
+
+ align:start position:0%
+and she said an old blue is a member of
+the faculty who looks like yale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i understood that i mean it was abstract
+
+ align:start position:0%
+i understood that i mean it was abstract
+ 
+
+ align:start position:0%
+i understood that i mean it was abstract
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+uh and we concluded in the end they said
+
+ align:start position:0%
+uh and we concluded in the end they said
+ 
+
+ align:start position:0%
+uh and we concluded in the end they said
+they come into board meetings the board
+
+ align:start position:0%
+they come into board meetings the board
+ 
+
+ align:start position:0%
+they come into board meetings the board
+meet the board
+
+ align:start position:0%
+meet the board
+ 
+
+ align:start position:0%
+meet the board
+by some yale tradition
+
+ align:start position:0%
+by some yale tradition
+ 
+
+ align:start position:0%
+by some yale tradition
+is able to pick out who the old blues
+
+ align:start position:0%
+is able to pick out who the old blues
+ 
+
+ align:start position:0%
+is able to pick out who the old blues
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+and the board brings them into the board
+
+ align:start position:0%
+and the board brings them into the board
+ 
+
+ align:start position:0%
+and the board brings them into the board
+meeting
+
+ align:start position:0%
+meeting
+ 
+
+ align:start position:0%
+meeting
+and here's what really happens according
+
+ align:start position:0%
+and here's what really happens according
+ 
+
+ align:start position:0%
+and here's what really happens according
+to that conversation
+
+ align:start position:0%
+to that conversation
+ 
+
+ align:start position:0%
+to that conversation
+that 95 of the time the board is talking
+
+ align:start position:0%
+that 95 of the time the board is talking
+ 
+
+ align:start position:0%
+that 95 of the time the board is talking
+about what yale lives for
+
+ align:start position:0%
+about what yale lives for
+ 
+
+ align:start position:0%
+about what yale lives for
+but when they want to make a decision
+
+ align:start position:0%
+but when they want to make a decision
+ 
+
+ align:start position:0%
+but when they want to make a decision
+where they can gain a lot
+
+ align:start position:0%
+where they can gain a lot
+ 
+
+ align:start position:0%
+where they can gain a lot
+maybe they want to know what yale is
+
+ align:start position:0%
+maybe they want to know what yale is
+ 
+
+ align:start position:0%
+maybe they want to know what yale is
+willing to die for
+
+ align:start position:0%
+willing to die for
+ 
+
+ align:start position:0%
+willing to die for
+then they turn to the old blue should we
+
+ align:start position:0%
+then they turn to the old blue should we
+ 
+
+ align:start position:0%
+then they turn to the old blue should we
+take this take on this project
+
+ align:start position:0%
+take this take on this project
+ 
+
+ align:start position:0%
+take this take on this project
+should we have a course in here on islam
+
+ align:start position:0%
+should we have a course in here on islam
+ 
+
+ align:start position:0%
+should we have a course in here on islam
+uh should we have um
+
+ align:start position:0%
+uh should we have um
+ 
+
+ align:start position:0%
+uh should we have um
+uh jerry falwell on the faculty
+
+ align:start position:0%
+uh jerry falwell on the faculty
+ 
+
+ align:start position:0%
+uh jerry falwell on the faculty
+they look to the old blues and the
+
+ align:start position:0%
+they look to the old blues and the
+ 
+
+ align:start position:0%
+they look to the old blues and the
+answer is not right or wrong answers is
+
+ align:start position:0%
+answer is not right or wrong answers is
+ 
+
+ align:start position:0%
+answer is not right or wrong answers is
+this yeah
+
+ align:start position:0%
+this yeah
+ 
+
+ align:start position:0%
+this yeah
+if we do this will we have yale at the
+
+ align:start position:0%
+if we do this will we have yale at the
+ 
+
+ align:start position:0%
+if we do this will we have yale at the
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well that's a good start of yale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this tradition i'm talking about is
+
+ align:start position:0%
+this tradition i'm talking about is
+ 
+
+ align:start position:0%
+this tradition i'm talking about is
+yale's mythology
+
+ align:start position:0%
+yale's mythology
+ 
+
+ align:start position:0%
+yale's mythology
+mythology will give you these old blues
+
+ align:start position:0%
+mythology will give you these old blues
+ 
+
+ align:start position:0%
+mythology will give you these old blues
+for a culture
+
+ align:start position:0%
+for a culture
+ 
+
+ align:start position:0%
+for a culture
+and if an old blue is representative of
+
+ align:start position:0%
+and if an old blue is representative of
+ 
+
+ align:start position:0%
+and if an old blue is representative of
+the whole
+
+ align:start position:0%
+the whole
+ 
+
+ align:start position:0%
+the whole
+then the old the old blue is
+
+ align:start position:0%
+then the old the old blue is
+ 
+
+ align:start position:0%
+then the old the old blue is
+has a part of each of us in
+
+ align:start position:0%
+has a part of each of us in
+ 
+
+ align:start position:0%
+has a part of each of us in
+him or her
+
+ align:start position:0%
+him or her
+ 
+
+ align:start position:0%
+him or her
+and once she has done whatever she has
+
+ align:start position:0%
+and once she has done whatever she has
+ 
+
+ align:start position:0%
+and once she has done whatever she has
+done no matter how bad it is
+
+ align:start position:0%
+done no matter how bad it is
+ 
+
+ align:start position:0%
+done no matter how bad it is
+we all have a tendency to say well
+
+ align:start position:0%
+we all have a tendency to say well
+ 
+
+ align:start position:0%
+we all have a tendency to say well
+maybe she needs to be punished but let's
+
+ align:start position:0%
+maybe she needs to be punished but let's
+ 
+
+ align:start position:0%
+maybe she needs to be punished but let's
+not be too harsh
+
+ align:start position:0%
+not be too harsh
+ 
+
+ align:start position:0%
+not be too harsh
+you know i mean i might have done that
+
+ align:start position:0%
+you know i mean i might have done that
+ 
+
+ align:start position:0%
+you know i mean i might have done that
+or you know
+
+ align:start position:0%
+or you know
+ 
+
+ align:start position:0%
+or you know
+we are decent people here but this is
+
+ align:start position:0%
+we are decent people here but this is
+ 
+
+ align:start position:0%
+we are decent people here but this is
+the best it gets with our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+family so if you pull out a cultural
+
+ align:start position:0%
+family so if you pull out a cultural
+ 
+
+ align:start position:0%
+family so if you pull out a cultural
+hero and imitate a cultural hero
+
+ align:start position:0%
+hero and imitate a cultural hero
+ 
+
+ align:start position:0%
+hero and imitate a cultural hero
+uh my argument has been and i'm not
+
+ align:start position:0%
+uh my argument has been and i'm not
+ 
+
+ align:start position:0%
+uh my argument has been and i'm not
+alone in this
+
+ align:start position:0%
+alone in this
+ 
+
+ align:start position:0%
+alone in this
+that whatever you do in the end
+
+ align:start position:0%
+that whatever you do in the end
+ 
+
+ align:start position:0%
+that whatever you do in the end
+uh and no matter what where
+
+ align:start position:0%
+uh and no matter what where
+ 
+
+ align:start position:0%
+uh and no matter what where
+whether the whether
+
+ align:start position:0%
+whether the whether
+ 
+
+ align:start position:0%
+whether the whether
+they want to punish you for it
+
+ align:start position:0%
+they want to punish you for it
+ 
+
+ align:start position:0%
+they want to punish you for it
+it will be a tendency
+
+ align:start position:0%
+it will be a tendency
+ 
+
+ align:start position:0%
+it will be a tendency
+for them to
+
+ align:start position:0%
+for them to
+ 
+
+ align:start position:0%
+for them to
+to side with you or to forgive you or to
+
+ align:start position:0%
+to side with you or to forgive you or to
+ 
+
+ align:start position:0%
+to side with you or to forgive you or to
+see the point of what you did or
+
+ align:start position:0%
+see the point of what you did or
+ 
+
+ align:start position:0%
+see the point of what you did or
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's really tough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i wonder if that's different like a
+
+ align:start position:0%
+and i wonder if that's different like a
+ 
+
+ align:start position:0%
+and i wonder if that's different like a
+cultural bureau to me would be someone
+
+ align:start position:0%
+cultural bureau to me would be someone
+ 
+
+ align:start position:0%
+cultural bureau to me would be someone
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+has faced decisions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh first of all uh you hit a very very a
+
+ align:start position:0%
+uh first of all uh you hit a very very a
+ 
+
+ align:start position:0%
+uh first of all uh you hit a very very a
+very um important nerve and that is that
+
+ align:start position:0%
+very um important nerve and that is that
+ 
+
+ align:start position:0%
+very um important nerve and that is that
+uh there's generational differences
+
+ align:start position:0%
+uh there's generational differences
+ 
+
+ align:start position:0%
+uh there's generational differences
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so the question is why is it
+
+ align:start position:0%
+so the question is why is it
+ 
+
+ align:start position:0%
+so the question is why is it
+that possible meant so much to me
+
+ align:start position:0%
+that possible meant so much to me
+ 
+
+ align:start position:0%
+that possible meant so much to me
+he was i was not in his generation
+
+ align:start position:0%
+he was i was not in his generation
+ 
+
+ align:start position:0%
+he was i was not in his generation
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and the key word
+
+ align:start position:0%
+and the key word
+ 
+
+ align:start position:0%
+and the key word
+in the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is metaphor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because i did now now listen to me
+
+ align:start position:0%
+because i did now now listen to me
+ 
+
+ align:start position:0%
+because i did now now listen to me
+carefully because i want to choose my
+
+ align:start position:0%
+carefully because i want to choose my
+ 
+
+ align:start position:0%
+carefully because i want to choose my
+words properly here because if i mess up
+
+ align:start position:0%
+words properly here because if i mess up
+ 
+
+ align:start position:0%
+words properly here because if i mess up
+i could really throw everybody off
+
+ align:start position:0%
+i could really throw everybody off
+ 
+
+ align:start position:0%
+i could really throw everybody off
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when i had to make that decision on my
+
+ align:start position:0%
+when i had to make that decision on my
+ 
+
+ align:start position:0%
+when i had to make that decision on my
+first day
+
+ align:start position:0%
+first day
+ 
+
+ align:start position:0%
+first day
+as an engineer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i didn't see any difference between
+
+ align:start position:0%
+i didn't see any difference between
+ 
+
+ align:start position:0%
+i didn't see any difference between
+parcel and my uncle rook
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+campbell says that the
+
+ align:start position:0%
+campbell says that the
+ 
+
+ align:start position:0%
+campbell says that the
+hero's journey
+
+ align:start position:0%
+hero's journey
+ 
+
+ align:start position:0%
+hero's journey
+has this path we just went through it
+
+ align:start position:0%
+has this path we just went through it
+ 
+
+ align:start position:0%
+has this path we just went through it
+first of all you hear a call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's really your unconscious trying to
+
+ align:start position:0%
+that's really your unconscious trying to
+ 
+
+ align:start position:0%
+that's really your unconscious trying to
+say look you better get down here
+
+ align:start position:0%
+say look you better get down here
+ 
+
+ align:start position:0%
+say look you better get down here
+uh you hear a call you don't really want
+
+ align:start position:0%
+uh you hear a call you don't really want
+ 
+
+ align:start position:0%
+uh you hear a call you don't really want
+to do it because somehow you know that
+
+ align:start position:0%
+to do it because somehow you know that
+ 
+
+ align:start position:0%
+to do it because somehow you know that
+this thing can be lethal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but some
+
+ align:start position:0%
+but some
+ 
+
+ align:start position:0%
+but some
+somebody else makes the case that if you
+
+ align:start position:0%
+somebody else makes the case that if you
+ 
+
+ align:start position:0%
+somebody else makes the case that if you
+don't go somebody else is going to
+
+ align:start position:0%
+don't go somebody else is going to
+ 
+
+ align:start position:0%
+don't go somebody else is going to
+suffer so you got to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first thing is to hear the call
+
+ align:start position:0%
+so the first thing is to hear the call
+ 
+
+ align:start position:0%
+so the first thing is to hear the call
+the second thing is the separation you
+
+ align:start position:0%
+the second thing is the separation you
+ 
+
+ align:start position:0%
+the second thing is the separation you
+have got to go away from the comfort
+
+ align:start position:0%
+have got to go away from the comfort
+ 
+
+ align:start position:0%
+have got to go away from the comfort
+zone
+
+ align:start position:0%
+zone
+ 
+
+ align:start position:0%
+zone
+and into the unknown
+
+ align:start position:0%
+and into the unknown
+ 
+
+ align:start position:0%
+and into the unknown
+and the fabulous that's very important
+
+ align:start position:0%
+and the fabulous that's very important
+ 
+
+ align:start position:0%
+and the fabulous that's very important
+fabulous fabulous not fabulous in terms
+
+ align:start position:0%
+fabulous fabulous not fabulous in terms
+ 
+
+ align:start position:0%
+fabulous fabulous not fabulous in terms
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+peacock feathers fabulous in terms of
+
+ align:start position:0%
+peacock feathers fabulous in terms of
+ 
+
+ align:start position:0%
+peacock feathers fabulous in terms of
+fable
+
+ align:start position:0%
+fable
+ 
+
+ align:start position:0%
+fable
+that there are things that you're going
+
+ align:start position:0%
+that there are things that you're going
+ 
+
+ align:start position:0%
+that there are things that you're going
+to encounter that are not of this
+
+ align:start position:0%
+to encounter that are not of this
+ 
+
+ align:start position:0%
+to encounter that are not of this
+conscious earth they're the demons in
+
+ align:start position:0%
+conscious earth they're the demons in
+ 
+
+ align:start position:0%
+conscious earth they're the demons in
+your country
+
+ align:start position:0%
+your country
+ 
+
+ align:start position:0%
+your country
+you got to slay a dragon because that's
+
+ align:start position:0%
+you got to slay a dragon because that's
+ 
+
+ align:start position:0%
+you got to slay a dragon because that's
+a that's a real thing in your
+
+ align:start position:0%
+a that's a real thing in your
+ 
+
+ align:start position:0%
+a that's a real thing in your
+unconscious
+
+ align:start position:0%
+unconscious
+ 
+
+ align:start position:0%
+unconscious
+and then when you slay the dragon you
+
+ align:start position:0%
+and then when you slay the dragon you
+ 
+
+ align:start position:0%
+and then when you slay the dragon you
+have to bring back something like the
+
+ align:start position:0%
+have to bring back something like the
+ 
+
+ align:start position:0%
+have to bring back something like the
+truth
+
+ align:start position:0%
+truth
+ 
+
+ align:start position:0%
+truth
+that's the holy grail
+
+ align:start position:0%
+that's the holy grail
+ 
+
+ align:start position:0%
+that's the holy grail
+you've got to bring the grail back and
+
+ align:start position:0%
+you've got to bring the grail back and
+ 
+
+ align:start position:0%
+you've got to bring the grail back and
+what do you do with the grail when you
+
+ align:start position:0%
+what do you do with the grail when you
+ 
+
+ align:start position:0%
+what do you do with the grail when you
+get back you share it with everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so those that's the pattern of the
+
+ align:start position:0%
+okay so those that's the pattern of the
+ 
+
+ align:start position:0%
+okay so those that's the pattern of the
+hero's journey
+
+ align:start position:0%
+hero's journey
+ 
+
+ align:start position:0%
+hero's journey
+look at roy why was roy a
+
+ align:start position:0%
+look at roy why was roy a
+ 
+
+ align:start position:0%
+look at roy why was roy a
+hero well
+
+ align:start position:0%
+hero well
+ 
+
+ align:start position:0%
+hero well
+when they got back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+home found out that all their parents
+
+ align:start position:0%
+home found out that all their parents
+ 
+
+ align:start position:0%
+home found out that all their parents
+were dead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+they heard a call to do something
+
+ align:start position:0%
+they heard a call to do something
+ 
+
+ align:start position:0%
+they heard a call to do something
+for the children
+
+ align:start position:0%
+for the children
+ 
+
+ align:start position:0%
+for the children
+but it wasn't staying there
+
+ align:start position:0%
+but it wasn't staying there
+ 
+
+ align:start position:0%
+but it wasn't staying there
+working so they had to go out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh when they got down to oberlin that
+
+ align:start position:0%
+uh when they got down to oberlin that
+ 
+
+ align:start position:0%
+uh when they got down to oberlin that
+was just like being in a dream world for
+
+ align:start position:0%
+was just like being in a dream world for
+ 
+
+ align:start position:0%
+was just like being in a dream world for
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+i've heard them talk about it
+
+ align:start position:0%
+i've heard them talk about it
+ 
+
+ align:start position:0%
+i've heard them talk about it
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+when they got their degrees what did
+
+ align:start position:0%
+when they got their degrees what did
+ 
+
+ align:start position:0%
+when they got their degrees what did
+they do with the degrees they didn't go
+
+ align:start position:0%
+they do with the degrees they didn't go
+ 
+
+ align:start position:0%
+they do with the degrees they didn't go
+out and get a big job they brought the
+
+ align:start position:0%
+out and get a big job they brought the
+ 
+
+ align:start position:0%
+out and get a big job they brought the
+degree back home
+
+ align:start position:0%
+degree back home
+ 
+
+ align:start position:0%
+degree back home
+to help the others get out
+
+ align:start position:0%
+to help the others get out
+ 
+
+ align:start position:0%
+to help the others get out
+that was their holy grail it's the same
+
+ align:start position:0%
+that was their holy grail it's the same
+ 
+
+ align:start position:0%
+that was their holy grail it's the same
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh what you've got to do
+
+ align:start position:0%
+so uh what you've got to do
+ 
+
+ align:start position:0%
+so uh what you've got to do
+is to look around you and find somebody
+
+ align:start position:0%
+is to look around you and find somebody
+ 
+
+ align:start position:0%
+is to look around you and find somebody
+you know now you don't have to know them
+
+ align:start position:0%
+you know now you don't have to know them
+ 
+
+ align:start position:0%
+you know now you don't have to know them
+personally
+
+ align:start position:0%
+personally
+ 
+
+ align:start position:0%
+personally
+but find somebody you know who has had
+
+ align:start position:0%
+but find somebody you know who has had
+ 
+
+ align:start position:0%
+but find somebody you know who has had
+that same experience
+
+ align:start position:0%
+that same experience
+ 
+
+ align:start position:0%
+that same experience
+they don't have to be perfect people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right but if they have had that
+
+ align:start position:0%
+right but if they have had that
+ 
+
+ align:start position:0%
+right but if they have had that
+experience
+
+ align:start position:0%
+experience
+ 
+
+ align:start position:0%
+experience
+and they are heroes in the sense that
+
+ align:start position:0%
+and they are heroes in the sense that
+ 
+
+ align:start position:0%
+and they are heroes in the sense that
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+beautiful thing about these things is
+
+ align:start position:0%
+beautiful thing about these things is
+ 
+
+ align:start position:0%
+beautiful thing about these things is
+they don't hide as we just discussed
+
+ align:start position:0%
+they don't hide as we just discussed
+ 
+
+ align:start position:0%
+they don't hide as we just discussed
+the the negative sides of these people's
+
+ align:start position:0%
+the the negative sides of these people's
+ 
+
+ align:start position:0%
+the the negative sides of these people's
+characters i mean when you find out what
+
+ align:start position:0%
+characters i mean when you find out what
+ 
+
+ align:start position:0%
+characters i mean when you find out what
+is relevant in them that's heroic
+
+ align:start position:0%
+is relevant in them that's heroic
+ 
+
+ align:start position:0%
+is relevant in them that's heroic
+put them in one of your situations
+
+ align:start position:0%
+put them in one of your situations
+ 
+
+ align:start position:0%
+put them in one of your situations
+do your best or do what you think is
+
+ align:start position:0%
+do your best or do what you think is
+ 
+
+ align:start position:0%
+do your best or do what you think is
+right in terms of how you unless you can
+
+ align:start position:0%
+right in terms of how you unless you can
+ 
+
+ align:start position:0%
+right in terms of how you unless you can
+follow them
+
+ align:start position:0%
+follow them
+ 
+
+ align:start position:0%
+follow them
+then once you have done it everybody
+
+ align:start position:0%
+then once you have done it everybody
+ 
+
+ align:start position:0%
+then once you have done it everybody
+else even if it's only on an unconscious
+
+ align:start position:0%
+else even if it's only on an unconscious
+ 
+
+ align:start position:0%
+else even if it's only on an unconscious
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+will see some sense in it and have some
+
+ align:start position:0%
+will see some sense in it and have some
+ 
+
+ align:start position:0%
+will see some sense in it and have some
+compassion for you why you did it
+
+ align:start position:0%
+compassion for you why you did it
+ 
+
+ align:start position:0%
+compassion for you why you did it
+and we'll be inclined to say well you
+
+ align:start position:0%
+and we'll be inclined to say well you
+ 
+
+ align:start position:0%
+and we'll be inclined to say well you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+that's as good as get better as it gets
+
+ align:start position:0%
+that's as good as get better as it gets
+ 
+
+ align:start position:0%
+that's as good as get better as it gets
+with us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh you'll be the kind that if they
+
+ align:start position:0%
+and uh you'll be the kind that if they
+ 
+
+ align:start position:0%
+and uh you'll be the kind that if they
+sent the prison you get your own job
+
+ align:start position:0%
+sent the prison you get your own job
+ 
+
+ align:start position:0%
+sent the prison you get your own job
+back when you get out
+
+ align:start position:0%
+back when you get out
+ 
+
+ align:start position:0%
+back when you get out
+you see what i'm saying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you'll be
+
+ align:start position:0%
+you'll be
+ 
+
+ align:start position:0%
+you'll be
+uh like john brown at uh
+
+ align:start position:0%
+uh like john brown at uh
+ 
+
+ align:start position:0%
+uh like john brown at uh
+rugby was it rugby john john brown
+
+ align:start position:0%
+rugby was it rugby john john brown
+ 
+
+ align:start position:0%
+rugby was it rugby john john brown
+school days was at rugby i'm talking
+
+ align:start position:0%
+school days was at rugby i'm talking
+ 
+
+ align:start position:0%
+school days was at rugby i'm talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+this story about this american that goes
+
+ align:start position:0%
+this story about this american that goes
+ 
+
+ align:start position:0%
+this story about this american that goes
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+one of the british schools and he does
+
+ align:start position:0%
+one of the british schools and he does
+ 
+
+ align:start position:0%
+one of the british schools and he does
+something very heroic but he gets
+
+ align:start position:0%
+something very heroic but he gets
+ 
+
+ align:start position:0%
+something very heroic but he gets
+sent down for it gets kicked out of
+
+ align:start position:0%
+sent down for it gets kicked out of
+ 
+
+ align:start position:0%
+sent down for it gets kicked out of
+school for it
+
+ align:start position:0%
+school for it
+ 
+
+ align:start position:0%
+school for it
+coal
+
+ align:start position:0%
+coal
+ 
+
+ align:start position:0%
+coal
+yeah it's uh
+
+ align:start position:0%
+yeah it's uh
+ 
+
+ align:start position:0%
+yeah it's uh
+oxford it's it's uh john brown at oxford
+
+ align:start position:0%
+oxford it's it's uh john brown at oxford
+ 
+
+ align:start position:0%
+oxford it's it's uh john brown at oxford
+i think it's the name of it well anyway
+
+ align:start position:0%
+i think it's the name of it well anyway
+ 
+
+ align:start position:0%
+i think it's the name of it well anyway
+what happens is he gets sent down for it
+
+ align:start position:0%
+what happens is he gets sent down for it
+ 
+
+ align:start position:0%
+what happens is he gets sent down for it
+but when he's in the carriage leaving
+
+ align:start position:0%
+but when he's in the carriage leaving
+ 
+
+ align:start position:0%
+but when he's in the carriage leaving
+oxford on the way to the um
+
+ align:start position:0%
+oxford on the way to the um
+ 
+
+ align:start position:0%
+oxford on the way to the um
+to the uh port where he gets the boat
+
+ align:start position:0%
+to the uh port where he gets the boat
+ 
+
+ align:start position:0%
+to the uh port where he gets the boat
+home
+
+ align:start position:0%
+home
+ 
+
+ align:start position:0%
+home
+all of the oxford students out there
+
+ align:start position:0%
+all of the oxford students out there
+ 
+
+ align:start position:0%
+all of the oxford students out there
+cheering him on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the kind of hero i'm talking
+
+ align:start position:0%
+that's the kind of hero i'm talking
+ 
+
+ align:start position:0%
+that's the kind of hero i'm talking
+about if you gotta go
+
+ align:start position:0%
+about if you gotta go
+ 
+
+ align:start position:0%
+about if you gotta go
+you're still they still will treat you
+
+ align:start position:0%
+you're still they still will treat you
+ 
+
+ align:start position:0%
+you're still they still will treat you
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+you think what you do is
+
+ align:start position:0%
+you think what you do is
+ 
+
+ align:start position:0%
+you think what you do is
+well as good as it gets
+
+ align:start position:0%
+well as good as it gets
+ 
+
+ align:start position:0%
+well as good as it gets
+all right so um my point is that we can
+
+ align:start position:0%
+all right so um my point is that we can
+ 
+
+ align:start position:0%
+all right so um my point is that we can
+bring
+
+ align:start position:0%
+bring
+ 
+
+ align:start position:0%
+bring
+virtue ethics back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+mythology
+
+ align:start position:0%
+mythology
+ 
+
+ align:start position:0%
+mythology
+is the way to go and if you do mythology
+
+ align:start position:0%
+is the way to go and if you do mythology
+ 
+
+ align:start position:0%
+is the way to go and if you do mythology
+right and this is another one of the
+
+ align:start position:0%
+right and this is another one of the
+ 
+
+ align:start position:0%
+right and this is another one of the
+things that joseph campbell takes credit
+
+ align:start position:0%
+things that joseph campbell takes credit
+ 
+
+ align:start position:0%
+things that joseph campbell takes credit
+for that as a matter of fact this is
+
+ align:start position:0%
+for that as a matter of fact this is
+ 
+
+ align:start position:0%
+for that as a matter of fact this is
+really the
+
+ align:start position:0%
+really the
+ 
+
+ align:start position:0%
+really the
+the source of his fame that what he
+
+ align:start position:0%
+the source of his fame that what he
+ 
+
+ align:start position:0%
+the source of his fame that what he
+found out was
+
+ align:start position:0%
+found out was
+ 
+
+ align:start position:0%
+found out was
+that uh if you look at mythologies of
+
+ align:start position:0%
+that uh if you look at mythologies of
+ 
+
+ align:start position:0%
+that uh if you look at mythologies of
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+cultures you'll find a whole lot of
+
+ align:start position:0%
+cultures you'll find a whole lot of
+ 
+
+ align:start position:0%
+cultures you'll find a whole lot of
+things in common
+
+ align:start position:0%
+things in common
+ 
+
+ align:start position:0%
+things in common
+and the hero's journey is one of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there are different kinds of
+
+ align:start position:0%
+and there are different kinds of
+ 
+
+ align:start position:0%
+and there are different kinds of
+heroes journeys and all of that but uh
+
+ align:start position:0%
+heroes journeys and all of that but uh
+ 
+
+ align:start position:0%
+heroes journeys and all of that but uh
+so therefore
+
+ align:start position:0%
+so therefore
+ 
+
+ align:start position:0%
+so therefore
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+your challenge then is to find somebody
+
+ align:start position:0%
+your challenge then is to find somebody
+ 
+
+ align:start position:0%
+your challenge then is to find somebody
+that you like i said that you know
+
+ align:start position:0%
+that you like i said that you know
+ 
+
+ align:start position:0%
+that you like i said that you know
+you don't have to know him personally
+
+ align:start position:0%
+you don't have to know him personally
+ 
+
+ align:start position:0%
+you don't have to know him personally
+they don't even have to be alive you can
+
+ align:start position:0%
+they don't even have to be alive you can
+ 
+
+ align:start position:0%
+they don't even have to be alive you can
+read them out of books i know that
+
+ align:start position:0%
+read them out of books i know that
+ 
+
+ align:start position:0%
+read them out of books i know that
+person
+
+ align:start position:0%
+person
+ 
+
+ align:start position:0%
+person
+but and say that uh-huh that person fits
+
+ align:start position:0%
+but and say that uh-huh that person fits
+ 
+
+ align:start position:0%
+but and say that uh-huh that person fits
+the pattern
+
+ align:start position:0%
+the pattern
+ 
+
+ align:start position:0%
+the pattern
+and if i really get in some trouble and
+
+ align:start position:0%
+and if i really get in some trouble and
+ 
+
+ align:start position:0%
+and if i really get in some trouble and
+do what i think that person will do it
+
+ align:start position:0%
+do what i think that person will do it
+ 
+
+ align:start position:0%
+do what i think that person will do it
+may not be the right thing
+
+ align:start position:0%
+may not be the right thing
+ 
+
+ align:start position:0%
+may not be the right thing
+but somehow or another i will still fit
+
+ align:start position:0%
+but somehow or another i will still fit
+ 
+
+ align:start position:0%
+but somehow or another i will still fit
+in the culture when it's done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it will be probably the best you can do
+
+ align:start position:0%
+it will be probably the best you can do
+ 
+
+ align:start position:0%
+it will be probably the best you can do
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and i was hoping the only reason i
+
+ align:start position:0%
+and and i was hoping the only reason i
+ 
+
+ align:start position:0%
+and and i was hoping the only reason i
+was hoping that this would be a bigger
+
+ align:start position:0%
+was hoping that this would be a bigger
+ 
+
+ align:start position:0%
+was hoping that this would be a bigger
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+the only reason
+
+ align:start position:0%
+the only reason
+ 
+
+ align:start position:0%
+the only reason
+is that i was hoping that we'd have a
+
+ align:start position:0%
+is that i was hoping that we'd have a
+ 
+
+ align:start position:0%
+is that i was hoping that we'd have a
+whole lot of people in here saying well
+
+ align:start position:0%
+whole lot of people in here saying well
+ 
+
+ align:start position:0%
+whole lot of people in here saying well
+you know where i'm from
+
+ align:start position:0%
+you know where i'm from
+ 
+
+ align:start position:0%
+you know where i'm from
+uh we got another story
+
+ align:start position:0%
+uh we got another story
+ 
+
+ align:start position:0%
+uh we got another story
+and the hero didn't go out and
+
+ align:start position:0%
+and the hero didn't go out and
+ 
+
+ align:start position:0%
+and the hero didn't go out and
+uh killed dragon
+
+ align:start position:0%
+uh killed dragon
+ 
+
+ align:start position:0%
+uh killed dragon
+the the hero went out and killed uh
+
+ align:start position:0%
+the the hero went out and killed uh
+ 
+
+ align:start position:0%
+the the hero went out and killed uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+kill something else might be just as bad
+
+ align:start position:0%
+kill something else might be just as bad
+ 
+
+ align:start position:0%
+kill something else might be just as bad
+you know uh i've heard some stories from
+
+ align:start position:0%
+you know uh i've heard some stories from
+ 
+
+ align:start position:0%
+you know uh i've heard some stories from
+south americans where the person goes
+
+ align:start position:0%
+south americans where the person goes
+ 
+
+ align:start position:0%
+south americans where the person goes
+out and kills something in the forest
+
+ align:start position:0%
+out and kills something in the forest
+ 
+
+ align:start position:0%
+out and kills something in the forest
+well even
+
+ align:start position:0%
+well even
+ 
+
+ align:start position:0%
+well even
+even the even the anthropologists who
+
+ align:start position:0%
+even the even the anthropologists who
+ 
+
+ align:start position:0%
+even the even the anthropologists who
+study oedipus saying that
+
+ align:start position:0%
+study oedipus saying that
+ 
+
+ align:start position:0%
+study oedipus saying that
+he did not kill it was a sphinx that he
+
+ align:start position:0%
+he did not kill it was a sphinx that he
+ 
+
+ align:start position:0%
+he did not kill it was a sphinx that he
+killed
+
+ align:start position:0%
+killed
+ 
+
+ align:start position:0%
+killed
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh a line with a person's head that was
+
+ align:start position:0%
+uh a line with a person's head that was
+ 
+
+ align:start position:0%
+uh a line with a person's head that was
+terrorizing the terrorizing the populace
+
+ align:start position:0%
+terrorizing the terrorizing the populace
+ 
+
+ align:start position:0%
+terrorizing the terrorizing the populace
+what they what they did find something
+
+ align:start position:0%
+what they what they did find something
+ 
+
+ align:start position:0%
+what they what they did find something
+and i don't know how they did it but
+
+ align:start position:0%
+and i don't know how they did it but
+ 
+
+ align:start position:0%
+and i don't know how they did it but
+they found something they said around
+
+ align:start position:0%
+they found something they said around
+ 
+
+ align:start position:0%
+they found something they said around
+that place at around that time
+
+ align:start position:0%
+that place at around that time
+ 
+
+ align:start position:0%
+that place at around that time
+there was a there was a pesticide
+
+ align:start position:0%
+there was a there was a pesticide
+ 
+
+ align:start position:0%
+there was a there was a pesticide
+a disease
+
+ align:start position:0%
+a disease
+ 
+
+ align:start position:0%
+a disease
+and somehow another this man came in
+
+ align:start position:0%
+and somehow another this man came in
+ 
+
+ align:start position:0%
+and somehow another this man came in
+from outside and walked among the people
+
+ align:start position:0%
+from outside and walked among the people
+ 
+
+ align:start position:0%
+from outside and walked among the people
+and helped care
+
+ align:start position:0%
+and helped care
+ 
+
+ align:start position:0%
+and helped care
+well how does it work
+
+ align:start position:0%
+well how does it work
+ 
+
+ align:start position:0%
+well how does it work
+12 generations later when it gets down
+
+ align:start position:0%
+12 generations later when it gets down
+ 
+
+ align:start position:0%
+12 generations later when it gets down
+in the unconscious into a story
+
+ align:start position:0%
+in the unconscious into a story
+ 
+
+ align:start position:0%
+in the unconscious into a story
+kill dragon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now what i want you to do um
+
+ align:start position:0%
+so now what i want you to do um
+ 
+
+ align:start position:0%
+so now what i want you to do um
+since y'all got all of this free time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uh to take this last paper that i've
+
+ align:start position:0%
+is uh to take this last paper that i've
+ 
+
+ align:start position:0%
+is uh to take this last paper that i've
+given you
+
+ align:start position:0%
+given you
+ 
+
+ align:start position:0%
+given you
+back and resubmitted but
+
+ align:start position:0%
+back and resubmitted but
+ 
+
+ align:start position:0%
+back and resubmitted but
+you can change it if you want to
+
+ align:start position:0%
+you can change it if you want to
+ 
+
+ align:start position:0%
+you can change it if you want to
+these are good papers but
+
+ align:start position:0%
+these are good papers but
+ 
+
+ align:start position:0%
+these are good papers but
+what i want you to do is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take the character that you analyze
+
+ align:start position:0%
+take the character that you analyze
+ 
+
+ align:start position:0%
+take the character that you analyze
+and substitute possible in there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if that doesn't work then substitute
+
+ align:start position:0%
+and if that doesn't work then substitute
+ 
+
+ align:start position:0%
+and if that doesn't work then substitute
+some kind of hero in there
+
+ align:start position:0%
+some kind of hero in there
+ 
+
+ align:start position:0%
+some kind of hero in there
+and see what that person would have done
+
+ align:start position:0%
+and see what that person would have done
+ 
+
+ align:start position:0%
+and see what that person would have done
+in that situation
+
+ align:start position:0%
+in that situation
+ 
+
+ align:start position:0%
+in that situation
+what would have been the consequences to
+
+ align:start position:0%
+what would have been the consequences to
+ 
+
+ align:start position:0%
+what would have been the consequences to
+that person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what i would like for you to do is to
+
+ align:start position:0%
+what i would like for you to do is to
+ 
+
+ align:start position:0%
+what i would like for you to do is to
+try possible first
+
+ align:start position:0%
+try possible first
+ 
+
+ align:start position:0%
+try possible first
+if it does not work for you then choose
+
+ align:start position:0%
+if it does not work for you then choose
+ 
+
+ align:start position:0%
+if it does not work for you then choose
+another one
+
+ align:start position:0%
+another one
+ 
+
+ align:start position:0%
+another one
+but justify why that person is a mythic
+
+ align:start position:0%
+but justify why that person is a mythic
+ 
+
+ align:start position:0%
+but justify why that person is a mythic
+hero
+
+ align:start position:0%
+hero
+ 
+
+ align:start position:0%
+hero
+a mythic hero of some sort or another
+
+ align:start position:0%
+a mythic hero of some sort or another
+ 
+
+ align:start position:0%
+a mythic hero of some sort or another
+they have to like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like my uncle roy and those they they
+
+ align:start position:0%
+like my uncle roy and those they they
+ 
+
+ align:start position:0%
+like my uncle roy and those they they
+had the they followed the pattern
+
+ align:start position:0%
+had the they followed the pattern
+ 
+
+ align:start position:0%
+had the they followed the pattern
+they heard the call they went out for a
+
+ align:start position:0%
+they heard the call they went out for a
+ 
+
+ align:start position:0%
+they heard the call they went out for a
+higher cause
+
+ align:start position:0%
+higher cause
+ 
+
+ align:start position:0%
+higher cause
+they had this fabulous experience
+
+ align:start position:0%
+they had this fabulous experience
+ 
+
+ align:start position:0%
+they had this fabulous experience
+they killed the dragon they brought the
+
+ align:start position:0%
+they killed the dragon they brought the
+ 
+
+ align:start position:0%
+they killed the dragon they brought the
+grail home and shared it with everybody
+
+ align:start position:0%
+grail home and shared it with everybody
+ 
+
+ align:start position:0%
+grail home and shared it with everybody
+there's the pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so see if the if that if that doesn't
+
+ align:start position:0%
+so see if the if that if that doesn't
+ 
+
+ align:start position:0%
+so see if the if that if that doesn't
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+then pick another another case
+
+ align:start position:0%
+then pick another another case
+ 
+
+ align:start position:0%
+then pick another another case
+the a7d or some other case that you've
+
+ align:start position:0%
+the a7d or some other case that you've
+ 
+
+ align:start position:0%
+the a7d or some other case that you've
+already studied
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now i don't want to as we all know
+
+ align:start position:0%
+okay now i don't want to as we all know
+ 
+
+ align:start position:0%
+okay now i don't want to as we all know
+none of these methods will work
+
+ align:start position:0%
+none of these methods will work
+ 
+
+ align:start position:0%
+none of these methods will work
+every time on every
+
+ align:start position:0%
+every time on every
+ 
+
+ align:start position:0%
+every time on every
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+but uh so but i'd like for you to try
+
+ align:start position:0%
+but uh so but i'd like for you to try
+ 
+
+ align:start position:0%
+but uh so but i'd like for you to try
+possible honest on chernobyl
\ No newline at end of file
diff --git a/4r1xgrWbALg.txt b/4r1xgrWbALg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..41b276b2e1daeb1d06e99f1dd00ad9e3f4b814d2
--- /dev/null
+++ b/4r1xgrWbALg.txt
@@ -0,0 +1,475 @@
+align:start position:0%
+ 
+so I would like to now consider the
+
+ align:start position:0%
+so I would like to now consider the
+ 
+
+ align:start position:0%
+so I would like to now consider the
+wheel that is rolling without slipping
+
+ align:start position:0%
+wheel that is rolling without slipping
+ 
+
+ align:start position:0%
+wheel that is rolling without slipping
+and what I'd like to do is
+
+ align:start position:0%
+and what I'd like to do is
+ 
+
+ align:start position:0%
+and what I'd like to do is
+consider let's draw the wheel rolling
+
+ align:start position:0%
+consider let's draw the wheel rolling
+ 
+
+ align:start position:0%
+consider let's draw the wheel rolling
+without slipping and I'd like to
+
+ align:start position:0%
+without slipping and I'd like to
+ 
+
+ align:start position:0%
+without slipping and I'd like to
+consider the contact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point between the
+
+ align:start position:0%
+point between the
+ 
+
+ align:start position:0%
+point between the
+wheel and the
+
+ align:start position:0%
+wheel and the
+ 
+
+ align:start position:0%
+wheel and the
+ground and I'd like to understand what
+
+ align:start position:0%
+ground and I'd like to understand what
+ 
+
+ align:start position:0%
+ground and I'd like to understand what
+the velocity of that contact point is
+
+ align:start position:0%
+the velocity of that contact point is
+ 
+
+ align:start position:0%
+the velocity of that contact point is
+and the result is surprising now we know
+
+ align:start position:0%
+and the result is surprising now we know
+ 
+
+ align:start position:0%
+and the result is surprising now we know
+by our law of additional velocities
+
+ align:start position:0%
+by our law of additional velocities
+ 
+
+ align:start position:0%
+by our law of additional velocities
+let's call that the point P that the
+
+ align:start position:0%
+let's call that the point P that the
+ 
+
+ align:start position:0%
+let's call that the point P that the
+velocity of p is the velocity of the
+
+ align:start position:0%
+velocity of p is the velocity of the
+ 
+
+ align:start position:0%
+velocity of p is the velocity of the
+center of mass and that pointed this way
+
+ align:start position:0%
+center of mass and that pointed this way
+ 
+
+ align:start position:0%
+center of mass and that pointed this way
+plus the velocity of the point p as seen
+
+ align:start position:0%
+plus the velocity of the point p as seen
+ 
+
+ align:start position:0%
+plus the velocity of the point p as seen
+in the center of Mass frame and in that
+
+ align:start position:0%
+in the center of Mass frame and in that
+ 
+
+ align:start position:0%
+in the center of Mass frame and in that
+frame every single point on the rim was
+
+ align:start position:0%
+frame every single point on the rim was
+ 
+
+ align:start position:0%
+frame every single point on the rim was
+just doing circular motion so that
+
+ align:start position:0%
+just doing circular motion so that
+ 
+
+ align:start position:0%
+just doing circular motion so that
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+is in the opposite direction and the
+
+ align:start position:0%
+is in the opposite direction and the
+ 
+
+ align:start position:0%
+is in the opposite direction and the
+vector sum is the velocity of this point
+
+ align:start position:0%
+vector sum is the velocity of this point
+ 
+
+ align:start position:0%
+vector sum is the velocity of this point
+p as seen in the ground
+
+ align:start position:0%
+p as seen in the ground
+ 
+
+ align:start position:0%
+p as seen in the ground
+frame so we want to consider the
+
+ align:start position:0%
+frame so we want to consider the
+ 
+
+ align:start position:0%
+frame so we want to consider the
+magnitudes of these two terms the
+
+ align:start position:0%
+magnitudes of these two terms the
+ 
+
+ align:start position:0%
+magnitudes of these two terms the
+Velocity in the center of Mass frame of
+
+ align:start position:0%
+Velocity in the center of Mass frame of
+ 
+
+ align:start position:0%
+Velocity in the center of Mass frame of
+a point in the rim has a magnitude equal
+
+ align:start position:0%
+a point in the rim has a magnitude equal
+ 
+
+ align:start position:0%
+a point in the rim has a magnitude equal
+to our
+
+ align:start position:0%
+to our
+ 
+
+ align:start position:0%
+to our
+Omega and we said that the
+
+ align:start position:0%
+Omega and we said that the
+ 
+
+ align:start position:0%
+Omega and we said that the
+velocity of this a center of mass we
+
+ align:start position:0%
+velocity of this a center of mass we
+ 
+
+ align:start position:0%
+velocity of this a center of mass we
+call that V CM now the
+
+ align:start position:0%
+call that V CM now the
+ 
+
+ align:start position:0%
+call that V CM now the
+rolling without spping condition was
+
+ align:start position:0%
+rolling without spping condition was
+ 
+
+ align:start position:0%
+rolling without spping condition was
+that these two magnitudes were equal vcm
+
+ align:start position:0%
+that these two magnitudes were equal vcm
+ 
+
+ align:start position:0%
+that these two magnitudes were equal vcm
+equals R Omega or the velocity of the
+
+ align:start position:0%
+equals R Omega or the velocity of the
+ 
+
+ align:start position:0%
+equals R Omega or the velocity of the
+point on the rim in the center of Mass
+
+ align:start position:0%
+point on the rim in the center of Mass
+ 
+
+ align:start position:0%
+point on the rim in the center of Mass
+frame is equal to the center Mass
+
+ align:start position:0%
+frame is equal to the center Mass
+ 
+
+ align:start position:0%
+frame is equal to the center Mass
+velocity of the wheel and therefore the
+
+ align:start position:0%
+velocity of the wheel and therefore the
+ 
+
+ align:start position:0%
+velocity of the wheel and therefore the
+velocity P which is the sum of these two
+
+ align:start position:0%
+velocity P which is the sum of these two
+ 
+
+ align:start position:0%
+velocity P which is the sum of these two
+vectors for the contact
+
+ align:start position:0%
+vectors for the contact
+ 
+
+ align:start position:0%
+vectors for the contact
+point so that's when p
+
+ align:start position:0%
+point so that's when p
+ 
+
+ align:start position:0%
+point so that's when p
+is in contact with the ground is equal
+
+ align:start position:0%
+is in contact with the ground is equal
+ 
+
+ align:start position:0%
+is in contact with the ground is equal
+to zero so what we say is that the
+
+ align:start position:0%
+to zero so what we say is that the
+ 
+
+ align:start position:0%
+to zero so what we say is that the
+contact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instantaneously at
+
+ align:start position:0%
+instantaneously at
+ 
+
+ align:start position:0%
+instantaneously at
+rest
+
+ align:start position:0%
+rest
+ 
+
+ align:start position:0%
+rest
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+respect to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ground and that's what really is the
+
+ align:start position:0%
+ground and that's what really is the
+ 
+
+ align:start position:0%
+ground and that's what really is the
+mystery of a wheel that's rolling
+
+ align:start position:0%
+mystery of a wheel that's rolling
+ 
+
+ align:start position:0%
+mystery of a wheel that's rolling
+without slipping that this contact point
+
+ align:start position:0%
+without slipping that this contact point
+ 
+
+ align:start position:0%
+without slipping that this contact point
+is the sum of these two vectors and it's
+
+ align:start position:0%
+is the sum of these two vectors and it's
+ 
+
+ align:start position:0%
+is the sum of these two vectors and it's
+instantaneously at rest with the ground
+
+ align:start position:0%
+instantaneously at rest with the ground
+ 
+
+ align:start position:0%
+instantaneously at rest with the ground
+when the Reel is rolling without
+
+ align:start position:0%
+when the Reel is rolling without
+ 
+
+ align:start position:0%
+when the Reel is rolling without
+slipping the other points are certainly
+
+ align:start position:0%
+slipping the other points are certainly
+ 
+
+ align:start position:0%
+slipping the other points are certainly
+not remember up here these two vectors
+
+ align:start position:0%
+not remember up here these two vectors
+ 
+
+ align:start position:0%
+not remember up here these two vectors
+pointed in the same
+
+ align:start position:0%
+pointed in the same
+ 
+
+ align:start position:0%
+pointed in the same
+direction so that that Vector has twice
+
+ align:start position:0%
+direction so that that Vector has twice
+ 
+
+ align:start position:0%
+direction so that that Vector has twice
+the magnitude of either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
\ No newline at end of file
diff --git a/5RqTJWf1l_A.txt b/5RqTJWf1l_A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..85cea9d6ab71ddf48438e37d2fabaf64800f88a2
--- /dev/null
+++ b/5RqTJWf1l_A.txt
@@ -0,0 +1,4491 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right all right so we're
+
+ align:start position:0%
+ocw.mit.edu all right all right so we're
+ 
+
+ align:start position:0%
+ocw.mit.edu all right all right so we're
+going to continue now and kind of get
+
+ align:start position:0%
+going to continue now and kind of get
+ 
+
+ align:start position:0%
+going to continue now and kind of get
+into the examples part of the uh of the
+
+ align:start position:0%
+into the examples part of the uh of the
+ 
+
+ align:start position:0%
+into the examples part of the uh of the
+course and again this is really the part
+
+ align:start position:0%
+course and again this is really the part
+ 
+
+ align:start position:0%
+course and again this is really the part
+that uh people should really I I I
+
+ align:start position:0%
+that uh people should really I I I
+ 
+
+ align:start position:0%
+that uh people should really I I I
+strongly encourage people doing the
+
+ align:start position:0%
+strongly encourage people doing the
+ 
+
+ align:start position:0%
+strongly encourage people doing the
+examples how many people got a chance to
+
+ align:start position:0%
+examples how many people got a chance to
+ 
+
+ align:start position:0%
+examples how many people got a chance to
+try the examples in the very good and we
+
+ align:start position:0%
+try the examples in the very good and we
+ 
+
+ align:start position:0%
+try the examples in the very good and we
+got a couple of questions for people and
+
+ align:start position:0%
+got a couple of questions for people and
+ 
+
+ align:start position:0%
+got a couple of questions for people and
+and most of the time we got another
+
+ align:start position:0%
+and most of the time we got another
+ 
+
+ align:start position:0%
+and most of the time we got another
+email from them right away that said
+
+ align:start position:0%
+email from them right away that said
+ 
+
+ align:start position:0%
+email from them right away that said
+oops no got it to work so we're very
+
+ align:start position:0%
+oops no got it to work so we're very
+ 
+
+ align:start position:0%
+oops no got it to work so we're very
+pleased about that uh very you know the
+
+ align:start position:0%
+pleased about that uh very you know the
+ 
+
+ align:start position:0%
+pleased about that uh very you know the
+great thing about working at Lincoln
+
+ align:start position:0%
+great thing about working at Lincoln
+ 
+
+ align:start position:0%
+great thing about working at Lincoln
+Labs is people are pretty good at figur
+
+ align:start position:0%
+Labs is people are pretty good at figur
+ 
+
+ align:start position:0%
+Labs is people are pretty good at figur
+ing stuff out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we have some experiened this and
+
+ align:start position:0%
+um we have some experiened this and
+ 
+
+ align:start position:0%
+um we have some experiened this and
+before obviously our parallel matlb
+
+ align:start position:0%
+before obviously our parallel matlb
+ 
+
+ align:start position:0%
+before obviously our parallel matlb
+technology we've released that out many
+
+ align:start position:0%
+technology we've released that out many
+ 
+
+ align:start position:0%
+technology we've released that out many
+many people use it and for the most part
+
+ align:start position:0%
+many people use it and for the most part
+ 
+
+ align:start position:0%
+many people use it and for the most part
+we're proud to say that whenever we get
+
+ align:start position:0%
+we're proud to say that whenever we get
+ 
+
+ align:start position:0%
+we're proud to say that whenever we get
+a a question from the outside world and
+
+ align:start position:0%
+a a question from the outside world and
+ 
+
+ align:start position:0%
+a a question from the outside world and
+it's not working it's it's usually the
+
+ align:start position:0%
+it's not working it's it's usually the
+ 
+
+ align:start position:0%
+it's not working it's it's usually the
+person has taken severely active steps
+
+ align:start position:0%
+person has taken severely active steps
+ 
+
+ align:start position:0%
+person has taken severely active steps
+to ignore the
+
+ align:start position:0%
+to ignore the
+ 
+
+ align:start position:0%
+to ignore the
+documentation you know and uh and uh and
+
+ align:start position:0%
+documentation you know and uh and uh and
+ 
+
+ align:start position:0%
+documentation you know and uh and uh and
+but if they they follow it at all
+
+ align:start position:0%
+but if they they follow it at all
+ 
+
+ align:start position:0%
+but if they they follow it at all
+they're generally pretty pretty safe
+
+ align:start position:0%
+they're generally pretty pretty safe
+ 
+
+ align:start position:0%
+they're generally pretty pretty safe
+so I'm going to get into the example
+
+ align:start position:0%
+so I'm going to get into the example
+ 
+
+ align:start position:0%
+so I'm going to get into the example
+code here so the example code this is oh
+
+ align:start position:0%
+code here so the example code this is oh
+ 
+
+ align:start position:0%
+code here so the example code this is oh
+that's not d4m user share that's
+
+ align:start position:0%
+that's not d4m user share that's
+ 
+
+ align:start position:0%
+that's not d4m user share that's
+incorrect it's tools lowercase examples
+
+ align:start position:0%
+incorrect it's tools lowercase examples
+ 
+
+ align:start position:0%
+incorrect it's tools lowercase examples
+I should correct these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh nice there we
+
+ align:start position:0%
+oh nice there we
+ 
+
+ align:start position:0%
+oh nice there we
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+great it is an X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right oh yes thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great all right so this is where the
+
+ align:start position:0%
+great all right so this is where the
+ 
+
+ align:start position:0%
+great all right so this is where the
+example code is uh but we're going to go
+
+ align:start position:0%
+example code is uh but we're going to go
+ 
+
+ align:start position:0%
+example code is uh but we're going to go
+over here um your assignment should you
+
+ align:start position:0%
+over here um your assignment should you
+ 
+
+ align:start position:0%
+over here um your assignment should you
+choose to undertake it um is to
+
+ align:start position:0%
+choose to undertake it um is to
+ 
+
+ align:start position:0%
+choose to undertake it um is to
+um pick a
+
+ align:start position:0%
+um pick a
+ 
+
+ align:start position:0%
+um pick a
+picture hopefully someone that's
+
+ align:start position:0%
+picture hopefully someone that's
+ 
+
+ align:start position:0%
+picture hopefully someone that's
+interesting to you doesn't have to be
+
+ align:start position:0%
+interesting to you doesn't have to be
+ 
+
+ align:start position:0%
+interesting to you doesn't have to be
+straight lines it could be anything
+
+ align:start position:0%
+straight lines it could be anything
+ 
+
+ align:start position:0%
+straight lines it could be anything
+where you could create draw edges or
+
+ align:start position:0%
+where you could create draw edges or
+ 
+
+ align:start position:0%
+where you could create draw edges or
+something you take some photo and put it
+
+ align:start position:0%
+something you take some photo and put it
+ 
+
+ align:start position:0%
+something you take some photo and put it
+through one of those photosho effects
+
+ align:start position:0%
+through one of those photosho effects
+ 
+
+ align:start position:0%
+through one of those photosho effects
+and turn it into a line drawing or
+
+ align:start position:0%
+and turn it into a line drawing or
+ 
+
+ align:start position:0%
+and turn it into a line drawing or
+something and then start labeling
+
+ align:start position:0%
+something and then start labeling
+ 
+
+ align:start position:0%
+something and then start labeling
+vertices
+
+ align:start position:0%
+vertices
+ 
+
+ align:start position:0%
+vertices
+um you do want to limit the number of
+
+ align:start position:0%
+um you do want to limit the number of
+ 
+
+ align:start position:0%
+um you do want to limit the number of
+lines though I would recommend 20 would
+
+ align:start position:0%
+lines though I would recommend 20 would
+ 
+
+ align:start position:0%
+lines though I would recommend 20 would
+be the most number of lines you do
+
+ align:start position:0%
+be the most number of lines you do
+ 
+
+ align:start position:0%
+be the most number of lines you do
+because this can get fairly involved you
+
+ align:start position:0%
+because this can get fairly involved you
+ 
+
+ align:start position:0%
+because this can get fairly involved you
+might start with something fairly small
+
+ align:start position:0%
+might start with something fairly small
+ 
+
+ align:start position:0%
+might start with something fairly small
+so select a picture label the edges and
+
+ align:start position:0%
+so select a picture label the edges and
+ 
+
+ align:start position:0%
+so select a picture label the edges and
+vertices create an incidence
+
+ align:start position:0%
+vertices create an incidence
+ 
+
+ align:start position:0%
+vertices create an incidence
+Matrix okay and then just compute The
+
+ align:start position:0%
+Matrix okay and then just compute The
+ 
+
+ align:start position:0%
+Matrix okay and then just compute The
+adjacency Matrix from the incidence
+
+ align:start position:0%
+adjacency Matrix from the incidence
+ 
+
+ align:start position:0%
+adjacency Matrix from the incidence
+Matrix using this this formula you can
+
+ align:start position:0%
+Matrix using this this formula you can
+ 
+
+ align:start position:0%
+Matrix using this this formula you can
+certainly use d4m if you want to do that
+
+ align:start position:0%
+certainly use d4m if you want to do that
+ 
+
+ align:start position:0%
+certainly use d4m if you want to do that
+but it's fine to do it by hand it's fine
+
+ align:start position:0%
+but it's fine to do it by hand it's fine
+ 
+
+ align:start position:0%
+but it's fine to do it by hand it's fine
+to do it by hand just in which case you
+
+ align:start position:0%
+to do it by hand just in which case you
+ 
+
+ align:start position:0%
+to do it by hand just in which case you
+would want to do a very small one just
+
+ align:start position:0%
+would want to do a very small one just
+ 
+
+ align:start position:0%
+would want to do a very small one just
+you know do doing it once by hand is is
+
+ align:start position:0%
+you know do doing it once by hand is is
+ 
+
+ align:start position:0%
+you know do doing it once by hand is is
+useful you know twice marginally and
+
+ align:start position:0%
+useful you know twice marginally and
+ 
+
+ align:start position:0%
+useful you know twice marginally and
+then the third time not not useful but
+
+ align:start position:0%
+then the third time not not useful but
+ 
+
+ align:start position:0%
+then the third time not not useful but
+just like in high school right they make
+
+ align:start position:0%
+just like in high school right they make
+ 
+
+ align:start position:0%
+just like in high school right they make
+you do Matrix multiply by hand
+
+ align:start position:0%
+you do Matrix multiply by hand
+ 
+
+ align:start position:0%
+you do Matrix multiply by hand
+like actually a lot you know a lot
+
+ align:start position:0%
+like actually a lot you know a lot
+ 
+
+ align:start position:0%
+like actually a lot you know a lot
+so so uh so that's the example and the
+
+ align:start position:0%
+so so uh so that's the example and the
+ 
+
+ align:start position:0%
+so so uh so that's the example and the
+assignment
+
+ align:start position:0%
+assignment
+ 
+
+ align:start position:0%
+assignment
+um if
+
+ align:start position:0%
+um if
+ 
+
+ align:start position:0%
+um if
+you do this on a piece of paper and scan
+
+ align:start position:0%
+you do this on a piece of paper and scan
+ 
+
+ align:start position:0%
+you do this on a piece of paper and scan
+it and email it to me before the next
+
+ align:start position:0%
+it and email it to me before the next
+ 
+
+ align:start position:0%
+it and email it to me before the next
+lecture I will get you give you some
+
+ align:start position:0%
+lecture I will get you give you some
+ 
+
+ align:start position:0%
+lecture I will get you give you some
+feedback on it before the following
+
+ align:start position:0%
+feedback on it before the following
+ 
+
+ align:start position:0%
+feedback on it before the following
+lecture so you know you say to get give
+
+ align:start position:0%
+lecture so you know you say to get give
+ 
+
+ align:start position:0%
+lecture so you know you say to get give
+it to me after
+
+ align:start position:0%
+it to me after
+ 
+
+ align:start position:0%
+it to me after
+that too bad right no I just won't give
+
+ align:start position:0%
+that too bad right no I just won't give
+ 
+
+ align:start position:0%
+that too bad right no I just won't give
+you feedback you know so there's no
+
+ align:start position:0%
+you feedback you know so there's no
+ 
+
+ align:start position:0%
+you feedback you know so there's no
+credit but you know this gives you some
+
+ align:start position:0%
+credit but you know this gives you some
+ 
+
+ align:start position:0%
+credit but you know this gives you some
+incentive to get it done if you want
+
+ align:start position:0%
+incentive to get it done if you want
+ 
+
+ align:start position:0%
+incentive to get it done if you want
+feedback from me about you know what
+
+ align:start position:0%
+feedback from me about you know what
+ 
+
+ align:start position:0%
+feedback from me about you know what
+what what you did make sense or if you
+
+ align:start position:0%
+what what you did make sense or if you
+ 
+
+ align:start position:0%
+what what you did make sense or if you
+encountered like I picked this picture
+
+ align:start position:0%
+encountered like I picked this picture
+ 
+
+ align:start position:0%
+encountered like I picked this picture
+and now I don't understand you know I
+
+ align:start position:0%
+and now I don't understand you know I
+ 
+
+ align:start position:0%
+and now I don't understand you know I
+did my best but I have questions about
+
+ align:start position:0%
+did my best but I have questions about
+ 
+
+ align:start position:0%
+did my best but I have questions about
+how I did this you know doesn't make
+
+ align:start position:0%
+how I did this you know doesn't make
+ 
+
+ align:start position:0%
+how I did this you know doesn't make
+sense I'd be happy to do that so just
+
+ align:start position:0%
+sense I'd be happy to do that so just
+ 
+
+ align:start position:0%
+sense I'd be happy to do that so just
+scan it email it to me or if it is
+
+ align:start position:0%
+scan it email it to me or if it is
+ 
+
+ align:start position:0%
+scan it email it to me or if it is
+electronic format you know you can do
+
+ align:start position:0%
+electronic format you know you can do
+ 
+
+ align:start position:0%
+electronic format you know you can do
+that as well so the lecture portion and
+
+ align:start position:0%
+that as well so the lecture portion and
+ 
+
+ align:start position:0%
+that as well so the lecture portion and
+now go back
+
+ align:start position:0%
+now go back
+ 
+
+ align:start position:0%
+now go back
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and let's see here we go to
+
+ align:start position:0%
+and let's see here we go to
+ 
+
+ align:start position:0%
+and let's see here we go to
+examples all right so we're in the
+
+ align:start position:0%
+examples all right so we're in the
+ 
+
+ align:start position:0%
+examples all right so we're in the
+intro the Edge Art
+
+ align:start position:0%
+intro the Edge Art
+ 
+
+ align:start position:0%
+intro the Edge Art
+directory start my at lab shell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place takes about 15 seconds for it to
+
+ align:start position:0%
+place takes about 15 seconds for it to
+ 
+
+ align:start position:0%
+place takes about 15 seconds for it to
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this uh this particular thing always CDs
+
+ align:start position:0%
+this uh this particular thing always CDs
+ 
+
+ align:start position:0%
+this uh this particular thing always CDs
+me to the the location of the directory
+
+ align:start position:0%
+me to the the location of the directory
+ 
+
+ align:start position:0%
+me to the the location of the directory
+you need to do that in order to see the
+
+ align:start position:0%
+you need to do that in order to see the
+ 
+
+ align:start position:0%
+you need to do that in order to see the
+examples um I think most mat lab users
+
+ align:start position:0%
+examples um I think most mat lab users
+ 
+
+ align:start position:0%
+examples um I think most mat lab users
+are familiar with that but just some
+
+ align:start position:0%
+are familiar with that but just some
+ 
+
+ align:start position:0%
+are familiar with that but just some
+that some that are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not hide that here is the actual
+
+ align:start position:0%
+not hide that here is the actual
+ 
+
+ align:start position:0%
+not hide that here is the actual
+adjacency
+
+ align:start position:0%
+adjacency
+ 
+
+ align:start position:0%
+adjacency
+Matrix of that
+
+ align:start position:0%
+Matrix of that
+ 
+
+ align:start position:0%
+Matrix of that
+painting so there it is same thing we
+
+ align:start position:0%
+painting so there it is same thing we
+ 
+
+ align:start position:0%
+painting so there it is same thing we
+just saw so this is the data set that
+
+ align:start position:0%
+just saw so this is the data set that
+ 
+
+ align:start position:0%
+just saw so this is the data set that
+we're going to work with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here all right so I'm going to do ea1
+
+ align:start position:0%
+here all right so I'm going to do ea1
+ 
+
+ align:start position:0%
+here all right so I'm going to do ea1
+again the numbered one you know the
+
+ align:start position:0%
+again the numbered one you know the
+ 
+
+ align:start position:0%
+again the numbered one you know the
+courses all the examples are numbered in
+
+ align:start position:0%
+courses all the examples are numbered in
+ 
+
+ align:start position:0%
+courses all the examples are numbered in
+order kind of that you're supposed to
+
+ align:start position:0%
+order kind of that you're supposed to
+ 
+
+ align:start position:0%
+order kind of that you're supposed to
+proceed through them and if you see kind
+
+ align:start position:0%
+proceed through them and if you see kind
+ 
+
+ align:start position:0%
+proceed through them and if you see kind
+of a file in a directory that's like
+
+ align:start position:0%
+of a file in a directory that's like
+ 
+
+ align:start position:0%
+of a file in a directory that's like
+Capital couple Capital levers which are
+
+ align:start position:0%
+Capital couple Capital levers which are
+ 
+
+ align:start position:0%
+Capital couple Capital levers which are
+the first two letters of the the
+
+ align:start position:0%
+the first two letters of the the
+ 
+
+ align:start position:0%
+the first two letters of the the
+directory or the abbreviation of the
+
+ align:start position:0%
+directory or the abbreviation of the
+ 
+
+ align:start position:0%
+directory or the abbreviation of the
+directory and a test that is the
+
+ align:start position:0%
+directory and a test that is the
+ 
+
+ align:start position:0%
+directory and a test that is the
+examples the other files are just
+
+ align:start position:0%
+examples the other files are just
+ 
+
+ align:start position:0%
+examples the other files are just
+supporting files you don't aren't
+
+ align:start position:0%
+supporting files you don't aren't
+ 
+
+ align:start position:0%
+supporting files you don't aren't
+expected to run
+
+ align:start position:0%
+expected to run
+ 
+
+ align:start position:0%
+expected to run
+those try running them but they'll
+
+ align:start position:0%
+those try running them but they'll
+ 
+
+ align:start position:0%
+those try running them but they'll
+probably C you problems if you run them
+
+ align:start position:0%
+probably C you problems if you run them
+ 
+
+ align:start position:0%
+probably C you problems if you run them
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+themselves all right here we go so we
+
+ align:start position:0%
+themselves all right here we go so we
+ 
+
+ align:start position:0%
+themselves all right here we go so we
+just ran that
+
+ align:start position:0%
+just ran that
+ 
+
+ align:start position:0%
+just ran that
+example let's see what we
+
+ align:start position:0%
+example let's see what we
+ 
+
+ align:start position:0%
+example let's see what we
+got and let me
+
+ align:start position:0%
+got and let me
+ 
+
+ align:start position:0%
+got and let me
+uh this a little bit
+
+ align:start position:0%
+uh this a little bit
+ 
+
+ align:start position:0%
+uh this a little bit
+smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+all right I think that worked all right
+
+ align:start position:0%
+all right I think that worked all right
+ 
+
+ align:start position:0%
+all right I think that worked all right
+so first thing we did here is we read in
+
+ align:start position:0%
+so first thing we did here is we read in
+ 
+
+ align:start position:0%
+so first thing we did here is we read in
+our data so we have this read CSV very
+
+ align:start position:0%
+our data so we have this read CSV very
+ 
+
+ align:start position:0%
+our data so we have this read CSV very
+useful
+
+ align:start position:0%
+useful
+ 
+
+ align:start position:0%
+useful
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+um not necessarily the fastest in some
+
+ align:start position:0%
+um not necessarily the fastest in some
+ 
+
+ align:start position:0%
+um not necessarily the fastest in some
+of the later
+
+ align:start position:0%
+of the later
+ 
+
+ align:start position:0%
+of the later
+examples uh we have a sort of a super
+
+ align:start position:0%
+examples uh we have a sort of a super
+ 
+
+ align:start position:0%
+examples uh we have a sort of a super
+fast reader which does almost no
+
+ align:start position:0%
+fast reader which does almost no
+ 
+
+ align:start position:0%
+fast reader which does almost no
+formatting for you so of just reads in
+
+ align:start position:0%
+formatting for you so of just reads in
+ 
+
+ align:start position:0%
+formatting for you so of just reads in
+the triples as raw triples because a lot
+
+ align:start position:0%
+the triples as raw triples because a lot
+ 
+
+ align:start position:0%
+the triples as raw triples because a lot
+of times if you're reading a very large
+
+ align:start position:0%
+of times if you're reading a very large
+ 
+
+ align:start position:0%
+of times if you're reading a very large
+CSV
+
+ align:start position:0%
+CSV
+ 
+
+ align:start position:0%
+CSV
+file you may not want to construct the
+
+ align:start position:0%
+file you may not want to construct the
+ 
+
+ align:start position:0%
+file you may not want to construct the
+full associative array out of the way we
+
+ align:start position:0%
+full associative array out of the way we
+ 
+
+ align:start position:0%
+full associative array out of the way we
+would just sort of do it by default and
+
+ align:start position:0%
+would just sort of do it by default and
+ 
+
+ align:start position:0%
+would just sort of do it by default and
+you can just read in the triples very
+
+ align:start position:0%
+you can just read in the triples very
+ 
+
+ align:start position:0%
+you can just read in the triples very
+quickly and then do some manipulations
+
+ align:start position:0%
+quickly and then do some manipulations
+ 
+
+ align:start position:0%
+quickly and then do some manipulations
+or a lot of times the first thing you'll
+
+ align:start position:0%
+or a lot of times the first thing you'll
+ 
+
+ align:start position:0%
+or a lot of times the first thing you'll
+do is recreate an associative array and
+
+ align:start position:0%
+do is recreate an associative array and
+ 
+
+ align:start position:0%
+do is recreate an associative array and
+then get the triples out of it because
+
+ align:start position:0%
+then get the triples out of it because
+ 
+
+ align:start position:0%
+then get the triples out of it because
+you want to work on the triples directly
+
+ align:start position:0%
+you want to work on the triples directly
+ 
+
+ align:start position:0%
+you want to work on the triples directly
+and so so we do have ways for doing that
+
+ align:start position:0%
+and so so we do have ways for doing that
+ 
+
+ align:start position:0%
+and so so we do have ways for doing that
+so this is the uh we now created the
+
+ align:start position:0%
+so this is the uh we now created the
+ 
+
+ align:start position:0%
+so this is the uh we now created the
+incidence Matrix into an associative
+
+ align:start position:0%
+incidence Matrix into an associative
+ 
+
+ align:start position:0%
+incidence Matrix into an associative
+array
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me go down here let me just show
+
+ align:start position:0%
+and let me go down here let me just show
+ 
+
+ align:start position:0%
+and let me go down here let me just show
+you that so if I go
+
+ align:start position:0%
+you that so if I go
+ 
+
+ align:start position:0%
+you that so if I go
+disp so that shows you the incidence
+
+ align:start position:0%
+disp so that shows you the incidence
+ 
+
+ align:start position:0%
+disp so that shows you the incidence
+Matrix these are its internal structures
+
+ align:start position:0%
+Matrix these are its internal structures
+ 
+
+ align:start position:0%
+Matrix these are its internal structures
+here these are the row keys so those are
+
+ align:start position:0%
+here these are the row keys so those are
+ 
+
+ align:start position:0%
+here these are the row keys so those are
+the recall the uh the labels of the
+
+ align:start position:0%
+the recall the uh the labels of the
+ 
+
+ align:start position:0%
+the recall the uh the labels of the
+edges they have been converted to lexor
+
+ align:start position:0%
+edges they have been converted to lexor
+ 
+
+ align:start position:0%
+edges they have been converted to lexor
+graphically sorted
+
+ align:start position:0%
+graphically sorted
+ 
+
+ align:start position:0%
+graphically sorted
+order we have the column keys but
+
+ align:start position:0%
+order we have the column keys but
+ 
+
+ align:start position:0%
+order we have the column keys but
+there's so many that that mat lab
+
+ align:start position:0%
+there's so many that that mat lab
+ 
+
+ align:start position:0%
+there's so many that that mat lab
+chooses not to print out the full list
+
+ align:start position:0%
+chooses not to print out the full list
+ 
+
+ align:start position:0%
+chooses not to print out the full list
+here but it's again a lexographic sorted
+
+ align:start position:0%
+here but it's again a lexographic sorted
+ 
+
+ align:start position:0%
+here but it's again a lexographic sorted
+list of the unique column labels these
+
+ align:start position:0%
+list of the unique column labels these
+ 
+
+ align:start position:0%
+list of the unique column labels these
+are the different values that we
+
+ align:start position:0%
+are the different values that we
+ 
+
+ align:start position:0%
+are the different values that we
+have so this is you remember we had an
+
+ align:start position:0%
+have so this is you remember we had an
+ 
+
+ align:start position:0%
+have so this is you remember we had an
+order column which is one two three blue
+
+ align:start position:0%
+order column which is one two three blue
+ 
+
+ align:start position:0%
+order column which is one two three blue
+green orange pink silver
+
+ align:start position:0%
+green orange pink silver
+ 
+
+ align:start position:0%
+green orange pink silver
+Etc and here uh you know and then the
+
+ align:start position:0%
+Etc and here uh you know and then the
+ 
+
+ align:start position:0%
+Etc and here uh you know and then the
+overall adjacency Matrix which connects
+
+ align:start position:0%
+overall adjacency Matrix which connects
+ 
+
+ align:start position:0%
+overall adjacency Matrix which connects
+the row keys to their value keys
+
+ align:start position:0%
+the row keys to their value keys
+ 
+
+ align:start position:0%
+the row keys to their value keys
+is 19 by
+
+ align:start position:0%
+is 19 by
+ 
+
+ align:start position:0%
+is 19 by
+21 19 19 rows by 21 columns this
+
+ align:start position:0%
+21 19 19 rows by 21 columns this
+ 
+
+ align:start position:0%
+21 19 19 rows by 21 columns this
+actually shows a mixed use right some of
+
+ align:start position:0%
+actually shows a mixed use right some of
+ 
+
+ align:start position:0%
+actually shows a mixed use right some of
+these are essentially exploded right the
+
+ align:start position:0%
+these are essentially exploded right the
+ 
+
+ align:start position:0%
+these are essentially exploded right the
+fact that we have each each Edge but
+
+ align:start position:0%
+fact that we have each each Edge but
+ 
+
+ align:start position:0%
+fact that we have each each Edge but
+some of the values are actually storing
+
+ align:start position:0%
+some of the values are actually storing
+ 
+
+ align:start position:0%
+some of the values are actually storing
+real stuff here blue green orange Etc so
+
+ align:start position:0%
+real stuff here blue green orange Etc so
+ 
+
+ align:start position:0%
+real stuff here blue green orange Etc so
+you don't have to go all the way with
+
+ align:start position:0%
+you don't have to go all the way with
+ 
+
+ align:start position:0%
+you don't have to go all the way with
+one you can mix them to around you can
+
+ align:start position:0%
+one you can mix them to around you can
+ 
+
+ align:start position:0%
+one you can mix them to around you can
+create dense matrices that look more
+
+ align:start position:0%
+create dense matrices that look more
+ 
+
+ align:start position:0%
+create dense matrices that look more
+like traditional tables and there's
+
+ align:start position:0%
+like traditional tables and there's
+ 
+
+ align:start position:0%
+like traditional tables and there's
+sometimes that you want to do that and
+
+ align:start position:0%
+sometimes that you want to do that and
+ 
+
+ align:start position:0%
+sometimes that you want to do that and
+other times you can sort of completely
+
+ align:start position:0%
+other times you can sort of completely
+ 
+
+ align:start position:0%
+other times you can sort of completely
+explode it out and do things like that
+
+ align:start position:0%
+explode it out and do things like that
+ 
+
+ align:start position:0%
+explode it out and do things like that
+as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so we go
+
+ align:start position:0%
+so so we go
+ 
+
+ align:start position:0%
+so so we go
+back um we just want to work with the
+
+ align:start position:0%
+back um we just want to work with the
+ 
+
+ align:start position:0%
+back um we just want to work with the
+vertices okay so we're going to ignore
+
+ align:start position:0%
+vertices okay so we're going to ignore
+ 
+
+ align:start position:0%
+vertices okay so we're going to ignore
+this color and Order column so we're
+
+ align:start position:0%
+this color and Order column so we're
+ 
+
+ align:start position:0%
+this color and Order column so we're
+going to create our first projection is
+
+ align:start position:0%
+going to create our first projection is
+ 
+
+ align:start position:0%
+going to create our first projection is
+to just work with the vertices so we
+
+ align:start position:0%
+to just work with the vertices so we
+ 
+
+ align:start position:0%
+to just work with the vertices so we
+have this little short hand here called
+
+ align:start position:0%
+have this little short hand here called
+ 
+
+ align:start position:0%
+have this little short hand here called
+starts with if you give it a a character
+
+ align:start position:0%
+starts with if you give it a a character
+ 
+
+ align:start position:0%
+starts with if you give it a a character
+and it will create a little query
+
+ align:start position:0%
+and it will create a little query
+ 
+
+ align:start position:0%
+and it will create a little query
+that'll that will get just things that
+
+ align:start position:0%
+that'll that will get just things that
+ 
+
+ align:start position:0%
+that'll that will get just things that
+start with that and very useful thing is
+
+ align:start position:0%
+start with that and very useful thing is
+ 
+
+ align:start position:0%
+start with that and very useful thing is
+very efficient too it actually formally
+
+ align:start position:0%
+very efficient too it actually formally
+ 
+
+ align:start position:0%
+very efficient too it actually formally
+creates the two bounding it figures out
+
+ align:start position:0%
+creates the two bounding it figures out
+ 
+
+ align:start position:0%
+creates the two bounding it figures out
+what the maximum range is for that and
+
+ align:start position:0%
+what the maximum range is for that and
+ 
+
+ align:start position:0%
+what the maximum range is for that and
+then it just needs to look up you know
+
+ align:start position:0%
+then it just needs to look up you know
+ 
+
+ align:start position:0%
+then it just needs to look up you know
+the beginning and the end it can assume
+
+ align:start position:0%
+the beginning and the end it can assume
+ 
+
+ align:start position:0%
+the beginning and the end it can assume
+lexor graphical order and then it can
+
+ align:start position:0%
+lexor graphical order and then it can
+ 
+
+ align:start position:0%
+lexor graphical order and then it can
+just grab the middle so much we have a
+
+ align:start position:0%
+just grab the middle so much we have a
+ 
+
+ align:start position:0%
+just grab the middle so much we have a
+regular expression approach too which
+
+ align:start position:0%
+regular expression approach too which
+ 
+
+ align:start position:0%
+regular expression approach too which
+works fine on small associative arrays
+
+ align:start position:0%
+works fine on small associative arrays
+ 
+
+ align:start position:0%
+works fine on small associative arrays
+but this is much more efficient because
+
+ align:start position:0%
+but this is much more efficient because
+ 
+
+ align:start position:0%
+but this is much more efficient because
+it's just basically two lookups and go
+
+ align:start position:0%
+it's just basically two lookups and go
+ 
+
+ align:start position:0%
+it's just basically two lookups and go
+um it also works if this e was actually
+
+ align:start position:0%
+um it also works if this e was actually
+ 
+
+ align:start position:0%
+um it also works if this e was actually
+a binding to a table in a database you
+
+ align:start position:0%
+a binding to a table in a database you
+ 
+
+ align:start position:0%
+a binding to a table in a database you
+can use the same syntax while the
+
+ align:start position:0%
+can use the same syntax while the
+ 
+
+ align:start position:0%
+can use the same syntax while the
+regular expression syntax doesn't really
+
+ align:start position:0%
+regular expression syntax doesn't really
+ 
+
+ align:start position:0%
+regular expression syntax doesn't really
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so that's the delimiter of the
+
+ align:start position:0%
+yes so that's the delimiter of the
+ 
+
+ align:start position:0%
+yes so that's the delimiter of the
+string so it's a string list with one
+
+ align:start position:0%
+string so it's a string list with one
+ 
+
+ align:start position:0%
+string so it's a string list with one
+entry in it so this is a string list all
+
+ align:start position:0%
+entry in it so this is a string list all
+ 
+
+ align:start position:0%
+entry in it so this is a string list all
+our strings list here well because this
+
+ align:start position:0%
+our strings list here well because this
+ 
+
+ align:start position:0%
+our strings list here well because this
+also allows me could have been anything
+
+ align:start position:0%
+also allows me could have been anything
+ 
+
+ align:start position:0%
+also allows me could have been anything
+that was that was unique to that okay
+
+ align:start position:0%
+that was that was unique to that okay
+ 
+
+ align:start position:0%
+that was that was unique to that okay
+and didn't have to be the same delimiter
+
+ align:start position:0%
+and didn't have to be the same delimiter
+ 
+
+ align:start position:0%
+and didn't have to be the same delimiter
+that was the one inside could have been
+
+ align:start position:0%
+that was the one inside could have been
+ 
+
+ align:start position:0%
+that was the one inside could have been
+a new line could have been a tab could
+
+ align:start position:0%
+a new line could have been a tab could
+ 
+
+ align:start position:0%
+a new line could have been a tab could
+whatever I just picked comma because it
+
+ align:start position:0%
+whatever I just picked comma because it
+ 
+
+ align:start position:0%
+whatever I just picked comma because it
+was convenient but could have been a
+
+ align:start position:0%
+was convenient but could have been a
+ 
+
+ align:start position:0%
+was convenient but could have been a
+space um because you can have multiple
+
+ align:start position:0%
+space um because you can have multiple
+ 
+
+ align:start position:0%
+space um because you can have multiple
+arguments to the starts with if you want
+
+ align:start position:0%
+arguments to the starts with if you want
+ 
+
+ align:start position:0%
+arguments to the starts with if you want
+to say I want starts with this and
+
+ align:start position:0%
+to say I want starts with this and
+ 
+
+ align:start position:0%
+to say I want starts with this and
+starts with this and starts with this
+
+ align:start position:0%
+starts with this and starts with this
+ 
+
+ align:start position:0%
+starts with this and starts with this
+you just give it a whole list and we'll
+
+ align:start position:0%
+you just give it a whole list and we'll
+ 
+
+ align:start position:0%
+you just give it a whole list and we'll
+go and do that all for you um and so
+
+ align:start position:0%
+go and do that all for you um and so
+ 
+
+ align:start position:0%
+go and do that all for you um and so
+that's why we do it that way wherever
+
+ align:start position:0%
+that's why we do it that way wherever
+ 
+
+ align:start position:0%
+that's why we do it that way wherever
+possible we try and accept a list of
+
+ align:start position:0%
+possible we try and accept a list of
+ 
+
+ align:start position:0%
+possible we try and accept a list of
+strings and then do kind of the right
+
+ align:start position:0%
+strings and then do kind of the right
+ 
+
+ align:start position:0%
+strings and then do kind of the right
+thing so basically this is saying get
+
+ align:start position:0%
+thing so basically this is saying get
+ 
+
+ align:start position:0%
+thing so basically this is saying get
+get me all columns that start with V so
+
+ align:start position:0%
+get me all columns that start with V so
+ 
+
+ align:start position:0%
+get me all columns that start with V so
+that will be all the vertices and this
+
+ align:start position:0%
+that will be all the vertices and this
+ 
+
+ align:start position:0%
+that will be all the vertices and this
+is the colon which says you know and I
+
+ align:start position:0%
+is the colon which says you know and I
+ 
+
+ align:start position:0%
+is the colon which says you know and I
+want the full row of
+
+ align:start position:0%
+want the full row of
+ 
+
+ align:start position:0%
+want the full row of
+that these had these values of um which
+
+ align:start position:0%
+that these had these values of um which
+ 
+
+ align:start position:0%
+that these had these values of um which
+were the the order group that they were
+
+ align:start position:0%
+were the the order group that they were
+ 
+
+ align:start position:0%
+were the the order group that they were
+in and uh and so we don't care about
+
+ align:start position:0%
+in and uh and so we don't care about
+ 
+
+ align:start position:0%
+in and uh and so we don't care about
+those we want to convert them back to
+
+ align:start position:0%
+those we want to convert them back to
+ 
+
+ align:start position:0%
+those we want to convert them back to
+regular numeric numbers and so we have
+
+ align:start position:0%
+regular numeric numbers and so we have
+ 
+
+ align:start position:0%
+regular numeric numbers and so we have
+this shorthand here called double Loi
+
+ align:start position:0%
+this shorthand here called double Loi
+ 
+
+ align:start position:0%
+this shorthand here called double Loi
+which basically just takes the logical
+
+ align:start position:0%
+which basically just takes the logical
+ 
+
+ align:start position:0%
+which basically just takes the logical
+and then does the double I think
+
+ align:start position:0%
+and then does the double I think
+ 
+
+ align:start position:0%
+and then does the double I think
+mathematically formally you would use
+
+ align:start position:0%
+mathematically formally you would use
+ 
+
+ align:start position:0%
+mathematically formally you would use
+call this the infinity Norm on strings
+
+ align:start position:0%
+call this the infinity Norm on strings
+ 
+
+ align:start position:0%
+call this the infinity Norm on strings
+if that even makes sense um but it
+
+ align:start position:0%
+if that even makes sense um but it
+ 
+
+ align:start position:0%
+if that even makes sense um but it
+basically just says if there's a value
+
+ align:start position:0%
+basically just says if there's a value
+ 
+
+ align:start position:0%
+basically just says if there's a value
+there convert it to a you know a double
+
+ align:start position:0%
+there convert it to a you know a double
+ 
+
+ align:start position:0%
+there convert it to a you know a double
+Precision one if there's not a value
+
+ align:start position:0%
+Precision one if there's not a value
+ 
+
+ align:start position:0%
+Precision one if there's not a value
+there it's just a sparse zero not not
+
+ align:start position:0%
+there it's just a sparse zero not not
+ 
+
+ align:start position:0%
+there it's just a sparse zero not not
+and we do this all the time because a
+
+ align:start position:0%
+and we do this all the time because a
+ 
+
+ align:start position:0%
+and we do this all the time because a
+lot of times we want to do math on these
+
+ align:start position:0%
+lot of times we want to do math on these
+ 
+
+ align:start position:0%
+lot of times we want to do math on these
+things it's like regular math uh we want
+
+ align:start position:0%
+things it's like regular math uh we want
+ 
+
+ align:start position:0%
+things it's like regular math uh we want
+to compute the vertex adjacency graph so
+
+ align:start position:0%
+to compute the vertex adjacency graph so
+ 
+
+ align:start position:0%
+to compute the vertex adjacency graph so
+we do that with our Square in function
+
+ align:start position:0%
+we do that with our Square in function
+ 
+
+ align:start position:0%
+we do that with our Square in function
+here our inner square product so that
+
+ align:start position:0%
+here our inner square product so that
+ 
+
+ align:start position:0%
+here our inner square product so that
+basically takes our Matrix and use the
+
+ align:start position:0%
+basically takes our Matrix and use the
+ 
+
+ align:start position:0%
+basically takes our Matrix and use the
+edge as the common key to to to join
+
+ align:start position:0%
+edge as the common key to to to join
+ 
+
+ align:start position:0%
+edge as the common key to to to join
+them together and we use our display
+
+ align:start position:0%
+them together and we use our display
+ 
+
+ align:start position:0%
+them together and we use our display
+full function to actually show what we
+
+ align:start position:0%
+full function to actually show what we
+ 
+
+ align:start position:0%
+full function to actually show what we
+got and so now you see the
+
+ align:start position:0%
+got and so now you see the
+ 
+
+ align:start position:0%
+got and so now you see the
+vertex vertex adjacency Matrix here and
+
+ align:start position:0%
+vertex vertex adjacency Matrix here and
+ 
+
+ align:start position:0%
+vertex vertex adjacency Matrix here and
+then the number is the number of times
+
+ align:start position:0%
+then the number is the number of times
+ 
+
+ align:start position:0%
+then the number is the number of times
+those vertices are on the same Edge so
+
+ align:start position:0%
+those vertices are on the same Edge so
+ 
+
+ align:start position:0%
+those vertices are on the same Edge so
+it's obviously symmetric and you see
+
+ align:start position:0%
+it's obviously symmetric and you see
+ 
+
+ align:start position:0%
+it's obviously symmetric and you see
+here some you know these vertices here
+
+ align:start position:0%
+here some you know these vertices here
+ 
+
+ align:start position:0%
+here some you know these vertices here
+which are part of this common hyper Edge
+
+ align:start position:0%
+which are part of this common hyper Edge
+ 
+
+ align:start position:0%
+which are part of this common hyper Edge
+you know we have this sort of 696
+
+ align:start position:0%
+you know we have this sort of 696
+ 
+
+ align:start position:0%
+you know we have this sort of 696
+structure here various other types of
+
+ align:start position:0%
+structure here various other types of
+ 
+
+ align:start position:0%
+structure here various other types of
+symmetric structures going on here
+
+ align:start position:0%
+symmetric structures going on here
+ 
+
+ align:start position:0%
+symmetric structures going on here
+showing you the counts how many times
+
+ align:start position:0%
+showing you the counts how many times
+ 
+
+ align:start position:0%
+showing you the counts how many times
+those vertices appeared on the same Edge
+
+ align:start position:0%
+those vertices appeared on the same Edge
+ 
+
+ align:start position:0%
+those vertices appeared on the same Edge
+these are obviously clicks because they
+
+ align:start position:0%
+these are obviously clicks because they
+ 
+
+ align:start position:0%
+these are obviously clicks because they
+are all vertices that are on the same
+
+ align:start position:0%
+are all vertices that are on the same
+ 
+
+ align:start position:0%
+are all vertices that are on the same
+hyperedge line so if you have a same
+
+ align:start position:0%
+hyperedge line so if you have a same
+ 
+
+ align:start position:0%
+hyperedge line so if you have a same
+hyperedge line whenever you do the
+
+ align:start position:0%
+hyperedge line whenever you do the
+ 
+
+ align:start position:0%
+hyperedge line whenever you do the
+squaring operation
+
+ align:start position:0%
+squaring operation
+ 
+
+ align:start position:0%
+squaring operation
+you create you see it as this cck uh in
+
+ align:start position:0%
+you create you see it as this cck uh in
+ 
+
+ align:start position:0%
+you create you see it as this cck uh in
+this in this uh in this operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+right we can also do the square
+
+ align:start position:0%
+right we can also do the square
+ 
+
+ align:start position:0%
+right we can also do the square
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+function okay which computes The Edge
+
+ align:start position:0%
+function okay which computes The Edge
+ 
+
+ align:start position:0%
+function okay which computes The Edge
+adjacency Matrix so now we want to ask
+
+ align:start position:0%
+adjacency Matrix so now we want to ask
+ 
+
+ align:start position:0%
+adjacency Matrix so now we want to ask
+which edges share common
+
+ align:start position:0%
+which edges share common
+ 
+
+ align:start position:0%
+which edges share common
+vertices and so that's this structure
+
+ align:start position:0%
+vertices and so that's this structure
+ 
+
+ align:start position:0%
+vertices and so that's this structure
+here shows you the these are the various
+
+ align:start position:0%
+here shows you the these are the various
+ 
+
+ align:start position:0%
+here shows you the these are the various
+edges and again it's symmetric and you
+
+ align:start position:0%
+edges and again it's symmetric and you
+ 
+
+ align:start position:0%
+edges and again it's symmetric and you
+can see all kinds of structures in here
+
+ align:start position:0%
+can see all kinds of structures in here
+ 
+
+ align:start position:0%
+can see all kinds of structures in here
+about which vertices share I mean which
+
+ align:start position:0%
+about which vertices share I mean which
+ 
+
+ align:start position:0%
+about which vertices share I mean which
+edges share common common vertices so
+
+ align:start position:0%
+edges share common common vertices so
+ 
+
+ align:start position:0%
+edges share common common vertices so
+and that is pretty much it for this
+
+ align:start position:0%
+and that is pretty much it for this
+ 
+
+ align:start position:0%
+and that is pretty much it for this
+example very simple example uh hopefully
+
+ align:start position:0%
+example very simple example uh hopefully
+ 
+
+ align:start position:0%
+example very simple example uh hopefully
+gets you to the point where you can
+
+ align:start position:0%
+gets you to the point where you can
+ 
+
+ align:start position:0%
+gets you to the point where you can
+begin to try out the homework assignment
+
+ align:start position:0%
+begin to try out the homework assignment
+ 
+
+ align:start position:0%
+begin to try out the homework assignment
+and if there's any questions that people
+
+ align:start position:0%
+and if there's any questions that people
+ 
+
+ align:start position:0%
+and if there's any questions that people
+have you know uh you know let's try this
+
+ align:start position:0%
+have you know uh you know let's try this
+ 
+
+ align:start position:0%
+have you know uh you know let's try this
+here one thing that's fun to do spy
+
+ align:start position:0%
+here one thing that's fun to do spy
+ 
+
+ align:start position:0%
+here one thing that's fun to do spy
+e where that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops come on gu I think between
+
+ align:start position:0%
+oops come on gu I think between
+ 
+
+ align:start position:0%
+oops come on gu I think between
+PowerPoint quick time and everything
+
+ align:start position:0%
+PowerPoint quick time and everything
+ 
+
+ align:start position:0%
+PowerPoint quick time and everything
+else it's just
+
+ align:start position:0%
+else it's just
+ 
+
+ align:start position:0%
+else it's just
+about ah there it is wow that took a
+
+ align:start position:0%
+about ah there it is wow that took a
+ 
+
+ align:start position:0%
+about ah there it is wow that took a
+long time so this shows that adjacency
+
+ align:start position:0%
+long time so this shows that adjacency
+ 
+
+ align:start position:0%
+long time so this shows that adjacency
+Matrix so spy works I think we I don't
+
+ align:start position:0%
+Matrix so spy works I think we I don't
+ 
+
+ align:start position:0%
+Matrix so spy works I think we I don't
+know if we showed that in the first
+
+ align:start position:0%
+know if we showed that in the first
+ 
+
+ align:start position:0%
+know if we showed that in the first
+example but the Spy function the
+
+ align:start position:0%
+example but the Spy function the
+ 
+
+ align:start position:0%
+example but the Spy function the
+standard M mat lab sparse plotting
+
+ align:start position:0%
+standard M mat lab sparse plotting
+ 
+
+ align:start position:0%
+standard M mat lab sparse plotting
+function very useful way to just sort of
+
+ align:start position:0%
+function very useful way to just sort of
+ 
+
+ align:start position:0%
+function very useful way to just sort of
+look at the stuff all those previous
+
+ align:start position:0%
+look at the stuff all those previous
+ 
+
+ align:start position:0%
+look at the stuff all those previous
+charts I showed you on the examples
+
+ align:start position:0%
+charts I showed you on the examples
+ 
+
+ align:start position:0%
+charts I showed you on the examples
+where we' done this thing and a little
+
+ align:start position:0%
+where we' done this thing and a little
+ 
+
+ align:start position:0%
+where we' done this thing and a little
+feature that sometimes causes mat lab to
+
+ align:start position:0%
+feature that sometimes causes mat lab to
+ 
+
+ align:start position:0%
+feature that sometimes causes mat lab to
+crash because it doesn't really like
+
+ align:start position:0%
+crash because it doesn't really like
+ 
+
+ align:start position:0%
+crash because it doesn't really like
+doing things too aggressively but if you
+
+ align:start position:0%
+doing things too aggressively but if you
+ 
+
+ align:start position:0%
+doing things too aggressively but if you
+click on
+
+ align:start position:0%
+click on
+ 
+
+ align:start position:0%
+click on
+it it shows you the row and the column
+
+ align:start position:0%
+it it shows you the row and the column
+ 
+
+ align:start position:0%
+it it shows you the row and the column
+and the value associated with that and
+
+ align:start position:0%
+and the value associated with that and
+ 
+
+ align:start position:0%
+and the value associated with that and
+also prints it out here likewise here so
+
+ align:start position:0%
+also prints it out here likewise here so
+ 
+
+ align:start position:0%
+also prints it out here likewise here so
+you see row column that gives you the
+
+ align:start position:0%
+you see row column that gives you the
+ 
+
+ align:start position:0%
+you see row column that gives you the
+order and this tells you you know the
+
+ align:start position:0%
+order and this tells you you know the
+ 
+
+ align:start position:0%
+order and this tells you you know the
+row is G2 its column is color its value
+
+ align:start position:0%
+row is G2 its column is color its value
+ 
+
+ align:start position:0%
+row is G2 its column is color its value
+is green so actually I lied to you that
+
+ align:start position:0%
+is green so actually I lied to you that
+ 
+
+ align:start position:0%
+is green so actually I lied to you that
+was just the first
+
+ align:start position:0%
+was just the first
+ 
+
+ align:start position:0%
+was just the first
+example see senior moment there we have
+
+ align:start position:0%
+example see senior moment there we have
+ 
+
+ align:start position:0%
+example see senior moment there we have
+two more to go a lot more fun see you're
+
+ align:start position:0%
+two more to go a lot more fun see you're
+ 
+
+ align:start position:0%
+two more to go a lot more fun see you're
+all you're all excited the class ended
+
+ align:start position:0%
+all you're all excited the class ended
+ 
+
+ align:start position:0%
+all you're all excited the class ended
+early so all right here's the other
+
+ align:start position:0%
+early so all right here's the other
+ 
+
+ align:start position:0%
+early so all right here's the other
+examples so again what we do is uh we're
+
+ align:start position:0%
+examples so again what we do is uh we're
+ 
+
+ align:start position:0%
+examples so again what we do is uh we're
+reading in the data set we're displaying
+
+ align:start position:0%
+reading in the data set we're displaying
+ 
+
+ align:start position:0%
+reading in the data set we're displaying
+the full thing so you can see there's
+
+ align:start position:0%
+the full thing so you can see there's
+ 
+
+ align:start position:0%
+the full thing so you can see there's
+the full Beast I just showed you with
+
+ align:start position:0%
+the full Beast I just showed you with
+ 
+
+ align:start position:0%
+the full Beast I just showed you with
+the Spy plot now I'm going to do some
+
+ align:start position:0%
+the Spy plot now I'm going to do some
+ 
+
+ align:start position:0%
+the Spy plot now I'm going to do some
+analytics on this so one thing I want to
+
+ align:start position:0%
+analytics on this so one thing I want to
+ 
+
+ align:start position:0%
+analytics on this so one thing I want to
+do is just get the orange edges so I can
+
+ align:start position:0%
+do is just get the orange edges so I can
+ 
+
+ align:start position:0%
+do is just get the orange edges so I can
+say get me the column
+
+ align:start position:0%
+say get me the column
+ 
+
+ align:start position:0%
+say get me the column
+color and because orange is held in the
+
+ align:start position:0%
+color and because orange is held in the
+ 
+
+ align:start position:0%
+color and because orange is held in the
+value I can actually compare it with the
+
+ align:start position:0%
+value I can actually compare it with the
+ 
+
+ align:start position:0%
+value I can actually compare it with the
+string so I say return me the Matrix the
+
+ align:start position:0%
+string so I say return me the Matrix the
+ 
+
+ align:start position:0%
+string so I say return me the Matrix the
+associative array of the row
+
+ align:start position:0%
+associative array of the row
+ 
+
+ align:start position:0%
+associative array of the row
+color and everything equal to Orange so
+
+ align:start position:0%
+color and everything equal to Orange so
+ 
+
+ align:start position:0%
+color and everything equal to Orange so
+that returns me another associative
+
+ align:start position:0%
+that returns me another associative
+ 
+
+ align:start position:0%
+that returns me another associative
+array the result of this whole logical
+
+ align:start position:0%
+array the result of this whole logical
+ 
+
+ align:start position:0%
+array the result of this whole logical
+expression is another associative array
+
+ align:start position:0%
+expression is another associative array
+ 
+
+ align:start position:0%
+expression is another associative array
+I can then get the rows of those
+
+ align:start position:0%
+I can then get the rows of those
+ 
+
+ align:start position:0%
+I can then get the rows of those
+associative arrays that associative
+
+ align:start position:0%
+associative arrays that associative
+ 
+
+ align:start position:0%
+associative arrays that associative
+array so I've found
+
+ align:start position:0%
+array so I've found
+ 
+
+ align:start position:0%
+array so I've found
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+um edges that are
+
+ align:start position:0%
+um edges that are
+ 
+
+ align:start position:0%
+um edges that are
+orange and I uh can then pass that get
+
+ align:start position:0%
+orange and I uh can then pass that get
+ 
+
+ align:start position:0%
+orange and I uh can then pass that get
+those rows and pass that back into the
+
+ align:start position:0%
+those rows and pass that back into the
+ 
+
+ align:start position:0%
+those rows and pass that back into the
+original one to get just the orange
+
+ align:start position:0%
+original one to get just the orange
+ 
+
+ align:start position:0%
+original one to get just the orange
+edges so this just shows you sort of
+
+ align:start position:0%
+edges so this just shows you sort of
+ 
+
+ align:start position:0%
+edges so this just shows you sort of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+composable ability that's very powerful
+
+ align:start position:0%
+composable ability that's very powerful
+ 
+
+ align:start position:0%
+composable ability that's very powerful
+same same ability that mat lab has one
+
+ align:start position:0%
+same same ability that mat lab has one
+ 
+
+ align:start position:0%
+same same ability that mat lab has one
+does similar statements in mat lab all
+
+ align:start position:0%
+does similar statements in mat lab all
+ 
+
+ align:start position:0%
+does similar statements in mat lab all
+the time and so it's very composable
+
+ align:start position:0%
+the time and so it's very composable
+ 
+
+ align:start position:0%
+the time and so it's very composable
+this would be a very complex query to do
+
+ align:start position:0%
+this would be a very complex query to do
+ 
+
+ align:start position:0%
+this would be a very complex query to do
+in other approaches and you can do it
+
+ align:start position:0%
+in other approaches and you can do it
+ 
+
+ align:start position:0%
+in other approaches and you can do it
+very quickly here yes question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh no it
+
+ align:start position:0%
+uh no it
+ 
+
+ align:start position:0%
+uh no it
+doesn't it doesn't what we could do is
+
+ align:start position:0%
+doesn't it doesn't what we could do is
+ 
+
+ align:start position:0%
+doesn't it doesn't what we could do is
+overload it so if you pass in an
+
+ align:start position:0%
+overload it so if you pass in an
+ 
+
+ align:start position:0%
+overload it so if you pass in an
+associative array with just a single
+
+ align:start position:0%
+associative array with just a single
+ 
+
+ align:start position:0%
+associative array with just a single
+argument and have it behave like when
+
+ align:start position:0%
+argument and have it behave like when
+ 
+
+ align:start position:0%
+argument and have it behave like when
+you pass in the mat lab logical and do
+
+ align:start position:0%
+you pass in the mat lab logical and do
+ 
+
+ align:start position:0%
+you pass in the mat lab logical and do
+that kind of intersection we could think
+
+ align:start position:0%
+that kind of intersection we could think
+ 
+
+ align:start position:0%
+that kind of intersection we could think
+about that but mat lab actually relies
+
+ align:start position:0%
+about that but mat lab actually relies
+ 
+
+ align:start position:0%
+about that but mat lab actually relies
+on then converting The Matrix to a
+
+ align:start position:0%
+on then converting The Matrix to a
+ 
+
+ align:start position:0%
+on then converting The Matrix to a
+vector and then using the
+
+ align:start position:0%
+vector and then using the
+ 
+
+ align:start position:0%
+vector and then using the
+singular basically it takes that logical
+
+ align:start position:0%
+singular basically it takes that logical
+ 
+
+ align:start position:0%
+singular basically it takes that logical
+converts it to a singular index which
+
+ align:start position:0%
+converts it to a singular index which
+ 
+
+ align:start position:0%
+converts it to a singular index which
+kind of gets us into an area where it's
+
+ align:start position:0%
+kind of gets us into an area where it's
+ 
+
+ align:start position:0%
+kind of gets us into an area where it's
+very fuzzy and gray so we've definitely
+
+ align:start position:0%
+very fuzzy and gray so we've definitely
+ 
+
+ align:start position:0%
+very fuzzy and gray so we've definitely
+thought about that and it's it's it's
+
+ align:start position:0%
+thought about that and it's it's it's
+ 
+
+ align:start position:0%
+thought about that and it's it's it's
+it's there are places where we line up
+
+ align:start position:0%
+it's there are places where we line up
+ 
+
+ align:start position:0%
+it's there are places where we line up
+with matab very nicely because the
+
+ align:start position:0%
+with matab very nicely because the
+ 
+
+ align:start position:0%
+with matab very nicely because the
+mathematics of associative arrays and
+
+ align:start position:0%
+mathematics of associative arrays and
+ 
+
+ align:start position:0%
+mathematics of associative arrays and
+linear algebra really line up very
+
+ align:start position:0%
+linear algebra really line up very
+ 
+
+ align:start position:0%
+linear algebra really line up very
+nicely and then there's there's there's
+
+ align:start position:0%
+nicely and then there's there's there's
+ 
+
+ align:start position:0%
+nicely and then there's there's there's
+and there's places where they intersect
+
+ align:start position:0%
+and there's places where they intersect
+ 
+
+ align:start position:0%
+and there's places where they intersect
+there's things you can do in with
+
+ align:start position:0%
+there's things you can do in with
+ 
+
+ align:start position:0%
+there's things you can do in with
+associative arrays that can't do with
+
+ align:start position:0%
+associative arrays that can't do with
+ 
+
+ align:start position:0%
+associative arrays that can't do with
+linear algebra for example we can mult
+
+ align:start position:0%
+linear algebra for example we can mult
+ 
+
+ align:start position:0%
+linear algebra for example we can mult
+Matrix multiply any two associative
+
+ align:start position:0%
+Matrix multiply any two associative
+ 
+
+ align:start position:0%
+Matrix multiply any two associative
+arrays there's no conformance
+
+ align:start position:0%
+arrays there's no conformance
+ 
+
+ align:start position:0%
+arrays there's no conformance
+requirement that they don't have the
+
+ align:start position:0%
+requirement that they don't have the
+ 
+
+ align:start position:0%
+requirement that they don't have the
+same normally when you multiply two
+
+ align:start position:0%
+same normally when you multiply two
+ 
+
+ align:start position:0%
+same normally when you multiply two
+matrices the number of the dimensions
+
+ align:start position:0%
+matrices the number of the dimensions
+ 
+
+ align:start position:0%
+matrices the number of the dimensions
+have to the inner Dimensions have to
+
+ align:start position:0%
+have to the inner Dimensions have to
+ 
+
+ align:start position:0%
+have to the inner Dimensions have to
+match basically The Columns of the left
+
+ align:start position:0%
+match basically The Columns of the left
+ 
+
+ align:start position:0%
+match basically The Columns of the left
+argument and the rows of the right
+
+ align:start position:0%
+argument and the rows of the right
+ 
+
+ align:start position:0%
+argument and the rows of the right
+argument must be the same length and
+
+ align:start position:0%
+argument must be the same length and
+ 
+
+ align:start position:0%
+argument must be the same length and
+Associate arrays that that requirement
+
+ align:start position:0%
+Associate arrays that that requirement
+ 
+
+ align:start position:0%
+Associate arrays that that requirement
+doesn't exist you can multiply or add
+
+ align:start position:0%
+doesn't exist you can multiply or add
+ 
+
+ align:start position:0%
+doesn't exist you can multiply or add
+any two associative arrays we'll get
+
+ align:start position:0%
+any two associative arrays we'll get
+ 
+
+ align:start position:0%
+any two associative arrays we'll get
+into that much more in the next class
+
+ align:start position:0%
+into that much more in the next class
+ 
+
+ align:start position:0%
+into that much more in the next class
+but that's a very powerful feature that
+
+ align:start position:0%
+but that's a very powerful feature that
+ 
+
+ align:start position:0%
+but that's a very powerful feature that
+people like but there's other places
+
+ align:start position:0%
+people like but there's other places
+ 
+
+ align:start position:0%
+people like but there's other places
+where it doesn't really make sense so uh
+
+ align:start position:0%
+where it doesn't really make sense so uh
+ 
+
+ align:start position:0%
+where it doesn't really make sense so uh
+things like what is the upper triangular
+
+ align:start position:0%
+things like what is the upper triangular
+ 
+
+ align:start position:0%
+things like what is the upper triangular
+section of an associative array gets to
+
+ align:start position:0%
+section of an associative array gets to
+ 
+
+ align:start position:0%
+section of an associative array gets to
+be a little bit huh what's that mean so
+
+ align:start position:0%
+be a little bit huh what's that mean so
+ 
+
+ align:start position:0%
+be a little bit huh what's that mean so
+excellent question though excellent
+
+ align:start position:0%
+excellent question though excellent
+ 
+
+ align:start position:0%
+excellent question though excellent
+question though so we can display this
+
+ align:start position:0%
+question though so we can display this
+ 
+
+ align:start position:0%
+question though so we can display this
+so this just shows we found all the
+
+ align:start position:0%
+so this just shows we found all the
+ 
+
+ align:start position:0%
+so this just shows we found all the
+edges that had color
+
+ align:start position:0%
+edges that had color
+ 
+
+ align:start position:0%
+edges that had color
+orange um but we don't have to just you
+
+ align:start position:0%
+orange um but we don't have to just you
+ 
+
+ align:start position:0%
+orange um but we don't have to just you
+know that's a way of using the values to
+
+ align:start position:0%
+know that's a way of using the values to
+ 
+
+ align:start position:0%
+know that's a way of using the values to
+select we could have of course used
+
+ align:start position:0%
+select we could have of course used
+ 
+
+ align:start position:0%
+select we could have of course used
+starts with in the rows just say starts
+
+ align:start position:0%
+starts with in the rows just say starts
+ 
+
+ align:start position:0%
+starts with in the rows just say starts
+with o and G I just happened to label
+
+ align:start position:0%
+with o and G I just happened to label
+ 
+
+ align:start position:0%
+with o and G I just happened to label
+all my rows that orange rows began with
+
+ align:start position:0%
+all my rows that orange rows began with
+ 
+
+ align:start position:0%
+all my rows that orange rows began with
+O and green rows begin with G so we can
+
+ align:start position:0%
+O and green rows begin with G so we can
+ 
+
+ align:start position:0%
+O and green rows begin with G so we can
+do starts with OG so that's example of
+
+ align:start position:0%
+do starts with OG so that's example of
+ 
+
+ align:start position:0%
+do starts with OG so that's example of
+those two range queries being done at
+
+ align:start position:0%
+those two range queries being done at
+ 
+
+ align:start position:0%
+those two range queries being done at
+the same time and so that gives us EOG
+
+ align:start position:0%
+the same time and so that gives us EOG
+ 
+
+ align:start position:0%
+the same time and so that gives us EOG
+and again we can see now we
+
+ align:start position:0%
+and again we can see now we
+ 
+
+ align:start position:0%
+and again we can see now we
+get the orange and green row
+
+ align:start position:0%
+get the orange and green row
+ 
+
+ align:start position:0%
+get the orange and green row
+so that just shows you that and then
+
+ align:start position:0%
+so that just shows you that and then
+ 
+
+ align:start position:0%
+so that just shows you that and then
+we'll wrap up here with the last example
+
+ align:start position:0%
+we'll wrap up here with the last example
+ 
+
+ align:start position:0%
+we'll wrap up here with the last example
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ea3 all right now we get to do some
+
+ align:start position:0%
+ea3 all right now we get to do some
+ 
+
+ align:start position:0%
+ea3 all right now we get to do some
+really fun stuff again we're reading in
+
+ align:start position:0%
+really fun stuff again we're reading in
+ 
+
+ align:start position:0%
+really fun stuff again we're reading in
+Reading in our data set converting just
+
+ align:start position:0%
+Reading in our data set converting just
+ 
+
+ align:start position:0%
+Reading in our data set converting just
+getting the
+
+ align:start position:0%
+getting the
+ 
+
+ align:start position:0%
+getting the
+vertices okay and then converting it to
+
+ align:start position:0%
+vertices okay and then converting it to
+ 
+
+ align:start position:0%
+vertices okay and then converting it to
+numeric zeros and ones I'm going to now
+
+ align:start position:0%
+numeric zeros and ones I'm going to now
+ 
+
+ align:start position:0%
+numeric zeros and ones I'm going to now
+just get the orange edges and I'm going
+
+ align:start position:0%
+just get the orange edges and I'm going
+ 
+
+ align:start position:0%
+just get the orange edges and I'm going
+to get the green
+
+ align:start position:0%
+to get the green
+ 
+
+ align:start position:0%
+to get the green
+edges all right and now I'm going to
+
+ align:start position:0%
+edges all right and now I'm going to
+ 
+
+ align:start position:0%
+edges all right and now I'm going to
+essentially do the
+
+ align:start position:0%
+essentially do the
+ 
+
+ align:start position:0%
+essentially do the
+crosscorrelation of the orange and green
+
+ align:start position:0%
+crosscorrelation of the orange and green
+ 
+
+ align:start position:0%
+crosscorrelation of the orange and green
+edges so I'm going to transpose one of
+
+ align:start position:0%
+edges so I'm going to transpose one of
+ 
+
+ align:start position:0%
+edges so I'm going to transpose one of
+them and Matrix multiply with the other
+
+ align:start position:0%
+them and Matrix multiply with the other
+ 
+
+ align:start position:0%
+them and Matrix multiply with the other
+ones we don't do Square in here because
+
+ align:start position:0%
+ones we don't do Square in here because
+ 
+
+ align:start position:0%
+ones we don't do Square in here because
+they're different matrices in fact I
+
+ align:start position:0%
+they're different matrices in fact I
+ 
+
+ align:start position:0%
+they're different matrices in fact I
+would say that people often do the cross
+
+ align:start position:0%
+would say that people often do the cross
+ 
+
+ align:start position:0%
+would say that people often do the cross
+correlation more often than they just
+
+ align:start position:0%
+correlation more often than they just
+ 
+
+ align:start position:0%
+correlation more often than they just
+Square The Matrix with itself you have
+
+ align:start position:0%
+Square The Matrix with itself you have
+ 
+
+ align:start position:0%
+Square The Matrix with itself you have
+one set with another set and you want to
+
+ align:start position:0%
+one set with another set and you want to
+ 
+
+ align:start position:0%
+one set with another set and you want to
+cross-correlate them a very common
+
+ align:start position:0%
+cross-correlate them a very common
+ 
+
+ align:start position:0%
+cross-correlate them a very common
+operation and so that's just transpose
+
+ align:start position:0%
+operation and so that's just transpose
+ 
+
+ align:start position:0%
+operation and so that's just transpose
+you know evg here and that gets
+
+ align:start position:0%
+you know evg here and that gets
+ 
+
+ align:start position:0%
+you know evg here and that gets
+that and as you can see the results of
+
+ align:start position:0%
+that and as you can see the results of
+ 
+
+ align:start position:0%
+that and as you can see the results of
+that inner product was
+
+ align:start position:0%
+that inner product was
+ 
+
+ align:start position:0%
+that inner product was
+empty all right but the result of the
+
+ align:start position:0%
+empty all right but the result of the
+ 
+
+ align:start position:0%
+empty all right but the result of the
+outer product is full so that just and
+
+ align:start position:0%
+outer product is full so that just and
+ 
+
+ align:start position:0%
+outer product is full so that just and
+you guys can think about why that
+
+ align:start position:0%
+you guys can think about why that
+ 
+
+ align:start position:0%
+you guys can think about why that
+is and so this just shows you the uh the
+
+ align:start position:0%
+is and so this just shows you the uh the
+ 
+
+ align:start position:0%
+is and so this just shows you the uh the
+uh the uh common how many um
+
+ align:start position:0%
+uh the uh common how many um
+ 
+
+ align:start position:0%
+uh the uh common how many um
+edges these appeared with
+
+ align:start position:0%
+edges these appeared with
+ 
+
+ align:start position:0%
+edges these appeared with
+together this shows you that there was
+
+ align:start position:0%
+together this shows you that there was
+ 
+
+ align:start position:0%
+together this shows you that there was
+no well you guys can figure that out
+
+ align:start position:0%
+no well you guys can figure that out
+ 
+
+ align:start position:0%
+no well you guys can figure that out
+I'll let you yeah now another thing that
+
+ align:start position:0%
+I'll let you yeah now another thing that
+ 
+
+ align:start position:0%
+I'll let you yeah now another thing that
+we often want to do is basically this
+
+ align:start position:0%
+we often want to do is basically this
+ 
+
+ align:start position:0%
+we often want to do is basically this
+showed us which um edges had common
+
+ align:start position:0%
+showed us which um edges had common
+ 
+
+ align:start position:0%
+showed us which um edges had common
+vertices you know shared vertices
+
+ align:start position:0%
+vertices you know shared vertices
+ 
+
+ align:start position:0%
+vertices you know shared vertices
+together okay but it didn't tell us we
+
+ align:start position:0%
+together okay but it didn't tell us we
+ 
+
+ align:start position:0%
+together okay but it didn't tell us we
+lost we lost the actual vertices we just
+
+ align:start position:0%
+lost we lost the actual vertices we just
+ 
+
+ align:start position:0%
+lost we lost the actual vertices we just
+know that there's three and a lot of
+
+ align:start position:0%
+know that there's three and a lot of
+ 
+
+ align:start position:0%
+know that there's three and a lot of
+times we want them this is sometimes
+
+ align:start position:0%
+times we want them this is sometimes
+ 
+
+ align:start position:0%
+times we want them this is sometimes
+called the pedigree you do a correlation
+
+ align:start position:0%
+called the pedigree you do a correlation
+ 
+
+ align:start position:0%
+called the pedigree you do a correlation
+and then you would like but but you say
+
+ align:start position:0%
+and then you would like but but you say
+ 
+
+ align:start position:0%
+and then you would like but but you say
+these two things are correlated I want
+
+ align:start position:0%
+these two things are correlated I want
+ 
+
+ align:start position:0%
+these two things are correlated I want
+to get the the connector back to the
+
+ align:start position:0%
+to get the the connector back to the
+ 
+
+ align:start position:0%
+to get the the connector back to the
+original record so I can go back to my e
+
+ align:start position:0%
+original record so I can go back to my e
+ 
+
+ align:start position:0%
+original record so I can go back to my e
+Matrix and really find that out and
+
+ align:start position:0%
+Matrix and really find that out and
+ 
+
+ align:start position:0%
+Matrix and really find that out and
+present that as the evidence that these
+
+ align:start position:0%
+present that as the evidence that these
+ 
+
+ align:start position:0%
+present that as the evidence that these
+things are connected together and we
+
+ align:start position:0%
+things are connected together and we
+ 
+
+ align:start position:0%
+things are connected together and we
+don't want to lose that so we have
+
+ align:start position:0%
+don't want to lose that so we have
+ 
+
+ align:start position:0%
+don't want to lose that so we have
+invented special new Matrix
+
+ align:start position:0%
+invented special new Matrix
+ 
+
+ align:start position:0%
+invented special new Matrix
+multiplies in the land of associative
+
+ align:start position:0%
+multiplies in the land of associative
+ 
+
+ align:start position:0%
+multiplies in the land of associative
+arrays one of them we call Cat key mul
+
+ align:start position:0%
+arrays one of them we call Cat key mul
+ 
+
+ align:start position:0%
+arrays one of them we call Cat key mul
+okay okay which if you view the Matrix
+
+ align:start position:0%
+okay okay which if you view the Matrix
+ 
+
+ align:start position:0%
+okay okay which if you view the Matrix
+multiply as sort of there's a key a
+
+ align:start position:0%
+multiply as sort of there's a key a
+ 
+
+ align:start position:0%
+multiply as sort of there's a key a
+common key this row column key that's
+
+ align:start position:0%
+common key this row column key that's
+ 
+
+ align:start position:0%
+common key this row column key that's
+being sort of joined together well we
+
+ align:start position:0%
+being sort of joined together well we
+ 
+
+ align:start position:0%
+being sort of joined together well we
+can preserve that and store that in the
+
+ align:start position:0%
+can preserve that and store that in the
+ 
+
+ align:start position:0%
+can preserve that and store that in the
+value instead of say the count or
+
+ align:start position:0%
+value instead of say the count or
+ 
+
+ align:start position:0%
+value instead of say the count or
+something like that so we do cat key
+
+ align:start position:0%
+something like that so we do cat key
+ 
+
+ align:start position:0%
+something like that so we do cat key
+mole ev0 transpose evg and then when we
+
+ align:start position:0%
+mole ev0 transpose evg and then when we
+ 
+
+ align:start position:0%
+mole ev0 transpose evg and then when we
+display that we not only
+
+ align:start position:0%
+display that we not only
+ 
+
+ align:start position:0%
+display that we not only
+see which edges were connected but we
+
+ align:start position:0%
+see which edges were connected but we
+ 
+
+ align:start position:0%
+see which edges were connected but we
+also have preserved
+
+ align:start position:0%
+also have preserved
+ 
+
+ align:start position:0%
+also have preserved
+the list of the vertices is essentially
+
+ align:start position:0%
+the list of the vertices is essentially
+ 
+
+ align:start position:0%
+the list of the vertices is essentially
+a concatenated list of those keys very
+
+ align:start position:0%
+a concatenated list of those keys very
+ 
+
+ align:start position:0%
+a concatenated list of those keys very
+useful thing
+
+ align:start position:0%
+useful thing
+ 
+
+ align:start position:0%
+useful thing
+um one has to be so very powerful
+
+ align:start position:0%
+um one has to be so very powerful
+ 
+
+ align:start position:0%
+um one has to be so very powerful
+Technique One definitely has to be
+
+ align:start position:0%
+Technique One definitely has to be
+ 
+
+ align:start position:0%
+Technique One definitely has to be
+careful about using this technique if it
+
+ align:start position:0%
+careful about using this technique if it
+ 
+
+ align:start position:0%
+careful about using this technique if it
+generate it's going to generate
+
+ align:start position:0%
+generate it's going to generate
+ 
+
+ align:start position:0%
+generate it's going to generate
+extremely oops extremely long lists here
+
+ align:start position:0%
+extremely oops extremely long lists here
+ 
+
+ align:start position:0%
+extremely oops extremely long lists here
+that can really cause this to behave
+
+ align:start position:0%
+that can really cause this to behave
+ 
+
+ align:start position:0%
+that can really cause this to behave
+very slowly uh in particular one has to
+
+ align:start position:0%
+very slowly uh in particular one has to
+ 
+
+ align:start position:0%
+very slowly uh in particular one has to
+be careful of if you do a cat key mole
+
+ align:start position:0%
+be careful of if you do a cat key mole
+ 
+
+ align:start position:0%
+be careful of if you do a cat key mole
+on a matrix with itself why do you think
+
+ align:start position:0%
+on a matrix with itself why do you think
+ 
+
+ align:start position:0%
+on a matrix with itself why do you think
+you would have to be careful with that
+
+ align:start position:0%
+you would have to be careful with that
+ 
+
+ align:start position:0%
+you would have to be careful with that
+anyone remember that dense diagonal that
+
+ align:start position:0%
+anyone remember that dense diagonal that
+ 
+
+ align:start position:0%
+anyone remember that dense diagonal that
+happened whenever we squared matrices so
+
+ align:start position:0%
+happened whenever we squared matrices so
+ 
+
+ align:start position:0%
+happened whenever we squared matrices so
+that means this thing will have an
+
+ align:start position:0%
+that means this thing will have an
+ 
+
+ align:start position:0%
+that means this thing will have an
+enormous number of entries along the
+
+ align:start position:0%
+enormous number of entries along the
+ 
+
+ align:start position:0%
+enormous number of entries along the
+diagonal so you have to be very careful
+
+ align:start position:0%
+diagonal so you have to be very careful
+ 
+
+ align:start position:0%
+diagonal so you have to be very careful
+when you use this kind of function to
+
+ align:start position:0%
+when you use this kind of function to
+ 
+
+ align:start position:0%
+when you use this kind of function to
+correlate something with itself it's
+
+ align:start position:0%
+correlate something with itself it's
+ 
+
+ align:start position:0%
+correlate something with itself it's
+better to correlate two distinct sets
+
+ align:start position:0%
+better to correlate two distinct sets
+ 
+
+ align:start position:0%
+better to correlate two distinct sets
+because they tend to not have that that
+
+ align:start position:0%
+because they tend to not have that that
+ 
+
+ align:start position:0%
+because they tend to not have that that
+dense diagonal which can be a little bit
+
+ align:start position:0%
+dense diagonal which can be a little bit
+ 
+
+ align:start position:0%
+dense diagonal which can be a little bit
+of a problem there's ways to get around
+
+ align:start position:0%
+of a problem there's ways to get around
+ 
+
+ align:start position:0%
+of a problem there's ways to get around
+that I mean there's hacks and tricks and
+
+ align:start position:0%
+that I mean there's hacks and tricks and
+ 
+
+ align:start position:0%
+that I mean there's hacks and tricks and
+stuff like that but at a certain level
+
+ align:start position:0%
+stuff like that but at a certain level
+ 
+
+ align:start position:0%
+stuff like that but at a certain level
+really dense diagonals I mean you
+
+ align:start position:0%
+really dense diagonals I mean you
+ 
+
+ align:start position:0%
+really dense diagonals I mean you
+essentially be listing every single
+
+ align:start position:0%
+essentially be listing every single
+ 
+
+ align:start position:0%
+essentially be listing every single
+vertex in your data set you could be
+
+ align:start position:0%
+vertex in your data set you could be
+ 
+
+ align:start position:0%
+vertex in your data set you could be
+listing every single vertex in your data
+
+ align:start position:0%
+listing every single vertex in your data
+ 
+
+ align:start position:0%
+listing every single vertex in your data
+set almost every single time you know
+
+ align:start position:0%
+set almost every single time you know
+ 
+
+ align:start position:0%
+set almost every single time you know
+multiple times along the diagonal that
+
+ align:start position:0%
+multiple times along the diagonal that
+ 
+
+ align:start position:0%
+multiple times along the diagonal that
+would be get very very bulky so just a
+
+ align:start position:0%
+would be get very very bulky so just a
+ 
+
+ align:start position:0%
+would be get very very bulky so just a
+little word of caution there and so now
+
+ align:start position:0%
+little word of caution there and so now
+ 
+
+ align:start position:0%
+little word of caution there and so now
+i' I've baited you once but this really
+
+ align:start position:0%
+i' I've baited you once but this really
+ 
+
+ align:start position:0%
+i' I've baited you once but this really
+is the end so um are there any questions
+
+ align:start position:0%
+is the end so um are there any questions
+ 
+
+ align:start position:0%
+is the end so um are there any questions
+on the examples before we cut it off
+
+ align:start position:0%
+on the examples before we cut it off
+ 
+
+ align:start position:0%
+on the examples before we cut it off
+here was there a question back here
+
+ align:start position:0%
+here was there a question back here
+ 
+
+ align:start position:0%
+here was there a question back here
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+no all right great thank you very much I
+
+ align:start position:0%
+no all right great thank you very much I
+ 
+
+ align:start position:0%
+no all right great thank you very much I
+appreciate it and we'll see you next
+
+ align:start position:0%
+appreciate it and we'll see you next
+ 
+
+ align:start position:0%
+appreciate it and we'll see you next
+week and uh again think of a picture
+
+ align:start position:0%
+week and uh again think of a picture
+ 
+
+ align:start position:0%
+week and uh again think of a picture
+draw some lines make an incidence
+
+ align:start position:0%
+draw some lines make an incidence
+ 
+
+ align:start position:0%
+draw some lines make an incidence
+Matrix have fun with
+
+ align:start position:0%
+Matrix have fun with
+ 
+
+ align:start position:0%
+Matrix have fun with
+it compute the degree of your
+
+ align:start position:0%
+it compute the degree of your
+ 
+
+ align:start position:0%
+it compute the degree of your
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+other idea bad idea yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
\ No newline at end of file
diff --git a/6S3BJSsc72Q.txt b/6S3BJSsc72Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..06d4f7424fc2636c0e50c73d6d015d0890e13f9d
--- /dev/null
+++ b/6S3BJSsc72Q.txt
@@ -0,0 +1,3011 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+what I'd like us to do is work on
+
+ align:start position:0%
+what I'd like us to do is work on
+ 
+
+ align:start position:0%
+what I'd like us to do is work on
+understanding Simply Connected regions
+
+ align:start position:0%
+understanding Simply Connected regions
+ 
+
+ align:start position:0%
+understanding Simply Connected regions
+in three dimensions well there's one
+
+ align:start position:0%
+in three dimensions well there's one
+ 
+
+ align:start position:0%
+in three dimensions well there's one
+two-dimensional one but the rest are
+
+ align:start position:0%
+two-dimensional one but the rest are
+ 
+
+ align:start position:0%
+two-dimensional one but the rest are
+three dimensions so what I want you to
+
+ align:start position:0%
+three dimensions so what I want you to
+ 
+
+ align:start position:0%
+three dimensions so what I want you to
+do is for each of the following there
+
+ align:start position:0%
+do is for each of the following there
+ 
+
+ align:start position:0%
+do is for each of the following there
+are six different regions determine
+
+ align:start position:0%
+are six different regions determine
+ 
+
+ align:start position:0%
+are six different regions determine
+whether or not each of them is Simply
+
+ align:start position:0%
+whether or not each of them is Simply
+ 
+
+ align:start position:0%
+whether or not each of them is Simply
+Connected so the first one is R3 the
+
+ align:start position:0%
+Connected so the first one is R3 the
+ 
+
+ align:start position:0%
+Connected so the first one is R3 the
+second one is if I take R3 and I remove
+
+ align:start position:0%
+second one is if I take R3 and I remove
+ 
+
+ align:start position:0%
+second one is if I take R3 and I remove
+the entire Z axis the third one is if I
+
+ align:start position:0%
+the entire Z axis the third one is if I
+ 
+
+ align:start position:0%
+the entire Z axis the third one is if I
+take R3 and I remove zero the fourth one
+
+ align:start position:0%
+take R3 and I remove zero the fourth one
+ 
+
+ align:start position:0%
+take R3 and I remove zero the fourth one
+is if I take R3 and remove a
+
+ align:start position:0%
+is if I take R3 and remove a
+ 
+
+ align:start position:0%
+is if I take R3 and remove a
+circle sorry the fourth yeah the fourth
+
+ align:start position:0%
+circle sorry the fourth yeah the fourth
+ 
+
+ align:start position:0%
+circle sorry the fourth yeah the fourth
+one the fifth one is R2 minus a line
+
+ align:start position:0%
+one the fifth one is R2 minus a line
+ 
+
+ align:start position:0%
+one the fifth one is R2 minus a line
+segment and the sixth one is a solid
+
+ align:start position:0%
+segment and the sixth one is a solid
+ 
+
+ align:start position:0%
+segment and the sixth one is a solid
+Taurus so a solid Taurus is it looks
+
+ align:start position:0%
+Taurus so a solid Taurus is it looks
+ 
+
+ align:start position:0%
+Taurus so a solid Taurus is it looks
+like a donut and it includes the the
+
+ align:start position:0%
+like a donut and it includes the the
+ 
+
+ align:start position:0%
+like a donut and it includes the the
+inside of the donut so hopefully you can
+
+ align:start position:0%
+inside of the donut so hopefully you can
+ 
+
+ align:start position:0%
+inside of the donut so hopefully you can
+see this looks like a donut hopefully to
+
+ align:start position:0%
+see this looks like a donut hopefully to
+ 
+
+ align:start position:0%
+see this looks like a donut hopefully to
+you and it's it's not Hollow it includes
+
+ align:start position:0%
+you and it's it's not Hollow it includes
+ 
+
+ align:start position:0%
+you and it's it's not Hollow it includes
+the inside so what I'd like you to do
+
+ align:start position:0%
+the inside so what I'd like you to do
+ 
+
+ align:start position:0%
+the inside so what I'd like you to do
+again is determine whether or not each
+
+ align:start position:0%
+again is determine whether or not each
+ 
+
+ align:start position:0%
+again is determine whether or not each
+of these regions is Simply Connected and
+
+ align:start position:0%
+of these regions is Simply Connected and
+ 
+
+ align:start position:0%
+of these regions is Simply Connected and
+uh and why don't you pause the video
+
+ align:start position:0%
+uh and why don't you pause the video
+ 
+
+ align:start position:0%
+uh and why don't you pause the video
+while you work on that and then bring
+
+ align:start position:0%
+while you work on that and then bring
+ 
+
+ align:start position:0%
+while you work on that and then bring
+the video back up when you're ready to
+
+ align:start position:0%
+the video back up when you're ready to
+ 
+
+ align:start position:0%
+the video back up when you're ready to
+check your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work okay welcome back so again what
+
+ align:start position:0%
+work okay welcome back so again what
+ 
+
+ align:start position:0%
+work okay welcome back so again what
+we're interested in doing is
+
+ align:start position:0%
+we're interested in doing is
+ 
+
+ align:start position:0%
+we're interested in doing is
+understanding simply connectedness in
+
+ align:start position:0%
+understanding simply connectedness in
+ 
+
+ align:start position:0%
+understanding simply connectedness in
+another dimension we did something
+
+ align:start position:0%
+another dimension we did something
+ 
+
+ align:start position:0%
+another dimension we did something
+already a while back with two dimensions
+
+ align:start position:0%
+already a while back with two dimensions
+ 
+
+ align:start position:0%
+already a while back with two dimensions
+and so now we want to understand it
+
+ align:start position:0%
+and so now we want to understand it
+ 
+
+ align:start position:0%
+and so now we want to understand it
+better in three dimensions so let's
+
+ align:start position:0%
+better in three dimensions so let's
+ 
+
+ align:start position:0%
+better in three dimensions so let's
+let's work through these well I'm not
+
+ align:start position:0%
+let's work through these well I'm not
+ 
+
+ align:start position:0%
+let's work through these well I'm not
+going to write anything down for number
+
+ align:start position:0%
+going to write anything down for number
+ 
+
+ align:start position:0%
+going to write anything down for number
+one because you should already know that
+
+ align:start position:0%
+one because you should already know that
+ 
+
+ align:start position:0%
+one because you should already know that
+R3 is Simply Connected but if you
+
+ align:start position:0%
+R3 is Simply Connected but if you
+ 
+
+ align:start position:0%
+R3 is Simply Connected but if you
+weren't sure about it you could think
+
+ align:start position:0%
+weren't sure about it you could think
+ 
+
+ align:start position:0%
+weren't sure about it you could think
+any any closed curve I draw in R3 I can
+
+ align:start position:0%
+any any closed curve I draw in R3 I can
+ 
+
+ align:start position:0%
+any any closed curve I draw in R3 I can
+certainly get all of the inside of it
+
+ align:start position:0%
+certainly get all of the inside of it
+ 
+
+ align:start position:0%
+certainly get all of the inside of it
+contained in R3 another way to think
+
+ align:start position:0%
+contained in R3 another way to think
+ 
+
+ align:start position:0%
+contained in R3 another way to think
+about it is that I can take that curve
+
+ align:start position:0%
+about it is that I can take that curve
+ 
+
+ align:start position:0%
+about it is that I can take that curve
+and I can collapse it down to a point
+
+ align:start position:0%
+and I can collapse it down to a point
+ 
+
+ align:start position:0%
+and I can collapse it down to a point
+and remain in R3 but let's start on so
+
+ align:start position:0%
+and remain in R3 but let's start on so
+ 
+
+ align:start position:0%
+and remain in R3 but let's start on so
+the first one is an easy yes to Simply
+
+ align:start position:0%
+the first one is an easy yes to Simply
+ 
+
+ align:start position:0%
+the first one is an easy yes to Simply
+connectedness okay so let's start on the
+
+ align:start position:0%
+connectedness okay so let's start on the
+ 
+
+ align:start position:0%
+connectedness okay so let's start on the
+second one and I'm going to draw a
+
+ align:start position:0%
+second one and I'm going to draw a
+ 
+
+ align:start position:0%
+second one and I'm going to draw a
+little picture for us so the second one
+
+ align:start position:0%
+little picture for us so the second one
+ 
+
+ align:start position:0%
+little picture for us so the second one
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+R3 oops R3 I should go this way this is
+
+ align:start position:0%
+R3 oops R3 I should go this way this is
+ 
+
+ align:start position:0%
+R3 oops R3 I should go this way this is
+XYZ but then I remove the entire z-axis
+
+ align:start position:0%
+XYZ but then I remove the entire z-axis
+ 
+
+ align:start position:0%
+XYZ but then I remove the entire z-axis
+so I should make this real dark so we
+
+ align:start position:0%
+so I should make this real dark so we
+ 
+
+ align:start position:0%
+so I should make this real dark so we
+know this stuff
+
+ align:start position:0%
+know this stuff
+ 
+
+ align:start position:0%
+know this stuff
+is we're removing that part from R3 and
+
+ align:start position:0%
+is we're removing that part from R3 and
+ 
+
+ align:start position:0%
+is we're removing that part from R3 and
+I'm removing it all the way up to minus
+
+ align:start position:0%
+I'm removing it all the way up to minus
+ 
+
+ align:start position:0%
+I'm removing it all the way up to minus
+minus Infinity in the Z Direction and
+
+ align:start position:0%
+minus Infinity in the Z Direction and
+ 
+
+ align:start position:0%
+minus Infinity in the Z Direction and
+plus infinity in the Z Direction now the
+
+ align:start position:0%
+plus infinity in the Z Direction now the
+ 
+
+ align:start position:0%
+plus infinity in the Z Direction now the
+question is can I find any closed curve
+
+ align:start position:0%
+question is can I find any closed curve
+ 
+
+ align:start position:0%
+question is can I find any closed curve
+that when I try and try and compress
+
+ align:start position:0%
+that when I try and try and compress
+ 
+
+ align:start position:0%
+that when I try and try and compress
+that closed curve down to a point I
+
+ align:start position:0%
+that closed curve down to a point I
+ 
+
+ align:start position:0%
+that closed curve down to a point I
+can't do it while remaining inside this
+
+ align:start position:0%
+can't do it while remaining inside this
+ 
+
+ align:start position:0%
+can't do it while remaining inside this
+region that is all of our three minus
+
+ align:start position:0%
+region that is all of our three minus
+ 
+
+ align:start position:0%
+region that is all of our three minus
+the z-axis and the answer is there is a
+
+ align:start position:0%
+the z-axis and the answer is there is a
+ 
+
+ align:start position:0%
+the z-axis and the answer is there is a
+whole family of curves that do this if I
+
+ align:start position:0%
+whole family of curves that do this if I
+ 
+
+ align:start position:0%
+whole family of curves that do this if I
+take a curve that goes around the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z-axis you'll notice that there's
+
+ align:start position:0%
+z-axis you'll notice that there's
+ 
+
+ align:start position:0%
+z-axis you'll notice that there's
+something on the inside of it regardless
+
+ align:start position:0%
+something on the inside of it regardless
+ 
+
+ align:start position:0%
+something on the inside of it regardless
+of you know if I slide it up or down
+
+ align:start position:0%
+of you know if I slide it up or down
+ 
+
+ align:start position:0%
+of you know if I slide it up or down
+there's a point on the inside of this
+
+ align:start position:0%
+there's a point on the inside of this
+ 
+
+ align:start position:0%
+there's a point on the inside of this
+this curve that is not in the region I'm
+
+ align:start position:0%
+this curve that is not in the region I'm
+ 
+
+ align:start position:0%
+this curve that is not in the region I'm
+interested in the region again is R3
+
+ align:start position:0%
+interested in the region again is R3
+ 
+
+ align:start position:0%
+interested in the region again is R3
+minus the z-axis so there's two ways to
+
+ align:start position:0%
+minus the z-axis so there's two ways to
+ 
+
+ align:start position:0%
+minus the z-axis so there's two ways to
+think about this you can think about you
+
+ align:start position:0%
+think about this you can think about you
+ 
+
+ align:start position:0%
+think about this you can think about you
+know if I were to take this curve and I
+
+ align:start position:0%
+know if I were to take this curve and I
+ 
+
+ align:start position:0%
+know if I were to take this curve and I
+were to to put a surface across this
+
+ align:start position:0%
+were to to put a surface across this
+ 
+
+ align:start position:0%
+were to to put a surface across this
+curve so it was like a disc there would
+
+ align:start position:0%
+curve so it was like a disc there would
+ 
+
+ align:start position:0%
+curve so it was like a disc there would
+be a point on the z-axis that would
+
+ align:start position:0%
+be a point on the z-axis that would
+ 
+
+ align:start position:0%
+be a point on the z-axis that would
+intersect it or you can think about it
+
+ align:start position:0%
+intersect it or you can think about it
+ 
+
+ align:start position:0%
+intersect it or you can think about it
+as saying I have this curve and if I try
+
+ align:start position:0%
+as saying I have this curve and if I try
+ 
+
+ align:start position:0%
+as saying I have this curve and if I try
+and squeeze it down to to a to as small
+
+ align:start position:0%
+and squeeze it down to to a to as small
+ 
+
+ align:start position:0%
+and squeeze it down to to a to as small
+as I can get it I can't get it as small
+
+ align:start position:0%
+as I can get it I can't get it as small
+ 
+
+ align:start position:0%
+as I can get it I can't get it as small
+as I want without hitting the Z axis at
+
+ align:start position:0%
+as I want without hitting the Z axis at
+ 
+
+ align:start position:0%
+as I want without hitting the Z axis at
+some point I'm always going to have the
+
+ align:start position:0%
+some point I'm always going to have the
+ 
+
+ align:start position:0%
+some point I'm always going to have the
+z-axis is kind of in the way
+
+ align:start position:0%
+z-axis is kind of in the way
+ 
+
+ align:start position:0%
+z-axis is kind of in the way
+right now uh number three is a little
+
+ align:start position:0%
+right now uh number three is a little
+ 
+
+ align:start position:0%
+right now uh number three is a little
+different situation because number three
+
+ align:start position:0%
+different situation because number three
+ 
+
+ align:start position:0%
+different situation because number three
+I take this exact same picture but
+
+ align:start position:0%
+I take this exact same picture but
+ 
+
+ align:start position:0%
+I take this exact same picture but
+instead of removing the whole z- axis I
+
+ align:start position:0%
+instead of removing the whole z- axis I
+ 
+
+ align:start position:0%
+instead of removing the whole z- axis I
+just remove the origin so let me try and
+
+ align:start position:0%
+just remove the origin so let me try and
+ 
+
+ align:start position:0%
+just remove the origin so let me try and
+draw a picture of
+
+ align:start position:0%
+draw a picture of
+ 
+
+ align:start position:0%
+draw a picture of
+that so I'm going to make this there's a
+
+ align:start position:0%
+that so I'm going to make this there's a
+ 
+
+ align:start position:0%
+that so I'm going to make this there's a
+big open circle at the origin that's not
+
+ align:start position:0%
+big open circle at the origin that's not
+ 
+
+ align:start position:0%
+big open circle at the origin that's not
+included in in our domain in our
+
+ align:start position:0%
+included in in our domain in our
+ 
+
+ align:start position:0%
+included in in our domain in our
+region so our region is all of our three
+
+ align:start position:0%
+region so our region is all of our three
+ 
+
+ align:start position:0%
+region so our region is all of our three
+except the origin
+
+ align:start position:0%
+except the origin
+ 
+
+ align:start position:0%
+except the origin
+and in two-dimensional space this was
+
+ align:start position:0%
+and in two-dimensional space this was
+ 
+
+ align:start position:0%
+and in two-dimensional space this was
+not Simply Connected but in
+
+ align:start position:0%
+not Simply Connected but in
+ 
+
+ align:start position:0%
+not Simply Connected but in
+three-dimensional space it is simply
+
+ align:start position:0%
+three-dimensional space it is simply
+ 
+
+ align:start position:0%
+three-dimensional space it is simply
+connected so this is a little different
+
+ align:start position:0%
+connected so this is a little different
+ 
+
+ align:start position:0%
+connected so this is a little different
+situation than what you had previously
+
+ align:start position:0%
+situation than what you had previously
+ 
+
+ align:start position:0%
+situation than what you had previously
+and so the idea is here if I take a
+
+ align:start position:0%
+and so the idea is here if I take a
+ 
+
+ align:start position:0%
+and so the idea is here if I take a
+curve even if I take a curve that's kind
+
+ align:start position:0%
+curve even if I take a curve that's kind
+ 
+
+ align:start position:0%
+curve even if I take a curve that's kind
+of sitting in the XY plane that goes
+
+ align:start position:0%
+of sitting in the XY plane that goes
+ 
+
+ align:start position:0%
+of sitting in the XY plane that goes
+around the origin the point is I can
+
+ align:start position:0%
+around the origin the point is I can
+ 
+
+ align:start position:0%
+around the origin the point is I can
+keep this curve in three-dimensional
+
+ align:start position:0%
+keep this curve in three-dimensional
+ 
+
+ align:start position:0%
+keep this curve in three-dimensional
+space and I can wiggle it around so that
+
+ align:start position:0%
+space and I can wiggle it around so that
+ 
+
+ align:start position:0%
+space and I can wiggle it around so that
+I can shrink it down to a point and the
+
+ align:start position:0%
+I can shrink it down to a point and the
+ 
+
+ align:start position:0%
+I can shrink it down to a point and the
+origin doesn't get in the way it doesn't
+
+ align:start position:0%
+origin doesn't get in the way it doesn't
+ 
+
+ align:start position:0%
+origin doesn't get in the way it doesn't
+keep me from doing that okay it doesn't
+
+ align:start position:0%
+keep me from doing that okay it doesn't
+ 
+
+ align:start position:0%
+keep me from doing that okay it doesn't
+keep me from doing that so this actually
+
+ align:start position:0%
+keep me from doing that so this actually
+ 
+
+ align:start position:0%
+keep me from doing that so this actually
+this region even though in
+
+ align:start position:0%
+this region even though in
+ 
+
+ align:start position:0%
+this region even though in
+two-dimensional space it was not Simply
+
+ align:start position:0%
+two-dimensional space it was not Simply
+ 
+
+ align:start position:0%
+two-dimensional space it was not Simply
+Connected in threedimensional space it
+
+ align:start position:0%
+Connected in threedimensional space it
+ 
+
+ align:start position:0%
+Connected in threedimensional space it
+is and let's see if we understand the
+
+ align:start position:0%
+is and let's see if we understand the
+ 
+
+ align:start position:0%
+is and let's see if we understand the
+difference the difference is in
+
+ align:start position:0%
+difference the difference is in
+ 
+
+ align:start position:0%
+difference the difference is in
+two-dimensional space if I drew a curve
+
+ align:start position:0%
+two-dimensional space if I drew a curve
+ 
+
+ align:start position:0%
+two-dimensional space if I drew a curve
+on the XY plane and I around the origin
+
+ align:start position:0%
+on the XY plane and I around the origin
+ 
+
+ align:start position:0%
+on the XY plane and I around the origin
+and I wanted to squish it down to a
+
+ align:start position:0%
+and I wanted to squish it down to a
+ 
+
+ align:start position:0%
+and I wanted to squish it down to a
+point the only way to do that would be
+
+ align:start position:0%
+point the only way to do that would be
+ 
+
+ align:start position:0%
+point the only way to do that would be
+to bring the curve somehow through the
+
+ align:start position:0%
+to bring the curve somehow through the
+ 
+
+ align:start position:0%
+to bring the curve somehow through the
+origin right I would be stuck having to
+
+ align:start position:0%
+origin right I would be stuck having to
+ 
+
+ align:start position:0%
+origin right I would be stuck having to
+pass the curve through the origin to
+
+ align:start position:0%
+pass the curve through the origin to
+ 
+
+ align:start position:0%
+pass the curve through the origin to
+shrink it down to a point
+
+ align:start position:0%
+shrink it down to a point
+ 
+
+ align:start position:0%
+shrink it down to a point
+but in three space I have another
+
+ align:start position:0%
+but in three space I have another
+ 
+
+ align:start position:0%
+but in three space I have another
+dimension so a curve that sits on the XY
+
+ align:start position:0%
+dimension so a curve that sits on the XY
+ 
+
+ align:start position:0%
+dimension so a curve that sits on the XY
+plane I can just kind of lift it a
+
+ align:start position:0%
+plane I can just kind of lift it a
+ 
+
+ align:start position:0%
+plane I can just kind of lift it a
+little bit away from the origin and then
+
+ align:start position:0%
+little bit away from the origin and then
+ 
+
+ align:start position:0%
+little bit away from the origin and then
+I can shink it down to a point without
+
+ align:start position:0%
+I can shink it down to a point without
+ 
+
+ align:start position:0%
+I can shink it down to a point without
+without getting the origin getting in
+
+ align:start position:0%
+without getting the origin getting in
+ 
+
+ align:start position:0%
+without getting the origin getting in
+the way so having that extra Dimension
+
+ align:start position:0%
+the way so having that extra Dimension
+ 
+
+ align:start position:0%
+the way so having that extra Dimension
+means even though I remove one point
+
+ align:start position:0%
+means even though I remove one point
+ 
+
+ align:start position:0%
+means even though I remove one point
+it's still actually a Simply Connected
+
+ align:start position:0%
+it's still actually a Simply Connected
+ 
+
+ align:start position:0%
+it's still actually a Simply Connected
+region so this is maybe this is the
+
+ align:start position:0%
+region so this is maybe this is the
+ 
+
+ align:start position:0%
+region so this is maybe this is the
+first place we see that the third three
+
+ align:start position:0%
+first place we see that the third three
+ 
+
+ align:start position:0%
+first place we see that the third three
+dimensions we have a different case than
+
+ align:start position:0%
+dimensions we have a different case than
+ 
+
+ align:start position:0%
+dimensions we have a different case than
+we had uh in two Dimensions removing the
+
+ align:start position:0%
+we had uh in two Dimensions removing the
+ 
+
+ align:start position:0%
+we had uh in two Dimensions removing the
+same kind of object so I realize now I
+
+ align:start position:0%
+same kind of object so I realize now I
+ 
+
+ align:start position:0%
+same kind of object so I realize now I
+haven't been writing down whether these
+
+ align:start position:0%
+haven't been writing down whether these
+ 
+
+ align:start position:0%
+haven't been writing down whether these
+are Simply Connected or or not so I
+
+ align:start position:0%
+are Simply Connected or or not so I
+ 
+
+ align:start position:0%
+are Simply Connected or or not so I
+should write down this as Simply
+
+ align:start position:0%
+should write down this as Simply
+ 
+
+ align:start position:0%
+should write down this as Simply
+Connected and maybe for number two I
+
+ align:start position:0%
+Connected and maybe for number two I
+ 
+
+ align:start position:0%
+Connected and maybe for number two I
+should go back and formally right you
+
+ align:start position:0%
+should go back and formally right you
+ 
+
+ align:start position:0%
+should go back and formally right you
+know not simply connecting so that we
+
+ align:start position:0%
+know not simply connecting so that we
+ 
+
+ align:start position:0%
+know not simply connecting so that we
+have this for
+
+ align:start position:0%
+have this for
+ 
+
+ align:start position:0%
+have this for
+posterity now the fourth one is R3 minus
+
+ align:start position:0%
+posterity now the fourth one is R3 minus
+ 
+
+ align:start position:0%
+posterity now the fourth one is R3 minus
+a circle so let me see if I can draw a
+
+ align:start position:0%
+a circle so let me see if I can draw a
+ 
+
+ align:start position:0%
+a circle so let me see if I can draw a
+picture of
+
+ align:start position:0%
+picture of
+ 
+
+ align:start position:0%
+picture of
+that and the circle it doesn't really
+
+ align:start position:0%
+that and the circle it doesn't really
+ 
+
+ align:start position:0%
+that and the circle it doesn't really
+matter where it
+
+ align:start position:0%
+matter where it
+ 
+
+ align:start position:0%
+matter where it
+is I'm just going to draw one
+
+ align:start position:0%
+is I'm just going to draw one
+ 
+
+ align:start position:0%
+is I'm just going to draw one
+somewhere so I'll draw a circle say
+
+ align:start position:0%
+somewhere so I'll draw a circle say
+ 
+
+ align:start position:0%
+somewhere so I'll draw a circle say
+here's my circle so everything is in my
+
+ align:start position:0%
+here's my circle so everything is in my
+ 
+
+ align:start position:0%
+here's my circle so everything is in my
+region except this circle and the
+
+ align:start position:0%
+region except this circle and the
+ 
+
+ align:start position:0%
+region except this circle and the
+question is is it Simply Connected and
+
+ align:start position:0%
+question is is it Simply Connected and
+ 
+
+ align:start position:0%
+question is is it Simply Connected and
+the answer is no the region is not
+
+ align:start position:0%
+the answer is no the region is not
+ 
+
+ align:start position:0%
+the answer is no the region is not
+Simply Connected because of one
+
+ align:start position:0%
+Simply Connected because of one
+ 
+
+ align:start position:0%
+Simply Connected because of one
+particular problem it's actually the
+
+ align:start position:0%
+particular problem it's actually the
+ 
+
+ align:start position:0%
+particular problem it's actually the
+same kind of problem you have when you
+
+ align:start position:0%
+same kind of problem you have when you
+ 
+
+ align:start position:0%
+same kind of problem you have when you
+remove the z-axis and that is if I draw
+
+ align:start position:0%
+remove the z-axis and that is if I draw
+ 
+
+ align:start position:0%
+remove the z-axis and that is if I draw
+a curve that goes around this
+
+ align:start position:0%
+a curve that goes around this
+ 
+
+ align:start position:0%
+a curve that goes around this
+circle right any curve that goes around
+
+ align:start position:0%
+circle right any curve that goes around
+ 
+
+ align:start position:0%
+circle right any curve that goes around
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+circle notice that any way I try and
+
+ align:start position:0%
+circle notice that any way I try and
+ 
+
+ align:start position:0%
+circle notice that any way I try and
+move this curve curve and and shrink it
+
+ align:start position:0%
+move this curve curve and and shrink it
+ 
+
+ align:start position:0%
+move this curve curve and and shrink it
+down to a point this circle is going to
+
+ align:start position:0%
+down to a point this circle is going to
+ 
+
+ align:start position:0%
+down to a point this circle is going to
+get in the way for the same reason that
+
+ align:start position:0%
+get in the way for the same reason that
+ 
+
+ align:start position:0%
+get in the way for the same reason that
+the z-axis got in the way because this
+
+ align:start position:0%
+the z-axis got in the way because this
+ 
+
+ align:start position:0%
+the z-axis got in the way because this
+circle is closed I can't like Slide the
+
+ align:start position:0%
+circle is closed I can't like Slide the
+ 
+
+ align:start position:0%
+circle is closed I can't like Slide the
+the the curve I'm interested in away
+
+ align:start position:0%
+the the curve I'm interested in away
+ 
+
+ align:start position:0%
+the the curve I'm interested in away
+from the away from the circle and then
+
+ align:start position:0%
+from the away from the circle and then
+ 
+
+ align:start position:0%
+from the away from the circle and then
+shrink it down okay there's there's some
+
+ align:start position:0%
+shrink it down okay there's there's some
+ 
+
+ align:start position:0%
+shrink it down okay there's there's some
+sort of obstruction right here and so
+
+ align:start position:0%
+sort of obstruction right here and so
+ 
+
+ align:start position:0%
+sort of obstruction right here and so
+it's fundamentally different than the
+
+ align:start position:0%
+it's fundamentally different than the
+ 
+
+ align:start position:0%
+it's fundamentally different than the
+case where we just had the origin
+
+ align:start position:0%
+case where we just had the origin
+ 
+
+ align:start position:0%
+case where we just had the origin
+because we could take any curve and we
+
+ align:start position:0%
+because we could take any curve and we
+ 
+
+ align:start position:0%
+because we could take any curve and we
+could move it away from the origin and
+
+ align:start position:0%
+could move it away from the origin and
+ 
+
+ align:start position:0%
+could move it away from the origin and
+then shrink it down to a point and the
+
+ align:start position:0%
+then shrink it down to a point and the
+ 
+
+ align:start position:0%
+then shrink it down to a point and the
+origin didn't get in the way but here
+
+ align:start position:0%
+origin didn't get in the way but here
+ 
+
+ align:start position:0%
+origin didn't get in the way but here
+anywhere I try and move this curve it's
+
+ align:start position:0%
+anywhere I try and move this curve it's
+ 
+
+ align:start position:0%
+anywhere I try and move this curve it's
+going to have to it's going to have to
+
+ align:start position:0%
+going to have to it's going to have to
+ 
+
+ align:start position:0%
+going to have to it's going to have to
+hit the circle if I want to move it away
+
+ align:start position:0%
+hit the circle if I want to move it away
+ 
+
+ align:start position:0%
+hit the circle if I want to move it away
+so I can shrink it to a point in my
+
+ align:start position:0%
+so I can shrink it to a point in my
+ 
+
+ align:start position:0%
+so I can shrink it to a point in my
+region so this circle is kind of
+
+ align:start position:0%
+region so this circle is kind of
+ 
+
+ align:start position:0%
+region so this circle is kind of
+preventing me from from shrinking it
+
+ align:start position:0%
+preventing me from from shrinking it
+ 
+
+ align:start position:0%
+preventing me from from shrinking it
+down okay and then there are two more
+
+ align:start position:0%
+down okay and then there are two more
+ 
+
+ align:start position:0%
+down okay and then there are two more
+the fifth one is R2 minus a line
+
+ align:start position:0%
+the fifth one is R2 minus a line
+ 
+
+ align:start position:0%
+the fifth one is R2 minus a line
+segment so now we're in two- dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space okay and let me just pick a
+
+ align:start position:0%
+space okay and let me just pick a
+ 
+
+ align:start position:0%
+space okay and let me just pick a
+segment
+
+ align:start position:0%
+segment
+ 
+
+ align:start position:0%
+segment
+okay now this one is interesting oops
+
+ align:start position:0%
+okay now this one is interesting oops
+ 
+
+ align:start position:0%
+okay now this one is interesting oops
+again I did it I forgot to write whether
+
+ align:start position:0%
+again I did it I forgot to write whether
+ 
+
+ align:start position:0%
+again I did it I forgot to write whether
+it's Simply Connected or not let me come
+
+ align:start position:0%
+it's Simply Connected or not let me come
+ 
+
+ align:start position:0%
+it's Simply Connected or not let me come
+back over to four for posterity not
+
+ align:start position:0%
+back over to four for posterity not
+ 
+
+ align:start position:0%
+back over to four for posterity not
+Simply Connected okay sorry about that
+
+ align:start position:0%
+Simply Connected okay sorry about that
+ 
+
+ align:start position:0%
+Simply Connected okay sorry about that
+the fifth
+
+ align:start position:0%
+the fifth
+ 
+
+ align:start position:0%
+the fifth
+one because I'm in two Dimensions it's
+
+ align:start position:0%
+one because I'm in two Dimensions it's
+ 
+
+ align:start position:0%
+one because I'm in two Dimensions it's
+going to be not Simply Connected but if
+
+ align:start position:0%
+going to be not Simply Connected but if
+ 
+
+ align:start position:0%
+going to be not Simply Connected but if
+I add a third dimension it would become
+
+ align:start position:0%
+I add a third dimension it would become
+ 
+
+ align:start position:0%
+I add a third dimension it would become
+Simply Connected so I want to I want to
+
+ align:start position:0%
+Simply Connected so I want to I want to
+ 
+
+ align:start position:0%
+Simply Connected so I want to I want to
+explain why it's not Simply Connected
+
+ align:start position:0%
+explain why it's not Simply Connected
+ 
+
+ align:start position:0%
+explain why it's not Simply Connected
+here and then I want to show you why in
+
+ align:start position:0%
+here and then I want to show you why in
+ 
+
+ align:start position:0%
+here and then I want to show you why in
+a third dimension it it become Simply
+
+ align:start position:0%
+a third dimension it it become Simply
+ 
+
+ align:start position:0%
+a third dimension it it become Simply
+Connected okay the problem curves are
+
+ align:start position:0%
+Connected okay the problem curves are
+ 
+
+ align:start position:0%
+Connected okay the problem curves are
+the curves that do this that go around
+
+ align:start position:0%
+the curves that do this that go around
+ 
+
+ align:start position:0%
+the curves that do this that go around
+this line
+
+ align:start position:0%
+this line
+ 
+
+ align:start position:0%
+this line
+segment because notice if I want to try
+
+ align:start position:0%
+segment because notice if I want to try
+ 
+
+ align:start position:0%
+segment because notice if I want to try
+and contract this curve down to a point
+
+ align:start position:0%
+and contract this curve down to a point
+ 
+
+ align:start position:0%
+and contract this curve down to a point
+and I don't want to intersect that line
+
+ align:start position:0%
+and I don't want to intersect that line
+ 
+
+ align:start position:0%
+and I don't want to intersect that line
+segment in order to do it I actually
+
+ align:start position:0%
+segment in order to do it I actually
+ 
+
+ align:start position:0%
+segment in order to do it I actually
+have to move it away from the line
+
+ align:start position:0%
+have to move it away from the line
+ 
+
+ align:start position:0%
+have to move it away from the line
+segment I'd have to pass through the
+
+ align:start position:0%
+segment I'd have to pass through the
+ 
+
+ align:start position:0%
+segment I'd have to pass through the
+line segment at some point this curve
+
+ align:start position:0%
+line segment at some point this curve
+ 
+
+ align:start position:0%
+line segment at some point this curve
+would intersect that segment in order to
+
+ align:start position:0%
+would intersect that segment in order to
+ 
+
+ align:start position:0%
+would intersect that segment in order to
+be able to shrink it to a point in a
+
+ align:start position:0%
+be able to shrink it to a point in a
+ 
+
+ align:start position:0%
+be able to shrink it to a point in a
+region in the region I'm interested in
+
+ align:start position:0%
+region in the region I'm interested in
+ 
+
+ align:start position:0%
+region in the region I'm interested in
+so this
+
+ align:start position:0%
+so this
+ 
+
+ align:start position:0%
+so this
+this segment is sort of getting in the
+
+ align:start position:0%
+this segment is sort of getting in the
+ 
+
+ align:start position:0%
+this segment is sort of getting in the
+way we can think of it that way of
+
+ align:start position:0%
+way we can think of it that way of
+ 
+
+ align:start position:0%
+way we can think of it that way of
+allowing me to contract this down to a
+
+ align:start position:0%
+allowing me to contract this down to a
+ 
+
+ align:start position:0%
+allowing me to contract this down to a
+point actually also when we talked about
+
+ align:start position:0%
+point actually also when we talked about
+ 
+
+ align:start position:0%
+point actually also when we talked about
+simply connectedness in two Dimensions
+
+ align:start position:0%
+simply connectedness in two Dimensions
+ 
+
+ align:start position:0%
+simply connectedness in two Dimensions
+it was easier because we could say if we
+
+ align:start position:0%
+it was easier because we could say if we
+ 
+
+ align:start position:0%
+it was easier because we could say if we
+take any curve and we look at the the uh
+
+ align:start position:0%
+take any curve and we look at the the uh
+ 
+
+ align:start position:0%
+take any curve and we look at the the uh
+disc that's spanned by this curve so we
+
+ align:start position:0%
+disc that's spanned by this curve so we
+ 
+
+ align:start position:0%
+disc that's spanned by this curve so we
+say or it's the boundary of this curve
+
+ align:start position:0%
+say or it's the boundary of this curve
+ 
+
+ align:start position:0%
+say or it's the boundary of this curve
+we look at the region the curve
+
+ align:start position:0%
+we look at the region the curve
+ 
+
+ align:start position:0%
+we look at the region the curve
+encloses notice that this segment is in
+
+ align:start position:0%
+encloses notice that this segment is in
+ 
+
+ align:start position:0%
+encloses notice that this segment is in
+that region and there's no way of
+
+ align:start position:0%
+that region and there's no way of
+ 
+
+ align:start position:0%
+that region and there's no way of
+drawing this kind of curve without the
+
+ align:start position:0%
+drawing this kind of curve without the
+ 
+
+ align:start position:0%
+drawing this kind of curve without the
+segment being in that region
+
+ align:start position:0%
+segment being in that region
+ 
+
+ align:start position:0%
+segment being in that region
+and that's how we know it's not Simply
+
+ align:start position:0%
+and that's how we know it's not Simply
+ 
+
+ align:start position:0%
+and that's how we know it's not Simply
+Connected now in three dimensions what
+
+ align:start position:0%
+Connected now in three dimensions what
+ 
+
+ align:start position:0%
+Connected now in three dimensions what
+happens what if I took this exact same
+
+ align:start position:0%
+happens what if I took this exact same
+ 
+
+ align:start position:0%
+happens what if I took this exact same
+picture and I just made the z-axis come
+
+ align:start position:0%
+picture and I just made the z-axis come
+ 
+
+ align:start position:0%
+picture and I just made the z-axis come
+out from the board why is that suddenly
+
+ align:start position:0%
+out from the board why is that suddenly
+ 
+
+ align:start position:0%
+out from the board why is that suddenly
+Simply Connected whereas in the
+
+ align:start position:0%
+Simply Connected whereas in the
+ 
+
+ align:start position:0%
+Simply Connected whereas in the
+two-dimensional case it's not and the
+
+ align:start position:0%
+two-dimensional case it's not and the
+ 
+
+ align:start position:0%
+two-dimensional case it's not and the
+reason is because this same picture I
+
+ align:start position:0%
+reason is because this same picture I
+ 
+
+ align:start position:0%
+reason is because this same picture I
+could take this same curve and I could
+
+ align:start position:0%
+could take this same curve and I could
+ 
+
+ align:start position:0%
+could take this same curve and I could
+take this sort of shaded thing and I
+
+ align:start position:0%
+take this sort of shaded thing and I
+ 
+
+ align:start position:0%
+take this sort of shaded thing and I
+could push the Shaded thing out of the
+
+ align:start position:0%
+could push the Shaded thing out of the
+ 
+
+ align:start position:0%
+could push the Shaded thing out of the
+XY plane and so I'd still have the same
+
+ align:start position:0%
+XY plane and so I'd still have the same
+ 
+
+ align:start position:0%
+XY plane and so I'd still have the same
+boundary curve but I'd have the Shaded
+
+ align:start position:0%
+boundary curve but I'd have the Shaded
+ 
+
+ align:start position:0%
+boundary curve but I'd have the Shaded
+portion not hitting the segment and so I
+
+ align:start position:0%
+portion not hitting the segment and so I
+ 
+
+ align:start position:0%
+portion not hitting the segment and so I
+can find some surface with this boundary
+
+ align:start position:0%
+can find some surface with this boundary
+ 
+
+ align:start position:0%
+can find some surface with this boundary
+that doesn't have this segment in in the
+
+ align:start position:0%
+that doesn't have this segment in in the
+ 
+
+ align:start position:0%
+that doesn't have this segment in in the
+interior of the surface and that's
+
+ align:start position:0%
+interior of the surface and that's
+ 
+
+ align:start position:0%
+interior of the surface and that's
+another way of thinking about simply
+
+ align:start position:0%
+another way of thinking about simply
+ 
+
+ align:start position:0%
+another way of thinking about simply
+connectedness so in the two-dimensional
+
+ align:start position:0%
+connectedness so in the two-dimensional
+ 
+
+ align:start position:0%
+connectedness so in the two-dimensional
+case it is not Simply
+
+ align:start position:0%
+case it is not Simply
+ 
+
+ align:start position:0%
+case it is not Simply
+Connected but if I were to add a third
+
+ align:start position:0%
+Connected but if I were to add a third
+ 
+
+ align:start position:0%
+Connected but if I were to add a third
+dimension this region would become
+
+ align:start position:0%
+dimension this region would become
+ 
+
+ align:start position:0%
+dimension this region would become
+Simply Connected okay because I would
+
+ align:start position:0%
+Simply Connected okay because I would
+ 
+
+ align:start position:0%
+Simply Connected okay because I would
+have no problem with finding for any
+
+ align:start position:0%
+have no problem with finding for any
+ 
+
+ align:start position:0%
+have no problem with finding for any
+curve finding some surface that had that
+
+ align:start position:0%
+curve finding some surface that had that
+ 
+
+ align:start position:0%
+curve finding some surface that had that
+curve as a boundary that didn't
+
+ align:start position:0%
+curve as a boundary that didn't
+ 
+
+ align:start position:0%
+curve as a boundary that didn't
+intersect this segment so I could keep
+
+ align:start position:0%
+intersect this segment so I could keep
+ 
+
+ align:start position:0%
+intersect this segment so I could keep
+the the surface in the region I was
+
+ align:start position:0%
+the the surface in the region I was
+ 
+
+ align:start position:0%
+the the surface in the region I was
+interested in okay so that would tell me
+
+ align:start position:0%
+interested in okay so that would tell me
+ 
+
+ align:start position:0%
+interested in okay so that would tell me
+it was simply connected and then the
+
+ align:start position:0%
+it was simply connected and then the
+ 
+
+ align:start position:0%
+it was simply connected and then the
+last one is a solid Taurus okay and this
+
+ align:start position:0%
+last one is a solid Taurus okay and this
+ 
+
+ align:start position:0%
+last one is a solid Taurus okay and this
+one we might not have dealt with solid
+
+ align:start position:0%
+one we might not have dealt with solid
+ 
+
+ align:start position:0%
+one we might not have dealt with solid
+torai before but this is kind of an
+
+ align:start position:0%
+torai before but this is kind of an
+ 
+
+ align:start position:0%
+torai before but this is kind of an
+interesting problem okay so there are
+
+ align:start position:0%
+interesting problem okay so there are
+ 
+
+ align:start position:0%
+interesting problem okay so there are
+really fundamentally we we say in math
+
+ align:start position:0%
+really fundamentally we we say in math
+ 
+
+ align:start position:0%
+really fundamentally we we say in math
+it's sort of like there are two classes
+
+ align:start position:0%
+it's sort of like there are two classes
+ 
+
+ align:start position:0%
+it's sort of like there are two classes
+of curves that are interesting we won't
+
+ align:start position:0%
+of curves that are interesting we won't
+ 
+
+ align:start position:0%
+of curves that are interesting we won't
+get into a uh the exact terminology of
+
+ align:start position:0%
+get into a uh the exact terminology of
+ 
+
+ align:start position:0%
+get into a uh the exact terminology of
+what's happening but there are sort of
+
+ align:start position:0%
+what's happening but there are sort of
+ 
+
+ align:start position:0%
+what's happening but there are sort of
+two types of Curves on the Taurus one
+
+ align:start position:0%
+two types of Curves on the Taurus one
+ 
+
+ align:start position:0%
+two types of Curves on the Taurus one
+type of curve is the kind that goes
+
+ align:start position:0%
+type of curve is the kind that goes
+ 
+
+ align:start position:0%
+type of curve is the kind that goes
+around right here okay so it loops
+
+ align:start position:0%
+around right here okay so it loops
+ 
+
+ align:start position:0%
+around right here okay so it loops
+around the dut in that in that that
+
+ align:start position:0%
+around the dut in that in that that
+ 
+
+ align:start position:0%
+around the dut in that in that that
+direction but that type of curve is nice
+
+ align:start position:0%
+direction but that type of curve is nice
+ 
+
+ align:start position:0%
+direction but that type of curve is nice
+because notice that if I look at a
+
+ align:start position:0%
+because notice that if I look at a
+ 
+
+ align:start position:0%
+because notice that if I look at a
+surface the surface in there right it's
+
+ align:start position:0%
+surface the surface in there right it's
+ 
+
+ align:start position:0%
+surface the surface in there right it's
+it's all inside the solid Taurus so
+
+ align:start position:0%
+it's all inside the solid Taurus so
+ 
+
+ align:start position:0%
+it's all inside the solid Taurus so
+that's good so that seems like that's a
+
+ align:start position:0%
+that's good so that seems like that's a
+ 
+
+ align:start position:0%
+that's good so that seems like that's a
+curve that that promotes simply
+
+ align:start position:0%
+curve that that promotes simply
+ 
+
+ align:start position:0%
+curve that that promotes simply
+connectedness it seems to imply
+
+ align:start position:0%
+connectedness it seems to imply
+ 
+
+ align:start position:0%
+connectedness it seems to imply
+or it's not it's not telling us it's not
+
+ align:start position:0%
+or it's not it's not telling us it's not
+ 
+
+ align:start position:0%
+or it's not it's not telling us it's not
+Simply Connected we'll say that but
+
+ align:start position:0%
+Simply Connected we'll say that but
+ 
+
+ align:start position:0%
+Simply Connected we'll say that but
+there's another class of Curves on the
+
+ align:start position:0%
+there's another class of Curves on the
+ 
+
+ align:start position:0%
+there's another class of Curves on the
+Taurus and that's the class of curves
+
+ align:start position:0%
+Taurus and that's the class of curves
+ 
+
+ align:start position:0%
+Taurus and that's the class of curves
+that goes around this is a little harder
+
+ align:start position:0%
+that goes around this is a little harder
+ 
+
+ align:start position:0%
+that goes around this is a little harder
+to draw but say around the top but
+
+ align:start position:0%
+to draw but say around the top but
+ 
+
+ align:start position:0%
+to draw but say around the top but
+around the hole okay around the hole now
+
+ align:start position:0%
+around the hole okay around the hole now
+ 
+
+ align:start position:0%
+around the hole okay around the hole now
+any surface I have that I try
+
+ align:start position:0%
+any surface I have that I try
+ 
+
+ align:start position:0%
+any surface I have that I try
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+draw any surface that's going to have
+
+ align:start position:0%
+draw any surface that's going to have
+ 
+
+ align:start position:0%
+draw any surface that's going to have
+that curve as a boundary is at some
+
+ align:start position:0%
+that curve as a boundary is at some
+ 
+
+ align:start position:0%
+that curve as a boundary is at some
+point forced to leave the solid Taurus
+
+ align:start position:0%
+point forced to leave the solid Taurus
+ 
+
+ align:start position:0%
+point forced to leave the solid Taurus
+and the reason is really because of the
+
+ align:start position:0%
+and the reason is really because of the
+ 
+
+ align:start position:0%
+and the reason is really because of the
+hole in the middle right that's really
+
+ align:start position:0%
+hole in the middle right that's really
+ 
+
+ align:start position:0%
+hole in the middle right that's really
+the reason it happens okay and so you
+
+ align:start position:0%
+the reason it happens okay and so you
+ 
+
+ align:start position:0%
+the reason it happens okay and so you
+can sort of see the part right in here
+
+ align:start position:0%
+can sort of see the part right in here
+ 
+
+ align:start position:0%
+can sort of see the part right in here
+is on the surface but it's not in the
+
+ align:start position:0%
+is on the surface but it's not in the
+ 
+
+ align:start position:0%
+is on the surface but it's not in the
+it's not in the solid Taurus so because
+
+ align:start position:0%
+it's not in the solid Taurus so because
+ 
+
+ align:start position:0%
+it's not in the solid Taurus so because
+I have a curve that any surface I draw
+
+ align:start position:0%
+I have a curve that any surface I draw
+ 
+
+ align:start position:0%
+I have a curve that any surface I draw
+that has that curve as a boundary is
+
+ align:start position:0%
+that has that curve as a boundary is
+ 
+
+ align:start position:0%
+that has that curve as a boundary is
+forced to leave the solid T Taurus it's
+
+ align:start position:0%
+forced to leave the solid T Taurus it's
+ 
+
+ align:start position:0%
+forced to leave the solid T Taurus it's
+a non-s Simply Connected region so we
+
+ align:start position:0%
+a non-s Simply Connected region so we
+ 
+
+ align:start position:0%
+a non-s Simply Connected region so we
+say not Simply Connected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I just I'm going to go back
+
+ align:start position:0%
+okay so I just I'm going to go back
+ 
+
+ align:start position:0%
+okay so I just I'm going to go back
+through real quick and just remind us
+
+ align:start position:0%
+through real quick and just remind us
+ 
+
+ align:start position:0%
+through real quick and just remind us
+what was happening and maybe um maybe
+
+ align:start position:0%
+what was happening and maybe um maybe
+ 
+
+ align:start position:0%
+what was happening and maybe um maybe
+use the language I was using at the end
+
+ align:start position:0%
+use the language I was using at the end
+ 
+
+ align:start position:0%
+use the language I was using at the end
+to describe the first examples because
+
+ align:start position:0%
+to describe the first examples because
+ 
+
+ align:start position:0%
+to describe the first examples because
+that might help a little better so let's
+
+ align:start position:0%
+that might help a little better so let's
+ 
+
+ align:start position:0%
+that might help a little better so let's
+go back to the first examples okay in
+
+ align:start position:0%
+go back to the first examples okay in
+ 
+
+ align:start position:0%
+go back to the first examples okay in
+the R3 example again number one we know
+
+ align:start position:0%
+the R3 example again number one we know
+ 
+
+ align:start position:0%
+the R3 example again number one we know
+it's Simply Connected we're not going to
+
+ align:start position:0%
+it's Simply Connected we're not going to
+ 
+
+ align:start position:0%
+it's Simply Connected we're not going to
+worry about it okay but let me draw in
+
+ align:start position:0%
+worry about it okay but let me draw in
+ 
+
+ align:start position:0%
+worry about it okay but let me draw in
+number two Let Me point out maybe if I
+
+ align:start position:0%
+number two Let Me point out maybe if I
+ 
+
+ align:start position:0%
+number two Let Me point out maybe if I
+draw some shaded region this will help
+
+ align:start position:0%
+draw some shaded region this will help
+ 
+
+ align:start position:0%
+draw some shaded region this will help
+us understand it a little bit better
+
+ align:start position:0%
+us understand it a little bit better
+ 
+
+ align:start position:0%
+us understand it a little bit better
+number two establish is not simply
+
+ align:start position:0%
+number two establish is not simply
+ 
+
+ align:start position:0%
+number two establish is not simply
+connected and if you think about it if
+
+ align:start position:0%
+connected and if you think about it if
+ 
+
+ align:start position:0%
+connected and if you think about it if
+you have a curve that goes around the
+
+ align:start position:0%
+you have a curve that goes around the
+ 
+
+ align:start position:0%
+you have a curve that goes around the
+z-axis and you want to look at a surface
+
+ align:start position:0%
+z-axis and you want to look at a surface
+ 
+
+ align:start position:0%
+z-axis and you want to look at a surface
+that has that curve as its
+
+ align:start position:0%
+that has that curve as its
+ 
+
+ align:start position:0%
+that has that curve as its
+boundary this surface certainly
+
+ align:start position:0%
+boundary this surface certainly
+ 
+
+ align:start position:0%
+boundary this surface certainly
+intersects the z-axis the question is
+
+ align:start position:0%
+intersects the z-axis the question is
+ 
+
+ align:start position:0%
+intersects the z-axis the question is
+can I keep this curve the way it is and
+
+ align:start position:0%
+can I keep this curve the way it is and
+ 
+
+ align:start position:0%
+can I keep this curve the way it is and
+sort of pull the surface away and have
+
+ align:start position:0%
+sort of pull the surface away and have
+ 
+
+ align:start position:0%
+sort of pull the surface away and have
+it not intersect the z-axis and the
+
+ align:start position:0%
+it not intersect the z-axis and the
+ 
+
+ align:start position:0%
+it not intersect the z-axis and the
+answer is no any way I move this any way
+
+ align:start position:0%
+answer is no any way I move this any way
+ 
+
+ align:start position:0%
+answer is no any way I move this any way
+I move the inside of the curve basically
+
+ align:start position:0%
+I move the inside of the curve basically
+ 
+
+ align:start position:0%
+I move the inside of the curve basically
+what looks like a disc it's still going
+
+ align:start position:0%
+what looks like a disc it's still going
+ 
+
+ align:start position:0%
+what looks like a disc it's still going
+to intersect the z-axis somewhere right
+
+ align:start position:0%
+to intersect the z-axis somewhere right
+ 
+
+ align:start position:0%
+to intersect the z-axis somewhere right
+and so it's definitely not simply
+
+ align:start position:0%
+and so it's definitely not simply
+ 
+
+ align:start position:0%
+and so it's definitely not simply
+connected and the thing I was trying to
+
+ align:start position:0%
+connected and the thing I was trying to
+ 
+
+ align:start position:0%
+connected and the thing I was trying to
+point out in this second or the the
+
+ align:start position:0%
+point out in this second or the the
+ 
+
+ align:start position:0%
+point out in this second or the the
+number three that it is Simply Connected
+
+ align:start position:0%
+number three that it is Simply Connected
+ 
+
+ align:start position:0%
+number three that it is Simply Connected
+is you know if I if I shade the boundary
+
+ align:start position:0%
+is you know if I if I shade the boundary
+ 
+
+ align:start position:0%
+is you know if I if I shade the boundary
+of a curve sitting in the XY plane and
+
+ align:start position:0%
+of a curve sitting in the XY plane and
+ 
+
+ align:start position:0%
+of a curve sitting in the XY plane and
+then I take that sort of shaded disc and
+
+ align:start position:0%
+then I take that sort of shaded disc and
+ 
+
+ align:start position:0%
+then I take that sort of shaded disc and
+I push it up a little then it no longer
+
+ align:start position:0%
+I push it up a little then it no longer
+ 
+
+ align:start position:0%
+I push it up a little then it no longer
+hits the origin and I haven't and I
+
+ align:start position:0%
+hits the origin and I haven't and I
+ 
+
+ align:start position:0%
+hits the origin and I haven't and I
+haven't fundamentally changed my curve
+
+ align:start position:0%
+haven't fundamentally changed my curve
+ 
+
+ align:start position:0%
+haven't fundamentally changed my curve
+at all and so that that's a way of
+
+ align:start position:0%
+at all and so that that's a way of
+ 
+
+ align:start position:0%
+at all and so that that's a way of
+understanding that it is actually Simply
+
+ align:start position:0%
+understanding that it is actually Simply
+ 
+
+ align:start position:0%
+understanding that it is actually Simply
+Connected okay so there's sort of a
+
+ align:start position:0%
+Connected okay so there's sort of a
+ 
+
+ align:start position:0%
+Connected okay so there's sort of a
+couple ways to think about it and um and
+
+ align:start position:0%
+couple ways to think about it and um and
+ 
+
+ align:start position:0%
+couple ways to think about it and um and
+without being sort of incredibly
+
+ align:start position:0%
+without being sort of incredibly
+ 
+
+ align:start position:0%
+without being sort of incredibly
+mathematically precise these are sort of
+
+ align:start position:0%
+mathematically precise these are sort of
+ 
+
+ align:start position:0%
+mathematically precise these are sort of
+the best ways we have of thinking about
+
+ align:start position:0%
+the best ways we have of thinking about
+ 
+
+ align:start position:0%
+the best ways we have of thinking about
+understanding Simply Connected or not
+
+ align:start position:0%
+understanding Simply Connected or not
+ 
+
+ align:start position:0%
+understanding Simply Connected or not
+Simply Connected so again we had six
+
+ align:start position:0%
+Simply Connected so again we had six
+ 
+
+ align:start position:0%
+Simply Connected so again we had six
+examples removing the z-axis from R3 was
+
+ align:start position:0%
+examples removing the z-axis from R3 was
+ 
+
+ align:start position:0%
+examples removing the z-axis from R3 was
+not Simply Connected removing the origin
+
+ align:start position:0%
+not Simply Connected removing the origin
+ 
+
+ align:start position:0%
+not Simply Connected removing the origin
+from R3 was still Simply
+
+ align:start position:0%
+from R3 was still Simply
+ 
+
+ align:start position:0%
+from R3 was still Simply
+Connected removing a circle from R3 was
+
+ align:start position:0%
+Connected removing a circle from R3 was
+ 
+
+ align:start position:0%
+Connected removing a circle from R3 was
+not Simply Connected for the same region
+
+ align:start position:0%
+not Simply Connected for the same region
+ 
+
+ align:start position:0%
+not Simply Connected for the same region
+region reason as the z-axis problem CU
+
+ align:start position:0%
+region reason as the z-axis problem CU
+ 
+
+ align:start position:0%
+region reason as the z-axis problem CU
+here was my here was my disc and
+
+ align:start position:0%
+here was my here was my disc and
+ 
+
+ align:start position:0%
+here was my here was my disc and
+anywhere any way I try to sort of move
+
+ align:start position:0%
+anywhere any way I try to sort of move
+ 
+
+ align:start position:0%
+anywhere any way I try to sort of move
+the Shaded surface I can't I can't keep
+
+ align:start position:0%
+the Shaded surface I can't I can't keep
+ 
+
+ align:start position:0%
+the Shaded surface I can't I can't keep
+it from intersecting this
+
+ align:start position:0%
+it from intersecting this
+ 
+
+ align:start position:0%
+it from intersecting this
+circle and then number five was R2 minus
+
+ align:start position:0%
+circle and then number five was R2 minus
+ 
+
+ align:start position:0%
+circle and then number five was R2 minus
+a segment not Simply Connected but if I
+
+ align:start position:0%
+a segment not Simply Connected but if I
+ 
+
+ align:start position:0%
+a segment not Simply Connected but if I
+add another dimension it is Simply
+
+ align:start position:0%
+add another dimension it is Simply
+ 
+
+ align:start position:0%
+add another dimension it is Simply
+Connected for the same kind of reason
+
+ align:start position:0%
+Connected for the same kind of reason
+ 
+
+ align:start position:0%
+Connected for the same kind of reason
+that R3 minus the origin was and then
+
+ align:start position:0%
+that R3 minus the origin was and then
+ 
+
+ align:start position:0%
+that R3 minus the origin was and then
+number six was the solid Taurus which
+
+ align:start position:0%
+number six was the solid Taurus which
+ 
+
+ align:start position:0%
+number six was the solid Taurus which
+now it's kind of hard to see with the
+
+ align:start position:0%
+now it's kind of hard to see with the
+ 
+
+ align:start position:0%
+now it's kind of hard to see with the
+solid taus looks
+
+ align:start position:0%
+solid taus looks
+ 
+
+ align:start position:0%
+solid taus looks
+like but we said there's one one curve
+
+ align:start position:0%
+like but we said there's one one curve
+ 
+
+ align:start position:0%
+like but we said there's one one curve
+kind of curve that behaves fine but the
+
+ align:start position:0%
+kind of curve that behaves fine but the
+ 
+
+ align:start position:0%
+kind of curve that behaves fine but the
+curve that goes all the way around the
+
+ align:start position:0%
+curve that goes all the way around the
+ 
+
+ align:start position:0%
+curve that goes all the way around the
+hole shows it's in fact not Simply
+
+ align:start position:0%
+hole shows it's in fact not Simply
+ 
+
+ align:start position:0%
+hole shows it's in fact not Simply
+Connected so hopefully that was
+
+ align:start position:0%
+Connected so hopefully that was
+ 
+
+ align:start position:0%
+Connected so hopefully that was
+informative and that's where I'll
+
+ align:start position:0%
+informative and that's where I'll
+ 
+
+ align:start position:0%
+informative and that's where I'll
+stop
\ No newline at end of file
diff --git a/6b83DypBeYg.txt b/6b83DypBeYg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5903044708d3e378464ba9a84b54f7753267bc51
--- /dev/null
+++ b/6b83DypBeYg.txt
@@ -0,0 +1,4113 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of
+MIT courses, visit
+
+MIT at
+OpenCourseWare@oce.mit.edu.
+
+PROFESSOR: OK, in that
+case, let's get started.
+
+As usual, I like
+to begin by giving
+
+a review of what we
+talked about last time.
+
+This time on slides instead
+of on the blackboard.
+
+We're talking mainly
+about relativistic energy,
+
+or relativistic energy and
+momentum, and pressure,
+
+sometimes.
+
+The key equation is probably
+the most famous equation
+
+in physics, Einstein's
+e equals m c squared.
+
+And I gave some
+numerical examples.
+
+I actually looked up some
+more numbers since then,
+
+when I was revising
+the lecture notes.
+
+So these are slightly
+more up to date.
+
+But it's still true that
+if you could burn matter
+
+at the rate of one
+kilogram per hour,
+
+you would have about
+one and a half times
+
+the total power
+output of the world.
+
+And that's apparently
+still valid in 2011.
+
+I only had 2008 figures,
+actually, at the lecture
+
+last time.
+
+And if you imagine the
+15-gallon tank of gasoline,
+
+and you could figure out how
+much that-- what it's mass is,
+
+and convert that to
+energy, it turns out
+
+that a 15-gallon
+tank of gasoline
+
+could power the world for about
+two and half days, if you could
+
+convert all of it into energy.
+
+The catch, of course, is
+that we can't convert matter
+
+into energy.
+
+We can't get around the problem
+that, at least at the energies
+
+that we deal with,
+baryon number.
+
+And that number of protons
+and neutrons is conserved,
+
+so we can't make protons
+and neutrons disappear.
+
+And that means that we're
+limited in what we can do.
+
+In particular, one of the most
+efficient things we can do
+
+is fission uranium 235.
+
+But when uranium 235 undergoes
+fission, less than 1/10
+
+of 1% of the mass is
+actually converted
+
+into energy, which is why we
+can't actually avail ourselves
+
+of these fantastic
+numbers that would apply,
+
+if we could literally just
+convert matter into energy.
+
+We went on to talk about
+the relativistic definitions
+
+of energy and momentum,
+and how they come together
+
+to form a Lorentz four vector,
+and the underlying theme here
+
+is that we consider ourselves
+users of special relativity.
+
+Most of you I know have taken
+special relativity courses,
+
+and for those of you who
+have, this is a review.
+
+For those you who have not,
+and there are some of those
+
+also, no need to panic.
+
+I intend to tell you
+every fact that you
+
+need to know about
+special relativity.
+
+I won't tell you how
+to derive them all,
+
+but I'll tell you all you'll
+need to know for this class.
+
+So in particular, it's
+useful for this class
+
+to recognize that energy and
+momentum can be put together
+
+into a four vector, where
+the zeroth component
+
+is the energy divided
+by the speed of light.
+
+And the three spatial components
+are just the three components
+
+of the spatial
+momentum, although they
+
+have to be defined
+relativistically.
+
+The relativistic
+definition of momentum,
+
+at least how it
+relates to velocity,
+
+is that it's equal to
+gamma times the rest
+
+mass times the velocity, where
+gamma is the famous factor
+
+that we've been
+seeing all along when
+
+we've talked about relativity.
+
+The Lorentz
+contraction factor, one
+
+over the square root of 1
+minus v squared over c squared.
+
+The energy of a particle,
+relativistically,
+
+is the same gamma, times m
+0 times c squared, and it
+
+can also be written as
+the square root of m 0
+
+c squared squared, plus
+the momentum squared,
+
+times c squared.
+
+Since the momentum
+forms a four vector,
+
+its Lorentz and variant square
+should be Lorentz and variant,
+
+and that means that
+the momentum squared
+
+minus p 0 squared should be the
+same in all inertial reference
+
+frames.
+
+And that's just
+equal when you put
+
+in what p 0 means,
+the momentum squared
+
+minus the energy squared,
+divided by c 0 squared.
+
+And to know what value it's
+equal to in all frames,
+
+it's efficient to know what
+it's equal to in one frame.
+
+And the one frame
+where we do know
+
+what it's equal to is the
+rest frame of a particle.
+
+So in the rest frame,
+the momentum vanishes,
+
+and the energy is
+just m 0 c squared.
+
+So in the rest frame,
+we can evaluate this,
+
+and we get minus m
+0 c squared squared.
+
+And that means that has to
+be the value in every frame.
+
+And this in fact is
+the easy way to derive
+
+the relationship between
+energy and momentum.
+
+If we go back, the
+equation we had
+
+relating energy and momentum is
+really exactly that equation,
+
+rearranged.
+
+Just to give an example of how
+this works, when we actually
+
+have energy exchanges,
+I pointed out
+
+that we could talk about the
+energy of a hydrogen atom.
+
+And because energy and
+mass are equivalent,
+
+the hydrogen atom clearly
+has a little bit less energy
+
+than an isolated proton,
+plus an isolated electron.
+
+Because when you
+bring them together
+
+there's a binding energy,
+and that binding energy
+
+is called delta e, and has
+a value of 13.6 electron
+
+volts for the ground
+state of hydrogen.
+
+So that tells us the
+mass of an hydrogen atom
+
+is not the sum of
+the two masses,
+
+but rather has this
+correction factor,
+
+because we've taken out a little
+bit of energy for the binding.
+
+And that means we've taken
+out a little bit of mass.
+
+OK, then we talked about the
+mass density of radiation
+
+and how-- building up to how
+that will affect the universe.
+
+And we said that the
+mass density of radiation
+
+is just the energy density
+divided by c squared.
+
+And that can be taken, really,
+as a definition of what
+
+we call relativistic
+mass, and hence
+
+relativistic mass density.
+
+But the important point is
+that this mass density actually
+
+does gravitate the
+same as any other mass
+
+density of the same value.
+
+It really does create
+gravity in the same way.
+
+Now I mentioned that things are
+much more complicated if you
+
+want to talk about the
+gravitational field produced
+
+by a single moving particle.
+
+That's asymmetric, the
+velocity of the particle
+
+shows up in the equations that
+describe the metric surrounding
+
+a single moving particle.
+
+But if you have a gas
+of particles moving
+
+at high velocities, where
+the velocities nonetheless
+
+average to zero, which
+tends to happen, in a gas
+
+at least in the rest
+frame of the gas.
+
+Then that gas will produce
+gravitational fields,
+
+just like a static mass density.
+
+Where the mass density is this
+relativistic energy divided
+
+by c squared, the relativistic
+definition of the mass density.
+
+It's also useful to know
+that the photon-- if we want
+
+to describe it as a particle,
+is a particle of zero rest mass.
+
+Which means that it
+can never be at rest,
+
+it always moves at
+the speed of light.
+
+And it also means that its
+energy can be arbitrarily
+
+small, because the energy
+is proportional of momentum,
+
+and the momentum of a photon
+can be as small as you like.
+
+For giving frequency, of
+course, the energy of a photon
+
+is fixed.
+
+It's h times nu but
+if you're allowed
+
+to vary the frequency,
+which you can do if you just
+
+look at it in
+different frames, you
+
+can make the energy
+as small as you like.
+
+And the famous equation
+then, p squared minus e
+
+squared c squared, which
+would have on the right,
+
+minus m 0 squared
+c to the 4th m 0
+
+squared c squared, excuse me--
+has zero on the right hand
+
+side, because m 0
+is 0 And that means
+
+that for photons, the energy is
+just the speed of light times
+
+the momentum.
+
+And that's a famous
+relationship that photons obey.
+
+Now, thinking about
+how this gas of photons
+
+will behave in the universe,
+we realized immediately
+
+that it does not
+behave the same way
+
+as a mass density of ordinary
+non-relativistic particles.
+
+Which is what we have
+been dealing with to date.
+
+The important difference
+is that in both cases,
+
+the number density falls
+off like 1 over a cubed,
+
+as the universe expands,
+these particles are not
+
+created and destroyed
+in significant numbers,
+
+they just persevere.
+
+So the number density of either
+non-relativistic particles,
+
+or photons, just falls off
+like one over the volume,
+
+as the volume increases and
+the number density dilutes.
+
+But what makes photons
+different from non-relativistic
+
+particles, is that a
+non-relativistic particle
+
+will maintain the
+energy of that particle
+
+as the universe
+expands, but photons
+
+will redshift as the
+universe expands.
+
+So each photon will
+itself lose energy.
+
+And it loses energy proportional
+to one over the scale factor.
+
+And that's just because the
+frequency shift proportionally
+
+to the scale factor.
+
+And that means that
+the energy per photon
+
+shifts, because
+quantum mechanically
+
+we know that the
+energy of a photon
+
+is proportional
+to its frequency.
+
+So if the frequency
+redshifts so must the energy.
+
+In exactly the same
+way, 1 over a f t.
+
+Yes, question?
+
+AUDIENCE: You said
+previously that neutrinos
+
+behave like radiation
+in the sense
+
+that theta energy
+falls is 1 over a.
+
+What is it about them
+that makes this happen?
+
+Because there are also particles
+with standard kinetic energy,
+
+right?
+
+PROFESSOR: OK, the question,
+in case you didn't hear it,
+
+is why-- how did
+neutrinos fit in here?
+
+I've made the claim that
+neutrinos act like radiation
+
+in the early universe, but
+neutrinos have a non-zero mass,
+
+so they should obey the
+standard formulas for particles
+
+with nonzero masses.
+
+The answer to that
+is-- there is,
+
+I think, a simple answer,
+which is that as long
+
+as the energy is large
+compared to the mass,
+
+particles with masses will still
+act like massless particles.
+
+It doesn't really matter
+if the mass is zero or not,
+
+the key thing, really,
+is this equation.
+
+So if the term on
+the right hand side
+
+is small compared to either
+of the two on the left,
+
+it's not much different
+from being zero.
+
+And that's what
+happens for neutrinos
+
+in the early universe.
+
+And we'll see soon that if
+you go to early enough times,
+
+it's true even for
+electron-positron pairs.
+
+They will also act
+like radiation.
+
+Any particle will
+act like radiation
+
+as long as the energy is large
+compared to the rest energy.
+
+So getting back
+to the discussion
+
+of the early universe, if
+the energy of each photon
+
+falls off like one
+over the scale factor,
+
+and the number density falls off
+like one over the scale factor
+
+cubed, it means that
+the energy density,
+
+and hence, the mass
+density of radiation
+
+will fall off like one
+over a to the fourth,
+
+in contrast to the one over
+a cubed, that we found when
+
+we were talking about
+non-relativistic matter.
+
+And that, of course, is
+going to make a difference.
+
+Because those issues play a
+key role in our discussions
+
+about how the universe evolved.
+
+An important feature,
+which we see immediately,
+
+is that if we extrapolate
+backwards in time,
+
+since the radiation mass density
+is falling off like one over a
+
+to the fourth, and the
+matter density is falling off
+
+like one over a cubed, it means
+that as you go back in time,
+
+the radiation becomes
+more and more important
+
+relative to the matter, by
+factor of the scale factor.
+
+So if we go back far
+enough, we will even
+
+find a time when the
+mass density in radiation
+
+equaled the mass density
+in non-relativistic matter.
+
+And we calculated about
+when that would be.
+
+We said that the energy
+density in radiation today
+
+is given by this number, 7
+times 10 to the minus 14,
+
+joules per meter cubed.
+
+And I just gave you this
+number, I didn't derive it yet.
+
+We will derive it,
+probably later today.
+
+But for now, we're
+just accepting it.
+
+And that implies
+we can calculate
+
+from that the ratio
+of the mass densities
+
+in radiation and
+ordinary matter.
+
+Here, we use the fact
+that ordinary matter
+
+can be described
+by having an omega
+
+ratio to the critical
+density of about 0.3.
+
+And we know how to calculate
+the critical density,
+
+and that allowed us to calculate
+the density of ordinary matter.
+
+And then this ratio turned
+out to be 3.1 times 10
+
+to the minus four.
+
+So radiation in
+today's universe is
+
+almost negligible
+in its contribution
+
+to the overall energy
+balance, compared
+
+to non-relativistic matter.
+
+But if you
+extrapolate backwards,
+
+we know that this ratio will
+vary as one over the scale
+
+factor.
+
+And we could figure
+out what constants
+
+to put this equation by
+putting in the right constant,
+
+so that this equation gives
+us the right value today.
+
+Where the right value today is
+3.1 times 10 to the minus four.
+
+And notice that
+this works, if we
+
+let t be equal to t sub
+zero, this factors one
+
+and we get 3.1 times
+10 to the minus four.
+
+So these two factors
+together they
+
+have t zero and the 3.1
+times 10 to the minus four,
+
+are just the right
+factors to put in
+
+to give us the right
+constant of proportionality
+
+in that equation.
+
+Having this
+equation, we can then
+
+ask, how far back do we
+have to go, how much we have
+
+to change t, for
+the ratio to be one?
+
+And that's a
+straightforward calculation.
+
+And the ratio of the a is
+then just one over 3.1 times
+
+10 to the minus four, or 3,200.
+
+So if we talk about it in
+terms of a redshift, which
+
+is how astronomers always talk
+about distances, or times,
+
+we're talking about going
+back to a redshift of 3,200.
+
+We can figure out what time,
+then, corresponds to also,
+
+if we know how a f
+t depends on time.
+
+And we do, approximately.
+
+For this calculation,
+I assume for now, we
+
+could do better
+later, and we will--
+
+but I assume for now
+that we could just
+
+treat the period between matter
+radiation equality, so-called t
+
+x and now as being
+entirely described
+
+by a matter-dominated universe.
+
+That's only a crude
+approximation,
+
+but it will get us the
+right order of magnitude.
+
+And we'll learn how to do
+better later in the course.
+
+So if we assume that, then t x
+is just this number to the 3/2
+
+power, cancelling the 2/3, times
+the age of universe, t naught.
+
+And that turned out to
+be about 75,000 years.
+
+So somewhere in the range of
+100,000 years, 50,000 years,
+
+is the time in the history of
+the universe when radiation
+
+ceased to be more
+important than matter.
+
+And for earlier times than
+that, the radiation dominated.
+
+And that's what we refer to as
+the radiation dominated era.
+
+Any questions?
+
+OK, now I think we get
+on to what is really
+
+the important subject that
+we want to understand,
+
+and most of this you did
+yourself on the homework.
+
+But I'll summarize
+the argument here.
+
+We want to understand
+what this tells us
+
+about the Friedmann Equations.
+
+And first, we'd
+like to understand
+
+what it says about pressure.
+
+Because it turns
+out that pressure
+
+is the crucial
+issue in determining
+
+how fast row falls
+off as a expands.
+
+So if row is proportional
+to one over a cubed,
+
+we can just differentiate
+that, putting
+
+in a constant proportionality
+temporarily, just
+
+to keep track of
+what we're doing.
+
+Since we know how to
+differentiate qualities
+
+and we're less familiar
+with how to differentiate
+
+proportionalities.
+
+But what we find immediately,
+is that row dot is then minus 3,
+
+where that 3 is that 3,
+times a dot over a times row.
+
+On the other hand, if
+row of t falls like one
+
+over a to the fourth,
+row dot is minus 4 times
+
+a dot over a times row,
+just by differentiation.
+
+So we get different
+expressions from row dot,
+
+between radiation and matter.
+
+And we want to explore
+the consequences
+
+of that difference.
+
+It's related to the
+pressure of the gas,
+
+because we can relate
+the pressure to row dot.
+
+Because we know that
+as a gas expands,
+
+it loses energy, which is
+just equal in amount to pdV.
+
+And we illustrated this by
+a piston thought experiment,
+
+but it's true in general.
+
+So we can apply this famous
+formula, dU equals minus pdV,
+
+to a patch of the
+expanding universe.
+
+And by a patch I mean some fixed
+region and coordinate space.
+
+So the total energy in that
+region of coordinate space
+
+will be the physical
+volume, which
+
+will be a cubed times
+the coordinate volume.
+
+Which is going to cancel out
+of this equation on both sides.
+
+So it's a cubed times
+the coordinate volume
+
+times the energy density,
+which is row c squared.
+
+The rate of change
+of that is Du.
+
+And then on the
+right hand side, we
+
+have minus p minus
+b times dV, which
+
+is the rate of change
+of a cubed, again
+
+times the coordinate volume
+that we're talking about.
+
+But that will cancel out on
+the two sides of the equation.
+
+So this is really
+just a description
+
+for the universe of the dU
+equals minus pdV equation.
+
+And this can just be rearranged,
+expanding the time derivatives,
+
+to give us row dot, and
+we get minus 3 a dot
+
+over a, times row
+plus p over c squared.
+
+So this tells us how to relate
+row dot to the pressure.
+
+And it tells us that the
+formula that we started
+
+with a long time ago, which
+just said that row fell off
+
+like 1 over a cubed, was
+synonymous with saying
+
+the pressure is zero, for a gas
+of non-relativistic particles,
+
+the pressure is negligible.
+
+But for radiation,
+clearly if we're
+
+going to get a four
+instead of a three,
+
+the pressure will
+be non-negligible.
+
+And in fact, it implies
+that the pressure
+
+is exactly equal to
+one third of the energy
+
+density for a gas of radiation.
+
+OK, knowing that, we can now
+look back at the Friedmann
+
+equations and ask,
+how do they stand up?
+
+Are they still consistent, or
+do we have to modify something?
+
+And this is really
+the crucial point.
+
+What we know are
+these three equations,
+
+which are the two
+Friedmann equations
+
+and the equation for row dot.
+
+And we could see immediately
+that those equations are not
+
+independent of each other.
+
+The easiest thing
+to see is that if we
+
+start with the top equation,
+we could differentiate it.
+
+And since the top
+equation has a dot in it,
+
+when we differentiate, we'll get
+an equation for a double dot.
+
+But the equation will
+also involve row dot,
+
+if we take the time derivative
+of that top equation.
+
+But if we know
+what row dot is, we
+
+could put that
+in, and in the end
+
+we'll get an equation for
+a double dot by itself.
+
+And it will in fact
+agree with the equation
+
+on the middle line.
+
+Again, things would
+be inconsistent.
+
+Things are consistent, we
+didn't make any mistakes.
+
+If we derive the
+equation for a double dot
+
+by using the first and
+third of those equations,
+
+then we'll get the second
+of those equations.
+
+But the catch is
+that now we want
+
+to modify the third
+of those equations,
+
+the equations for row dot.
+
+And then the Friedmann
+equations as we've
+
+written them will not
+be consistent anymore.
+
+Because we'll have a different
+equation for row dot,
+
+we'll get a different
+equation for a double dot.
+
+So we have to decide what gives.
+
+What can we change to make
+everything consistent?
+
+And here, the rigorous
+way of proceeding
+
+is to look at general
+relativity and see what it says,
+
+and the answer we're
+going to write down
+
+is exactly what general
+relativity says.
+
+But we can motivate
+the answer in, I think,
+
+a pretty sensible
+way, by noticing
+
+that as the universe
+expands, we'd
+
+expect the energy density
+to vary continuously,
+
+because energies are conserved.
+
+And we also expect a dot
+to vary continuously,
+
+because basically, the
+mechanics of the universe
+
+are like ton's laws.
+
+And velocities don't
+change discontinuously.
+
+You can apply a
+force, and that causes
+
+velocities to have
+a rate of change.
+
+But velocities don't
+change instantaneously,
+
+unless you somehow
+apply an infinite force.
+
+And the same thing will
+be true with the universe.
+
+On the other hand, accelerations
+can change instantaneously.
+
+You could change the force
+acting on a particle,
+
+in principle, as
+fast as you want,
+
+and the acceleration
+of the particle
+
+will change at that same rate.
+
+So if we look at
+these equations,
+
+we would expect that the first
+equation and the third equation
+
+would not be allowed to
+involve the pressure.
+
+Because the pressure basically
+is a measure of a force.
+
+Pressures can change
+instantaneously.
+
+So what you need to
+do, if we're going
+
+to make these equations
+consistent in the presence
+
+of pressure-- which changes
+the row dot equation,
+
+the only equation we can
+change is the second one.
+
+And then we can
+ask ourselves, what
+
+do we have to change it to make
+the three equations consistent?
+
+And this is what you
+looked at on your homework.
+
+And the answer is that
+the a double dot equation
+
+has to be modified
+to give the equation
+
+at the bottom of
+the screen here.
+
+And this is the correct form
+of the a double dot equation
+
+in cosmology.
+
+And this is what we'll be
+using for the rest of the term,
+
+this is exactly what you would
+get from general relativity.
+
+As long as we're talking
+about homogeneous
+
+and isotropic universes,
+this formula as exact
+
+as far as we know.
+
+OK, any questions about that?
+
+Yes.
+
+AUDIENCE: Why when we derive
+that equation do we use--
+
+PROFESSOR: This equation?
+
+AUDIENCE: Or the one above that.
+
+PROFESSOR: Yeah.
+
+AUDIENCE: We use dU
+equals minus pdV?
+
+I mean, I agree with
+that, but couldn't we
+
+use a more complete version?
+
+Like, the complete
+version of the first law
+
+of thermodynamics, that
+dU equals TDS minus pdV.
+
+PROFESSOR: OK, yeah.
+
+The question was when we wrote
+down dU equals minus pdV,
+
+why did we not include
+a plus TDS term here,
+
+which could also be relevant.
+
+The answer is that
+for the applications
+
+we're interested in--
+you're quite right,
+
+it could be important,
+but for the applications
+
+that we're interested in,
+which is the expanding
+
+gas in the universe, the
+expanding gas in the universe
+
+will be making use of this fact.
+
+It really does expand
+adiabatically, that is,
+
+there's nothing
+putting heat in or out,
+
+and everything is remaining very
+close to thermal equilibrium,
+
+which means that entropy does
+not spontaneously change.
+
+So the TDS term we will be
+assuming is very, very small,
+
+and that's accurate.
+
+And you're right, if
+that were not the case,
+
+there would be further
+complications in terms
+
+of figuring out what row dot is.
+
+Let me point out here that
+this equation actually
+
+does contain a somewhat
+startling perhaps fact
+
+about gravity it says
+that in the context
+
+of general relativity.
+
+And that's really the
+context that we're in,
+
+even though we haven't learned
+a lot of general relativity.
+
+But it says that in the
+context of general relativity,
+
+pressures, as well
+as mass densities,
+
+contribute to the
+gravitational field.
+
+A double dot is
+basically a measure
+
+of how fast gravity is
+slowing down the universe.
+
+And this says that
+there's a pressure.
+
+It can also help to
+slow down the universe.
+
+Meaning that pressure itself can
+create a gravitational field.
+
+In the early universe,
+where we go back
+
+to this radiation
+dominated period,
+
+we know that the pressure is
+one third of the energy density.
+
+That says that
+this pressure term
+
+is the same size exactly
+as the mass density term.
+
+So in the radiation
+dominated phase,
+
+the pressure is just
+as important in effect
+
+for slowing down the universe
+as is the mass density.
+
+In today's universe
+it's negligible.
+
+Well, we'll come back that.
+
+The dark energy has a
+non-trivial pressure,
+
+but the pressure of ordinary
+matter in today's universe
+
+is negligible.
+
+The other important
+fact about this equation
+
+is that energy densities,
+so far as we know,
+
+are always positive.
+
+We don't know for sure what
+the ultimate laws of physics
+
+are, but for all the laws
+of physics that we know,
+
+energy densities are positive.
+
+On the other hand,
+pressures actually
+
+can be negative for
+some kinds of material.
+
+And we'll talk a little
+bit more about how
+
+to get a negative
+pressure later.
+
+But this formula tells us
+that positive pressures
+
+act the same way as
+positive mass densities,
+
+creating an attractive
+gravitational field which
+
+slows down the expansion
+of the universe.
+
+But if there could be a material
+with a negative pressure,
+
+this same equation, which
+would presumably still hold,
+
+and believe it
+does, would tell us
+
+that that negative
+pressure would actually
+
+cause the universe to
+accelerate, because
+
+of its gravitational effects.
+
+Now, we're not talking
+about the mechanical effects
+
+of the pressure.
+
+Mechanical effects
+of pressure only
+
+show up when there are
+pressure gradients, when
+
+the pressure is uneven.
+
+So the very large air
+pressure in this room,
+
+which really is quite
+large, we don't feel all,
+
+because it's acting
+equally in all directions.
+
+Uniform pressures do
+not produce forces.
+
+So the mechanical effects of the
+pressure in the early universe,
+
+which we're assuming is
+completely homogeneous,
+
+is zilch.
+
+There is no mechanical effect.
+
+But what we're seeing
+in this equation
+
+is a gravitational effect
+caused by the pressure.
+
+And it's obviously
+gravitational,
+
+business the effect is
+proportional to Newton's
+
+capital G, a
+constant determining
+
+the strength of gravity.
+
+So the equation is telling
+us that a positive pressure
+
+creates a gravitational
+attraction, which
+
+would cause the universe to
+slow down in its expansion.
+
+But a negative
+pressure would produce
+
+a gravitational repulsion,
+which would cause universe
+
+to speed up.
+
+And we now know that,
+today-- in fact,
+
+for the last five billion
+years or so-- our universe
+
+itself is actually accelerating
+under the influence
+
+of something.
+
+And the only
+explanation we have is
+
+that the something that's
+causing the universe
+
+to accelerate is the
+repulsive gravity caused
+
+by some kind of a negative
+pressure material.
+
+And that negative
+pressure material
+
+is what we call the dark energy.
+
+And we'll talk a little
+more later about what it is.
+
+It's very likely
+just vacuum energy.
+
+But we'll come back to
+that later in the course.
+
+Yes?
+
+AUDIENCE: When we looked at
+the toy example of the piston
+
+in the cavity, the
+pressure of the gas
+
+was pushing outwards against
+the wall of the container.
+
+But we can't have that view
+of the universe, really,
+
+because there's no
+exteriors in the universe.
+
+PROFESSOR: There's
+no walls, right.
+
+AUDIENCE: So how should we view
+pressure in the sense that--
+
+PROFESSOR: OK.
+
+Yeah.
+
+OK, the question is, in our toy
+problem involving the piston,
+
+we had walls for the
+pressure to push against.
+
+And that was where
+the energy went.
+
+It went into pushing the walls.
+
+When we're talking about the
+universe, there are no walls.
+
+How does that analogy work?
+
+What plays the
+role of the walls?
+
+And the answer, I think, is
+that the role of the walls, when
+
+we're talking about the
+universe, first of all, you
+
+can ignore it if you just
+took in a small region.
+
+You could still just
+say, the small region
+
+is pushing out on the
+regions around it.
+
+And I think that's enough
+to make the logic clear.
+
+But it still leaves open
+the question of, ultimately,
+
+where does this energy go?
+
+So saying it goes
+from here to there
+
+doesn't help you
+unless you know where
+
+it goes after it goes
+from and there and there.
+
+So you might want to ask
+the question more generally,
+
+where does the energy
+ultimately end up?
+
+And then I think the
+answer is that it ends up
+
+in gravitational
+potential energy.
+
+You could certainly build
+a toy model, where you just
+
+have a gas in a finite region,
+self-contained under gravity.
+
+And then you'd have to make
+up some kind of a mechanism
+
+to cause it to expand.
+
+But when you cause
+it to expand, you'll
+
+be pulling particles
+apart, which
+
+are attracting each
+other gravitationally.
+
+And that means
+you'll be increasing
+
+the gravitational
+potential energy
+
+as you pull the gas apart.
+
+So I think, ultimately, the
+answer is the energy imbalance
+
+that we seem to be
+seeing here is taken up
+
+by the gravitational field
+so that, all in all, energy
+
+still conserved.
+
+Any other questions?
+
+OK, in that case, let us
+continue on the blackboard.
+
+OK, first thing I
+want to look at it
+
+is just the behavior of a
+radiation-dominated flat
+
+universe.
+
+So a flat universe
+is going to obey
+
+H squared equals
+8 pi over 3 G rho,
+
+and then the potential minus
+kc squared over a squared.
+
+Hard to write dotted
+lines on the blackboard.
+
+But this potential term is
+not there, because k equals 0.
+
+We're talking about
+the flat case.
+
+So for a flat case, we could
+just express H in terms of rho.
+
+And we know how rho
+behaves for radiation.
+
+Rho falls off as
+1/a to the fourth.
+
+So H squared is proportional
+to 1/a to the fourth.
+
+That means that H itself is
+proportional to 1/a squared.
+
+So we can do that.
+
+a-dot over a is equal to
+some constant over a squared,
+
+a-dot over a being H. And now
+we can multiply both sides
+
+by a, of course.
+
+And we get a-dot is equal
+to a constant over a.
+
+And this we can integrate.
+
+The way to integrate is
+to put all the a's on one
+
+side and all of the
+dt's on the other side.
+
+So we get ada,
+writing this as da/dt.
+
+So ada is equal to
+the constant times dt.
+
+And then, as we've
+done before, when
+
+we're talking about matter,
+it's the same calculation there.
+
+I just did different
+power of a appears
+
+so we'd know how to do it.
+
+Integrating, we get 1/2a squared
+is equal to the constant times
+
+t, and then plus a new constant
+of integration, constant prime.
+
+Now we make the same argument
+as we've made in the past.
+
+We have not yet
+said anything that
+
+determines how our clocks
+are going to be set.
+
+So we can choose to set our
+clocks in the standard way,
+
+which is to set our
+clocks so that t equals
+
+0 corresponds to the moment
+where a is equal to 0.
+
+And if a is going to be equal
+to 0 when t is equal to 0,
+
+it means constant prime
+is going to be equal to 0.
+
+So by choosing the
+value of constant prime,
+
+we really are just
+determining how
+
+we're going to set
+our clocks, how
+
+we're going to
+choose the 0 of time.
+
+And we'll do that by setting
+constant prime equal to 0.
+
+And then we get
+the famous formula
+
+for a radiation-dominated
+universe, a of t
+
+is just proportional to
+the square root of t,
+
+or t to the 1/2 power.
+
+And this is for a
+radiation-dominated flat
+
+universe, replacing
+the t to the 2/3
+
+that we have for the
+matter-dominated flat universe.
+
+Once we know that
+a is proportional
+
+to the square root of t--
+and for the flat universe,
+
+the constant proportionality
+mean nothing, by the way.
+
+It's not that we haven't
+been smart enough
+
+to figure out what it is.
+
+It really has no
+meaning whatever.
+
+You could set it equal
+to whatever you want,
+
+and it just determines
+your definition
+
+of the notch, your
+definition of how you're
+
+going to measure the
+comoving coordinate system.
+
+Once we know this, we should
+know pretty much everything.
+
+So in particular,
+we can calculate
+
+h, which a-dot over a.
+
+And the constant
+proportionality drops
+
+when we compute a-dot over a.
+
+As we expect, it has no meaning.
+
+So it should not appear in
+the equation for anything
+
+that does have physical meaning.
+
+So H is just 1/2t,
+the 1/2 here coming
+
+from differentiating
+the t the 1/2 power.
+
+We can also compute
+the horizon distance.
+
+So the physical horizon
+distance, l sub p horizon,
+
+where p stands for physical,
+is equal to the scale factor
+
+times the coordinate
+horizon distance.
+
+And the coordinate
+horizon distance
+
+is just the total
+coordinate distance
+
+that light could travel from
+the beginning of the universe.
+
+And we know the coordinate
+velocity of light
+
+is c divided by a.
+
+So we just integrate that to get
+the total coordinate distance.
+
+So it's the integral
+from 0 to t of c
+
+over a of t prime dt prime.
+
+And since a of t is
+just t to the 1/2,
+
+this is a trivial
+integral to do.
+
+And the answer is
+2 times c times t.
+
+So in a radiation-dominated
+universe,
+
+the horizon's distance
+is twice c times t.
+
+For a static universe,
+the horizon distance
+
+would just be c times t.
+
+It would just be the distance
+light can travel in time t,
+
+but more complicated in
+an expanding universe.
+
+For the matter-dominated
+case, we
+
+discovered that the
+horizon distance was 3ct,
+
+if you remember.
+
+For the radiation-dominated
+case, it's 2ct.
+
+And finally, an
+important equation
+
+is that, going back to
+here, where we started,
+
+this equation relates H to rho.
+
+We found out that,
+merely by knowing
+
+the universe is
+radiation-dominated,
+
+without even caring about
+what kind of radiation
+
+it is, how much neutrinos,
+how much photons, whatever--
+
+doesn't matter-- merely
+by knowing the universe
+
+is radiation-dominated, we were
+able to tell that H is 1/2t.
+
+And if we know what H
+is, that formula tells us
+
+we also know what rho is.
+
+So without even knowing
+what kind of radiation
+
+is contributing, we know that,
+for a radiation-dominated
+
+universe, rho is just
+equal to 3 over 32
+
+pi Newton's constant G times
+time, little t, squared.
+
+It's rather amazing that we
+can write down that formula
+
+without even knowing what kind
+of radiation is contributing.
+
+But as long as that
+radiation falls
+
+off as 1 over the scale
+factor to the fourth,
+
+and as long as we know
+the universe is flat,
+
+then we know what that
+energy density has to be.
+
+This is crucial
+here, by the way.
+
+The energy could be
+anything if we did not
+
+assume that the
+universe was flat.
+
+OK, any questions about this?
+
+Yes?
+
+AUDIENCE: If we assumed
+that it was almost flat,
+
+would we be able to
+have any bounds on it?
+
+PROFESSOR: OK, question
+is, if we assumed
+
+that it was almost
+flat, would we
+
+be able to have
+any bounds on it?
+
+The answer is, yeah, if
+you were quantitative
+
+about what you meant
+by "almost flat,"
+
+you could know how almost true
+that formula would have to be.
+
+OK, if there are
+no other questions,
+
+I want to switch
+gears slightly now
+
+and go back to talk about some
+of the basic underlying physics
+
+that we are going to need,
+and in particular, the physics
+
+of black-body radiation.
+
+So this is really just a little
+chapter of a stat mech course
+
+that we're inserting
+here, because we need it.
+
+And because it comes
+from another course,
+
+we're not going try to
+do it in complete detail.
+
+But I'll try to write down
+formulas that make sense.
+
+And that will give us what
+we need to know to proceed.
+
+So that will be the goal.
+
+So what is black-body radiation?
+
+The physical phenomenon
+is that, if one imagines
+
+a box with a cavity
+in it-- that's
+
+supposed to be a box
+with a cavity in it,
+
+in case you can't recognize the
+picture-- if the box is held
+
+at some uniform temperature
+t-- t is temperature--
+
+then is claimed and
+verified experimentally
+
+that the cavity will fill up
+with radiation-- in this case,
+
+we're really just talking about
+electromagnetic radiation--
+
+the calving will fill up with
+electromagnetic radiation
+
+whose characteristics
+would be determined solely
+
+by that temperature
+t and will therefore
+
+be totally independent of the
+material that makes up the box.
+
+Roughly speaking,
+I think the way
+
+to think about it is to say
+that the box will fill up
+
+with radiation at temperature t.
+
+And saying that the
+radiation has temperature t
+
+is enough to completely
+describe the radiation.
+
+It doesn't matter
+what kind of a box
+
+that radiation is sitting in.
+
+So the box will fill with
+radiation at temperature t.
+
+And that radiation is
+called black-body radiation.
+
+Like many things in physics,
+it has a variety of names,
+
+just to confuse us all.
+
+So it's also called
+cavity radiation,
+
+which makes a lot
+of sense, given
+
+the description we just gave.
+
+And it's also sometimes called
+just thermal equilibrium
+
+radiation.
+
+This is radiation
+at temperature t.
+
+I haven't really justified
+the word "black-body"
+
+radiation yet, so let me
+try to do that quickly.
+
+The reason why it can be called
+black-body radiation-- and this
+
+will be important for
+some things in cosmology;
+
+I'm not sure if it will
+be important to us or not,
+
+but certainly important to
+know-- the reason why it's
+
+called black-body radiation is
+because we imagine inserting
+
+into this cavity a black
+body, in the literal sense.
+
+What is the literal
+sense of a black body?
+
+It's a body which is
+black in the sense
+
+that all radiation that
+hits it is absorbed.
+
+Now, this black body
+is still going to glow.
+
+If you heat a piece
+of iron or something
+
+to very high temperatures,
+you see it glow.
+
+That glow is not reflection.
+
+That glow is emission
+by the hot atoms
+
+in the piece of
+iron or whatever.
+
+Emission is different
+from reflection.
+
+When we say it
+absorbs everything,
+
+we mean it does not
+reflect anything.
+
+But it will still admit
+by thermal de-excitation.
+
+The crucial distinction between
+reflection and thermal emission
+
+is that reflection
+is instantaneous.
+
+When a light beam comes
+in, if it's reflected,
+
+it just goes back
+out instantaneously.
+
+Emission, thermal emission,
+is a slower process.
+
+Atoms get excited,
+and eventually, they
+
+de-excite and emit radiation.
+
+So it takes time.
+
+And that's the distinction.
+
+We're going to assume that
+this body is black in the sense
+
+that there's no reflection.
+
+OK, now we're going to
+make use of the fact
+
+that we know that thermal
+equilibrium works.
+
+That is, if you let any
+isolated system sit long enough,
+
+it will approach a unique
+state of thermal equilibrium
+
+determined by its constituents,
+which you've put in
+
+to begin with, but otherwise
+independent of how exactly
+
+you arrange those constituents.
+
+So if we put in, for
+example, a cold black body,
+
+it will start to get
+harder, warming up
+
+to the same temperature
+as everything else.
+
+If we put in an
+extra hot black body,
+
+it would emit energy
+and start to cool down
+
+to the temperature
+of everything else.
+
+But eventually,
+this black body will
+
+be at the same temperature
+as everything else.
+
+And we're going to be assuming
+here that the box itself
+
+is being held at some
+fixed temperature t.
+
+So wherever energy
+exchange occurs
+
+because of this
+black body, it will
+
+be absorbed by
+whatever is holding
+
+the outer box at the
+fixed temperature.
+
+So in the end, if
+we wait long enough,
+
+this black body is going to
+acquire the same temperature
+
+as everything else and
+hold that temperature.
+
+Now, if it's holding
+that temperature,
+
+it means that the energy input
+to the box, to the black body,
+
+will have to be the
+same as the energy
+
+output of the black body.
+
+Now, the black body is going
+to be absorbing radiation,
+
+because we have
+radiation here, and we
+
+said that any radiation
+that hits it is absorbed.
+
+That was the
+definition of "black."
+
+So it's clearly
+absorbing energy.
+
+If it's not going
+to be heating up--
+
+and we know that it's
+not, because it's
+
+in thermal equilibrium; the
+temperature will remain fixed--
+
+in order for it
+to not heat up, it
+
+has to radiate energy, as well.
+
+And the energy it radiates
+has to be exactly the same
+
+as the energy it's
+absorbing once it
+
+reaches thermal equilibrium.
+
+So in equilibrium, the black
+body, BB, radiates at same rate
+
+that it absorbs energy.
+
+This radiation process
+is this slow process
+
+of thermal emission.
+
+There are atoms inside this
+black body that are excited.
+
+Those atoms will
+de-excite over time,
+
+releasing photons
+that will go off.
+
+And the important thing
+about that slow mechanism
+
+is that, if we imagine
+taking this black body out
+
+of its cavity, but not waiting
+long enough for its temperature
+
+to change-- so we'll
+assume its temperature
+
+is still the same, t.
+
+So this is a picture of the same
+black body at temperature t,
+
+but now outside the cavity.
+
+Its radiation rate is not
+going to change when we take it
+
+outside the cavity, because the
+radiation was caused by things
+
+happening inside the black body,
+which are not changed when we
+
+put it in or out of the cavity.
+
+So it will continue to radiate
+at exactly the same rate
+
+that it was radiating
+when it was in the cavity.
+
+And that means it's
+going to radiate
+
+at exactly the same
+rate as the energy
+
+that it would have
+absorbed if it were bathed
+
+by this black-body radiation.
+
+So essentially, it means it
+will emit black-body radiation
+
+with exactly the intensity that
+the black-body radiation would
+
+have on the outside if
+the black body were still
+
+inside the cavity.
+
+So it radiates with exactly the
+same intensity as the energy
+
+that it would receive if
+it were inside the cavity.
+
+And furthermore, you
+could even elaborate a bit
+
+on his argument to show that
+the radiation that it radiates
+
+has exactly the same spectrum,
+exactly the same decomposition
+
+into wavelengths, as
+the black-body radiation
+
+inside the cavity.
+
+And the way to see
+that is to imagine
+
+surrounding this black body by
+absorption filters that only
+
+let through certain frequencies.
+
+And the point is that, no
+matter what frequencies
+
+you limit going
+through this filter,
+
+you have to stay in equilibrium.
+
+It will never get
+hotter or colder.
+
+So that means that each
+frequency by itself
+
+has to balance, has to have
+exactly the same emission
+
+as it would have abortion
+if the black body were just
+
+exposed to black-body
+radiation surrounding it.
+
+So it radiates
+black-body radiation.
+
+And the intensity
+and spectrum must
+
+match what we call black-body
+or cavity radiation.
+
+So the cavity radiation
+has to exactly mimic
+
+the radiation emitted
+by this black body.
+
+And that's the
+motivation for calling it
+
+black-body radiation.
+
+Now, if this black body
+absorbed some radiation
+
+and reflected some, then it
+would emit different radiation.
+
+So it is important
+that this body
+
+be black, in the sense that
+it doesn't reflect anything.
+
+All radiation hitting
+it is absorbed.
+
+And only under
+that assumption do
+
+we know exactly what
+it's going to emit.
+
+Yes?
+
+AUDIENCE: So is this
+only true for right
+
+after you take it out?
+
+PROFESSOR: Well, it will start
+to cool after you take it out.
+
+And as it cools, its
+temperature will change.
+
+But if you account for
+the changing temperature,
+
+it will be true at
+anytime, actually.
+
+But the temperature will change.
+
+AUDIENCE: Because,
+in the black cavity,
+
+it has things exciting it.
+
+And when you take
+it out, there's
+
+no photons, no constant
+radiation to excite it.
+
+So it can radiate--
+
+PROFESSOR: Yes.
+
+Once you take it out, it's
+no longer being excited.
+
+And I think, technically,
+you're right.
+
+Once you take it out,
+it will not only cool,
+
+but it will cease to be
+at a uniform temperature.
+
+And that's basically
+what we're saying
+
+if we're saying that the
+atoms that are excited
+
+won't necessarily be in the
+right thermal distribution
+
+as they would be if
+it was on the inside.
+
+That would be a
+statement that is not
+
+any longer in
+thermal equilibrium.
+
+But as long as the
+radiation is slow,
+
+you could just account for
+the changing temperature.
+
+You would know how it radiates.
+
+And I think that's a
+very good approximation.
+
+Although in principle,
+it will cease
+
+to be in thermal equilibrium,
+as soon as you take it out,
+
+the edges will be cool,
+and the center will be hot.
+
+And you'd have to take into
+account all of those things
+
+to be able to understand
+how it radiates.
+
+Any other questions?
+
+OK, next, I want to
+talk a little bit
+
+about what this
+black-body radiation is.
+
+And one can begin by
+trying to understand
+
+it purely classically,
+which, of course,
+
+is what happened historically.
+
+In the 1800s, people tried to
+understand cavity radiation
+
+or black-body radiation using
+classical physics, Maxwell's
+
+equations, to describe
+the radiation.
+
+And then, in a
+nutshell-- we're just
+
+trying to establish
+basic ideas here--
+
+one can try to treat a field
+statistical-mechanically
+
+by imagining not
+fields in empty space,
+
+but fields in some
+kind of a box.
+
+In this case, it
+doesn't necessarily
+
+have to be the cavity
+that we're talking about.
+
+It could be a big box that just
+enclosed the system somehow
+
+to make it easier to talk about.
+
+And in the end,
+you could imagine
+
+taking that box to infinity,
+this theoretical box
+
+that you use to
+simplify the problem.
+
+But once you put
+the system in a box,
+
+then a field, like the
+electromagnetic field,
+
+can always be broken
+up into normal modes,
+
+standing wave patterns that have
+an integer or a half integer
+
+number of wavelengths
+inside the box.
+
+And no matter how complicated
+the field is inside the box,
+
+you could always describe
+it as a superposition
+
+of some set of standing waves.
+
+In general, it takes
+an infinite number
+
+of standing wave components
+to describe an arbitrary
+
+field-- that is, with shorter
+and shorter wavelengths.
+
+But you can always-- and
+this is Fourier's theorem--
+
+you can always
+describe an arbitrary
+
+field in terms of
+the standing waves.
+
+And that's good for
+the point of view
+
+of thinking about
+statistical mechanics,
+
+because you could think
+about each standing wave
+
+almost as if it were a particle.
+
+It really is a
+harmonic oscillator.
+
+So if you think you know
+the statistical mechanics
+
+of harmonic oscillators,
+each standing wave in the box
+
+is just a harmonic
+oscillator, so simple.
+
+We now try to ask what
+is the thermodynamics
+
+of this system of
+harmonic oscillators.
+
+And the rule for harmonic
+oscillator is simple.
+
+Stat mech tells
+you that you have
+
+1/2 kT per degree of freedom
+in thermal equilibrium.
+
+The energy of a
+system should just
+
+be 1/2 kT per degree of freedom.
+
+Having said that, all
+the complicate questions
+
+come about by asking
+ourselves what
+
+is meant by degree of freedom.
+
+But for the harmonic oscillator,
+that has a simple answer.
+
+A harmonic oscillator
+has two degrees
+
+of freedom-- the kinetic energy
+and the potential energy.
+
+So the energy of a
+harmonic oscillator
+
+should just be kT per
+degree of freedom.
+
+And we could apply that to our
+gas in the box and we could,
+
+ask how much energy
+should the gas absorb
+
+at a given temperature?
+
+What should be the energy
+density of the gas at a given
+
+temperature-- this
+gas of photons.
+
+But it was noticed in
+the 1900-- the 1800s
+
+that this doesn't work because
+there's no limit to how short
+
+the wavelengths can be.
+
+And therefore, there's
+not just some finite set
+
+of harmonic oscillators.
+
+There's an infinite
+set of harmonic
+
+oscillators where you have
+more and more harmonic
+
+oscillators at shorter
+and shorter wavelengths
+
+ad infinitum, no limit.
+
+And that came to be
+known as Jean's Paradox.
+
+So what it suggests is that
+if this classical stat mech
+
+worked-- which obviously
+it's not working.
+
+But if it did
+work, it would mean
+
+that as you tried to put a gas
+in just an empty box in contact
+
+with something at a
+fixed temperature,
+
+the box would absorb more and
+more energy without limit.
+
+And ultimately, it
+would presumably
+
+cause the temperature
+of the whatever
+
+is trying to maintain
+the temperature
+
+to go to 0 as energy
+gets siphoned off
+
+to shorter and shorter
+wavelengths of excitations.
+
+That obviously isn't the
+way the world behaves.
+
+We'd all freeze to
+death if it did.
+
+So something has to
+happen to save it.
+
+And it wasn't at all
+obvious for many years
+
+what it was that saves it.
+
+But this Jean's
+Paradox turns out
+
+to be saved by
+quantum mechanics.
+
+And the important implication
+of quantum mechanics
+
+is that the energy of
+a harmonic oscillator
+
+is no longer allowed to
+have any possible value,
+
+but is now quantized
+as some integer times
+
+h times nu, the
+frequency-- h being
+
+Planck's constant,
+nu being frequency, n
+
+being some integer where
+this integer might be called
+
+the excitation level of
+the harmonic oscillator.
+
+Depending how you choose your
+0, you might have an n plus 1/2
+
+there.
+
+But that's not important
+for us right now.
+
+It will be important
+later actually.
+
+But for now, we'll just allow
+ourselves to readjust the 0
+
+and just think of it as n
+times h nu, or h bar omega.
+
+Now, this makes
+all the difference,
+
+statistical mechanically.
+
+One can apply
+statistical mechanics
+
+using basically
+the same principles
+
+to the quantum
+mechanical system.
+
+And the key thing now is that
+for the very short wavelengths,
+
+which are the ones that
+were giving us trouble--
+
+the infinities came
+to short wavelengths.
+
+For the short wavelengths
+where nu is high, h nu is high.
+
+And it means that
+there's a minimum ante
+
+that you could put in to
+excite those short wavelength
+
+harmonic oscillators.
+
+And it's a large number.
+
+You either put in a large
+amount of energy or none at all.
+
+Quantum mechanics doesn't let
+you do anything in between.
+
+Now remember, the
+classical mechanics answer
+
+was that you have kT in
+each harmonic oscillator.
+
+And kT would be small
+compared to h nu,
+
+if we're talking about
+a very short wavelength.
+
+So the classic
+answer is just not
+
+allowed by quantum mechanics.
+
+You either have to put in
+nothing or an amount much, much
+
+larger than the
+classical answer.
+
+And when you do the statistical
+mechanics quantum mechanically,
+
+which is not a big
+deal really, you
+
+find that when you're
+confronted with that choice,
+
+the most likely answer is
+to put in no energy at all.
+
+So quantum mechanics freezes out
+these short wavelength modes.
+
+And then the n produces
+a finite energy density
+
+for a gas of photons.
+
+Yes?
+
+AUDIENCE: Seems like
+if you were to sum over
+
+like all the possible
+wave numbers, that-- well,
+
+so the energy is inversely
+related to wavelength, right?
+
+So even if you quantize it,
+like for large wavelengths,
+
+isn't the sum still like a sum
+of one over lambda wavelength,
+
+with its derivative?
+
+PROFESSOR: You're
+saying, isn't there also
+
+a divergence at the
+large wavelength n?
+
+AUDIENCE: Because
+that sum doesn't
+
+seem like it would work.
+
+PROFESSOR: Right.
+
+No, that's important.
+
+The reason that's
+not a problem is
+
+that if you're talking
+about the energy in a box,
+
+the wavelength can't
+be bigger than the box.
+
+The largest possible
+wavelength is twice the box so
+
+that half a wavelength
+fits in the box.
+
+If you're talking about the
+energy in the whole infinite
+
+universe, then we expect
+the answer to infinite.
+
+And it is.
+
+There's no problem with
+having infinite total energy
+
+if you want to have
+a finite energy
+
+density throughout
+an infinite universe.
+
+So the size of the box cuts
+off the large wavelengths.
+
+And quantum mechanics cuts
+off the small wavelengths.
+
+So in the end, one does
+get a finite answer
+
+for the energy density
+of black-body radiation.
+
+And that's crucial
+for our survival,
+
+crucial for the
+existence of the universe
+
+as we know it, and also
+crucial for the calculations
+
+that we're about to do.
+
+OK, so when one does these
+calculations initially
+
+for photons only, what we'd
+find is that the energy density
+
+is equal to a fudge factor,
+which I'm going to call g.
+
+And you'll see later why I'm
+introducing a fudge factor.
+
+For now, g is just 2.
+
+But later, we'll generalize the
+application of this formula,
+
+and g will have
+different values.
+
+But for now, we're
+dealing with photons.
+
+There's a factor of 2 there,
+but I'm going to write 2 as g,
+
+writing g equals 2 underneath.
+
+And then the pi
+squared over 30--
+
+you can really
+calculate this-- times
+
+kT to the fourth power divided
+by h bar c cubed, h bar
+
+being Plank's constant
+divided by 2 pi and little k
+
+being Boltzmann constant.
+
+So this is calculated just by
+thinking of the gas in a box
+
+as a lot of harmonic oscillators
+and applying standard stat
+
+mech to each
+harmonic oscillator,
+
+but you apply the quantum
+mechanical version of the stat
+
+mech to each
+harmonic oscillator.
+
+And you can also find, by doing
+the same kind of analysis,
+
+that the pressure is
+1/3 the energy density,
+
+which we also derived
+earlier by different means.
+
+And it's all consistent so you
+get the same answer every time,
+
+even if you think
+about it differently.
+
+So here, I have mine deriving
+it directly from the stat mech.
+
+You can also, from
+the stat mech,
+
+calculate the number density of
+photons in thermal equilibrium.
+
+And that will be equal to --
+again, there's a factor of 2.
+
+But this time, I'll
+call the factor
+
+of 2 g star, where g star
+also equals 2 for photons.
+
+But when we generalize
+these formulas,
+
+g will not necessarily
+equal g star,
+
+which is why I'm
+giving it two names.
+
+And this g star
+multiplies zeta of 3,
+
+where zeta refers to the
+Riemann zeta function, which
+
+I'll define in a second,
+divided by pi squared times
+
+kT cubed divided
+by h bar c cubed.
+
+OK.
+
+OK, so I need to
+define this zeta of 3.
+
+It's 1 over 1 cubed plus 1 over
+2 cubed plus 1 over 3 cubed
+
+plus dot dot dot.
+
+It's an infinite series.
+
+And if you sum up
+that infinite series,
+
+at least to three decimal
+places, it's 1.202.
+
+OK, then there's
+one other formula
+
+that will be of interest to us.
+
+And that'll be a formula
+for the entropy density.
+
+Now, if you've had
+a stat mech course,
+
+you have some idea of what
+entropy density means.
+
+If you have not, suffice
+it to say for this class
+
+that it is some measure of
+the disorder in the sense
+
+of the total number of
+different quantum states
+
+that contribute to a given
+macroscopic description.
+
+The more different
+microstates there
+
+are that contribute to a
+macroscopic description,
+
+the higher the entropy.
+
+And the other important
+thing about entropy to us
+
+besides that vague definition--
+which will be enough--
+
+but the important
+thing for us is
+
+that under most circumstances,
+entropy will be conserved.
+
+It's conserved as
+long as things stay
+
+at or near thermal equilibrium.
+
+And in the early universe
+as the universe expands,
+
+that's the case.
+
+So for us, the
+entropy of our gas
+
+will simply be a
+conserved quantity
+
+that we can make use of.
+
+And we will make use of
+it in some important ways.
+
+And we could write
+down a formula
+
+for the entropy
+density of photons.
+
+And it's g, where this g in
+fact the same g as over there.
+
+It is related to the energy.
+
+So it's the same g that
+appears in two cases, 2
+
+in both cases for
+protons by themselves.
+
+And then there are factors
+that you can calculate--
+
+2 pi squared over 45 times k to
+the fourth T cubed over h bar
+
+c cubed.
+
+OK, this time, the number
+of k's and T's do not match.
+
+That's mainly due to
+the conventions about
+
+how entropy is defined.
+
+It's not really anything deep.
+
+I might mention at
+this point that the 2's
+
+that I've been writing for
+everything-- g equals 2,
+
+g star equals 2-- the
+reason those 2's are written
+
+explicitly rather than just
+absorbing the factor of 2
+
+into the other factors is
+that photons are characterized
+
+by the fact that there are
+two polarizations of photons.
+
+So if I have a beam
+of photons, they
+
+could be right-handed
+or left-handed.
+
+And anything else
+could be considered
+
+a superposition of those two.
+
+So there are two
+independent polarizations.
+
+And it's useful to keep
+track of these formulas
+
+as the amount of energy
+density per polarization.
+
+Thus, different
+kinds of particles
+
+will have different
+numbers of polarizations.
+
+So if we know the
+amount per polarization,
+
+we'll be able to more easily
+apply it to other particles.
+
+Yes?
+
+AUDIENCE: Sorry, just to kind
+of bring up the same question,
+
+if we-- I read that
+in the early universe,
+
+the temperature is constantly
+changing or it's cooling.
+
+PROFESSOR: Right.
+
+AUDIENCE: So then if the
+temperature is changing,
+
+then how can we say that
+the entropy is constant?
+
+PROFESSOR: OK,
+important question--
+
+we'll be getting
+to it very soon.
+
+But since you asked the
+question, I'll ask it now.
+
+The question was if the
+universe is expanding,
+
+and the entropy
+density is going down
+
+because it thins,
+how can that happen--
+
+I guess it was asked
+the other way around.
+
+If the temperature
+is falling, how
+
+can entropy be
+conserved if this is
+
+the formula for entropy density?
+
+And the answer-- when I tell
+you, you'll see it's obvious.
+
+We don't expect
+the entropy density
+
+to be conserved if the
+entropy is conserved.
+
+The entropy thins out
+as the universe expands.
+
+So if we just had a gas
+with nothing else changing,
+
+we expect the entropy density
+to go down like 1 over the scale
+
+factor cubed, just like the
+number density of particles.
+
+So if s is going to go down like
+1 over the scale factor cubed,
+
+that would be consistent
+with this formula
+
+if the temperature also fell
+as 1 over the scale factor.
+
+So that to cubing it
+made things match.
+
+And that's what we'll find.
+
+The temperature falls off,
+like 1 over the scale factor.
+
+And that's consistent
+with everything
+
+that we said about energy
+densities and so on.
+
+OK.
+
+Next thing I want
+to talk about is
+
+neutrinos, which
+I told you earlier
+
+contributes in a significant
+way to the radiation energy
+
+density in the universe today.
+
+Neutrinos are particles
+which for a long time,
+
+were thought to be massless.
+
+Until around 2000
+or so, neutrinos
+
+were thought to be massless.
+
+Now we know that in fact, they
+have a very small mass, which
+
+complicates the
+description here.
+
+It turns out that
+cosmologically, neutrinos
+
+still act as if
+they were massless
+
+for almost all purposes
+and for really all purposes
+
+that we'll be dealing with in
+this class, although if we were
+
+interested in the effects
+of neutrinos on structure
+
+formation, we'd be
+interested in whether or not
+
+the neutrinos have a
+small mass or whether it's
+
+smaller than that.
+
+We know it's non-zero.
+
+We don't know what the
+neutrino mass is, by the way.
+
+What we actually know
+from observations
+
+is that there are three
+types of neutrinos.
+
+And those are called flavors.
+
+And I'll use the letter
+nu for the word neutrino.
+
+And those three
+types of neutrinos
+
+are called nu sub e, called
+the electron neutrino;
+
+nu subbed mu, called the muon
+neutrino, and nu sub tau,
+
+called the tau neutrino.
+
+And these letters e, mu, and tau
+link to the names of particles.
+
+This is the electron neutrino.
+
+This is the muon
+neutrino connected
+
+to a particle called
+the muon, which
+
+is like the electron but
+heavier and different.
+
+And this is linked to a particle
+called the tau, which is also
+
+like the electron but much more
+heavier but otherwise similar
+
+in its properties.
+
+And the neutrinos are
+linked in the sense
+
+that when a neutrino
+is produced, depending
+
+on how you start, it is
+very typically produced
+
+in conjunction with one
+of these other particles.
+
+So an electron
+neutrino is typically
+
+produced in conjunction
+with an electron.
+
+And similarly, a muon
+neutrino is typically
+
+produced in conjunction
+with a muon.
+
+And a tau neutrino is typically
+produced in conjunction
+
+with a tau.
+
+Now, what does this have
+to do with neutrino masses?
+
+We've never actually measured
+the mass of neutrino.
+
+So we only know that they
+have mass indirectly.
+
+What we have seen is one
+flavor of neutrino turn
+
+into another flavor.
+
+And it turns out, in the
+context of quantum field theory
+
+and I think this does make
+a certain amount of sense
+
+just by intuition, if
+a particle is massless,
+
+it can never change
+into anything.
+
+The process by which
+one changes into another
+
+is pretty quantum
+mechanical and a little hard
+
+to understand anyway.
+
+But if the particles
+were really massless,
+
+they would move at
+the speed of light.
+
+And if the particles were
+moving at the speed of light,
+
+if the particle had any kind
+of a clock on the particle,
+
+that clock would literally
+stop with the particle
+
+moving at the speed of light.
+
+So if particles are massless,
+any internal workings
+
+that that particle
+might have to be frozen.
+
+That is, if it's a
+clock, it has to be
+
+a clock that's
+stopped completely.
+
+And for reasons that
+are essentially that,
+
+although they can be made
+more formal and more rigorous,
+
+a truly massless
+particle could never
+
+undergo any kind
+of change whatever.
+
+It would have to
+stay exactly like it
+
+looks like to start with.
+
+Because it just has no time.
+
+So the fact that these
+neutrinos turn into each other
+
+implies that they must
+have a nonzero mass.
+
+It must not really be moving
+at quite the speed of light.
+
+And that's the way
+the formalism works.
+
+And we could set
+limits on the masses
+
+based on what we know about
+the transitions between one
+
+kind of neutrino and another.
+
+Yes?
+
+AUDIENCE: How do we
+explain photon decaying
+
+to an electron-positron
+pair then?
+
+PROFESSOR: A photon decaying
+to an electron-positron pair?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: The answer is a
+free photon never does decay
+
+to an electron-positron pair.
+
+Photons can collide
+with something
+
+and produce an
+electron-positron pair.
+
+But that collision, that's
+a more complicated process.
+
+What I'm saying is-- I'm sorry.
+
+This process of conversion--
+maybe I should have clarified--
+
+happens just as the
+neutrinos travel.
+
+It's not due to collisions.
+
+Due to collsions,
+complicated things
+
+can happen whether the
+particle is massless or not.
+
+But a massless particle simply
+in transit cannot undergo any
+
+kind of transition.
+
+And these neutrinos are seen
+to undergo transitions simply
+
+being in transit
+without any collisions.
+
+In terms of my clock
+analogy and a stopped clock,
+
+I think the reason
+the photon can convert
+
+into electron-positron pairs
+if it collides with something
+
+is that when it collides, it
+essentially breaks the clock.
+
+You don't have a
+photon that's just
+
+moving along without
+time anymore.
+
+OK, so these
+neutrinos have masses.
+
+And maybe I should,
+at this point,
+
+write down some bounds
+on these masses.
+
+m squared 21 times c to the
+fourth is equal to 7.50 plus
+
+or minus 0.2 times 10 to the
+minus 5 electron volts squared.
+
+These numbers come from the
+latest particle data tables,
+
+which I gave references
+for in the notes.
+
+So this is the difference
+of the mass squared.
+
+And delta m 23 squared
+times c to the fourth
+
+to turn it into the
+square of an energy
+
+is 2.32 plus 0.12
+minus 0.08 times 10
+
+to the minus third
+electron volts squared.
+
+So one thing you
+notice immediately
+
+is that these are
+incredibly small masses.
+
+Remember, the proton
+weighs 938 MeV,
+
+three million electron volts.
+
+And these are fractions
+of one electron volt.
+
+So by the standards
+of particle physics,
+
+these are unbelievably
+small energies,
+
+unbelievably small
+mass differences.
+
+But they're there.
+
+They have to be there for the
+physics we know to make sense.
+
+The other thing
+that you may notice
+
+about this notation-- which
+I don't want to elaborate
+
+on but I'll just mention--
+this is called 21.
+
+This is called 23.
+
+There's no 1, 2, or 3 there.
+
+There's an e and a mu and a tau.
+
+The complication here is
+something very quantum
+
+mechanical.
+
+The e, mu and tau
+labels are labels
+
+which basically label
+the neutrino according
+
+to how the neutrino is created.
+
+It turns out that their mass
+eigenstates-- states which
+
+actually have a
+definite mass-- are not
+
+the e, the mu or the tau.
+
+In fact, if the e
+had a definite mass,
+
+that would be saying
+that an e would just
+
+propagate as a particle
+with a certain mass.
+
+It would not convert
+into anything else.
+
+The fact that an e converts
+into other particles--
+
+a nu sub e converts
+into other particles
+
+is really the statement
+that nu sub e is not
+
+a state with a definite mass.
+
+But there are states
+with definite masses
+
+which could be expressed quantum
+mechanically as superpositions
+
+of these flavor eigenstates.
+
+So nu sub 1, nu
+sub 2 and nu sub 3
+
+are states of neutrinos
+that have definite masses.
+
+And each one of them is
+a superposition of nu sub
+
+e, nu sub mu and nu sub tau.
+
+Yes?
+
+AUDIENCE: How come we don't
+have a delta n from 31?
+
+PROFESSOR: Good question.
+
+I think it's just the
+lack of knowledge.
+
+I don't think there's any
+reason it's not defined.
+
+I'm sure it is defined.
+
+I think it's just
+lack of knowledge.
+
+And if I knew more details about
+how these things were measured,
+
+I could give you a
+better story about that.
+
+But I don't, frankly.
+
+So in the end, it's a rather
+complicated quantum mechanical
+
+system which we're not going
+to go into any details about.
+
+What more should I say today?
+
+OK, let me just
+mention for today
+
+and we'll continue next
+time after the quiz,
+
+for our purposes, we're going
+to treat these neutrinos
+
+as if they're massless.
+
+And it turns out that that's
+actually extraordinarily
+
+accurate from the point
+of view of cosmology,
+
+at least for the
+kind of cosmology
+
+that we're doing
+where we're just
+
+interested in the effect
+of these neutrinos
+
+on the expansion
+rate of the universe.
+
+And treating them as
+massless particles,
+
+I will shortly give
+you the formulas
+
+for how they contribute to
+the black-body radiation.
+
+But it I think there's no
+point in my writing them now.
+
+I'll just write them again in
+the beginning of next period.
+
+But they do contribute to
+the black-body radiation
+
+and in a way that we actually
+know how to calculate.
+
+And they have a
+noticeable effect
+
+on the evolution
+of our universe.
+
+OK, that's all for today.
+
+Good luck on the
+quiz on Thursday.
+
+I'll be here to help proctor.
+
+I think Tim [INAUDIBLE]
+will be here too.
+
+And I'll see you more intimately
+either at my office hour
+
+tomorrow or at lecture
+a week from now.
\ No newline at end of file
diff --git a/6mndLA1SceA.txt b/6mndLA1SceA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e44aab1af3e057ea992186064f0081848247d460
--- /dev/null
+++ b/6mndLA1SceA.txt
@@ -0,0 +1,1131 @@
+align:start position:0%
+ 
+hi there my name is Gloria chair and for
+
+ align:start position:0%
+hi there my name is Gloria chair and for
+ 
+
+ align:start position:0%
+hi there my name is Gloria chair and for
+the next few minutes I'll be talking
+
+ align:start position:0%
+the next few minutes I'll be talking
+ 
+
+ align:start position:0%
+the next few minutes I'll be talking
+about how to find the perfect diamond
+
+ align:start position:0%
+about how to find the perfect diamond
+ 
+
+ align:start position:0%
+about how to find the perfect diamond
+and why that might actually be
+
+ align:start position:0%
+and why that might actually be
+ 
+
+ align:start position:0%
+and why that might actually be
+impossible let's start with what a
+
+ align:start position:0%
+impossible let's start with what a
+ 
+
+ align:start position:0%
+impossible let's start with what a
+perfect diamond looks like a quick
+
+ align:start position:0%
+perfect diamond looks like a quick
+ 
+
+ align:start position:0%
+perfect diamond looks like a quick
+google image search for the perfect
+
+ align:start position:0%
+google image search for the perfect
+ 
+
+ align:start position:0%
+google image search for the perfect
+diamond you've just asked as the first
+
+ align:start position:0%
+diamond you've just asked as the first
+ 
+
+ align:start position:0%
+diamond you've just asked as the first
+result and it does look pretty perfect
+
+ align:start position:0%
+result and it does look pretty perfect
+ 
+
+ align:start position:0%
+result and it does look pretty perfect
+but just because it looks perfect
+
+ align:start position:0%
+but just because it looks perfect
+ 
+
+ align:start position:0%
+but just because it looks perfect
+doesn't mean that it actually is to
+
+ align:start position:0%
+doesn't mean that it actually is to
+ 
+
+ align:start position:0%
+doesn't mean that it actually is to
+determine if a diamond is really perfect
+
+ align:start position:0%
+determine if a diamond is really perfect
+ 
+
+ align:start position:0%
+determine if a diamond is really perfect
+we have to look at its structure a
+
+ align:start position:0%
+we have to look at its structure a
+ 
+
+ align:start position:0%
+we have to look at its structure a
+diamond consists of carbon atoms
+
+ align:start position:0%
+diamond consists of carbon atoms
+ 
+
+ align:start position:0%
+diamond consists of carbon atoms
+arranged in what we call a crystal
+
+ align:start position:0%
+arranged in what we call a crystal
+ 
+
+ align:start position:0%
+arranged in what we call a crystal
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+more specifically diamonds from diamonds
+
+ align:start position:0%
+more specifically diamonds from diamonds
+ 
+
+ align:start position:0%
+more specifically diamonds from diamonds
+form a cubic crystal structure made up
+
+ align:start position:0%
+form a cubic crystal structure made up
+ 
+
+ align:start position:0%
+form a cubic crystal structure made up
+of tetrahedrally arranged atoms as shown
+
+ align:start position:0%
+of tetrahedrally arranged atoms as shown
+ 
+
+ align:start position:0%
+of tetrahedrally arranged atoms as shown
+in this 2d depiction an important thing
+
+ align:start position:0%
+in this 2d depiction an important thing
+ 
+
+ align:start position:0%
+in this 2d depiction an important thing
+to note is that diamonds are not a
+
+ align:start position:0%
+to note is that diamonds are not a
+ 
+
+ align:start position:0%
+to note is that diamonds are not a
+stable form of carbon they're what we
+
+ align:start position:0%
+stable form of carbon they're what we
+ 
+
+ align:start position:0%
+stable form of carbon they're what we
+call metastable which means that they
+
+ align:start position:0%
+call metastable which means that they
+ 
+
+ align:start position:0%
+call metastable which means that they
+are energetically unfavorable but there
+
+ align:start position:0%
+are energetically unfavorable but there
+ 
+
+ align:start position:0%
+are energetically unfavorable but there
+is a high activation energy for it to
+
+ align:start position:0%
+is a high activation energy for it to
+ 
+
+ align:start position:0%
+is a high activation energy for it to
+decompose so it stays how it is for a
+
+ align:start position:0%
+decompose so it stays how it is for a
+ 
+
+ align:start position:0%
+decompose so it stays how it is for a
+very long time besides the fact that
+
+ align:start position:0%
+very long time besides the fact that
+ 
+
+ align:start position:0%
+very long time besides the fact that
+diamonds aren't forever
+
+ align:start position:0%
+diamonds aren't forever
+ 
+
+ align:start position:0%
+diamonds aren't forever
+what really makes finding the perfect
+
+ align:start position:0%
+what really makes finding the perfect
+ 
+
+ align:start position:0%
+what really makes finding the perfect
+one impossible is that it probably
+
+ align:start position:0%
+one impossible is that it probably
+ 
+
+ align:start position:0%
+one impossible is that it probably
+doesn't even exist what real diamonds
+
+ align:start position:0%
+doesn't even exist what real diamonds
+ 
+
+ align:start position:0%
+doesn't even exist what real diamonds
+look like it's something like this it's
+
+ align:start position:0%
+look like it's something like this it's
+ 
+
+ align:start position:0%
+look like it's something like this it's
+the same structure as the last slide but
+
+ align:start position:0%
+the same structure as the last slide but
+ 
+
+ align:start position:0%
+the same structure as the last slide but
+there's a carbon atom missing this is
+
+ align:start position:0%
+there's a carbon atom missing this is
+ 
+
+ align:start position:0%
+there's a carbon atom missing this is
+called the vacancy which is a type of
+
+ align:start position:0%
+called the vacancy which is a type of
+ 
+
+ align:start position:0%
+called the vacancy which is a type of
+defect that can exist in crystals like
+
+ align:start position:0%
+defect that can exist in crystals like
+ 
+
+ align:start position:0%
+defect that can exist in crystals like
+diamond defects are imperfections in
+
+ align:start position:0%
+diamond defects are imperfections in
+ 
+
+ align:start position:0%
+diamond defects are imperfections in
+crystals and vacancies are not the only
+
+ align:start position:0%
+crystals and vacancies are not the only
+ 
+
+ align:start position:0%
+crystals and vacancies are not the only
+kinds all crystals in the real world
+
+ align:start position:0%
+kinds all crystals in the real world
+ 
+
+ align:start position:0%
+kinds all crystals in the real world
+have a number of defects ranging from
+
+ align:start position:0%
+have a number of defects ranging from
+ 
+
+ align:start position:0%
+have a number of defects ranging from
+vacancies or grain boundaries to edge
+
+ align:start position:0%
+vacancies or grain boundaries to edge
+ 
+
+ align:start position:0%
+vacancies or grain boundaries to edge
+dislocations there's quite a number of
+
+ align:start position:0%
+dislocations there's quite a number of
+ 
+
+ align:start position:0%
+dislocations there's quite a number of
+them but for the purpose of this video
+
+ align:start position:0%
+them but for the purpose of this video
+ 
+
+ align:start position:0%
+them but for the purpose of this video
+I'll be referencing vacancies in
+
+ align:start position:0%
+I'll be referencing vacancies in
+ 
+
+ align:start position:0%
+I'll be referencing vacancies in
+diamonds
+
+ align:start position:0%
+diamonds
+ 
+
+ align:start position:0%
+diamonds
+keep in mind that anything I say about
+
+ align:start position:0%
+keep in mind that anything I say about
+ 
+
+ align:start position:0%
+keep in mind that anything I say about
+them also applies to other kinds of
+
+ align:start position:0%
+them also applies to other kinds of
+ 
+
+ align:start position:0%
+them also applies to other kinds of
+defects and other kinds of crystals okay
+
+ align:start position:0%
+defects and other kinds of crystals okay
+ 
+
+ align:start position:0%
+defects and other kinds of crystals okay
+so now that we know why crystals aren't
+
+ align:start position:0%
+so now that we know why crystals aren't
+ 
+
+ align:start position:0%
+so now that we know why crystals aren't
+perfect we want to know why this happens
+
+ align:start position:0%
+perfect we want to know why this happens
+ 
+
+ align:start position:0%
+perfect we want to know why this happens
+to begin with the reason that these
+
+ align:start position:0%
+to begin with the reason that these
+ 
+
+ align:start position:0%
+to begin with the reason that these
+defects form is because a crystal will
+
+ align:start position:0%
+defects form is because a crystal will
+ 
+
+ align:start position:0%
+defects form is because a crystal will
+always be tending to equilibrium
+
+ align:start position:0%
+always be tending to equilibrium
+ 
+
+ align:start position:0%
+always be tending to equilibrium
+also known as the state of lowest Gibbs
+
+ align:start position:0%
+also known as the state of lowest Gibbs
+ 
+
+ align:start position:0%
+also known as the state of lowest Gibbs
+free energy the formation of defects in
+
+ align:start position:0%
+free energy the formation of defects in
+ 
+
+ align:start position:0%
+free energy the formation of defects in
+a crystal may seem counterintuitive
+
+ align:start position:0%
+a crystal may seem counterintuitive
+ 
+
+ align:start position:0%
+a crystal may seem counterintuitive
+because it it costs energy which is not
+
+ align:start position:0%
+because it it costs energy which is not
+ 
+
+ align:start position:0%
+because it it costs energy which is not
+favorable
+
+ align:start position:0%
+favorable
+ 
+
+ align:start position:0%
+favorable
+but the formation of defects also
+
+ align:start position:0%
+but the formation of defects also
+ 
+
+ align:start position:0%
+but the formation of defects also
+increases the amount of entropy in which
+
+ align:start position:0%
+increases the amount of entropy in which
+ 
+
+ align:start position:0%
+increases the amount of entropy in which
+in the system which is favorable the
+
+ align:start position:0%
+in the system which is favorable the
+ 
+
+ align:start position:0%
+in the system which is favorable the
+entropy gain can sometimes outweigh the
+
+ align:start position:0%
+entropy gain can sometimes outweigh the
+ 
+
+ align:start position:0%
+entropy gain can sometimes outweigh the
+energy cost of forming a defect so a
+
+ align:start position:0%
+energy cost of forming a defect so a
+ 
+
+ align:start position:0%
+energy cost of forming a defect so a
+perfect crystal can actually decrease
+
+ align:start position:0%
+perfect crystal can actually decrease
+ 
+
+ align:start position:0%
+perfect crystal can actually decrease
+its Gibbs free energy by forming defects
+
+ align:start position:0%
+its Gibbs free energy by forming defects
+ 
+
+ align:start position:0%
+its Gibbs free energy by forming defects
+this can be seen in the following
+
+ align:start position:0%
+this can be seen in the following
+ 
+
+ align:start position:0%
+this can be seen in the following
+equation where Delta G equals Delta H
+
+ align:start position:0%
+equation where Delta G equals Delta H
+ 
+
+ align:start position:0%
+equation where Delta G equals Delta H
+minus T Delta s so formation of defects
+
+ align:start position:0%
+minus T Delta s so formation of defects
+ 
+
+ align:start position:0%
+minus T Delta s so formation of defects
+becomes a battle of enthalpy versus
+
+ align:start position:0%
+becomes a battle of enthalpy versus
+ 
+
+ align:start position:0%
+becomes a battle of enthalpy versus
+entropy if the enthalpy cost of forming
+
+ align:start position:0%
+entropy if the enthalpy cost of forming
+ 
+
+ align:start position:0%
+entropy if the enthalpy cost of forming
+a defect is greater than the entropy
+
+ align:start position:0%
+a defect is greater than the entropy
+ 
+
+ align:start position:0%
+a defect is greater than the entropy
+increase of the system then the defect
+
+ align:start position:0%
+increase of the system then the defect
+ 
+
+ align:start position:0%
+increase of the system then the defect
+does not form if the entropy increase of
+
+ align:start position:0%
+does not form if the entropy increase of
+ 
+
+ align:start position:0%
+does not form if the entropy increase of
+the system is greater than the cost of
+
+ align:start position:0%
+the system is greater than the cost of
+ 
+
+ align:start position:0%
+the system is greater than the cost of
+forming a defect then the defect does
+
+ align:start position:0%
+forming a defect then the defect does
+ 
+
+ align:start position:0%
+forming a defect then the defect does
+form the change in Gibbs energy of
+
+ align:start position:0%
+form the change in Gibbs energy of
+ 
+
+ align:start position:0%
+form the change in Gibbs energy of
+forming vacancies depends on several
+
+ align:start position:0%
+forming vacancies depends on several
+ 
+
+ align:start position:0%
+forming vacancies depends on several
+factors including the number of
+
+ align:start position:0%
+factors including the number of
+ 
+
+ align:start position:0%
+factors including the number of
+vacancies already present and the size
+
+ align:start position:0%
+vacancies already present and the size
+ 
+
+ align:start position:0%
+vacancies already present and the size
+of the crystal so the energy cost an
+
+ align:start position:0%
+of the crystal so the energy cost an
+ 
+
+ align:start position:0%
+of the crystal so the energy cost an
+entropy contribution of vacancy
+
+ align:start position:0%
+entropy contribution of vacancy
+ 
+
+ align:start position:0%
+entropy contribution of vacancy
+formation actually changes with each
+
+ align:start position:0%
+formation actually changes with each
+ 
+
+ align:start position:0%
+formation actually changes with each
+defect formed what we see is that
+
+ align:start position:0%
+defect formed what we see is that
+ 
+
+ align:start position:0%
+defect formed what we see is that
+there's actually happy spot for the
+
+ align:start position:0%
+there's actually happy spot for the
+ 
+
+ align:start position:0%
+there's actually happy spot for the
+equilibrium amounts of vacancies this
+
+ align:start position:0%
+equilibrium amounts of vacancies this
+ 
+
+ align:start position:0%
+equilibrium amounts of vacancies this
+here is a visualization of how the
+
+ align:start position:0%
+here is a visualization of how the
+ 
+
+ align:start position:0%
+here is a visualization of how the
+number of vacancies affect the Gibbs
+
+ align:start position:0%
+number of vacancies affect the Gibbs
+ 
+
+ align:start position:0%
+number of vacancies affect the Gibbs
+free energy of a crystal at various
+
+ align:start position:0%
+free energy of a crystal at various
+ 
+
+ align:start position:0%
+free energy of a crystal at various
+temperatures on the left is a plot of
+
+ align:start position:0%
+temperatures on the left is a plot of
+ 
+
+ align:start position:0%
+temperatures on the left is a plot of
+Gibbs free energy where x axis
+
+ align:start position:0%
+Gibbs free energy where x axis
+ 
+
+ align:start position:0%
+Gibbs free energy where x axis
+represents the number of vacancies that
+
+ align:start position:0%
+represents the number of vacancies that
+ 
+
+ align:start position:0%
+represents the number of vacancies that
+can occur in a crystal and the y axis
+
+ align:start position:0%
+can occur in a crystal and the y axis
+ 
+
+ align:start position:0%
+can occur in a crystal and the y axis
+represents two Gibbs energy of the
+
+ align:start position:0%
+represents two Gibbs energy of the
+ 
+
+ align:start position:0%
+represents two Gibbs energy of the
+system on the right is a visualization
+
+ align:start position:0%
+system on the right is a visualization
+ 
+
+ align:start position:0%
+system on the right is a visualization
+of what the lattice looks like at
+
+ align:start position:0%
+of what the lattice looks like at
+ 
+
+ align:start position:0%
+of what the lattice looks like at
+equilibrium in this demo the crystal is
+
+ align:start position:0%
+equilibrium in this demo the crystal is
+ 
+
+ align:start position:0%
+equilibrium in this demo the crystal is
+a square lattice made it for 400 atom
+
+ align:start position:0%
+a square lattice made it for 400 atom
+ 
+
+ align:start position:0%
+a square lattice made it for 400 atom
+sites I am using a 2d square lattice
+
+ align:start position:0%
+sites I am using a 2d square lattice
+ 
+
+ align:start position:0%
+sites I am using a 2d square lattice
+instead of a 3-dimensional diamond
+
+ align:start position:0%
+instead of a 3-dimensional diamond
+ 
+
+ align:start position:0%
+instead of a 3-dimensional diamond
+lattice for ease of viewing and
+
+ align:start position:0%
+lattice for ease of viewing and
+ 
+
+ align:start position:0%
+lattice for ease of viewing and
+understanding this topic these concepts
+
+ align:start position:0%
+understanding this topic these concepts
+ 
+
+ align:start position:0%
+understanding this topic these concepts
+applying the same way to Diamond
+
+ align:start position:0%
+applying the same way to Diamond
+ 
+
+ align:start position:0%
+applying the same way to Diamond
+crystals which are much more complicated
+
+ align:start position:0%
+crystals which are much more complicated
+ 
+
+ align:start position:0%
+crystals which are much more complicated
+as you can see already there is a
+
+ align:start position:0%
+as you can see already there is a
+ 
+
+ align:start position:0%
+as you can see already there is a
+vacancy present in the slot it may be a
+
+ align:start position:0%
+vacancy present in the slot it may be a
+ 
+
+ align:start position:0%
+vacancy present in the slot it may be a
+bit difficult to see on the left but
+
+ align:start position:0%
+bit difficult to see on the left but
+ 
+
+ align:start position:0%
+bit difficult to see on the left but
+this is because a at equilibrium the
+
+ align:start position:0%
+this is because a at equilibrium the
+ 
+
+ align:start position:0%
+this is because a at equilibrium the
+Gibbs free energy plant is actually not
+
+ align:start position:0%
+Gibbs free energy plant is actually not
+ 
+
+ align:start position:0%
+Gibbs free energy plant is actually not
+linear but curved it becomes more
+
+ align:start position:0%
+linear but curved it becomes more
+ 
+
+ align:start position:0%
+linear but curved it becomes more
+apparent as we increase the temperature
+
+ align:start position:0%
+apparent as we increase the temperature
+ 
+
+ align:start position:0%
+apparent as we increase the temperature
+higher temperatures provide greater
+
+ align:start position:0%
+higher temperatures provide greater
+ 
+
+ align:start position:0%
+higher temperatures provide greater
+entropy increase of defect formation so
+
+ align:start position:0%
+entropy increase of defect formation so
+ 
+
+ align:start position:0%
+entropy increase of defect formation so
+we see vacancies are more likely to form
+
+ align:start position:0%
+we see vacancies are more likely to form
+ 
+
+ align:start position:0%
+we see vacancies are more likely to form
+here we can see that the lowest Gibbs
+
+ align:start position:0%
+here we can see that the lowest Gibbs
+ 
+
+ align:start position:0%
+here we can see that the lowest Gibbs
+free energy doesn't occur at zero but
+
+ align:start position:0%
+free energy doesn't occur at zero but
+ 
+
+ align:start position:0%
+free energy doesn't occur at zero but
+actually at around 50 vacancies per 400
+
+ align:start position:0%
+actually at around 50 vacancies per 400
+ 
+
+ align:start position:0%
+actually at around 50 vacancies per 400
+sites this seems pretty high but if you
+
+ align:start position:0%
+sites this seems pretty high but if you
+ 
+
+ align:start position:0%
+sites this seems pretty high but if you
+think about it this is at 5000 Kelvin so
+
+ align:start position:0%
+think about it this is at 5000 Kelvin so
+ 
+
+ align:start position:0%
+think about it this is at 5000 Kelvin so
+the amount or so the atoms in the
+
+ align:start position:0%
+the amount or so the atoms in the
+ 
+
+ align:start position:0%
+the amount or so the atoms in the
+diamond crystal are actually moving
+
+ align:start position:0%
+diamond crystal are actually moving
+ 
+
+ align:start position:0%
+diamond crystal are actually moving
+around quite a bit so it makes sense
+
+ align:start position:0%
+around quite a bit so it makes sense
+ 
+
+ align:start position:0%
+around quite a bit so it makes sense
+that you won't find all of the atoms in
+
+ align:start position:0%
+that you won't find all of the atoms in
+ 
+
+ align:start position:0%
+that you won't find all of the atoms in
+the right places if you would like to
+
+ align:start position:0%
+the right places if you would like to
+ 
+
+ align:start position:0%
+the right places if you would like to
+see how this visualization was made the
+
+ align:start position:0%
+see how this visualization was made the
+ 
+
+ align:start position:0%
+see how this visualization was made the
+code is accompanied with this video in
+
+ align:start position:0%
+code is accompanied with this video in
+ 
+
+ align:start position:0%
+code is accompanied with this video in
+summary what we found is that the
+
+ align:start position:0%
+summary what we found is that the
+ 
+
+ align:start position:0%
+summary what we found is that the
+perfect crystals don't exist because the
+
+ align:start position:0%
+perfect crystals don't exist because the
+ 
+
+ align:start position:0%
+perfect crystals don't exist because the
+equilibrium state of lowest Gibbs free
+
+ align:start position:0%
+equilibrium state of lowest Gibbs free
+ 
+
+ align:start position:0%
+equilibrium state of lowest Gibbs free
+energy curves with some number of
+
+ align:start position:0%
+energy curves with some number of
+ 
+
+ align:start position:0%
+energy curves with some number of
+defects
+
+ align:start position:0%
+defects
+ 
+
+ align:start position:0%
+defects
+since diamonds are crystals it turns out
+
+ align:start position:0%
+since diamonds are crystals it turns out
+ 
+
+ align:start position:0%
+since diamonds are crystals it turns out
+that finding a perfect one is impossible
+
+ align:start position:0%
+that finding a perfect one is impossible
+ 
+
+ align:start position:0%
+that finding a perfect one is impossible
+but that doesn't mean we can't find a
+
+ align:start position:0%
+but that doesn't mean we can't find a
+ 
+
+ align:start position:0%
+but that doesn't mean we can't find a
+diamond that looks perfect thanks for
+
+ align:start position:0%
+diamond that looks perfect thanks for
+ 
+
+ align:start position:0%
+diamond that looks perfect thanks for
+listening and I hope this quick lesson
+
+ align:start position:0%
+listening and I hope this quick lesson
+ 
+
+ align:start position:0%
+listening and I hope this quick lesson
+has made understanding why defects form
+
+ align:start position:0%
+has made understanding why defects form
+ 
+
+ align:start position:0%
+has made understanding why defects form
+a little clearer the notebook that
+
+ align:start position:0%
+a little clearer the notebook that
+ 
+
+ align:start position:0%
+a little clearer the notebook that
+accompanies this video is a version of
+
+ align:start position:0%
+accompanies this video is a version of
+ 
+
+ align:start position:0%
+accompanies this video is a version of
+this video and with that I would like to
+
+ align:start position:0%
+this video and with that I would like to
+ 
+
+ align:start position:0%
+this video and with that I would like to
+thank professor Carter and professor
+
+ align:start position:0%
+thank professor Carter and professor
+ 
+
+ align:start position:0%
+thank professor Carter and professor
+King and the help of Durio 160 a's emma
+
+ align:start position:0%
+King and the help of Durio 160 a's emma
+ 
+
+ align:start position:0%
+King and the help of Durio 160 a's emma
+berhan and philippe
\ No newline at end of file
diff --git a/6vgHIImFwHo.txt b/6vgHIImFwHo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42f47eb87dbcc58a4f035f26ec0cec7fcb72bfd6
--- /dev/null
+++ b/6vgHIImFwHo.txt
@@ -0,0 +1,1715 @@
+align:start position:0%
+ 
+okay so how do we find these stable
+
+ align:start position:0%
+okay so how do we find these stable
+ 
+
+ align:start position:0%
+okay so how do we find these stable
+marriages well there's a procedure for
+
+ align:start position:0%
+marriages well there's a procedure for
+ 
+
+ align:start position:0%
+marriages well there's a procedure for
+doing it which is kind of elegantly
+
+ align:start position:0%
+doing it which is kind of elegantly
+ 
+
+ align:start position:0%
+doing it which is kind of elegantly
+described as a day-by-day mating ritual
+
+ align:start position:0%
+described as a day-by-day mating ritual
+ 
+
+ align:start position:0%
+described as a day-by-day mating ritual
+that the boys and the girls cooperate in
+
+ align:start position:0%
+that the boys and the girls cooperate in
+ 
+
+ align:start position:0%
+that the boys and the girls cooperate in
+so let's see what happens on the first
+
+ align:start position:0%
+so let's see what happens on the first
+ 
+
+ align:start position:0%
+so let's see what happens on the first
+day um on the morning of the first day
+
+ align:start position:0%
+day um on the morning of the first day
+ 
+
+ align:start position:0%
+day um on the morning of the first day
+each boy looks at his list of girls and
+
+ align:start position:0%
+each boy looks at his list of girls and
+ 
+
+ align:start position:0%
+each boy looks at his list of girls and
+picks the one that he likes the best at
+
+ align:start position:0%
+picks the one that he likes the best at
+ 
+
+ align:start position:0%
+picks the one that he likes the best at
+the top of his list and he goes off and
+
+ align:start position:0%
+the top of his list and he goes off and
+ 
+
+ align:start position:0%
+the top of his list and he goes off and
+serenades her or proposes to her
+
+ align:start position:0%
+serenades her or proposes to her
+ 
+
+ align:start position:0%
+serenades her or proposes to her
+so here we have Billy Bob and Brad
+
+ align:start position:0%
+so here we have Billy Bob and Brad
+ 
+
+ align:start position:0%
+so here we have Billy Bob and Brad
+proposing to Angelina that means that on
+
+ align:start position:0%
+proposing to Angelina that means that on
+ 
+
+ align:start position:0%
+proposing to Angelina that means that on
+the first day uh Angelina was at the top
+
+ align:start position:0%
+the first day uh Angelina was at the top
+ 
+
+ align:start position:0%
+the first day uh Angelina was at the top
+of both Brad's list and Billy Bob's list
+
+ align:start position:0%
+of both Brad's list and Billy Bob's list
+ 
+
+ align:start position:0%
+of both Brad's list and Billy Bob's list
+and they're both going to be proposing
+
+ align:start position:0%
+and they're both going to be proposing
+ 
+
+ align:start position:0%
+and they're both going to be proposing
+and asking if she's willing to marry
+
+ align:start position:0%
+and asking if she's willing to marry
+ 
+
+ align:start position:0%
+and asking if she's willing to marry
+them well in the afternoon uh each girl
+
+ align:start position:0%
+them well in the afternoon uh each girl
+ 
+
+ align:start position:0%
+them well in the afternoon uh each girl
+rejects all but her favorite Suitor so
+
+ align:start position:0%
+rejects all but her favorite Suitor so
+ 
+
+ align:start position:0%
+rejects all but her favorite Suitor so
+in this case Angelina likes Brad best
+
+ align:start position:0%
+in this case Angelina likes Brad best
+ 
+
+ align:start position:0%
+in this case Angelina likes Brad best
+ofal so she says to everybody else if
+
+ align:start position:0%
+ofal so she says to everybody else if
+ 
+
+ align:start position:0%
+ofal so she says to everybody else if
+you're not Brad take a hike and that's
+
+ align:start position:0%
+you're not Brad take a hike and that's
+ 
+
+ align:start position:0%
+you're not Brad take a hike and that's
+what happened at that stage and then in
+
+ align:start position:0%
+what happened at that stage and then in
+ 
+
+ align:start position:0%
+what happened at that stage and then in
+the evening here we look at rejected Boy
+
+ align:start position:0%
+the evening here we look at rejected Boy
+ 
+
+ align:start position:0%
+the evening here we look at rejected Boy
+Billy Bob a boy who's rejected crosses
+
+ align:start position:0%
+Billy Bob a boy who's rejected crosses
+ 
+
+ align:start position:0%
+Billy Bob a boy who's rejected crosses
+off the girl who rejected him so Billy
+
+ align:start position:0%
+off the girl who rejected him so Billy
+ 
+
+ align:start position:0%
+off the girl who rejected him so Billy
+Bob is going to cross Angelino off his
+
+ align:start position:0%
+Bob is going to cross Angelino off his
+ 
+
+ align:start position:0%
+Bob is going to cross Angelino off his
+list and then the whole ritual is going
+
+ align:start position:0%
+list and then the whole ritual is going
+ 
+
+ align:start position:0%
+list and then the whole ritual is going
+to repeat starting the next morning
+
+ align:start position:0%
+to repeat starting the next morning
+ 
+
+ align:start position:0%
+to repeat starting the next morning
+except that now Billy Bob will have a
+
+ align:start position:0%
+except that now Billy Bob will have a
+ 
+
+ align:start position:0%
+except that now Billy Bob will have a
+different woman at the top of his list
+
+ align:start position:0%
+different woman at the top of his list
+ 
+
+ align:start position:0%
+different woman at the top of his list
+because Angelina is gone
+
+ align:start position:0%
+because Angelina is gone
+ 
+
+ align:start position:0%
+because Angelina is gone
+forever okay this uh mating ritual
+
+ align:start position:0%
+forever okay this uh mating ritual
+ 
+
+ align:start position:0%
+forever okay this uh mating ritual
+continues until nothing changes and
+
+ align:start position:0%
+continues until nothing changes and
+ 
+
+ align:start position:0%
+continues until nothing changes and
+that's going to happen exactly when each
+
+ align:start position:0%
+that's going to happen exactly when each
+ 
+
+ align:start position:0%
+that's going to happen exactly when each
+girl has at most one Suitor cuz if she
+
+ align:start position:0%
+girl has at most one Suitor cuz if she
+ 
+
+ align:start position:0%
+girl has at most one Suitor cuz if she
+has more than one Suitor she's going to
+
+ align:start position:0%
+has more than one Suitor she's going to
+ 
+
+ align:start position:0%
+has more than one Suitor she's going to
+reject the less favorite ones so that is
+
+ align:start position:0%
+reject the less favorite ones so that is
+ 
+
+ align:start position:0%
+reject the less favorite ones so that is
+the definition of the stopping condition
+
+ align:start position:0%
+the definition of the stopping condition
+ 
+
+ align:start position:0%
+the definition of the stopping condition
+and on that day by definition no girl
+
+ align:start position:0%
+and on that day by definition no girl
+ 
+
+ align:start position:0%
+and on that day by definition no girl
+can have more than one Suitor so she
+
+ align:start position:0%
+can have more than one Suitor so she
+ 
+
+ align:start position:0%
+can have more than one Suitor so she
+will marry the one Suitor she has and
+
+ align:start position:0%
+will marry the one Suitor she has and
+ 
+
+ align:start position:0%
+will marry the one Suitor she has and
+that's the definition of the marriages
+
+ align:start position:0%
+that's the definition of the marriages
+ 
+
+ align:start position:0%
+that's the definition of the marriages
+that result if and when the mating
+
+ align:start position:0%
+that result if and when the mating
+ 
+
+ align:start position:0%
+that result if and when the mating
+ritual
+
+ align:start position:0%
+ritual
+ 
+
+ align:start position:0%
+ritual
+stops and we claim that they are going
+
+ align:start position:0%
+stops and we claim that they are going
+ 
+
+ align:start position:0%
+stops and we claim that they are going
+to be stable
+
+ align:start position:0%
+to be stable
+ 
+
+ align:start position:0%
+to be stable
+marriages now if we think about this
+
+ align:start position:0%
+marriages now if we think about this
+ 
+
+ align:start position:0%
+marriages now if we think about this
+process it's really a state machine in
+
+ align:start position:0%
+process it's really a state machine in
+ 
+
+ align:start position:0%
+process it's really a state machine in
+fact if you think about it what the
+
+ align:start position:0%
+fact if you think about it what the
+ 
+
+ align:start position:0%
+fact if you think about it what the
+states are is the is the set of girls on
+
+ align:start position:0%
+states are is the is the set of girls on
+ 
+
+ align:start position:0%
+states are is the is the set of girls on
+the boys list on any given morning and
+
+ align:start position:0%
+the boys list on any given morning and
+ 
+
+ align:start position:0%
+the boys list on any given morning and
+then uh those States evolve to a new
+
+ align:start position:0%
+then uh those States evolve to a new
+ 
+
+ align:start position:0%
+then uh those States evolve to a new
+list after the crossing out happens on
+
+ align:start position:0%
+list after the crossing out happens on
+ 
+
+ align:start position:0%
+list after the crossing out happens on
+the next morning so this is kind of a a
+
+ align:start position:0%
+the next morning so this is kind of a a
+ 
+
+ align:start position:0%
+the next morning so this is kind of a a
+memorable way to tell a story about the
+
+ align:start position:0%
+memorable way to tell a story about the
+ 
+
+ align:start position:0%
+memorable way to tell a story about the
+transitions of a state machine and we
+
+ align:start position:0%
+transitions of a state machine and we
+ 
+
+ align:start position:0%
+transitions of a state machine and we
+can bring our state machine Concepts to
+
+ align:start position:0%
+can bring our state machine Concepts to
+ 
+
+ align:start position:0%
+can bring our state machine Concepts to
+bear so the first thing we want to prove
+
+ align:start position:0%
+bear so the first thing we want to prove
+ 
+
+ align:start position:0%
+bear so the first thing we want to prove
+is that this state machine terminates
+
+ align:start position:0%
+is that this state machine terminates
+ 
+
+ align:start position:0%
+is that this state machine terminates
+that is to say there exists a wedding
+
+ align:start position:0%
+that is to say there exists a wedding
+ 
+
+ align:start position:0%
+that is to say there exists a wedding
+day um then we want to prove that this
+
+ align:start position:0%
+day um then we want to prove that this
+ 
+
+ align:start position:0%
+day um then we want to prove that this
+uh State machine is partially correct
+
+ align:start position:0%
+uh State machine is partially correct
+ 
+
+ align:start position:0%
+uh State machine is partially correct
+and what that means that uh when the
+
+ align:start position:0%
+and what that means that uh when the
+ 
+
+ align:start position:0%
+and what that means that uh when the
+machine stops everyone is married and
+
+ align:start position:0%
+machine stops everyone is married and
+ 
+
+ align:start position:0%
+machine stops everyone is married and
+that the marriages are stable so that's
+
+ align:start position:0%
+that the marriages are stable so that's
+ 
+
+ align:start position:0%
+that the marriages are stable so that's
+our task well termination easy because
+
+ align:start position:0%
+our task well termination easy because
+ 
+
+ align:start position:0%
+our task well termination easy because
+if you look at the state the state is
+
+ align:start position:0%
+if you look at the state the state is
+ 
+
+ align:start position:0%
+if you look at the state the state is
+the boys lists on a given morning and
+
+ align:start position:0%
+the boys lists on a given morning and
+ 
+
+ align:start position:0%
+the boys lists on a given morning and
+things evolve because boys get rejected
+
+ align:start position:0%
+things evolve because boys get rejected
+ 
+
+ align:start position:0%
+things evolve because boys get rejected
+and they cross girls off the list so
+
+ align:start position:0%
+and they cross girls off the list so
+ 
+
+ align:start position:0%
+and they cross girls off the list so
+what that means if we take the total
+
+ align:start position:0%
+what that means if we take the total
+ 
+
+ align:start position:0%
+what that means if we take the total
+number of names remaining on the boy
+
+ align:start position:0%
+number of names remaining on the boy
+ 
+
+ align:start position:0%
+number of names remaining on the boy
+lists On Any Given morning that is a
+
+ align:start position:0%
+lists On Any Given morning that is a
+ 
+
+ align:start position:0%
+lists On Any Given morning that is a
+strictly decreasing and non- negative
+
+ align:start position:0%
+strictly decreasing and non- negative
+ 
+
+ align:start position:0%
+strictly decreasing and non- negative
+integer valued variable so by the well-
+
+ align:start position:0%
+integer valued variable so by the well-
+ 
+
+ align:start position:0%
+integer valued variable so by the well-
+ordering principle that's strictly
+
+ align:start position:0%
+ordering principle that's strictly
+ 
+
+ align:start position:0%
+ordering principle that's strictly
+decreasing
+
+ align:start position:0%
+decreasing
+ 
+
+ align:start position:0%
+decreasing
+well-ordered um uh derive variable will
+
+ align:start position:0%
+well-ordered um uh derive variable will
+ 
+
+ align:start position:0%
+well-ordered um uh derive variable will
+reach a minimum value and by definition
+
+ align:start position:0%
+reach a minimum value and by definition
+ 
+
+ align:start position:0%
+reach a minimum value and by definition
+that's when the algorithm has to stop
+
+ align:start position:0%
+that's when the algorithm has to stop
+ 
+
+ align:start position:0%
+that's when the algorithm has to stop
+because it's strictly increasing so it
+
+ align:start position:0%
+because it's strictly increasing so it
+ 
+
+ align:start position:0%
+because it's strictly increasing so it
+can't move once it's reached its
+
+ align:start position:0%
+can't move once it's reached its
+ 
+
+ align:start position:0%
+can't move once it's reached its
+minimum so there's a wedding
+
+ align:start position:0%
+minimum so there's a wedding
+ 
+
+ align:start position:0%
+minimum so there's a wedding
+day all right so now let's examine
+
+ align:start position:0%
+day all right so now let's examine
+ 
+
+ align:start position:0%
+day all right so now let's examine
+correctness of this procedure and figure
+
+ align:start position:0%
+correctness of this procedure and figure
+ 
+
+ align:start position:0%
+correctness of this procedure and figure
+out what's supposed to happen on the
+
+ align:start position:0%
+out what's supposed to happen on the
+ 
+
+ align:start position:0%
+out what's supposed to happen on the
+wedding day we want to show that
+
+ align:start position:0%
+wedding day we want to show that
+ 
+
+ align:start position:0%
+wedding day we want to show that
+everybody's married and that the
+
+ align:start position:0%
+everybody's married and that the
+ 
+
+ align:start position:0%
+everybody's married and that the
+marriages are stable and in order to do
+
+ align:start position:0%
+marriages are stable and in order to do
+ 
+
+ align:start position:0%
+marriages are stable and in order to do
+that we're going to look at some more
+
+ align:start position:0%
+that we're going to look at some more
+ 
+
+ align:start position:0%
+that we're going to look at some more
+derive variables and an invariant that
+
+ align:start position:0%
+derive variables and an invariant that
+ 
+
+ align:start position:0%
+derive variables and an invariant that
+explains why the mating ritual works so
+
+ align:start position:0%
+explains why the mating ritual works so
+ 
+
+ align:start position:0%
+explains why the mating ritual works so
+the first remark is that the girls
+
+ align:start position:0%
+the first remark is that the girls
+ 
+
+ align:start position:0%
+the first remark is that the girls
+improve uh day by day or at least they
+
+ align:start position:0%
+improve uh day by day or at least they
+ 
+
+ align:start position:0%
+improve uh day by day or at least they
+don't get any worse namely a girl's
+
+ align:start position:0%
+don't get any worse namely a girl's
+ 
+
+ align:start position:0%
+don't get any worse namely a girl's
+favorite tomorrow will be at least as
+
+ align:start position:0%
+favorite tomorrow will be at least as
+ 
+
+ align:start position:0%
+favorite tomorrow will be at least as
+desirable to her as her favorite today
+
+ align:start position:0%
+desirable to her as her favorite today
+ 
+
+ align:start position:0%
+desirable to her as her favorite today
+that's for any given day if you look at
+
+ align:start position:0%
+that's for any given day if you look at
+ 
+
+ align:start position:0%
+that's for any given day if you look at
+a girl's favorite on this day and if
+
+ align:start position:0%
+a girl's favorite on this day and if
+ 
+
+ align:start position:0%
+a girl's favorite on this day and if
+there is a tomorrow then her favorite
+
+ align:start position:0%
+there is a tomorrow then her favorite
+ 
+
+ align:start position:0%
+there is a tomorrow then her favorite
+tomorrow is going to be at least as good
+
+ align:start position:0%
+tomorrow is going to be at least as good
+ 
+
+ align:start position:0%
+tomorrow is going to be at least as good
+as the one she has and why is that well
+
+ align:start position:0%
+as the one she has and why is that well
+ 
+
+ align:start position:0%
+as the one she has and why is that well
+because today's favorite will keep
+
+ align:start position:0%
+because today's favorite will keep
+ 
+
+ align:start position:0%
+because today's favorite will keep
+serenading her until he gets rejected
+
+ align:start position:0%
+serenading her until he gets rejected
+ 
+
+ align:start position:0%
+serenading her until he gets rejected
+and he only gets rejected when the girl
+
+ align:start position:0%
+and he only gets rejected when the girl
+ 
+
+ align:start position:0%
+and he only gets rejected when the girl
+that he's serenading gets yet a better
+
+ align:start position:0%
+that he's serenading gets yet a better
+ 
+
+ align:start position:0%
+that he's serenading gets yet a better
+Suitor and so the girls are always going
+
+ align:start position:0%
+Suitor and so the girls are always going
+ 
+
+ align:start position:0%
+Suitor and so the girls are always going
+to improve we could reformulate this uh
+
+ align:start position:0%
+to improve we could reformulate this uh
+ 
+
+ align:start position:0%
+to improve we could reformulate this uh
+in in state machine Language by saying
+
+ align:start position:0%
+in in state machine Language by saying
+ 
+
+ align:start position:0%
+in in state machine Language by saying
+that the rank of a girl's favorite where
+
+ align:start position:0%
+that the rank of a girl's favorite where
+ 
+
+ align:start position:0%
+that the rank of a girl's favorite where
+she uh rates the boy that's serting her
+
+ align:start position:0%
+she uh rates the boy that's serting her
+ 
+
+ align:start position:0%
+she uh rates the boy that's serting her
+on her own list of preferences is a
+
+ align:start position:0%
+on her own list of preferences is a
+ 
+
+ align:start position:0%
+on her own list of preferences is a
+weekly increasing variable it never gets
+
+ align:start position:0%
+weekly increasing variable it never gets
+ 
+
+ align:start position:0%
+weekly increasing variable it never gets
+any worse from one day to the
+
+ align:start position:0%
+any worse from one day to the
+ 
+
+ align:start position:0%
+any worse from one day to the
+next by the same reasoning or similar
+
+ align:start position:0%
+next by the same reasoning or similar
+ 
+
+ align:start position:0%
+next by the same reasoning or similar
+reasoning a boy's favorite uh tomorrow
+
+ align:start position:0%
+reasoning a boy's favorite uh tomorrow
+ 
+
+ align:start position:0%
+reasoning a boy's favorite uh tomorrow
+is going to be uh no better than today's
+
+ align:start position:0%
+is going to be uh no better than today's
+ 
+
+ align:start position:0%
+is going to be uh no better than today's
+it might be worse and so it's no more
+
+ align:start position:0%
+it might be worse and so it's no more
+ 
+
+ align:start position:0%
+it might be worse and so it's no more
+the woman that he going to say tomorrow
+
+ align:start position:0%
+the woman that he going to say tomorrow
+ 
+
+ align:start position:0%
+the woman that he going to say tomorrow
+is no more desirable to him than today
+
+ align:start position:0%
+is no more desirable to him than today
+ 
+
+ align:start position:0%
+is no more desirable to him than today
+is basically because he works straight
+
+ align:start position:0%
+is basically because he works straight
+ 
+
+ align:start position:0%
+is basically because he works straight
+down his list if he hasn't been rejected
+
+ align:start position:0%
+down his list if he hasn't been rejected
+ 
+
+ align:start position:0%
+down his list if he hasn't been rejected
+he'll keep Serena the same woman
+
+ align:start position:0%
+he'll keep Serena the same woman
+ 
+
+ align:start position:0%
+he'll keep Serena the same woman
+tomorrow if he has been rejected then uh
+
+ align:start position:0%
+tomorrow if he has been rejected then uh
+ 
+
+ align:start position:0%
+tomorrow if he has been rejected then uh
+he's got to be working on somebody lower
+
+ align:start position:0%
+he's got to be working on somebody lower
+ 
+
+ align:start position:0%
+he's got to be working on somebody lower
+on his list that's less desirable so
+
+ align:start position:0%
+on his list that's less desirable so
+ 
+
+ align:start position:0%
+on his list that's less desirable so
+again the rank of a girl on a boy that a
+
+ align:start position:0%
+again the rank of a girl on a boy that a
+ 
+
+ align:start position:0%
+again the rank of a girl on a boy that a
+boy serenades is a weekly decreasing
+
+ align:start position:0%
+boy serenades is a weekly decreasing
+ 
+
+ align:start position:0%
+boy serenades is a weekly decreasing
+deriv variable of this process and these
+
+ align:start position:0%
+deriv variable of this process and these
+ 
+
+ align:start position:0%
+deriv variable of this process and these
+observations lead us to an invariant
+
+ align:start position:0%
+observations lead us to an invariant
+ 
+
+ align:start position:0%
+observations lead us to an invariant
+that holds for the mating ritual and the
+
+ align:start position:0%
+that holds for the mating ritual and the
+ 
+
+ align:start position:0%
+that holds for the mating ritual and the
+invariant is that if you look at any
+
+ align:start position:0%
+invariant is that if you look at any
+ 
+
+ align:start position:0%
+invariant is that if you look at any
+girl G um and if there's a boy B and G
+
+ align:start position:0%
+girl G um and if there's a boy B and G
+ 
+
+ align:start position:0%
+girl G um and if there's a boy B and G
+is not on B's list that is g must have
+
+ align:start position:0%
+is not on B's list that is g must have
+ 
+
+ align:start position:0%
+is not on B's list that is g must have
+been crossed off by B at some point then
+
+ align:start position:0%
+been crossed off by B at some point then
+ 
+
+ align:start position:0%
+been crossed off by B at some point then
+uh the invariant is that the girl G has
+
+ align:start position:0%
+uh the invariant is that the girl G has
+ 
+
+ align:start position:0%
+uh the invariant is that the girl G has
+a favorite that is
+
+ align:start position:0%
+a favorite that is
+ 
+
+ align:start position:0%
+a favorite that is
+uh better than than b and the reason is
+
+ align:start position:0%
+uh better than than b and the reason is
+ 
+
+ align:start position:0%
+uh better than than b and the reason is
+that again when G rejected B she had a
+
+ align:start position:0%
+that again when G rejected B she had a
+ 
+
+ align:start position:0%
+that again when G rejected B she had a
+better Suitor than b and her suitors
+
+ align:start position:0%
+better Suitor than b and her suitors
+ 
+
+ align:start position:0%
+better Suitor than b and her suitors
+keep getting better by the uh weekly
+
+ align:start position:0%
+keep getting better by the uh weekly
+ 
+
+ align:start position:0%
+keep getting better by the uh weekly
+increasing property of her suitors and
+
+ align:start position:0%
+increasing property of her suitors and
+ 
+
+ align:start position:0%
+increasing property of her suitors and
+therefore uh she's going to have a
+
+ align:start position:0%
+therefore uh she's going to have a
+ 
+
+ align:start position:0%
+therefore uh she's going to have a
+Suitor that she likes at Le better than
+
+ align:start position:0%
+Suitor that she likes at Le better than
+ 
+
+ align:start position:0%
+Suitor that she likes at Le better than
+be whose list she's not on this holds
+
+ align:start position:0%
+be whose list she's not on this holds
+ 
+
+ align:start position:0%
+be whose list she's not on this holds
+for all G's and B's uh and that is an
+
+ align:start position:0%
+for all G's and B's uh and that is an
+ 
+
+ align:start position:0%
+for all G's and B's uh and that is an
+invariant from one day to the
+
+ align:start position:0%
+invariant from one day to the
+ 
+
+ align:start position:0%
+invariant from one day to the
+next so let's look at what happens on
+
+ align:start position:0%
+next so let's look at what happens on
+ 
+
+ align:start position:0%
+next so let's look at what happens on
+the wedding day and use the invariant to
+
+ align:start position:0%
+the wedding day and use the invariant to
+ 
+
+ align:start position:0%
+the wedding day and use the invariant to
+prove that everybody's married and that
+
+ align:start position:0%
+prove that everybody's married and that
+ 
+
+ align:start position:0%
+prove that everybody's married and that
+stability
+
+ align:start position:0%
+stability
+ 
+
+ align:start position:0%
+stability
+holds so the first remark is that each
+
+ align:start position:0%
+holds so the first remark is that each
+ 
+
+ align:start position:0%
+holds so the first remark is that each
+girl has at most one Suitor and we've
+
+ align:start position:0%
+girl has at most one Suitor and we've
+ 
+
+ align:start position:0%
+girl has at most one Suitor and we've
+observed that's by definition of a
+
+ align:start position:0%
+observed that's by definition of a
+ 
+
+ align:start position:0%
+observed that's by definition of a
+wedding day and now what we want to
+
+ align:start position:0%
+wedding day and now what we want to
+ 
+
+ align:start position:0%
+wedding day and now what we want to
+prove is that um uh each boy gets
+
+ align:start position:0%
+prove is that um uh each boy gets
+ 
+
+ align:start position:0%
+prove is that um uh each boy gets
+married well what's going on with a boy
+
+ align:start position:0%
+married well what's going on with a boy
+ 
+
+ align:start position:0%
+married well what's going on with a boy
+um a boy is either married because he's
+
+ align:start position:0%
+um a boy is either married because he's
+ 
+
+ align:start position:0%
+um a boy is either married because he's
+seraing the top woman on his list
+
+ align:start position:0%
+seraing the top woman on his list
+ 
+
+ align:start position:0%
+seraing the top woman on his list
+or maybe all the all the women on his
+
+ align:start position:0%
+or maybe all the all the women on his
+ 
+
+ align:start position:0%
+or maybe all the all the women on his
+List have been crossed off then he's not
+
+ align:start position:0%
+List have been crossed off then he's not
+ 
+
+ align:start position:0%
+List have been crossed off then he's not
+seren Serena anybody so that's the only
+
+ align:start position:0%
+seren Serena anybody so that's the only
+ 
+
+ align:start position:0%
+seren Serena anybody so that's the only
+way that he could be not married now the
+
+ align:start position:0%
+way that he could be not married now the
+ 
+
+ align:start position:0%
+way that he could be not married now the
+reason that this is the case is that
+
+ align:start position:0%
+reason that this is the case is that
+ 
+
+ align:start position:0%
+reason that this is the case is that
+there's no bigamy here so um boys
+
+ align:start position:0%
+there's no bigamy here so um boys
+ 
+
+ align:start position:0%
+there's no bigamy here so um boys
+serenate only one girl at a time so um
+
+ align:start position:0%
+serenate only one girl at a time so um
+ 
+
+ align:start position:0%
+serenate only one girl at a time so um
+if a boy uh is married there's only one
+
+ align:start position:0%
+if a boy uh is married there's only one
+ 
+
+ align:start position:0%
+if a boy uh is married there's only one
+possible woman that he can be married to
+
+ align:start position:0%
+possible woman that he can be married to
+ 
+
+ align:start position:0%
+possible woman that he can be married to
+and a woman's only married to one
+
+ align:start position:0%
+and a woman's only married to one
+ 
+
+ align:start position:0%
+and a woman's only married to one
+possible boy so let's now put these
+
+ align:start position:0%
+possible boy so let's now put these
+ 
+
+ align:start position:0%
+possible boy so let's now put these
+facts together and ARG AR that everybody
+
+ align:start position:0%
+facts together and ARG AR that everybody
+ 
+
+ align:start position:0%
+facts together and ARG AR that everybody
+is married on the wedding day and the
+
+ align:start position:0%
+is married on the wedding day and the
+ 
+
+ align:start position:0%
+is married on the wedding day and the
+proof is by
+
+ align:start position:0%
+proof is by
+ 
+
+ align:start position:0%
+proof is by
+contradiction suppose there's some boy
+
+ align:start position:0%
+contradiction suppose there's some boy
+ 
+
+ align:start position:0%
+contradiction suppose there's some boy
+be That's not married well that happens
+
+ align:start position:0%
+be That's not married well that happens
+ 
+
+ align:start position:0%
+be That's not married well that happens
+exactly when his list is empty otherwise
+
+ align:start position:0%
+exactly when his list is empty otherwise
+ 
+
+ align:start position:0%
+exactly when his list is empty otherwise
+he'd be serenading somebody and be
+
+ align:start position:0%
+he'd be serenading somebody and be
+ 
+
+ align:start position:0%
+he'd be serenading somebody and be
+married to her but if his list is empty
+
+ align:start position:0%
+married to her but if his list is empty
+ 
+
+ align:start position:0%
+married to her but if his list is empty
+by the invariant every girl has a a
+
+ align:start position:0%
+by the invariant every girl has a a
+ 
+
+ align:start position:0%
+by the invariant every girl has a a
+Suitor that she likes better than be
+
+ align:start position:0%
+Suitor that she likes better than be
+ 
+
+ align:start position:0%
+Suitor that she likes better than be
+which means she's going to be married to
+
+ align:start position:0%
+which means she's going to be married to
+ 
+
+ align:start position:0%
+which means she's going to be married to
+somebody that she likes better than be
+
+ align:start position:0%
+somebody that she likes better than be
+ 
+
+ align:start position:0%
+somebody that she likes better than be
+every girl's married but there are the
+
+ align:start position:0%
+every girl's married but there are the
+ 
+
+ align:start position:0%
+every girl's married but there are the
+same number of boys and girls so in fact
+
+ align:start position:0%
+same number of boys and girls so in fact
+ 
+
+ align:start position:0%
+same number of boys and girls so in fact
+given that there's no bigamy all the
+
+ align:start position:0%
+given that there's no bigamy all the
+ 
+
+ align:start position:0%
+given that there's no bigamy all the
+boys have to be married too and that
+
+ align:start position:0%
+boys have to be married too and that
+ 
+
+ align:start position:0%
+boys have to be married too and that
+settles that one so the next crucial
+
+ align:start position:0%
+settles that one so the next crucial
+ 
+
+ align:start position:0%
+settles that one so the next crucial
+property that we're interested in is
+
+ align:start position:0%
+property that we're interested in is
+ 
+
+ align:start position:0%
+property that we're interested in is
+stability that in fact this set of
+
+ align:start position:0%
+stability that in fact this set of
+ 
+
+ align:start position:0%
+stability that in fact this set of
+marriages which must come into being on
+
+ align:start position:0%
+marriages which must come into being on
+ 
+
+ align:start position:0%
+marriages which must come into being on
+the wedding day um are all stable and
+
+ align:start position:0%
+the wedding day um are all stable and
+ 
+
+ align:start position:0%
+the wedding day um are all stable and
+the argument for stability uh has two
+
+ align:start position:0%
+the argument for stability uh has two
+ 
+
+ align:start position:0%
+the argument for stability uh has two
+cases both of them trivial and that
+
+ align:start position:0%
+cases both of them trivial and that
+ 
+
+ align:start position:0%
+cases both of them trivial and that
+follow immediately from the invariant um
+
+ align:start position:0%
+follow immediately from the invariant um
+ 
+
+ align:start position:0%
+follow immediately from the invariant um
+first of all let's look at an arbitrary
+
+ align:start position:0%
+first of all let's look at an arbitrary
+ 
+
+ align:start position:0%
+first of all let's look at an arbitrary
+boy Bob uh I claim that won't be in a
+
+ align:start position:0%
+boy Bob uh I claim that won't be in a
+ 
+
+ align:start position:0%
+boy Bob uh I claim that won't be in a
+rogue couple with case one any girl G
+
+ align:start position:0%
+rogue couple with case one any girl G
+ 
+
+ align:start position:0%
+rogue couple with case one any girl G
+that's on his final list because if a
+
+ align:start position:0%
+that's on his final list because if a
+ 
+
+ align:start position:0%
+that's on his final list because if a
+girl is on his final list then uh he's
+
+ align:start position:0%
+girl is on his final list then uh he's
+ 
+
+ align:start position:0%
+girl is on his final list then uh he's
+already married to the best of them he
+
+ align:start position:0%
+already married to the best of them he
+ 
+
+ align:start position:0%
+already married to the best of them he
+marries the girl at the top of his list
+
+ align:start position:0%
+marries the girl at the top of his list
+ 
+
+ align:start position:0%
+marries the girl at the top of his list
+so he's not going to be tempted to
+
+ align:start position:0%
+so he's not going to be tempted to
+ 
+
+ align:start position:0%
+so he's not going to be tempted to
+switch uh to be part of a rogue couple
+
+ align:start position:0%
+switch uh to be part of a rogue couple
+ 
+
+ align:start position:0%
+switch uh to be part of a rogue couple
+with some girl that's uh still on his
+
+ align:start position:0%
+with some girl that's uh still on his
+ 
+
+ align:start position:0%
+with some girl that's uh still on his
+list case two is he's not going to be in
+
+ align:start position:0%
+list case two is he's not going to be in
+ 
+
+ align:start position:0%
+list case two is he's not going to be in
+a rogue couple with a girl that's not on
+
+ align:start position:0%
+a rogue couple with a girl that's not on
+ 
+
+ align:start position:0%
+a rogue couple with a girl that's not on
+his list Because by the invariant she's
+
+ align:start position:0%
+his list Because by the invariant she's
+ 
+
+ align:start position:0%
+his list Because by the invariant she's
+married to somebody she likes better
+
+ align:start position:0%
+married to somebody she likes better
+ 
+
+ align:start position:0%
+married to somebody she likes better
+than him so there's no available girl
+
+ align:start position:0%
+than him so there's no available girl
+ 
+
+ align:start position:0%
+than him so there's no available girl
+either way for Bob to be in a rogue
+
+ align:start position:0%
+either way for Bob to be in a rogue
+ 
+
+ align:start position:0%
+either way for Bob to be in a rogue
+couple with Bob of course is an
+
+ align:start position:0%
+couple with Bob of course is an
+ 
+
+ align:start position:0%
+couple with Bob of course is an
+arbitrary um uh boy and therefore no boy
+
+ align:start position:0%
+arbitrary um uh boy and therefore no boy
+ 
+
+ align:start position:0%
+arbitrary um uh boy and therefore no boy
+is in a rogue couple and indeed there
+
+ align:start position:0%
+is in a rogue couple and indeed there
+ 
+
+ align:start position:0%
+is in a rogue couple and indeed there
+are no roog couples
\ No newline at end of file
diff --git a/70auqrv84y8.txt b/70auqrv84y8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a9d697bffb074c044e644e9f89f7aae9bbd62f7c
--- /dev/null
+++ b/70auqrv84y8.txt
@@ -0,0 +1,274 @@
+What we'd like to do is to create a single
+abstraction that can be used to address all
+
+our synchronization needs.
+
+In the early 1960's, the Dutch computer scientist
+Edsger Dijkstra proposed a new abstract data
+
+type called the semaphore, which has an integer
+value greater than or equal to 0.
+
+A programmer can declare a semaphore as shown
+here, specifying its initial value.
+
+The semaphore lives in a memory location shared
+by all the processes that need to synchronize
+
+their operation.
+
+The semaphore is accessed with two operations:
+WAIT and SIGNAL.
+
+The WAIT operation will wait until the specified
+semaphore has a value greater than 0, then
+
+it will decrement the semaphore value and
+return to the calling program.
+
+If the semaphore value is 0 when WAIT is called,
+conceptually execution is suspended until
+
+the semaphore value is non-zero.
+
+In a simple (inefficient) implementation,
+the WAIT routine loops, periodically testing
+
+the value of the semaphore, proceeding when
+its value is non-zero.
+
+The SIGNAL operation increments the value
+of the specified semaphore.
+
+If there any processes WAITing on that semaphore,
+exactly one of them may now proceed.
+
+We'll have to be careful with the implementation
+of SIGNAL and WAIT to ensure that the "exactly
+
+one" constraint is satisfied,
+i.e., that two processes both WAITing on the
+
+same semaphore won't both think they can decrement
+it and proceed after a SIGNAL.
+
+A semaphore initialized with the value K guarantees
+that the i_th call to SIGNAL will precede
+
+(i+K)_th call to WAIT.
+
+In a moment, we'll see some concrete examples
+that will make this clear.
+
+Note that in 6.004, we're ruling out semaphores
+with negative values.
+
+In the literature, you may see P(s) used in
+place of WAIT(s) and V(s) used in place of
+
+SIGNAL(s).
+
+These operation names are derived from the
+Dutch words for "test" and "increase".
+
+Let's see how to use semaphores to implement
+precedence constraints.
+
+Here are two processes, each running a program
+with 5 statements.
+
+Execution proceeds sequentially within each
+process, so A1 executes before A2, and so
+
+on.
+
+But there are no constraints on the order
+of execution between the processes, so statement
+
+B1 in Process B might be executed before or
+after any of the statements in Process A.
+
+Even if A and B are running in a timeshared
+environment on a single physical processor,
+
+execution may switch at any time between processes
+A and B.
+
+Suppose we wish to impose the constraint that
+the execution of statement A2 completes before
+
+execution of statement B4 begins.
+
+The red arrow shows the constraint we want.
+
+Here's the recipe for implementing this sort
+of simple precedence constraint using semaphores.
+
+First, declare a semaphore (called "s" in
+this example) and initialize its value to
+
+0.
+
+Place a call to signal(s) at the start of
+the arrow.
+
+In this example, signal(s) is placed after
+the statement A2 in process A.
+
+Then place a call to wait(s) at the end of
+the arrow.
+
+In this example, wait(s) is placed before
+the statement B4 in process B.
+
+With these modifications, process A executes
+as before, with the signal to semaphore s
+
+happening after statement A2 is executed.
+
+Statements B1 through B3 also execute as before,
+but when the wait(s) is executed, execution
+
+of process B is suspended until the signal(s)
+statement has finished execution.
+
+This guarantees that execution of B4 will
+start only after execution of A2 has completed.
+
+By initializing the semaphore s to 0, we enforced
+the constraint that the first call to signal(s)
+
+had to complete before the first call to wait(s)
+would succeed.
+
+Another way to think about semaphores is as
+a management tool for a shared pool of K resources,
+
+where K is the initial value of the semaphore.
+
+You use the SIGNAL operation to add or return
+resources to the shared pool.
+
+And you use the WAIT operation to allocate
+a resource for your exclusive use.
+
+At any given time, the value of the semaphore
+gives the number of unallocated resources
+
+still available in the shared pool.
+
+Note that the WAIT and SIGNAL operations can
+be in the same process, or they may be in
+
+different processes, depending on when the
+resource is allocated and returned.
+
+We can use semaphores to manage our N-character
+FIFO buffer.
+
+Here we've defined a semaphore CHARS and initialized
+it to 0.
+
+The value of CHARS will tell us how many characters
+are in the buffer.
+
+So SEND does a signal(CHARS) after it has
+added a character to the buffer, indicating
+
+the buffer now contains an additional character.
+
+And RCV does a wait(CHARS) to ensure the buffer
+has at least one character before reading
+
+from the buffer.
+
+Since CHARS was initialized to 0, we've enforced
+the constraint that the i_th call to signal(CHARS)
+
+precedes the completion of the i_th call to
+wait(CHARS).
+
+In other words, RCV can't consume a character
+until it has been placed in the buffer by
+
+SEND.
+
+Does this mean our producer and consumer are
+now properly synchronized?
+
+Using the CHARS semaphore, we implemented
+*one* of the two precedence constraints we
+
+identified as being necessary for correct
+operation.
+
+Next we'll see how to implement the other
+precedence constraint.
+
+What keeps the producer from putting more
+than N characters into the N-character buffer?
+
+Nothing.
+
+Oops, the producer can start to overwrite
+characters placed in the buffer earlier even
+
+though they haven't yet been read by the consumer.
+
+This is called buffer overflow and the sequence
+of characters transmitted from producer to
+
+consumer becomes hopelessly corrupted.
+
+What we've guaranteed so far is that the consumer
+can read a character only after the producer
+
+has placed it in the buffer, i.e., the consumer
+can't read from an empty buffer.
+
+What we still need to guarantee is that the
+producer can't get too far ahead of the consumer.
+
+Since the buffer holds at most N characters,
+the producer can't send the (i+N)th character
+
+until the consumer has read the i_th character.
+
+Here we've added a second semaphore, SPACES,
+to manage the number of spaces in the buffer.
+
+Initially the buffer is empty, so it has N
+spaces.
+
+The producer must WAIT for a space to be available.
+
+When SPACES in non-zero, the WAIT succeeds,
+decrementing the number of available spaces
+
+by one and then the producer fills that space
+with the next character.
+
+The consumer signals the availability of another
+space after it reads a character from the
+
+buffer.
+
+There's a nice symmetry here.
+
+The producer consumes spaces and produces
+characters.
+
+The consumer consumes characters and produces
+spaces.
+
+Semaphores are used to track the availability
+of both resources (i.e., characters and spaces),
+
+synchronizing the execution of the producer
+and consumer.
+
+This works great when there is a single producer
+process and a single consumer process.
+
+Next we'll think about what will happen if
+we have multiple producers and multiple consumers.
\ No newline at end of file
diff --git a/7Y5me3mwXpA.txt b/7Y5me3mwXpA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..173544f3b6bdaf6ce04bd680867c30fba6b2dcdd
--- /dev/null
+++ b/7Y5me3mwXpA.txt
@@ -0,0 +1,2419 @@
+align:start position:0%
+ 
+today we continue with our discussion of
+
+ align:start position:0%
+today we continue with our discussion of
+ 
+
+ align:start position:0%
+today we continue with our discussion of
+wkb so a few matters regarding wkb were
+
+ align:start position:0%
+wkb so a few matters regarding wkb were
+ 
+
+ align:start position:0%
+wkb so a few matters regarding wkb were
+explained in the last few segments we
+
+ align:start position:0%
+explained in the last few segments we
+ 
+
+ align:start position:0%
+explained in the last few segments we
+discussed that there would be a useful
+
+ align:start position:0%
+discussed that there would be a useful
+ 
+
+ align:start position:0%
+discussed that there would be a useful
+to define a position dependent momentum
+
+ align:start position:0%
+to define a position dependent momentum
+ 
+
+ align:start position:0%
+to define a position dependent momentum
+for a particle that is moving in a
+
+ align:start position:0%
+for a particle that is moving in a
+ 
+
+ align:start position:0%
+for a particle that is moving in a
+potential that was a completely
+
+ align:start position:0%
+potential that was a completely
+ 
+
+ align:start position:0%
+potential that was a completely
+classical notion but helped our
+
+ align:start position:0%
+classical notion but helped our
+ 
+
+ align:start position:0%
+classical notion but helped our
+terminology in solving the Schrodinger
+
+ align:start position:0%
+terminology in solving the Schrodinger
+ 
+
+ align:start position:0%
+terminology in solving the Schrodinger
+equation and set up the stage for some
+
+ align:start position:0%
+equation and set up the stage for some
+ 
+
+ align:start position:0%
+equation and set up the stage for some
+definitions for example a position
+
+ align:start position:0%
+definitions for example a position
+ 
+
+ align:start position:0%
+definitions for example a position
+dependent the Broglie wavelength that
+
+ align:start position:0%
+dependent the Broglie wavelength that
+ 
+
+ align:start position:0%
+dependent the Broglie wavelength that
+would be given by in terms of the
+
+ align:start position:0%
+would be given by in terms of the
+ 
+
+ align:start position:0%
+would be given by in terms of the
+position dependent momentum by the
+
+ align:start position:0%
+position dependent momentum by the
+ 
+
+ align:start position:0%
+position dependent momentum by the
+classic formula that they broadly use
+
+ align:start position:0%
+classic formula that they broadly use
+ 
+
+ align:start position:0%
+classic formula that they broadly use
+for particles that move with constant
+
+ align:start position:0%
+for particles that move with constant
+ 
+
+ align:start position:0%
+for particles that move with constant
+momentum then in this language the
+
+ align:start position:0%
+momentum then in this language the
+ 
+
+ align:start position:0%
+momentum then in this language the
+Schrodinger equation took the form of
+
+ align:start position:0%
+Schrodinger equation took the form of
+ 
+
+ align:start position:0%
+Schrodinger equation took the form of
+equation the time independent
+
+ align:start position:0%
+equation the time independent
+ 
+
+ align:start position:0%
+equation the time independent
+Schrodinger equation to the form P
+
+ align:start position:0%
+Schrodinger equation to the form P
+ 
+
+ align:start position:0%
+Schrodinger equation to the form P
+squared on sy is equal to P squared of x
+
+ align:start position:0%
+squared on sy is equal to P squared of x
+ 
+
+ align:start position:0%
+squared on sy is equal to P squared of x
+times Phi this is Phi of X and we
+
+ align:start position:0%
+times Phi this is Phi of X and we
+ 
+
+ align:start position:0%
+times Phi this is Phi of X and we
+mentioned that was kind of nice that the
+
+ align:start position:0%
+mentioned that was kind of nice that the
+ 
+
+ align:start position:0%
+mentioned that was kind of nice that the
+momentum operator ended up having sort
+
+ align:start position:0%
+momentum operator ended up having sort
+ 
+
+ align:start position:0%
+momentum operator ended up having sort
+of in the style of an eigenvalue vagin
+
+ align:start position:0%
+of in the style of an eigenvalue vagin
+ 
+
+ align:start position:0%
+of in the style of an eigenvalue vagin
+value P of X we then spoke about wave
+
+ align:start position:0%
+value P of X we then spoke about wave
+ 
+
+ align:start position:0%
+value P of X we then spoke about wave
+functions that in the wkb approximation
+
+ align:start position:0%
+functions that in the wkb approximation
+ 
+
+ align:start position:0%
+functions that in the wkb approximation
+would take form of an exponential with a
+
+ align:start position:0%
+would take form of an exponential with a
+ 
+
+ align:start position:0%
+would take form of an exponential with a
+face and a magnitude so the usual
+
+ align:start position:0%
+face and a magnitude so the usual
+ 
+
+ align:start position:0%
+face and a magnitude so the usual
+notation we have for complex numbers so
+
+ align:start position:0%
+notation we have for complex numbers so
+ 
+
+ align:start position:0%
+notation we have for complex numbers so
+the PSI of X and T would be written as
+
+ align:start position:0%
+the PSI of X and T would be written as
+ 
+
+ align:start position:0%
+the PSI of X and T would be written as
+Rho of X and T e to the I over H bar s
+
+ align:start position:0%
+Rho of X and T e to the I over H bar s
+ 
+
+ align:start position:0%
+Rho of X and T e to the I over H bar s
+of X and T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a typical form of a wkb
+
+ align:start position:0%
+that's a typical form of a wkb
+ 
+
+ align:start position:0%
+that's a typical form of a wkb
+wavefunction adieu we'll see soon and
+
+ align:start position:0%
+wavefunction adieu we'll see soon and
+ 
+
+ align:start position:0%
+wavefunction adieu we'll see soon and
+for such wave functions it's kind of
+
+ align:start position:0%
+for such wave functions it's kind of
+ 
+
+ align:start position:0%
+for such wave functions it's kind of
+manifest that row here is the charge
+
+ align:start position:0%
+manifest that row here is the charge
+ 
+
+ align:start position:0%
+manifest that row here is the charge
+density because if you think the norm
+
+ align:start position:0%
+density because if you think the norm
+ 
+
+ align:start position:0%
+density because if you think the norm
+squared of sy that gives you exactly ro
+
+ align:start position:0%
+squared of sy that gives you exactly ro
+ 
+
+ align:start position:0%
+squared of sy that gives you exactly ro
+the face cancels on the other hand the
+
+ align:start position:0%
+the face cancels on the other hand the
+ 
+
+ align:start position:0%
+the face cancels on the other hand the
+computation of the current was a little
+
+ align:start position:0%
+computation of the current was a little
+ 
+
+ align:start position:0%
+computation of the current was a little
+more interesting and they gave you Rho
+
+ align:start position:0%
+more interesting and they gave you Rho
+ 
+
+ align:start position:0%
+more interesting and they gave you Rho
+times gradient of s over m the mass of
+
+ align:start position:0%
+times gradient of s over m the mass of
+ 
+
+ align:start position:0%
+times gradient of s over m the mass of
+the particle so we identified the
+
+ align:start position:0%
+the particle so we identified the
+ 
+
+ align:start position:0%
+the particle so we identified the
+current as perpendicular to the surfaces
+
+ align:start position:0%
+current as perpendicular to the surfaces
+ 
+
+ align:start position:0%
+current as perpendicular to the surfaces
+of constant s or constant face in the
+
+ align:start position:0%
+of constant s or constant face in the
+ 
+
+ align:start position:0%
+of constant s or constant face in the
+exponent of the wkb equation our last
+
+ align:start position:0%
+exponent of the wkb equation our last
+ 
+
+ align:start position:0%
+exponent of the wkb equation our last
+comments had to do with lambda and we've
+
+ align:start position:0%
+comments had to do with lambda and we've
+ 
+
+ align:start position:0%
+comments had to do with lambda and we've
+said that we suspect that the semi
+
+ align:start position:0%
+said that we suspect that the semi
+ 
+
+ align:start position:0%
+said that we suspect that the semi
+classical approximation is valid in some
+
+ align:start position:0%
+classical approximation is valid in some
+ 
+
+ align:start position:0%
+classical approximation is valid in some
+way when lambda is small compared to
+
+ align:start position:0%
+way when lambda is small compared to
+ 
+
+ align:start position:0%
+way when lambda is small compared to
+physical length of a system or for
+
+ align:start position:0%
+physical length of a system or for
+ 
+
+ align:start position:0%
+physical length of a system or for
+lambda changes slowly as a function of
+
+ align:start position:0%
+lambda changes slowly as a function of
+ 
+
+ align:start position:0%
+lambda changes slowly as a function of
+position and those things we have not
+
+ align:start position:0%
+position and those things we have not
+ 
+
+ align:start position:0%
+position and those things we have not
+quite yet determined precisely how they
+
+ align:start position:0%
+quite yet determined precisely how they
+ 
+
+ align:start position:0%
+quite yet determined precisely how they
+go and some of what we have to do today
+
+ align:start position:0%
+go and some of what we have to do today
+ 
+
+ align:start position:0%
+go and some of what we have to do today
+is understand more concretely the nature
+
+ align:start position:0%
+is understand more concretely the nature
+ 
+
+ align:start position:0%
+is understand more concretely the nature
+of the approximation so the
+
+ align:start position:0%
+of the approximation so the
+ 
+
+ align:start position:0%
+of the approximation so the
+semi-classical approximation has
+
+ align:start position:0%
+semi-classical approximation has
+ 
+
+ align:start position:0%
+semi-classical approximation has
+something to do with lambda slowly
+
+ align:start position:0%
+something to do with lambda slowly
+ 
+
+ align:start position:0%
+something to do with lambda slowly
+varying varying and with lambda small in
+
+ align:start position:0%
+varying varying and with lambda small in
+ 
+
+ align:start position:0%
+varying varying and with lambda small in
+some sense and since you have an H bar
+
+ align:start position:0%
+some sense and since you have an H bar
+ 
+
+ align:start position:0%
+some sense and since you have an H bar
+in here that would make it small if H
+
+ align:start position:0%
+in here that would make it small if H
+ 
+
+ align:start position:0%
+in here that would make it small if H
+bar is small we also mentioned we would
+
+ align:start position:0%
+bar is small we also mentioned we would
+ 
+
+ align:start position:0%
+bar is small we also mentioned we would
+end up considering the limit as a sort
+
+ align:start position:0%
+end up considering the limit as a sort
+ 
+
+ align:start position:0%
+end up considering the limit as a sort
+of imaginary
+
+ align:start position:0%
+of imaginary
+ 
+
+ align:start position:0%
+of imaginary
+or fictitious limit in which h bar goes
+
+ align:start position:0%
+or fictitious limit in which h bar goes
+ 
+
+ align:start position:0%
+or fictitious limit in which h bar goes
+to zero so it's time to try to really do
+
+ align:start position:0%
+to zero so it's time to try to really do
+ 
+
+ align:start position:0%
+to zero so it's time to try to really do
+the approximation let let's try to write
+
+ align:start position:0%
+the approximation let let's try to write
+ 
+
+ align:start position:0%
+the approximation let let's try to write
+something and approximate the solution
+
+ align:start position:0%
+something and approximate the solution
+ 
+
+ align:start position:0%
+something and approximate the solution
+now we had a nice instructive form of
+
+ align:start position:0%
+now we had a nice instructive form of
+ 
+
+ align:start position:0%
+now we had a nice instructive form of
+the wavefunction there but I will take a
+
+ align:start position:0%
+the wavefunction there but I will take a
+ 
+
+ align:start position:0%
+the wavefunction there but I will take a
+simpler form in which the wave function
+
+ align:start position:0%
+simpler form in which the wave function
+ 
+
+ align:start position:0%
+simpler form in which the wave function
+will be just a pure exponential so
+
+ align:start position:0%
+will be just a pure exponential so
+ 
+
+ align:start position:0%
+will be just a pure exponential so
+setting the approximation scheme so
+
+ align:start position:0%
+setting the approximation scheme so
+ 
+
+ align:start position:0%
+setting the approximation scheme so
+approximation scheme so before I had the
+
+ align:start position:0%
+approximation scheme so before I had the
+ 
+
+ align:start position:0%
+approximation scheme so before I had the
+wave function that had a norm and a face
+
+ align:start position:0%
+wave function that had a norm and a face
+ 
+
+ align:start position:0%
+wave function that had a norm and a face
+now I want a wave function that looks
+
+ align:start position:0%
+now I want a wave function that looks
+ 
+
+ align:start position:0%
+now I want a wave function that looks
+like it just has a face you would say of
+
+ align:start position:0%
+like it just has a face you would say of
+ 
+
+ align:start position:0%
+like it just has a face you would say of
+course that's impossible so we will use
+
+ align:start position:0%
+course that's impossible so we will use
+ 
+
+ align:start position:0%
+course that's impossible so we will use
+for all for the time independent
+
+ align:start position:0%
+for all for the time independent
+ 
+
+ align:start position:0%
+for all for the time independent
+Schrodinger equation so we will use an S
+
+ align:start position:0%
+Schrodinger equation so we will use an S
+ 
+
+ align:start position:0%
+Schrodinger equation so we will use an S
+of X and we will write up side effects
+
+ align:start position:0%
+of X and we will write up side effects
+ 
+
+ align:start position:0%
+of X and we will write up side effects
+in the firm e to the I H bar s of X and
+
+ align:start position:0%
+in the firm e to the I H bar s of X and
+ 
+
+ align:start position:0%
+in the firm e to the I H bar s of X and
+you say no that's not true my usual wave
+
+ align:start position:0%
+you say no that's not true my usual wave
+ 
+
+ align:start position:0%
+you say no that's not true my usual wave
+functions are more than just faces are
+
+ align:start position:0%
+functions are more than just faces are
+ 
+
+ align:start position:0%
+functions are more than just faces are
+not just faces we've seen wave functions
+
+ align:start position:0%
+not just faces we've seen wave functions
+ 
+
+ align:start position:0%
+not just faces we've seen wave functions
+of different magnitude here that wave
+
+ align:start position:0%
+of different magnitude here that wave
+ 
+
+ align:start position:0%
+of different magnitude here that wave
+function would have always density equal
+
+ align:start position:0%
+function would have always density equal
+ 
+
+ align:start position:0%
+function would have always density equal
+to one but that is avoided that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+criticism is voided if you just simply
+
+ align:start position:0%
+criticism is voided if you just simply
+ 
+
+ align:start position:0%
+criticism is voided if you just simply
+say that s now may be a complex number
+
+ align:start position:0%
+say that s now may be a complex number
+ 
+
+ align:start position:0%
+say that s now may be a complex number
+so if s is itself a complex number the
+
+ align:start position:0%
+so if s is itself a complex number the
+ 
+
+ align:start position:0%
+so if s is itself a complex number the
+imaginary part of s provides the norm of
+
+ align:start position:0%
+imaginary part of s provides the norm of
+ 
+
+ align:start position:0%
+imaginary part of s provides the norm of
+the wave function so it's possible to do
+
+ align:start position:0%
+the wave function so it's possible to do
+ 
+
+ align:start position:0%
+the wave function so it's possible to do
+that any function can move any row up
+
+ align:start position:0%
+that any function can move any row up
+ 
+
+ align:start position:0%
+that any function can move any row up
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+can be written as the exponential of the
+
+ align:start position:0%
+can be written as the exponential of the
+ 
+
+ align:start position:0%
+can be written as the exponential of the
+log of something and then can be brought
+
+ align:start position:0%
+log of something and then can be brought
+ 
+
+ align:start position:0%
+log of something and then can be brought
+in the exponent and there's no loss of
+
+ align:start position:0%
+in the exponent and there's no loss of
+ 
+
+ align:start position:0%
+in the exponent and there's no loss of
+generality in writing something like
+
+ align:start position:0%
+generality in writing something like
+ 
+
+ align:start position:0%
+generality in writing something like
+that if s is complex now we have the
+
+ align:start position:0%
+that if s is complex now we have the
+ 
+
+ align:start position:0%
+that if s is complex now we have the
+Schrodinger equation and the sheraton
+
+ align:start position:0%
+Schrodinger equation and the sheraton
+ 
+
+ align:start position:0%
+Schrodinger equation and the sheraton
+equation was written there so it's minus
+
+ align:start position:0%
+equation was written there so it's minus
+ 
+
+ align:start position:0%
+equation was written there so it's minus
+H squared ii the x squared of Phi of X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to P squared of X e to the I
+
+ align:start position:0%
+is equal to P squared of X e to the I
+ 
+
+ align:start position:0%
+is equal to P squared of X e to the I
+over H bar s now when we differentiate
+
+ align:start position:0%
+over H bar s now when we differentiate
+ 
+
+ align:start position:0%
+over H bar s now when we differentiate
+an exponential we differentiate it two
+
+ align:start position:0%
+an exponential we differentiate it two
+ 
+
+ align:start position:0%
+an exponential we differentiate it two
+times we will have a couple of things we
+
+ align:start position:0%
+times we will have a couple of things we
+ 
+
+ align:start position:0%
+times we will have a couple of things we
+can differentiate the first time Brinson
+
+ align:start position:0%
+can differentiate the first time Brinson
+ 
+
+ align:start position:0%
+can differentiate the first time Brinson
+s prime down and the second time you can
+
+ align:start position:0%
+s prime down and the second time you can
+ 
+
+ align:start position:0%
+s prime down and the second time you can
+differentiate the exponential you can
+
+ align:start position:0%
+differentiate the exponential you can
+ 
+
+ align:start position:0%
+differentiate the exponential you can
+differentiate what is down already so
+
+ align:start position:0%
+differentiate what is down already so
+ 
+
+ align:start position:0%
+differentiate what is down already so
+it's two terms the first one would be
+
+ align:start position:0%
+it's two terms the first one would be
+ 
+
+ align:start position:0%
+it's two terms the first one would be
+imagine differentiating the first one s
+
+ align:start position:0%
+imagine differentiating the first one s
+ 
+
+ align:start position:0%
+imagine differentiating the first one s
+goes down and then the derivative acts
+
+ align:start position:0%
+goes down and then the derivative acts
+ 
+
+ align:start position:0%
+goes down and then the derivative acts
+on the S so you get I over H bar s
+
+ align:start position:0%
+on the S so you get I over H bar s
+ 
+
+ align:start position:0%
+on the S so you get I over H bar s
+double prime which is prime notation and
+
+ align:start position:0%
+double prime which is prime notation and
+ 
+
+ align:start position:0%
+double prime which is prime notation and
+the other one is when you differentiate
+
+ align:start position:0%
+the other one is when you differentiate
+ 
+
+ align:start position:0%
+the other one is when you differentiate
+once here it brings a factor down again
+
+ align:start position:0%
+once here it brings a factor down again
+ 
+
+ align:start position:0%
+once here it brings a factor down again
+there so it's plus I over H bar s prime
+
+ align:start position:0%
+there so it's plus I over H bar s prime
+ 
+
+ align:start position:0%
+there so it's plus I over H bar s prime
+squared and then the face is still there
+
+ align:start position:0%
+squared and then the face is still there
+ 
+
+ align:start position:0%
+squared and then the face is still there
+and it can cancel between the left and
+
+ align:start position:0%
+and it can cancel between the left and
+ 
+
+ align:start position:0%
+and it can cancel between the left and
+the right so this is equal to P squared
+
+ align:start position:0%
+the right so this is equal to P squared
+ 
+
+ align:start position:0%
+the right so this is equal to P squared
+of X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I took the derivative and canceled
+
+ align:start position:0%
+so I took the derivative and canceled
+ 
+
+ align:start position:0%
+so I took the derivative and canceled
+the Exponential's so cleaning this up a
+
+ align:start position:0%
+the Exponential's so cleaning this up a
+ 
+
+ align:start position:0%
+the Exponential's so cleaning this up a
+little bit will have this term over here
+
+ align:start position:0%
+little bit will have this term over here
+ 
+
+ align:start position:0%
+little bit will have this term over here
+that the ages cancel the sign cancels
+
+ align:start position:0%
+that the ages cancel the sign cancels
+ 
+
+ align:start position:0%
+that the ages cancel the sign cancels
+and you get s prime of x squared minus I
+
+ align:start position:0%
+and you get s prime of x squared minus I
+ 
+
+ align:start position:0%
+and you get s prime of x squared minus I
+h-bar is double prime is equal to P
+
+ align:start position:0%
+h-bar is double prime is equal to P
+ 
+
+ align:start position:0%
+h-bar is double prime is equal to P
+squared of X okay simple enough we have
+
+ align:start position:0%
+squared of X okay simple enough we have
+ 
+
+ align:start position:0%
+squared of X okay simple enough we have
+a derivation of that equation and the
+
+ align:start position:0%
+a derivation of that equation and the
+ 
+
+ align:start position:0%
+a derivation of that equation and the
+first thing that you say is it looks
+
+ align:start position:0%
+first thing that you say is it looks
+ 
+
+ align:start position:0%
+first thing that you say is it looks
+like we've gone backwards we've gone
+
+ align:start position:0%
+like we've gone backwards we've gone
+ 
+
+ align:start position:0%
+like we've gone backwards we've gone
+from our reasonably simple equation
+
+ align:start position:0%
+from our reasonably simple equation
+ 
+
+ align:start position:0%
+from our reasonably simple equation
+destroying our equation second order
+
+ align:start position:0%
+destroying our equation second order
+ 
+
+ align:start position:0%
+destroying our equation second order
+linear differential equation to a
+
+ align:start position:0%
+linear differential equation to a
+ 
+
+ align:start position:0%
+linear differential equation to a
+nonlinear equation here is the function
+
+ align:start position:0%
+nonlinear equation here is the function
+ 
+
+ align:start position:0%
+nonlinear equation here is the function
+squared the derivative square second
+
+ align:start position:0%
+squared the derivative square second
+ 
+
+ align:start position:0%
+squared the derivative square second
+derivative no fun is nothing linear
+
+ align:start position:0%
+derivative no fun is nothing linear
+ 
+
+ align:start position:0%
+derivative no fun is nothing linear
+about this equation in s if you have one
+
+ align:start position:0%
+about this equation in s if you have one
+ 
+
+ align:start position:0%
+about this equation in s if you have one
+solution for an S and another solution
+
+ align:start position:0%
+solution for an S and another solution
+ 
+
+ align:start position:0%
+solution for an S and another solution
+you cannot add them so this happens
+
+ align:start position:0%
+you cannot add them so this happens
+ 
+
+ align:start position:0%
+you cannot add them so this happens
+because we put everything in the
+
+ align:start position:0%
+because we put everything in the
+ 
+
+ align:start position:0%
+because we put everything in the
+exponential when you think double
+
+ align:start position:0%
+exponential when you think double
+ 
+
+ align:start position:0%
+exponential when you think double
+derivatives of an exponential you get a
+
+ align:start position:0%
+derivatives of an exponential you get a
+ 
+
+ align:start position:0%
+derivatives of an exponential you get a
+term with double derivatives in a term
+
+ align:start position:0%
+term with double derivatives in a term
+ 
+
+ align:start position:0%
+term with double derivatives in a term
+with a derivative squared there's
+
+ align:start position:0%
+with a derivative squared there's
+ 
+
+ align:start position:0%
+with a derivative squared there's
+nothing you can do and this still
+
+ align:start position:0%
+nothing you can do and this still
+ 
+
+ align:start position:0%
+nothing you can do and this still
+represents progress in some way even
+
+ align:start position:0%
+represents progress in some way even
+ 
+
+ align:start position:0%
+represents progress in some way even
+though it has become an equation that
+
+ align:start position:0%
+though it has become an equation that
+ 
+
+ align:start position:0%
+though it has become an equation that
+looks more difficult it can be tracted
+
+ align:start position:0%
+looks more difficult it can be tracted
+ 
+
+ align:start position:0%
+looks more difficult it can be tracted
+in some other way so the first and most
+
+ align:start position:0%
+in some other way so the first and most
+ 
+
+ align:start position:0%
+in some other way so the first and most
+important thing we want to say about
+
+ align:start position:0%
+important thing we want to say about
+ 
+
+ align:start position:0%
+important thing we want to say about
+this equation is that it's nonlinear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differential equation the h-bar term
+
+ align:start position:0%
+differential equation the h-bar term
+ 
+
+ align:start position:0%
+differential equation the h-bar term
+appears in just one position here and
+
+ align:start position:0%
+appears in just one position here and
+ 
+
+ align:start position:0%
+appears in just one position here and
+let's consider a following claim I will
+
+ align:start position:0%
+let's consider a following claim I will
+ 
+
+ align:start position:0%
+let's consider a following claim I will
+claim that I h-bar s double prime this
+
+ align:start position:0%
+claim that I h-bar s double prime this
+ 
+
+ align:start position:0%
+claim that I h-bar s double prime this
+term is small when V of X is slowly
+
+ align:start position:0%
+term is small when V of X is slowly
+ 
+
+ align:start position:0%
+term is small when V of X is slowly
+varying you see we're having in mind the
+
+ align:start position:0%
+varying you see we're having in mind the
+ 
+
+ align:start position:0%
+varying you see we're having in mind the
+situation with which a particle is
+
+ align:start position:0%
+situation with which a particle is
+ 
+
+ align:start position:0%
+situation with which a particle is
+moving in a potential a quantum particle
+
+ align:start position:0%
+moving in a potential a quantum particle
+ 
+
+ align:start position:0%
+moving in a potential a quantum particle
+so there it is P of X is well-defined
+
+ align:start position:0%
+so there it is P of X is well-defined
+ 
+
+ align:start position:0%
+so there it is P of X is well-defined
+that's the term that goes into this
+
+ align:start position:0%
+that's the term that goes into this
+ 
+
+ align:start position:0%
+that's the term that goes into this
+equation so this is partly known you may
+
+ align:start position:0%
+equation so this is partly known you may
+ 
+
+ align:start position:0%
+equation so this is partly known you may
+not know the energy but the potential
+
+ align:start position:0%
+not know the energy but the potential
+ 
+
+ align:start position:0%
+not know the energy but the potential
+you know and my claim and perhaps a very
+
+ align:start position:0%
+you know and my claim and perhaps a very
+ 
+
+ align:start position:0%
+you know and my claim and perhaps a very
+important claim about this equation that
+
+ align:start position:0%
+important claim about this equation that
+ 
+
+ align:start position:0%
+important claim about this equation that
+sets you going clearly is that when V of
+
+ align:start position:0%
+sets you going clearly is that when V of
+ 
+
+ align:start position:0%
+sets you going clearly is that when V of
+s is slowly varying this term is almost
+
+ align:start position:0%
+s is slowly varying this term is almost
+ 
+
+ align:start position:0%
+s is slowly varying this term is almost
+irrelevant okay that's the first thing
+
+ align:start position:0%
+irrelevant okay that's the first thing
+ 
+
+ align:start position:0%
+irrelevant okay that's the first thing
+we want to make sure we understand so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's assume indeed let's take V of X is
+
+ align:start position:0%
+let's assume indeed let's take V of X is
+ 
+
+ align:start position:0%
+let's assume indeed let's take V of X is
+equal to v-0 a constant so this is the
+
+ align:start position:0%
+equal to v-0 a constant so this is the
+ 
+
+ align:start position:0%
+equal to v-0 a constant so this is the
+extreme case of a slowly varying
+
+ align:start position:0%
+extreme case of a slowly varying
+ 
+
+ align:start position:0%
+extreme case of a slowly varying
+potential but just doesn't vary at all
+
+ align:start position:0%
+potential but just doesn't vary at all
+ 
+
+ align:start position:0%
+potential but just doesn't vary at all
+in that case P of X is going to be a
+
+ align:start position:0%
+in that case P of X is going to be a
+ 
+
+ align:start position:0%
+in that case P of X is going to be a
+constant and that constant is square
+
+ align:start position:0%
+constant and that constant is square
+ 
+
+ align:start position:0%
+constant and that constant is square
+root of 2m e minus V not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what do we have here we have a free
+
+ align:start position:0%
+and what do we have here we have a free
+ 
+
+ align:start position:0%
+and what do we have here we have a free
+particle this V of X is a constant so
+
+ align:start position:0%
+particle this V of X is a constant so
+ 
+
+ align:start position:0%
+particle this V of X is a constant so
+the solution of the Schrodinger equation
+
+ align:start position:0%
+the solution of the Schrodinger equation
+ 
+
+ align:start position:0%
+the solution of the Schrodinger equation
+that you know in general is that sigh of
+
+ align:start position:0%
+that you know in general is that sigh of
+ 
+
+ align:start position:0%
+that you know in general is that sigh of
+X is e to the I P naught X over H bar
+
+ align:start position:0%
+X is e to the I P naught X over H bar
+ 
+
+ align:start position:0%
+X is e to the I P naught X over H bar
+that solves the Schrodinger equation now
+
+ align:start position:0%
+that solves the Schrodinger equation now
+ 
+
+ align:start position:0%
+that solves the Schrodinger equation now
+we were talking about this equation so
+
+ align:start position:0%
+we were talking about this equation so
+ 
+
+ align:start position:0%
+we were talking about this equation so
+to connect to that equation in this
+
+ align:start position:0%
+to connect to that equation in this
+ 
+
+ align:start position:0%
+to connect to that equation in this
+situation of constant potential constant
+
+ align:start position:0%
+situation of constant potential constant
+ 
+
+ align:start position:0%
+situation of constant potential constant
+momentum in the classical sense and free
+
+ align:start position:0%
+momentum in the classical sense and free
+ 
+
+ align:start position:0%
+momentum in the classical sense and free
+particle with that constant momentum
+
+ align:start position:0%
+particle with that constant momentum
+ 
+
+ align:start position:0%
+particle with that constant momentum
+remember that s is the term here in the
+
+ align:start position:0%
+remember that s is the term here in the
+ 
+
+ align:start position:0%
+remember that s is the term here in the
+exponential so for this solution here s
+
+ align:start position:0%
+exponential so for this solution here s
+ 
+
+ align:start position:0%
+exponential so for this solution here s
+of X is equal to p0 X that's all it is
+
+ align:start position:0%
+of X is equal to p0 X that's all it is
+ 
+
+ align:start position:0%
+of X is equal to p0 X that's all it is
+it's whatever is left when you single
+
+ align:start position:0%
+it's whatever is left when you single
+ 
+
+ align:start position:0%
+it's whatever is left when you single
+out the I over H bar and let's look at
+
+ align:start position:0%
+out the I over H bar and let's look at
+ 
+
+ align:start position:0%
+out the I over H bar and let's look at
+that thing that should be a solution you
+
+ align:start position:0%
+that thing that should be a solution you
+ 
+
+ align:start position:0%
+that thing that should be a solution you
+see we've constructed the solution of
+
+ align:start position:0%
+see we've constructed the solution of
+ 
+
+ align:start position:0%
+see we've constructed the solution of
+the Schrodinger equation for constant
+
+ align:start position:0%
+the Schrodinger equation for constant
+ 
+
+ align:start position:0%
+the Schrodinger equation for constant
+potential we've read what s of X is that
+
+ align:start position:0%
+potential we've read what s of X is that
+ 
+
+ align:start position:0%
+potential we've read what s of X is that
+should solve this equation and how does
+
+ align:start position:0%
+should solve this equation and how does
+ 
+
+ align:start position:0%
+should solve this equation and how does
+it manage to solve it it manages to
+
+ align:start position:0%
+it manage to solve it it manages to
+ 
+
+ align:start position:0%
+it manage to solve it it manages to
+solve it because s prime of X then s
+
+ align:start position:0%
+solve it because s prime of X then s
+ 
+
+ align:start position:0%
+solve it because s prime of X then s
+prime of X is equal to P naught s double
+
+ align:start position:0%
+prime of X is equal to P naught s double
+ 
+
+ align:start position:0%
+prime of X is equal to P naught s double
+prime of X is equal to 0 and the
+
+ align:start position:0%
+prime of X is equal to 0 and the
+ 
+
+ align:start position:0%
+prime of X is equal to 0 and the
+equation works out with the first term
+
+ align:start position:0%
+equation works out with the first term
+ 
+
+ align:start position:0%
+equation works out with the first term
+squared P naught squared equal to P of x
+
+ align:start position:0%
+squared P naught squared equal to P of x
+ 
+
+ align:start position:0%
+squared P naught squared equal to P of x
+squared which is P naught squared so
+
+ align:start position:0%
+squared which is P naught squared so
+ 
+
+ align:start position:0%
+squared which is P naught squared so
+this term first term in the left hand
+
+ align:start position:0%
+this term first term in the left hand
+ 
+
+ align:start position:0%
+this term first term in the left hand
+side is equal to the right hand side
+
+ align:start position:0%
+side is equal to the right hand side
+ 
+
+ align:start position:0%
+side is equal to the right hand side
+this term is identically 0 so when the
+
+ align:start position:0%
+this term is identically 0 so when the
+ 
+
+ align:start position:0%
+this term is identically 0 so when the
+potential is constant that term IH bar s
+
+ align:start position:0%
+potential is constant that term IH bar s
+ 
+
+ align:start position:0%
+potential is constant that term IH bar s
+double prime plays no role it's 0
+
+ align:start position:0%
+double prime plays no role it's 0
+ 
+
+ align:start position:0%
+double prime plays no role it's 0
+so when so the term I h-bar s double
+
+ align:start position:0%
+so when so the term I h-bar s double
+ 
+
+ align:start position:0%
+so when so the term I h-bar s double
+prime is equal to zero so the claim now
+
+ align:start position:0%
+prime is equal to zero so the claim now
+ 
+
+ align:start position:0%
+prime is equal to zero so the claim now
+follows from fairly intuitive result if
+
+ align:start position:0%
+follows from fairly intuitive result if
+ 
+
+ align:start position:0%
+follows from fairly intuitive result if
+the potential is constant that term in
+
+ align:start position:0%
+the potential is constant that term in
+ 
+
+ align:start position:0%
+the potential is constant that term in
+the solution is zero if the potential
+
+ align:start position:0%
+the solution is zero if the potential
+ 
+
+ align:start position:0%
+the solution is zero if the potential
+will be extremely slowly varying that
+
+ align:start position:0%
+will be extremely slowly varying that
+ 
+
+ align:start position:0%
+will be extremely slowly varying that
+term should be very small you know you
+
+ align:start position:0%
+term should be very small you know you
+ 
+
+ align:start position:0%
+term should be very small you know you
+cannot expect that the constant
+
+ align:start position:0%
+cannot expect that the constant
+ 
+
+ align:start position:0%
+cannot expect that the constant
+potential has a solution and you doubt
+
+ align:start position:0%
+potential has a solution and you doubt
+ 
+
+ align:start position:0%
+potential has a solution and you doubt
+infinitesimal variation of your
+
+ align:start position:0%
+infinitesimal variation of your
+ 
+
+ align:start position:0%
+infinitesimal variation of your
+potential and suddenly this term becomes
+
+ align:start position:0%
+potential and suddenly this term becomes
+ 
+
+ align:start position:0%
+potential and suddenly this term becomes
+very big so for constant V I H bar s
+
+ align:start position:0%
+very big so for constant V I H bar s
+ 
+
+ align:start position:0%
+very big so for constant V I H bar s
+double prime equal zero so for four
+
+ align:start position:0%
+double prime equal zero so for four
+ 
+
+ align:start position:0%
+double prime equal zero so for four
+slowly varying V of X I H bar of s
+
+ align:start position:0%
+slowly varying V of X I H bar of s
+ 
+
+ align:start position:0%
+slowly varying V of X I H bar of s
+double prime should be small in the
+
+ align:start position:0%
+double prime should be small in the
+ 
+
+ align:start position:0%
+double prime should be small in the
+sense that this solution is
+
+ align:start position:0%
+sense that this solution is
+ 
+
+ align:start position:0%
+sense that this solution is
+approximately correct so if we do say
+
+ align:start position:0%
+approximately correct so if we do say
+ 
+
+ align:start position:0%
+approximately correct so if we do say
+that we've identified the term in the
+
+ align:start position:0%
+that we've identified the term in the
+ 
+
+ align:start position:0%
+that we've identified the term in the
+equation that is small when potentials
+
+ align:start position:0%
+equation that is small when potentials
+ 
+
+ align:start position:0%
+equation that is small when potentials
+are slowly vary therefore we will take
+
+ align:start position:0%
+are slowly vary therefore we will take
+ 
+
+ align:start position:0%
+are slowly vary therefore we will take
+that term as being the small term in
+
+ align:start position:0%
+that term as being the small term in
+ 
+
+ align:start position:0%
+that term as being the small term in
+that equation and this will be nicely
+
+ align:start position:0%
+that equation and this will be nicely
+ 
+
+ align:start position:0%
+that equation and this will be nicely
+implemented by considering as we said H
+
+ align:start position:0%
+implemented by considering as we said H
+ 
+
+ align:start position:0%
+implemented by considering as we said H
+bar going to 0 or H as a small parameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we will learn as we do the approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how to quantify what something that we
+
+ align:start position:0%
+how to quantify what something that we
+ 
+
+ align:start position:0%
+how to quantify what something that we
+call slowly varying is but we will take
+
+ align:start position:0%
+call slowly varying is but we will take
+ 
+
+ align:start position:0%
+call slowly varying is but we will take
+H now as a small parameter
+
+ align:start position:0%
+H now as a small parameter
+ 
+
+ align:start position:0%
+H now as a small parameter
+that makes that term small and set up an
+
+ align:start position:0%
+that makes that term small and set up an
+ 
+
+ align:start position:0%
+that makes that term small and set up an
+expansion to solve this equation that is
+
+ align:start position:0%
+expansion to solve this equation that is
+ 
+
+ align:start position:0%
+expansion to solve this equation that is
+our goal now so how do we set it up we
+
+ align:start position:0%
+our goal now so how do we set it up we
+ 
+
+ align:start position:0%
+our goal now so how do we set it up we
+set up like this we say as effects as
+
+ align:start position:0%
+set up like this we say as effects as
+ 
+
+ align:start position:0%
+set up like this we say as effects as
+we've learned in perturbation theories
+
+ align:start position:0%
+we've learned in perturbation theories
+ 
+
+ align:start position:0%
+we've learned in perturbation theories
+as 0 of X plus h bar as 1 of X the first
+
+ align:start position:0%
+as 0 of X plus h bar as 1 of X the first
+ 
+
+ align:start position:0%
+as 0 of X plus h bar as 1 of X the first
+correction plus h bar squared is 2 of X
+
+ align:start position:0%
+correction plus h bar squared is 2 of X
+ 
+
+ align:start position:0%
+correction plus h bar squared is 2 of X
+and higher order now H bar I'm sorry s
+
+ align:start position:0%
+and higher order now H bar I'm sorry s
+ 
+
+ align:start position:0%
+and higher order now H bar I'm sorry s
+already has units of H bar units of H
+
+ align:start position:0%
+already has units of H bar units of H
+ 
+
+ align:start position:0%
+already has units of H bar units of H
+bar so as 0 will have units of H bar to
+
+ align:start position:0%
+bar so as 0 will have units of H bar to
+ 
+
+ align:start position:0%
+bar so as 0 will have units of H bar to
+s 1 for example has no units so each
+
+ align:start position:0%
+s 1 for example has no units so each
+ 
+
+ align:start position:0%
+s 1 for example has no units so each
+term has a different set of units and
+
+ align:start position:0%
+term has a different set of units and
+ 
+
+ align:start position:0%
+term has a different set of units and
+that's okay because H bar has units and
+
+ align:start position:0%
+that's okay because H bar has units and
+ 
+
+ align:start position:0%
+that's okay because H bar has units and
+this will go like 1 over H bar units of
+
+ align:start position:0%
+this will go like 1 over H bar units of
+ 
+
+ align:start position:0%
+this will go like 1 over H bar units of
+1 over H bar and so for and so on so we
+
+ align:start position:0%
+1 over H bar and so for and so on so we
+ 
+
+ align:start position:0%
+1 over H bar and so for and so on so we
+have an expansion and this will call our
+
+ align:start position:0%
+have an expansion and this will call our
+ 
+
+ align:start position:0%
+have an expansion and this will call our
+semi-classical expansion as we applied
+
+ align:start position:0%
+semi-classical expansion as we applied
+ 
+
+ align:start position:0%
+semi-classical expansion as we applied
+now this expansion to that equation we
+
+ align:start position:0%
+now this expansion to that equation we
+ 
+
+ align:start position:0%
+now this expansion to that equation we
+should treat H as we treat at lambda in
+
+ align:start position:0%
+should treat H as we treat at lambda in
+ 
+
+ align:start position:0%
+should treat H as we treat at lambda in
+perturbation theory that is we imagine
+
+ align:start position:0%
+perturbation theory that is we imagine
+ 
+
+ align:start position:0%
+perturbation theory that is we imagine
+that this must be hald order by order in
+
+ align:start position:0%
+that this must be hald order by order in
+ 
+
+ align:start position:0%
+that this must be hald order by order in
+H bar because we imagine we have the
+
+ align:start position:0%
+H bar because we imagine we have the
+ 
+
+ align:start position:0%
+H bar because we imagine we have the
+flexibility of changing H bar
+
+ align:start position:0%
+flexibility of changing H bar
+ 
+
+ align:start position:0%
+flexibility of changing H bar
+so let's do this what do we have an
+
+ align:start position:0%
+so let's do this what do we have an
+ 
+
+ align:start position:0%
+so let's do this what do we have an
+equation we have s prime so the equation
+
+ align:start position:0%
+equation we have s prime so the equation
+ 
+
+ align:start position:0%
+equation we have s prime so the equation
+has s 0 prime plus h bar s 1 prime now I
+
+ align:start position:0%
+has s 0 prime plus h bar s 1 prime now I
+ 
+
+ align:start position:0%
+has s 0 prime plus h bar s 1 prime now I
+will keep terms up to order H bar so I
+
+ align:start position:0%
+will keep terms up to order H bar so I
+ 
+
+ align:start position:0%
+will keep terms up to order H bar so I
+will stop here plus order H bar squared
+
+ align:start position:0%
+will stop here plus order H bar squared
+ 
+
+ align:start position:0%
+will stop here plus order H bar squared
+squared minus IH bar s double prime so
+
+ align:start position:0%
+squared minus IH bar s double prime so
+ 
+
+ align:start position:0%
+squared minus IH bar s double prime so
+that should be s 0 double prime plus
+
+ align:start position:0%
+that should be s 0 double prime plus
+ 
+
+ align:start position:0%
+that should be s 0 double prime plus
+order H bar equal P squared of X so
+
+ align:start position:0%
+order H bar equal P squared of X so
+ 
+
+ align:start position:0%
+order H bar equal P squared of X so
+let's organize our terms we have s 0
+
+ align:start position:0%
+let's organize our terms we have s 0
+ 
+
+ align:start position:0%
+let's organize our terms we have s 0
+prime squared on the left hand side
+
+ align:start position:0%
+prime squared on the left hand side
+ 
+
+ align:start position:0%
+prime squared on the left hand side
+minus P squared of X I bring the P to
+
+ align:start position:0%
+minus P squared of X I bring the P to
+ 
+
+ align:start position:0%
+minus P squared of X I bring the P to
+the left hand side plus h bar so these
+
+ align:start position:0%
+the left hand side plus h bar so these
+ 
+
+ align:start position:0%
+the left hand side plus h bar so these
+are terms that have no H bar and when we
+
+ align:start position:0%
+are terms that have no H bar and when we
+ 
+
+ align:start position:0%
+are terms that have no H bar and when we
+look at H bar from the first term there
+
+ align:start position:0%
+look at H bar from the first term there
+ 
+
+ align:start position:0%
+look at H bar from the first term there
+we expand we square this thing so you
+
+ align:start position:0%
+we expand we square this thing so you
+ 
+
+ align:start position:0%
+we expand we square this thing so you
+can get the cross product between the s
+
+ align:start position:0%
+can get the cross product between the s
+ 
+
+ align:start position:0%
+can get the cross product between the s
+0 Prime and s y prime so you get 2 well
+
+ align:start position:0%
+0 Prime and s y prime so you get 2 well
+ 
+
+ align:start position:0%
+0 Prime and s y prime so you get 2 well
+to the H Prime already there to s 0
+
+ align:start position:0%
+to the H Prime already there to s 0
+ 
+
+ align:start position:0%
+to the H Prime already there to s 0
+prime s 1 Prime and from the second term
+
+ align:start position:0%
+prime s 1 Prime and from the second term
+ 
+
+ align:start position:0%
+prime s 1 Prime and from the second term
+you get minus I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s0 double prime plus order h squared
+
+ align:start position:0%
+s0 double prime plus order h squared
+ 
+
+ align:start position:0%
+s0 double prime plus order h squared
+equals zero so I just collected all the
+
+ align:start position:0%
+equals zero so I just collected all the
+ 
+
+ align:start position:0%
+equals zero so I just collected all the
+terms there so if we're believing in
+
+ align:start position:0%
+terms there so if we're believing in
+ 
+
+ align:start position:0%
+terms there so if we're believing in
+this expansion the first thing we should
+
+ align:start position:0%
+this expansion the first thing we should
+ 
+
+ align:start position:0%
+this expansion the first thing we should
+say that each coefficient in the power
+
+ align:start position:0%
+say that each coefficient in the power
+ 
+
+ align:start position:0%
+say that each coefficient in the power
+series of H bar is zero so we get two
+
+ align:start position:0%
+series of H bar is zero so we get two
+ 
+
+ align:start position:0%
+series of H bar is zero so we get two
+equations first one is s0 prime squared
+
+ align:start position:0%
+equations first one is s0 prime squared
+ 
+
+ align:start position:0%
+equations first one is s0 prime squared
+is equal to P squared of X it's one
+
+ align:start position:0%
+is equal to P squared of X it's one
+ 
+
+ align:start position:0%
+is equal to P squared of X it's one
+that's this term equal to zero and here
+
+ align:start position:0%
+that's this term equal to zero and here
+ 
+
+ align:start position:0%
+that's this term equal to zero and here
+we get let's write it in a way that we
+
+ align:start position:0%
+we get let's write it in a way that we
+ 
+
+ align:start position:0%
+we get let's write it in a way that we
+solve for the unknown supposedly from
+
+ align:start position:0%
+solve for the unknown supposedly from
+ 
+
+ align:start position:0%
+solve for the unknown supposedly from
+this first equation we can solve for x
+
+ align:start position:0%
+this first equation we can solve for x
+ 
+
+ align:start position:0%
+this first equation we can solve for x
+cs0
+
+ align:start position:0%
+cs0
+ 
+
+ align:start position:0%
+cs0
+if you know it's 0 what do you want now
+
+ align:start position:0%
+if you know it's 0 what do you want now
+ 
+
+ align:start position:0%
+if you know it's 0 what do you want now
+to know it says 1 prime so let's write
+
+ align:start position:0%
+to know it says 1 prime so let's write
+ 
+
+ align:start position:0%
+to know it says 1 prime so let's write
+this as s 1 prime is equal to I as 0
+
+ align:start position:0%
+this as s 1 prime is equal to I as 0
+ 
+
+ align:start position:0%
+this as s 1 prime is equal to I as 0
+double prime over to s 0 prime so these
+
+ align:start position:0%
+double prime over to s 0 prime so these
+ 
+
+ align:start position:0%
+double prime over to s 0 prime so these
+are my two equations
\ No newline at end of file
diff --git a/88tKZLGOr3M.txt b/88tKZLGOr3M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8a4f791f9748922523fdfda6a938ee1092674315
--- /dev/null
+++ b/88tKZLGOr3M.txt
@@ -0,0 +1,11739 @@
+align:start position:0%
+ 
+today we're going to continue building
+
+ align:start position:0%
+today we're going to continue building
+ 
+
+ align:start position:0%
+today we're going to continue building
+our equivalent circuit model of a neuron
+
+ align:start position:0%
+our equivalent circuit model of a neuron
+ 
+
+ align:start position:0%
+our equivalent circuit model of a neuron
+again this is the hodgkin-huxley model
+
+ align:start position:0%
+again this is the hodgkin-huxley model
+ 
+
+ align:start position:0%
+again this is the hodgkin-huxley model
+and it's the model was really developed
+
+ align:start position:0%
+and it's the model was really developed
+ 
+
+ align:start position:0%
+and it's the model was really developed
+around explaining how neurons generate
+
+ align:start position:0%
+around explaining how neurons generate
+ 
+
+ align:start position:0%
+around explaining how neurons generate
+action potentials there are two key ion
+
+ align:start position:0%
+action potentials there are two key ion
+ 
+
+ align:start position:0%
+action potentials there are two key ion
+channels that are associated with making
+
+ align:start position:0%
+channels that are associated with making
+ 
+
+ align:start position:0%
+channels that are associated with making
+spikes there's a sodium a sodium channel
+
+ align:start position:0%
+spikes there's a sodium a sodium channel
+ 
+
+ align:start position:0%
+spikes there's a sodium a sodium channel
+that that we model as a conductance in
+
+ align:start position:0%
+that that we model as a conductance in
+ 
+
+ align:start position:0%
+that that we model as a conductance in
+in series with a battery and there's a
+
+ align:start position:0%
+in series with a battery and there's a
+ 
+
+ align:start position:0%
+in series with a battery and there's a
+potassium conductance that we model the
+
+ align:start position:0%
+potassium conductance that we model the
+ 
+
+ align:start position:0%
+potassium conductance that we model the
+same way and again those two
+
+ align:start position:0%
+same way and again those two
+ 
+
+ align:start position:0%
+same way and again those two
+conductances cooperate to produce an
+
+ align:start position:0%
+conductances cooperate to produce an
+ 
+
+ align:start position:0%
+conductances cooperate to produce an
+action potential and we saw essentially
+
+ align:start position:0%
+action potential and we saw essentially
+ 
+
+ align:start position:0%
+action potential and we saw essentially
+how those two conductances together with
+
+ align:start position:0%
+how those two conductances together with
+ 
+
+ align:start position:0%
+how those two conductances together with
+their batteries the sodium battery is up
+
+ align:start position:0%
+their batteries the sodium battery is up
+ 
+
+ align:start position:0%
+their batteries the sodium battery is up
+at plus 50 or so millivolts the
+
+ align:start position:0%
+at plus 50 or so millivolts the
+ 
+
+ align:start position:0%
+at plus 50 or so millivolts the
+potassium battery is down at minus 75 or
+
+ align:start position:0%
+potassium battery is down at minus 75 or
+ 
+
+ align:start position:0%
+potassium battery is down at minus 75 or
+so millivolts and those two conductances
+
+ align:start position:0%
+so millivolts and those two conductances
+ 
+
+ align:start position:0%
+so millivolts and those two conductances
+then work to connect essentially connect
+
+ align:start position:0%
+then work to connect essentially connect
+ 
+
+ align:start position:0%
+then work to connect essentially connect
+the inside of the neuron to the plus
+
+ align:start position:0%
+the inside of the neuron to the plus
+ 
+
+ align:start position:0%
+the inside of the neuron to the plus
+battery and then to the minus battery to
+
+ align:start position:0%
+battery and then to the minus battery to
+ 
+
+ align:start position:0%
+battery and then to the minus battery to
+give you an action potential and you may
+
+ align:start position:0%
+give you an action potential and you may
+ 
+
+ align:start position:0%
+give you an action potential and you may
+remember that we saw what that looks
+
+ align:start position:0%
+remember that we saw what that looks
+ 
+
+ align:start position:0%
+remember that we saw what that looks
+like so here is plotting membrane
+
+ align:start position:0%
+like so here is plotting membrane
+ 
+
+ align:start position:0%
+like so here is plotting membrane
+potential in blue here we turn on this
+
+ align:start position:0%
+potential in blue here we turn on this
+ 
+
+ align:start position:0%
+potential in blue here we turn on this
+sodium conductance the voltage of the
+
+ align:start position:0%
+sodium conductance the voltage of the
+ 
+
+ align:start position:0%
+sodium conductance the voltage of the
+cell races up to about plus 55 then we
+
+ align:start position:0%
+cell races up to about plus 55 then we
+ 
+
+ align:start position:0%
+cell races up to about plus 55 then we
+turn off the sodium we turn on the
+
+ align:start position:0%
+turn off the sodium we turn on the
+ 
+
+ align:start position:0%
+turn off the sodium we turn on the
+potassium the voltage goes down to minus
+
+ align:start position:0%
+potassium the voltage goes down to minus
+ 
+
+ align:start position:0%
+potassium the voltage goes down to minus
+75 or so and then we turn off both
+
+ align:start position:0%
+75 or so and then we turn off both
+ 
+
+ align:start position:0%
+75 or so and then we turn off both
+conductances and the cell recover so you
+
+ align:start position:0%
+conductances and the cell recover so you
+ 
+
+ align:start position:0%
+conductances and the cell recover so you
+can see that that basically produces
+
+ align:start position:0%
+can see that that basically produces
+ 
+
+ align:start position:0%
+can see that that basically produces
+what looks like an action potential
+
+ align:start position:0%
+what looks like an action potential
+ 
+
+ align:start position:0%
+what looks like an action potential
+that's the basis of produced action
+
+ align:start position:0%
+that's the basis of produced action
+ 
+
+ align:start position:0%
+that's the basis of produced action
+potential production but we need in
+
+ align:start position:0%
+potential production but we need in
+ 
+
+ align:start position:0%
+potential production but we need in
+order to understand how these things
+
+ align:start position:0%
+order to understand how these things
+ 
+
+ align:start position:0%
+order to understand how these things
+turn on and off in the time course that
+
+ align:start position:0%
+turn on and off in the time course that
+ 
+
+ align:start position:0%
+turn on and off in the time course that
+they do we need to understand a little
+
+ align:start position:0%
+they do we need to understand a little
+ 
+
+ align:start position:0%
+they do we need to understand a little
+bit more about how these sodium and
+
+ align:start position:0%
+bit more about how these sodium and
+ 
+
+ align:start position:0%
+bit more about how these sodium and
+potassium conductances work and that's
+
+ align:start position:0%
+potassium conductances work and that's
+ 
+
+ align:start position:0%
+potassium conductances work and that's
+what we're going to focus on today so
+
+ align:start position:0%
+what we're going to focus on today so
+ 
+
+ align:start position:0%
+what we're going to focus on today so
+let's just start building our models so
+
+ align:start position:0%
+let's just start building our models so
+ 
+
+ align:start position:0%
+let's just start building our models so
+each one of those conductances with a
+
+ align:start position:0%
+each one of those conductances with a
+ 
+
+ align:start position:0%
+each one of those conductances with a
+with a battery is associated with a
+
+ align:start position:0%
+with a battery is associated with a
+ 
+
+ align:start position:0%
+with a battery is associated with a
+current there's a current that goes
+
+ align:start position:0%
+current there's a current that goes
+ 
+
+ align:start position:0%
+current there's a current that goes
+through each of those conductances the
+
+ align:start position:0%
+through each of those conductances the
+ 
+
+ align:start position:0%
+through each of those conductances the
+total current through the membrane the
+
+ align:start position:0%
+total current through the membrane the
+ 
+
+ align:start position:0%
+total current through the membrane the
+ionic current through the
+
+ align:start position:0%
+ionic current through the
+ 
+
+ align:start position:0%
+ionic current through the
+membrane in the hodgkin-huxley model is
+
+ align:start position:0%
+membrane in the hodgkin-huxley model is
+ 
+
+ align:start position:0%
+membrane in the hodgkin-huxley model is
+a sum of three components actually a
+
+ align:start position:0%
+a sum of three components actually a
+ 
+
+ align:start position:0%
+a sum of three components actually a
+sodium current a potassium current those
+
+ align:start position:0%
+sodium current a potassium current those
+ 
+
+ align:start position:0%
+sodium current a potassium current those
+two we just talked about and a leak
+
+ align:start position:0%
+two we just talked about and a leak
+ 
+
+ align:start position:0%
+two we just talked about and a leak
+current that is just a fixed current so
+
+ align:start position:0%
+current that is just a fixed current so
+ 
+
+ align:start position:0%
+current that is just a fixed current so
+the sodium and potassium currents are
+
+ align:start position:0%
+the sodium and potassium currents are
+ 
+
+ align:start position:0%
+the sodium and potassium currents are
+functions of time and voltage the leak
+
+ align:start position:0%
+functions of time and voltage the leak
+ 
+
+ align:start position:0%
+functions of time and voltage the leak
+current the leak conductance is just
+
+ align:start position:0%
+current the leak conductance is just
+ 
+
+ align:start position:0%
+current the leak conductance is just
+fixed and it has a battery of about
+
+ align:start position:0%
+fixed and it has a battery of about
+ 
+
+ align:start position:0%
+fixed and it has a battery of about
+minus 50 millivolts and it just tends to
+
+ align:start position:0%
+minus 50 millivolts and it just tends to
+ 
+
+ align:start position:0%
+minus 50 millivolts and it just tends to
+keep the cell sort of hyper polarized
+
+ align:start position:0%
+keep the cell sort of hyper polarized
+ 
+
+ align:start position:0%
+keep the cell sort of hyper polarized
+and these two these two currents these
+
+ align:start position:0%
+and these two these two currents these
+ 
+
+ align:start position:0%
+and these two these two currents these
+two conductances do the job of making an
+
+ align:start position:0%
+two conductances do the job of making an
+ 
+
+ align:start position:0%
+two conductances do the job of making an
+action potential so the total current
+
+ align:start position:0%
+action potential so the total current
+ 
+
+ align:start position:0%
+action potential so the total current
+membrane current is just a sum of those
+
+ align:start position:0%
+membrane current is just a sum of those
+ 
+
+ align:start position:0%
+membrane current is just a sum of those
+three parts and now we can just take
+
+ align:start position:0%
+three parts and now we can just take
+ 
+
+ align:start position:0%
+three parts and now we can just take
+that membrane current and plug it into
+
+ align:start position:0%
+that membrane current and plug it into
+ 
+
+ align:start position:0%
+that membrane current and plug it into
+this equation for the voltage as a
+
+ align:start position:0%
+this equation for the voltage as a
+ 
+
+ align:start position:0%
+this equation for the voltage as a
+function of of current now and solve
+
+ align:start position:0%
+function of of current now and solve
+ 
+
+ align:start position:0%
+function of of current now and solve
+that differential equation to get the
+
+ align:start position:0%
+that differential equation to get the
+ 
+
+ align:start position:0%
+that differential equation to get the
+voltage how to calculate how the voltage
+
+ align:start position:0%
+voltage how to calculate how the voltage
+ 
+
+ align:start position:0%
+voltage how to calculate how the voltage
+evolves in time in the presence of these
+
+ align:start position:0%
+evolves in time in the presence of these
+ 
+
+ align:start position:0%
+evolves in time in the presence of these
+membrane currents okay all right so you
+
+ align:start position:0%
+membrane currents okay all right so you
+ 
+
+ align:start position:0%
+membrane currents okay all right so you
+recall from the last lecture that you
+
+ align:start position:0%
+recall from the last lecture that you
+ 
+
+ align:start position:0%
+recall from the last lecture that you
+watched on video that these currents can
+
+ align:start position:0%
+watched on video that these currents can
+ 
+
+ align:start position:0%
+watched on video that these currents can
+be written down as a conductance so that
+
+ align:start position:0%
+be written down as a conductance so that
+ 
+
+ align:start position:0%
+be written down as a conductance so that
+let's just start here this is the most
+
+ align:start position:0%
+let's just start here this is the most
+ 
+
+ align:start position:0%
+let's just start here this is the most
+similar one to the one that you saw in
+
+ align:start position:0%
+similar one to the one that you saw in
+ 
+
+ align:start position:0%
+similar one to the one that you saw in
+the in the previous lecture the current
+
+ align:start position:0%
+the in the previous lecture the current
+ 
+
+ align:start position:0%
+the in the previous lecture the current
+is just a conductance times a driving
+
+ align:start position:0%
+is just a conductance times a driving
+ 
+
+ align:start position:0%
+is just a conductance times a driving
+potential and we described how that
+
+ align:start position:0%
+potential and we described how that
+ 
+
+ align:start position:0%
+potential and we described how that
+equation can be summarized in electrical
+
+ align:start position:0%
+equation can be summarized in electrical
+ 
+
+ align:start position:0%
+equation can be summarized in electrical
+circuit components as a resistor which
+
+ align:start position:0%
+circuit components as a resistor which
+ 
+
+ align:start position:0%
+circuit components as a resistor which
+is one over the conductance times a
+
+ align:start position:0%
+is one over the conductance times a
+ 
+
+ align:start position:0%
+is one over the conductance times a
+driving potential which is basically
+
+ align:start position:0%
+driving potential which is basically
+ 
+
+ align:start position:0%
+driving potential which is basically
+just the voltage drop across the
+
+ align:start position:0%
+just the voltage drop across the
+ 
+
+ align:start position:0%
+just the voltage drop across the
+conductance okay now each of these
+
+ align:start position:0%
+conductance okay now each of these
+ 
+
+ align:start position:0%
+conductance okay now each of these
+conductance is each of these currents is
+
+ align:start position:0%
+conductance is each of these currents is
+ 
+
+ align:start position:0%
+conductance is each of these currents is
+going to be written down by a very
+
+ align:start position:0%
+going to be written down by a very
+ 
+
+ align:start position:0%
+going to be written down by a very
+similar equation so the potassium
+
+ align:start position:0%
+similar equation so the potassium
+ 
+
+ align:start position:0%
+similar equation so the potassium
+current is just the potassium
+
+ align:start position:0%
+current is just the potassium
+ 
+
+ align:start position:0%
+current is just the potassium
+conductance times the driving potential
+
+ align:start position:0%
+conductance times the driving potential
+ 
+
+ align:start position:0%
+conductance times the driving potential
+for potassium which is just the membrane
+
+ align:start position:0%
+for potassium which is just the membrane
+ 
+
+ align:start position:0%
+for potassium which is just the membrane
+potential minus the ek and the sodium
+
+ align:start position:0%
+potential minus the ek and the sodium
+ 
+
+ align:start position:0%
+potential minus the ek and the sodium
+current is just the sodium conductance
+
+ align:start position:0%
+current is just the sodium conductance
+ 
+
+ align:start position:0%
+current is just the sodium conductance
+times the driving potential for sodium
+
+ align:start position:0%
+times the driving potential for sodium
+ 
+
+ align:start position:0%
+times the driving potential for sodium
+which is the membrane potential minus
+
+ align:start position:0%
+which is the membrane potential minus
+ 
+
+ align:start position:0%
+which is the membrane potential minus
+the sodium batter any questions yes yes
+
+ align:start position:0%
+the sodium batter any questions yes yes
+ 
+
+ align:start position:0%
+the sodium batter any questions yes yes
+so so unless I've made a mistake I've
+
+ align:start position:0%
+so so unless I've made a mistake I've
+ 
+
+ align:start position:0%
+so so unless I've made a mistake I've
+tried to put these remember that the
+
+ align:start position:0%
+tried to put these remember that the
+ 
+
+ align:start position:0%
+tried to put these remember that the
+potassium battery is is minus is
+
+ align:start position:0%
+potassium battery is is minus is
+ 
+
+ align:start position:0%
+potassium battery is is minus is
+negative right and the sodium battery is
+
+ align:start position:0%
+negative right and the sodium battery is
+ 
+
+ align:start position:0%
+negative right and the sodium battery is
+positive so I've tried to show that by
+
+ align:start position:0%
+positive so I've tried to show that by
+ 
+
+ align:start position:0%
+positive so I've tried to show that by
+putting the batteries in the opposite
+
+ align:start position:0%
+putting the batteries in the opposite
+ 
+
+ align:start position:0%
+putting the batteries in the opposite
+direction right so the battery symbol
+
+ align:start position:0%
+direction right so the battery symbol
+ 
+
+ align:start position:0%
+direction right so the battery symbol
+has one side that's that's supposed to
+
+ align:start position:0%
+has one side that's that's supposed to
+ 
+
+ align:start position:0%
+has one side that's that's supposed to
+indicate a positive voltage and the
+
+ align:start position:0%
+indicate a positive voltage and the
+ 
+
+ align:start position:0%
+indicate a positive voltage and the
+other side is negative so because they
+
+ align:start position:0%
+other side is negative so because they
+ 
+
+ align:start position:0%
+other side is negative so because they
+have the opposite sign I put them in
+
+ align:start position:0%
+have the opposite sign I put them in
+ 
+
+ align:start position:0%
+have the opposite sign I put them in
+backwards in the opposite direction does
+
+ align:start position:0%
+backwards in the opposite direction does
+ 
+
+ align:start position:0%
+backwards in the opposite direction does
+that make sense don't worry about that
+
+ align:start position:0%
+that make sense don't worry about that
+ 
+
+ align:start position:0%
+that make sense don't worry about that
+too much if I you know if I ask you to
+
+ align:start position:0%
+too much if I you know if I ask you to
+ 
+
+ align:start position:0%
+too much if I you know if I ask you to
+draw this I don't really care that much
+
+ align:start position:0%
+draw this I don't really care that much
+ 
+
+ align:start position:0%
+draw this I don't really care that much
+which way these things go I just want
+
+ align:start position:0%
+which way these things go I just want
+ 
+
+ align:start position:0%
+which way these things go I just want
+you to know that this one is negative on
+
+ align:start position:0%
+you to know that this one is negative on
+ 
+
+ align:start position:0%
+you to know that this one is negative on
+the inside and the the sodium is
+
+ align:start position:0%
+the inside and the the sodium is
+ 
+
+ align:start position:0%
+the inside and the the sodium is
+positive on the inside this is the
+
+ align:start position:0%
+positive on the inside this is the
+ 
+
+ align:start position:0%
+positive on the inside this is the
+inside of this out here right okay
+
+ align:start position:0%
+inside of this out here right okay
+ 
+
+ align:start position:0%
+inside of this out here right okay
+the sodium battery drives the inside of
+
+ align:start position:0%
+the sodium battery drives the inside of
+ 
+
+ align:start position:0%
+the sodium battery drives the inside of
+the cell toward positive voltage because
+
+ align:start position:0%
+the cell toward positive voltage because
+ 
+
+ align:start position:0%
+the cell toward positive voltage because
+you have positive ions flowing into the
+
+ align:start position:0%
+you have positive ions flowing into the
+ 
+
+ align:start position:0%
+you have positive ions flowing into the
+cell so you can see now that the
+
+ align:start position:0%
+cell so you can see now that the
+ 
+
+ align:start position:0%
+cell so you can see now that the
+membrane potential here depends on the
+
+ align:start position:0%
+membrane potential here depends on the
+ 
+
+ align:start position:0%
+membrane potential here depends on the
+membrane currents right through this
+
+ align:start position:0%
+membrane currents right through this
+ 
+
+ align:start position:0%
+membrane currents right through this
+differential equation but the membrane
+
+ align:start position:0%
+differential equation but the membrane
+ 
+
+ align:start position:0%
+differential equation but the membrane
+currents the sodium potassium and leak
+
+ align:start position:0%
+currents the sodium potassium and leak
+ 
+
+ align:start position:0%
+currents the sodium potassium and leak
+cards all depend on these conductances
+
+ align:start position:0%
+cards all depend on these conductances
+ 
+
+ align:start position:0%
+cards all depend on these conductances
+right and these conductances for the
+
+ align:start position:0%
+right and these conductances for the
+ 
+
+ align:start position:0%
+right and these conductances for the
+sodium and potassium are voltage
+
+ align:start position:0%
+sodium and potassium are voltage
+ 
+
+ align:start position:0%
+sodium and potassium are voltage
+dependent and time dependent so you can
+
+ align:start position:0%
+dependent and time dependent so you can
+ 
+
+ align:start position:0%
+dependent and time dependent so you can
+see that the conductances depend on the
+
+ align:start position:0%
+see that the conductances depend on the
+ 
+
+ align:start position:0%
+see that the conductances depend on the
+voltage right so the membrane potential
+
+ align:start position:0%
+voltage right so the membrane potential
+ 
+
+ align:start position:0%
+voltage right so the membrane potential
+depends on current current depends on
+
+ align:start position:0%
+depends on current current depends on
+ 
+
+ align:start position:0%
+depends on current current depends on
+conductances but the conductance is
+
+ align:start position:0%
+conductances but the conductance is
+ 
+
+ align:start position:0%
+conductances but the conductance is
+depend on the membrane potential so it
+
+ align:start position:0%
+depend on the membrane potential so it
+ 
+
+ align:start position:0%
+depend on the membrane potential so it
+goes around and around and around right
+
+ align:start position:0%
+goes around and around and around right
+ 
+
+ align:start position:0%
+goes around and around and around right
+so those things all depend on each other
+
+ align:start position:0%
+so those things all depend on each other
+ 
+
+ align:start position:0%
+so those things all depend on each other
+and so what we are setting out to do is
+
+ align:start position:0%
+and so what we are setting out to do is
+ 
+
+ align:start position:0%
+and so what we are setting out to do is
+to write down the way those things
+
+ align:start position:0%
+to write down the way those things
+ 
+
+ align:start position:0%
+to write down the way those things
+depend on each other the way you can
+
+ align:start position:0%
+depend on each other the way you can
+ 
+
+ align:start position:0%
+depend on each other the way you can
+think about that system evolving in time
+
+ align:start position:0%
+think about that system evolving in time
+ 
+
+ align:start position:0%
+think about that system evolving in time
+so let me just show you what the planet
+
+ align:start position:0%
+so let me just show you what the planet
+ 
+
+ align:start position:0%
+so let me just show you what the planet
+so the plan is to write down an
+
+ align:start position:0%
+so the plan is to write down an
+ 
+
+ align:start position:0%
+so the plan is to write down an
+algorithm basically a for loop
+
+ align:start position:0%
+algorithm basically a for loop
+ 
+
+ align:start position:0%
+algorithm basically a for loop
+that describes how the membrane how the
+
+ align:start position:0%
+that describes how the membrane how the
+ 
+
+ align:start position:0%
+that describes how the membrane how the
+neuron generates an action potential let
+
+ align:start position:0%
+neuron generates an action potential let
+ 
+
+ align:start position:0%
+neuron generates an action potential let
+me just walk you through the steps of
+
+ align:start position:0%
+me just walk you through the steps of
+ 
+
+ align:start position:0%
+me just walk you through the steps of
+that and then I'll get to your question
+
+ align:start position:0%
+that and then I'll get to your question
+ 
+
+ align:start position:0%
+that and then I'll get to your question
+so we're going to start with some
+
+ align:start position:0%
+so we're going to start with some
+ 
+
+ align:start position:0%
+so we're going to start with some
+membrane potential V and we're going to
+
+ align:start position:0%
+membrane potential V and we're going to
+ 
+
+ align:start position:0%
+membrane potential V and we're going to
+calculate the the voltage dependent
+
+ align:start position:0%
+calculate the the voltage dependent
+ 
+
+ align:start position:0%
+calculate the the voltage dependent
+parameters of the sodium and potassium
+
+ align:start position:0%
+parameters of the sodium and potassium
+ 
+
+ align:start position:0%
+parameters of the sodium and potassium
+conductance using that membrane
+
+ align:start position:0%
+conductance using that membrane
+ 
+
+ align:start position:0%
+conductance using that membrane
+potential and once we have those
+
+ align:start position:0%
+potential and once we have those
+ 
+
+ align:start position:0%
+potential and once we have those
+parameters we can actually calculate the
+
+ align:start position:0%
+parameters we can actually calculate the
+ 
+
+ align:start position:0%
+parameters we can actually calculate the
+conductance for each of those for the
+
+ align:start position:0%
+conductance for each of those for the
+ 
+
+ align:start position:0%
+conductance for each of those for the
+sodium and potassium once you know the
+
+ align:start position:0%
+sodium and potassium once you know the
+ 
+
+ align:start position:0%
+sodium and potassium once you know the
+conductance you can get the currents
+
+ align:start position:0%
+conductance you can get the currents
+ 
+
+ align:start position:0%
+conductance you can get the currents
+once you have the currents you can
+
+ align:start position:0%
+once you have the currents you can
+ 
+
+ align:start position:0%
+once you have the currents you can
+compute the total membrane current just
+
+ align:start position:0%
+compute the total membrane current just
+ 
+
+ align:start position:0%
+compute the total membrane current just
+by adding them all together then you can
+
+ align:start position:0%
+by adding them all together then you can
+ 
+
+ align:start position:0%
+by adding them all together then you can
+compute once you have all those currents
+
+ align:start position:0%
+compute once you have all those currents
+ 
+
+ align:start position:0%
+compute once you have all those currents
+you just compute V infinity which is
+
+ align:start position:0%
+you just compute V infinity which is
+ 
+
+ align:start position:0%
+you just compute V infinity which is
+just the current times the resistance
+
+ align:start position:0%
+just the current times the resistance
+ 
+
+ align:start position:0%
+just the current times the resistance
+the effective resistance then we're
+
+ align:start position:0%
+the effective resistance then we're
+ 
+
+ align:start position:0%
+the effective resistance then we're
+going to integrate our first-order
+
+ align:start position:0%
+going to integrate our first-order
+ 
+
+ align:start position:0%
+going to integrate our first-order
+linear differential equation to get a
+
+ align:start position:0%
+linear differential equation to get a
+ 
+
+ align:start position:0%
+linear differential equation to get a
+new voltage as a function of being a
+
+ align:start position:0%
+new voltage as a function of being a
+ 
+
+ align:start position:0%
+new voltage as a function of being a
+time and B infinity and then we're just
+
+ align:start position:0%
+time and B infinity and then we're just
+ 
+
+ align:start position:0%
+time and B infinity and then we're just
+going to go back and start again so
+
+ align:start position:0%
+going to go back and start again so
+ 
+
+ align:start position:0%
+going to go back and start again so
+that's the algorithm that a neuron uses
+
+ align:start position:0%
+that's the algorithm that a neuron uses
+ 
+
+ align:start position:0%
+that's the algorithm that a neuron uses
+to generate a spike okay and that's what
+
+ align:start position:0%
+to generate a spike okay and that's what
+ 
+
+ align:start position:0%
+to generate a spike okay and that's what
+we're going to work out now we've talked
+
+ align:start position:0%
+we're going to work out now we've talked
+ 
+
+ align:start position:0%
+we're going to work out now we've talked
+about these things over the last few
+
+ align:start position:0%
+about these things over the last few
+ 
+
+ align:start position:0%
+about these things over the last few
+lectures how you can how you can relate
+
+ align:start position:0%
+lectures how you can how you can relate
+ 
+
+ align:start position:0%
+lectures how you can how you can relate
+total current to V infinity and then
+
+ align:start position:0%
+total current to V infinity and then
+ 
+
+ align:start position:0%
+total current to V infinity and then
+integrate a first-order linear
+
+ align:start position:0%
+integrate a first-order linear
+ 
+
+ align:start position:0%
+integrate a first-order linear
+differential equation which is just
+
+ align:start position:0%
+differential equation which is just
+ 
+
+ align:start position:0%
+differential equation which is just
+relaxing exponentially toward the
+
+ align:start position:0%
+relaxing exponentially toward the
+ 
+
+ align:start position:0%
+relaxing exponentially toward the
+infinity but now we're going to put
+
+ align:start position:0%
+infinity but now we're going to put
+ 
+
+ align:start position:0%
+infinity but now we're going to put
+these things in figure out the voltage
+
+ align:start position:0%
+these things in figure out the voltage
+ 
+
+ align:start position:0%
+these things in figure out the voltage
+and time dependence of the sodium and
+
+ align:start position:0%
+and time dependence of the sodium and
+ 
+
+ align:start position:0%
+and time dependence of the sodium and
+potassium conductances yes yes it's
+
+ align:start position:0%
+potassium conductances yes yes it's
+ 
+
+ align:start position:0%
+potassium conductances yes yes it's
+primarily potassium it has a negative
+
+ align:start position:0%
+primarily potassium it has a negative
+ 
+
+ align:start position:0%
+primarily potassium it has a negative
+potential but it's just constant so
+
+ align:start position:0%
+potential but it's just constant so
+ 
+
+ align:start position:0%
+potential but it's just constant so
+we're not really going to pay much
+
+ align:start position:0%
+we're not really going to pay much
+ 
+
+ align:start position:0%
+we're not really going to pay much
+attention to it okay so if the sodium
+
+ align:start position:0%
+attention to it okay so if the sodium
+ 
+
+ align:start position:0%
+attention to it okay so if the sodium
+and potassium currents are off then the
+
+ align:start position:0%
+and potassium currents are off then the
+ 
+
+ align:start position:0%
+and potassium currents are off then the
+leak current still keeps the cell
+
+ align:start position:0%
+leak current still keeps the cell
+ 
+
+ align:start position:0%
+leak current still keeps the cell
+hyperpolarized okay
+
+ align:start position:0%
+hyperpolarized okay
+ 
+
+ align:start position:0%
+hyperpolarized okay
+all right any questions that's the big
+
+ align:start position:0%
+all right any questions that's the big
+ 
+
+ align:start position:0%
+all right any questions that's the big
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+okay so here are our learning objectives
+
+ align:start position:0%
+okay so here are our learning objectives
+ 
+
+ align:start position:0%
+okay so here are our learning objectives
+I'd like you to be able to draw that
+
+ align:start position:0%
+I'd like you to be able to draw that
+ 
+
+ align:start position:0%
+I'd like you to be able to draw that
+circuit diagram not worrying about the
+
+ align:start position:0%
+circuit diagram not worrying about the
+ 
+
+ align:start position:0%
+circuit diagram not worrying about the
+long and short sides of the battery I'm
+
+ align:start position:0%
+long and short sides of the battery I'm
+ 
+
+ align:start position:0%
+long and short sides of the battery I'm
+going to we're going to talk about how
+
+ align:start position:0%
+going to we're going to talk about how
+ 
+
+ align:start position:0%
+going to we're going to talk about how
+we measure the properties of ion
+
+ align:start position:0%
+we measure the properties of ion
+ 
+
+ align:start position:0%
+we measure the properties of ion
+channels
+
+ align:start position:0%
+channels
+ 
+
+ align:start position:0%
+channels
+that's called a voltage clamp so I want
+
+ align:start position:0%
+that's called a voltage clamp so I want
+ 
+
+ align:start position:0%
+that's called a voltage clamp so I want
+you to be able to describe what that is
+
+ align:start position:0%
+you to be able to describe what that is
+ 
+
+ align:start position:0%
+you to be able to describe what that is
+I'd like you to be able to plot the
+
+ align:start position:0%
+I'd like you to be able to plot the
+ 
+
+ align:start position:0%
+I'd like you to be able to plot the
+voltage and time dependence of of the
+
+ align:start position:0%
+voltage and time dependence of of the
+ 
+
+ align:start position:0%
+voltage and time dependence of of the
+potassium current for today the next
+
+ align:start position:0%
+potassium current for today the next
+ 
+
+ align:start position:0%
+potassium current for today the next
+lecture we'll talk about the sodium
+
+ align:start position:0%
+lecture we'll talk about the sodium
+ 
+
+ align:start position:0%
+lecture we'll talk about the sodium
+current so we'll add that to our list of
+
+ align:start position:0%
+current so we'll add that to our list of
+ 
+
+ align:start position:0%
+current so we'll add that to our list of
+things that we need to know but for
+
+ align:start position:0%
+things that we need to know but for
+ 
+
+ align:start position:0%
+things that we need to know but for
+today I'd like you to be able to plot
+
+ align:start position:0%
+today I'd like you to be able to plot
+ 
+
+ align:start position:0%
+today I'd like you to be able to plot
+the voltage and time dependence of the
+
+ align:start position:0%
+the voltage and time dependence of the
+ 
+
+ align:start position:0%
+the voltage and time dependence of the
+potassium current and conductance and be
+
+ align:start position:0%
+potassium current and conductance and be
+ 
+
+ align:start position:0%
+potassium current and conductance and be
+able to explain biophysically where the
+
+ align:start position:0%
+able to explain biophysically where the
+ 
+
+ align:start position:0%
+able to explain biophysically where the
+time and voltage dependence of that
+
+ align:start position:0%
+time and voltage dependence of that
+ 
+
+ align:start position:0%
+time and voltage dependence of that
+potassium conductance comes from and be
+
+ align:start position:0%
+potassium conductance comes from and be
+ 
+
+ align:start position:0%
+potassium conductance comes from and be
+able to write it down in terms of
+
+ align:start position:0%
+able to write it down in terms of
+ 
+
+ align:start position:0%
+able to write it down in terms of
+quantities that we're going to call that
+
+ align:start position:0%
+quantities that we're going to call that
+ 
+
+ align:start position:0%
+quantities that we're going to call that
+are called the hodgkin-huxley gating
+
+ align:start position:0%
+are called the hodgkin-huxley gating
+ 
+
+ align:start position:0%
+are called the hodgkin-huxley gating
+variables okay so that's that's the plan
+
+ align:start position:0%
+variables okay so that's that's the plan
+ 
+
+ align:start position:0%
+variables okay so that's that's the plan
+all right so let's come back to our
+
+ align:start position:0%
+all right so let's come back to our
+ 
+
+ align:start position:0%
+all right so let's come back to our
+circuit again we have a sodium current
+
+ align:start position:0%
+circuit again we have a sodium current
+ 
+
+ align:start position:0%
+circuit again we have a sodium current
+that's the sodium conductance times the
+
+ align:start position:0%
+that's the sodium conductance times the
+ 
+
+ align:start position:0%
+that's the sodium conductance times the
+sodium driving potential the conductance
+
+ align:start position:0%
+sodium driving potential the conductance
+ 
+
+ align:start position:0%
+sodium driving potential the conductance
+is voltage and time dependent the
+
+ align:start position:0%
+is voltage and time dependent the
+ 
+
+ align:start position:0%
+is voltage and time dependent the
+equilibrium potential for sodium again
+
+ align:start position:0%
+equilibrium potential for sodium again
+ 
+
+ align:start position:0%
+equilibrium potential for sodium again
+is plus 55 millivolts the potassium
+
+ align:start position:0%
+is plus 55 millivolts the potassium
+ 
+
+ align:start position:0%
+is plus 55 millivolts the potassium
+current is just potassium conductance
+
+ align:start position:0%
+current is just potassium conductance
+ 
+
+ align:start position:0%
+current is just potassium conductance
+times the potassium driving potential
+
+ align:start position:0%
+times the potassium driving potential
+ 
+
+ align:start position:0%
+times the potassium driving potential
+that the driving potential is reference
+
+ align:start position:0%
+that the driving potential is reference
+ 
+
+ align:start position:0%
+that the driving potential is reference
+to a battery and equilibrium potential
+
+ align:start position:0%
+to a battery and equilibrium potential
+ 
+
+ align:start position:0%
+to a battery and equilibrium potential
+at minus 75 and the leak has a battery
+
+ align:start position:0%
+at minus 75 and the leak has a battery
+ 
+
+ align:start position:0%
+at minus 75 and the leak has a battery
+at minus 50 millivolts okay so those are
+
+ align:start position:0%
+at minus 50 millivolts okay so those are
+ 
+
+ align:start position:0%
+at minus 50 millivolts okay so those are
+the parts we're going to use we're going
+
+ align:start position:0%
+the parts we're going to use we're going
+ 
+
+ align:start position:0%
+the parts we're going to use we're going
+to describe now the experiments that
+
+ align:start position:0%
+to describe now the experiments that
+ 
+
+ align:start position:0%
+to describe now the experiments that
+hodgkin and huxley did to extract the
+
+ align:start position:0%
+hodgkin and huxley did to extract the
+ 
+
+ align:start position:0%
+hodgkin and huxley did to extract the
+parameters of the sodium and potassium
+
+ align:start position:0%
+parameters of the sodium and potassium
+ 
+
+ align:start position:0%
+parameters of the sodium and potassium
+conductances today we're going to focus
+
+ align:start position:0%
+conductances today we're going to focus
+ 
+
+ align:start position:0%
+conductances today we're going to focus
+on the potassium conductances and then
+
+ align:start position:0%
+on the potassium conductances and then
+ 
+
+ align:start position:0%
+on the potassium conductances and then
+on next Tuesday I guess we're going to
+
+ align:start position:0%
+on next Tuesday I guess we're going to
+ 
+
+ align:start position:0%
+on next Tuesday I guess we're going to
+do the sodium all right so the reason
+
+ align:start position:0%
+do the sodium all right so the reason
+ 
+
+ align:start position:0%
+do the sodium all right so the reason
+hodgkin and huxley studied so so they
+
+ align:start position:0%
+hodgkin and huxley studied so so they
+ 
+
+ align:start position:0%
+hodgkin and huxley studied so so they
+studied these but these channels that
+
+ align:start position:0%
+studied these but these channels that
+ 
+
+ align:start position:0%
+studied these but these channels that
+potassium and sodium channels in the
+
+ align:start position:0%
+potassium and sodium channels in the
+ 
+
+ align:start position:0%
+potassium and sodium channels in the
+giant squid axon now this is most of our
+
+ align:start position:0%
+giant squid axon now this is most of our
+ 
+
+ align:start position:0%
+giant squid axon now this is most of our
+axons are about a microp most of the
+
+ align:start position:0%
+axons are about a microp most of the
+ 
+
+ align:start position:0%
+axons are about a microp most of the
+axons in our brain are about a micron
+
+ align:start position:0%
+axons in our brain are about a micron
+ 
+
+ align:start position:0%
+axons in our brain are about a micron
+across
+
+ align:start position:0%
+across
+ 
+
+ align:start position:0%
+across
+this axon is about a millimeter across
+
+ align:start position:0%
+this axon is about a millimeter across
+ 
+
+ align:start position:0%
+this axon is about a millimeter across
+action potentials propagate much faster
+
+ align:start position:0%
+action potentials propagate much faster
+ 
+
+ align:start position:0%
+action potentials propagate much faster
+in large axons and this axon is involved
+
+ align:start position:0%
+in large axons and this axon is involved
+ 
+
+ align:start position:0%
+in large axons and this axon is involved
+in transmitting an action potential from
+
+ align:start position:0%
+in transmitting an action potential from
+ 
+
+ align:start position:0%
+in transmitting an action potential from
+the brain to the tail that drives an
+
+ align:start position:0%
+the brain to the tail that drives an
+ 
+
+ align:start position:0%
+the brain to the tail that drives an
+escape reflex that the squid squirts
+
+ align:start position:0%
+escape reflex that the squid squirts
+ 
+
+ align:start position:0%
+escape reflex that the squid squirts
+water out of a sort of a chamber that
+
+ align:start position:0%
+water out of a sort of a chamber that
+ 
+
+ align:start position:0%
+water out of a sort of a chamber that
+has water in it if the squid senses
+
+ align:start position:0%
+has water in it if the squid senses
+ 
+
+ align:start position:0%
+has water in it if the squid senses
+danger it contracts muscles that squeeze
+
+ align:start position:0%
+danger it contracts muscles that squeeze
+ 
+
+ align:start position:0%
+danger it contracts muscles that squeeze
+water out of that and it makes a jet and
+
+ align:start position:0%
+water out of that and it makes a jet and
+ 
+
+ align:start position:0%
+water out of that and it makes a jet and
+it squirts the squid forward away from
+
+ align:start position:0%
+it squirts the squid forward away from
+ 
+
+ align:start position:0%
+it squirts the squid forward away from
+danger okay so that action potential has
+
+ align:start position:0%
+danger okay so that action potential has
+ 
+
+ align:start position:0%
+danger okay so that action potential has
+to propagate very quickly from the brain
+
+ align:start position:0%
+to propagate very quickly from the brain
+ 
+
+ align:start position:0%
+to propagate very quickly from the brain
+to the tail and it does that through
+
+ align:start position:0%
+to the tail and it does that through
+ 
+
+ align:start position:0%
+to the tail and it does that through
+this enormous axon that axon is so big
+
+ align:start position:0%
+this enormous axon that axon is so big
+ 
+
+ align:start position:0%
+this enormous axon that axon is so big
+you can now put multiple wires inside of
+
+ align:start position:0%
+you can now put multiple wires inside of
+ 
+
+ align:start position:0%
+you can now put multiple wires inside of
+it you don't even need to pull these
+
+ align:start position:0%
+it you don't even need to pull these
+ 
+
+ align:start position:0%
+it you don't even need to pull these
+glass electrodes you can just take
+
+ align:start position:0%
+glass electrodes you can just take
+ 
+
+ align:start position:0%
+glass electrodes you can just take
+little wires and stick them and chop out
+
+ align:start position:0%
+little wires and stick them and chop out
+ 
+
+ align:start position:0%
+little wires and stick them and chop out
+a little piece of the axon and stick
+
+ align:start position:0%
+a little piece of the axon and stick
+ 
+
+ align:start position:0%
+a little piece of the axon and stick
+wires inside of it and study it yes yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's that you eat that part and you
+
+ align:start position:0%
+that's that you eat that part and you
+ 
+
+ align:start position:0%
+that's that you eat that part and you
+eat that part not that that you throw
+
+ align:start position:0%
+eat that part not that that you throw
+ 
+
+ align:start position:0%
+eat that part not that that you throw
+away the most interesting part okay any
+
+ align:start position:0%
+away the most interesting part okay any
+ 
+
+ align:start position:0%
+away the most interesting part okay any
+other questions okay all right so now
+
+ align:start position:0%
+other questions okay all right so now
+ 
+
+ align:start position:0%
+other questions okay all right so now
+we're setting out to measure these
+
+ align:start position:0%
+we're setting out to measure these
+ 
+
+ align:start position:0%
+we're setting out to measure these
+sodium and potassium conductances okay
+
+ align:start position:0%
+sodium and potassium conductances okay
+ 
+
+ align:start position:0%
+sodium and potassium conductances okay
+so how do we do that so what we really
+
+ align:start position:0%
+so how do we do that so what we really
+ 
+
+ align:start position:0%
+so how do we do that so what we really
+want to do is to set we want to measure
+
+ align:start position:0%
+want to do is to set we want to measure
+ 
+
+ align:start position:0%
+want to do is to set we want to measure
+conductance which is the relation
+
+ align:start position:0%
+conductance which is the relation
+ 
+
+ align:start position:0%
+conductance which is the relation
+between voltage and current so we'd like
+
+ align:start position:0%
+between voltage and current so we'd like
+ 
+
+ align:start position:0%
+between voltage and current so we'd like
+to do is to be able to set the voltage
+
+ align:start position:0%
+to do is to be able to set the voltage
+ 
+
+ align:start position:0%
+to do is to be able to set the voltage
+at a certain level and measure the
+
+ align:start position:0%
+at a certain level and measure the
+ 
+
+ align:start position:0%
+at a certain level and measure the
+current that flows through these
+
+ align:start position:0%
+current that flows through these
+ 
+
+ align:start position:0%
+current that flows through these
+channels okay so you really want to plot
+
+ align:start position:0%
+channels okay so you really want to plot
+ 
+
+ align:start position:0%
+channels okay so you really want to plot
+the IV curve right you want to set the
+
+ align:start position:0%
+the IV curve right you want to set the
+ 
+
+ align:start position:0%
+the IV curve right you want to set the
+voltage measure the current and do that
+
+ align:start position:0%
+voltage measure the current and do that
+ 
+
+ align:start position:0%
+voltage measure the current and do that
+at a bunch of different voltages and you
+
+ align:start position:0%
+at a bunch of different voltages and you
+ 
+
+ align:start position:0%
+at a bunch of different voltages and you
+recall that the conductance is basically
+
+ align:start position:0%
+recall that the conductance is basically
+ 
+
+ align:start position:0%
+recall that the conductance is basically
+just the slope of that curve right that
+
+ align:start position:0%
+just the slope of that curve right that
+ 
+
+ align:start position:0%
+just the slope of that curve right that
+line okay so the job is set voltage
+
+ align:start position:0%
+line okay so the job is set voltage
+ 
+
+ align:start position:0%
+line okay so the job is set voltage
+measure current extract conductance now
+
+ align:start position:0%
+measure current extract conductance now
+ 
+
+ align:start position:0%
+measure current extract conductance now
+the problem with that is that as soon as
+
+ align:start position:0%
+the problem with that is that as soon as
+ 
+
+ align:start position:0%
+the problem with that is that as soon as
+you set the voltage of the cell of the
+
+ align:start position:0%
+you set the voltage of the cell of the
+ 
+
+ align:start position:0%
+you set the voltage of the cell of the
+axon somewhere up here in an interest
+
+ align:start position:0%
+axon somewhere up here in an interest
+ 
+
+ align:start position:0%
+axon somewhere up here in an interest
+in range the thing begins to spike and
+
+ align:start position:0%
+in range the thing begins to spike and
+ 
+
+ align:start position:0%
+in range the thing begins to spike and
+then the voltage is no longer constant
+
+ align:start position:0%
+then the voltage is no longer constant
+ 
+
+ align:start position:0%
+then the voltage is no longer constant
+right so it becomes really hard to make
+
+ align:start position:0%
+right so it becomes really hard to make
+ 
+
+ align:start position:0%
+right so it becomes really hard to make
+measurements like this if you depolarize
+
+ align:start position:0%
+measurements like this if you depolarize
+ 
+
+ align:start position:0%
+measurements like this if you depolarize
+the cell a little bit to set try to set
+
+ align:start position:0%
+the cell a little bit to set try to set
+ 
+
+ align:start position:0%
+the cell a little bit to set try to set
+the voltage and all of a sudden it's
+
+ align:start position:0%
+the voltage and all of a sudden it's
+ 
+
+ align:start position:0%
+the voltage and all of a sudden it's
+like generating spikes okay so what do
+
+ align:start position:0%
+like generating spikes okay so what do
+ 
+
+ align:start position:0%
+like generating spikes okay so what do
+you do so the trick is to develop a
+
+ align:start position:0%
+you do so the trick is to develop a
+ 
+
+ align:start position:0%
+you do so the trick is to develop a
+device called the voltage clamp this
+
+ align:start position:0%
+device called the voltage clamp this
+ 
+
+ align:start position:0%
+device called the voltage clamp this
+thing basically holds the member so look
+
+ align:start position:0%
+thing basically holds the member so look
+ 
+
+ align:start position:0%
+thing basically holds the member so look
+if you were if the action potential were
+
+ align:start position:0%
+if you were if the action potential were
+ 
+
+ align:start position:0%
+if you were if the action potential were
+really really slow then you could
+
+ align:start position:0%
+really really slow then you could
+ 
+
+ align:start position:0%
+really really slow then you could
+actually set the voltage but you could
+
+ align:start position:0%
+actually set the voltage but you could
+ 
+
+ align:start position:0%
+actually set the voltage but you could
+inject change the current being injected
+
+ align:start position:0%
+inject change the current being injected
+ 
+
+ align:start position:0%
+inject change the current being injected
+into the cell by hand you say okay I'm
+
+ align:start position:0%
+into the cell by hand you say okay I'm
+ 
+
+ align:start position:0%
+into the cell by hand you say okay I'm
+trying to set the voltage at zero oh it
+
+ align:start position:0%
+trying to set the voltage at zero oh it
+ 
+
+ align:start position:0%
+trying to set the voltage at zero oh it
+got a little bit too high so I turn the
+
+ align:start position:0%
+got a little bit too high so I turn the
+ 
+
+ align:start position:0%
+got a little bit too high so I turn the
+current down now the voltage has gone
+
+ align:start position:0%
+current down now the voltage has gone
+ 
+
+ align:start position:0%
+current down now the voltage has gone
+too low so now I turn the current up
+
+ align:start position:0%
+too low so now I turn the current up
+ 
+
+ align:start position:0%
+too low so now I turn the current up
+like you could do it by hand if the
+
+ align:start position:0%
+like you could do it by hand if the
+ 
+
+ align:start position:0%
+like you could do it by hand if the
+action potential were super slow if it
+
+ align:start position:0%
+action potential were super slow if it
+ 
+
+ align:start position:0%
+action potential were super slow if it
+took a minute to generate right but the
+
+ align:start position:0%
+took a minute to generate right but the
+ 
+
+ align:start position:0%
+took a minute to generate right but the
+action potential takes a millisecond so
+
+ align:start position:0%
+action potential takes a millisecond so
+ 
+
+ align:start position:0%
+action potential takes a millisecond so
+that's just too fast for you to follow
+
+ align:start position:0%
+that's just too fast for you to follow
+ 
+
+ align:start position:0%
+that's just too fast for you to follow
+so you just make a little electrical
+
+ align:start position:0%
+so you just make a little electrical
+ 
+
+ align:start position:0%
+so you just make a little electrical
+circuit that does that job for you okay
+
+ align:start position:0%
+circuit that does that job for you okay
+ 
+
+ align:start position:0%
+circuit that does that job for you okay
+it uses feedback to set the voltage
+
+ align:start position:0%
+it uses feedback to set the voltage
+ 
+
+ align:start position:0%
+it uses feedback to set the voltage
+where you want so you put up you here's
+
+ align:start position:0%
+where you want so you put up you here's
+ 
+
+ align:start position:0%
+where you want so you put up you here's
+yourself
+
+ align:start position:0%
+yourself
+ 
+
+ align:start position:0%
+yourself
+here's your membrane put your membrane
+
+ align:start position:0%
+here's your membrane put your membrane
+ 
+
+ align:start position:0%
+here's your membrane put your membrane
+resistance or conductance that you're
+
+ align:start position:0%
+resistance or conductance that you're
+ 
+
+ align:start position:0%
+resistance or conductance that you're
+trying to measure
+
+ align:start position:0%
+trying to measure
+ 
+
+ align:start position:0%
+trying to measure
+you put a electrode in the cell you put
+
+ align:start position:0%
+you put a electrode in the cell you put
+ 
+
+ align:start position:0%
+you put a electrode in the cell you put
+it into a little amplifier called an
+
+ align:start position:0%
+it into a little amplifier called an
+ 
+
+ align:start position:0%
+it into a little amplifier called an
+operational amplifier so and then on the
+
+ align:start position:0%
+operational amplifier so and then on the
+ 
+
+ align:start position:0%
+operational amplifier so and then on the
+other side of that amplifier the
+
+ align:start position:0%
+other side of that amplifier the
+ 
+
+ align:start position:0%
+other side of that amplifier the
+differential amplifier you you put the
+
+ align:start position:0%
+differential amplifier you you put the
+ 
+
+ align:start position:0%
+differential amplifier you you put the
+command voltage that you're trying to
+
+ align:start position:0%
+command voltage that you're trying to
+ 
+
+ align:start position:0%
+command voltage that you're trying to
+set so here's the way it works basically
+
+ align:start position:0%
+set so here's the way it works basically
+ 
+
+ align:start position:0%
+set so here's the way it works basically
+this thing tries to set the membrane
+
+ align:start position:0%
+this thing tries to set the membrane
+ 
+
+ align:start position:0%
+this thing tries to set the membrane
+potential it tries to make this value
+
+ align:start position:0%
+potential it tries to make this value
+ 
+
+ align:start position:0%
+potential it tries to make this value
+this voltage equal to that voltage and
+
+ align:start position:0%
+this voltage equal to that voltage and
+ 
+
+ align:start position:0%
+this voltage equal to that voltage and
+it does that by feeding current back
+
+ align:start position:0%
+it does that by feeding current back
+ 
+
+ align:start position:0%
+it does that by feeding current back
+into this zone does that make sense okay
+
+ align:start position:0%
+into this zone does that make sense okay
+ 
+
+ align:start position:0%
+into this zone does that make sense okay
+so you use an operational amplifier an
+
+ align:start position:0%
+so you use an operational amplifier an
+ 
+
+ align:start position:0%
+so you use an operational amplifier an
+op amp has two inputs a plus input a
+
+ align:start position:0%
+op amp has two inputs a plus input a
+ 
+
+ align:start position:0%
+op amp has two inputs a plus input a
+minus input the output is just a gain
+
+ align:start position:0%
+minus input the output is just a gain
+ 
+
+ align:start position:0%
+minus input the output is just a gain
+times that plus input minus the positive
+
+ align:start position:0%
+times that plus input minus the positive
+ 
+
+ align:start position:0%
+times that plus input minus the positive
+input minus the negative input and the
+
+ align:start position:0%
+input minus the negative input and the
+ 
+
+ align:start position:0%
+input minus the negative input and the
+gain is really big it's about a million
+
+ align:start position:0%
+gain is really big it's about a million
+ 
+
+ align:start position:0%
+gain is really big it's about a million
+so if this input is a little bit above
+
+ align:start position:0%
+so if this input is a little bit above
+ 
+
+ align:start position:0%
+so if this input is a little bit above
+that import this output is big and
+
+ align:start position:0%
+that import this output is big and
+ 
+
+ align:start position:0%
+that import this output is big and
+positive if this input is less than that
+
+ align:start position:0%
+positive if this input is less than that
+ 
+
+ align:start position:0%
+positive if this input is less than that
+input you can see this is negative and
+
+ align:start position:0%
+input you can see this is negative and
+ 
+
+ align:start position:0%
+input you can see this is negative and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+output is big and negative any questions
+
+ align:start position:0%
+output is big and negative any questions
+ 
+
+ align:start position:0%
+output is big and negative any questions
+okay so don't get confused here that G
+
+ align:start position:0%
+okay so don't get confused here that G
+ 
+
+ align:start position:0%
+okay so don't get confused here that G
+is gain not not conductance okay just
+
+ align:start position:0%
+is gain not not conductance okay just
+ 
+
+ align:start position:0%
+is gain not not conductance okay just
+just for the next few slides okay so how
+
+ align:start position:0%
+just for the next few slides okay so how
+ 
+
+ align:start position:0%
+just for the next few slides okay so how
+does this work you can see that if the
+
+ align:start position:0%
+does this work you can see that if the
+ 
+
+ align:start position:0%
+does this work you can see that if the
+membrane potential is less than the
+
+ align:start position:0%
+membrane potential is less than the
+ 
+
+ align:start position:0%
+membrane potential is less than the
+command voltage then the output voltage
+
+ align:start position:0%
+command voltage then the output voltage
+ 
+
+ align:start position:0%
+command voltage then the output voltage
+is is positive and big that drives
+
+ align:start position:0%
+is is positive and big that drives
+ 
+
+ align:start position:0%
+is is positive and big that drives
+current into the cell which increases
+
+ align:start position:0%
+current into the cell which increases
+ 
+
+ align:start position:0%
+current into the cell which increases
+the membrane potential and makes it
+
+ align:start position:0%
+the membrane potential and makes it
+ 
+
+ align:start position:0%
+the membrane potential and makes it
+approach the command voltage if the
+
+ align:start position:0%
+approach the command voltage if the
+ 
+
+ align:start position:0%
+approach the command voltage if the
+membrane potential is larger than the
+
+ align:start position:0%
+membrane potential is larger than the
+ 
+
+ align:start position:0%
+membrane potential is larger than the
+command voltage then this thing this is
+
+ align:start position:0%
+command voltage then this thing this is
+ 
+
+ align:start position:0%
+command voltage then this thing this is
+bigger than this so this is negative and
+
+ align:start position:0%
+bigger than this so this is negative and
+ 
+
+ align:start position:0%
+bigger than this so this is negative and
+that pulse current out of the neuron and
+
+ align:start position:0%
+that pulse current out of the neuron and
+ 
+
+ align:start position:0%
+that pulse current out of the neuron and
+decreases the membrane potential and in
+
+ align:start position:0%
+decreases the membrane potential and in
+ 
+
+ align:start position:0%
+decreases the membrane potential and in
+both cases the membrane potential is
+
+ align:start position:0%
+both cases the membrane potential is
+ 
+
+ align:start position:0%
+both cases the membrane potential is
+being pulled toward the command voltage
+
+ align:start position:0%
+being pulled toward the command voltage
+ 
+
+ align:start position:0%
+being pulled toward the command voltage
+and you can show if you just plug in
+
+ align:start position:0%
+and you can show if you just plug in
+ 
+
+ align:start position:0%
+and you can show if you just plug in
+these variables into into a couple of
+
+ align:start position:0%
+these variables into into a couple of
+ 
+
+ align:start position:0%
+these variables into into a couple of
+equations that as long as the gain is
+
+ align:start position:0%
+equations that as long as the gain is
+ 
+
+ align:start position:0%
+equations that as long as the gain is
+big enough the membrane potential is
+
+ align:start position:0%
+big enough the membrane potential is
+ 
+
+ align:start position:0%
+big enough the membrane potential is
+forced to be very close to the command
+
+ align:start position:0%
+forced to be very close to the command
+ 
+
+ align:start position:0%
+forced to be very close to the command
+voltage all right so that's the voltage
+
+ align:start position:0%
+voltage all right so that's the voltage
+ 
+
+ align:start position:0%
+voltage all right so that's the voltage
+clamp it drives whatever current is
+
+ align:start position:0%
+clamp it drives whatever current is
+ 
+
+ align:start position:0%
+clamp it drives whatever current is
+necessary to clamp the voltage of the
+
+ align:start position:0%
+necessary to clamp the voltage of the
+ 
+
+ align:start position:0%
+necessary to clamp the voltage of the
+cell at the command voltage and then
+
+ align:start position:0%
+cell at the command voltage and then
+ 
+
+ align:start position:0%
+cell at the command voltage and then
+what we do is during an experiment we
+
+ align:start position:0%
+what we do is during an experiment we
+ 
+
+ align:start position:0%
+what we do is during an experiment we
+step the command voltage around the cell
+
+ align:start position:0%
+step the command voltage around the cell
+ 
+
+ align:start position:0%
+step the command voltage around the cell
+tries to spike those currents turn on
+
+ align:start position:0%
+tries to spike those currents turn on
+ 
+
+ align:start position:0%
+tries to spike those currents turn on
+the cell tries to spike but this thing
+
+ align:start position:0%
+the cell tries to spike but this thing
+ 
+
+ align:start position:0%
+the cell tries to spike but this thing
+keeps the voltage locked at whatever it
+
+ align:start position:0%
+keeps the voltage locked at whatever it
+ 
+
+ align:start position:0%
+keeps the voltage locked at whatever it
+is that you want we want the voltage to
+
+ align:start position:0%
+is that you want we want the voltage to
+ 
+
+ align:start position:0%
+is that you want we want the voltage to
+be okay and then you measure the amount
+
+ align:start position:0%
+be okay and then you measure the amount
+ 
+
+ align:start position:0%
+be okay and then you measure the amount
+of current required you just measure the
+
+ align:start position:0%
+of current required you just measure the
+ 
+
+ align:start position:0%
+of current required you just measure the
+amount of current flowing through this
+
+ align:start position:0%
+amount of current flowing through this
+ 
+
+ align:start position:0%
+amount of current flowing through this
+resistor here that's required to hold
+
+ align:start position:0%
+resistor here that's required to hold
+ 
+
+ align:start position:0%
+resistor here that's required to hold
+the the cell at any voltage all right
+
+ align:start position:0%
+the the cell at any voltage all right
+ 
+
+ align:start position:0%
+the the cell at any voltage all right
+any questions voltage clamp very cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+gain is just the multiplier here in this
+
+ align:start position:0%
+gain is just the multiplier here in this
+ 
+
+ align:start position:0%
+gain is just the multiplier here in this
+equation so if there's a tiny difference
+
+ align:start position:0%
+equation so if there's a tiny difference
+ 
+
+ align:start position:0%
+equation so if there's a tiny difference
+between the two inputs the output is big
+
+ align:start position:0%
+between the two inputs the output is big
+ 
+
+ align:start position:0%
+between the two inputs the output is big
+that's that's what gain means right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if there's a mite if the gain is a
+
+ align:start position:0%
+so if there's a mite if the gain is a
+ 
+
+ align:start position:0%
+so if there's a mite if the gain is a
+million if there's a microvolt
+
+ align:start position:0%
+million if there's a microvolt
+ 
+
+ align:start position:0%
+million if there's a microvolt
+difference between the two inputs the
+
+ align:start position:0%
+difference between the two inputs the
+ 
+
+ align:start position:0%
+difference between the two inputs the
+output will be about a volt and it'll be
+
+ align:start position:0%
+output will be about a volt and it'll be
+ 
+
+ align:start position:0%
+output will be about a volt and it'll be
+plus or minus depending on which of
+
+ align:start position:0%
+plus or minus depending on which of
+ 
+
+ align:start position:0%
+plus or minus depending on which of
+those two was was more positive okay
+
+ align:start position:0%
+those two was was more positive okay
+ 
+
+ align:start position:0%
+those two was was more positive okay
+okay so now let's get to the actual
+
+ align:start position:0%
+okay so now let's get to the actual
+ 
+
+ align:start position:0%
+okay so now let's get to the actual
+voltage clamp experiment that hodgkin
+
+ align:start position:0%
+voltage clamp experiment that hodgkin
+ 
+
+ align:start position:0%
+voltage clamp experiment that hodgkin
+and huxley did we have here we had two
+
+ align:start position:0%
+and huxley did we have here we had two
+ 
+
+ align:start position:0%
+and huxley did we have here we had two
+wires in our cell one to measure voltage
+
+ align:start position:0%
+wires in our cell one to measure voltage
+ 
+
+ align:start position:0%
+wires in our cell one to measure voltage
+and the other one to inject current
+
+ align:start position:0%
+and the other one to inject current
+ 
+
+ align:start position:0%
+and the other one to inject current
+that's exactly what they did there's one
+
+ align:start position:0%
+that's exactly what they did there's one
+ 
+
+ align:start position:0%
+that's exactly what they did there's one
+wire here that's a little piece of axon
+
+ align:start position:0%
+wire here that's a little piece of axon
+ 
+
+ align:start position:0%
+wire here that's a little piece of axon
+you can literally take the cut the squid
+
+ align:start position:0%
+you can literally take the cut the squid
+ 
+
+ align:start position:0%
+you can literally take the cut the squid
+open find that axon it's a big white
+
+ align:start position:0%
+open find that axon it's a big white
+ 
+
+ align:start position:0%
+open find that axon it's a big white
+looking tube about a millimeter across
+
+ align:start position:0%
+looking tube about a millimeter across
+ 
+
+ align:start position:0%
+looking tube about a millimeter across
+cut two pieces of it take two wires
+
+ align:start position:0%
+cut two pieces of it take two wires
+ 
+
+ align:start position:0%
+cut two pieces of it take two wires
+stick one in each end and I drew that
+
+ align:start position:0%
+stick one in each end and I drew that
+ 
+
+ align:start position:0%
+stick one in each end and I drew that
+like this but if you did it that way
+
+ align:start position:0%
+like this but if you did it that way
+ 
+
+ align:start position:0%
+like this but if you did it that way
+they'd probably short together so then
+
+ align:start position:0%
+they'd probably short together so then
+ 
+
+ align:start position:0%
+they'd probably short together so then
+one of those measures the voltage you
+
+ align:start position:0%
+one of those measures the voltage you
+ 
+
+ align:start position:0%
+one of those measures the voltage you
+set a command and the other wire allows
+
+ align:start position:0%
+set a command and the other wire allows
+ 
+
+ align:start position:0%
+set a command and the other wire allows
+you to inject current inside the axon it
+
+ align:start position:0%
+you to inject current inside the axon it
+ 
+
+ align:start position:0%
+you to inject current inside the axon it
+and then you seal the ends with a little
+
+ align:start position:0%
+and then you seal the ends with a little
+ 
+
+ align:start position:0%
+and then you seal the ends with a little
+bit of Vaseline okay yes we see is the
+
+ align:start position:0%
+bit of Vaseline okay yes we see is the
+ 
+
+ align:start position:0%
+bit of Vaseline okay yes we see is the
+command voltage that you're trying to
+
+ align:start position:0%
+command voltage that you're trying to
+ 
+
+ align:start position:0%
+command voltage that you're trying to
+set the inside of the cell to okay
+
+ align:start position:0%
+set the inside of the cell to okay
+ 
+
+ align:start position:0%
+set the inside of the cell to okay
+remember here we're setting the the V
+
+ align:start position:0%
+remember here we're setting the the V
+ 
+
+ align:start position:0%
+remember here we're setting the the V
+the VC is what you're controlling as the
+
+ align:start position:0%
+the VC is what you're controlling as the
+ 
+
+ align:start position:0%
+the VC is what you're controlling as the
+experimenter you're setting the voltage
+
+ align:start position:0%
+experimenter you're setting the voltage
+ 
+
+ align:start position:0%
+experimenter you're setting the voltage
+with that command okay the current so
+
+ align:start position:0%
+with that command okay the current so
+ 
+
+ align:start position:0%
+with that command okay the current so
+the voltage clamp then holds the inside
+
+ align:start position:0%
+the voltage clamp then holds the inside
+ 
+
+ align:start position:0%
+the voltage clamp then holds the inside
+of the cell at that command voltage and
+
+ align:start position:0%
+of the cell at that command voltage and
+ 
+
+ align:start position:0%
+of the cell at that command voltage and
+then you're measuring the current with
+
+ align:start position:0%
+then you're measuring the current with
+ 
+
+ align:start position:0%
+then you're measuring the current with
+this device that there's a readout that
+
+ align:start position:0%
+this device that there's a readout that
+ 
+
+ align:start position:0%
+this device that there's a readout that
+tells you how much current it's putting
+
+ align:start position:0%
+tells you how much current it's putting
+ 
+
+ align:start position:0%
+tells you how much current it's putting
+into the cellar goes on to an
+
+ align:start position:0%
+into the cellar goes on to an
+ 
+
+ align:start position:0%
+into the cellar goes on to an
+oscilloscope because it's time dependent
+
+ align:start position:0%
+oscilloscope because it's time dependent
+ 
+
+ align:start position:0%
+oscilloscope because it's time dependent
+okay okay so let's do an experiment
+
+ align:start position:0%
+okay okay so let's do an experiment
+ 
+
+ align:start position:0%
+okay okay so let's do an experiment
+here's an example of an experiment they
+
+ align:start position:0%
+here's an example of an experiment they
+ 
+
+ align:start position:0%
+here's an example of an experiment they
+hold the command at minus 65 and
+
+ align:start position:0%
+hold the command at minus 65 and
+ 
+
+ align:start position:0%
+hold the command at minus 65 and
+suddenly they drop the command voltage
+
+ align:start position:0%
+suddenly they drop the command voltage
+ 
+
+ align:start position:0%
+suddenly they drop the command voltage
+to minus 130 what is the what is the
+
+ align:start position:0%
+to minus 130 what is the what is the
+ 
+
+ align:start position:0%
+to minus 130 what is the what is the
+cell do what is the current nothing okay
+
+ align:start position:0%
+cell do what is the current nothing okay
+ 
+
+ align:start position:0%
+cell do what is the current nothing okay
+there's a little transient here which is
+
+ align:start position:0%
+there's a little transient here which is
+ 
+
+ align:start position:0%
+there's a little transient here which is
+the amount of current it took to charge
+
+ align:start position:0%
+the amount of current it took to charge
+ 
+
+ align:start position:0%
+the amount of current it took to charge
+that capacitor up to minus 130
+
+ align:start position:0%
+that capacitor up to minus 130
+ 
+
+ align:start position:0%
+that capacitor up to minus 130
+millivolts and then nothing happens
+
+ align:start position:0%
+millivolts and then nothing happens
+ 
+
+ align:start position:0%
+millivolts and then nothing happens
+all right let's do another experiment
+
+ align:start position:0%
+all right let's do another experiment
+ 
+
+ align:start position:0%
+all right let's do another experiment
+now we're going to take we're gonna
+
+ align:start position:0%
+now we're going to take we're gonna
+ 
+
+ align:start position:0%
+now we're going to take we're gonna
+start our cell at minus 65 and suddenly
+
+ align:start position:0%
+start our cell at minus 65 and suddenly
+ 
+
+ align:start position:0%
+start our cell at minus 65 and suddenly
+jump the voltage up to zero so we're
+
+ align:start position:0%
+jump the voltage up to zero so we're
+ 
+
+ align:start position:0%
+jump the voltage up to zero so we're
+gonna depolarize our cell and now
+
+ align:start position:0%
+gonna depolarize our cell and now
+ 
+
+ align:start position:0%
+gonna depolarize our cell and now
+something happens you get a big pulse of
+
+ align:start position:0%
+something happens you get a big pulse of
+ 
+
+ align:start position:0%
+something happens you get a big pulse of
+current that's negative what does
+
+ align:start position:0%
+current that's negative what does
+ 
+
+ align:start position:0%
+current that's negative what does
+negative mean anybody remember what
+
+ align:start position:0%
+negative mean anybody remember what
+ 
+
+ align:start position:0%
+negative mean anybody remember what
+negative current means by our definition
+
+ align:start position:0%
+negative current means by our definition
+ 
+
+ align:start position:0%
+negative current means by our definition
+negative means that there are positive
+
+ align:start position:0%
+negative means that there are positive
+ 
+
+ align:start position:0%
+negative means that there are positive
+ions going into the cell okay so it's
+
+ align:start position:0%
+ions going into the cell okay so it's
+ 
+
+ align:start position:0%
+ions going into the cell okay so it's
+charging the cell up okay this is
+
+ align:start position:0%
+charging the cell up okay this is
+ 
+
+ align:start position:0%
+charging the cell up okay this is
+membrane current now okay so you just
+
+ align:start position:0%
+membrane current now okay so you just
+ 
+
+ align:start position:0%
+membrane current now okay so you just
+have to remember that definition
+
+ align:start position:0%
+have to remember that definition
+ 
+
+ align:start position:0%
+have to remember that definition
+negative membrane current means that
+
+ align:start position:0%
+negative membrane current means that
+ 
+
+ align:start position:0%
+negative membrane current means that
+positive charges are going into the cell
+
+ align:start position:0%
+positive charges are going into the cell
+ 
+
+ align:start position:0%
+positive charges are going into the cell
+and that's chart that's depolarizing in
+
+ align:start position:0%
+and that's chart that's depolarizing in
+ 
+
+ align:start position:0%
+and that's chart that's depolarizing in
+the film okay and then that negative
+
+ align:start position:0%
+the film okay and then that negative
+ 
+
+ align:start position:0%
+the film okay and then that negative
+current lasts for a few milliseconds and
+
+ align:start position:0%
+current lasts for a few milliseconds and
+ 
+
+ align:start position:0%
+current lasts for a few milliseconds and
+then the current reverses sign and
+
+ align:start position:0%
+then the current reverses sign and
+ 
+
+ align:start position:0%
+then the current reverses sign and
+becomes positive and stays on okay so
+
+ align:start position:0%
+becomes positive and stays on okay so
+ 
+
+ align:start position:0%
+becomes positive and stays on okay so
+what is that so the first thing that
+
+ align:start position:0%
+what is that so the first thing that
+ 
+
+ align:start position:0%
+what is that so the first thing that
+hodgkin-huxley did was they tried to
+
+ align:start position:0%
+hodgkin-huxley did was they tried to
+ 
+
+ align:start position:0%
+hodgkin-huxley did was they tried to
+figure out what causes that pattern of
+
+ align:start position:0%
+figure out what causes that pattern of
+ 
+
+ align:start position:0%
+figure out what causes that pattern of
+currents okay so here's what they did
+
+ align:start position:0%
+currents okay so here's what they did
+ 
+
+ align:start position:0%
+currents okay so here's what they did
+they had this idea that part of this
+
+ align:start position:0%
+they had this idea that part of this
+ 
+
+ align:start position:0%
+they had this idea that part of this
+might be due to sodium and so what they
+
+ align:start position:0%
+might be due to sodium and so what they
+ 
+
+ align:start position:0%
+might be due to sodium and so what they
+did was they did an experiment where
+
+ align:start position:0%
+did was they did an experiment where
+ 
+
+ align:start position:0%
+did was they did an experiment where
+they were placed sodium outside the cell
+
+ align:start position:0%
+they were placed sodium outside the cell
+ 
+
+ align:start position:0%
+they were placed sodium outside the cell
+outside the axon with an ion with they
+
+ align:start position:0%
+outside the axon with an ion with they
+ 
+
+ align:start position:0%
+outside the axon with an ion with they
+replaced this they kept the chloride but
+
+ align:start position:0%
+replaced this they kept the chloride but
+ 
+
+ align:start position:0%
+replaced this they kept the chloride but
+they replaced the sodium with choline so
+
+ align:start position:0%
+they replaced the sodium with choline so
+ 
+
+ align:start position:0%
+they replaced the sodium with choline so
+they used choline chloride so it's a
+
+ align:start position:0%
+they used choline chloride so it's a
+ 
+
+ align:start position:0%
+they used choline chloride so it's a
+salt solution but it has no sodium in it
+
+ align:start position:0%
+salt solution but it has no sodium in it
+ 
+
+ align:start position:0%
+salt solution but it has no sodium in it
+and here's and then they redid that
+
+ align:start position:0%
+and here's and then they redid that
+ 
+
+ align:start position:0%
+and here's and then they redid that
+experiment and here's what they found
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what they found was so here it is with
+
+ align:start position:0%
+what they found was so here it is with
+ 
+
+ align:start position:0%
+what they found was so here it is with
+sodium and if they replace the sodium
+
+ align:start position:0%
+sodium and if they replace the sodium
+ 
+
+ align:start position:0%
+sodium and if they replace the sodium
+they find that they get almost the same
+
+ align:start position:0%
+they find that they get almost the same
+ 
+
+ align:start position:0%
+they find that they get almost the same
+thing except that initial negative pulse
+
+ align:start position:0%
+thing except that initial negative pulse
+ 
+
+ align:start position:0%
+thing except that initial negative pulse
+goes away okay so you can subtract and
+
+ align:start position:0%
+goes away okay so you can subtract and
+ 
+
+ align:start position:0%
+goes away okay so you can subtract and
+so they hypothesized that that part is
+
+ align:start position:0%
+so they hypothesized that that part is
+ 
+
+ align:start position:0%
+so they hypothesized that that part is
+due to sodium and so now you just
+
+ align:start position:0%
+due to sodium and so now you just
+ 
+
+ align:start position:0%
+due to sodium and so now you just
+subtract this from this to get the
+
+ align:start position:0%
+subtract this from this to get the
+ 
+
+ align:start position:0%
+subtract this from this to get the
+difference and that is the sodium
+
+ align:start position:0%
+difference and that is the sodium
+ 
+
+ align:start position:0%
+difference and that is the sodium
+current that makes sense okay so that's
+
+ align:start position:0%
+current that makes sense okay so that's
+ 
+
+ align:start position:0%
+current that makes sense okay so that's
+and then one other thing through another
+
+ align:start position:0%
+and then one other thing through another
+ 
+
+ align:start position:0%
+and then one other thing through another
+set of experiments they were able to
+
+ align:start position:0%
+set of experiments they were able to
+ 
+
+ align:start position:0%
+set of experiments they were able to
+show that this part that's left after
+
+ align:start position:0%
+show that this part that's left after
+ 
+
+ align:start position:0%
+show that this part that's left after
+you block or remove sodium is that due
+
+ align:start position:0%
+you block or remove sodium is that due
+ 
+
+ align:start position:0%
+you block or remove sodium is that due
+to potassium okay so this is the
+
+ align:start position:0%
+to potassium okay so this is the
+ 
+
+ align:start position:0%
+to potassium okay so this is the
+potassium current that is a sodium
+
+ align:start position:0%
+potassium current that is a sodium
+ 
+
+ align:start position:0%
+potassium current that is a sodium
+current okay so by doing different kinds
+
+ align:start position:0%
+current okay so by doing different kinds
+ 
+
+ align:start position:0%
+current okay so by doing different kinds
+of experiments so one of the things that
+
+ align:start position:0%
+of experiments so one of the things that
+ 
+
+ align:start position:0%
+of experiments so one of the things that
+you're able to do that they didn't do
+
+ align:start position:0%
+you're able to do that they didn't do
+ 
+
+ align:start position:0%
+you're able to do that they didn't do
+initially but later they were able to do
+
+ align:start position:0%
+initially but later they were able to do
+ 
+
+ align:start position:0%
+initially but later they were able to do
+things like take that little piece of
+
+ align:start position:0%
+things like take that little piece of
+ 
+
+ align:start position:0%
+things like take that little piece of
+axon take a little miniature paint
+
+ align:start position:0%
+axon take a little miniature paint
+ 
+
+ align:start position:0%
+axon take a little miniature paint
+roller squish the axon roll the roller
+
+ align:start position:0%
+roller squish the axon roll the roller
+ 
+
+ align:start position:0%
+roller squish the axon roll the roller
+over the axon squish its guts out and
+
+ align:start position:0%
+over the axon squish its guts out and
+ 
+
+ align:start position:0%
+over the axon squish its guts out and
+then fill it up again with solutions
+
+ align:start position:0%
+then fill it up again with solutions
+ 
+
+ align:start position:0%
+then fill it up again with solutions
+that they control that have different
+
+ align:start position:0%
+that they control that have different
+ 
+
+ align:start position:0%
+that they control that have different
+ions in them and so they're able to
+
+ align:start position:0%
+ions in them and so they're able to
+ 
+
+ align:start position:0%
+ions in them and so they're able to
+study you know just do multiple
+
+ align:start position:0%
+study you know just do multiple
+ 
+
+ align:start position:0%
+study you know just do multiple
+different kinds of experiments to be
+
+ align:start position:0%
+different kinds of experiments to be
+ 
+
+ align:start position:0%
+different kinds of experiments to be
+sure that this slow thing that turns on
+
+ align:start position:0%
+sure that this slow thing that turns on
+ 
+
+ align:start position:0%
+sure that this slow thing that turns on
+a slow positive current is potassium and
+
+ align:start position:0%
+a slow positive current is potassium and
+ 
+
+ align:start position:0%
+a slow positive current is potassium and
+this fast negative current is sodium all
+
+ align:start position:0%
+this fast negative current is sodium all
+ 
+
+ align:start position:0%
+this fast negative current is sodium all
+right okay so now what you can do is you
+
+ align:start position:0%
+right okay so now what you can do is you
+ 
+
+ align:start position:0%
+right okay so now what you can do is you
+can do this experiment at different
+
+ align:start position:0%
+can do this experiment at different
+ 
+
+ align:start position:0%
+can do this experiment at different
+voltages here right we want to measure
+
+ align:start position:0%
+voltages here right we want to measure
+ 
+
+ align:start position:0%
+voltages here right we want to measure
+how these currents depend on voltage
+
+ align:start position:0%
+how these currents depend on voltage
+ 
+
+ align:start position:0%
+how these currents depend on voltage
+right we can see here how they depend on
+
+ align:start position:0%
+right we can see here how they depend on
+ 
+
+ align:start position:0%
+right we can see here how they depend on
+time we can also see how they depend on
+
+ align:start position:0%
+time we can also see how they depend on
+ 
+
+ align:start position:0%
+time we can also see how they depend on
+voltage by doing this experiment at
+
+ align:start position:0%
+voltage by doing this experiment at
+ 
+
+ align:start position:0%
+voltage by doing this experiment at
+different voltages you start at some
+
+ align:start position:0%
+different voltages you start at some
+ 
+
+ align:start position:0%
+different voltages you start at some
+negative potential you step the voltage
+
+ align:start position:0%
+negative potential you step the voltage
+ 
+
+ align:start position:0%
+negative potential you step the voltage
+up to minus 40 or you step it up to zero
+
+ align:start position:0%
+up to minus 40 or you step it up to zero
+ 
+
+ align:start position:0%
+up to minus 40 or you step it up to zero
+or you step it up to 40 and now you can
+
+ align:start position:0%
+or you step it up to 40 and now you can
+ 
+
+ align:start position:0%
+or you step it up to 40 and now you can
+measure that potassium current as a
+
+ align:start position:0%
+measure that potassium current as a
+ 
+
+ align:start position:0%
+measure that potassium current as a
+function of time or the sodium current
+
+ align:start position:0%
+function of time or the sodium current
+ 
+
+ align:start position:0%
+function of time or the sodium current
+as a function of time
+
+ align:start position:0%
+as a function of time
+ 
+
+ align:start position:0%
+as a function of time
+all right at different voltages okay all
+
+ align:start position:0%
+all right at different voltages okay all
+ 
+
+ align:start position:0%
+all right at different voltages okay all
+right so those look kind of weird
+
+ align:start position:0%
+right so those look kind of weird
+ 
+
+ align:start position:0%
+right so those look kind of weird
+especially that one that looks kind of
+
+ align:start position:0%
+especially that one that looks kind of
+ 
+
+ align:start position:0%
+especially that one that looks kind of
+scary like what the heck is going on
+
+ align:start position:0%
+scary like what the heck is going on
+ 
+
+ align:start position:0%
+scary like what the heck is going on
+there okay but it turns out that both of
+
+ align:start position:0%
+there okay but it turns out that both of
+ 
+
+ align:start position:0%
+there okay but it turns out that both of
+both of these things are actually pretty
+
+ align:start position:0%
+both of these things are actually pretty
+ 
+
+ align:start position:0%
+both of these things are actually pretty
+simple once we dig a little bit more
+
+ align:start position:0%
+simple once we dig a little bit more
+ 
+
+ align:start position:0%
+simple once we dig a little bit more
+into into how these currents are
+
+ align:start position:0%
+into into how these currents are
+ 
+
+ align:start position:0%
+into into how these currents are
+produced you're gonna see that there's a
+
+ align:start position:0%
+produced you're gonna see that there's a
+ 
+
+ align:start position:0%
+produced you're gonna see that there's a
+very simple way to understand what
+
+ align:start position:0%
+very simple way to understand what
+ 
+
+ align:start position:0%
+very simple way to understand what
+what's happening there
+
+ align:start position:0%
+what's happening there
+ 
+
+ align:start position:0%
+what's happening there
+all right any questions they're with me
+
+ align:start position:0%
+all right any questions they're with me
+ 
+
+ align:start position:0%
+all right any questions they're with me
+okay so this so now what we want to do
+
+ align:start position:0%
+okay so this so now what we want to do
+ 
+
+ align:start position:0%
+okay so this so now what we want to do
+is we want to measure the voltage
+
+ align:start position:0%
+is we want to measure the voltage
+ 
+
+ align:start position:0%
+is we want to measure the voltage
+dependence of these things kind of
+
+ align:start position:0%
+dependence of these things kind of
+ 
+
+ align:start position:0%
+dependence of these things kind of
+separately from the time dependence so
+
+ align:start position:0%
+separately from the time dependence so
+ 
+
+ align:start position:0%
+separately from the time dependence so
+what we're gonna do is we're gonna
+
+ align:start position:0%
+what we're gonna do is we're gonna
+ 
+
+ align:start position:0%
+what we're gonna do is we're gonna
+measure the peak potassium current kind
+
+ align:start position:0%
+measure the peak potassium current kind
+ 
+
+ align:start position:0%
+measure the peak potassium current kind
+of this steady state seem current as a
+
+ align:start position:0%
+of this steady state seem current as a
+ 
+
+ align:start position:0%
+of this steady state seem current as a
+function of voltage okay so here's our
+
+ align:start position:0%
+function of voltage okay so here's our
+ 
+
+ align:start position:0%
+function of voltage okay so here's our
+IV curve that I promised that we were
+
+ align:start position:0%
+IV curve that I promised that we were
+ 
+
+ align:start position:0%
+IV curve that I promised that we were
+going to plot peak current as a function
+
+ align:start position:0%
+going to plot peak current as a function
+ 
+
+ align:start position:0%
+going to plot peak current as a function
+of voltage and you can see that it's
+
+ align:start position:0%
+of voltage and you can see that it's
+ 
+
+ align:start position:0%
+of voltage and you can see that it's
+approximately linear above minus 50 or
+
+ align:start position:0%
+approximately linear above minus 50 or
+ 
+
+ align:start position:0%
+approximately linear above minus 50 or
+so millivolts the sodium current looks
+
+ align:start position:0%
+so millivolts the sodium current looks
+ 
+
+ align:start position:0%
+so millivolts the sodium current looks
+kind of weird we're gonna plot the peak
+
+ align:start position:0%
+kind of weird we're gonna plot the peak
+ 
+
+ align:start position:0%
+kind of weird we're gonna plot the peak
+sodium current as a function of voltage
+
+ align:start position:0%
+sodium current as a function of voltage
+ 
+
+ align:start position:0%
+sodium current as a function of voltage
+and we see that the peak sodium current
+
+ align:start position:0%
+and we see that the peak sodium current
+ 
+
+ align:start position:0%
+and we see that the peak sodium current
+has this weird shape it's sort of linear
+
+ align:start position:0%
+has this weird shape it's sort of linear
+ 
+
+ align:start position:0%
+has this weird shape it's sort of linear
+up here at positive voltages and then it
+
+ align:start position:0%
+up here at positive voltages and then it
+ 
+
+ align:start position:0%
+up here at positive voltages and then it
+crashes down to zero I'd make all
+
+ align:start position:0%
+crashes down to zero I'd make all
+ 
+
+ align:start position:0%
+crashes down to zero I'd make all
+teachers okay all right still kind of
+
+ align:start position:0%
+teachers okay all right still kind of
+ 
+
+ align:start position:0%
+teachers okay all right still kind of
+weird and scary so let's see if we can
+
+ align:start position:0%
+weird and scary so let's see if we can
+ 
+
+ align:start position:0%
+weird and scary so let's see if we can
+understand where this comes from
+
+ align:start position:0%
+understand where this comes from
+ 
+
+ align:start position:0%
+understand where this comes from
+I just reap lotted them here so now
+
+ align:start position:0%
+I just reap lotted them here so now
+ 
+
+ align:start position:0%
+I just reap lotted them here so now
+remember that we use this voltage clamp
+
+ align:start position:0%
+remember that we use this voltage clamp
+ 
+
+ align:start position:0%
+remember that we use this voltage clamp
+to measure current as a voltage but what
+
+ align:start position:0%
+to measure current as a voltage but what
+ 
+
+ align:start position:0%
+to measure current as a voltage but what
+is it that we're really trying to
+
+ align:start position:0%
+is it that we're really trying to
+ 
+
+ align:start position:0%
+is it that we're really trying to
+understand we're really trying to
+
+ align:start position:0%
+understand we're really trying to
+ 
+
+ align:start position:0%
+understand we're really trying to
+understand the conductances those
+
+ align:start position:0%
+understand the conductances those
+ 
+
+ align:start position:0%
+understand the conductances those
+resistors but right we're under trying
+
+ align:start position:0%
+resistors but right we're under trying
+ 
+
+ align:start position:0%
+resistors but right we're under trying
+to understand the voltage and time
+
+ align:start position:0%
+to understand the voltage and time
+ 
+
+ align:start position:0%
+to understand the voltage and time
+dependence of those conductances all
+
+ align:start position:0%
+dependence of those conductances all
+ 
+
+ align:start position:0%
+dependence of those conductances all
+right so we're trying to extract
+
+ align:start position:0%
+right so we're trying to extract
+ 
+
+ align:start position:0%
+right so we're trying to extract
+conductance as a function of voltage and
+
+ align:start position:0%
+conductance as a function of voltage and
+ 
+
+ align:start position:0%
+conductance as a function of voltage and
+remember that
+
+ align:start position:0%
+remember that
+ 
+
+ align:start position:0%
+remember that
+it'sjust conductance times a driving
+
+ align:start position:0%
+it'sjust conductance times a driving
+ 
+
+ align:start position:0%
+it'sjust conductance times a driving
+potential for potassium sodium current
+
+ align:start position:0%
+potential for potassium sodium current
+ 
+
+ align:start position:0%
+potential for potassium sodium current
+is just sodium conductance times the
+
+ align:start position:0%
+is just sodium conductance times the
+ 
+
+ align:start position:0%
+is just sodium conductance times the
+sodium driving potential so we can
+
+ align:start position:0%
+sodium driving potential so we can
+ 
+
+ align:start position:0%
+sodium driving potential so we can
+extract inductance as current divided by
+
+ align:start position:0%
+extract inductance as current divided by
+ 
+
+ align:start position:0%
+extract inductance as current divided by
+the driving potential okay so that's
+
+ align:start position:0%
+the driving potential okay so that's
+ 
+
+ align:start position:0%
+the driving potential okay so that's
+this is what we're really trying to find
+
+ align:start position:0%
+this is what we're really trying to find
+ 
+
+ align:start position:0%
+this is what we're really trying to find
+rather than doing this rather than doing
+
+ align:start position:0%
+rather than doing this rather than doing
+ 
+
+ align:start position:0%
+rather than doing this rather than doing
+this division because this one over this
+
+ align:start position:0%
+this division because this one over this
+ 
+
+ align:start position:0%
+this division because this one over this
+thing goes to zero at the places where
+
+ align:start position:0%
+thing goes to zero at the places where
+ 
+
+ align:start position:0%
+thing goes to zero at the places where
+the voltage is equal to the equilibrium
+
+ align:start position:0%
+the voltage is equal to the equilibrium
+ 
+
+ align:start position:0%
+the voltage is equal to the equilibrium
+potential so we don't want to do that
+
+ align:start position:0%
+potential so we don't want to do that
+ 
+
+ align:start position:0%
+potential so we don't want to do that
+we're gonna solve this problem
+
+ align:start position:0%
+we're gonna solve this problem
+ 
+
+ align:start position:0%
+we're gonna solve this problem
+graphically so here's the driving
+
+ align:start position:0%
+graphically so here's the driving
+ 
+
+ align:start position:0%
+graphically so here's the driving
+potential right Li minus ek it goes to
+
+ align:start position:0%
+potential right Li minus ek it goes to
+ 
+
+ align:start position:0%
+potential right Li minus ek it goes to
+zero at minus at ek right and we want to
+
+ align:start position:0%
+zero at minus at ek right and we want to
+ 
+
+ align:start position:0%
+zero at minus at ek right and we want to
+find a conductance that makes this look
+
+ align:start position:0%
+find a conductance that makes this look
+ 
+
+ align:start position:0%
+find a conductance that makes this look
+like this so if this is kind of a
+
+ align:start position:0%
+like this so if this is kind of a
+ 
+
+ align:start position:0%
+like this so if this is kind of a
+straight line if the current as a
+
+ align:start position:0%
+straight line if the current as a
+ 
+
+ align:start position:0%
+straight line if the current as a
+function of voltage is kind of a
+
+ align:start position:0%
+function of voltage is kind of a
+ 
+
+ align:start position:0%
+function of voltage is kind of a
+straight line and this is a straight
+
+ align:start position:0%
+straight line and this is a straight
+ 
+
+ align:start position:0%
+straight line and this is a straight
+line what does that tell us about the
+
+ align:start position:0%
+line what does that tell us about the
+ 
+
+ align:start position:0%
+line what does that tell us about the
+conductance in this region up here it's
+
+ align:start position:0%
+conductance in this region up here it's
+ 
+
+ align:start position:0%
+conductance in this region up here it's
+constant excellent now if the if the
+
+ align:start position:0%
+constant excellent now if the if the
+ 
+
+ align:start position:0%
+constant excellent now if the if the
+driving potential is very negative here
+
+ align:start position:0%
+driving potential is very negative here
+ 
+
+ align:start position:0%
+driving potential is very negative here
+but the current is zero then what's the
+
+ align:start position:0%
+but the current is zero then what's the
+ 
+
+ align:start position:0%
+but the current is zero then what's the
+conductance driving potential is big and
+
+ align:start position:0%
+conductance driving potential is big and
+ 
+
+ align:start position:0%
+conductance driving potential is big and
+negative current is zero what does that
+
+ align:start position:0%
+negative current is zero what does that
+ 
+
+ align:start position:0%
+negative current is zero what does that
+tell us about the conductance it's zero
+
+ align:start position:0%
+tell us about the conductance it's zero
+ 
+
+ align:start position:0%
+tell us about the conductance it's zero
+okay so not not so hard right we have
+
+ align:start position:0%
+okay so not not so hard right we have
+ 
+
+ align:start position:0%
+okay so not not so hard right we have
+some 0 here and constant here so can
+
+ align:start position:0%
+some 0 here and constant here so can
+ 
+
+ align:start position:0%
+some 0 here and constant here so can
+anyone just show me what that might look
+
+ align:start position:0%
+anyone just show me what that might look
+ 
+
+ align:start position:0%
+anyone just show me what that might look
+like good it could be like a jump it
+
+ align:start position:0%
+like good it could be like a jump it
+ 
+
+ align:start position:0%
+like good it could be like a jump it
+could be kind of smooth and that's
+
+ align:start position:0%
+could be kind of smooth and that's
+ 
+
+ align:start position:0%
+could be kind of smooth and that's
+exactly what it looks like okay so the
+
+ align:start position:0%
+exactly what it looks like okay so the
+ 
+
+ align:start position:0%
+exactly what it looks like okay so the
+conductance is zero here which it has to
+
+ align:start position:0%
+conductance is zero here which it has to
+ 
+
+ align:start position:0%
+conductance is zero here which it has to
+be because the current is zero even the
+
+ align:start position:0%
+be because the current is zero even the
+ 
+
+ align:start position:0%
+be because the current is zero even the
+potential is negative and the
+
+ align:start position:0%
+potential is negative and the
+ 
+
+ align:start position:0%
+potential is negative and the
+conductance here is constant because the
+
+ align:start position:0%
+conductance here is constant because the
+ 
+
+ align:start position:0%
+conductance here is constant because the
+driving potential is constant here the
+
+ align:start position:0%
+driving potential is constant here the
+ 
+
+ align:start position:0%
+driving potential is constant here the
+driving potential is linear and the
+
+ align:start position:0%
+driving potential is linear and the
+ 
+
+ align:start position:0%
+driving potential is linear and the
+current is linear so this needs to be
+
+ align:start position:0%
+current is linear so this needs to be
+ 
+
+ align:start position:0%
+current is linear so this needs to be
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+all right so the conductance is very
+
+ align:start position:0%
+all right so the conductance is very
+ 
+
+ align:start position:0%
+all right so the conductance is very
+simple it turns off at negative voltages
+
+ align:start position:0%
+simple it turns off at negative voltages
+ 
+
+ align:start position:0%
+simple it turns off at negative voltages
+and turns on and then stays on at higher
+
+ align:start position:0%
+and turns on and then stays on at higher
+ 
+
+ align:start position:0%
+and turns on and then stays on at higher
+voltages let's do that for sodium this
+
+ align:start position:0%
+voltages let's do that for sodium this
+ 
+
+ align:start position:0%
+voltages let's do that for sodium this
+thing looks crazy weird right but let's
+
+ align:start position:0%
+thing looks crazy weird right but let's
+ 
+
+ align:start position:0%
+thing looks crazy weird right but let's
+go through the same operation here's our
+
+ align:start position:0%
+go through the same operation here's our
+ 
+
+ align:start position:0%
+go through the same operation here's our
+driving potential for sodium remember
+
+ align:start position:0%
+driving potential for sodium remember
+ 
+
+ align:start position:0%
+driving potential for sodium remember
+it's got a reversal at plus 55 but it's
+
+ align:start position:0%
+it's got a reversal at plus 55 but it's
+ 
+
+ align:start position:0%
+it's got a reversal at plus 55 but it's
+it's a straight line right that's a
+
+ align:start position:0%
+it's a straight line right that's a
+ 
+
+ align:start position:0%
+it's a straight line right that's a
+battery and a resistor so there's our
+
+ align:start position:0%
+battery and a resistor so there's our
+ 
+
+ align:start position:0%
+battery and a resistor so there's our
+driving potential now this is linear
+
+ align:start position:0%
+driving potential now this is linear
+ 
+
+ align:start position:0%
+driving potential now this is linear
+this is linear so what does the
+
+ align:start position:0%
+this is linear so what does the
+ 
+
+ align:start position:0%
+this is linear so what does the
+conductance look like up here good this
+
+ align:start position:0%
+conductance look like up here good this
+ 
+
+ align:start position:0%
+conductance look like up here good this
+is zero but this is big and negative so
+
+ align:start position:0%
+is zero but this is big and negative so
+ 
+
+ align:start position:0%
+is zero but this is big and negative so
+what does this look like down here good
+
+ align:start position:0%
+what does this look like down here good
+ 
+
+ align:start position:0%
+what does this look like down here good
+starting to look pretty familiar right
+
+ align:start position:0%
+starting to look pretty familiar right
+ 
+
+ align:start position:0%
+starting to look pretty familiar right
+boom it's exactly the same both of these
+
+ align:start position:0%
+boom it's exactly the same both of these
+ 
+
+ align:start position:0%
+boom it's exactly the same both of these
+conductances are off at negative
+
+ align:start position:0%
+conductances are off at negative
+ 
+
+ align:start position:0%
+conductances are off at negative
+potentials and they turn on at positive
+
+ align:start position:0%
+potentials and they turn on at positive
+ 
+
+ align:start position:0%
+potentials and they turn on at positive
+voltages and remain constant okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great great question because the sodium
+
+ align:start position:0%
+great great question because the sodium
+ 
+
+ align:start position:0%
+great great question because the sodium
+conductance turns on and then it shuts
+
+ align:start position:0%
+conductance turns on and then it shuts
+ 
+
+ align:start position:0%
+conductance turns on and then it shuts
+off right away and the shutting off is a
+
+ align:start position:0%
+off right away and the shutting off is a
+ 
+
+ align:start position:0%
+off right away and the shutting off is a
+different mechanism so we're trying to
+
+ align:start position:0%
+different mechanism so we're trying to
+ 
+
+ align:start position:0%
+different mechanism so we're trying to
+figure out how to ignore that and just
+
+ align:start position:0%
+figure out how to ignore that and just
+ 
+
+ align:start position:0%
+figure out how to ignore that and just
+understand the voltage dependence of how
+
+ align:start position:0%
+understand the voltage dependence of how
+ 
+
+ align:start position:0%
+understand the voltage dependence of how
+it turns on does that make sense yeah
+
+ align:start position:0%
+it turns on does that make sense yeah
+ 
+
+ align:start position:0%
+it turns on does that make sense yeah
+and we'll get into that next Tuesday but
+
+ align:start position:0%
+and we'll get into that next Tuesday but
+ 
+
+ align:start position:0%
+and we'll get into that next Tuesday but
+I'm showing both of these at the same
+
+ align:start position:0%
+I'm showing both of these at the same
+ 
+
+ align:start position:0%
+I'm showing both of these at the same
+time because they they look Miller at
+
+ align:start position:0%
+time because they they look Miller at
+ 
+
+ align:start position:0%
+time because they they look Miller at
+the level of the voltage dependence in
+
+ align:start position:0%
+the level of the voltage dependence in
+ 
+
+ align:start position:0%
+the level of the voltage dependence in
+fact the way they turn on is very
+
+ align:start position:0%
+fact the way they turn on is very
+ 
+
+ align:start position:0%
+fact the way they turn on is very
+similar okay it's just that the sodium
+
+ align:start position:0%
+similar okay it's just that the sodium
+ 
+
+ align:start position:0%
+similar okay it's just that the sodium
+has some other weird thing that shuts it
+
+ align:start position:0%
+has some other weird thing that shuts it
+ 
+
+ align:start position:0%
+has some other weird thing that shuts it
+off after a few milliseconds so we'll
+
+ align:start position:0%
+off after a few milliseconds so we'll
+ 
+
+ align:start position:0%
+off after a few milliseconds so we'll
+talk about that next time yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nope it's not but any non-linearity here
+
+ align:start position:0%
+nope it's not but any non-linearity here
+ 
+
+ align:start position:0%
+nope it's not but any non-linearity here
+we're going to account for by changes by
+
+ align:start position:0%
+we're going to account for by changes by
+ 
+
+ align:start position:0%
+we're going to account for by changes by
+voltage dependence of the conductance
+
+ align:start position:0%
+voltage dependence of the conductance
+ 
+
+ align:start position:0%
+voltage dependence of the conductance
+okay so great point is that a subtlety
+
+ align:start position:0%
+okay so great point is that a subtlety
+ 
+
+ align:start position:0%
+okay so great point is that a subtlety
+that that we have kind of imposed by
+
+ align:start position:0%
+that that we have kind of imposed by
+ 
+
+ align:start position:0%
+that that we have kind of imposed by
+this way of writing down the voltage
+
+ align:start position:0%
+this way of writing down the voltage
+ 
+
+ align:start position:0%
+this way of writing down the voltage
+dependence of the of the current any
+
+ align:start position:0%
+dependence of the of the current any
+ 
+
+ align:start position:0%
+dependence of the of the current any
+other questions no okay
+
+ align:start position:0%
+other questions no okay
+ 
+
+ align:start position:0%
+other questions no okay
+pushing on so this kind of gradual
+
+ align:start position:0%
+pushing on so this kind of gradual
+ 
+
+ align:start position:0%
+pushing on so this kind of gradual
+turning on this sort of zero conductance
+
+ align:start position:0%
+turning on this sort of zero conductance
+ 
+
+ align:start position:0%
+turning on this sort of zero conductance
+down here and a constants up here that's
+
+ align:start position:0%
+down here and a constants up here that's
+ 
+
+ align:start position:0%
+down here and a constants up here that's
+called a sigmoid volvulus
+
+ align:start position:0%
+called a sigmoid volvulus
+ 
+
+ align:start position:0%
+called a sigmoid volvulus
+it's how these channels turn on okay and
+
+ align:start position:0%
+it's how these channels turn on okay and
+ 
+
+ align:start position:0%
+it's how these channels turn on okay and
+as I said before we're going to deal
+
+ align:start position:0%
+as I said before we're going to deal
+ 
+
+ align:start position:0%
+as I said before we're going to deal
+with how they the other properties of
+
+ align:start position:0%
+with how they the other properties of
+ 
+
+ align:start position:0%
+with how they the other properties of
+the sodium channel that turn it off
+
+ align:start position:0%
+the sodium channel that turn it off
+ 
+
+ align:start position:0%
+the sodium channel that turn it off
+later so both have a sigmoidal voltage
+
+ align:start position:0%
+later so both have a sigmoidal voltage
+ 
+
+ align:start position:0%
+later so both have a sigmoidal voltage
+dependence of activation okay and if you
+
+ align:start position:0%
+dependence of activation okay and if you
+ 
+
+ align:start position:0%
+dependence of activation okay and if you
+plot this you can see that if you plot
+
+ align:start position:0%
+plot this you can see that if you plot
+ 
+
+ align:start position:0%
+plot this you can see that if you plot
+this on a on a log scale here log scale
+
+ align:start position:0%
+this on a on a log scale here log scale
+ 
+
+ align:start position:0%
+this on a on a log scale here log scale
+on conductance linear here on potential
+
+ align:start position:0%
+on conductance linear here on potential
+ 
+
+ align:start position:0%
+on conductance linear here on potential
+you can see that both of these curves
+
+ align:start position:0%
+you can see that both of these curves
+ 
+
+ align:start position:0%
+you can see that both of these curves
+both the potassium and the sodium have
+
+ align:start position:0%
+both the potassium and the sodium have
+ 
+
+ align:start position:0%
+both the potassium and the sodium have
+this very characteristic exponential
+
+ align:start position:0%
+this very characteristic exponential
+ 
+
+ align:start position:0%
+this very characteristic exponential
+turn on followed by this saturation a
+
+ align:start position:0%
+turn on followed by this saturation a
+ 
+
+ align:start position:0%
+turn on followed by this saturation a
+constant constant conductance at higher
+
+ align:start position:0%
+constant constant conductance at higher
+ 
+
+ align:start position:0%
+constant constant conductance at higher
+voltages alright any questions that's
+
+ align:start position:0%
+voltages alright any questions that's
+ 
+
+ align:start position:0%
+voltages alright any questions that's
+voltage dependence now we're going to
+
+ align:start position:0%
+voltage dependence now we're going to
+ 
+
+ align:start position:0%
+voltage dependence now we're going to
+turn to time dependence okay so you can
+
+ align:start position:0%
+turn to time dependence okay so you can
+ 
+
+ align:start position:0%
+turn to time dependence okay so you can
+see that the time dependence so this
+
+ align:start position:0%
+see that the time dependence so this
+ 
+
+ align:start position:0%
+see that the time dependence so this
+driving potential that's just constant
+
+ align:start position:0%
+driving potential that's just constant
+ 
+
+ align:start position:0%
+driving potential that's just constant
+that just depends on the voltage and the
+
+ align:start position:0%
+that just depends on the voltage and the
+ 
+
+ align:start position:0%
+that just depends on the voltage and the
+reversal potential and so we can
+
+ align:start position:0%
+reversal potential and so we can
+ 
+
+ align:start position:0%
+reversal potential and so we can
+separate out that that this thing is
+
+ align:start position:0%
+separate out that that this thing is
+ 
+
+ align:start position:0%
+separate out that that this thing is
+just any time dependence this has is
+
+ align:start position:0%
+just any time dependence this has is
+ 
+
+ align:start position:0%
+just any time dependence this has is
+dependent on the time dependence of the
+
+ align:start position:0%
+dependent on the time dependence of the
+ 
+
+ align:start position:0%
+dependent on the time dependence of the
+voltage but in our in our voltage clamp
+
+ align:start position:0%
+voltage but in our in our voltage clamp
+ 
+
+ align:start position:0%
+voltage but in our in our voltage clamp
+experiments the voltage is constant so
+
+ align:start position:0%
+experiments the voltage is constant so
+ 
+
+ align:start position:0%
+experiments the voltage is constant so
+this thing is constant so anytime
+
+ align:start position:0%
+this thing is constant so anytime
+ 
+
+ align:start position:0%
+this thing is constant so anytime
+Penance current has to be due to time
+
+ align:start position:0%
+Penance current has to be due to time
+ 
+
+ align:start position:0%
+Penance current has to be due to time
+dependence of the conductance right and
+
+ align:start position:0%
+dependence of the conductance right and
+ 
+
+ align:start position:0%
+dependence of the conductance right and
+what that means is we can just look at
+
+ align:start position:0%
+what that means is we can just look at
+ 
+
+ align:start position:0%
+what that means is we can just look at
+the shape of this potassium current
+
+ align:start position:0%
+the shape of this potassium current
+ 
+
+ align:start position:0%
+the shape of this potassium current
+remember this is the potassium current
+
+ align:start position:0%
+remember this is the potassium current
+ 
+
+ align:start position:0%
+remember this is the potassium current
+here that time dependence is just due to
+
+ align:start position:0%
+here that time dependence is just due to
+ 
+
+ align:start position:0%
+here that time dependence is just due to
+time dependence of the conductance that
+
+ align:start position:0%
+time dependence of the conductance that
+ 
+
+ align:start position:0%
+time dependence of the conductance that
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+so what's happening is the potassium
+
+ align:start position:0%
+so what's happening is the potassium
+ 
+
+ align:start position:0%
+so what's happening is the potassium
+conductance is starting at zero the
+
+ align:start position:0%
+conductance is starting at zero the
+ 
+
+ align:start position:0%
+conductance is starting at zero the
+moment you step the voltage up that
+
+ align:start position:0%
+moment you step the voltage up that
+ 
+
+ align:start position:0%
+moment you step the voltage up that
+thing begins to grow gradually and then
+
+ align:start position:0%
+thing begins to grow gradually and then
+ 
+
+ align:start position:0%
+thing begins to grow gradually and then
+runs up to a constant potassium
+
+ align:start position:0%
+runs up to a constant potassium
+ 
+
+ align:start position:0%
+runs up to a constant potassium
+conductance in time it starts off ramps
+
+ align:start position:0%
+conductance in time it starts off ramps
+ 
+
+ align:start position:0%
+conductance in time it starts off ramps
+up and then becomes constant alright so
+
+ align:start position:0%
+up and then becomes constant alright so
+ 
+
+ align:start position:0%
+up and then becomes constant alright so
+that's the time dependence alright sort
+
+ align:start position:0%
+that's the time dependence alright sort
+ 
+
+ align:start position:0%
+that's the time dependence alright sort
+of gracefully turns on that process of
+
+ align:start position:0%
+of gracefully turns on that process of
+ 
+
+ align:start position:0%
+of gracefully turns on that process of
+turning on is called activation the
+
+ align:start position:0%
+turning on is called activation the
+ 
+
+ align:start position:0%
+turning on is called activation the
+sodium conductance their current the
+
+ align:start position:0%
+sodium conductance their current the
+ 
+
+ align:start position:0%
+sodium conductance their current the
+same thing the sodium current is just
+
+ align:start position:0%
+same thing the sodium current is just
+ 
+
+ align:start position:0%
+same thing the sodium current is just
+the sodium conductance the sodium
+
+ align:start position:0%
+the sodium conductance the sodium
+ 
+
+ align:start position:0%
+the sodium conductance the sodium
+current as a function is the sodium
+
+ align:start position:0%
+current as a function is the sodium
+ 
+
+ align:start position:0%
+current as a function is the sodium
+conductance as a function of time times
+
+ align:start position:0%
+conductance as a function of time times
+ 
+
+ align:start position:0%
+conductance as a function of time times
+a constant in our voltage clamp
+
+ align:start position:0%
+a constant in our voltage clamp
+ 
+
+ align:start position:0%
+a constant in our voltage clamp
+experiment again this voltage is
+
+ align:start position:0%
+experiment again this voltage is
+ 
+
+ align:start position:0%
+experiment again this voltage is
+constant so that the sodium conductance
+
+ align:start position:0%
+constant so that the sodium conductance
+ 
+
+ align:start position:0%
+constant so that the sodium conductance
+turns on
+
+ align:start position:0%
+turns on
+ 
+
+ align:start position:0%
+turns on
+that's activation but then it turns off
+
+ align:start position:0%
+that's activation but then it turns off
+ 
+
+ align:start position:0%
+that's activation but then it turns off
+and that's called inactivation all right
+
+ align:start position:0%
+and that's called inactivation all right
+ 
+
+ align:start position:0%
+and that's called inactivation all right
+so the sodium current has but in
+
+ align:start position:0%
+so the sodium current has but in
+ 
+
+ align:start position:0%
+so the sodium current has but in
+conductance has two things going on
+
+ align:start position:0%
+conductance has two things going on
+ 
+
+ align:start position:0%
+conductance has two things going on
+one activation and the second is
+
+ align:start position:0%
+one activation and the second is
+ 
+
+ align:start position:0%
+one activation and the second is
+inactivation okay and it turns out these
+
+ align:start position:0%
+inactivation okay and it turns out these
+ 
+
+ align:start position:0%
+inactivation okay and it turns out these
+are two separate biophysical mechanisms
+
+ align:start position:0%
+are two separate biophysical mechanisms
+ 
+
+ align:start position:0%
+are two separate biophysical mechanisms
+and we're gonna spend more time on this
+
+ align:start position:0%
+and we're gonna spend more time on this
+ 
+
+ align:start position:0%
+and we're gonna spend more time on this
+next week okay so
+
+ align:start position:0%
+next week okay so
+ 
+
+ align:start position:0%
+next week okay so
+notice something interesting the sodium
+
+ align:start position:0%
+notice something interesting the sodium
+ 
+
+ align:start position:0%
+notice something interesting the sodium
+conductance turns on you depolarize the
+
+ align:start position:0%
+conductance turns on you depolarize the
+ 
+
+ align:start position:0%
+conductance turns on you depolarize the
+cell sodium conductance turns on right
+
+ align:start position:0%
+cell sodium conductance turns on right
+ 
+
+ align:start position:0%
+cell sodium conductance turns on right
+away and then shuts off the potassium
+
+ align:start position:0%
+away and then shuts off the potassium
+ 
+
+ align:start position:0%
+away and then shuts off the potassium
+conductance has a delay and then it
+
+ align:start position:0%
+conductance has a delay and then it
+ 
+
+ align:start position:0%
+conductance has a delay and then it
+turns on does that look familiar that
+
+ align:start position:0%
+turns on does that look familiar that
+ 
+
+ align:start position:0%
+turns on does that look familiar that
+looks an awful lot like like this right
+
+ align:start position:0%
+looks an awful lot like like this right
+ 
+
+ align:start position:0%
+looks an awful lot like like this right
+here's the sodium conductance turns on
+
+ align:start position:0%
+here's the sodium conductance turns on
+ 
+
+ align:start position:0%
+here's the sodium conductance turns on
+and then shuts off and then the
+
+ align:start position:0%
+and then shuts off and then the
+ 
+
+ align:start position:0%
+and then shuts off and then the
+potassium conductance turns on with a
+
+ align:start position:0%
+potassium conductance turns on with a
+ 
+
+ align:start position:0%
+potassium conductance turns on with a
+delay yeah and that gives us an action
+
+ align:start position:0%
+delay yeah and that gives us an action
+ 
+
+ align:start position:0%
+delay yeah and that gives us an action
+potential so you can see that when you
+
+ align:start position:0%
+potential so you can see that when you
+ 
+
+ align:start position:0%
+potential so you can see that when you
+use voltage clamp and to sect it out the
+
+ align:start position:0%
+use voltage clamp and to sect it out the
+ 
+
+ align:start position:0%
+use voltage clamp and to sect it out the
+tightness of the of the sodium and
+
+ align:start position:0%
+tightness of the of the sodium and
+ 
+
+ align:start position:0%
+tightness of the of the sodium and
+potassium conductance it looks just like
+
+ align:start position:0%
+potassium conductance it looks just like
+ 
+
+ align:start position:0%
+potassium conductance it looks just like
+the thing we concocted earlier just sort
+
+ align:start position:0%
+the thing we concocted earlier just sort
+ 
+
+ align:start position:0%
+the thing we concocted earlier just sort
+of a toy example for how to make an
+
+ align:start position:0%
+of a toy example for how to make an
+ 
+
+ align:start position:0%
+of a toy example for how to make an
+action potential pretty cool right okay
+
+ align:start position:0%
+action potential pretty cool right okay
+ 
+
+ align:start position:0%
+action potential pretty cool right okay
+it's starting to come together piece by
+
+ align:start position:0%
+it's starting to come together piece by
+ 
+
+ align:start position:0%
+it's starting to come together piece by
+piece
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're now going to dig in a
+
+ align:start position:0%
+okay so we're now going to dig in a
+ 
+
+ align:start position:0%
+okay so we're now going to dig in a
+little bit deeper into the biophysics of
+
+ align:start position:0%
+little bit deeper into the biophysics of
+ 
+
+ align:start position:0%
+little bit deeper into the biophysics of
+how you get these voltage and time
+
+ align:start position:0%
+how you get these voltage and time
+ 
+
+ align:start position:0%
+how you get these voltage and time
+dependencies okay so we're going to
+
+ align:start position:0%
+dependencies okay so we're going to
+ 
+
+ align:start position:0%
+dependencies okay so we're going to
+derive the equation for the voltage
+
+ align:start position:0%
+derive the equation for the voltage
+ 
+
+ align:start position:0%
+derive the equation for the voltage
+dependence anybody want to take a crazy
+
+ align:start position:0%
+dependence anybody want to take a crazy
+ 
+
+ align:start position:0%
+dependence anybody want to take a crazy
+guess on how we're gonna do that just a
+
+ align:start position:0%
+guess on how we're gonna do that just a
+ 
+
+ align:start position:0%
+guess on how we're gonna do that just a
+wild guess how you might derive the
+
+ align:start position:0%
+wild guess how you might derive the
+ 
+
+ align:start position:0%
+wild guess how you might derive the
+voltage dependence of something No okay
+
+ align:start position:0%
+voltage dependence of something No okay
+ 
+
+ align:start position:0%
+voltage dependence of something No okay
+we're gonna use the Boltzmann equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're gonna derive different
+
+ align:start position:0%
+and we're gonna derive different
+ 
+
+ align:start position:0%
+and we're gonna derive different
+equations that describe the way those
+
+ align:start position:0%
+equations that describe the way those
+ 
+
+ align:start position:0%
+equations that describe the way those
+channels turn on okay how those
+
+ align:start position:0%
+channels turn on okay how those
+ 
+
+ align:start position:0%
+channels turn on okay how those
+conductances turn on alright and once we
+
+ align:start position:0%
+conductances turn on alright and once we
+ 
+
+ align:start position:0%
+conductances turn on alright and once we
+do that we're gonna have a simple set of
+
+ align:start position:0%
+do that we're gonna have a simple set of
+ 
+
+ align:start position:0%
+do that we're gonna have a simple set of
+equations and not just equations we're
+
+ align:start position:0%
+equations and not just equations we're
+ 
+
+ align:start position:0%
+equations and not just equations we're
+gonna have a set of processes that we
+
+ align:start position:0%
+gonna have a set of processes that we
+ 
+
+ align:start position:0%
+gonna have a set of processes that we
+can think of as happening a loop in a
+
+ align:start position:0%
+can think of as happening a loop in a
+ 
+
+ align:start position:0%
+can think of as happening a loop in a
+for loop that's our algorithm for an
+
+ align:start position:0%
+for loop that's our algorithm for an
+ 
+
+ align:start position:0%
+for loop that's our algorithm for an
+action potential okay all right so let's
+
+ align:start position:0%
+action potential okay all right so let's
+ 
+
+ align:start position:0%
+action potential okay all right so let's
+dive into single channels and see see
+
+ align:start position:0%
+dive into single channels and see see
+ 
+
+ align:start position:0%
+dive into single channels and see see
+how they worked so of course
+
+ align:start position:0%
+how they worked so of course
+ 
+
+ align:start position:0%
+how they worked so of course
+currents are result from ionic flow
+
+ align:start position:0%
+currents are result from ionic flow
+ 
+
+ align:start position:0%
+currents are result from ionic flow
+through ion channels it's actually
+
+ align:start position:0%
+through ion channels it's actually
+ 
+
+ align:start position:0%
+through ion channels it's actually
+possible to record currents from single
+
+ align:start position:0%
+possible to record currents from single
+ 
+
+ align:start position:0%
+possible to record currents from single
+ion channels we can actually make a
+
+ align:start position:0%
+ion channels we can actually make a
+ 
+
+ align:start position:0%
+ion channels we can actually make a
+version of our voltage clamp that we can
+
+ align:start position:0%
+version of our voltage clamp that we can
+ 
+
+ align:start position:0%
+version of our voltage clamp that we can
+attach to a single ion channel and the
+
+ align:start position:0%
+attach to a single ion channel and the
+ 
+
+ align:start position:0%
+attach to a single ion channel and the
+way you do that is it's so when you take
+
+ align:start position:0%
+way you do that is it's so when you take
+ 
+
+ align:start position:0%
+way you do that is it's so when you take
+this piece of glass and you pull it
+
+ align:start position:0%
+this piece of glass and you pull it
+ 
+
+ align:start position:0%
+this piece of glass and you pull it
+instead of poking it through the cell
+
+ align:start position:0%
+instead of poking it through the cell
+ 
+
+ align:start position:0%
+instead of poking it through the cell
+instead of making it really sharp and
+
+ align:start position:0%
+instead of making it really sharp and
+ 
+
+ align:start position:0%
+instead of making it really sharp and
+poking it through the cell what you do
+
+ align:start position:0%
+poking it through the cell what you do
+ 
+
+ align:start position:0%
+poking it through the cell what you do
+is you make it a little bit blunter okay
+
+ align:start position:0%
+is you make it a little bit blunter okay
+ 
+
+ align:start position:0%
+is you make it a little bit blunter okay
+so it's got kind of a rough end and then
+
+ align:start position:0%
+so it's got kind of a rough end and then
+ 
+
+ align:start position:0%
+so it's got kind of a rough end and then
+you can fire polish you can hold the end
+
+ align:start position:0%
+you can fire polish you can hold the end
+ 
+
+ align:start position:0%
+you can fire polish you can hold the end
+of that electrode into a flame okay
+
+ align:start position:0%
+of that electrode into a flame okay
+ 
+
+ align:start position:0%
+of that electrode into a flame okay
+quite it's usually a filament that heats
+
+ align:start position:0%
+quite it's usually a filament that heats
+ 
+
+ align:start position:0%
+quite it's usually a filament that heats
+up hot you hold the end of the electrode
+
+ align:start position:0%
+up hot you hold the end of the electrode
+ 
+
+ align:start position:0%
+up hot you hold the end of the electrode
+near this hot and it melts the tip into
+
+ align:start position:0%
+near this hot and it melts the tip into
+ 
+
+ align:start position:0%
+near this hot and it melts the tip into
+a nice round it's still a tube but the
+
+ align:start position:0%
+a nice round it's still a tube but the
+ 
+
+ align:start position:0%
+a nice round it's still a tube but the
+edges of the tube are nice and smooth
+
+ align:start position:0%
+edges of the tube are nice and smooth
+ 
+
+ align:start position:0%
+edges of the tube are nice and smooth
+okay and now when you take that tube and
+
+ align:start position:0%
+okay and now when you take that tube and
+ 
+
+ align:start position:0%
+okay and now when you take that tube and
+you press it up against the cell
+
+ align:start position:0%
+you press it up against the cell
+ 
+
+ align:start position:0%
+you press it up against the cell
+actually you attach all
+
+ align:start position:0%
+actually you attach all
+ 
+
+ align:start position:0%
+actually you attach all
+a little plastic tube to the end of the
+
+ align:start position:0%
+a little plastic tube to the end of the
+ 
+
+ align:start position:0%
+a little plastic tube to the end of the
+glass and you press the the electrode
+
+ align:start position:0%
+glass and you press the the electrode
+ 
+
+ align:start position:0%
+glass and you press the the electrode
+it's the selling you actually you
+
+ align:start position:0%
+it's the selling you actually you
+ 
+
+ align:start position:0%
+it's the selling you actually you
+literally suck on it with your mouth
+
+ align:start position:0%
+literally suck on it with your mouth
+ 
+
+ align:start position:0%
+literally suck on it with your mouth
+onto that tube and it sucks the membrane
+
+ align:start position:0%
+onto that tube and it sucks the membrane
+ 
+
+ align:start position:0%
+onto that tube and it sucks the membrane
+up against that smooth end of the
+
+ align:start position:0%
+up against that smooth end of the
+ 
+
+ align:start position:0%
+up against that smooth end of the
+electrode and it sticks the lipids of
+
+ align:start position:0%
+electrode and it sticks the lipids of
+ 
+
+ align:start position:0%
+electrode and it sticks the lipids of
+the membrane actually sealed themselves
+
+ align:start position:0%
+the membrane actually sealed themselves
+ 
+
+ align:start position:0%
+the membrane actually sealed themselves
+onto the end of the glass so now no
+
+ align:start position:0%
+onto the end of the glass so now no
+ 
+
+ align:start position:0%
+onto the end of the glass so now no
+currents can flow out through the
+
+ align:start position:0%
+currents can flow out through the
+ 
+
+ align:start position:0%
+currents can flow out through the
+through these edges here all right and
+
+ align:start position:0%
+through these edges here all right and
+ 
+
+ align:start position:0%
+through these edges here all right and
+then you hook it up to a very sensitive
+
+ align:start position:0%
+then you hook it up to a very sensitive
+ 
+
+ align:start position:0%
+then you hook it up to a very sensitive
+current amplifier and now you can
+
+ align:start position:0%
+current amplifier and now you can
+ 
+
+ align:start position:0%
+current amplifier and now you can
+control the voltage you can actually
+
+ align:start position:0%
+control the voltage you can actually
+ 
+
+ align:start position:0%
+control the voltage you can actually
+just rip that off of the cell so now
+
+ align:start position:0%
+just rip that off of the cell so now
+ 
+
+ align:start position:0%
+just rip that off of the cell so now
+there's no more cell you just have an
+
+ align:start position:0%
+there's no more cell you just have an
+ 
+
+ align:start position:0%
+there's no more cell you just have an
+ion channel sitting there on a piece and
+
+ align:start position:0%
+ion channel sitting there on a piece and
+ 
+
+ align:start position:0%
+ion channel sitting there on a piece and
+the end of your glass and now you can do
+
+ align:start position:0%
+the end of your glass and now you can do
+ 
+
+ align:start position:0%
+the end of your glass and now you can do
+a voltage clamp experiment and study the
+
+ align:start position:0%
+a voltage clamp experiment and study the
+ 
+
+ align:start position:0%
+a voltage clamp experiment and study the
+current the voltage dependence of the
+
+ align:start position:0%
+current the voltage dependence of the
+ 
+
+ align:start position:0%
+current the voltage dependence of the
+current through that ion channel so
+
+ align:start position:0%
+current through that ion channel so
+ 
+
+ align:start position:0%
+current through that ion channel so
+here's what this looks like here's one
+
+ align:start position:0%
+here's what this looks like here's one
+ 
+
+ align:start position:0%
+here's what this looks like here's one
+experiment we're gonna start at minus
+
+ align:start position:0%
+experiment we're gonna start at minus
+ 
+
+ align:start position:0%
+experiment we're gonna start at minus
+100 this is a potassium channel you
+
+ align:start position:0%
+100 this is a potassium channel you
+ 
+
+ align:start position:0%
+100 this is a potassium channel you
+depolarize the potassium channel up to
+
+ align:start position:0%
+depolarize the potassium channel up to
+ 
+
+ align:start position:0%
+depolarize the potassium channel up to
+50 millivolts and you see that the
+
+ align:start position:0%
+50 millivolts and you see that the
+ 
+
+ align:start position:0%
+50 millivolts and you see that the
+current through that single channel
+
+ align:start position:0%
+current through that single channel
+ 
+
+ align:start position:0%
+current through that single channel
+starts flickering on and off okay here's
+
+ align:start position:0%
+starts flickering on and off okay here's
+ 
+
+ align:start position:0%
+starts flickering on and off okay here's
+another trial turns on turns off turns
+
+ align:start position:0%
+another trial turns on turns off turns
+ 
+
+ align:start position:0%
+another trial turns on turns off turns
+on turns off you can do that a bunch of
+
+ align:start position:0%
+on turns off you can do that a bunch of
+ 
+
+ align:start position:0%
+on turns off you can do that a bunch of
+times you can see something interesting
+
+ align:start position:0%
+times you can see something interesting
+ 
+
+ align:start position:0%
+times you can see something interesting
+the current is either off doesn't turn
+
+ align:start position:0%
+the current is either off doesn't turn
+ 
+
+ align:start position:0%
+the current is either off doesn't turn
+on gradually doesn't change smoothly it
+
+ align:start position:0%
+on gradually doesn't change smoothly it
+ 
+
+ align:start position:0%
+on gradually doesn't change smoothly it
+just flickers between on and off it's a
+
+ align:start position:0%
+just flickers between on and off it's a
+ 
+
+ align:start position:0%
+just flickers between on and off it's a
+very important aspect of ion channels
+
+ align:start position:0%
+very important aspect of ion channels
+ 
+
+ align:start position:0%
+very important aspect of ion channels
+but if you average all those trials
+
+ align:start position:0%
+but if you average all those trials
+ 
+
+ align:start position:0%
+but if you average all those trials
+together you see that you get an average
+
+ align:start position:0%
+together you see that you get an average
+ 
+
+ align:start position:0%
+together you see that you get an average
+current that looks just like the current
+
+ align:start position:0%
+current that looks just like the current
+ 
+
+ align:start position:0%
+current that looks just like the current
+that hodgkin-huxley measured in the
+
+ align:start position:0%
+that hodgkin-huxley measured in the
+ 
+
+ align:start position:0%
+that hodgkin-huxley measured in the
+whole axon how is that possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah good so basically what we're doing
+
+ align:start position:0%
+yeah good so basically what we're doing
+ 
+
+ align:start position:0%
+yeah good so basically what we're doing
+is we're measuring one ion channel many
+
+ align:start position:0%
+is we're measuring one ion channel many
+ 
+
+ align:start position:0%
+is we're measuring one ion channel many
+times but on a cell you're measuring a
+
+ align:start position:0%
+times but on a cell you're measuring a
+ 
+
+ align:start position:0%
+times but on a cell you're measuring a
+bunch of ion channels each of which is
+
+ align:start position:0%
+bunch of ion channels each of which is
+ 
+
+ align:start position:0%
+bunch of ion channels each of which is
+doing something like this but there have
+
+ align:start position:0%
+doing something like this but there have
+ 
+
+ align:start position:0%
+doing something like this but there have
+at the same time and the current is
+
+ align:start position:0%
+at the same time and the current is
+ 
+
+ align:start position:0%
+at the same time and the current is
+being averaged so here we're averaging
+
+ align:start position:0%
+being averaged so here we're averaging
+ 
+
+ align:start position:0%
+being averaged so here we're averaging
+the current one at a time and on a whole
+
+ align:start position:0%
+the current one at a time and on a whole
+ 
+
+ align:start position:0%
+the current one at a time and on a whole
+cell were just averaging a bunch of them
+
+ align:start position:0%
+cell were just averaging a bunch of them
+ 
+
+ align:start position:0%
+cell were just averaging a bunch of them
+at once okay it's called ergot disa T in
+
+ align:start position:0%
+at once okay it's called ergot disa T in
+ 
+
+ align:start position:0%
+at once okay it's called ergot disa T in
+physics that's called the ensemble
+
+ align:start position:0%
+physics that's called the ensemble
+ 
+
+ align:start position:0%
+physics that's called the ensemble
+average okay you can do the same thing
+
+ align:start position:0%
+average okay you can do the same thing
+ 
+
+ align:start position:0%
+average okay you can do the same thing
+for sodium you take your patch a new
+
+ align:start position:0%
+for sodium you take your patch a new
+ 
+
+ align:start position:0%
+for sodium you take your patch a new
+patch electrode fire polish it push it
+
+ align:start position:0%
+patch electrode fire polish it push it
+ 
+
+ align:start position:0%
+patch electrode fire polish it push it
+up to a cell by some suction glues on
+
+ align:start position:0%
+up to a cell by some suction glues on
+ 
+
+ align:start position:0%
+up to a cell by some suction glues on
+this time we had a sodium channel okay
+
+ align:start position:0%
+this time we had a sodium channel okay
+ 
+
+ align:start position:0%
+this time we had a sodium channel okay
+and now you can see that the thing again
+
+ align:start position:0%
+and now you can see that the thing again
+ 
+
+ align:start position:0%
+and now you can see that the thing again
+flickers on flickers flickers on
+
+ align:start position:0%
+flickers on flickers flickers on
+ 
+
+ align:start position:0%
+flickers on flickers flickers on
+flickers off but now they all flicker on
+
+ align:start position:0%
+flickers off but now they all flicker on
+ 
+
+ align:start position:0%
+flickers off but now they all flicker on
+right at the beginning and then they
+
+ align:start position:0%
+right at the beginning and then they
+ 
+
+ align:start position:0%
+right at the beginning and then they
+flicker off and stay off and if you
+
+ align:start position:0%
+flicker off and stay off and if you
+ 
+
+ align:start position:0%
+flicker off and stay off and if you
+average all those different trials you
+
+ align:start position:0%
+average all those different trials you
+ 
+
+ align:start position:0%
+average all those different trials you
+see an average an ensemble average
+
+ align:start position:0%
+see an average an ensemble average
+ 
+
+ align:start position:0%
+see an average an ensemble average
+sodium current that looks just like when
+
+ align:start position:0%
+sodium current that looks just like when
+ 
+
+ align:start position:0%
+sodium current that looks just like when
+you measure the sodium current on a
+
+ align:start position:0%
+you measure the sodium current on a
+ 
+
+ align:start position:0%
+you measure the sodium current on a
+whole act okay but the key thing is that
+
+ align:start position:0%
+whole act okay but the key thing is that
+ 
+
+ align:start position:0%
+whole act okay but the key thing is that
+these channels have two states on and
+
+ align:start position:0%
+these channels have two states on and
+ 
+
+ align:start position:0%
+these channels have two states on and
+off and they flicker back and forth
+
+ align:start position:0%
+off and they flicker back and forth
+ 
+
+ align:start position:0%
+off and they flicker back and forth
+between those two states conducting and
+
+ align:start position:0%
+between those two states conducting and
+ 
+
+ align:start position:0%
+between those two states conducting and
+non conducting so we can now write down
+
+ align:start position:0%
+non conducting so we can now write down
+ 
+
+ align:start position:0%
+non conducting so we can now write down
+we could start now working with this
+
+ align:start position:0%
+we could start now working with this
+ 
+
+ align:start position:0%
+we could start now working with this
+idea that our ion channels are eating
+
+ align:start position:0%
+idea that our ion channels are eating
+ 
+
+ align:start position:0%
+idea that our ion channels are eating
+open or closed and we can think of a
+
+ align:start position:0%
+open or closed and we can think of a
+ 
+
+ align:start position:0%
+open or closed and we can think of a
+probability that the channel is being
+
+ align:start position:0%
+probability that the channel is being
+ 
+
+ align:start position:0%
+probability that the channel is being
+open that the channel is open we can
+
+ align:start position:0%
+open that the channel is open we can
+ 
+
+ align:start position:0%
+open that the channel is open we can
+have a total number of channels the
+
+ align:start position:0%
+have a total number of channels the
+ 
+
+ align:start position:0%
+have a total number of channels the
+probability the number of open channels
+
+ align:start position:0%
+probability the number of open channels
+ 
+
+ align:start position:0%
+probability the number of open channels
+is just the number of channels you have
+
+ align:start position:0%
+is just the number of channels you have
+ 
+
+ align:start position:0%
+is just the number of channels you have
+times the probability that any one of
+
+ align:start position:0%
+times the probability that any one of
+ 
+
+ align:start position:0%
+times the probability that any one of
+them is open if G is the conductance of
+
+ align:start position:0%
+them is open if G is the conductance of
+ 
+
+ align:start position:0%
+them is open if G is the conductance of
+one open channel then we can write down
+
+ align:start position:0%
+one open channel then we can write down
+ 
+
+ align:start position:0%
+one open channel then we can write down
+the total potassium conductance as the
+
+ align:start position:0%
+the total potassium conductance as the
+ 
+
+ align:start position:0%
+the total potassium conductance as the
+probability that any given ion channel
+
+ align:start position:0%
+probability that any given ion channel
+ 
+
+ align:start position:0%
+probability that any given ion channel
+is open times the number of channels
+
+ align:start position:0%
+is open times the number of channels
+ 
+
+ align:start position:0%
+is open times the number of channels
+times the conductance of one open
+
+ align:start position:0%
+times the conductance of one open
+ 
+
+ align:start position:0%
+times the conductance of one open
+channel
+
+ align:start position:0%
+channel
+ 
+
+ align:start position:0%
+channel
+there makes sense and now to claim here
+
+ align:start position:0%
+there makes sense and now to claim here
+ 
+
+ align:start position:0%
+there makes sense and now to claim here
+all of the interesting voltage and time
+
+ align:start position:0%
+all of the interesting voltage and time
+ 
+
+ align:start position:0%
+all of the interesting voltage and time
+dependence of these channels happens
+
+ align:start position:0%
+dependence of these channels happens
+ 
+
+ align:start position:0%
+dependence of these channels happens
+here obviously the number of them isn't
+
+ align:start position:0%
+here obviously the number of them isn't
+ 
+
+ align:start position:0%
+here obviously the number of them isn't
+changing very rapidly the conductance
+
+ align:start position:0%
+changing very rapidly the conductance
+ 
+
+ align:start position:0%
+changing very rapidly the conductance
+per channel is constant per open channel
+
+ align:start position:0%
+per channel is constant per open channel
+ 
+
+ align:start position:0%
+per channel is constant per open channel
+so the interesting stuff is in the
+
+ align:start position:0%
+so the interesting stuff is in the
+ 
+
+ align:start position:0%
+so the interesting stuff is in the
+probability that the channel okay and
+
+ align:start position:0%
+probability that the channel okay and
+ 
+
+ align:start position:0%
+probability that the channel okay and
+when we want to get the current we're
+
+ align:start position:0%
+when we want to get the current we're
+ 
+
+ align:start position:0%
+when we want to get the current we're
+just going to plug this conductance into
+
+ align:start position:0%
+just going to plug this conductance into
+ 
+
+ align:start position:0%
+just going to plug this conductance into
+here okay all right so let's start with
+
+ align:start position:0%
+here okay all right so let's start with
+ 
+
+ align:start position:0%
+here okay all right so let's start with
+a potassium channel let's dig in a
+
+ align:start position:0%
+a potassium channel let's dig in a
+ 
+
+ align:start position:0%
+a potassium channel let's dig in a
+little bit deeper into what the
+
+ align:start position:0%
+little bit deeper into what the
+ 
+
+ align:start position:0%
+little bit deeper into what the
+potassium channel looks like potassium
+
+ align:start position:0%
+potassium channel looks like potassium
+ 
+
+ align:start position:0%
+potassium channel looks like potassium
+channel is formed by four identical
+
+ align:start position:0%
+channel is formed by four identical
+ 
+
+ align:start position:0%
+channel is formed by four identical
+subunits there they're produced
+
+ align:start position:0%
+subunits there they're produced
+ 
+
+ align:start position:0%
+subunits there they're produced
+separately by by ribosomes they they
+
+ align:start position:0%
+separately by by ribosomes they they
+ 
+
+ align:start position:0%
+separately by by ribosomes they they
+form a heterodimer a tetramer
+
+ align:start position:0%
+form a heterodimer a tetramer
+ 
+
+ align:start position:0%
+form a heterodimer a tetramer
+and that tetra mer has a hole that runs
+
+ align:start position:0%
+and that tetra mer has a hole that runs
+ 
+
+ align:start position:0%
+and that tetra mer has a hole that runs
+down the middle of it which is where the
+
+ align:start position:0%
+down the middle of it which is where the
+ 
+
+ align:start position:0%
+down the middle of it which is where the
+where the ions flow each of these
+
+ align:start position:0%
+where the ions flow each of these
+ 
+
+ align:start position:0%
+where the ions flow each of these
+subunits has a voltage sensor that
+
+ align:start position:0%
+subunits has a voltage sensor that
+ 
+
+ align:start position:0%
+subunits has a voltage sensor that
+allows it to turn on and off and in
+
+ align:start position:0%
+allows it to turn on and off and in
+ 
+
+ align:start position:0%
+allows it to turn on and off and in
+order for the channel to be on all four
+
+ align:start position:0%
+order for the channel to be on all four
+ 
+
+ align:start position:0%
+order for the channel to be on all four
+of those subunits has to be open so each
+
+ align:start position:0%
+of those subunits has to be open so each
+ 
+
+ align:start position:0%
+of those subunits has to be open so each
+subunit has an open state and a closed
+
+ align:start position:0%
+subunit has an open state and a closed
+ 
+
+ align:start position:0%
+subunit has an open state and a closed
+state and for the channel to be open all
+
+ align:start position:0%
+state and for the channel to be open all
+ 
+
+ align:start position:0%
+state and for the channel to be open all
+four of them have to be in the open
+
+ align:start position:0%
+four of them have to be in the open
+ 
+
+ align:start position:0%
+four of them have to be in the open
+state okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if n is the probability that any one
+
+ align:start position:0%
+so if n is the probability that any one
+ 
+
+ align:start position:0%
+so if n is the probability that any one
+subunit is open I meant to ask me make
+
+ align:start position:0%
+subunit is open I meant to ask me make
+ 
+
+ align:start position:0%
+subunit is open I meant to ask me make
+you guys answer this question before I
+
+ align:start position:0%
+you guys answer this question before I
+ 
+
+ align:start position:0%
+you guys answer this question before I
+show the answer but is it clear how if
+
+ align:start position:0%
+show the answer but is it clear how if
+ 
+
+ align:start position:0%
+show the answer but is it clear how if
+any one subunit has a probability of
+
+ align:start position:0%
+any one subunit has a probability of
+ 
+
+ align:start position:0%
+any one subunit has a probability of
+being open of n then the probability
+
+ align:start position:0%
+being open of n then the probability
+ 
+
+ align:start position:0%
+being open of n then the probability
+that the whole channel is open is n to
+
+ align:start position:0%
+that the whole channel is open is n to
+ 
+
+ align:start position:0%
+that the whole channel is open is n to
+the four okay this n is called a gating
+
+ align:start position:0%
+the four okay this n is called a gating
+ 
+
+ align:start position:0%
+the four okay this n is called a gating
+variable I would like you to be able to
+
+ align:start position:0%
+variable I would like you to be able to
+ 
+
+ align:start position:0%
+variable I would like you to be able to
+I would like you to know that the
+
+ align:start position:0%
+I would like you to know that the
+ 
+
+ align:start position:0%
+I would like you to know that the
+probability that a sodium potassium
+
+ align:start position:0%
+probability that a sodium potassium
+ 
+
+ align:start position:0%
+probability that a sodium potassium
+channel is open is n to the four that's
+
+ align:start position:0%
+channel is open is n to the four that's
+ 
+
+ align:start position:0%
+channel is open is n to the four that's
+an important thing for you to remember
+
+ align:start position:0%
+an important thing for you to remember
+ 
+
+ align:start position:0%
+an important thing for you to remember
+that assumes that those four subunits
+
+ align:start position:0%
+that assumes that those four subunits
+ 
+
+ align:start position:0%
+that assumes that those four subunits
+are independent okay and in potassium
+
+ align:start position:0%
+are independent okay and in potassium
+ 
+
+ align:start position:0%
+are independent okay and in potassium
+channels that's a very good
+
+ align:start position:0%
+channels that's a very good
+ 
+
+ align:start position:0%
+channels that's a very good
+approximation so we can now write down
+
+ align:start position:0%
+approximation so we can now write down
+ 
+
+ align:start position:0%
+approximation so we can now write down
+the conductance of our potassium channel
+
+ align:start position:0%
+the conductance of our potassium channel
+ 
+
+ align:start position:0%
+the conductance of our potassium channel
+something times n to the 4 where that
+
+ align:start position:0%
+something times n to the 4 where that
+ 
+
+ align:start position:0%
+something times n to the 4 where that
+something is that conductance of 1 ion
+
+ align:start position:0%
+something is that conductance of 1 ion
+ 
+
+ align:start position:0%
+something is that conductance of 1 ion
+channel okay so we can now write down
+
+ align:start position:0%
+channel okay so we can now write down
+ 
+
+ align:start position:0%
+channel okay so we can now write down
+the current as n open conductance times
+
+ align:start position:0%
+the current as n open conductance times
+ 
+
+ align:start position:0%
+the current as n open conductance times
+n to the 4 times a driving potential and
+
+ align:start position:0%
+n to the 4 times a driving potential and
+ 
+
+ align:start position:0%
+n to the 4 times a driving potential and
+that n is called the gating variable for
+
+ align:start position:0%
+that n is called the gating variable for
+ 
+
+ align:start position:0%
+that n is called the gating variable for
+the potassium conductance all right any
+
+ align:start position:0%
+the potassium conductance all right any
+ 
+
+ align:start position:0%
+the potassium conductance all right any
+questions no yes and absolutely does
+
+ align:start position:0%
+questions no yes and absolutely does
+ 
+
+ align:start position:0%
+questions no yes and absolutely does
+depend on voltage very good that's where
+
+ align:start position:0%
+depend on voltage very good that's where
+ 
+
+ align:start position:0%
+depend on voltage very good that's where
+we're going next okay okay but before we
+
+ align:start position:0%
+we're going next okay okay but before we
+ 
+
+ align:start position:0%
+we're going next okay okay but before we
+go on to that I want to do one other
+
+ align:start position:0%
+go on to that I want to do one other
+ 
+
+ align:start position:0%
+go on to that I want to do one other
+thing which I think is is really cool
+
+ align:start position:0%
+thing which I think is is really cool
+ 
+
+ align:start position:0%
+thing which I think is is really cool
+we're gonna do the voltage dependence of
+
+ align:start position:0%
+we're gonna do the voltage dependence of
+ 
+
+ align:start position:0%
+we're gonna do the voltage dependence of
+a potassium channel using the Boltzmann
+
+ align:start position:0%
+a potassium channel using the Boltzmann
+ 
+
+ align:start position:0%
+a potassium channel using the Boltzmann
+equation okay
+
+ align:start position:0%
+equation okay
+ 
+
+ align:start position:0%
+equation okay
+so here's the way you think about a
+
+ align:start position:0%
+so here's the way you think about a
+ 
+
+ align:start position:0%
+so here's the way you think about a
+potassium channel working here's a
+
+ align:start position:0%
+potassium channel working here's a
+ 
+
+ align:start position:0%
+potassium channel working here's a
+potassium channel we're showing a
+
+ align:start position:0%
+potassium channel we're showing a
+ 
+
+ align:start position:0%
+potassium channel we're showing a
+cross-section here it is here's the
+
+ align:start position:0%
+cross-section here it is here's the
+ 
+
+ align:start position:0%
+cross-section here it is here's the
+membrane the lipid bilayer here's our
+
+ align:start position:0%
+membrane the lipid bilayer here's our
+ 
+
+ align:start position:0%
+membrane the lipid bilayer here's our
+potassium channel sitting in the in the
+
+ align:start position:0%
+potassium channel sitting in the in the
+ 
+
+ align:start position:0%
+potassium channel sitting in the in the
+membrane and we're taking a
+
+ align:start position:0%
+membrane and we're taking a
+ 
+
+ align:start position:0%
+membrane and we're taking a
+cross-section through that tetramer that
+
+ align:start position:0%
+cross-section through that tetramer that
+ 
+
+ align:start position:0%
+cross-section through that tetramer that
+shows two subunits and I'm showing the
+
+ align:start position:0%
+shows two subunits and I'm showing the
+ 
+
+ align:start position:0%
+shows two subunits and I'm showing the
+voltage sent of showing the mechanism
+
+ align:start position:0%
+voltage sent of showing the mechanism
+ 
+
+ align:start position:0%
+voltage sent of showing the mechanism
+that that opens and closes one of those
+
+ align:start position:0%
+that that opens and closes one of those
+ 
+
+ align:start position:0%
+that that opens and closes one of those
+subunits okay this this subunit will
+
+ align:start position:0%
+subunits okay this this subunit will
+ 
+
+ align:start position:0%
+subunits okay this this subunit will
+also have a voltage sensor and a gate
+
+ align:start position:0%
+also have a voltage sensor and a gate
+ 
+
+ align:start position:0%
+also have a voltage sensor and a gate
+that looks the same okay so look the
+
+ align:start position:0%
+that looks the same okay so look the
+ 
+
+ align:start position:0%
+that looks the same okay so look the
+voltage sensor how do you sense voltage
+
+ align:start position:0%
+voltage sensor how do you sense voltage
+ 
+
+ align:start position:0%
+voltage sensor how do you sense voltage
+you sense voltage with charge right
+
+ align:start position:0%
+you sense voltage with charge right
+ 
+
+ align:start position:0%
+you sense voltage with charge right
+voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differences I should say you sense with
+
+ align:start position:0%
+differences I should say you sense with
+ 
+
+ align:start position:0%
+differences I should say you sense with
+a charge because voltage gradients are
+
+ align:start position:0%
+a charge because voltage gradients are
+ 
+
+ align:start position:0%
+a charge because voltage gradients are
+electric fields and electric fields push
+
+ align:start position:0%
+electric fields and electric fields push
+ 
+
+ align:start position:0%
+electric fields and electric fields push
+on charges so if we want to detect the
+
+ align:start position:0%
+on charges so if we want to detect the
+ 
+
+ align:start position:0%
+on charges so if we want to detect the
+voltage difference across this membrane
+
+ align:start position:0%
+voltage difference across this membrane
+ 
+
+ align:start position:0%
+voltage difference across this membrane
+we put a charge in the membrane when the
+
+ align:start position:0%
+we put a charge in the membrane when the
+ 
+
+ align:start position:0%
+we put a charge in the membrane when the
+voltage difference is zero there's
+
+ align:start position:0%
+voltage difference is zero there's
+ 
+
+ align:start position:0%
+voltage difference is zero there's
+little force on the on those charges now
+
+ align:start position:0%
+little force on the on those charges now
+ 
+
+ align:start position:0%
+little force on the on those charges now
+if we suddenly hyperpolarize the cell so
+
+ align:start position:0%
+if we suddenly hyperpolarize the cell so
+ 
+
+ align:start position:0%
+if we suddenly hyperpolarize the cell so
+it's very negative
+
+ align:start position:0%
+it's very negative
+ 
+
+ align:start position:0%
+it's very negative
+now there's an electric field inside the
+
+ align:start position:0%
+now there's an electric field inside the
+ 
+
+ align:start position:0%
+now there's an electric field inside the
+membrane that points toward the inside
+
+ align:start position:0%
+membrane that points toward the inside
+ 
+
+ align:start position:0%
+membrane that points toward the inside
+of the cell which pushes those charges
+
+ align:start position:0%
+of the cell which pushes those charges
+ 
+
+ align:start position:0%
+of the cell which pushes those charges
+toward the inside of the cell and now
+
+ align:start position:0%
+toward the inside of the cell and now
+ 
+
+ align:start position:0%
+toward the inside of the cell and now
+you can just have a little mechanical
+
+ align:start position:0%
+you can just have a little mechanical
+ 
+
+ align:start position:0%
+you can just have a little mechanical
+linkage that's not really what it looks
+
+ align:start position:0%
+linkage that's not really what it looks
+ 
+
+ align:start position:0%
+linkage that's not really what it looks
+like but there's some consumnes is in
+
+ align:start position:0%
+like but there's some consumnes is in
+ 
+
+ align:start position:0%
+like but there's some consumnes is in
+the protein are configured so that when
+
+ align:start position:0%
+the protein are configured so that when
+ 
+
+ align:start position:0%
+the protein are configured so that when
+those charges get pushed on it closes a
+
+ align:start position:0%
+those charges get pushed on it closes a
+ 
+
+ align:start position:0%
+those charges get pushed on it closes a
+gate and now that current can no longer
+
+ align:start position:0%
+gate and now that current can no longer
+ 
+
+ align:start position:0%
+gate and now that current can no longer
+flow through the ion channel okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we're gonna derive how this
+
+ align:start position:0%
+okay so now we're gonna derive how this
+ 
+
+ align:start position:0%
+okay so now we're gonna derive how this
+we're gonna see how to derive this
+
+ align:start position:0%
+we're gonna see how to derive this
+ 
+
+ align:start position:0%
+we're gonna see how to derive this
+voltage dependence from the Boltzmann
+
+ align:start position:0%
+voltage dependence from the Boltzmann
+ 
+
+ align:start position:0%
+voltage dependence from the Boltzmann
+equation alright so everybody this is
+
+ align:start position:0%
+equation alright so everybody this is
+ 
+
+ align:start position:0%
+equation alright so everybody this is
+just for fun I don't to know how to do
+
+ align:start position:0%
+just for fun I don't to know how to do
+ 
+
+ align:start position:0%
+just for fun I don't to know how to do
+this I just want you to see it because I
+
+ align:start position:0%
+this I just want you to see it because I
+ 
+
+ align:start position:0%
+this I just want you to see it because I
+personally get chills when I see this
+
+ align:start position:0%
+personally get chills when I see this
+ 
+
+ align:start position:0%
+personally get chills when I see this
+it's really cool but I'm not expecting
+
+ align:start position:0%
+it's really cool but I'm not expecting
+ 
+
+ align:start position:0%
+it's really cool but I'm not expecting
+you to be able to reproduce it okay
+
+ align:start position:0%
+you to be able to reproduce it okay
+ 
+
+ align:start position:0%
+you to be able to reproduce it okay
+so just watch okay so again the
+
+ align:start position:0%
+so just watch okay so again the
+ 
+
+ align:start position:0%
+so just watch okay so again the
+Boltzmann equation says that the
+
+ align:start position:0%
+Boltzmann equation says that the
+ 
+
+ align:start position:0%
+Boltzmann equation says that the
+probability of being in two states open
+
+ align:start position:0%
+probability of being in two states open
+ 
+
+ align:start position:0%
+probability of being in two states open
+or closed depends on the energy
+
+ align:start position:0%
+or closed depends on the energy
+ 
+
+ align:start position:0%
+or closed depends on the energy
+difference between them okay so we have
+
+ align:start position:0%
+difference between them okay so we have
+ 
+
+ align:start position:0%
+difference between them okay so we have
+an open state and a closed state and
+
+ align:start position:0%
+an open state and a closed state and
+ 
+
+ align:start position:0%
+an open state and a closed state and
+when the voltage inside the cell is zero
+
+ align:start position:0%
+when the voltage inside the cell is zero
+ 
+
+ align:start position:0%
+when the voltage inside the cell is zero
+when the voltage difference between the
+
+ align:start position:0%
+when the voltage difference between the
+ 
+
+ align:start position:0%
+when the voltage difference between the
+inside and the outside cell of the cell
+
+ align:start position:0%
+inside and the outside cell of the cell
+ 
+
+ align:start position:0%
+inside and the outside cell of the cell
+is zero you know that the sodium channel
+
+ align:start position:0%
+is zero you know that the sodium channel
+ 
+
+ align:start position:0%
+is zero you know that the sodium channel
+likes to be open so what that means is
+
+ align:start position:0%
+likes to be open so what that means is
+ 
+
+ align:start position:0%
+likes to be open so what that means is
+that the open state has a lower energy
+
+ align:start position:0%
+that the open state has a lower energy
+ 
+
+ align:start position:0%
+that the open state has a lower energy
+than the closed state right sodium
+
+ align:start position:0%
+than the closed state right sodium
+ 
+
+ align:start position:0%
+than the closed state right sodium
+channel likes to open when the cell is
+
+ align:start position:0%
+channel likes to open when the cell is
+ 
+
+ align:start position:0%
+channel likes to open when the cell is
+depolarize that means the voltage inside
+
+ align:start position:0%
+depolarize that means the voltage inside
+ 
+
+ align:start position:0%
+depolarize that means the voltage inside
+and outside are close to each other
+
+ align:start position:0%
+and outside are close to each other
+ 
+
+ align:start position:0%
+and outside are close to each other
+right open state has a lower energy than
+
+ align:start position:0%
+right open state has a lower energy than
+ 
+
+ align:start position:0%
+right open state has a lower energy than
+the closed State let's call that energy
+
+ align:start position:0%
+the closed State let's call that energy
+ 
+
+ align:start position:0%
+the closed State let's call that energy
+difference Delta U okay and it's close
+
+ align:start position:0%
+difference Delta U okay and it's close
+ 
+
+ align:start position:0%
+difference Delta U okay and it's close
+to KT because when it's open this cell
+
+ align:start position:0%
+to KT because when it's open this cell
+ 
+
+ align:start position:0%
+to KT because when it's open this cell
+kind of the channel kind of flickers
+
+ align:start position:0%
+kind of the channel kind of flickers
+ 
+
+ align:start position:0%
+kind of the channel kind of flickers
+back and forth between open and closed
+
+ align:start position:0%
+back and forth between open and closed
+ 
+
+ align:start position:0%
+back and forth between open and closed
+that makes sense okay now now let's put
+
+ align:start position:0%
+that makes sense okay now now let's put
+ 
+
+ align:start position:0%
+that makes sense okay now now let's put
+on let's hyperpolarize the inside of our
+
+ align:start position:0%
+on let's hyperpolarize the inside of our
+ 
+
+ align:start position:0%
+on let's hyperpolarize the inside of our
+cells so now the voltage inside is low
+
+ align:start position:0%
+cells so now the voltage inside is low
+ 
+
+ align:start position:0%
+cells so now the voltage inside is low
+there's a voltage gradient an electric
+
+ align:start position:0%
+there's a voltage gradient an electric
+ 
+
+ align:start position:0%
+there's a voltage gradient an electric
+field that that is is trying to push
+
+ align:start position:0%
+field that that is is trying to push
+ 
+
+ align:start position:0%
+field that that is is trying to push
+those charges in now you can see that
+
+ align:start position:0%
+those charges in now you can see that
+ 
+
+ align:start position:0%
+those charges in now you can see that
+those charges here are sitting at a
+
+ align:start position:0%
+those charges here are sitting at a
+ 
+
+ align:start position:0%
+those charges here are sitting at a
+lower voltage so in the close date those
+
+ align:start position:0%
+lower voltage so in the close date those
+ 
+
+ align:start position:0%
+lower voltage so in the close date those
+charges are down here at a lower
+
+ align:start position:0%
+charges are down here at a lower
+ 
+
+ align:start position:0%
+charges are down here at a lower
+potential what does that mean for the
+
+ align:start position:0%
+potential what does that mean for the
+ 
+
+ align:start position:0%
+potential what does that mean for the
+energy of the closed State when the cell
+
+ align:start position:0%
+energy of the closed State when the cell
+ 
+
+ align:start position:0%
+energy of the closed State when the cell
+is hyperpolarized it's lower right the
+
+ align:start position:0%
+is hyperpolarized it's lower right the
+ 
+
+ align:start position:0%
+is hyperpolarized it's lower right the
+energy of the closed State is low
+
+ align:start position:0%
+energy of the closed State is low
+ 
+
+ align:start position:0%
+energy of the closed State is low
+because those charges are
+
+ align:start position:0%
+because those charges are
+ 
+
+ align:start position:0%
+because those charges are
+toward the inside of the cell and then
+
+ align:start position:0%
+toward the inside of the cell and then
+ 
+
+ align:start position:0%
+toward the inside of the cell and then
+and the voltage is low okay now what
+
+ align:start position:0%
+and the voltage is low okay now what
+ 
+
+ align:start position:0%
+and the voltage is low okay now what
+happens if the cell is hyperpolarized
+
+ align:start position:0%
+happens if the cell is hyperpolarized
+ 
+
+ align:start position:0%
+happens if the cell is hyperpolarized
+but it happens to be in the open state
+
+ align:start position:0%
+but it happens to be in the open state
+ 
+
+ align:start position:0%
+but it happens to be in the open state
+you can see those charges are closer
+
+ align:start position:0%
+you can see those charges are closer
+ 
+
+ align:start position:0%
+you can see those charges are closer
+this way so that you can see that the
+
+ align:start position:0%
+this way so that you can see that the
+ 
+
+ align:start position:0%
+this way so that you can see that the
+energy of these these charges are still
+
+ align:start position:0%
+energy of these these charges are still
+ 
+
+ align:start position:0%
+energy of these these charges are still
+sitting in a voltage that's lower than
+
+ align:start position:0%
+sitting in a voltage that's lower than
+ 
+
+ align:start position:0%
+sitting in a voltage that's lower than
+outside so that open state has a
+
+ align:start position:0%
+outside so that open state has a
+ 
+
+ align:start position:0%
+outside so that open state has a
+slightly lower energy but you can see
+
+ align:start position:0%
+slightly lower energy but you can see
+ 
+
+ align:start position:0%
+slightly lower energy but you can see
+that the closed state still has a much
+
+ align:start position:0%
+that the closed state still has a much
+ 
+
+ align:start position:0%
+that the closed state still has a much
+lower energy than the open state okay
+
+ align:start position:0%
+lower energy than the open state okay
+ 
+
+ align:start position:0%
+lower energy than the open state okay
+and we can write down that voltage
+
+ align:start position:0%
+and we can write down that voltage
+ 
+
+ align:start position:0%
+and we can write down that voltage
+difference as a gating charge times this
+
+ align:start position:0%
+difference as a gating charge times this
+ 
+
+ align:start position:0%
+difference as a gating charge times this
+voltage prints okay so now let's just
+
+ align:start position:0%
+voltage prints okay so now let's just
+ 
+
+ align:start position:0%
+voltage prints okay so now let's just
+take here's it an open state that has an
+
+ align:start position:0%
+take here's it an open state that has an
+ 
+
+ align:start position:0%
+take here's it an open state that has an
+energy difference of a little a little
+
+ align:start position:0%
+energy difference of a little a little
+ 
+
+ align:start position:0%
+energy difference of a little a little
+amount W open state is lower than close
+
+ align:start position:0%
+amount W open state is lower than close
+ 
+
+ align:start position:0%
+amount W open state is lower than close
+by an amount W when the voltage inside
+
+ align:start position:0%
+by an amount W when the voltage inside
+ 
+
+ align:start position:0%
+by an amount W when the voltage inside
+the cell is low we've decreased the
+
+ align:start position:0%
+the cell is low we've decreased the
+ 
+
+ align:start position:0%
+the cell is low we've decreased the
+energy of the closed state by this
+
+ align:start position:0%
+energy of the closed state by this
+ 
+
+ align:start position:0%
+energy of the closed state by this
+amount gating charge times membrane
+
+ align:start position:0%
+amount gating charge times membrane
+ 
+
+ align:start position:0%
+amount gating charge times membrane
+potential okay and now we have an energy
+
+ align:start position:0%
+potential okay and now we have an energy
+ 
+
+ align:start position:0%
+potential okay and now we have an energy
+difference in the open State and the
+
+ align:start position:0%
+difference in the open State and the
+ 
+
+ align:start position:0%
+difference in the open State and the
+close the energy difference between the
+
+ align:start position:0%
+close the energy difference between the
+ 
+
+ align:start position:0%
+close the energy difference between the
+open state and closed state as a
+
+ align:start position:0%
+open state and closed state as a
+ 
+
+ align:start position:0%
+open state and closed state as a
+function of voltage yes we have a simple
+
+ align:start position:0%
+function of voltage yes we have a simple
+ 
+
+ align:start position:0%
+function of voltage yes we have a simple
+equation that describes the energy
+
+ align:start position:0%
+equation that describes the energy
+ 
+
+ align:start position:0%
+equation that describes the energy
+difference between the open and closed
+
+ align:start position:0%
+difference between the open and closed
+ 
+
+ align:start position:0%
+difference between the open and closed
+State as a function of the membrane
+
+ align:start position:0%
+State as a function of the membrane
+ 
+
+ align:start position:0%
+State as a function of the membrane
+potential and now we can just plug that
+
+ align:start position:0%
+potential and now we can just plug that
+ 
+
+ align:start position:0%
+potential and now we can just plug that
+into the Boltzmann equation and derive
+
+ align:start position:0%
+into the Boltzmann equation and derive
+ 
+
+ align:start position:0%
+into the Boltzmann equation and derive
+the probability of being open and closed
+
+ align:start position:0%
+the probability of being open and closed
+ 
+
+ align:start position:0%
+the probability of being open and closed
+okay so we just plug that Delta u into
+
+ align:start position:0%
+okay so we just plug that Delta u into
+ 
+
+ align:start position:0%
+okay so we just plug that Delta u into
+here w- gating charge times voltage now
+
+ align:start position:0%
+here w- gating charge times voltage now
+ 
+
+ align:start position:0%
+here w- gating charge times voltage now
+let's calculate the probability of being
+
+ align:start position:0%
+let's calculate the probability of being
+ 
+
+ align:start position:0%
+let's calculate the probability of being
+open this gives us the ratio of open to
+
+ align:start position:0%
+open this gives us the ratio of open to
+ 
+
+ align:start position:0%
+open this gives us the ratio of open to
+closed how do we calculate the
+
+ align:start position:0%
+closed how do we calculate the
+ 
+
+ align:start position:0%
+closed how do we calculate the
+probability of being open well n is the
+
+ align:start position:0%
+probability of being open well n is the
+ 
+
+ align:start position:0%
+probability of being open well n is the
+probability of being open that's just
+
+ align:start position:0%
+probability of being open that's just
+ 
+
+ align:start position:0%
+probability of being open that's just
+probably open / open + closed
+
+ align:start position:0%
+probably open / open + closed
+ 
+
+ align:start position:0%
+probably open / open + closed
+what's probability of being open +
+
+ align:start position:0%
+what's probability of being open +
+ 
+
+ align:start position:0%
+what's probability of being open +
+probability being closed well if it's it
+
+ align:start position:0%
+probability being closed well if it's it
+ 
+
+ align:start position:0%
+probability being closed well if it's it
+if it's in one or the other then the sum
+
+ align:start position:0%
+if it's in one or the other then the sum
+ 
+
+ align:start position:0%
+if it's in one or the other then the sum
+of those has to be one okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now divide both side top and bottom
+
+ align:start position:0%
+and now divide both side top and bottom
+ 
+
+ align:start position:0%
+and now divide both side top and bottom
+by P not the probability of being open
+
+ align:start position:0%
+by P not the probability of being open
+ 
+
+ align:start position:0%
+by P not the probability of being open
+is just 1 over 1 plus P closed over P
+
+ align:start position:0%
+is just 1 over 1 plus P closed over P
+ 
+
+ align:start position:0%
+is just 1 over 1 plus P closed over P
+open which is just the inverse of this
+
+ align:start position:0%
+open which is just the inverse of this
+ 
+
+ align:start position:0%
+open which is just the inverse of this
+and that's equal to that okay all right
+
+ align:start position:0%
+and that's equal to that okay all right
+ 
+
+ align:start position:0%
+and that's equal to that okay all right
+that may have gone by a little bit too
+
+ align:start position:0%
+that may have gone by a little bit too
+ 
+
+ align:start position:0%
+that may have gone by a little bit too
+fast and I wasn't very smooth on that
+
+ align:start position:0%
+fast and I wasn't very smooth on that
+ 
+
+ align:start position:0%
+fast and I wasn't very smooth on that
+you can see the idea right it's about
+
+ align:start position:0%
+you can see the idea right it's about
+ 
+
+ align:start position:0%
+you can see the idea right it's about
+estimating it's estimating how the
+
+ align:start position:0%
+estimating it's estimating how the
+ 
+
+ align:start position:0%
+estimating it's estimating how the
+energy difference between the open and
+
+ align:start position:0%
+energy difference between the open and
+ 
+
+ align:start position:0%
+energy difference between the open and
+closed state depends on the voltage of
+
+ align:start position:0%
+closed state depends on the voltage of
+ 
+
+ align:start position:0%
+closed state depends on the voltage of
+the cell and it's just an energy
+
+ align:start position:0%
+the cell and it's just an energy
+ 
+
+ align:start position:0%
+the cell and it's just an energy
+difference so it has to be a charge
+
+ align:start position:0%
+difference so it has to be a charge
+ 
+
+ align:start position:0%
+difference so it has to be a charge
+times a voltage yeah and that's right
+
+ align:start position:0%
+times a voltage yeah and that's right
+ 
+
+ align:start position:0%
+times a voltage yeah and that's right
+charge times a voltage and now we're
+
+ align:start position:0%
+charge times a voltage and now we're
+ 
+
+ align:start position:0%
+charge times a voltage and now we're
+just doing a little bit of algebra to
+
+ align:start position:0%
+just doing a little bit of algebra to
+ 
+
+ align:start position:0%
+just doing a little bit of algebra to
+extract probability of open from open
+
+ align:start position:0%
+extract probability of open from open
+ 
+
+ align:start position:0%
+extract probability of open from open
+divided by closed okay and and now if we
+
+ align:start position:0%
+divided by closed okay and and now if we
+ 
+
+ align:start position:0%
+divided by closed okay and and now if we
+just plug that into there we get this
+
+ align:start position:0%
+just plug that into there we get this
+ 
+
+ align:start position:0%
+just plug that into there we get this
+alright so now let's see how that
+
+ align:start position:0%
+alright so now let's see how that
+ 
+
+ align:start position:0%
+alright so now let's see how that
+compares to the actual answer
+
+ align:start position:0%
+compares to the actual answer
+ 
+
+ align:start position:0%
+compares to the actual answer
+probability of open it's just 1 over e 1
+
+ align:start position:0%
+probability of open it's just 1 over e 1
+ 
+
+ align:start position:0%
+probability of open it's just 1 over e 1
+1 over 1 plus this exponential here's
+
+ align:start position:0%
+1 over 1 plus this exponential here's
+ 
+
+ align:start position:0%
+1 over 1 plus this exponential here's
+what that data looked like remember that
+
+ align:start position:0%
+what that data looked like remember that
+ 
+
+ align:start position:0%
+what that data looked like remember that
+was the data for the open product for
+
+ align:start position:0%
+was the data for the open product for
+ 
+
+ align:start position:0%
+was the data for the open product for
+the conductance as a function of voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's a fit to a functional form that
+
+ align:start position:0%
+here's a fit to a functional form that
+ 
+
+ align:start position:0%
+here's a fit to a functional form that
+looks like that and here is the
+
+ align:start position:0%
+looks like that and here is the
+ 
+
+ align:start position:0%
+looks like that and here is the
+prediction from Boltzmann ok you can see
+
+ align:start position:0%
+prediction from Boltzmann ok you can see
+ 
+
+ align:start position:0%
+prediction from Boltzmann ok you can see
+that it almost exactly fits and you can
+
+ align:start position:0%
+that it almost exactly fits and you can
+ 
+
+ align:start position:0%
+that it almost exactly fits and you can
+actually extract biophysically what the
+
+ align:start position:0%
+actually extract biophysically what the
+ 
+
+ align:start position:0%
+actually extract biophysically what the
+gating charges inside this tiny little
+
+ align:start position:0%
+gating charges inside this tiny little
+ 
+
+ align:start position:0%
+gating charges inside this tiny little
+protein simply by looking by fitting
+
+ align:start position:0%
+protein simply by looking by fitting
+ 
+
+ align:start position:0%
+protein simply by looking by fitting
+this to the data okay pretty cool right
+
+ align:start position:0%
+this to the data okay pretty cool right
+ 
+
+ align:start position:0%
+this to the data okay pretty cool right
+yes W is it's the energy difference
+
+ align:start position:0%
+yes W is it's the energy difference
+ 
+
+ align:start position:0%
+yes W is it's the energy difference
+between the open and closed state when
+
+ align:start position:0%
+between the open and closed state when
+ 
+
+ align:start position:0%
+between the open and closed state when
+the voltage is 0 so you kind of have to
+
+ align:start position:0%
+the voltage is 0 so you kind of have to
+ 
+
+ align:start position:0%
+the voltage is 0 so you kind of have to
+fit that too okay it's it's
+
+ align:start position:0%
+fit that too okay it's it's
+ 
+
+ align:start position:0%
+fit that too okay it's it's
+voltage is zero it's the it's the energy
+
+ align:start position:0%
+voltage is zero it's the it's the energy
+ 
+
+ align:start position:0%
+voltage is zero it's the it's the energy
+difference between the open and closed
+
+ align:start position:0%
+difference between the open and closed
+ 
+
+ align:start position:0%
+difference between the open and closed
+state when the voltage is zero okay and
+
+ align:start position:0%
+state when the voltage is zero okay and
+ 
+
+ align:start position:0%
+state when the voltage is zero okay and
+then you subtract from that the energy
+
+ align:start position:0%
+then you subtract from that the energy
+ 
+
+ align:start position:0%
+then you subtract from that the energy
+of the gating charge as a function of
+
+ align:start position:0%
+of the gating charge as a function of
+ 
+
+ align:start position:0%
+of the gating charge as a function of
+voltage inside the cell okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes each has the sensor and they all
+
+ align:start position:0%
+yes yes each has the sensor and they all
+ 
+
+ align:start position:0%
+yes yes each has the sensor and they all
+have to be open for the ion channel to
+
+ align:start position:0%
+have to be open for the ion channel to
+ 
+
+ align:start position:0%
+have to be open for the ion channel to
+be open yes nope because this is the
+
+ align:start position:0%
+be open yes nope because this is the
+ 
+
+ align:start position:0%
+be open yes nope because this is the
+problem that one subunit is open yeah
+
+ align:start position:0%
+problem that one subunit is open yeah
+ 
+
+ align:start position:0%
+problem that one subunit is open yeah
+but that's a good point if you want to
+
+ align:start position:0%
+but that's a good point if you want to
+ 
+
+ align:start position:0%
+but that's a good point if you want to
+compare that to the okay so you're right
+
+ align:start position:0%
+compare that to the okay so you're right
+ 
+
+ align:start position:0%
+compare that to the okay so you're right
+if you want to compared it that to the
+
+ align:start position:0%
+if you want to compared it that to the
+ 
+
+ align:start position:0%
+if you want to compared it that to the
+conductance of the whole channel then it
+
+ align:start position:0%
+conductance of the whole channel then it
+ 
+
+ align:start position:0%
+conductance of the whole channel then it
+has to be raised to the power of four
+
+ align:start position:0%
+has to be raised to the power of four
+ 
+
+ align:start position:0%
+has to be raised to the power of four
+and that's been accounted for here good
+
+ align:start position:0%
+and that's been accounted for here good
+ 
+
+ align:start position:0%
+and that's been accounted for here good
+good question any other questions
+
+ align:start position:0%
+good question any other questions
+ 
+
+ align:start position:0%
+good question any other questions
+Boltzmann equation is pretty cool if you
+
+ align:start position:0%
+Boltzmann equation is pretty cool if you
+ 
+
+ align:start position:0%
+Boltzmann equation is pretty cool if you
+if you know the the mass of a nitrogen
+
+ align:start position:0%
+if you know the the mass of a nitrogen
+ 
+
+ align:start position:0%
+if you know the the mass of a nitrogen
+molecule and acceleration due to gravity
+
+ align:start position:0%
+molecule and acceleration due to gravity
+ 
+
+ align:start position:0%
+molecule and acceleration due to gravity
+what can you calculate with the
+
+ align:start position:0%
+what can you calculate with the
+ 
+
+ align:start position:0%
+what can you calculate with the
+Boltzmann equation any idea the mass of
+
+ align:start position:0%
+Boltzmann equation any idea the mass of
+ 
+
+ align:start position:0%
+Boltzmann equation any idea the mass of
+a nitrogen molecule and the acceleration
+
+ align:start position:0%
+a nitrogen molecule and the acceleration
+ 
+
+ align:start position:0%
+a nitrogen molecule and the acceleration
+due to gravity close you can calculate
+
+ align:start position:0%
+due to gravity close you can calculate
+ 
+
+ align:start position:0%
+due to gravity close you can calculate
+the height of the atmosphere you do all
+
+ align:start position:0%
+the height of the atmosphere you do all
+ 
+
+ align:start position:0%
+the height of the atmosphere you do all
+kinds of really cool stuff with the
+
+ align:start position:0%
+kinds of really cool stuff with the
+ 
+
+ align:start position:0%
+kinds of really cool stuff with the
+Boltzmann equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there was another question here no
+
+ align:start position:0%
+okay there was another question here no
+ 
+
+ align:start position:0%
+okay there was another question here no
+okay okay so you can extract actually
+
+ align:start position:0%
+okay okay so you can extract actually
+ 
+
+ align:start position:0%
+okay okay so you can extract actually
+these quantities the gating charge and
+
+ align:start position:0%
+these quantities the gating charge and
+ 
+
+ align:start position:0%
+these quantities the gating charge and
+this energy difference in the zero
+
+ align:start position:0%
+this energy difference in the zero
+ 
+
+ align:start position:0%
+this energy difference in the zero
+voltage state okay so and the fit is
+
+ align:start position:0%
+voltage state okay so and the fit is
+ 
+
+ align:start position:0%
+voltage state okay so and the fit is
+very good okay so that's voltage
+
+ align:start position:0%
+very good okay so that's voltage
+ 
+
+ align:start position:0%
+very good okay so that's voltage
+dependence I highlighted these slides
+
+ align:start position:0%
+dependence I highlighted these slides
+ 
+
+ align:start position:0%
+dependence I highlighted these slides
+that I don't expect you to be able to
+
+ align:start position:0%
+that I don't expect you to be able to
+ 
+
+ align:start position:0%
+that I don't expect you to be able to
+you know to reproduce in blue okay so
+
+ align:start position:0%
+you know to reproduce in blue okay so
+ 
+
+ align:start position:0%
+you know to reproduce in blue okay so
+you can just make it more clear what you
+
+ align:start position:0%
+you can just make it more clear what you
+ 
+
+ align:start position:0%
+you can just make it more clear what you
+know for your review what you have to
+
+ align:start position:0%
+know for your review what you have to
+ 
+
+ align:start position:0%
+know for your review what you have to
+focus on okay let's look at the time
+
+ align:start position:0%
+focus on okay let's look at the time
+ 
+
+ align:start position:0%
+focus on okay let's look at the time
+dependence the time dependence is pretty
+
+ align:start position:0%
+dependence the time dependence is pretty
+ 
+
+ align:start position:0%
+dependence the time dependence is pretty
+simple it's going to just involve a
+
+ align:start position:0%
+simple it's going to just involve a
+ 
+
+ align:start position:0%
+simple it's going to just involve a
+linear first order differential equation
+
+ align:start position:0%
+linear first order differential equation
+ 
+
+ align:start position:0%
+linear first order differential equation
+you guys are all like super experts on
+
+ align:start position:0%
+you guys are all like super experts on
+ 
+
+ align:start position:0%
+you guys are all like super experts on
+that now right okay so we have an ion
+
+ align:start position:0%
+that now right okay so we have an ion
+ 
+
+ align:start position:0%
+that now right okay so we have an ion
+channel sorry a subunit that's either
+
+ align:start position:0%
+channel sorry a subunit that's either
+ 
+
+ align:start position:0%
+channel sorry a subunit that's either
+open or closed right we have an open
+
+ align:start position:0%
+open or closed right we have an open
+ 
+
+ align:start position:0%
+open or closed right we have an open
+state closed state what we're gonna do
+
+ align:start position:0%
+state closed state what we're gonna do
+ 
+
+ align:start position:0%
+state closed state what we're gonna do
+is so the way to think about this is the
+
+ align:start position:0%
+is so the way to think about this is the
+ 
+
+ align:start position:0%
+is so the way to think about this is the
+ion channel the subunit if the cell is
+
+ align:start position:0%
+ion channel the subunit if the cell is
+ 
+
+ align:start position:0%
+ion channel the subunit if the cell is
+hyperpolarized is sitting in the closed
+
+ align:start position:0%
+hyperpolarized is sitting in the closed
+ 
+
+ align:start position:0%
+hyperpolarized is sitting in the closed
+State right when you depolarize the
+
+ align:start position:0%
+State right when you depolarize the
+ 
+
+ align:start position:0%
+State right when you depolarize the
+neuron that changes the energy levels so
+
+ align:start position:0%
+neuron that changes the energy levels so
+ 
+
+ align:start position:0%
+neuron that changes the energy levels so
+which way wasn't I forget okay the
+
+ align:start position:0%
+which way wasn't I forget okay the
+ 
+
+ align:start position:0%
+which way wasn't I forget okay the
+closed state has a lower energy now when
+
+ align:start position:0%
+closed state has a lower energy now when
+ 
+
+ align:start position:0%
+closed state has a lower energy now when
+you depolarize the cell the closed State
+
+ align:start position:0%
+you depolarize the cell the closed State
+ 
+
+ align:start position:0%
+you depolarize the cell the closed State
+suddenly has a much higher energy and as
+
+ align:start position:0%
+suddenly has a much higher energy and as
+ 
+
+ align:start position:0%
+suddenly has a much higher energy and as
+close as close to the open state and so
+
+ align:start position:0%
+close as close to the open state and so
+ 
+
+ align:start position:0%
+close as close to the open state and so
+at some point subunit will jump over to
+
+ align:start position:0%
+at some point subunit will jump over to
+ 
+
+ align:start position:0%
+at some point subunit will jump over to
+the open state right but that takes time
+
+ align:start position:0%
+the open state right but that takes time
+ 
+
+ align:start position:0%
+the open state right but that takes time
+you change the energy levels but it
+
+ align:start position:0%
+you change the energy levels but it
+ 
+
+ align:start position:0%
+you change the energy levels but it
+takes time for the system to jump into
+
+ align:start position:0%
+takes time for the system to jump into
+ 
+
+ align:start position:0%
+takes time for the system to jump into
+the open state why is that because that
+
+ align:start position:0%
+the open state why is that because that
+ 
+
+ align:start position:0%
+the open state why is that because that
+transition is caused by thermal
+
+ align:start position:0%
+transition is caused by thermal
+ 
+
+ align:start position:0%
+transition is caused by thermal
+fluctuations okay
+
+ align:start position:0%
+fluctuations okay
+ 
+
+ align:start position:0%
+fluctuations okay
+so you have to wait for one of those
+
+ align:start position:0%
+so you have to wait for one of those
+ 
+
+ align:start position:0%
+so you have to wait for one of those
+fluctuations to kick you over into the
+
+ align:start position:0%
+fluctuations to kick you over into the
+ 
+
+ align:start position:0%
+fluctuations to kick you over into the
+open state okay so we're going to model
+
+ align:start position:0%
+open state okay so we're going to model
+ 
+
+ align:start position:0%
+open state okay so we're going to model
+those transitions between open and
+
+ align:start position:0%
+those transitions between open and
+ 
+
+ align:start position:0%
+those transitions between open and
+closed States with a simple rate
+
+ align:start position:0%
+closed States with a simple rate
+ 
+
+ align:start position:0%
+closed States with a simple rate
+equation that's voltage dependent we
+
+ align:start position:0%
+equation that's voltage dependent we
+ 
+
+ align:start position:0%
+equation that's voltage dependent we
+have an open state and we imagine that n
+
+ align:start position:0%
+have an open state and we imagine that n
+ 
+
+ align:start position:0%
+have an open state and we imagine that n
+is the probability of being in the open
+
+ align:start position:0%
+is the probability of being in the open
+ 
+
+ align:start position:0%
+is the probability of being in the open
+state and and we can equivalently think
+
+ align:start position:0%
+state and and we can equivalently think
+ 
+
+ align:start position:0%
+state and and we can equivalently think
+of it is if we have a population of
+
+ align:start position:0%
+of it is if we have a population of
+ 
+
+ align:start position:0%
+of it is if we have a population of
+subunits and let's think of it as more
+
+ align:start position:0%
+subunits and let's think of it as more
+ 
+
+ align:start position:0%
+subunits and let's think of it as more
+as the fraction it's it's also
+
+ align:start position:0%
+as the fraction it's it's also
+ 
+
+ align:start position:0%
+as the fraction it's it's also
+equivalent to the just whichever way you
+
+ align:start position:0%
+equivalent to the just whichever way you
+ 
+
+ align:start position:0%
+equivalent to the just whichever way you
+want to think about it either works well
+
+ align:start position:0%
+want to think about it either works well
+ 
+
+ align:start position:0%
+want to think about it either works well
+but you can also think of it as the
+
+ align:start position:0%
+but you can also think of it as the
+ 
+
+ align:start position:0%
+but you can also think of it as the
+probability of being in the open state
+
+ align:start position:0%
+probability of being in the open state
+ 
+
+ align:start position:0%
+probability of being in the open state
+or the number of subunits that are in
+
+ align:start position:0%
+or the number of subunits that are in
+ 
+
+ align:start position:0%
+or the number of subunits that are in
+the open state you know population okay
+
+ align:start position:0%
+the open state you know population okay
+ 
+
+ align:start position:0%
+the open state you know population okay
+you also have a closed state so if n is
+
+ align:start position:0%
+you also have a closed state so if n is
+ 
+
+ align:start position:0%
+you also have a closed state so if n is
+the probability of being in the open
+
+ align:start position:0%
+the probability of being in the open
+ 
+
+ align:start position:0%
+the probability of being in the open
+state of a closed state with probability
+
+ align:start position:0%
+state of a closed state with probability
+ 
+
+ align:start position:0%
+state of a closed state with probability
+1 minus n right if you're in the closed
+
+ align:start position:0%
+1 minus n right if you're in the closed
+ 
+
+ align:start position:0%
+1 minus n right if you're in the closed
+state you have some transition rate
+
+ align:start position:0%
+state you have some transition rate
+ 
+
+ align:start position:0%
+state you have some transition rate
+probability per unit time of going from
+
+ align:start position:0%
+probability per unit time of going from
+ 
+
+ align:start position:0%
+probability per unit time of going from
+the closed state to the open state and
+
+ align:start position:0%
+the closed state to the open state and
+ 
+
+ align:start position:0%
+the closed state to the open state and
+if you're in the open state you have
+
+ align:start position:0%
+if you're in the open state you have
+ 
+
+ align:start position:0%
+if you're in the open state you have
+some probability per unit time beta of
+
+ align:start position:0%
+some probability per unit time beta of
+ 
+
+ align:start position:0%
+some probability per unit time beta of
+going into the closed state okay so
+
+ align:start position:0%
+going into the closed state okay so
+ 
+
+ align:start position:0%
+going into the closed state okay so
+those things have units of per second
+
+ align:start position:0%
+those things have units of per second
+ 
+
+ align:start position:0%
+those things have units of per second
+probability per second yes Rebecca right
+
+ align:start position:0%
+probability per second yes Rebecca right
+ 
+
+ align:start position:0%
+probability per second yes Rebecca right
+yeah just warmth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these things are voltage dependent
+
+ align:start position:0%
+and these things are voltage dependent
+ 
+
+ align:start position:0%
+and these things are voltage dependent
+remember those depend on the energy
+
+ align:start position:0%
+remember those depend on the energy
+ 
+
+ align:start position:0%
+remember those depend on the energy
+difference between that open and closed
+
+ align:start position:0%
+difference between that open and closed
+ 
+
+ align:start position:0%
+difference between that open and closed
+state okay all right
+
+ align:start position:0%
+state okay all right
+ 
+
+ align:start position:0%
+state okay all right
+let's develop our first-order linear
+
+ align:start position:0%
+let's develop our first-order linear
+ 
+
+ align:start position:0%
+let's develop our first-order linear
+equation it's gonna be very simple we
+
+ align:start position:0%
+equation it's gonna be very simple we
+ 
+
+ align:start position:0%
+equation it's gonna be very simple we
+have a closed state an open state the
+
+ align:start position:0%
+have a closed state an open state the
+ 
+
+ align:start position:0%
+have a closed state an open state the
+change in the number of open states is
+
+ align:start position:0%
+change in the number of open states is
+ 
+
+ align:start position:0%
+change in the number of open states is
+just going to be the number of closed
+
+ align:start position:0%
+just going to be the number of closed
+ 
+
+ align:start position:0%
+just going to be the number of closed
+States the number of closed sub units
+
+ align:start position:0%
+States the number of closed sub units
+ 
+
+ align:start position:0%
+States the number of closed sub units
+that open minus the number of open
+
+ align:start position:0%
+that open minus the number of open
+ 
+
+ align:start position:0%
+that open minus the number of open
+subunits that closed that makes sense
+
+ align:start position:0%
+subunits that closed that makes sense
+ 
+
+ align:start position:0%
+subunits that closed that makes sense
+all right that's simple enough the
+
+ align:start position:0%
+all right that's simple enough the
+ 
+
+ align:start position:0%
+all right that's simple enough the
+change in the number of open sub units
+
+ align:start position:0%
+change in the number of open sub units
+ 
+
+ align:start position:0%
+change in the number of open sub units
+per unit time is going to be the number
+
+ align:start position:0%
+per unit time is going to be the number
+ 
+
+ align:start position:0%
+per unit time is going to be the number
+of closed
+
+ align:start position:0%
+of closed
+ 
+
+ align:start position:0%
+of closed
+sub units that there are times the
+
+ align:start position:0%
+sub units that there are times the
+ 
+
+ align:start position:0%
+sub units that there are times the
+probability that a closed sub unit opens
+
+ align:start position:0%
+probability that a closed sub unit opens
+ 
+
+ align:start position:0%
+probability that a closed sub unit opens
+per unit time that's alpha minus
+
+ align:start position:0%
+per unit time that's alpha minus
+ 
+
+ align:start position:0%
+per unit time that's alpha minus
+remember the number of closed sub units
+
+ align:start position:0%
+remember the number of closed sub units
+ 
+
+ align:start position:0%
+remember the number of closed sub units
+that open is the number of closed sub
+
+ align:start position:0%
+that open is the number of closed sub
+ 
+
+ align:start position:0%
+that open is the number of closed sub
+units times the probability of per unit
+
+ align:start position:0%
+units times the probability of per unit
+ 
+
+ align:start position:0%
+units times the probability of per unit
+time that are closed sub unit opens all
+
+ align:start position:0%
+time that are closed sub unit opens all
+ 
+
+ align:start position:0%
+time that are closed sub unit opens all
+right and the number of open sub units
+
+ align:start position:0%
+right and the number of open sub units
+ 
+
+ align:start position:0%
+right and the number of open sub units
+that closed is just the number of open
+
+ align:start position:0%
+that closed is just the number of open
+ 
+
+ align:start position:0%
+that closed is just the number of open
+sub units times the probability that any
+
+ align:start position:0%
+sub units times the probability that any
+ 
+
+ align:start position:0%
+sub units times the probability that any
+one of them closes per unit time that
+
+ align:start position:0%
+one of them closes per unit time that
+ 
+
+ align:start position:0%
+one of them closes per unit time that
+makes sense okay a lot of words but the
+
+ align:start position:0%
+makes sense okay a lot of words but the
+ 
+
+ align:start position:0%
+makes sense okay a lot of words but the
+equation ends up being very simple the
+
+ align:start position:0%
+equation ends up being very simple the
+ 
+
+ align:start position:0%
+equation ends up being very simple the
+change per unit time of n is just the
+
+ align:start position:0%
+change per unit time of n is just the
+ 
+
+ align:start position:0%
+change per unit time of n is just the
+number of closed sub units 1 times the
+
+ align:start position:0%
+number of closed sub units 1 times the
+ 
+
+ align:start position:0%
+number of closed sub units 1 times the
+probability that those open per unit
+
+ align:start position:0%
+probability that those open per unit
+ 
+
+ align:start position:0%
+probability that those open per unit
+time alpha minus beta times n okay
+
+ align:start position:0%
+time alpha minus beta times n okay
+ 
+
+ align:start position:0%
+time alpha minus beta times n okay
+alpha times 1 minus n minus beta times n
+
+ align:start position:0%
+alpha times 1 minus n minus beta times n
+ 
+
+ align:start position:0%
+alpha times 1 minus n minus beta times n
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions about that alpha beta are
+
+ align:start position:0%
+any questions about that alpha beta are
+ 
+
+ align:start position:0%
+any questions about that alpha beta are
+voltage-dependent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I've rewritten that equation and
+
+ align:start position:0%
+okay so I've rewritten that equation and
+ 
+
+ align:start position:0%
+okay so I've rewritten that equation and
+it's the probability that a subunit is
+
+ align:start position:0%
+it's the probability that a subunit is
+ 
+
+ align:start position:0%
+it's the probability that a subunit is
+open okay let's just rewrite this let's
+
+ align:start position:0%
+open okay let's just rewrite this let's
+ 
+
+ align:start position:0%
+open okay let's just rewrite this let's
+expand this alpha minus alpha times M my
+
+ align:start position:0%
+expand this alpha minus alpha times M my
+ 
+
+ align:start position:0%
+expand this alpha minus alpha times M my
+beta times n factor out the end so you
+
+ align:start position:0%
+beta times n factor out the end so you
+ 
+
+ align:start position:0%
+beta times n factor out the end so you
+have DN DT equals alpha minus alpha plus
+
+ align:start position:0%
+have DN DT equals alpha minus alpha plus
+ 
+
+ align:start position:0%
+have DN DT equals alpha minus alpha plus
+beta times n divide both sides by 1 over
+
+ align:start position:0%
+beta times n divide both sides by 1 over
+ 
+
+ align:start position:0%
+beta times n divide both sides by 1 over
+alpha plus beta
+
+ align:start position:0%
+alpha plus beta
+ 
+
+ align:start position:0%
+alpha plus beta
+what's the steady state of this steady
+
+ align:start position:0%
+what's the steady state of this steady
+ 
+
+ align:start position:0%
+what's the steady state of this steady
+state solution of this equation that is
+
+ align:start position:0%
+state solution of this equation that is
+ 
+
+ align:start position:0%
+state solution of this equation that is
+the steady state solution right da if
+
+ align:start position:0%
+the steady state solution right da if
+ 
+
+ align:start position:0%
+the steady state solution right da if
+you set the nd T equal to zero that n is
+
+ align:start position:0%
+you set the nd T equal to zero that n is
+ 
+
+ align:start position:0%
+you set the nd T equal to zero that n is
+equal to that just an infinity and
+
+ align:start position:0%
+equal to that just an infinity and
+ 
+
+ align:start position:0%
+equal to that just an infinity and
+what's that alpha and beta have units of
+
+ align:start position:0%
+what's that alpha and beta have units of
+ 
+
+ align:start position:0%
+what's that alpha and beta have units of
+per unit time so what is 1 what units do
+
+ align:start position:0%
+per unit time so what is 1 what units do
+ 
+
+ align:start position:0%
+per unit time so what is 1 what units do
+1 over alpha plus beta have time so what
+
+ align:start position:0%
+1 over alpha plus beta have time so what
+ 
+
+ align:start position:0%
+1 over alpha plus beta have time so what
+might that be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tau it's a time constant okay so after
+
+ align:start position:0%
+tau it's a time constant okay so after
+ 
+
+ align:start position:0%
+tau it's a time constant okay so after
+all of this what we end up with is an
+
+ align:start position:0%
+all of this what we end up with is an
+ 
+
+ align:start position:0%
+all of this what we end up with is an
+equation that looks exactly like what we
+
+ align:start position:0%
+equation that looks exactly like what we
+ 
+
+ align:start position:0%
+equation that looks exactly like what we
+had for we have a first-order linear
+
+ align:start position:0%
+had for we have a first-order linear
+ 
+
+ align:start position:0%
+had for we have a first-order linear
+differential equation actly the same
+
+ align:start position:0%
+differential equation actly the same
+ 
+
+ align:start position:0%
+differential equation actly the same
+form as the equation we used to
+
+ align:start position:0%
+form as the equation we used to
+ 
+
+ align:start position:0%
+form as the equation we used to
+understand the way the voltage changes
+
+ align:start position:0%
+understand the way the voltage changes
+ 
+
+ align:start position:0%
+understand the way the voltage changes
+in a cell in response to current
+
+ align:start position:0%
+in a cell in response to current
+ 
+
+ align:start position:0%
+in a cell in response to current
+injection okay so if we change and
+
+ align:start position:0%
+injection okay so if we change and
+ 
+
+ align:start position:0%
+injection okay so if we change and
+infinity what is this thing going to do
+
+ align:start position:0%
+infinity what is this thing going to do
+ 
+
+ align:start position:0%
+infinity what is this thing going to do
+it's going to what is n going to do it's
+
+ align:start position:0%
+it's going to what is n going to do it's
+ 
+
+ align:start position:0%
+it's going to what is n going to do it's
+going to relax exponentially okay with a
+
+ align:start position:0%
+going to relax exponentially okay with a
+ 
+
+ align:start position:0%
+going to relax exponentially okay with a
+time constant tau
+
+ align:start position:0%
+time constant tau
+ 
+
+ align:start position:0%
+time constant tau
+and all of these things the Tao is tau
+
+ align:start position:0%
+and all of these things the Tao is tau
+ 
+
+ align:start position:0%
+and all of these things the Tao is tau
+sub n because it's for the end gating
+
+ align:start position:0%
+sub n because it's for the end gating
+ 
+
+ align:start position:0%
+sub n because it's for the end gating
+variable so that's why this has an end
+
+ align:start position:0%
+variable so that's why this has an end
+ 
+
+ align:start position:0%
+variable so that's why this has an end
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+so an infinity and tau are voltage
+
+ align:start position:0%
+so an infinity and tau are voltage
+ 
+
+ align:start position:0%
+so an infinity and tau are voltage
+dependent because they come from alpha
+
+ align:start position:0%
+dependent because they come from alpha
+ 
+
+ align:start position:0%
+dependent because they come from alpha
+and beta which are voltage dependent
+
+ align:start position:0%
+and beta which are voltage dependent
+ 
+
+ align:start position:0%
+and beta which are voltage dependent
+okay but we actually just derived the
+
+ align:start position:0%
+okay but we actually just derived the
+ 
+
+ align:start position:0%
+okay but we actually just derived the
+steady state voltage dependence of the
+
+ align:start position:0%
+steady state voltage dependence of the
+ 
+
+ align:start position:0%
+steady state voltage dependence of the
+potassium conductance right from the
+
+ align:start position:0%
+potassium conductance right from the
+ 
+
+ align:start position:0%
+potassium conductance right from the
+Boltzmann equation what is n infinity
+
+ align:start position:0%
+Boltzmann equation what is n infinity
+ 
+
+ align:start position:0%
+Boltzmann equation what is n infinity
+for very negative voltages do you
+
+ align:start position:0%
+for very negative voltages do you
+ 
+
+ align:start position:0%
+for very negative voltages do you
+remember just approximately big-small
+
+ align:start position:0%
+remember just approximately big-small
+ 
+
+ align:start position:0%
+remember just approximately big-small
+1/2 what is the steady state what's the
+
+ align:start position:0%
+1/2 what is the steady state what's the
+ 
+
+ align:start position:0%
+1/2 what is the steady state what's the
+probability that a potassium channel is
+
+ align:start position:0%
+probability that a potassium channel is
+ 
+
+ align:start position:0%
+probability that a potassium channel is
+open that a subunit is open at very
+
+ align:start position:0%
+open that a subunit is open at very
+ 
+
+ align:start position:0%
+open that a subunit is open at very
+negative voltages do you remember zero
+
+ align:start position:0%
+negative voltages do you remember zero
+ 
+
+ align:start position:0%
+negative voltages do you remember zero
+it's off for look big voltage and
+
+ align:start position:0%
+it's off for look big voltage and
+ 
+
+ align:start position:0%
+it's off for look big voltage and
+infinity has to be if we think of it as
+
+ align:start position:0%
+infinity has to be if we think of it as
+ 
+
+ align:start position:0%
+infinity has to be if we think of it as
+a probability it's close to 1 so n
+
+ align:start position:0%
+a probability it's close to 1 so n
+ 
+
+ align:start position:0%
+a probability it's close to 1 so n
+infinity goes from zero at negative
+
+ align:start position:0%
+infinity goes from zero at negative
+ 
+
+ align:start position:0%
+infinity goes from zero at negative
+voltages sigmoid activation up to one at
+
+ align:start position:0%
+voltages sigmoid activation up to one at
+ 
+
+ align:start position:0%
+voltages sigmoid activation up to one at
+high voltages ok okay so now let's let's
+
+ align:start position:0%
+high voltages ok okay so now let's let's
+ 
+
+ align:start position:0%
+high voltages ok okay so now let's let's
+look at how n changes as a function of
+
+ align:start position:0%
+look at how n changes as a function of
+ 
+
+ align:start position:0%
+look at how n changes as a function of
+time so here's our our potential we're
+
+ align:start position:0%
+time so here's our our potential we're
+ 
+
+ align:start position:0%
+time so here's our our potential we're
+gonna do a voltage clamp experiment
+
+ align:start position:0%
+gonna do a voltage clamp experiment
+ 
+
+ align:start position:0%
+gonna do a voltage clamp experiment
+we're going to start at minus eighty
+
+ align:start position:0%
+we're going to start at minus eighty
+ 
+
+ align:start position:0%
+we're going to start at minus eighty
+millivolts and step up to zero okay so
+
+ align:start position:0%
+millivolts and step up to zero okay so
+ 
+
+ align:start position:0%
+millivolts and step up to zero okay so
+what is an infinity going to do an
+
+ align:start position:0%
+what is an infinity going to do an
+ 
+
+ align:start position:0%
+what is an infinity going to do an
+infinity is just a function of voltage
+
+ align:start position:0%
+infinity is just a function of voltage
+ 
+
+ align:start position:0%
+infinity is just a function of voltage
+right it's like those energy levels they
+
+ align:start position:0%
+right it's like those energy levels they
+ 
+
+ align:start position:0%
+right it's like those energy levels they
+change immediately so what is an
+
+ align:start position:0%
+change immediately so what is an
+ 
+
+ align:start position:0%
+change immediately so what is an
+infinity going to do good it's gonna
+
+ align:start position:0%
+infinity going to do good it's gonna
+ 
+
+ align:start position:0%
+infinity going to do good it's gonna
+start at close to zero jump up to one
+
+ align:start position:0%
+start at close to zero jump up to one
+ 
+
+ align:start position:0%
+start at close to zero jump up to one
+and then jump back to close to zero
+
+ align:start position:0%
+and then jump back to close to zero
+ 
+
+ align:start position:0%
+and then jump back to close to zero
+immediately following the voltage okay
+
+ align:start position:0%
+immediately following the voltage okay
+ 
+
+ align:start position:0%
+immediately following the voltage okay
+but what is n going to do now let's plot
+
+ align:start position:0%
+but what is n going to do now let's plot
+ 
+
+ align:start position:0%
+but what is n going to do now let's plot
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+and it's going to start at zero when you
+
+ align:start position:0%
+and it's going to start at zero when you
+ 
+
+ align:start position:0%
+and it's going to start at zero when you
+jump the when you step the voltage up
+
+ align:start position:0%
+jump the when you step the voltage up
+ 
+
+ align:start position:0%
+jump the when you step the voltage up
+and infinity will jump up and n will
+
+ align:start position:0%
+and infinity will jump up and n will
+ 
+
+ align:start position:0%
+and infinity will jump up and n will
+relax exponentially to a high end
+
+ align:start position:0%
+relax exponentially to a high end
+ 
+
+ align:start position:0%
+relax exponentially to a high end
+infinity close to one right and then
+
+ align:start position:0%
+infinity close to one right and then
+ 
+
+ align:start position:0%
+infinity close to one right and then
+when we turn back and infinity jumps
+
+ align:start position:0%
+when we turn back and infinity jumps
+ 
+
+ align:start position:0%
+when we turn back and infinity jumps
+back down to zero and n relaxes
+
+ align:start position:0%
+back down to zero and n relaxes
+ 
+
+ align:start position:0%
+back down to zero and n relaxes
+exponentially back yes yes but but for a
+
+ align:start position:0%
+exponentially back yes yes but but for a
+ 
+
+ align:start position:0%
+exponentially back yes yes but but for a
+voltage around zero and infinity is
+
+ align:start position:0%
+voltage around zero and infinity is
+ 
+
+ align:start position:0%
+voltage around zero and infinity is
+going to be close to one okay any any
+
+ align:start position:0%
+going to be close to one okay any any
+ 
+
+ align:start position:0%
+going to be close to one okay any any
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is called activation that's the
+
+ align:start position:0%
+that is called activation that's the
+ 
+
+ align:start position:0%
+that is called activation that's the
+that's the activation now this this
+
+ align:start position:0%
+that's the activation now this this
+ 
+
+ align:start position:0%
+that's the activation now this this
+looks a little funny right this this
+
+ align:start position:0%
+looks a little funny right this this
+ 
+
+ align:start position:0%
+looks a little funny right this this
+thing is turning on immediately it
+
+ align:start position:0%
+thing is turning on immediately it
+ 
+
+ align:start position:0%
+thing is turning on immediately it
+doesn't have that nice sigmoid alape
+
+ align:start position:0%
+doesn't have that nice sigmoid alape
+ 
+
+ align:start position:0%
+doesn't have that nice sigmoid alape
+that the potassium current had right or
+
+ align:start position:0%
+that the potassium current had right or
+ 
+
+ align:start position:0%
+that the potassium current had right or
+the protectants why is that what are we
+
+ align:start position:0%
+the protectants why is that what are we
+ 
+
+ align:start position:0%
+the protectants why is that what are we
+looking at here we're plotting n what is
+
+ align:start position:0%
+looking at here we're plotting n what is
+ 
+
+ align:start position:0%
+looking at here we're plotting n what is
+the potassium conductance or the current
+
+ align:start position:0%
+the potassium conductance or the current
+ 
+
+ align:start position:0%
+the potassium conductance or the current
+how does that relate to n n to the
+
+ align:start position:0%
+how does that relate to n n to the
+ 
+
+ align:start position:0%
+how does that relate to n n to the
+fourth so what do we do to plot the
+
+ align:start position:0%
+fourth so what do we do to plot the
+ 
+
+ align:start position:0%
+fourth so what do we do to plot the
+potassium current or the potassium
+
+ align:start position:0%
+potassium current or the potassium
+ 
+
+ align:start position:0%
+potassium current or the potassium
+conductance we just take this right so
+
+ align:start position:0%
+conductance we just take this right so
+ 
+
+ align:start position:0%
+conductance we just take this right so
+what does that look like this process of
+
+ align:start position:0%
+what does that look like this process of
+ 
+
+ align:start position:0%
+what does that look like this process of
+turning off the gating variable getting
+
+ align:start position:0%
+turning off the gating variable getting
+ 
+
+ align:start position:0%
+turning off the gating variable getting
+bigger is called activation the gating
+
+ align:start position:0%
+bigger is called activation the gating
+ 
+
+ align:start position:0%
+bigger is called activation the gating
+variable getting smaller and getting
+
+ align:start position:0%
+variable getting smaller and getting
+ 
+
+ align:start position:0%
+variable getting smaller and getting
+smaller is called dis activation okay so
+
+ align:start position:0%
+smaller is called dis activation okay so
+ 
+
+ align:start position:0%
+smaller is called dis activation okay so
+now let's plot this to the fourth so
+
+ align:start position:0%
+now let's plot this to the fourth so
+ 
+
+ align:start position:0%
+now let's plot this to the fourth so
+this conductance turns on gradually but
+
+ align:start position:0%
+this conductance turns on gradually but
+ 
+
+ align:start position:0%
+this conductance turns on gradually but
+the conductance is proportional to n to
+
+ align:start position:0%
+the conductance is proportional to n to
+ 
+
+ align:start position:0%
+the conductance is proportional to n to
+the fourth so let's plot that so if we
+
+ align:start position:0%
+the fourth so let's plot that so if we
+ 
+
+ align:start position:0%
+the fourth so let's plot that so if we
+plot N to the fourth you can see that
+
+ align:start position:0%
+plot N to the fourth you can see that
+ 
+
+ align:start position:0%
+plot N to the fourth you can see that
+that that function now turns on smoothly
+
+ align:start position:0%
+that that function now turns on smoothly
+ 
+
+ align:start position:0%
+that that function now turns on smoothly
+in time this is time now right so that
+
+ align:start position:0%
+in time this is time now right so that
+ 
+
+ align:start position:0%
+in time this is time now right so that
+gating variable ends relaxes
+
+ align:start position:0%
+gating variable ends relaxes
+ 
+
+ align:start position:0%
+gating variable ends relaxes
+exponentially but the conductance goes
+
+ align:start position:0%
+exponentially but the conductance goes
+ 
+
+ align:start position:0%
+exponentially but the conductance goes
+as the gating variable to the fourth and
+
+ align:start position:0%
+as the gating variable to the fourth and
+ 
+
+ align:start position:0%
+as the gating variable to the fourth and
+so it has this nice graceful turn on
+
+ align:start position:0%
+so it has this nice graceful turn on
+ 
+
+ align:start position:0%
+so it has this nice graceful turn on
+right because it's the gating
+
+ align:start position:0%
+right because it's the gating
+ 
+
+ align:start position:0%
+right because it's the gating
+exponential to the fourth looks exactly
+
+ align:start position:0%
+exponential to the fourth looks exactly
+ 
+
+ align:start position:0%
+exponential to the fourth looks exactly
+like this okay in fact that's how
+
+ align:start position:0%
+like this okay in fact that's how
+ 
+
+ align:start position:0%
+like this okay in fact that's how
+Hodgkin and Huxley figured out that its
+
+ align:start position:0%
+Hodgkin and Huxley figured out that its
+ 
+
+ align:start position:0%
+Hodgkin and Huxley figured out that its
+end to the four because they knew that
+
+ align:start position:0%
+end to the four because they knew that
+ 
+
+ align:start position:0%
+end to the four because they knew that
+they if they assume that it's a
+
+ align:start position:0%
+they if they assume that it's a
+ 
+
+ align:start position:0%
+they if they assume that it's a
+exponentially decaying gating variable
+
+ align:start position:0%
+exponentially decaying gating variable
+ 
+
+ align:start position:0%
+exponentially decaying gating variable
+that the only way they could fit the
+
+ align:start position:0%
+that the only way they could fit the
+ 
+
+ align:start position:0%
+that the only way they could fit the
+turn on of the conductance was by
+
+ align:start position:0%
+turn on of the conductance was by
+ 
+
+ align:start position:0%
+turn on of the conductance was by
+raising it to the fourth power if they
+
+ align:start position:0%
+raising it to the fourth power if they
+ 
+
+ align:start position:0%
+raising it to the fourth power if they
+raised it to the second power it was
+
+ align:start position:0%
+raised it to the second power it was
+ 
+
+ align:start position:0%
+raised it to the second power it was
+still too sudden if they raised it to
+
+ align:start position:0%
+still too sudden if they raised it to
+ 
+
+ align:start position:0%
+still too sudden if they raised it to
+the third power it was still not quite
+
+ align:start position:0%
+the third power it was still not quite
+ 
+
+ align:start position:0%
+the third power it was still not quite
+right but if they raised it to the fifth
+
+ align:start position:0%
+right but if they raised it to the fifth
+ 
+
+ align:start position:0%
+right but if they raised it to the fifth
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+oops it's too delayed if they were
+
+ align:start position:0%
+oops it's too delayed if they were
+ 
+
+ align:start position:0%
+oops it's too delayed if they were
+horsepower it exactly fits the shape of
+
+ align:start position:0%
+horsepower it exactly fits the shape of
+ 
+
+ align:start position:0%
+horsepower it exactly fits the shape of
+the conductance turning on and so they
+
+ align:start position:0%
+the conductance turning on and so they
+ 
+
+ align:start position:0%
+the conductance turning on and so they
+inferred they didn't know about subunits
+
+ align:start position:0%
+inferred they didn't know about subunits
+ 
+
+ align:start position:0%
+inferred they didn't know about subunits
+they just had a piece of axon you know a
+
+ align:start position:0%
+they just had a piece of axon you know a
+ 
+
+ align:start position:0%
+they just had a piece of axon you know a
+piece of squid line and a table in front
+
+ align:start position:0%
+piece of squid line and a table in front
+ 
+
+ align:start position:0%
+piece of squid line and a table in front
+of them and they figure out that there
+
+ align:start position:0%
+of them and they figure out that there
+ 
+
+ align:start position:0%
+of them and they figure out that there
+were four independent processes that
+
+ align:start position:0%
+were four independent processes that
+ 
+
+ align:start position:0%
+were four independent processes that
+turn on the potassium conductance pretty
+
+ align:start position:0%
+turn on the potassium conductance pretty
+ 
+
+ align:start position:0%
+turn on the potassium conductance pretty
+cool right that's what you get by doing
+
+ align:start position:0%
+cool right that's what you get by doing
+ 
+
+ align:start position:0%
+cool right that's what you get by doing
+things quantitatively so they could the
+
+ align:start position:0%
+things quantitatively so they could the
+ 
+
+ align:start position:0%
+things quantitatively so they could the
+shape of that potassium conductance
+
+ align:start position:0%
+shape of that potassium conductance
+ 
+
+ align:start position:0%
+shape of that potassium conductance
+turning on by this exponential gating
+
+ align:start position:0%
+turning on by this exponential gating
+ 
+
+ align:start position:0%
+turning on by this exponential gating
+variable raised to the fourth power and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from that they were able to infer that
+
+ align:start position:0%
+from that they were able to infer that
+ 
+
+ align:start position:0%
+from that they were able to infer that
+it's for independent first-order
+
+ align:start position:0%
+it's for independent first-order
+ 
+
+ align:start position:0%
+it's for independent first-order
+processes that combine to produce that
+
+ align:start position:0%
+processes that combine to produce that
+ 
+
+ align:start position:0%
+processes that combine to produce that
+activation okay the offset also fits if
+
+ align:start position:0%
+activation okay the offset also fits if
+ 
+
+ align:start position:0%
+activation okay the offset also fits if
+you raise it to the fourth power they
+
+ align:start position:0%
+you raise it to the fourth power they
+ 
+
+ align:start position:0%
+you raise it to the fourth power they
+were able to measure the size of the
+
+ align:start position:0%
+were able to measure the size of the
+ 
+
+ align:start position:0%
+were able to measure the size of the
+potassium conductance to measure an
+
+ align:start position:0%
+potassium conductance to measure an
+ 
+
+ align:start position:0%
+potassium conductance to measure an
+infinity directly so we derived it using
+
+ align:start position:0%
+infinity directly so we derived it using
+ 
+
+ align:start position:0%
+infinity directly so we derived it using
+the Boltzmann equation but they measured
+
+ align:start position:0%
+the Boltzmann equation but they measured
+ 
+
+ align:start position:0%
+the Boltzmann equation but they measured
+it directly just by the size of the
+
+ align:start position:0%
+it directly just by the size of the
+ 
+
+ align:start position:0%
+it directly just by the size of the
+conductance and you can also measure the
+
+ align:start position:0%
+conductance and you can also measure the
+ 
+
+ align:start position:0%
+conductance and you can also measure the
+time course you don't need to worry
+
+ align:start position:0%
+time course you don't need to worry
+ 
+
+ align:start position:0%
+time course you don't need to worry
+about this I'm not expecting you should
+
+ align:start position:0%
+about this I'm not expecting you should
+ 
+
+ align:start position:0%
+about this I'm not expecting you should
+know this I'm just showing you that just
+
+ align:start position:0%
+know this I'm just showing you that just
+ 
+
+ align:start position:0%
+know this I'm just showing you that just
+for fun you don't need to know that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can extract these towels just by
+
+ align:start position:0%
+and you can extract these towels just by
+ 
+
+ align:start position:0%
+and you can extract these towels just by
+measuring this exponential decay at
+
+ align:start position:0%
+measuring this exponential decay at
+ 
+
+ align:start position:0%
+measuring this exponential decay at
+different voltages or measuring these
+
+ align:start position:0%
+different voltages or measuring these
+ 
+
+ align:start position:0%
+different voltages or measuring these
+the inferred first order process you can
+
+ align:start position:0%
+the inferred first order process you can
+ 
+
+ align:start position:0%
+the inferred first order process you can
+infer the time constant of the first
+
+ align:start position:0%
+infer the time constant of the first
+ 
+
+ align:start position:0%
+infer the time constant of the first
+order process so on the onset and the
+
+ align:start position:0%
+order process so on the onset and the
+ 
+
+ align:start position:0%
+order process so on the onset and the
+offset to extract these towels as a
+
+ align:start position:0%
+offset to extract these towels as a
+ 
+
+ align:start position:0%
+offset to extract these towels as a
+function of volt this is tau as a
+
+ align:start position:0%
+function of volt this is tau as a
+ 
+
+ align:start position:0%
+function of volt this is tau as a
+function of voltage okay you can also
+
+ align:start position:0%
+function of voltage okay you can also
+ 
+
+ align:start position:0%
+function of voltage okay you can also
+from these two quantities you can
+
+ align:start position:0%
+from these two quantities you can
+ 
+
+ align:start position:0%
+from these two quantities you can
+actually extract alpha and beta
+
+ align:start position:0%
+actually extract alpha and beta
+ 
+
+ align:start position:0%
+actually extract alpha and beta
+and so you can write down a simple out
+
+ align:start position:0%
+and so you can write down a simple out
+ 
+
+ align:start position:0%
+and so you can write down a simple out
+algebraic expression for alpha and beta
+
+ align:start position:0%
+algebraic expression for alpha and beta
+ 
+
+ align:start position:0%
+algebraic expression for alpha and beta
+and that's the way they actually wrote
+
+ align:start position:0%
+and that's the way they actually wrote
+ 
+
+ align:start position:0%
+and that's the way they actually wrote
+those things down they wrote them down
+
+ align:start position:0%
+those things down they wrote them down
+ 
+
+ align:start position:0%
+those things down they wrote them down
+as alpha and beta rather than an
+
+ align:start position:0%
+as alpha and beta rather than an
+ 
+
+ align:start position:0%
+as alpha and beta rather than an
+infinity Intel okay so you can actually
+
+ align:start position:0%
+infinity Intel okay so you can actually
+ 
+
+ align:start position:0%
+infinity Intel okay so you can actually
+those are simple expressions for alpha
+
+ align:start position:0%
+those are simple expressions for alpha
+ 
+
+ align:start position:0%
+those are simple expressions for alpha
+and beta in units of per millisecond as
+
+ align:start position:0%
+and beta in units of per millisecond as
+ 
+
+ align:start position:0%
+and beta in units of per millisecond as
+a function of voltage in units of
+
+ align:start position:0%
+a function of voltage in units of
+ 
+
+ align:start position:0%
+a function of voltage in units of
+millivolts okay I think I think yeah
+
+ align:start position:0%
+millivolts okay I think I think yeah
+ 
+
+ align:start position:0%
+millivolts okay I think I think yeah
+it's millivolts yeah there it is right
+
+ align:start position:0%
+it's millivolts yeah there it is right
+ 
+
+ align:start position:0%
+it's millivolts yeah there it is right
+there okay so you can actually just take
+
+ align:start position:0%
+there okay so you can actually just take
+ 
+
+ align:start position:0%
+there okay so you can actually just take
+those parameters right and calculate n
+
+ align:start position:0%
+those parameters right and calculate n
+ 
+
+ align:start position:0%
+those parameters right and calculate n
+infinity and tau N and calculate the
+
+ align:start position:0%
+infinity and tau N and calculate the
+ 
+
+ align:start position:0%
+infinity and tau N and calculate the
+gating variable from that using that
+
+ align:start position:0%
+gating variable from that using that
+ 
+
+ align:start position:0%
+gating variable from that using that
+differential equation okay so we have
+
+ align:start position:0%
+differential equation okay so we have
+ 
+
+ align:start position:0%
+differential equation okay so we have
+these nice expressions for what the
+
+ align:start position:0%
+these nice expressions for what the
+ 
+
+ align:start position:0%
+these nice expressions for what the
+steady state and infinity and tau NR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now why did we yes yes they're per
+
+ align:start position:0%
+okay now why did we yes yes they're per
+ 
+
+ align:start position:0%
+okay now why did we yes yes they're per
+unit time yeah so they have units of per
+
+ align:start position:0%
+unit time yeah so they have units of per
+ 
+
+ align:start position:0%
+unit time yeah so they have units of per
+millisecond okay so now let's come back
+
+ align:start position:0%
+millisecond okay so now let's come back
+ 
+
+ align:start position:0%
+millisecond okay so now let's come back
+to our picture we have an infinity and
+
+ align:start position:0%
+to our picture we have an infinity and
+ 
+
+ align:start position:0%
+to our picture we have an infinity and
+tau n as a function of voltage now we
+
+ align:start position:0%
+tau n as a function of voltage now we
+ 
+
+ align:start position:0%
+tau n as a function of voltage now we
+just can plug those into this
+
+ align:start position:0%
+just can plug those into this
+ 
+
+ align:start position:0%
+just can plug those into this
+differential equation and solve for n
+
+ align:start position:0%
+differential equation and solve for n
+ 
+
+ align:start position:0%
+differential equation and solve for n
+well we already know what that does it
+
+ align:start position:0%
+well we already know what that does it
+ 
+
+ align:start position:0%
+well we already know what that does it
+just N relaxes exponentially toward an
+
+ align:start position:0%
+just N relaxes exponentially toward an
+ 
+
+ align:start position:0%
+just N relaxes exponentially toward an
+infinity with a time constant tau but
+
+ align:start position:0%
+infinity with a time constant tau but
+ 
+
+ align:start position:0%
+infinity with a time constant tau but
+you can integrate that numerically you
+
+ align:start position:0%
+you can integrate that numerically you
+ 
+
+ align:start position:0%
+you can integrate that numerically you
+get the potassium conductance as n to
+
+ align:start position:0%
+get the potassium conductance as n to
+ 
+
+ align:start position:0%
+get the potassium conductance as n to
+the 4G times n to the 4 you get the
+
+ align:start position:0%
+the 4G times n to the 4 you get the
+ 
+
+ align:start position:0%
+the 4G times n to the 4 you get the
+potassium current as GN to the 4 times
+
+ align:start position:0%
+potassium current as GN to the 4 times
+ 
+
+ align:start position:0%
+potassium current as GN to the 4 times
+the driving potential or V - EK okay and
+
+ align:start position:0%
+the driving potential or V - EK okay and
+ 
+
+ align:start position:0%
+the driving potential or V - EK okay and
+now let's come back to our algorithm for
+
+ align:start position:0%
+now let's come back to our algorithm for
+ 
+
+ align:start position:0%
+now let's come back to our algorithm for
+making an action potential so we have
+
+ align:start position:0%
+making an action potential so we have
+ 
+
+ align:start position:0%
+making an action potential so we have
+the parts related to the potassium
+
+ align:start position:0%
+the parts related to the potassium
+ 
+
+ align:start position:0%
+the parts related to the potassium
+current we still have to add the parts
+
+ align:start position:0%
+current we still have to add the parts
+ 
+
+ align:start position:0%
+current we still have to add the parts
+related to sodium but it's going to look
+
+ align:start position:0%
+related to sodium but it's going to look
+ 
+
+ align:start position:0%
+related to sodium but it's going to look
+very similar so here's the idea we start
+
+ align:start position:0%
+very similar so here's the idea we start
+ 
+
+ align:start position:0%
+very similar so here's the idea we start
+with the membrane potential at time step
+
+ align:start position:0%
+with the membrane potential at time step
+ 
+
+ align:start position:0%
+with the membrane potential at time step
+T we compute n infinity and tau n we
+
+ align:start position:0%
+T we compute n infinity and tau n we
+ 
+
+ align:start position:0%
+T we compute n infinity and tau n we
+integrate DN DT
+
+ align:start position:0%
+integrate DN DT
+ 
+
+ align:start position:0%
+integrate DN DT
+one time step to get the next n plug n
+
+ align:start position:0%
+one time step to get the next n plug n
+ 
+
+ align:start position:0%
+one time step to get the next n plug n
+into our equation to get the potassium
+
+ align:start position:0%
+into our equation to get the potassium
+ 
+
+ align:start position:0%
+into our equation to get the potassium
+current we then add that to all the
+
+ align:start position:0%
+current we then add that to all the
+ 
+
+ align:start position:0%
+current we then add that to all the
+other currents to get the total membrane
+
+ align:start position:0%
+other currents to get the total membrane
+ 
+
+ align:start position:0%
+other currents to get the total membrane
+current we compute the infinity of the
+
+ align:start position:0%
+current we compute the infinity of the
+ 
+
+ align:start position:0%
+current we compute the infinity of the
+cell we integrate dv/dt one time step to
+
+ align:start position:0%
+cell we integrate dv/dt one time step to
+ 
+
+ align:start position:0%
+cell we integrate dv/dt one time step to
+get the next voltage and you plug that
+
+ align:start position:0%
+get the next voltage and you plug that
+ 
+
+ align:start position:0%
+get the next voltage and you plug that
+in and calculate the next and infinity
+
+ align:start position:0%
+in and calculate the next and infinity
+ 
+
+ align:start position:0%
+in and calculate the next and infinity
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so we still have to add the sodium parts
+
+ align:start position:0%
+so we still have to add the sodium parts
+ 
+
+ align:start position:0%
+so we still have to add the sodium parts
+but you can see we've gone through all
+
+ align:start position:0%
+but you can see we've gone through all
+ 
+
+ align:start position:0%
+but you can see we've gone through all
+of these steps for the potassium okay
+
+ align:start position:0%
+of these steps for the potassium okay
+ 
+
+ align:start position:0%
+of these steps for the potassium okay
+and so work just this shy of having a
+
+ align:start position:0%
+and so work just this shy of having a
+ 
+
+ align:start position:0%
+and so work just this shy of having a
+full-blown algorithm for an action
+
+ align:start position:0%
+full-blown algorithm for an action
+ 
+
+ align:start position:0%
+full-blown algorithm for an action
+potential in a neuron okay and not only
+
+ align:start position:0%
+potential in a neuron okay and not only
+ 
+
+ align:start position:0%
+potential in a neuron okay and not only
+do you understand all the little steps
+
+ align:start position:0%
+do you understand all the little steps
+ 
+
+ align:start position:0%
+do you understand all the little steps
+but you understand that fundamental
+
+ align:start position:0%
+but you understand that fundamental
+ 
+
+ align:start position:0%
+but you understand that fundamental
+biophysics that leads to that voltage
+
+ align:start position:0%
+biophysics that leads to that voltage
+ 
+
+ align:start position:0%
+biophysics that leads to that voltage
+and time dependence okay all right so
+
+ align:start position:0%
+and time dependence okay all right so
+ 
+
+ align:start position:0%
+and time dependence okay all right so
+again what I'd like you to be able to do
+
+ align:start position:0%
+again what I'd like you to be able to do
+ 
+
+ align:start position:0%
+again what I'd like you to be able to do
+is to draw that circuit the
+
+ align:start position:0%
+is to draw that circuit the
+ 
+
+ align:start position:0%
+is to draw that circuit the
+hodgkin-huxley model I'd like you to be
+
+ align:start position:0%
+hodgkin-huxley model I'd like you to be
+ 
+
+ align:start position:0%
+hodgkin-huxley model I'd like you to be
+able to explain at a basic level what a
+
+ align:start position:0%
+able to explain at a basic level what a
+ 
+
+ align:start position:0%
+able to explain at a basic level what a
+voltage clamp is and how it works
+
+ align:start position:0%
+voltage clamp is and how it works
+ 
+
+ align:start position:0%
+voltage clamp is and how it works
+we'd like you to be able to plot the
+
+ align:start position:0%
+we'd like you to be able to plot the
+ 
+
+ align:start position:0%
+we'd like you to be able to plot the
+voltage and time dependence of the
+
+ align:start position:0%
+voltage and time dependence of the
+ 
+
+ align:start position:0%
+voltage and time dependence of the
+potassium current remember this sigmoid
+
+ align:start position:0%
+potassium current remember this sigmoid
+ 
+
+ align:start position:0%
+potassium current remember this sigmoid
+'el activation of the potassium current
+
+ align:start position:0%
+'el activation of the potassium current
+ 
+
+ align:start position:0%
+'el activation of the potassium current
+and the conductance voltage and time
+
+ align:start position:0%
+and the conductance voltage and time
+ 
+
+ align:start position:0%
+and the conductance voltage and time
+dependence and be able to explain the
+
+ align:start position:0%
+dependence and be able to explain the
+ 
+
+ align:start position:0%
+dependence and be able to explain the
+time and voltage depends to the
+
+ align:start position:0%
+time and voltage depends to the
+ 
+
+ align:start position:0%
+time and voltage depends to the
+potassium conductance in terms of the
+
+ align:start position:0%
+potassium conductance in terms of the
+ 
+
+ align:start position:0%
+potassium conductance in terms of the
+hodgkin-huxley gating variables okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/8MLEYc3PLUc.txt b/8MLEYc3PLUc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3762f8d2bc740aafd7dfb6b5c5134b89b1c7c2fc
--- /dev/null
+++ b/8MLEYc3PLUc.txt
@@ -0,0 +1,1051 @@
+align:start position:0%
+ 
+we're speaking today with Heidi
+
+ align:start position:0%
+we're speaking today with Heidi
+ 
+
+ align:start position:0%
+we're speaking today with Heidi
+scherholz the chief Economist at the US
+
+ align:start position:0%
+scherholz the chief Economist at the US
+ 
+
+ align:start position:0%
+scherholz the chief Economist at the US
+Department of Labor Heidi follows the
+
+ align:start position:0%
+Department of Labor Heidi follows the
+ 
+
+ align:start position:0%
+Department of Labor Heidi follows the
+job Trends and occupational
+
+ align:start position:0%
+job Trends and occupational
+ 
+
+ align:start position:0%
+job Trends and occupational
+opportunities uh around the country and
+
+ align:start position:0%
+opportunities uh around the country and
+ 
+
+ align:start position:0%
+opportunities uh around the country and
+so this is a good opportunity to discuss
+
+ align:start position:0%
+so this is a good opportunity to discuss
+ 
+
+ align:start position:0%
+so this is a good opportunity to discuss
+where some of the good jobs are so Heidi
+
+ align:start position:0%
+where some of the good jobs are so Heidi
+ 
+
+ align:start position:0%
+where some of the good jobs are so Heidi
+thank you for joining us today it's my
+
+ align:start position:0%
+thank you for joining us today it's my
+ 
+
+ align:start position:0%
+thank you for joining us today it's my
+pleasure I wonder if you could start by
+
+ align:start position:0%
+pleasure I wonder if you could start by
+ 
+
+ align:start position:0%
+pleasure I wonder if you could start by
+telling us what do you see as some of
+
+ align:start position:0%
+telling us what do you see as some of
+ 
+
+ align:start position:0%
+telling us what do you see as some of
+the good job opportunities for young
+
+ align:start position:0%
+the good job opportunities for young
+ 
+
+ align:start position:0%
+the good job opportunities for young
+people entering the labor force today I
+
+ align:start position:0%
+people entering the labor force today I
+ 
+
+ align:start position:0%
+people entering the labor force today I
+think it's important to know that there
+
+ align:start position:0%
+think it's important to know that there
+ 
+
+ align:start position:0%
+think it's important to know that there
+are a lot of good jobs being created
+
+ align:start position:0%
+are a lot of good jobs being created
+ 
+
+ align:start position:0%
+are a lot of good jobs being created
+there are a lot of good opportunities
+
+ align:start position:0%
+there are a lot of good opportunities
+ 
+
+ align:start position:0%
+there are a lot of good opportunities
+and if you look our Bureau of Labor
+
+ align:start position:0%
+and if you look our Bureau of Labor
+ 
+
+ align:start position:0%
+and if you look our Bureau of Labor
+Statistics does these employment
+
+ align:start position:0%
+Statistics does these employment
+ 
+
+ align:start position:0%
+Statistics does these employment
+projections where you can look and see
+
+ align:start position:0%
+projections where you can look and see
+ 
+
+ align:start position:0%
+projections where you can look and see
+what kind of jobs are growing strongly
+
+ align:start position:0%
+what kind of jobs are growing strongly
+ 
+
+ align:start position:0%
+what kind of jobs are growing strongly
+for the next 10 years what kind of wages
+
+ align:start position:0%
+for the next 10 years what kind of wages
+ 
+
+ align:start position:0%
+for the next 10 years what kind of wages
+will those jobs have and there's some
+
+ align:start position:0%
+will those jobs have and there's some
+ 
+
+ align:start position:0%
+will those jobs have and there's some
+trends that come out of that that you
+
+ align:start position:0%
+trends that come out of that that you
+ 
+
+ align:start position:0%
+trends that come out of that that you
+can see so some of the fastest growing
+
+ align:start position:0%
+can see so some of the fastest growing
+ 
+
+ align:start position:0%
+can see so some of the fastest growing
+jobs our jobs in the health sector
+
+ align:start position:0%
+jobs our jobs in the health sector
+ 
+
+ align:start position:0%
+jobs our jobs in the health sector
+particularly nurses really strong wages
+
+ align:start position:0%
+particularly nurses really strong wages
+ 
+
+ align:start position:0%
+particularly nurses really strong wages
+and really strong strong job growth we
+
+ align:start position:0%
+and really strong strong job growth we
+ 
+
+ align:start position:0%
+and really strong strong job growth we
+also see good job growth in the tech
+
+ align:start position:0%
+also see good job growth in the tech
+ 
+
+ align:start position:0%
+also see good job growth in the tech
+sector so software engineering software
+
+ align:start position:0%
+sector so software engineering software
+ 
+
+ align:start position:0%
+sector so software engineering software
+development those kinds of jobs are
+
+ align:start position:0%
+development those kinds of jobs are
+ 
+
+ align:start position:0%
+development those kinds of jobs are
+growing quickly you also see projected
+
+ align:start position:0%
+growing quickly you also see projected
+ 
+
+ align:start position:0%
+growing quickly you also see projected
+growth in some jobs in professional and
+
+ align:start position:0%
+growth in some jobs in professional and
+ 
+
+ align:start position:0%
+growth in some jobs in professional and
+business services like accountant jobs
+
+ align:start position:0%
+business services like accountant jobs
+ 
+
+ align:start position:0%
+business services like accountant jobs
+and auditing jobs sort of those old
+
+ align:start position:0%
+and auditing jobs sort of those old
+ 
+
+ align:start position:0%
+and auditing jobs sort of those old
+standbys we're going to always need them
+
+ align:start position:0%
+standbys we're going to always need them
+ 
+
+ align:start position:0%
+standbys we're going to always need them
+and they're really decent paying jobs so
+
+ align:start position:0%
+and they're really decent paying jobs so
+ 
+
+ align:start position:0%
+and they're really decent paying jobs so
+that's at the high end of the labor
+
+ align:start position:0%
+that's at the high end of the labor
+ 
+
+ align:start position:0%
+that's at the high end of the labor
+force how about at the middle tier of
+
+ align:start position:0%
+force how about at the middle tier of
+ 
+
+ align:start position:0%
+force how about at the middle tier of
+the labor force what's happening there
+
+ align:start position:0%
+the labor force what's happening there
+ 
+
+ align:start position:0%
+the labor force what's happening there
+one of the phenomenons that we're seeing
+
+ align:start position:0%
+one of the phenomenons that we're seeing
+ 
+
+ align:start position:0%
+one of the phenomenons that we're seeing
+there is there's this big group of
+
+ align:start position:0%
+there is there's this big group of
+ 
+
+ align:start position:0%
+there is there's this big group of
+people who are hitting retirement age
+
+ align:start position:0%
+people who are hitting retirement age
+ 
+
+ align:start position:0%
+people who are hitting retirement age
+the Baby Boomers and as that continues
+
+ align:start position:0%
+the Baby Boomers and as that continues
+ 
+
+ align:start position:0%
+the Baby Boomers and as that continues
+to happen there's going to be a lot of
+
+ align:start position:0%
+to happen there's going to be a lot of
+ 
+
+ align:start position:0%
+to happen there's going to be a lot of
+job turnover in some of these really
+
+ align:start position:0%
+job turnover in some of these really
+ 
+
+ align:start position:0%
+job turnover in some of these really
+good middleclass jobs like carpenter
+
+ align:start position:0%
+good middleclass jobs like carpenter
+ 
+
+ align:start position:0%
+good middleclass jobs like carpenter
+jobs electrician jobs um utility workers
+
+ align:start position:0%
+jobs electrician jobs um utility workers
+ 
+
+ align:start position:0%
+jobs electrician jobs um utility workers
+uh welders those kinds of jobs that
+
+ align:start position:0%
+uh welders those kinds of jobs that
+ 
+
+ align:start position:0%
+uh welders those kinds of jobs that
+historically people got a lot of
+
+ align:start position:0%
+historically people got a lot of
+ 
+
+ align:start position:0%
+historically people got a lot of
+training in those kind of jobs through
+
+ align:start position:0%
+training in those kind of jobs through
+ 
+
+ align:start position:0%
+training in those kind of jobs through
+their unions in apprenticeship programs
+
+ align:start position:0%
+their unions in apprenticeship programs
+ 
+
+ align:start position:0%
+their unions in apprenticeship programs
+as we have the this group of people that
+
+ align:start position:0%
+as we have the this group of people that
+ 
+
+ align:start position:0%
+as we have the this group of people that
+was trained in that way hitting
+
+ align:start position:0%
+was trained in that way hitting
+ 
+
+ align:start position:0%
+was trained in that way hitting
+retirement age we have to really figure
+
+ align:start position:0%
+retirement age we have to really figure
+ 
+
+ align:start position:0%
+retirement age we have to really figure
+out how we're going to refill those jobs
+
+ align:start position:0%
+out how we're going to refill those jobs
+ 
+
+ align:start position:0%
+out how we're going to refill those jobs
+one of the things the Department of
+
+ align:start position:0%
+one of the things the Department of
+ 
+
+ align:start position:0%
+one of the things the Department of
+Labor is doing is really doing
+
+ align:start position:0%
+Labor is doing is really doing
+ 
+
+ align:start position:0%
+Labor is doing is really doing
+everything we can to support
+
+ align:start position:0%
+everything we can to support
+ 
+
+ align:start position:0%
+everything we can to support
+apprenticeship programs they can help
+
+ align:start position:0%
+apprenticeship programs they can help
+ 
+
+ align:start position:0%
+apprenticeship programs they can help
+train up people to get into those jobs
+
+ align:start position:0%
+train up people to get into those jobs
+ 
+
+ align:start position:0%
+train up people to get into those jobs
+because those are really good middle
+
+ align:start position:0%
+because those are really good middle
+ 
+
+ align:start position:0%
+because those are really good middle
+class jobs that are going to be very in
+
+ align:start position:0%
+class jobs that are going to be very in
+ 
+
+ align:start position:0%
+class jobs that are going to be very in
+demand going forward well that's great
+
+ align:start position:0%
+demand going forward well that's great
+ 
+
+ align:start position:0%
+demand going forward well that's great
+because apprenticeships have such a
+
+ align:start position:0%
+because apprenticeships have such a
+ 
+
+ align:start position:0%
+because apprenticeships have such a
+positive records so rebuilding those is
+
+ align:start position:0%
+positive records so rebuilding those is
+ 
+
+ align:start position:0%
+positive records so rebuilding those is
+so critical to our economy and the
+
+ align:start position:0%
+so critical to our economy and the
+ 
+
+ align:start position:0%
+so critical to our economy and the
+future Workforce research shows
+
+ align:start position:0%
+future Workforce research shows
+ 
+
+ align:start position:0%
+future Workforce research shows
+apprenticeship has the highest rate of
+
+ align:start position:0%
+apprenticeship has the highest rate of
+ 
+
+ align:start position:0%
+apprenticeship has the highest rate of
+return as far as investment in workers
+
+ align:start position:0%
+return as far as investment in workers
+ 
+
+ align:start position:0%
+return as far as investment in workers
+what pays off for the economy for their
+
+ align:start position:0%
+what pays off for the economy for their
+ 
+
+ align:start position:0%
+what pays off for the economy for their
+future earnings so it's a really good um
+
+ align:start position:0%
+future earnings so it's a really good um
+ 
+
+ align:start position:0%
+future earnings so it's a really good um
+it's a really good route for our country
+
+ align:start position:0%
+it's a really good route for our country
+ 
+
+ align:start position:0%
+it's a really good route for our country
+to invest in and for people to take
+
+ align:start position:0%
+to invest in and for people to take
+ 
+
+ align:start position:0%
+to invest in and for people to take
+advantage of as they're thinking about
+
+ align:start position:0%
+advantage of as they're thinking about
+ 
+
+ align:start position:0%
+advantage of as they're thinking about
+what their careers are going to look
+
+ align:start position:0%
+what their careers are going to look
+ 
+
+ align:start position:0%
+what their careers are going to look
+like going forward and what about at the
+
+ align:start position:0%
+like going forward and what about at the
+ 
+
+ align:start position:0%
+like going forward and what about at the
+lower end of the occupational
+
+ align:start position:0%
+lower end of the occupational
+ 
+
+ align:start position:0%
+lower end of the occupational
+distribution the projections show that
+
+ align:start position:0%
+distribution the projections show that
+ 
+
+ align:start position:0%
+distribution the projections show that
+we are expeced to add a lot of jobs that
+
+ align:start position:0%
+we are expeced to add a lot of jobs that
+ 
+
+ align:start position:0%
+we are expeced to add a lot of jobs that
+at this point are low-wage jobs home
+
+ align:start position:0%
+at this point are low-wage jobs home
+ 
+
+ align:start position:0%
+at this point are low-wage jobs home
+health aids food prep workers in
+
+ align:start position:0%
+health aids food prep workers in
+ 
+
+ align:start position:0%
+health aids food prep workers in
+restaurants and bars child care workers
+
+ align:start position:0%
+restaurants and bars child care workers
+ 
+
+ align:start position:0%
+restaurants and bars child care workers
+janitors maids and housekeeping cleaners
+
+ align:start position:0%
+janitors maids and housekeeping cleaners
+ 
+
+ align:start position:0%
+janitors maids and housekeeping cleaners
+so some of these lower-end jobs are
+
+ align:start position:0%
+so some of these lower-end jobs are
+ 
+
+ align:start position:0%
+so some of these lower-end jobs are
+projected to see strong growth going
+
+ align:start position:0%
+projected to see strong growth going
+ 
+
+ align:start position:0%
+projected to see strong growth going
+forward so what I think that's a really
+
+ align:start position:0%
+forward so what I think that's a really
+ 
+
+ align:start position:0%
+forward so what I think that's a really
+important segment of the labor market to
+
+ align:start position:0%
+important segment of the labor market to
+ 
+
+ align:start position:0%
+important segment of the labor market to
+think about and that's where policy can
+
+ align:start position:0%
+think about and that's where policy can
+ 
+
+ align:start position:0%
+think about and that's where policy can
+come in to help make sure that those are
+
+ align:start position:0%
+come in to help make sure that those are
+ 
+
+ align:start position:0%
+come in to help make sure that those are
+better jobs so things like making sure
+
+ align:start position:0%
+better jobs so things like making sure
+ 
+
+ align:start position:0%
+better jobs so things like making sure
+um we have a decent minimum wage
+
+ align:start position:0%
+um we have a decent minimum wage
+ 
+
+ align:start position:0%
+um we have a decent minimum wage
+increasing the minimum wage making sure
+
+ align:start position:0%
+increasing the minimum wage making sure
+ 
+
+ align:start position:0%
+increasing the minimum wage making sure
+people have overtime protections um
+
+ align:start position:0%
+people have overtime protections um
+ 
+
+ align:start position:0%
+people have overtime protections um
+making sure that people have paid leave
+
+ align:start position:0%
+making sure that people have paid leave
+ 
+
+ align:start position:0%
+making sure that people have paid leave
+the president just announced um
+
+ align:start position:0%
+the president just announced um
+ 
+
+ align:start position:0%
+the president just announced um
+initiatives to bolster paid leave in the
+
+ align:start position:0%
+initiatives to bolster paid leave in the
+ 
+
+ align:start position:0%
+initiatives to bolster paid leave in the
+United States those kinds of policies
+
+ align:start position:0%
+United States those kinds of policies
+ 
+
+ align:start position:0%
+United States those kinds of policies
+can help um ensure that even jobs that
+
+ align:start position:0%
+can help um ensure that even jobs that
+ 
+
+ align:start position:0%
+can help um ensure that even jobs that
+that that we have high quality jobs for
+
+ align:start position:0%
+that that we have high quality jobs for
+ 
+
+ align:start position:0%
+that that we have high quality jobs for
+people at all levels of Education and
+
+ align:start position:0%
+people at all levels of Education and
+ 
+
+ align:start position:0%
+people at all levels of Education and
+Training certainly important that we
+
+ align:start position:0%
+Training certainly important that we
+ 
+
+ align:start position:0%
+Training certainly important that we
+really help to improve those low wage
+
+ align:start position:0%
+really help to improve those low wage
+ 
+
+ align:start position:0%
+really help to improve those low wage
+jobs and provide career opportunities
+
+ align:start position:0%
+jobs and provide career opportunities
+ 
+
+ align:start position:0%
+jobs and provide career opportunities
+for growth and so on what else would you
+
+ align:start position:0%
+for growth and so on what else would you
+ 
+
+ align:start position:0%
+for growth and so on what else would you
+say that young people need to do to
+
+ align:start position:0%
+say that young people need to do to
+ 
+
+ align:start position:0%
+say that young people need to do to
+prepare for the good jobs of the future
+
+ align:start position:0%
+prepare for the good jobs of the future
+ 
+
+ align:start position:0%
+prepare for the good jobs of the future
+thinking about investments in your own
+
+ align:start position:0%
+thinking about investments in your own
+ 
+
+ align:start position:0%
+thinking about investments in your own
+training and education over the course
+
+ align:start position:0%
+training and education over the course
+ 
+
+ align:start position:0%
+training and education over the course
+of your career is just a really smart
+
+ align:start position:0%
+of your career is just a really smart
+ 
+
+ align:start position:0%
+of your career is just a really smart
+idea um one of the things people should
+
+ align:start position:0%
+idea um one of the things people should
+ 
+
+ align:start position:0%
+idea um one of the things people should
+be doing is asking their employers for
+
+ align:start position:0%
+be doing is asking their employers for
+ 
+
+ align:start position:0%
+be doing is asking their employers for
+what opportunities there are for
+
+ align:start position:0%
+what opportunities there are for
+ 
+
+ align:start position:0%
+what opportunities there are for
+advancement asking your union what can
+
+ align:start position:0%
+advancement asking your union what can
+ 
+
+ align:start position:0%
+advancement asking your union what can
+you do to help help support these kind
+
+ align:start position:0%
+you do to help help support these kind
+ 
+
+ align:start position:0%
+you do to help help support these kind
+of career ladders looking into things
+
+ align:start position:0%
+of career ladders looking into things
+ 
+
+ align:start position:0%
+of career ladders looking into things
+like joint Union and management programs
+
+ align:start position:0%
+like joint Union and management programs
+ 
+
+ align:start position:0%
+like joint Union and management programs
+that support these kind of career Lads
+
+ align:start position:0%
+that support these kind of career Lads
+ 
+
+ align:start position:0%
+that support these kind of career Lads
+for example there's there's programs
+
+ align:start position:0%
+for example there's there's programs
+ 
+
+ align:start position:0%
+for example there's there's programs
+that will help people go from a nursing
+
+ align:start position:0%
+that will help people go from a nursing
+ 
+
+ align:start position:0%
+that will help people go from a nursing
+assistant to an LPN to a registered
+
+ align:start position:0%
+assistant to an LPN to a registered
+ 
+
+ align:start position:0%
+assistant to an LPN to a registered
+nurse and if you can think of supporting
+
+ align:start position:0%
+nurse and if you can think of supporting
+ 
+
+ align:start position:0%
+nurse and if you can think of supporting
+those kinds of trajectories you can
+
+ align:start position:0%
+those kinds of trajectories you can
+ 
+
+ align:start position:0%
+those kinds of trajectories you can
+really carve out a career that you
+
+ align:start position:0%
+really carve out a career that you
+ 
+
+ align:start position:0%
+really carve out a career that you
+really lets let you punch punch the
+
+ align:start position:0%
+really lets let you punch punch the
+ 
+
+ align:start position:0%
+really lets let you punch punch the
+ticket to the middle class I think
+
+ align:start position:0%
+ticket to the middle class I think
+ 
+
+ align:start position:0%
+ticket to the middle class I think
+that's that's good advice uh young
+
+ align:start position:0%
+that's that's good advice uh young
+ 
+
+ align:start position:0%
+that's that's good advice uh young
+people have lots of opportunities and
+
+ align:start position:0%
+people have lots of opportunities and
+ 
+
+ align:start position:0%
+people have lots of opportunities and
+they have to create new ones uh along
+
+ align:start position:0%
+they have to create new ones uh along
+ 
+
+ align:start position:0%
+they have to create new ones uh along
+with the partnership of the Department
+
+ align:start position:0%
+with the partnership of the Department
+ 
+
+ align:start position:0%
+with the partnership of the Department
+of Labor and good employers and good
+
+ align:start position:0%
+of Labor and good employers and good
+ 
+
+ align:start position:0%
+of Labor and good employers and good
+labor organizations so thank you very
+
+ align:start position:0%
+labor organizations so thank you very
+ 
+
+ align:start position:0%
+labor organizations so thank you very
+much it's been my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pleasure
\ No newline at end of file
diff --git a/9iJryWzLDIw.txt b/9iJryWzLDIw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fa2abd84879393c2c6397b0fde5a27f0c74b63b0
--- /dev/null
+++ b/9iJryWzLDIw.txt
@@ -0,0 +1,7400 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so I've got Quiz 2 to
+
+ align:start position:0%
+ocw.mit.edu okay so I've got Quiz 2 to
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so I've got Quiz 2 to
+give back to you with good scores so
+
+ align:start position:0%
+give back to you with good scores so
+ 
+
+ align:start position:0%
+give back to you with good scores so
+it's Christmas early uh or good work on
+
+ align:start position:0%
+it's Christmas early uh or good work on
+ 
+
+ align:start position:0%
+it's Christmas early uh or good work on
+that exam that's fine and uh so we all
+
+ align:start position:0%
+that exam that's fine and uh so we all
+ 
+
+ align:start position:0%
+that exam that's fine and uh so we all
+know 4A series is like a central topic
+
+ align:start position:0%
+know 4A series is like a central topic
+ 
+
+ align:start position:0%
+know 4A series is like a central topic
+on the final uh third of the course and
+
+ align:start position:0%
+on the final uh third of the course and
+ 
+
+ align:start position:0%
+on the final uh third of the course and
+I'll just keep going on 4 Series I'll
+
+ align:start position:0%
+I'll just keep going on 4 Series I'll
+ 
+
+ align:start position:0%
+I'll just keep going on 4 Series I'll
+give you a homework on 4.1 and
+
+ align:start position:0%
+give you a homework on 4.1 and
+ 
+
+ align:start position:0%
+give you a homework on 4.1 and
+4.2 so 4.1 is what we complete today the
+
+ align:start position:0%
+4.2 so 4.1 is what we complete today the
+ 
+
+ align:start position:0%
+4.2 so 4.1 is what we complete today the
+fora series 4.2 is the discret fora
+
+ align:start position:0%
+fora series 4.2 is the discret fora
+ 
+
+ align:start position:0%
+fora series 4.2 is the discret fora
+series uh so those are two major major
+
+ align:start position:0%
+series uh so those are two major major
+ 
+
+ align:start position:0%
+series uh so those are two major major
+topics for uh this part of the course
+
+ align:start position:0%
+topics for uh this part of the course
+ 
+
+ align:start position:0%
+topics for uh this part of the course
+the the this is the periodic one and 42
+
+ align:start position:0%
+the the this is the periodic one and 42
+ 
+
+ align:start position:0%
+the the this is the periodic one and 42
+will be the finite one with a forier
+
+ align:start position:0%
+will be the finite one with a forier
+ 
+
+ align:start position:0%
+will be the finite one with a forier
+matrix showing up okay so can I pick up
+
+ align:start position:0%
+matrix showing up okay so can I pick up
+ 
+
+ align:start position:0%
+matrix showing up okay so can I pick up
+I made a list of topics last time to
+
+ align:start position:0%
+I made a list of topics last time to
+ 
+
+ align:start position:0%
+I made a list of topics last time to
+that that were important for 4.1 for 4A
+
+ align:start position:0%
+that that were important for 4.1 for 4A
+ 
+
+ align:start position:0%
+that that were important for 4.1 for 4A
+series and I think these are the
+
+ align:start position:0%
+series and I think these are the
+ 
+
+ align:start position:0%
+series and I think these are the
+remaining uh entries on the
+
+ align:start position:0%
+remaining uh entries on the
+ 
+
+ align:start position:0%
+remaining uh entries on the
+list uh I did the
+
+ align:start position:0%
+list uh I did the
+ 
+
+ align:start position:0%
+list uh I did the
+um the F series for the odd uh Square
+
+ align:start position:0%
+um the F series for the odd uh Square
+ 
+
+ align:start position:0%
+um the F series for the odd uh Square
+wave the minus one stepping up to plus
+
+ align:start position:0%
+wave the minus one stepping up to plus
+ 
+
+ align:start position:0%
+wave the minus one stepping up to plus
+one and you remember that uh well I'll
+
+ align:start position:0%
+one and you remember that uh well I'll
+ 
+
+ align:start position:0%
+one and you remember that uh well I'll
+just let me put that example down here
+
+ align:start position:0%
+just let me put that example down here
+ 
+
+ align:start position:0%
+just let me put that example down here
+that was the step function uh easier if
+
+ align:start position:0%
+that was the step function uh easier if
+ 
+
+ align:start position:0%
+that was the step function uh easier if
+I draw it than if I try to write
+
+ align:start position:0%
+I draw it than if I try to write
+ 
+
+ align:start position:0%
+I draw it than if I try to write
+equation so it was minus1 up to Plus one
+
+ align:start position:0%
+equation so it was minus1 up to Plus one
+ 
+
+ align:start position:0%
+equation so it was minus1 up to Plus one
+at Pi ending of course period 2 pi and I
+
+ align:start position:0%
+at Pi ending of course period 2 pi and I
+ 
+
+ align:start position:0%
+at Pi ending of course period 2 pi and I
+guess we called that S ofx for S
+
+ align:start position:0%
+guess we called that S ofx for S
+ 
+
+ align:start position:0%
+guess we called that S ofx for S
+signaling step function s signaling
+
+ align:start position:0%
+signaling step function s signaling
+ 
+
+ align:start position:0%
+signaling step function s signaling
+Square wave and S the general uh signal
+
+ align:start position:0%
+Square wave and S the general uh signal
+ 
+
+ align:start position:0%
+Square wave and S the general uh signal
+that the function is odd and that means
+
+ align:start position:0%
+that the function is odd and that means
+ 
+
+ align:start position:0%
+that the function is odd and that means
+that it goes with s functions and I
+
+ align:start position:0%
+that it goes with s functions and I
+ 
+
+ align:start position:0%
+that it goes with s functions and I
+think the amounts the numbers that we
+
+ align:start position:0%
+think the amounts the numbers that we
+ 
+
+ align:start position:0%
+think the amounts the numbers that we
+found from the formula was
+
+ align:start position:0%
+found from the formula was
+ 
+
+ align:start position:0%
+found from the formula was
+uh sin x over 1 sin 3x over 3 sin 5x
+
+ align:start position:0%
+uh sin x over 1 sin 3x over 3 sin 5x
+ 
+
+ align:start position:0%
+uh sin x over 1 sin 3x over 3 sin 5x
+over five that's it's just a great one
+
+ align:start position:0%
+over five that's it's just a great one
+ 
+
+ align:start position:0%
+over five that's it's just a great one
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember yeah and that's the the uh uh
+
+ align:start position:0%
+remember yeah and that's the the uh uh
+ 
+
+ align:start position:0%
+remember yeah and that's the the uh uh
+the example that has the the important
+
+ align:start position:0%
+the example that has the the important
+ 
+
+ align:start position:0%
+the example that has the the important
+and I don't know if I wrote down Gibb's
+
+ align:start position:0%
+and I don't know if I wrote down Gibb's
+ 
+
+ align:start position:0%
+and I don't know if I wrote down Gibb's
+name he was the great physicist at Yale
+
+ align:start position:0%
+name he was the great physicist at Yale
+ 
+
+ align:start position:0%
+name he was the great physicist at Yale
+uh well 100 years ago or more and uh did
+
+ align:start position:0%
+uh well 100 years ago or more and uh did
+ 
+
+ align:start position:0%
+uh well 100 years ago or more and uh did
+uh this key idea in that that appears
+
+ align:start position:0%
+uh this key idea in that that appears
+ 
+
+ align:start position:0%
+uh this key idea in that that appears
+all the time that anytime you have a
+
+ align:start position:0%
+all the time that anytime you have a
+ 
+
+ align:start position:0%
+all the time that anytime you have a
+step function then the Fier Series has a
+
+ align:start position:0%
+step function then the Fier Series has a
+ 
+
+ align:start position:0%
+step function then the Fier Series has a
+well it does its
+
+ align:start position:0%
+well it does its
+ 
+
+ align:start position:0%
+well it does its
+best if I take a thousand terms it'll do
+
+ align:start position:0%
+best if I take a thousand terms it'll do
+ 
+
+ align:start position:0%
+best if I take a thousand terms it'll do
+its best but it will overshoot by an
+
+ align:start position:0%
+its best but it will overshoot by an
+ 
+
+ align:start position:0%
+its best but it will overshoot by an
+amount that Gibbs found and then it will
+
+ align:start position:0%
+amount that Gibbs found and then it will
+ 
+
+ align:start position:0%
+amount that Gibbs found and then it will
+get really close CL and then it will
+
+ align:start position:0%
+get really close CL and then it will
+ 
+
+ align:start position:0%
+get really close CL and then it will
+overshoot again and and then
+
+ align:start position:0%
+overshoot again and and then
+ 
+
+ align:start position:0%
+overshoot again and and then
+symmetrically or anti- symmetrically I
+
+ align:start position:0%
+symmetrically or anti- symmetrically I
+ 
+
+ align:start position:0%
+symmetrically or anti- symmetrically I
+should say so that's the Gibbs
+
+ align:start position:0%
+should say so that's the Gibbs
+ 
+
+ align:start position:0%
+should say so that's the Gibbs
+phenomenon of great importance okay I I
+
+ align:start position:0%
+phenomenon of great importance okay I I
+ 
+
+ align:start position:0%
+phenomenon of great importance okay I I
+write this one out because uh first it's
+
+ align:start position:0%
+write this one out because uh first it's
+ 
+
+ align:start position:0%
+write this one out because uh first it's
+a important one to remember uh second
+
+ align:start position:0%
+a important one to remember uh second
+ 
+
+ align:start position:0%
+a important one to remember uh second
+it'll give us a good example for this uh
+
+ align:start position:0%
+it'll give us a good example for this uh
+ 
+
+ align:start position:0%
+it'll give us a good example for this uh
+important equality uh that the energy in
+
+ align:start position:0%
+important equality uh that the energy in
+ 
+
+ align:start position:0%
+important equality uh that the energy in
+in in the function is the energy in the
+
+ align:start position:0%
+in in the function is the energy in the
+ 
+
+ align:start position:0%
+in in the function is the energy in the
+coefficients that'll be good okay
+
+ align:start position:0%
+coefficients that'll be good okay
+ 
+
+ align:start position:0%
+coefficients that'll be good okay
+actually maybe I should do that one
+
+ align:start position:0%
+actually maybe I should do that one
+ 
+
+ align:start position:0%
+actually maybe I should do that one
+first because the the Delta function has
+
+ align:start position:0%
+first because the the Delta function has
+ 
+
+ align:start position:0%
+first because the the Delta function has
+got infinite energy and and we don't
+
+ align:start position:0%
+got infinite energy and and we don't
+ 
+
+ align:start position:0%
+got infinite energy and and we don't
+learn anything from this equation so so
+
+ align:start position:0%
+learn anything from this equation so so
+ 
+
+ align:start position:0%
+learn anything from this equation so so
+let me let me jump to the energy in the
+
+ align:start position:0%
+let me let me jump to the energy in the
+ 
+
+ align:start position:0%
+let me let me jump to the energy in the
+function and the energy in the
+
+ align:start position:0%
+function and the energy in the
+ 
+
+ align:start position:0%
+function and the energy in the
+coefficients so what do I mean by
+
+ align:start position:0%
+coefficients so what do I mean by
+ 
+
+ align:start position:0%
+coefficients so what do I mean by
+energy well it's quadratic right that's
+
+ align:start position:0%
+energy well it's quadratic right that's
+ 
+
+ align:start position:0%
+energy well it's quadratic right that's
+it's the it's the it's the length
+
+ align:start position:0%
+it's the it's the it's the length
+ 
+
+ align:start position:0%
+it's the it's the it's the length
+squared here it's the length squar of
+
+ align:start position:0%
+squared here it's the length squar of
+ 
+
+ align:start position:0%
+squared here it's the length squar of
+the function so uh let me uh compute
+
+ align:start position:0%
+the function so uh let me uh compute
+ 
+
+ align:start position:0%
+the function so uh let me uh compute
+maybe I'll do it on this board
+
+ align:start position:0%
+maybe I'll do it on this board
+ 
+
+ align:start position:0%
+maybe I'll do it on this board
+underneath and leave space for the Delta
+
+ align:start position:0%
+underneath and leave space for the Delta
+ 
+
+ align:start position:0%
+underneath and leave space for the Delta
+function the energy in X space is just
+
+ align:start position:0%
+function the energy in X space is just
+ 
+
+ align:start position:0%
+function the energy in X space is just
+the integral it's the length squared the
+
+ align:start position:0%
+the integral it's the length squared the
+ 
+
+ align:start position:0%
+the integral it's the length squared the
+integral of s ofx
+
+ align:start position:0%
+integral of s ofx
+ 
+
+ align:start position:0%
+integral of s ofx
+squar
+
+ align:start position:0%
+squar
+ 
+
+ align:start position:0%
+squar
+DX it's just just what you
+
+ align:start position:0%
+DX it's just just what you
+ 
+
+ align:start position:0%
+DX it's just just what you
+would uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expect we have a function not a vector
+
+ align:start position:0%
+expect we have a function not a vector
+ 
+
+ align:start position:0%
+expect we have a function not a vector
+so we can't
+
+ align:start position:0%
+so we can't
+ 
+
+ align:start position:0%
+so we can't
+sum coefficient squared we instead we
+
+ align:start position:0%
+sum coefficient squared we instead we
+ 
+
+ align:start position:0%
+sum coefficient squared we instead we
+integrate all the values squared and of
+
+ align:start position:0%
+integrate all the values squared and of
+ 
+
+ align:start position:0%
+integrate all the values squared and of
+course this is a number that we can
+
+ align:start position:0%
+course this is a number that we can
+ 
+
+ align:start position:0%
+course this is a number that we can
+quickly compute for that function so
+
+ align:start position:0%
+quickly compute for that function so
+ 
+
+ align:start position:0%
+quickly compute for that function so
+what does it turn out to be well what is
+
+ align:start position:0%
+what does it turn out to be well what is
+ 
+
+ align:start position:0%
+what does it turn out to be well what is
+s ofx s for that
+
+ align:start position:0%
+s ofx s for that
+ 
+
+ align:start position:0%
+s ofx s for that
+function one obviously the function is
+
+ align:start position:0%
+function one obviously the function is
+ 
+
+ align:start position:0%
+function one obviously the function is
+one here I'm looking at the original s
+
+ align:start position:0%
+one here I'm looking at the original s
+ 
+
+ align:start position:0%
+one here I'm looking at the original s
+ofx not the
+
+ align:start position:0%
+ofx not the
+ 
+
+ align:start position:0%
+ofx not the
+series the function is one there and
+
+ align:start position:0%
+series the function is one there and
+ 
+
+ align:start position:0%
+series the function is one there and
+minus one there when I Square those It's
+
+ align:start position:0%
+minus one there when I Square those It's
+ 
+
+ align:start position:0%
+minus one there when I Square those It's
+s of x^2 is one everywhere so I'm
+
+ align:start position:0%
+s of x^2 is one everywhere so I'm
+ 
+
+ align:start position:0%
+s of x^2 is one everywhere so I'm
+integrating one everywhere from minus pi
+
+ align:start position:0%
+integrating one everywhere from minus pi
+ 
+
+ align:start position:0%
+integrating one everywhere from minus pi
+to Pi so I get the answer 2
+
+ align:start position:0%
+to Pi so I get the answer 2
+ 
+
+ align:start position:0%
+to Pi so I get the answer 2
+pi so that's a case where the energy in
+
+ align:start position:0%
+pi so that's a case where the energy in
+ 
+
+ align:start position:0%
+pi so that's a case where the energy in
+the physical space the X space was
+
+ align:start position:0%
+the physical space the X space was
+ 
+
+ align:start position:0%
+the physical space the X space was
+totally easy to compute now what about
+
+ align:start position:0%
+totally easy to compute now what about
+ 
+
+ align:start position:0%
+totally easy to compute now what about
+energy what is this equality this this
+
+ align:start position:0%
+energy what is this equality this this
+ 
+
+ align:start position:0%
+energy what is this equality this this
+really neat easy to remember equality
+
+ align:start position:0%
+really neat easy to remember equality
+ 
+
+ align:start position:0%
+really neat easy to remember equality
+it's what's the I I'm just going to find
+
+ align:start position:0%
+it's what's the I I'm just going to find
+ 
+
+ align:start position:0%
+it's what's the I I'm just going to find
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+by looking by taking this thing squared
+
+ align:start position:0%
+by looking by taking this thing squared
+ 
+
+ align:start position:0%
+by looking by taking this thing squared
+what's the integral of the right hand
+
+ align:start position:0%
+what's the integral of the right hand
+ 
+
+ align:start position:0%
+what's the integral of the right hand
+side the two are
+
+ align:start position:0%
+side the two are
+ 
+
+ align:start position:0%
+side the two are
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+so I suppose I just fire away I
+
+ align:start position:0%
+so I suppose I just fire away I
+ 
+
+ align:start position:0%
+so I suppose I just fire away I
+integrate the square of that infinite
+
+ align:start position:0%
+integrate the square of that infinite
+ 
+
+ align:start position:0%
+integrate the square of that infinite
+series you're going to say well that's
+
+ align:start position:0%
+series you're going to say well that's
+ 
+
+ align:start position:0%
+series you're going to say well that's
+going to take a while but uh uh uh
+
+ align:start position:0%
+going to take a while but uh uh uh
+ 
+
+ align:start position:0%
+going to take a while but uh uh uh
+what's going to be good the the key
+
+ align:start position:0%
+what's going to be good the the key
+ 
+
+ align:start position:0%
+what's going to be good the the key
+point the first point in in in last
+
+ align:start position:0%
+point the first point in in in last
+ 
+
+ align:start position:0%
+point the first point in in in last
+times's lecture the first point in every
+
+ align:start position:0%
+times's lecture the first point in every
+ 
+
+ align:start position:0%
+times's lecture the first point in every
+discussion of Fier series is
+
+ align:start position:0%
+discussion of Fier series is
+ 
+
+ align:start position:0%
+discussion of Fier series is
+orthogonality signs times other signs
+
+ align:start position:0%
+orthogonality signs times other signs
+ 
+
+ align:start position:0%
+orthogonality signs times other signs
+integrated are zero so that a whole lot
+
+ align:start position:0%
+integrated are zero so that a whole lot
+ 
+
+ align:start position:0%
+integrated are zero so that a whole lot
+of terms will go so I take that thing I
+
+ align:start position:0%
+of terms will go so I take that thing I
+ 
+
+ align:start position:0%
+of terms will go so I take that thing I
+Square it so let me uh let me do that
+
+ align:start position:0%
+Square it so let me uh let me do that
+ 
+
+ align:start position:0%
+Square it so let me uh let me do that
+one here the inte from minus pi to Pi
+
+ align:start position:0%
+one here the inte from minus pi to Pi
+ 
+
+ align:start position:0%
+one here the inte from minus pi to Pi
+may I take out the 4 over pi^ squar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just so I don't have it so it's not
+
+ align:start position:0%
+just so I don't have it so it's not
+ 
+
+ align:start position:0%
+just so I don't have it so it's not
+confusing the now this is the s x over 1
+
+ align:start position:0%
+confusing the now this is the s x over 1
+ 
+
+ align:start position:0%
+confusing the now this is the s x over 1
+sin 3x over 3 sin KX over K and so on
+
+ align:start position:0%
+sin 3x over 3 sin KX over K and so on
+ 
+
+ align:start position:0%
+sin 3x over 3 sin KX over K and so on
+all squared DX and so what do I get the
+
+ align:start position:0%
+all squared DX and so what do I get the
+ 
+
+ align:start position:0%
+all squared DX and so what do I get the
+4 over pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squar and now I've got a whole lot of
+
+ align:start position:0%
+squar and now I've got a whole lot of
+ 
+
+ align:start position:0%
+squar and now I've got a whole lot of
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+but the thing is I can do this because
+
+ align:start position:0%
+but the thing is I can do this because
+ 
+
+ align:start position:0%
+but the thing is I can do this because
+when I Square this I'll have a lot of
+
+ align:start position:0%
+when I Square this I'll have a lot of
+ 
+
+ align:start position:0%
+when I Square this I'll have a lot of
+terms like sinx sin 3x and when I
+
+ align:start position:0%
+terms like sinx sin 3x and when I
+ 
+
+ align:start position:0%
+terms like sinx sin 3x and when I
+integrate those I get zero so the only
+
+ align:start position:0%
+integrate those I get zero so the only
+ 
+
+ align:start position:0%
+integrate those I get zero so the only
+ones that I don't get zero are when sinx
+
+ align:start position:0%
+ones that I don't get zero are when sinx
+ 
+
+ align:start position:0%
+ones that I don't get zero are when sinx
+integrates against itself and sin 3x
+
+ align:start position:0%
+integrates against itself and sin 3x
+ 
+
+ align:start position:0%
+integrates against itself and sin 3x
+against itself so when sin x integrates
+
+ align:start position:0%
+against itself so when sin x integrates
+ 
+
+ align:start position:0%
+against itself so when sin x integrates
+against itself that's sin squared its
+
+ align:start position:0%
+against itself that's sin squared its
+ 
+
+ align:start position:0%
+against itself that's sin squared its
+integral is you remember the integral of
+
+ align:start position:0%
+integral is you remember the integral of
+ 
+
+ align:start position:0%
+integral is you remember the integral of
+sin squared which is
+
+ align:start position:0%
+sin squared which is
+ 
+
+ align:start position:0%
+sin squared which is
+it's it's its average value is a half
+
+ align:start position:0%
+it's it's its average value is a half
+ 
+
+ align:start position:0%
+it's it's its average value is a half
+we're over an interval I think I'm going
+
+ align:start position:0%
+we're over an interval I think I'm going
+ 
+
+ align:start position:0%
+we're over an interval I think I'm going
+to get Pi for S squared because sin
+
+ align:start position:0%
+to get Pi for S squared because sin
+ 
+
+ align:start position:0%
+to get Pi for S squared because sin
+squar we could do that calculation
+
+ align:start position:0%
+squar we could do that calculation
+ 
+
+ align:start position:0%
+squar we could do that calculation
+separately it's a standard integral the
+
+ align:start position:0%
+separately it's a standard integral the
+ 
+
+ align:start position:0%
+separately it's a standard integral the
+integral of sin squar is pi actually
+
+ align:start position:0%
+integral of sin squar is pi actually
+ 
+
+ align:start position:0%
+integral of sin squar is pi actually
+yeah it it just uses the fact that sin^2
+
+ align:start position:0%
+yeah it it just uses the fact that sin^2
+ 
+
+ align:start position:0%
+yeah it it just uses the fact that sin^2
+X is the same as whatever it is the same
+
+ align:start position:0%
+X is the same as whatever it is the same
+ 
+
+ align:start position:0%
+X is the same as whatever it is the same
+as U is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one minus cosine 2X or something over
+
+ align:start position:0%
+one minus cosine 2X or something over
+ 
+
+ align:start position:0%
+one minus cosine 2X or something over
+two or plus who cares because the yeah
+
+ align:start position:0%
+two or plus who cares because the yeah
+ 
+
+ align:start position:0%
+two or plus who cares because the yeah
+because the integral of whichever plus
+
+ align:start position:0%
+because the integral of whichever plus
+ 
+
+ align:start position:0%
+because the integral of whichever plus
+or minus let
+
+ align:start position:0%
+or minus let
+ 
+
+ align:start position:0%
+or minus let
+me well I suppose for history sake we
+
+ align:start position:0%
+me well I suppose for history sake we
+ 
+
+ align:start position:0%
+me well I suppose for history sake we
+should get it right which is it is it a
+
+ align:start position:0%
+should get it right which is it is it a
+ 
+
+ align:start position:0%
+should get it right which is it is it a
+minus so it's looks okay now okay all
+
+ align:start position:0%
+minus so it's looks okay now okay all
+ 
+
+ align:start position:0%
+minus so it's looks okay now okay all
+right if it's wrong I didn't say it's
+
+ align:start position:0%
+right if it's wrong I didn't say it's
+ 
+
+ align:start position:0%
+right if it's wrong I didn't say it's
+wrong okay but I'm going to integrate so
+
+ align:start position:0%
+wrong okay but I'm going to integrate so
+ 
+
+ align:start position:0%
+wrong okay but I'm going to integrate so
+the co integral the cosine is z Z and
+
+ align:start position:0%
+the co integral the cosine is z Z and
+ 
+
+ align:start position:0%
+the co integral the cosine is z Z and
+the integral of the 1/2 is the part that
+
+ align:start position:0%
+the integral of the 1/2 is the part that
+ 
+
+ align:start position:0%
+the integral of the 1/2 is the part that
+the part I'm talking about that 1/2 is
+
+ align:start position:0%
+the part I'm talking about that 1/2 is
+ 
+
+ align:start position:0%
+the part I'm talking about that 1/2 is
+there all the way from minus pi to Pi so
+
+ align:start position:0%
+there all the way from minus pi to Pi so
+ 
+
+ align:start position:0%
+there all the way from minus pi to Pi so
+I get a PI from all these signs and now
+
+ align:start position:0%
+I get a PI from all these signs and now
+ 
+
+ align:start position:0%
+I get a PI from all these signs and now
+what are the what are all the terms well
+
+ align:start position:0%
+what are the what are all the terms well
+ 
+
+ align:start position:0%
+what are the what are all the terms well
+one over one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squar that just had a coefficient one
+
+ align:start position:0%
+squar that just had a coefficient one
+ 
+
+ align:start position:0%
+squar that just had a coefficient one
+but what's the next guy you remember I'm
+
+ align:start position:0%
+but what's the next guy you remember I'm
+ 
+
+ align:start position:0%
+but what's the next guy you remember I'm
+squaring it I'm integrating but I have a
+
+ align:start position:0%
+squaring it I'm integrating but I have a
+ 
+
+ align:start position:0%
+squaring it I'm integrating but I have a
+1 over3
+
+ align:start position:0%
+1 over3
+ 
+
+ align:start position:0%
+1 over3
+squar and one over 5^ s and so
+
+ align:start position:0%
+squar and one over 5^ s and so
+ 
+
+ align:start position:0%
+squar and one over 5^ s and so
+on okay and here's the PO great Point
+
+ align:start position:0%
+on okay and here's the PO great Point
+ 
+
+ align:start position:0%
+on okay and here's the PO great Point
+these two are
+
+ align:start position:0%
+these two are
+ 
+
+ align:start position:0%
+these two are
+equal I I I've got the same function
+
+ align:start position:0%
+equal I I I've got the same function
+ 
+
+ align:start position:0%
+equal I I I've got the same function
+expressed in X space and here it's
+
+ align:start position:0%
+expressed in X space and here it's
+ 
+
+ align:start position:0%
+expressed in X space and here it's
+expressed in sign space you could say in
+
+ align:start position:0%
+expressed in sign space you could say in
+ 
+
+ align:start position:0%
+expressed in sign space you could say in
+in in harmonic space okay so that's
+
+ align:start position:0%
+in in harmonic space okay so that's
+ 
+
+ align:start position:0%
+in in harmonic space okay so that's
+equal and and that's the going to be the
+
+ align:start position:0%
+equal and and that's the going to be the
+ 
+
+ align:start position:0%
+equal and and that's the going to be the
+fact in general that the in general that
+
+ align:start position:0%
+fact in general that the in general that
+ 
+
+ align:start position:0%
+fact in general that the in general that
+the integral of s of X squar I mean so
+
+ align:start position:0%
+the integral of s of X squar I mean so
+ 
+
+ align:start position:0%
+the integral of s of X squar I mean so
+the general fact will be the integral of
+
+ align:start position:0%
+the general fact will be the integral of
+ 
+
+ align:start position:0%
+the general fact will be the integral of
+s of well I'll write it down below but
+
+ align:start position:0%
+s of well I'll write it down below but
+ 
+
+ align:start position:0%
+s of well I'll write it down below but
+let let's just see what we get for
+
+ align:start position:0%
+let let's just see what we get for
+ 
+
+ align:start position:0%
+let let's just see what we get for
+numbers here so I had Pi on both
+
+ align:start position:0%
+numbers here so I had Pi on both
+ 
+
+ align:start position:0%
+numbers here so I had Pi on both
+sides and so if I lift that over there I
+
+ align:start position:0%
+sides and so if I lift that over there I
+ 
+
+ align:start position:0%
+sides and so if I lift that over there I
+get something like what do I have pi^
+
+ align:start position:0%
+get something like what do I have pi^
+ 
+
+ align:start position:0%
+get something like what do I have pi^
+squar over 16 maybe I have pi^ squ over
+
+ align:start position:0%
+squar over 16 maybe I have pi^ squ over
+ 
+
+ align:start position:0%
+squar over 16 maybe I have pi^ squ over
+8 you just get like an
+
+ align:start position:0%
+8 you just get like an
+ 
+
+ align:start position:0%
+8 you just get like an
+amazing a remarkable formula putting
+
+ align:start position:0%
+amazing a remarkable formula putting
+ 
+
+ align:start position:0%
+amazing a remarkable formula putting
+that up there would be pi^ S over 16 and
+
+ align:start position:0%
+that up there would be pi^ S over 16 and
+ 
+
+ align:start position:0%
+that up there would be pi^ S over 16 and
+the two makes it an eight and here I
+
+ align:start position:0%
+the two makes it an eight and here I
+ 
+
+ align:start position:0%
+the two makes it an eight and here I
+have the sum of 1 over 1^ 2 + 1 over 3^
+
+ align:start position:0%
+have the sum of 1 over 1^ 2 + 1 over 3^
+ 
+
+ align:start position:0%
+have the sum of 1 over 1^ 2 + 1 over 3^
+2 + 1 over 5^ squ so you know that
+
+ align:start position:0%
+2 + 1 over 5^ squ so you know that
+ 
+
+ align:start position:0%
+2 + 1 over 5^ squ so you know that
+that's a an infinite sum that I would
+
+ align:start position:0%
+that's a an infinite sum that I would
+ 
+
+ align:start position:0%
+that's a an infinite sum that I would
+not have known how to how to
+
+ align:start position:0%
+not have known how to how to
+ 
+
+ align:start position:0%
+not have known how to how to
+do except it it appears here the sum of
+
+ align:start position:0%
+do except it it appears here the sum of
+ 
+
+ align:start position:0%
+do except it it appears here the sum of
+one over all those
+
+ align:start position:0%
+one over all those
+ 
+
+ align:start position:0%
+one over all those
+squares if I T picked another example I
+
+ align:start position:0%
+squares if I T picked another example I
+ 
+
+ align:start position:0%
+squares if I T picked another example I
+could get the sum oh this was all the
+
+ align:start position:0%
+could get the sum oh this was all the
+ 
+
+ align:start position:0%
+could get the sum oh this was all the
+odd numberers squared uh if I picked a
+
+ align:start position:0%
+odd numberers squared uh if I picked a
+ 
+
+ align:start position:0%
+odd numberers squared uh if I picked a
+different function I could have got one
+
+ align:start position:0%
+different function I could have got one
+ 
+
+ align:start position:0%
+different function I could have got one
+that that had all
+
+ align:start position:0%
+that that had all
+ 
+
+ align:start position:0%
+that that had all
+the that that also had the sin 2x over 2
+
+ align:start position:0%
+the that that also had the sin 2x over 2
+ 
+
+ align:start position:0%
+the that that also had the sin 2x over 2
+and the sin 4X over 4 so this would have
+
+ align:start position:0%
+and the sin 4X over 4 so this would have
+ 
+
+ align:start position:0%
+and the sin 4X over 4 so this would have
+been the sum of all the squares do you
+
+ align:start position:0%
+been the sum of all the squares do you
+ 
+
+ align:start position:0%
+been the sum of all the squares do you
+know happen to know what that comes out
+
+ align:start position:0%
+know happen to know what that comes out
+ 
+
+ align:start position:0%
+know happen to know what that comes out
+to be I mean it's here's a way to
+
+ align:start position:0%
+to be I mean it's here's a way to
+ 
+
+ align:start position:0%
+to be I mean it's here's a way to
+compute Pi we have a formula for pi here
+
+ align:start position:0%
+compute Pi we have a formula for pi here
+ 
+
+ align:start position:0%
+compute Pi we have a formula for pi here
+uh and and we'd have another formula
+
+ align:start position:0%
+uh and and we'd have another formula
+ 
+
+ align:start position:0%
+uh and and we'd have another formula
+that involved all the spons maybe I have
+
+ align:start position:0%
+that involved all the spons maybe I have
+ 
+
+ align:start position:0%
+that involved all the spons maybe I have
+room for it up here this this would be
+
+ align:start position:0%
+room for it up here this this would be
+ 
+
+ align:start position:0%
+room for it up here this this would be
+the sum of 1 over n^2 right if if I had
+
+ align:start position:0%
+the sum of 1 over n^2 right if if I had
+ 
+
+ align:start position:0%
+the sum of 1 over n^2 right if if I had
+all this here I have only the odd ones
+
+ align:start position:0%
+all this here I have only the odd ones
+ 
+
+ align:start position:0%
+all this here I have only the odd ones
+and I get pi^ 2 over 8 you happen to
+
+ align:start position:0%
+and I get pi^ 2 over 8 you happen to
+ 
+
+ align:start position:0%
+and I get pi^ 2 over 8 you happen to
+know what I get for for the all of them
+
+ align:start position:0%
+know what I get for for the all of them
+ 
+
+ align:start position:0%
+know what I get for for the all of them
+the E you know so I'm also including one
+
+ align:start position:0%
+the E you know so I'm also including one
+ 
+
+ align:start position:0%
+the E you know so I'm also including one
+over two squar there's a quarter also in
+
+ align:start position:0%
+over two squar there's a quarter also in
+ 
+
+ align:start position:0%
+over two squar there's a quarter also in
+here and also a 16th and also a 36 in in
+
+ align:start position:0%
+here and also a 16th and also a 36 in in
+ 
+
+ align:start position:0%
+here and also a 16th and also a 36 in in
+this one and the answer happens to be
+
+ align:start position:0%
+this one and the answer happens to be
+ 
+
+ align:start position:0%
+this one and the answer happens to be
+pi^ 2 over 6
+
+ align:start position:0%
+pi^ 2 over 6
+ 
+
+ align:start position:0%
+pi^ 2 over 6
+pi^ 2 over
+
+ align:start position:0%
+pi^ 2 over
+ 
+
+ align:start position:0%
+pi^ 2 over
+6 yeah so that's
+
+ align:start position:0%
+6 yeah so that's
+ 
+
+ align:start position:0%
+6 yeah so that's
+you it's nice I mean the the important
+
+ align:start position:0%
+you it's nice I mean the the important
+ 
+
+ align:start position:0%
+you it's nice I mean the the important
+point about this energy equality is not
+
+ align:start position:0%
+point about this energy equality is not
+ 
+
+ align:start position:0%
+point about this energy equality is not
+being able to get a few very remarkable
+
+ align:start position:0%
+being able to get a few very remarkable
+ 
+
+ align:start position:0%
+being able to get a few very remarkable
+formulas for pi uh and and there's will
+
+ align:start position:0%
+formulas for pi uh and and there's will
+ 
+
+ align:start position:0%
+formulas for pi uh and and there's will
+be another remarkable formula in the
+
+ align:start position:0%
+be another remarkable formula in the
+ 
+
+ align:start position:0%
+be another remarkable formula in the
+homework uh this is a little famous do
+
+ align:start position:0%
+homework uh this is a little famous do
+ 
+
+ align:start position:0%
+homework uh this is a little famous do
+you know what the what this is is this
+
+ align:start position:0%
+you know what the what this is is this
+ 
+
+ align:start position:0%
+you know what the what this is is this
+is the this is the famous reman zeta
+
+ align:start position:0%
+is the this is the famous reman zeta
+ 
+
+ align:start position:0%
+is the this is the famous reman zeta
+function one the sum of 1/ N to the x is
+
+ align:start position:0%
+function one the sum of 1/ N to the x is
+ 
+
+ align:start position:0%
+function one the sum of 1/ N to the x is
+the zeta function at X here's the zeta
+
+ align:start position:0%
+the zeta function at X here's the zeta
+ 
+
+ align:start position:0%
+the zeta function at X here's the zeta
+function at two so if I could draw a
+
+ align:start position:0%
+function at two so if I could draw a
+ 
+
+ align:start position:0%
+function at two so if I could draw a
+Zeta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe I there are some Greek guys in
+
+ align:start position:0%
+maybe I there are some Greek guys in
+ 
+
+ align:start position:0%
+maybe I there are some Greek guys in
+this class who could do it properly but
+
+ align:start position:0%
+this class who could do it properly but
+ 
+
+ align:start position:0%
+this class who could do it properly but
+anyway HH look how chicken out
+
+ align:start position:0%
+anyway HH look how chicken out
+ 
+
+ align:start position:0%
+anyway HH look how chicken out
+Zeta of of at the value two right Z of
+
+ align:start position:0%
+Zeta of of at the value two right Z of
+ 
+
+ align:start position:0%
+Zeta of of at the value two right Z of
+two so we know Z of two we know Z of
+
+ align:start position:0%
+two so we know Z of two we know Z of
+ 
+
+ align:start position:0%
+two so we know Z of two we know Z of
+four I don't think we know Z of three it
+
+ align:start position:0%
+four I don't think we know Z of three it
+ 
+
+ align:start position:0%
+four I don't think we know Z of three it
+doesn't come it's not a I think it's not
+
+ align:start position:0%
+doesn't come it's not a I think it's not
+ 
+
+ align:start position:0%
+doesn't come it's not a I think it's not
+a a special number like pi^ squ over 6
+
+ align:start position:0%
+a a special number like pi^ squ over 6
+ 
+
+ align:start position:0%
+a a special number like pi^ squ over 6
+um so the zeta function the sum over one
+
+ align:start position:0%
+um so the zeta function the sum over one
+ 
+
+ align:start position:0%
+um so the zeta function the sum over one
+to the one over n to this thing is uh
+
+ align:start position:0%
+to the one over n to this thing is uh
+ 
+
+ align:start position:0%
+to the one over n to this thing is uh
+that's the actually that's the subject
+
+ align:start position:0%
+that's the actually that's the subject
+ 
+
+ align:start position:0%
+that's the actually that's the subject
+of a a problem that remond did not solve
+
+ align:start position:0%
+of a a problem that remond did not solve
+ 
+
+ align:start position:0%
+of a a problem that remond did not solve
+there's a problem reman did not solve
+
+ align:start position:0%
+there's a problem reman did not solve
+ 
+
+ align:start position:0%
+there's a problem reman did not solve
+and nobody has succeeded to find it to
+
+ align:start position:0%
+and nobody has succeeded to find it to
+ 
+
+ align:start position:0%
+and nobody has succeeded to find it to
+solve it
+
+ align:start position:0%
+solve it
+ 
+
+ align:start position:0%
+solve it
+since there's a million doll prize for
+
+ align:start position:0%
+since there's a million doll prize for
+ 
+
+ align:start position:0%
+since there's a million doll prize for
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+solution um my neighbors think I should
+
+ align:start position:0%
+solution um my neighbors think I should
+ 
+
+ align:start position:0%
+solution um my neighbors think I should
+be working on this but I know better uh
+
+ align:start position:0%
+be working on this but I know better uh
+ 
+
+ align:start position:0%
+be working on this but I know better uh
+uh it's going to be solved one day but
+
+ align:start position:0%
+uh it's going to be solved one day but
+ 
+
+ align:start position:0%
+uh it's going to be solved one day but
+uh it's pretty difficult and that is to
+
+ align:start position:0%
+uh it's pretty difficult and that is to
+ 
+
+ align:start position:0%
+uh it's pretty difficult and that is to
+know where this Z function where it it's
+
+ align:start position:0%
+know where this Z function where it it's
+ 
+
+ align:start position:0%
+know where this Z function where it it's
+zero of course it isn't zero at two
+
+ align:start position:0%
+zero of course it isn't zero at two
+ 
+
+ align:start position:0%
+zero of course it isn't zero at two
+because it's pi^ squ over 6 and actually
+
+ align:start position:0%
+because it's pi^ squ over 6 and actually
+ 
+
+ align:start position:0%
+because it's pi^ squ over 6 and actually
+it's the conjecture is that it's zero
+
+ align:start position:0%
+it's the conjecture is that it's zero
+ 
+
+ align:start position:0%
+it's the conjecture is that it's zero
+all the zeros have are at points complex
+
+ align:start position:0%
+all the zeros have are at points complex
+ 
+
+ align:start position:0%
+all the zeros have are at points complex
+numbers with real part a half so they're
+
+ align:start position:0%
+numbers with real part a half so they're
+ 
+
+ align:start position:0%
+numbers with real part a half so they're
+on this famous line uh the imaginary
+
+ align:start position:0%
+on this famous line uh the imaginary
+ 
+
+ align:start position:0%
+on this famous line uh the imaginary
+line with real part a half and uh that's
+
+ align:start position:0%
+line with real part a half and uh that's
+ 
+
+ align:start position:0%
+line with real part a half and uh that's
+a that that's a the most important
+
+ align:start position:0%
+a that that's a the most important
+ 
+
+ align:start position:0%
+a that that's a the most important
+problem in pure mathematics actually
+
+ align:start position:0%
+problem in pure mathematics actually
+ 
+
+ align:start position:0%
+problem in pure mathematics actually
+yeah so here we go we got we got a
+
+ align:start position:0%
+yeah so here we go we got we got a
+ 
+
+ align:start position:0%
+yeah so here we go we got we got a
+formula for pi out of this energy
+
+ align:start position:0%
+formula for pi out of this energy
+ 
+
+ align:start position:0%
+formula for pi out of this energy
+identity and I'll write it again in the
+
+ align:start position:0%
+identity and I'll write it again in the
+ 
+
+ align:start position:0%
+identity and I'll write it again in the
+once I have the complex
+
+ align:start position:0%
+once I have the complex
+ 
+
+ align:start position:0%
+once I have the complex
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+okay so but you see where it comes from
+
+ align:start position:0%
+okay so but you see where it comes from
+ 
+
+ align:start position:0%
+okay so but you see where it comes from
+it just comes from orthogonality that
+
+ align:start position:0%
+it just comes from orthogonality that
+ 
+
+ align:start position:0%
+it just comes from orthogonality that
+the fact that we could integrate that
+
+ align:start position:0%
+the fact that we could integrate that
+ 
+
+ align:start position:0%
+the fact that we could integrate that
+square is the is is what what made it
+
+ align:start position:0%
+square is the is is what what made it
+ 
+
+ align:start position:0%
+square is the is is what what made it
+all work okay let's do uh the Delta
+
+ align:start position:0%
+all work okay let's do uh the Delta
+ 
+
+ align:start position:0%
+all work okay let's do uh the Delta
+function okay so that's an even function
+
+ align:start position:0%
+function okay so that's an even function
+ 
+
+ align:start position:0%
+function okay so that's an even function
+the Delta right now I'm looking at the
+
+ align:start position:0%
+the Delta right now I'm looking at the
+ 
+
+ align:start position:0%
+the Delta right now I'm looking at the
+Delta function us pi to Pi it has the
+
+ align:start position:0%
+Delta function us pi to Pi it has the
+ 
+
+ align:start position:0%
+Delta function us pi to Pi it has the
+spike at
+
+ align:start position:0%
+spike at
+ 
+
+ align:start position:0%
+spike at
+zero and it's certainly even so we'll we
+
+ align:start position:0%
+zero and it's certainly even so we'll we
+ 
+
+ align:start position:0%
+zero and it's certainly even so we'll we
+expect cosiness and what are the
+
+ align:start position:0%
+expect cosiness and what are the
+ 
+
+ align:start position:0%
+expect cosiness and what are the
+coefficients so it's just uh it's just
+
+ align:start position:0%
+coefficients so it's just uh it's just
+ 
+
+ align:start position:0%
+coefficients so it's just uh it's just
+important one to know very important
+
+ align:start position:0%
+important one to know very important
+ 
+
+ align:start position:0%
+important one to know very important
+example uh so what's a not in general
+
+ align:start position:0%
+example uh so what's a not in general
+ 
+
+ align:start position:0%
+example uh so what's a not in general
+the coefficient a not in the Fier series
+
+ align:start position:0%
+the coefficient a not in the Fier series
+ 
+
+ align:start position:0%
+the coefficient a not in the Fier series
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the if I have a function Delta of x s
+
+ align:start position:0%
+the if I have a function Delta of x s
+ 
+
+ align:start position:0%
+the if I have a function Delta of x s
+ofx whatever my function the a not
+
+ align:start position:0%
+ofx whatever my function the a not
+ 
+
+ align:start position:0%
+ofx whatever my function the a not
+coefficient is the average a for average
+
+ align:start position:0%
+coefficient is the average a for average
+ 
+
+ align:start position:0%
+coefficient is the average a for average
+there a not is the average value so what
+
+ align:start position:0%
+there a not is the average value so what
+ 
+
+ align:start position:0%
+there a not is the average value so what
+is so this has the this is 1 over 2 pi
+
+ align:start position:0%
+is so this has the this is 1 over 2 pi
+ 
+
+ align:start position:0%
+is so this has the this is 1 over 2 pi
+the integral from minus pi to Pi of my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function where did that come from I just
+
+ align:start position:0%
+function where did that come from I just
+ 
+
+ align:start position:0%
+function where did that come from I just
+integrate I just multiply both sides by
+
+ align:start position:0%
+integrate I just multiply both sides by
+ 
+
+ align:start position:0%
+integrate I just multiply both sides by
+one and and or or by 1 over two pi and
+
+ align:start position:0%
+one and and or or by 1 over two pi and
+ 
+
+ align:start position:0%
+one and and or or by 1 over two pi and
+integrated it
+
+ align:start position:0%
+integrated it
+ 
+
+ align:start position:0%
+integrated it
+and all those terms disappeared and I
+
+ align:start position:0%
+and all those terms disappeared and I
+ 
+
+ align:start position:0%
+and all those terms disappeared and I
+was left with a not and what's the
+
+ align:start position:0%
+was left with a not and what's the
+ 
+
+ align:start position:0%
+was left with a not and what's the
+answer everybody knows that
+
+ align:start position:0%
+answer everybody knows that
+ 
+
+ align:start position:0%
+answer everybody knows that
+integral the integral of the Delta
+
+ align:start position:0%
+integral the integral of the Delta
+ 
+
+ align:start position:0%
+integral the integral of the Delta
+function is one so I just get one over 2
+
+ align:start position:0%
+function is one so I just get one over 2
+ 
+
+ align:start position:0%
+function is one so I just get one over 2
+pi so one over 2 pi okay now ready for
+
+ align:start position:0%
+pi so one over 2 pi okay now ready for
+ 
+
+ align:start position:0%
+pi so one over 2 pi okay now ready for
+A1 how much how much of cosine X do I
+
+ align:start position:0%
+A1 how much how much of cosine X do I
+ 
+
+ align:start position:0%
+A1 how much how much of cosine X do I
+have can I just change this formula to
+
+ align:start position:0%
+have can I just change this formula to
+ 
+
+ align:start position:0%
+have can I just change this formula to
+to give me A1 and you can tell me what
+
+ align:start position:0%
+to give me A1 and you can tell me what
+ 
+
+ align:start position:0%
+to give me A1 and you can tell me what
+it gives well let me do it do it here
+
+ align:start position:0%
+it gives well let me do it do it here
+ 
+
+ align:start position:0%
+it gives well let me do it do it here
+here's A1
+
+ align:start position:0%
+here's A1
+ 
+
+ align:start position:0%
+here's A1
+what's the formula for
+
+ align:start position:0%
+what's the formula for
+ 
+
+ align:start position:0%
+what's the formula for
+A1 it's just like B1 like the sign
+
+ align:start position:0%
+A1 it's just like B1 like the sign
+ 
+
+ align:start position:0%
+A1 it's just like B1 like the sign
+formulas you have to remember you're
+
+ align:start position:0%
+formulas you have to remember you're
+ 
+
+ align:start position:0%
+formulas you have to remember you're
+only dividing by pi because that average
+
+ align:start position:0%
+only dividing by pi because that average
+ 
+
+ align:start position:0%
+only dividing by pi because that average
+value was a half as we saw and you then
+
+ align:start position:0%
+value was a half as we saw and you then
+ 
+
+ align:start position:0%
+value was a half as we saw and you then
+you have the integral of whatever your
+
+ align:start position:0%
+you have the integral of whatever your
+ 
+
+ align:start position:0%
+you have the integral of whatever your
+function is Delta of X in this case
+
+ align:start position:0%
+function is Delta of X in this case
+ 
+
+ align:start position:0%
+function is Delta of X in this case
+times the cosine of 1x if we're looking
+
+ align:start position:0%
+times the cosine of 1x if we're looking
+ 
+
+ align:start position:0%
+times the cosine of 1x if we're looking
+for A1 we've multiplied about both sides
+
+ align:start position:0%
+for A1 we've multiplied about both sides
+ 
+
+ align:start position:0%
+for A1 we've multiplied about both sides
+by cos x and integrated and what what
+
+ align:start position:0%
+by cos x and integrated and what what
+ 
+
+ align:start position:0%
+by cos x and integrated and what what
+answer do we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get for
+
+ align:start position:0%
+get for
+ 
+
+ align:start position:0%
+get for
+A1 what's the integral of Delta of X
+
+ align:start position:0%
+A1 what's the integral of Delta of X
+ 
+
+ align:start position:0%
+A1 what's the integral of Delta of X
+time cosine
+
+ align:start position:0%
+time cosine
+ 
+
+ align:start position:0%
+time cosine
+X DX which I should put in a DX and the
+
+ align:start position:0%
+X DX which I should put in a DX and the
+ 
+
+ align:start position:0%
+X DX which I should put in a DX and the
+answer is one also one the Delta
+
+ align:start position:0%
+answer is one also one the Delta
+ 
+
+ align:start position:0%
+answer is one also one the Delta
+function this Spike picks out the value
+
+ align:start position:0%
+function this Spike picks out the value
+ 
+
+ align:start position:0%
+function this Spike picks out the value
+of this function at the
+
+ align:start position:0%
+of this function at the
+ 
+
+ align:start position:0%
+of this function at the
+spike because of course it doesn't
+
+ align:start position:0%
+spike because of course it doesn't
+ 
+
+ align:start position:0%
+spike because of course it doesn't
+matter what that function is away from
+
+ align:start position:0%
+matter what that function is away from
+ 
+
+ align:start position:0%
+matter what that function is away from
+the spike because the other Factor Delta
+
+ align:start position:0%
+the spike because the other Factor Delta
+ 
+
+ align:start position:0%
+the spike because the other Factor Delta
+is zero everything is at that Spike all
+
+ align:start position:0%
+is zero everything is at that Spike all
+ 
+
+ align:start position:0%
+is zero everything is at that Spike all
+the action and this happens to be one at
+
+ align:start position:0%
+the action and this happens to be one at
+ 
+
+ align:start position:0%
+the action and this happens to be one at
+the spike so I get a one over
+
+ align:start position:0%
+the spike so I get a one over
+ 
+
+ align:start position:0%
+the spike so I get a one over
+pi and actually the same formula for all
+
+ align:start position:0%
+pi and actually the same formula for all
+ 
+
+ align:start position:0%
+pi and actually the same formula for all
+these guys this will be the same with
+
+ align:start position:0%
+these guys this will be the same with
+ 
+
+ align:start position:0%
+these guys this will be the same with
+cos x change to cos
+
+ align:start position:0%
+cos x change to cos
+ 
+
+ align:start position:0%
+cos x change to cos
+2X and what will be the answer
+
+ align:start position:0%
+2X and what will be the answer
+ 
+
+ align:start position:0%
+2X and what will be the answer
+now again one right it's the value this
+
+ align:start position:0%
+now again one right it's the value this
+ 
+
+ align:start position:0%
+now again one right it's the value this
+integral the formula for H 2 would have
+
+ align:start position:0%
+integral the formula for H 2 would have
+ 
+
+ align:start position:0%
+integral the formula for H 2 would have
+come by multiplying both sides by cos 2x
+
+ align:start position:0%
+come by multiplying both sides by cos 2x
+ 
+
+ align:start position:0%
+come by multiplying both sides by cos 2x
+integrating uh uh and the integral of
+
+ align:start position:0%
+integrating uh uh and the integral of
+ 
+
+ align:start position:0%
+integrating uh uh and the integral of
+cos squar would give me the pi and I'm
+
+ align:start position:0%
+cos squar would give me the pi and I'm
+ 
+
+ align:start position:0%
+cos squar would give me the pi and I'm
+dividing by the pi and I just need that
+
+ align:start position:0%
+dividing by the pi and I just need that
+ 
+
+ align:start position:0%
+dividing by the pi and I just need that
+integral and it's easy it's also one
+
+ align:start position:0%
+integral and it's easy it's also one
+ 
+
+ align:start position:0%
+integral and it's easy it's also one
+over Pi so all these are one over Pi let
+
+ align:start position:0%
+over Pi so all these are one over Pi let
+ 
+
+ align:start position:0%
+over Pi so all these are one over Pi let
+me just put in the Formula 1 over 2 pi
+
+ align:start position:0%
+me just put in the Formula 1 over 2 pi
+ 
+
+ align:start position:0%
+me just put in the Formula 1 over 2 pi
+and all the rest are one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+cos 3x there're all the cosiness are
+
+ align:start position:0%
+cos 3x there're all the cosiness are
+ 
+
+ align:start position:0%
+cos 3x there're all the cosiness are
+there all in the same
+
+ align:start position:0%
+there all in the same
+ 
+
+ align:start position:0%
+there all in the same
+amount uh and the constant term is uh uh
+
+ align:start position:0%
+amount uh and the constant term is uh uh
+ 
+
+ align:start position:0%
+amount uh and the constant term is uh uh
+slightly
+
+ align:start position:0%
+slightly
+ 
+
+ align:start position:0%
+slightly
+different okay that's
+
+ align:start position:0%
+different okay that's
+ 
+
+ align:start position:0%
+different okay that's
+the that's the formal fora series for
+
+ align:start position:0%
+the that's the formal fora series for
+ 
+
+ align:start position:0%
+the that's the formal fora series for
+the Delta function formal meaning you
+
+ align:start position:0%
+the Delta function formal meaning you
+ 
+
+ align:start position:0%
+the Delta function formal meaning you
+can use it to to uh compute uh of course
+
+ align:start position:0%
+can use it to to uh compute uh of course
+ 
+
+ align:start position:0%
+can use it to to uh compute uh of course
+some things will fail like what's the
+
+ align:start position:0%
+some things will fail like what's the
+ 
+
+ align:start position:0%
+some things will fail like what's the
+energy what's if I integrate if I try to
+
+ align:start position:0%
+energy what's if I integrate if I try to
+ 
+
+ align:start position:0%
+energy what's if I integrate if I try to
+do energy in X space of the Delta
+
+ align:start position:0%
+do energy in X space of the Delta
+ 
+
+ align:start position:0%
+do energy in X space of the Delta
+function or energy in k space what
+
+ align:start position:0%
+function or energy in k space what
+ 
+
+ align:start position:0%
+function or energy in k space what
+answer would I get well the right the
+
+ align:start position:0%
+answer would I get well the right the
+ 
+
+ align:start position:0%
+answer would I get well the right the
+integral of Delta squared its energy is
+
+ align:start position:0%
+integral of Delta squared its energy is
+ 
+
+ align:start position:0%
+integral of Delta squared its energy is
+infinite right the integral of Delta if
+
+ align:start position:0%
+infinite right the integral of Delta if
+ 
+
+ align:start position:0%
+infinite right the integral of Delta if
+I have Delta times Delta then I'm really
+
+ align:start position:0%
+I have Delta times Delta then I'm really
+ 
+
+ align:start position:0%
+I have Delta times Delta then I'm really
+in trouble right because because this
+
+ align:start position:0%
+in trouble right because because this
+ 
+
+ align:start position:0%
+in trouble right because because this
+Delta says if I can speak informally
+
+ align:start position:0%
+Delta says if I can speak informally
+ 
+
+ align:start position:0%
+Delta says if I can speak informally
+that Delta says take the value of this
+
+ align:start position:0%
+that Delta says take the value of this
+ 
+
+ align:start position:0%
+that Delta says take the value of this
+function at zero but of course that's
+
+ align:start position:0%
+function at zero but of course that's
+ 
+
+ align:start position:0%
+function at zero but of course that's
+infinite so so that would be infinite
+
+ align:start position:0%
+infinite so so that would be infinite
+ 
+
+ align:start position:0%
+infinite so so that would be infinite
+that would be that would be the energy
+
+ align:start position:0%
+that would be that would be the energy
+ 
+
+ align:start position:0%
+that would be that would be the energy
+in the in X space what about the energy
+
+ align:start position:0%
+in the in X space what about the energy
+ 
+
+ align:start position:0%
+in the in X space what about the energy
+in KS space well I
+
+ align:start position:0%
+in KS space well I
+ 
+
+ align:start position:0%
+in KS space well I
+haven't let's think what is what's the
+
+ align:start position:0%
+haven't let's think what is what's the
+ 
+
+ align:start position:0%
+haven't let's think what is what's the
+energy in k space I'm going to do the
+
+ align:start position:0%
+energy in k space I'm going to do the
+ 
+
+ align:start position:0%
+energy in k space I'm going to do the
+squares of the coefficients you remember
+
+ align:start position:0%
+squares of the coefficients you remember
+ 
+
+ align:start position:0%
+squares of the coefficients you remember
+that's what I had down
+
+ align:start position:0%
+that's what I had down
+ 
+
+ align:start position:0%
+that's what I had down
+here and I'll have it again in a moment
+
+ align:start position:0%
+here and I'll have it again in a moment
+ 
+
+ align:start position:0%
+here and I'll have it again in a moment
+it's the sum of the squares of the
+
+ align:start position:0%
+it's the sum of the squares of the
+ 
+
+ align:start position:0%
+it's the sum of the squares of the
+coefficients fixed up by factors of Pi
+
+ align:start position:0%
+coefficients fixed up by factors of Pi
+ 
+
+ align:start position:0%
+coefficients fixed up by factors of Pi
+uh and here all the coefficients are
+
+ align:start position:0%
+uh and here all the coefficients are
+ 
+
+ align:start position:0%
+uh and here all the coefficients are
+constant so that sum is infinite again
+
+ align:start position:0%
+constant so that sum is infinite again
+ 
+
+ align:start position:0%
+constant so that sum is infinite again
+it's the sum of squares of constant
+
+ align:start position:0%
+it's the sum of squares of constant
+ 
+
+ align:start position:0%
+it's the sum of squares of constant
+constant constant constant and that
+
+ align:start position:0%
+constant constant constant and that
+ 
+
+ align:start position:0%
+constant constant constant and that
+series doesn't converge it blows up so
+
+ align:start position:0%
+series doesn't converge it blows up so
+ 
+
+ align:start position:0%
+series doesn't converge it blows up so
+the energy is infinite that's that's
+
+ align:start position:0%
+the energy is infinite that's that's
+ 
+
+ align:start position:0%
+the energy is infinite that's that's
+okay the the key is that formula okay
+
+ align:start position:0%
+okay the the key is that formula okay
+ 
+
+ align:start position:0%
+okay the the key is that formula okay
+there's there's the formula to remember
+
+ align:start position:0%
+there's there's the formula to remember
+ 
+
+ align:start position:0%
+there's there's the formula to remember
+there's the formula on forever every
+
+ align:start position:0%
+there's the formula on forever every
+ 
+
+ align:start position:0%
+there's the formula on forever every
+frequency is in here uh to the to the
+
+ align:start position:0%
+frequency is in here uh to the to the
+ 
+
+ align:start position:0%
+frequency is in here uh to the to the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+amount yeah okay good that that's that's
+
+ align:start position:0%
+amount yeah okay good that that's that's
+ 
+
+ align:start position:0%
+amount yeah okay good that that's that's
+the Delta function example okay ready to
+
+ align:start position:0%
+the Delta function example okay ready to
+ 
+
+ align:start position:0%
+the Delta function example okay ready to
+go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complex yeah comp complex is no big deal
+
+ align:start position:0%
+complex yeah comp complex is no big deal
+ 
+
+ align:start position:0%
+complex yeah comp complex is no big deal
+because we know actually you can tell me
+
+ align:start position:0%
+because we know actually you can tell me
+ 
+
+ align:start position:0%
+because we know actually you can tell me
+the the the complex series for the Delta
+
+ align:start position:0%
+the the the complex series for the Delta
+ 
+
+ align:start position:0%
+the the the complex series for the Delta
+function I'll write it right underneath
+
+ align:start position:0%
+function I'll write it right underneath
+ 
+
+ align:start position:0%
+function I'll write it right underneath
+the complex series for the Delta
+
+ align:start position:0%
+the complex series for the Delta
+ 
+
+ align:start position:0%
+the complex series for the Delta
+function just turn these guys
+
+ align:start position:0%
+function just turn these guys
+ 
+
+ align:start position:0%
+function just turn these guys
+into e to the I Theta e to the I x's and
+
+ align:start position:0%
+into e to the I Theta e to the I x's and
+ 
+
+ align:start position:0%
+into e to the I Theta e to the I x's and
+e to the i 2 X's and e to the i e to the
+
+ align:start position:0%
+e to the i 2 X's and e to the i e to the
+ 
+
+ align:start position:0%
+e to the i 2 X's and e to the i e to the
+minus I 2x's just term by term just to
+
+ align:start position:0%
+minus I 2x's just term by term just to
+ 
+
+ align:start position:0%
+minus I 2x's just term by term just to
+see it you know see it clearly for this
+
+ align:start position:0%
+see it you know see it clearly for this
+ 
+
+ align:start position:0%
+see it you know see it clearly for this
+great example so what do what does
+
+ align:start position:0%
+great example so what do what does
+ 
+
+ align:start position:0%
+great example so what do what does
+cosine 2X look like in term terms of uh
+
+ align:start position:0%
+cosine 2X look like in term terms of uh
+ 
+
+ align:start position:0%
+cosine 2X look like in term terms of uh
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+exponentials everybody knows cost Cost
+
+ align:start position:0%
+exponentials everybody knows cost Cost
+ 
+
+ align:start position:0%
+exponentials everybody knows cost Cost
+cos x is the same
+
+ align:start position:0%
+cos x is the same
+ 
+
+ align:start position:0%
+cos x is the same
+as e to the
+
+ align:start position:0%
+as e to the
+ 
+
+ align:start position:0%
+as e to the
+iix and e to the minus IX right divided
+
+ align:start position:0%
+iix and e to the minus IX right divided
+ 
+
+ align:start position:0%
+iix and e to the minus IX right divided
+by two because this is cos x plus I sinx
+
+ align:start position:0%
+by two because this is cos x plus I sinx
+ 
+
+ align:start position:0%
+by two because this is cos x plus I sinx
+this is cos x minus I sinx when I add
+
+ align:start position:0%
+this is cos x minus I sinx when I add
+ 
+
+ align:start position:0%
+this is cos x minus I sinx when I add
+them I get two cosine X's so I must
+
+ align:start position:0%
+them I get two cosine X's so I must
+ 
+
+ align:start position:0%
+them I get two cosine X's so I must
+divide by two let me divide by two all
+
+ align:start position:0%
+divide by two let me divide by two all
+ 
+
+ align:start position:0%
+divide by two let me divide by two all
+the way so so I'm dividing this one over
+
+ align:start position:0%
+the way so so I'm dividing this one over
+ 
+
+ align:start position:0%
+the way so so I'm dividing this one over
+Pi by two you you'll see it's so much
+
+ align:start position:0%
+Pi by two you you'll see it's so much
+ 
+
+ align:start position:0%
+Pi by two you you'll see it's so much
+nicer so one over 2 pi * the one that's
+
+ align:start position:0%
+nicer so one over 2 pi * the one that's
+ 
+
+ align:start position:0%
+nicer so one over 2 pi * the one that's
+our first guy and now I've got the next
+
+ align:start position:0%
+our first guy and now I've got the next
+ 
+
+ align:start position:0%
+our first guy and now I've got the next
+guy right because I need to divide by
+
+ align:start position:0%
+guy right because I need to divide by
+ 
+
+ align:start position:0%
+guy right because I need to divide by
+the two to get the cosine and there's my
+
+ align:start position:0%
+the two to get the cosine and there's my
+ 
+
+ align:start position:0%
+the two to get the cosine and there's my
+two okay what's the next what do I have
+
+ align:start position:0%
+two okay what's the next what do I have
+ 
+
+ align:start position:0%
+two okay what's the next what do I have
+next from this guy one over pi
+
+ align:start position:0%
+next from this guy one over pi
+ 
+
+ align:start position:0%
+next from this guy one over pi
+still there what's cosine of 2x if I if
+
+ align:start position:0%
+still there what's cosine of 2x if I if
+ 
+
+ align:start position:0%
+still there what's cosine of 2x if I if
+I want to write it in terms of complex
+
+ align:start position:0%
+I want to write it in terms of complex
+ 
+
+ align:start position:0%
+I want to write it in terms of complex
+exponentials so this guy now I'm ready
+
+ align:start position:0%
+exponentials so this guy now I'm ready
+ 
+
+ align:start position:0%
+exponentials so this guy now I'm ready
+for him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is e to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i2x
+
+ align:start position:0%
+i2x
+ 
+
+ align:start position:0%
+i2x
+and e to the minus
+
+ align:start position:0%
+and e to the minus
+ 
+
+ align:start position:0%
+and e to the minus
+i2x divided by two and there's my two do
+
+ align:start position:0%
+i2x divided by two and there's my two do
+ 
+
+ align:start position:0%
+i2x divided by two and there's my two do
+you see what's happening it's like
+
+ align:start position:0%
+you see what's happening it's like
+ 
+
+ align:start position:0%
+you see what's happening it's like
+there's an example to show you why the
+
+ align:start position:0%
+there's an example to show you why the
+ 
+
+ align:start position:0%
+there's an example to show you why the
+complex case is so nice here we had to
+
+ align:start position:0%
+complex case is so nice here we had to
+ 
+
+ align:start position:0%
+complex case is so nice here we had to
+remember uh a different number for the
+
+ align:start position:0%
+remember uh a different number for the
+ 
+
+ align:start position:0%
+remember uh a different number for the
+for a not here it it it's just so the
+
+ align:start position:0%
+for a not here it it it's just so the
+ 
+
+ align:start position:0%
+for a not here it it it's just so the
+next one will be e to the i3x and e to
+
+ align:start position:0%
+next one will be e to the i3x and e to
+ 
+
+ align:start position:0%
+next one will be e to the i3x and e to
+the minus i3x so the the the the Delta
+
+ align:start position:0%
+the minus i3x so the the the the Delta
+ 
+
+ align:start position:0%
+the minus i3x so the the the the Delta
+function in the complex 4 a series all
+
+ align:start position:0%
+function in the complex 4 a series all
+ 
+
+ align:start position:0%
+function in the complex 4 a series all
+the terms have coefficients one divided
+
+ align:start position:0%
+the terms have coefficients one divided
+ 
+
+ align:start position:0%
+the terms have coefficients one divided
+the two Pi that's a great example great
+
+ align:start position:0%
+the two Pi that's a great example great
+ 
+
+ align:start position:0%
+the two Pi that's a great example great
+example yeah and of course we see again
+
+ align:start position:0%
+example yeah and of course we see again
+ 
+
+ align:start position:0%
+example yeah and of course we see again
+that uh the sum of squares oh yeah so
+
+ align:start position:0%
+that uh the sum of squares oh yeah so
+ 
+
+ align:start position:0%
+that uh the sum of squares oh yeah so
+let's get to the let's do the complex
+
+ align:start position:0%
+let's get to the let's do the complex
+ 
+
+ align:start position:0%
+let's get to the let's do the complex
+formula uh the complex formula by which
+
+ align:start position:0%
+formula uh the complex formula by which
+ 
+
+ align:start position:0%
+formula uh the complex formula by which
+I mean I'm taking any function
+
+ align:start position:0%
+I mean I'm taking any function
+ 
+
+ align:start position:0%
+I mean I'm taking any function
+f not
+
+ align:start position:0%
+f not
+ 
+
+ align:start position:0%
+f not
+necessarily even not necessarily odd not
+
+ align:start position:0%
+necessarily even not necessarily odd not
+ 
+
+ align:start position:0%
+necessarily even not necessarily odd not
+necessarily real any function it can now
+
+ align:start position:0%
+necessarily real any function it can now
+ 
+
+ align:start position:0%
+necessarily real any function it can now
+be a complex function because we're
+
+ align:start position:0%
+be a complex function because we're
+ 
+
+ align:start position:0%
+be a complex function because we're
+going to use complex things here so I'll
+
+ align:start position:0%
+going to use complex things here so I'll
+ 
+
+ align:start position:0%
+going to use complex things here so I'll
+have all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the complex exponentials for integer K
+
+ align:start position:0%
+the complex exponentials for integer K
+ 
+
+ align:start position:0%
+the complex exponentials for integer K
+this K is an integer but it can go
+
+ align:start position:0%
+this K is an integer but it can go
+ 
+
+ align:start position:0%
+this K is an integer but it can go
+from minus infinity to
+
+ align:start position:0%
+from minus infinity to
+ 
+
+ align:start position:0%
+from minus infinity to
+Infinity that's that's the complex form
+
+ align:start position:0%
+Infinity that's that's the complex form
+ 
+
+ align:start position:0%
+Infinity that's that's the complex form
+f ofx is the
+
+ align:start position:0%
+f ofx is the
+ 
+
+ align:start position:0%
+f ofx is the
+the the uh is a is a series again the
+
+ align:start position:0%
+the the uh is a is a series again the
+ 
+
+ align:start position:0%
+the the uh is a is a series again the
+beauty is that every term looks the
+
+ align:start position:0%
+beauty is that every term looks the
+ 
+
+ align:start position:0%
+beauty is that every term looks the
+same the thing you have to remember is
+
+ align:start position:0%
+same the thing you have to remember is
+ 
+
+ align:start position:0%
+same the thing you have to remember is
+that K negative K is allowed as well as
+
+ align:start position:0%
+that K negative K is allowed as well as
+ 
+
+ align:start position:0%
+that K negative K is allowed as well as
+positive K you see that we need we
+
+ align:start position:0%
+positive K you see that we need we
+ 
+
+ align:start position:0%
+positive K you see that we need we
+needed the negative K to get
+
+ align:start position:0%
+needed the negative K to get
+ 
+
+ align:start position:0%
+needed the negative K to get
+cosiness K was minus one there K was
+
+ align:start position:0%
+cosiness K was minus one there K was
+ 
+
+ align:start position:0%
+cosiness K was minus one there K was
+minus two there and for signs we would
+
+ align:start position:0%
+minus two there and for signs we would
+ 
+
+ align:start position:0%
+minus two there and for signs we would
+also need them so so cosiness go into it
+
+ align:start position:0%
+also need them so so cosiness go into it
+ 
+
+ align:start position:0%
+also need them so so cosiness go into it
+signs go into it f ofx could be complex
+
+ align:start position:0%
+signs go into it f ofx could be complex
+ 
+
+ align:start position:0%
+signs go into it f ofx could be complex
+that's the complex Series so maybe we
+
+ align:start position:0%
+that's the complex Series so maybe we
+ 
+
+ align:start position:0%
+that's the complex Series so maybe we
+should we could have started with that
+
+ align:start position:0%
+should we could have started with that
+ 
+
+ align:start position:0%
+should we could have started with that
+series but but we didn't we came to it
+
+ align:start position:0%
+series but but we didn't we came to it
+ 
+
+ align:start position:0%
+series but but we didn't we came to it
+here but let's what's the formula for
+
+ align:start position:0%
+here but let's what's the formula for
+ 
+
+ align:start position:0%
+here but let's what's the formula for
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+coefficients okay
+
+ align:start position:0%
+coefficients okay
+ 
+
+ align:start position:0%
+coefficients okay
+actually for the next half hour now we
+
+ align:start position:0%
+actually for the next half hour now we
+ 
+
+ align:start position:0%
+actually for the next half hour now we
+have to think complex and that will
+
+ align:start position:0%
+have to think complex and that will
+ 
+
+ align:start position:0%
+have to think complex and that will
+bring a few changes so watch for the
+
+ align:start position:0%
+bring a few changes so watch for the
+ 
+
+ align:start position:0%
+bring a few changes so watch for the
+changes you you see that it's we're
+
+ align:start position:0%
+changes you you see that it's we're
+ 
+
+ align:start position:0%
+changes you you see that it's we're
+almost in in the same
+
+ align:start position:0%
+almost in in the same
+ 
+
+ align:start position:0%
+almost in in the same
+uh ballp part but there are a couple of
+
+ align:start position:0%
+uh ballp part but there are a couple of
+ 
+
+ align:start position:0%
+uh ballp part but there are a couple of
+things to notice so let me write down
+
+ align:start position:0%
+things to notice so let me write down
+ 
+
+ align:start position:0%
+things to notice so let me write down
+that series again minus infinity to
+
+ align:start position:0%
+that series again minus infinity to
+ 
+
+ align:start position:0%
+that series again minus infinity to
+Infinity of some coefficient e to the I
+
+ align:start position:0%
+Infinity of some coefficient e to the I
+ 
+
+ align:start position:0%
+Infinity of some coefficient e to the I
+KX now what is
+
+ align:start position:0%
+KX now what is
+ 
+
+ align:start position:0%
+KX now what is
+CK what is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula for
+
+ align:start position:0%
+formula for
+ 
+
+ align:start position:0%
+formula for
+CK as soon as we answer that question
+
+ align:start position:0%
+CK as soon as we answer that question
+ 
+
+ align:start position:0%
+CK as soon as we answer that question
+you'll see the new the new aspect for
+
+ align:start position:0%
+you'll see the new the new aspect for
+ 
+
+ align:start position:0%
+you'll see the new the new aspect for
+complex how am I how do I find
+
+ align:start position:0%
+complex how am I how do I find
+ 
+
+ align:start position:0%
+complex how am I how do I find
+coefficients I multiply by something I
+
+ align:start position:0%
+coefficients I multiply by something I
+ 
+
+ align:start position:0%
+coefficients I multiply by something I
+integrate and I use orthogonality always
+
+ align:start position:0%
+integrate and I use orthogonality always
+ 
+
+ align:start position:0%
+integrate and I use orthogonality always
+same same ideas just repeat after repeat
+
+ align:start position:0%
+same same ideas just repeat after repeat
+ 
+
+ align:start position:0%
+same same ideas just repeat after repeat
+the question is what do I multiply with
+
+ align:start position:0%
+the question is what do I multiply with
+ 
+
+ align:start position:0%
+the question is what do I multiply with
+by if I wanted to know
+
+ align:start position:0%
+by if I wanted to know
+ 
+
+ align:start position:0%
+by if I wanted to know
+C3 suppose I want to know a formula for
+
+ align:start position:0%
+C3 suppose I want to know a formula for
+ 
+
+ align:start position:0%
+C3 suppose I want to know a formula for
+C3 the coefficient what am I going to
+
+ align:start position:0%
+C3 the coefficient what am I going to
+ 
+
+ align:start position:0%
+C3 the coefficient what am I going to
+multiply by I that's going to give me
+
+ align:start position:0%
+multiply by I that's going to give me
+ 
+
+ align:start position:0%
+multiply by I that's going to give me
+the orthogonality I need that all the
+
+ align:start position:0%
+the orthogonality I need that all the
+ 
+
+ align:start position:0%
+the orthogonality I need that all the
+other integrals are going to disappear
+
+ align:start position:0%
+other integrals are going to disappear
+ 
+
+ align:start position:0%
+other integrals are going to disappear
+that's the key I want to multiply by
+
+ align:start position:0%
+that's the key I want to multiply by
+ 
+
+ align:start position:0%
+that's the key I want to multiply by
+something so that when I integrate all
+
+ align:start position:0%
+something so that when I integrate all
+ 
+
+ align:start position:0%
+something so that when I integrate all
+the other integrals are going to
+
+ align:start position:0%
+the other integrals are going to
+ 
+
+ align:start position:0%
+the other integrals are going to
+disappear and let's just do it here
+
+ align:start position:0%
+disappear and let's just do it here
+ 
+
+ align:start position:0%
+disappear and let's just do it here
+suppose I have e to the
+
+ align:start position:0%
+suppose I have e to the
+ 
+
+ align:start position:0%
+suppose I have e to the
+I 5x and I would like
+
+ align:start position:0%
+I 5x and I would like
+ 
+
+ align:start position:0%
+I 5x and I would like
+that I'm looking for the the oh no sorry
+
+ align:start position:0%
+that I'm looking for the the oh no sorry
+ 
+
+ align:start position:0%
+that I'm looking for the the oh no sorry
+I'm looking for C3 so I'll look look at
+
+ align:start position:0%
+I'm looking for C3 so I'll look look at
+ 
+
+ align:start position:0%
+I'm looking for C3 so I'll look look at
+e to the by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3x so so
+
+ align:start position:0%
+3x so so
+ 
+
+ align:start position:0%
+3x so so
+watch this is the small point we have to
+
+ align:start position:0%
+watch this is the small point we have to
+ 
+
+ align:start position:0%
+watch this is the small point we have to
+make so so I'm looking for the E to the
+
+ align:start position:0%
+make so so I'm looking for the E to the
+ 
+
+ align:start position:0%
+make so so I'm looking for the E to the
+i3x so I'm going to multiply by
+
+ align:start position:0%
+i3x so I'm going to multiply by
+ 
+
+ align:start position:0%
+i3x so I'm going to multiply by
+something and I'm going to integrate and
+
+ align:start position:0%
+something and I'm going to integrate and
+ 
+
+ align:start position:0%
+something and I'm going to integrate and
+what would be the good thing to multiply
+
+ align:start position:0%
+what would be the good thing to multiply
+ 
+
+ align:start position:0%
+what would be the good thing to multiply
+by well you would say if you were just a
+
+ align:start position:0%
+by well you would say if you were just a
+ 
+
+ align:start position:0%
+by well you would say if you were just a
+real person you would say multiply by e
+
+ align:start position:0%
+real person you would say multiply by e
+ 
+
+ align:start position:0%
+real person you would say multiply by e
+to the i3x and integrate and hope for
+
+ align:start position:0%
+to the i3x and integrate and hope for
+ 
+
+ align:start position:0%
+to the i3x and integrate and hope for
+getting zero you won't get zero If I
+
+ align:start position:0%
+getting zero you won't get zero If I
+ 
+
+ align:start position:0%
+getting zero you won't get zero If I
+multiply e to the i3x I'm sorry you you
+
+ align:start position:0%
+multiply e to the i3x I'm sorry you you
+ 
+
+ align:start position:0%
+multiply e to the i3x I'm sorry you you
+might say m yeah what am I doing here I
+
+ align:start position:0%
+might say m yeah what am I doing here I
+ 
+
+ align:start position:0%
+might say m yeah what am I doing here I
+I I'm trying to check orthogonality let
+
+ align:start position:0%
+I I'm trying to check orthogonality let
+ 
+
+ align:start position:0%
+I I'm trying to check orthogonality let
+me let me instead of three use a a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KX okay so that's a typical complex one
+
+ align:start position:0%
+KX okay so that's a typical complex one
+ 
+
+ align:start position:0%
+KX okay so that's a typical complex one
+it's any one of these guys and I would
+
+ align:start position:0%
+it's any one of these guys and I would
+ 
+
+ align:start position:0%
+it's any one of these guys and I would
+like to multiply it I would I would I
+
+ align:start position:0%
+like to multiply it I would I would I
+ 
+
+ align:start position:0%
+like to multiply it I would I would I
+want to see what's
+
+ align:start position:0%
+want to see what's
+ 
+
+ align:start position:0%
+want to see what's
+orthogonality that's what I'm asking
+
+ align:start position:0%
+orthogonality that's what I'm asking
+ 
+
+ align:start position:0%
+orthogonality that's what I'm asking
+everything hinged on orthogonality we've
+
+ align:start position:0%
+everything hinged on orthogonality we've
+ 
+
+ align:start position:0%
+everything hinged on orthogonality we've
+got to have orthogonality here but let
+
+ align:start position:0%
+got to have orthogonality here but let
+ 
+
+ align:start position:0%
+got to have orthogonality here but let
+me show you what it is the thing you
+
+ align:start position:0%
+me show you what it is the thing you
+ 
+
+ align:start position:0%
+me show you what it is the thing you
+multiply is by to get the C3 is not e to
+
+ align:start position:0%
+multiply is by to get the C3 is not e to
+ 
+
+ align:start position:0%
+multiply is by to get the C3 is not e to
+the i3x it is e to the minus i3x you
+
+ align:start position:0%
+the i3x it is e to the minus i3x you
+ 
+
+ align:start position:0%
+the i3x it is e to the minus i3x you
+take the conjugate you change I to minus
+
+ align:start position:0%
+take the conjugate you change I to minus
+ 
+
+ align:start position:0%
+take the conjugate you change I to minus
+I in in in in the complex cas case so if
+
+ align:start position:0%
+I in in in in the complex cas case so if
+ 
+
+ align:start position:0%
+I in in in in the complex cas case so if
+I take e to the I KX time e to the minus
+
+ align:start position:0%
+I take e to the I KX time e to the minus
+ 
+
+ align:start position:0%
+I take e to the I KX time e to the minus
+I LX and notice that minus I claim that
+
+ align:start position:0%
+I LX and notice that minus I claim that
+ 
+
+ align:start position:0%
+I LX and notice that minus I claim that
+I get
+
+ align:start position:0%
+I get
+ 
+
+ align:start position:0%
+I get
+zero except if K is L or I get and when
+
+ align:start position:0%
+zero except if K is L or I get and when
+ 
+
+ align:start position:0%
+zero except if K is L or I get and when
+K is l i get I probably I get two Pi if
+
+ align:start position:0%
+K is l i get I probably I get two Pi if
+ 
+
+ align:start position:0%
+K is l i get I probably I get two Pi if
+K is
+
+ align:start position:0%
+K is
+ 
+
+ align:start position:0%
+K is
+l i get zero if K is not L that's the
+
+ align:start position:0%
+l i get zero if K is not L that's the
+ 
+
+ align:start position:0%
+l i get zero if K is not L that's the
+that's the beautiful orthogonality I'm
+
+ align:start position:0%
+that's the beautiful orthogonality I'm
+ 
+
+ align:start position:0%
+that's the beautiful orthogonality I'm
+not too worried about the two Pi I'll
+
+ align:start position:0%
+not too worried about the two Pi I'll
+ 
+
+ align:start position:0%
+not too worried about the two Pi I'll
+figure that out it's
+
+ align:start position:0%
+figure that out it's
+ 
+
+ align:start position:0%
+figure that out it's
+the so what I'm saying is when you're
+
+ align:start position:0%
+the so what I'm saying is when you're
+ 
+
+ align:start position:0%
+the so what I'm saying is when you're
+taking inner products dot products and
+
+ align:start position:0%
+taking inner products dot products and
+ 
+
+ align:start position:0%
+taking inner products dot products and
+you've got complex stuff one of the
+
+ align:start position:0%
+you've got complex stuff one of the
+ 
+
+ align:start position:0%
+you've got complex stuff one of the
+factors has to
+
+ align:start position:0%
+factors has to
+ 
+
+ align:start position:0%
+factors has to
+get take the complex conjugate change I
+
+ align:start position:0%
+get take the complex conjugate change I
+ 
+
+ align:start position:0%
+get take the complex conjugate change I
+to minus I do do you see that we've got
+
+ align:start position:0%
+to minus I do do you see that we've got
+ 
+
+ align:start position:0%
+to minus I do do you see that we've got
+a completely easy integral now what is
+
+ align:start position:0%
+a completely easy integral now what is
+ 
+
+ align:start position:0%
+a completely easy integral now what is
+the integral of this guy how do I how do
+
+ align:start position:0%
+the integral of this guy how do I how do
+ 
+
+ align:start position:0%
+the integral of this guy how do I how do
+I see that I really get zero so this is
+
+ align:start position:0%
+I see that I really get zero so this is
+ 
+
+ align:start position:0%
+I see that I really get zero so this is
+the the first time I'm actually doing an
+
+ align:start position:0%
+the the first time I'm actually doing an
+ 
+
+ align:start position:0%
+the the first time I'm actually doing an
+integration and seeing
+
+ align:start position:0%
+integration and seeing
+ 
+
+ align:start position:0%
+integration and seeing
+orthogonality like
+
+ align:start position:0%
+orthogonality like
+ 
+
+ align:start position:0%
+orthogonality like
+anybody likes integrating these things
+
+ align:start position:0%
+anybody likes integrating these things
+ 
+
+ align:start position:0%
+anybody likes integrating these things
+because they're they're so simple to
+
+ align:start position:0%
+because they're they're so simple to
+ 
+
+ align:start position:0%
+because they're they're so simple to
+integrate what's what's the integral of
+
+ align:start position:0%
+integrate what's what's the integral of
+ 
+
+ align:start position:0%
+integrate what's what's the integral of
+if I just before I plug in the limits
+
+ align:start position:0%
+if I just before I plug in the limits
+ 
+
+ align:start position:0%
+if I just before I plug in the limits
+what's the integral of this guy how do I
+
+ align:start position:0%
+what's the integral of this guy how do I
+ 
+
+ align:start position:0%
+what's the integral of this guy how do I
+how do I rewrite that to integrate it
+
+ align:start position:0%
+how do I rewrite that to integrate it
+ 
+
+ align:start position:0%
+how do I rewrite that to integrate it
+easily I put the two exponents together
+
+ align:start position:0%
+easily I put the two exponents together
+ 
+
+ align:start position:0%
+easily I put the two exponents together
+this is the same as e to the I K minus
+
+ align:start position:0%
+this is the same as e to the I K minus
+ 
+
+ align:start position:0%
+this is the same as e to the I K minus
+LX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right exponentials follow that rule If I
+
+ align:start position:0%
+right exponentials follow that rule If I
+ 
+
+ align:start position:0%
+right exponentials follow that rule If I
+multiply exponentials I combine the
+
+ align:start position:0%
+multiply exponentials I combine the
+ 
+
+ align:start position:0%
+multiply exponentials I combine the
+exponents and now I'm ready to integrate
+
+ align:start position:0%
+exponents and now I'm ready to integrate
+ 
+
+ align:start position:0%
+exponents and now I'm ready to integrate
+and so what is the integral of e to the
+
+ align:start position:0%
+and so what is the integral of e to the
+ 
+
+ align:start position:0%
+and so what is the integral of e to the
+i k minus
+
+ align:start position:0%
+i k minus
+ 
+
+ align:start position:0%
+i k minus
+LX when I integrate e to the i e to the
+
+ align:start position:0%
+LX when I integrate e to the i e to the
+ 
+
+ align:start position:0%
+LX when I integrate e to the i e to the
+something X I get that same thing again
+
+ align:start position:0%
+something X I get that same thing again
+ 
+
+ align:start position:0%
+something X I get that same thing again
+divided by the
+
+ align:start position:0%
+divided by the
+ 
+
+ align:start position:0%
+divided by the
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+right so now I've integrated and now I
+
+ align:start position:0%
+right so now I've integrated and now I
+ 
+
+ align:start position:0%
+right so now I've integrated and now I
+want I just want to go from 0 to 2 pi
+
+ align:start position:0%
+want I just want to go from 0 to 2 pi
+ 
+
+ align:start position:0%
+want I just want to go from 0 to 2 pi
+like in the limits from X = 0 to x = 2
+
+ align:start position:0%
+like in the limits from X = 0 to x = 2
+ 
+
+ align:start position:0%
+like in the limits from X = 0 to x = 2
+pi that's this is what the integral is
+
+ align:start position:0%
+pi that's this is what the integral is
+ 
+
+ align:start position:0%
+pi that's this is what the integral is
+asking me for so I'm actually doing the
+
+ align:start position:0%
+asking me for so I'm actually doing the
+ 
+
+ align:start position:0%
+asking me for so I'm actually doing the
+integral here I'm I put these together
+
+ align:start position:0%
+integral here I'm I put these together
+ 
+
+ align:start position:0%
+integral here I'm I put these together
+into that I integrated which just
+
+ align:start position:0%
+into that I integrated which just
+ 
+
+ align:start position:0%
+into that I integrated which just
+brought this term down below because the
+
+ align:start position:0%
+brought this term down below because the
+ 
+
+ align:start position:0%
+brought this term down below because the
+derivative will bring that term above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh they weren't meant to change they
+
+ align:start position:0%
+oh they weren't meant to change they
+ 
+
+ align:start position:0%
+oh they weren't meant to change they
+actually it's it's wrong but right to
+
+ align:start position:0%
+actually it's it's wrong but right to
+ 
+
+ align:start position:0%
+actually it's it's wrong but right to
+change those integration limits I mean
+
+ align:start position:0%
+change those integration limits I mean
+ 
+
+ align:start position:0%
+change those integration limits I mean
+any two Pi would work but thank you it's
+
+ align:start position:0%
+any two Pi would work but thank you it's
+ 
+
+ align:start position:0%
+any two Pi would work but thank you it's
+it's you're totally right I should have
+
+ align:start position:0%
+it's you're totally right I should have
+ 
+
+ align:start position:0%
+it's you're totally right I should have
+done minus pi to
+
+ align:start position:0%
+done minus pi to
+ 
+
+ align:start position:0%
+done minus pi to
+Pi why do we get zero that's the whole
+
+ align:start position:0%
+Pi why do we get zero that's the whole
+ 
+
+ align:start position:0%
+Pi why do we get zero that's the whole
+point here we we actually did the
+
+ align:start position:0%
+point here we we actually did the
+ 
+
+ align:start position:0%
+point here we we actually did the
+integral and uh we can just plug in xal
+
+ align:start position:0%
+integral and uh we can just plug in xal
+ 
+
+ align:start position:0%
+integral and uh we can just plug in xal
+pi and xal minus Pi or we could plug in
+
+ align:start position:0%
+pi and xal minus Pi or we could plug in
+ 
+
+ align:start position:0%
+pi and xal minus Pi or we could plug in
+zero and 2 pi or I could plug in any
+
+ align:start position:0%
+zero and 2 pi or I could plug in any
+ 
+
+ align:start position:0%
+zero and 2 pi or I could plug in any
+guys that were two Pi apart any period
+
+ align:start position:0%
+guys that were two Pi apart any period
+ 
+
+ align:start position:0%
+guys that were two Pi apart any period
+of 2 pi why do we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero do you have to do the plugging in
+
+ align:start position:0%
+zero do you have to do the plugging in
+ 
+
+ align:start position:0%
+zero do you have to do the plugging in
+part to see
+
+ align:start position:0%
+part to see
+ 
+
+ align:start position:0%
+part to see
+it you can certainly but the point is
+
+ align:start position:0%
+it you can certainly but the point is
+ 
+
+ align:start position:0%
+it you can certainly but the point is
+this function is
+
+ align:start position:0%
+this function is
+ 
+
+ align:start position:0%
+this function is
+periodic that's a function that has
+
+ align:start position:0%
+periodic that's a function that has
+ 
+
+ align:start position:0%
+periodic that's a function that has
+Period 2 pi so it has to be the the same
+
+ align:start position:0%
+Period 2 pi so it has to be the the same
+ 
+
+ align:start position:0%
+Period 2 pi so it has to be the the same
+at the lower and the upper limits that
+
+ align:start position:0%
+at the lower and the upper limits that
+ 
+
+ align:start position:0%
+at the lower and the upper limits that
+that's what it's coming to that's a
+
+ align:start position:0%
+that's what it's coming to that's a
+ 
+
+ align:start position:0%
+that's what it's coming to that's a
+periodic
+
+ align:start position:0%
+periodic
+ 
+
+ align:start position:0%
+periodic
+function it's equal at these two limits
+
+ align:start position:0%
+function it's equal at these two limits
+ 
+
+ align:start position:0%
+function it's equal at these two limits
+and therefore when I do the subtraction
+
+ align:start position:0%
+and therefore when I do the subtraction
+ 
+
+ align:start position:0%
+and therefore when I do the subtraction
+from you know I take it at the top limit
+
+ align:start position:0%
+from you know I take it at the top limit
+ 
+
+ align:start position:0%
+from you know I take it at the top limit
+minus the answer at the bottom limit
+
+ align:start position:0%
+minus the answer at the bottom limit
+ 
+
+ align:start position:0%
+minus the answer at the bottom limit
+it's the same at both so I get zero so
+
+ align:start position:0%
+it's the same at both so I get zero so
+ 
+
+ align:start position:0%
+it's the same at both so I get zero so
+there is the actual check of
+
+ align:start position:0%
+there is the actual check of
+ 
+
+ align:start position:0%
+there is the actual check of
+orthogonality so the the the key point
+
+ align:start position:0%
+orthogonality so the the the key point
+ 
+
+ align:start position:0%
+orthogonality so the the the key point
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+orthogonality or or in product for
+
+ align:start position:0%
+orthogonality or or in product for
+ 
+
+ align:start position:0%
+orthogonality or or in product for
+complex functions one of them has to
+
+ align:start position:0%
+complex functions one of them has to
+ 
+
+ align:start position:0%
+complex functions one of them has to
+take the complex conjugate let let me
+
+ align:start position:0%
+take the complex conjugate let let me
+ 
+
+ align:start position:0%
+take the complex conjugate let let me
+just do for vectors
+
+ align:start position:0%
+just do for vectors
+ 
+
+ align:start position:0%
+just do for vectors
+too complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors I may have mentioned let me take
+
+ align:start position:0%
+vectors I may have mentioned let me take
+ 
+
+ align:start position:0%
+vectors I may have mentioned let me take
+the vector one I as an extreme
+
+ align:start position:0%
+the vector one I as an extreme
+ 
+
+ align:start position:0%
+the vector one I as an extreme
+example and and suppose I want to define
+
+ align:start position:0%
+example and and suppose I want to define
+ 
+
+ align:start position:0%
+example and and suppose I want to define
+the inner product with
+
+ align:start position:0%
+the inner product with
+ 
+
+ align:start position:0%
+the inner product with
+itself which will be the length squared
+
+ align:start position:0%
+itself which will be the length squared
+ 
+
+ align:start position:0%
+itself which will be the length squared
+what's the inner product of that Vector
+
+ align:start position:0%
+what's the inner product of that Vector
+ 
+
+ align:start position:0%
+what's the inner product of that Vector
+that complex Vector one I with itself
+
+ align:start position:0%
+that complex Vector one I with itself
+ 
+
+ align:start position:0%
+that complex Vector one I with itself
+let me just raise it up so we see it
+
+ align:start position:0%
+let me just raise it up so we see it
+ 
+
+ align:start position:0%
+let me just raise it up so we see it
+focus on
+
+ align:start position:0%
+focus on
+ 
+
+ align:start position:0%
+focus on
+this usually the length squared would be
+
+ align:start position:0%
+this usually the length squared would be
+ 
+
+ align:start position:0%
+this usually the length squared would be
+1 2 + i
+
+ align:start position:0%
+1 2 + i
+ 
+
+ align:start position:0%
+1 2 + i
+s no good why why no
+
+ align:start position:0%
+s no good why why no
+ 
+
+ align:start position:0%
+s no good why why no
+good because it's zero 1 s plus I squ is
+
+ align:start position:0%
+good because it's zero 1 s plus I squ is
+ 
+
+ align:start position:0%
+good because it's zero 1 s plus I squ is
+zero it's just we we want we want
+
+ align:start position:0%
+zero it's just we we want we want
+ 
+
+ align:start position:0%
+zero it's just we we want we want
+absolute value
+
+ align:start position:0%
+absolute value
+ 
+
+ align:start position:0%
+absolute value
+squared absolute value
+
+ align:start position:0%
+squared absolute value
+ 
+
+ align:start position:0%
+squared absolute value
+we we need squares we need positive
+
+ align:start position:0%
+we we need squares we need positive
+ 
+
+ align:start position:0%
+we we need squares we need positive
+number here so the the length of this
+
+ align:start position:0%
+number here so the the length of this
+ 
+
+ align:start position:0%
+number here so the the length of this
+squared I would so let let me call that
+
+ align:start position:0%
+squared I would so let let me call that
+ 
+
+ align:start position:0%
+squared I would so let let me call that
+vector v i want to I want to take not V
+
+ align:start position:0%
+vector v i want to I want to take not V
+ 
+
+ align:start position:0%
+vector v i want to I want to take not V
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+V that's the thing that would give me
+
+ align:start position:0%
+V that's the thing that would give me
+ 
+
+ align:start position:0%
+V that's the thing that would give me
+zero if I did one
+
+ align:start position:0%
+zero if I did one
+ 
+
+ align:start position:0%
+zero if I did one
+I I have to take the complex conjugate
+
+ align:start position:0%
+I I have to take the complex conjugate
+ 
+
+ align:start position:0%
+I I have to take the complex conjugate
+one of the two factors and it's just a
+
+ align:start position:0%
+one of the two factors and it's just a
+ 
+
+ align:start position:0%
+one of the two factors and it's just a
+matter of convention which one you do
+
+ align:start position:0%
+matter of convention which one you do
+ 
+
+ align:start position:0%
+matter of convention which one you do
+this is the thing that gives me the
+
+ align:start position:0%
+this is the thing that gives me the
+ 
+
+ align:start position:0%
+this is the thing that gives me the
+length of v s and it's the same thing
+
+ align:start position:0%
+length of v s and it's the same thing
+ 
+
+ align:start position:0%
+length of v s and it's the same thing
+for functions it's the integral of f
+
+ align:start position:0%
+for functions it's the integral of f
+ 
+
+ align:start position:0%
+for functions it's the integral of f
+ofx do do you want me to write it as
+
+ align:start position:0%
+ofx do do you want me to write it as
+ 
+
+ align:start position:0%
+ofx do do you want me to write it as
+it's the integral of f ofx times its
+
+ align:start position:0%
+it's the integral of f ofx times its
+ 
+
+ align:start position:0%
+it's the integral of f ofx times its
+conjugate that gives me the length of f
+
+ align:start position:0%
+conjugate that gives me the length of f
+ 
+
+ align:start position:0%
+conjugate that gives me the length of f
+squared and of course I can rewrite that
+
+ align:start position:0%
+squared and of course I can rewrite that
+ 
+
+ align:start position:0%
+squared and of course I can rewrite that
+as the integral of f right we have the
+
+ align:start position:0%
+as the integral of f right we have the
+ 
+
+ align:start position:0%
+as the integral of f right we have the
+this handy notation for ftimes its
+
+ align:start position:0%
+this handy notation for ftimes its
+ 
+
+ align:start position:0%
+this handy notation for ftimes its
+conjugate is it's
+
+ align:start position:0%
+conjugate is it's
+ 
+
+ align:start position:0%
+conjugate is it's
+like it's like re to the I Theta time re
+
+ align:start position:0%
+like it's like re to the I Theta time re
+ 
+
+ align:start position:0%
+like it's like re to the I Theta time re
+e the minus I Theta the product of re to
+
+ align:start position:0%
+e the minus I Theta the product of re to
+ 
+
+ align:start position:0%
+e the minus I Theta the product of re to
+the I Theta
+
+ align:start position:0%
+the I Theta
+ 
+
+ align:start position:0%
+the I Theta
+time time r e the minus I Theta is
+
+ align:start position:0%
+time time r e the minus I Theta is
+ 
+
+ align:start position:0%
+time time r e the minus I Theta is
+what this is the function this is the
+
+ align:start position:0%
+what this is the function this is the
+ 
+
+ align:start position:0%
+what this is the function this is the
+complex number this is its conjugate
+
+ align:start position:0%
+complex number this is its conjugate
+ 
+
+ align:start position:0%
+complex number this is its conjugate
+when I multiply you notice that I went
+
+ align:start position:0%
+when I multiply you notice that I went
+ 
+
+ align:start position:0%
+when I multiply you notice that I went
+minus I when I drop below the imaginary
+
+ align:start position:0%
+minus I when I drop below the imaginary
+ 
+
+ align:start position:0%
+minus I when I drop below the imaginary
+axis I just the the real axis I just
+
+ align:start position:0%
+axis I just the the real axis I just
+ 
+
+ align:start position:0%
+axis I just the the real axis I just
+just change I to minus I so those cancel
+
+ align:start position:0%
+just change I to minus I so those cancel
+ 
+
+ align:start position:0%
+just change I to minus I so those cancel
+and I get R
+
+ align:start position:0%
+and I get R
+ 
+
+ align:start position:0%
+and I get R
+squ the length the size of the
+
+ align:start position:0%
+squ the length the size of the
+ 
+
+ align:start position:0%
+squ the length the size of the
+number it's just if you haven't thought
+
+ align:start position:0%
+number it's just if you haven't thought
+ 
+
+ align:start position:0%
+number it's just if you haven't thought
+complex just make this change and you're
+
+ align:start position:0%
+complex just make this change and you're
+ 
+
+ align:start position:0%
+complex just make this change and you're
+you're ready to go yeah just just V bar
+
+ align:start position:0%
+you're ready to go yeah just just V bar
+ 
+
+ align:start position:0%
+you're ready to go yeah just just V bar
+transpose V FB bar transpose F if you
+
+ align:start position:0%
+transpose V FB bar transpose F if you
+ 
+
+ align:start position:0%
+transpose V FB bar transpose F if you
+like or or f s
+
+ align:start position:0%
+like or or f s
+ 
+
+ align:start position:0%
+like or or f s
+so and when we make the correct change
+
+ align:start position:0%
+so and when we make the correct change
+ 
+
+ align:start position:0%
+so and when we make the correct change
+we have still have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonality
+
+ align:start position:0%
+orthogonality
+ 
+
+ align:start position:0%
+orthogonality
+okay so that's what orthogonality is now
+
+ align:start position:0%
+okay so that's what orthogonality is now
+ 
+
+ align:start position:0%
+okay so that's what orthogonality is now
+what's the
+
+ align:start position:0%
+what's the
+ 
+
+ align:start position:0%
+what's the
+coefficient so now after all that speech
+
+ align:start position:0%
+coefficient so now after all that speech
+ 
+
+ align:start position:0%
+coefficient so now after all that speech
+tell me what do I multiply both sides by
+
+ align:start position:0%
+tell me what do I multiply both sides by
+ 
+
+ align:start position:0%
+tell me what do I multiply both sides by
+let me start again and and remember here
+
+ align:start position:0%
+let me start again and and remember here
+ 
+
+ align:start position:0%
+let me start again and and remember here
+so I my f ofx is going to be the sum of
+
+ align:start position:0%
+so I my f ofx is going to be the sum of
+ 
+
+ align:start position:0%
+so I my f ofx is going to be the sum of
+c k e to the I
+
+ align:start position:0%
+c k e to the I
+ 
+
+ align:start position:0%
+c k e to the I
+KX and if I want
+
+ align:start position:0%
+KX and if I want
+ 
+
+ align:start position:0%
+KX and if I want
+to get a coefficient I'm looking for a
+
+ align:start position:0%
+to get a coefficient I'm looking for a
+ 
+
+ align:start position:0%
+to get a coefficient I'm looking for a
+formula for
+
+ align:start position:0%
+formula for
+ 
+
+ align:start position:0%
+formula for
+C3 so how do I find
+
+ align:start position:0%
+C3 so how do I find
+ 
+
+ align:start position:0%
+C3 so how do I find
+C3 let's let's let me slow down a second
+
+ align:start position:0%
+C3 let's let's let me slow down a second
+ 
+
+ align:start position:0%
+C3 let's let's let me slow down a second
+how to find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C3
+
+ align:start position:0%
+C3
+ 
+
+ align:start position:0%
+C3
+multiply both sides by what and and
+
+ align:start position:0%
+multiply both sides by what and and
+ 
+
+ align:start position:0%
+multiply both sides by what and and
+integrate and integrate minus pi to Pi
+
+ align:start position:0%
+integrate and integrate minus pi to Pi
+ 
+
+ align:start position:0%
+integrate and integrate minus pi to Pi
+what goes
+
+ align:start position:0%
+what goes
+ 
+
+ align:start position:0%
+what goes
+there if I want
+
+ align:start position:0%
+there if I want
+ 
+
+ align:start position:0%
+there if I want
+C3 I should multiply both sides by
+
+ align:start position:0%
+C3 I should multiply both sides by
+ 
+
+ align:start position:0%
+C3 I should multiply both sides by
+should I multiply both sides by e to the
+
+ align:start position:0%
+should I multiply both sides by e to the
+ 
+
+ align:start position:0%
+should I multiply both sides by e to the
+i3x nope e to the minus i3x multiply
+
+ align:start position:0%
+i3x nope e to the minus i3x multiply
+ 
+
+ align:start position:0%
+i3x nope e to the minus i3x multiply
+both sides by e to the minus i3x and
+
+ align:start position:0%
+both sides by e to the minus i3x and
+ 
+
+ align:start position:0%
+both sides by e to the minus i3x and
+integrate e the minus i3x DX and then on
+
+ align:start position:0%
+integrate e the minus i3x DX and then on
+ 
+
+ align:start position:0%
+integrate e the minus i3x DX and then on
+the right side I get what I get
+
+ align:start position:0%
+the right side I get what I get
+ 
+
+ align:start position:0%
+the right side I get what I get
+C3 because that'll be either the minus
+
+ align:start position:0%
+C3 because that'll be either the minus
+ 
+
+ align:start position:0%
+C3 because that'll be either the minus
+i3x * e plus i3x that'll be I'll be
+
+ align:start position:0%
+i3x * e plus i3x that'll be I'll be
+ 
+
+ align:start position:0%
+i3x * e plus i3x that'll be I'll be
+integrating one so I'll get a 2 pi and
+
+ align:start position:0%
+integrating one so I'll get a 2 pi and
+ 
+
+ align:start position:0%
+integrating one so I'll get a 2 pi and
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+zeros from all the other
+
+ align:start position:0%
+zeros from all the other
+ 
+
+ align:start position:0%
+zeros from all the other
+terms orthogonality doing its job again
+
+ align:start position:0%
+terms orthogonality doing its job again
+ 
+
+ align:start position:0%
+terms orthogonality doing its job again
+all these zeros from or by orthogonality
+
+ align:start position:0%
+all these zeros from or by orthogonality
+ 
+
+ align:start position:0%
+all these zeros from or by orthogonality
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+orthogonality by by exactly this
+
+ align:start position:0%
+orthogonality by by exactly this
+ 
+
+ align:start position:0%
+orthogonality by by exactly this
+integration that we did if if if K is
+
+ align:start position:0%
+integration that we did if if if K is
+ 
+
+ align:start position:0%
+integration that we did if if if K is
+three and L is s or k is seven and L is
+
+ align:start position:0%
+three and L is s or k is seven and L is
+ 
+
+ align:start position:0%
+three and L is s or k is seven and L is
+three the integral gives zero so so
+
+ align:start position:0%
+three the integral gives zero so so
+ 
+
+ align:start position:0%
+three the integral gives zero so so
+what's the formula then this is all gone
+
+ align:start position:0%
+what's the formula then this is all gone
+ 
+
+ align:start position:0%
+what's the formula then this is all gone
+divide by 2
+
+ align:start position:0%
+divide by 2
+ 
+
+ align:start position:0%
+divide by 2
+pi and you've got
+
+ align:start position:0%
+pi and you've got
+ 
+
+ align:start position:0%
+pi and you've got
+it there you are that's the
+
+ align:start position:0%
+it there you are that's the
+ 
+
+ align:start position:0%
+it there you are that's the
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+okay it just we have to move to complex
+
+ align:start position:0%
+okay it just we have to move to complex
+ 
+
+ align:start position:0%
+okay it just we have to move to complex
+numbers and now in those in the those 20
+
+ align:start position:0%
+numbers and now in those in the those 20
+ 
+
+ align:start position:0%
+numbers and now in those in the those 20
+minutes we've got the the only change to
+
+ align:start position:0%
+minutes we've got the the only change to
+ 
+
+ align:start position:0%
+minutes we've got the the only change to
+make is conjugate one of the one of the
+
+ align:start position:0%
+make is conjugate one of the one of the
+ 
+
+ align:start position:0%
+make is conjugate one of the one of the
+things you when when it can be complex
+
+ align:start position:0%
+things you when when it can be complex
+ 
+
+ align:start position:0%
+things you when when it can be complex
+okay good so that's the that's the
+
+ align:start position:0%
+okay good so that's the that's the
+ 
+
+ align:start position:0%
+okay good so that's the that's the
+complex series what is the uh what's the
+
+ align:start position:0%
+complex series what is the uh what's the
+ 
+
+ align:start position:0%
+complex series what is the uh what's the
+energy inequality now let me do the
+
+ align:start position:0%
+energy inequality now let me do the
+ 
+
+ align:start position:0%
+energy inequality now let me do the
+energy equality in X space and in X in k
+
+ align:start position:0%
+energy equality in X space and in X in k
+ 
+
+ align:start position:0%
+energy equality in X space and in X in k
+space if I take
+
+ align:start position:0%
+space if I take
+ 
+
+ align:start position:0%
+space if I take
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I'd like so that's an equality of
+
+ align:start position:0%
+now I'd like so that's an equality of
+ 
+
+ align:start position:0%
+now I'd like so that's an equality of
+two functions now I'd like to get
+
+ align:start position:0%
+two functions now I'd like to get
+ 
+
+ align:start position:0%
+two functions now I'd like to get
+it I I want to do
+
+ align:start position:0%
+it I I want to do
+ 
+
+ align:start position:0%
+it I I want to do
+energy this is fantastic and extremely
+
+ align:start position:0%
+energy this is fantastic and extremely
+ 
+
+ align:start position:0%
+energy this is fantastic and extremely
+practical and useful the fact that the
+
+ align:start position:0%
+practical and useful the fact that the
+ 
+
+ align:start position:0%
+practical and useful the fact that the
+energy is going to come out beautifully
+
+ align:start position:0%
+energy is going to come out beautifully
+ 
+
+ align:start position:0%
+energy is going to come out beautifully
+too so what I what am I going to do for
+
+ align:start position:0%
+too so what I what am I going to do for
+ 
+
+ align:start position:0%
+too so what I what am I going to do for
+energy I'm going to integrate f ofx
+
+ align:start position:0%
+energy I'm going to integrate f ofx
+ 
+
+ align:start position:0%
+energy I'm going to integrate f ofx
+s DX that's the
+
+ align:start position:0%
+s DX that's the
+ 
+
+ align:start position:0%
+s DX that's the
+energy that's the energy in X space in
+
+ align:start position:0%
+energy that's the energy in X space in
+ 
+
+ align:start position:0%
+energy that's the energy in X space in
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function what do I do now I I I
+
+ align:start position:0%
+function what do I do now I I I
+ 
+
+ align:start position:0%
+function what do I do now I I I
+integrate this the series c k e to the I
+
+ align:start position:0%
+integrate this the series c k e to the I
+ 
+
+ align:start position:0%
+integrate this the series c k e to the I
+kx2 oh no whoa if I put a square
+
+ align:start position:0%
+kx2 oh no whoa if I put a square
+ 
+
+ align:start position:0%
+kx2 oh no whoa if I put a square
+there right I'm fired uh right what do I
+
+ align:start position:0%
+there right I'm fired uh right what do I
+ 
+
+ align:start position:0%
+there right I'm fired uh right what do I
+have to do I will put a square there but
+
+ align:start position:0%
+have to do I will put a square there but
+ 
+
+ align:start position:0%
+have to do I will put a square there but
+I have to straighten out something what
+
+ align:start position:0%
+I have to straighten out something what
+ 
+
+ align:start position:0%
+I have to straighten out something what
+do I do those curvy lines
+
+ align:start position:0%
+do I do those curvy lines
+ 
+
+ align:start position:0%
+do I do those curvy lines
+which just meant take the thing in
+
+ align:start position:0%
+which just meant take the thing in
+ 
+
+ align:start position:0%
+which just meant take the thing in
+square should be changed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to straight just the matter of getting
+
+ align:start position:0%
+to straight just the matter of getting
+ 
+
+ align:start position:0%
+to straight just the matter of getting
+them straight straightening this out
+
+ align:start position:0%
+them straight straightening this out
+ 
+
+ align:start position:0%
+them straight straightening this out
+okay straight there we are okay now that
+
+ align:start position:0%
+okay straight there we are okay now that
+ 
+
+ align:start position:0%
+okay straight there we are okay now that
+means the thing times its conjugate
+
+ align:start position:0%
+means the thing times its conjugate
+ 
+
+ align:start position:0%
+means the thing times its conjugate
+that's the thing times its conjugate so
+
+ align:start position:0%
+that's the thing times its conjugate so
+ 
+
+ align:start position:0%
+that's the thing times its conjugate so
+what do I get all the terms disappear
+
+ align:start position:0%
+what do I get all the terms disappear
+ 
+
+ align:start position:0%
+what do I get all the terms disappear
+except the perfect the ones that are
+
+ align:start position:0%
+except the perfect the ones that are
+ 
+
+ align:start position:0%
+except the perfect the ones that are
+squared so what do I get
+
+ align:start position:0%
+squared so what do I get
+ 
+
+ align:start position:0%
+squared so what do I get
+here and the ones that are squared I'm
+
+ align:start position:0%
+here and the ones that are squared I'm
+ 
+
+ align:start position:0%
+here and the ones that are squared I'm
+integrating one so I get a 2 pi so
+
+ align:start position:0%
+integrating one so I get a 2 pi so
+ 
+
+ align:start position:0%
+integrating one so I get a 2 pi so
+there's a 2 pi the whole subject is full
+
+ align:start position:0%
+there's a 2 pi the whole subject is full
+ 
+
+ align:start position:0%
+there's a 2 pi the whole subject is full
+of these pies and two pies it's just
+
+ align:start position:0%
+of these pies and two pies it's just
+ 
+
+ align:start position:0%
+of these pies and two pies it's just
+part of the deal uh now what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left then now I'm looking only at the
+
+ align:start position:0%
+left then now I'm looking only at the
+ 
+
+ align:start position:0%
+left then now I'm looking only at the
+terms where I'm integrating something by
+
+ align:start position:0%
+terms where I'm integrating something by
+ 
+
+ align:start position:0%
+terms where I'm integrating something by
+its conjugate by its own conjugate and
+
+ align:start position:0%
+its conjugate by its own conjugate and
+ 
+
+ align:start position:0%
+its conjugate by its own conjugate and
+then I'm getting CK times its own
+
+ align:start position:0%
+then I'm getting CK times its own
+ 
+
+ align:start position:0%
+then I'm getting CK times its own
+conjugate so I'm getting all the terms
+
+ align:start position:0%
+conjugate so I'm getting all the terms
+ 
+
+ align:start position:0%
+conjugate so I'm getting all the terms
+I'm getting no cross terms just the
+
+ align:start position:0%
+I'm getting no cross terms just the
+ 
+
+ align:start position:0%
+I'm getting no cross terms just the
+terms that come from this from that
+
+ align:start position:0%
+terms that come from this from that
+ 
+
+ align:start position:0%
+terms that come from this from that
+times its own conjugate which is
+
+ align:start position:0%
+times its own conjugate which is
+ 
+
+ align:start position:0%
+times its own conjugate which is
+CK squar that's the energy in
+
+ align:start position:0%
+CK squar that's the energy in
+ 
+
+ align:start position:0%
+CK squar that's the energy in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+coefficients that's the energy in k
+
+ align:start position:0%
+coefficients that's the energy in k
+ 
+
+ align:start position:0%
+coefficients that's the energy in k
+space and of course that sum goes minus
+
+ align:start position:0%
+space and of course that sum goes minus
+ 
+
+ align:start position:0%
+space and of course that sum goes minus
+infinity to Infinity I've got them all
+
+ align:start position:0%
+infinity to Infinity I've got them all
+ 
+
+ align:start position:0%
+infinity to Infinity I've got them all
+that's the energy in kpace here's the
+
+ align:start position:0%
+that's the energy in kpace here's the
+ 
+
+ align:start position:0%
+that's the energy in kpace here's the
+energy in X space yeah yeah you can
+
+ align:start position:0%
+energy in X space yeah yeah you can
+ 
+
+ align:start position:0%
+energy in X space yeah yeah you can
+expect that this uh that this
+
+ align:start position:0%
+expect that this uh that this
+ 
+
+ align:start position:0%
+expect that this uh that this
+uh orthogonality is going to give you
+
+ align:start position:0%
+uh orthogonality is going to give you
+ 
+
+ align:start position:0%
+uh orthogonality is going to give you
+something nice for uh the for the energy
+
+ align:start position:0%
+something nice for uh the for the energy
+ 
+
+ align:start position:0%
+something nice for uh the for the energy
+for this the integral of the square all
+
+ align:start position:0%
+for this the integral of the square all
+ 
+
+ align:start position:0%
+for this the integral of the square all
+right so you saw that uh and uh let's
+
+ align:start position:0%
+right so you saw that uh and uh let's
+ 
+
+ align:start position:0%
+right so you saw that uh and uh let's
+see so we saw it for we actually got a
+
+ align:start position:0%
+see so we saw it for we actually got a
+ 
+
+ align:start position:0%
+see so we saw it for we actually got a
+good number for the for the square wave
+
+ align:start position:0%
+good number for the for the square wave
+ 
+
+ align:start position:0%
+good number for the for the square wave
+we got Infinity for the Delta function
+
+ align:start position:0%
+we got Infinity for the Delta function
+ 
+
+ align:start position:0%
+we got Infinity for the Delta function
+uh I've put on here as a last uh topic
+
+ align:start position:0%
+uh I've put on here as a last uh topic
+ 
+
+ align:start position:0%
+uh I've put on here as a last uh topic
+to just give the word function tell
+
+ align:start position:0%
+to just give the word function tell
+ 
+
+ align:start position:0%
+to just give the word function tell
+you you know part of what this course is
+
+ align:start position:0%
+you you know part of what this course is
+ 
+
+ align:start position:0%
+you you know part of what this course is
+doing is to speak the language teach the
+
+ align:start position:0%
+doing is to speak the language teach the
+ 
+
+ align:start position:0%
+doing is to speak the language teach the
+language
+
+ align:start position:0%
+language
+ 
+
+ align:start position:0%
+language
+of uh of Applied
+
+ align:start position:0%
+of uh of Applied
+ 
+
+ align:start position:0%
+of uh of Applied
+math so that when you see something you
+
+ align:start position:0%
+math so that when you see something you
+ 
+
+ align:start position:0%
+math so that when you see something you
+you see this you you you recognize hey
+
+ align:start position:0%
+you see this you you you recognize hey
+ 
+
+ align:start position:0%
+you see this you you you recognize hey
+I've seen that word
+
+ align:start position:0%
+I've seen that word
+ 
+
+ align:start position:0%
+I've seen that word
+before so so I want to know what's the
+
+ align:start position:0%
+before so so I want to know what's the
+ 
+
+ align:start position:0%
+before so so I want to know what's the
+right space of functions this is my
+
+ align:start position:0%
+right space of functions this is my
+ 
+
+ align:start position:0%
+right space of functions this is my
+measure for the length squar of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function my Square wave is
+
+ align:start position:0%
+function my Square wave is
+ 
+
+ align:start position:0%
+function my Square wave is
+great it's its length squared was
+
+ align:start position:0%
+great it's its length squared was
+ 
+
+ align:start position:0%
+great it's its length squared was
+whatever it was pi squ over something
+
+ align:start position:0%
+whatever it was pi squ over something
+ 
+
+ align:start position:0%
+whatever it was pi squ over something
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh that's its that's the its length
+
+ align:start position:0%
+uh that's its that's the its length
+ 
+
+ align:start position:0%
+uh that's its that's the its length
+squared the Delta
+
+ align:start position:0%
+squared the Delta
+ 
+
+ align:start position:0%
+squared the Delta
+function would gave Infinity so I'm not
+
+ align:start position:0%
+function would gave Infinity so I'm not
+ 
+
+ align:start position:0%
+function would gave Infinity so I'm not
+it's not going to be allowed into the
+
+ align:start position:0%
+it's not going to be allowed into the
+ 
+
+ align:start position:0%
+it's not going to be allowed into the
+function space it's it's a it's a vector
+
+ align:start position:0%
+function space it's it's a it's a vector
+ 
+
+ align:start position:0%
+function space it's it's a it's a vector
+of infinite length like the vector 11111
+
+ align:start position:0%
+of infinite length like the vector 11111
+ 
+
+ align:start position:0%
+of infinite length like the vector 11111
+forever too long we can't sum Pythagoras
+
+ align:start position:0%
+forever too long we can't sum Pythagoras
+ 
+
+ align:start position:0%
+forever too long we can't sum Pythagoras
+fails because we sum the squares we get
+
+ align:start position:0%
+fails because we sum the squares we get
+ 
+
+ align:start position:0%
+fails because we sum the squares we get
+infinite so what ve functions what
+
+ align:start position:0%
+infinite so what ve functions what
+ 
+
+ align:start position:0%
+infinite so what ve functions what
+vectors should we allow in our space so
+
+ align:start position:0%
+vectors should we allow in our space so
+ 
+
+ align:start position:0%
+vectors should we allow in our space so
+so we're going to have a a space it's
+
+ align:start position:0%
+so we're going to have a a space it's
+ 
+
+ align:start position:0%
+so we're going to have a a space it's
+going to be infinite dimensional because
+
+ align:start position:0%
+going to be infinite dimensional because
+ 
+
+ align:start position:0%
+going to be infinite dimensional because
+our vect our coefficients we've got
+
+ align:start position:0%
+our vect our coefficients we've got
+ 
+
+ align:start position:0%
+our vect our coefficients we've got
+infinitely many coefficients
+
+ align:start position:0%
+infinitely many coefficients
+ 
+
+ align:start position:0%
+infinitely many coefficients
+our functions have infinitely many
+
+ align:start position:0%
+our functions have infinitely many
+ 
+
+ align:start position:0%
+our functions have infinitely many
+values so we've moved up from n
+
+ align:start position:0%
+values so we've moved up from n
+ 
+
+ align:start position:0%
+values so we've moved up from n
+dimensional space to infinite
+
+ align:start position:0%
+dimensional space to infinite
+ 
+
+ align:start position:0%
+dimensional space to infinite
+dimensional space and everybody calls it
+
+ align:start position:0%
+dimensional space and everybody calls it
+ 
+
+ align:start position:0%
+dimensional space and everybody calls it
+after the guy who Hilbert
+
+ align:start position:0%
+after the guy who Hilbert
+ 
+
+ align:start position:0%
+after the guy who Hilbert
+space so I don't know if you've seen
+
+ align:start position:0%
+space so I don't know if you've seen
+ 
+
+ align:start position:0%
+space so I don't know if you've seen
+that word before H that name before
+
+ align:start position:0%
+that word before H that name before
+ 
+
+ align:start position:0%
+that word before H that name before
+Hilbert space it's the space of
+
+ align:start position:0%
+Hilbert space it's the space of
+ 
+
+ align:start position:0%
+Hilbert space it's the space of
+functions with finite energy finite
+
+ align:start position:0%
+functions with finite energy finite
+ 
+
+ align:start position:0%
+functions with finite energy finite
+length so this fun function is in it the
+
+ align:start position:0%
+length so this fun function is in it the
+ 
+
+ align:start position:0%
+length so this fun function is in it the
+Delta function is not in
+
+ align:start position:0%
+Delta function is not in
+ 
+
+ align:start position:0%
+Delta function is not in
+it uh and uh the point is that this
+
+ align:start position:0%
+it uh and uh the point is that this
+ 
+
+ align:start position:0%
+it uh and uh the point is that this
+space of functions we've got the these
+
+ align:start position:0%
+space of functions we've got the these
+ 
+
+ align:start position:0%
+space of functions we've got the these
+these guys are a great basis for the
+
+ align:start position:0%
+these guys are a great basis for the
+ 
+
+ align:start position:0%
+these guys are a great basis for the
+space of functions the signs and
+
+ align:start position:0%
+space of functions the signs and
+ 
+
+ align:start position:0%
+space of functions the signs and
+cosiness are another basis for this
+
+ align:start position:0%
+cosiness are another basis for this
+ 
+
+ align:start position:0%
+cosiness are another basis for this
+space of functions we just have a whole
+
+ align:start position:0%
+space of functions we just have a whole
+ 
+
+ align:start position:0%
+space of functions we just have a whole
+lot of functions and all the facts of
+
+ align:start position:0%
+lot of functions and all the facts of
+ 
+
+ align:start position:0%
+lot of functions and all the facts of
+n-dimensional space like so what are
+
+ align:start position:0%
+n-dimensional space like so what are
+ 
+
+ align:start position:0%
+n-dimensional space like so what are
+what are important facts about n
+
+ align:start position:0%
+what are important facts about n
+ 
+
+ align:start position:0%
+what are important facts about n
+dimensional space one that comes to mind
+
+ align:start position:0%
+dimensional space one that comes to mind
+ 
+
+ align:start position:0%
+dimensional space one that comes to mind
+is the that that's that involves length
+
+ align:start position:0%
+is the that that's that involves length
+ 
+
+ align:start position:0%
+is the that that's that involves length
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the a key fact about length
+
+ align:start position:0%
+the a key fact about length
+ 
+
+ align:start position:0%
+the a key fact about length
+is length and
+
+ align:start position:0%
+is length and
+ 
+
+ align:start position:0%
+is length and
+angle the key the the gra I could say
+
+ align:start position:0%
+angle the key the the gra I could say
+ 
+
+ align:start position:0%
+angle the key the the gra I could say
+actually this is many people would say
+
+ align:start position:0%
+actually this is many people would say
+ 
+
+ align:start position:0%
+actually this is many people would say
+this is the most important inequality in
+
+ align:start position:0%
+this is the most important inequality in
+ 
+
+ align:start position:0%
+this is the most important inequality in
+mathematics that the dotproduct of two
+
+ align:start position:0%
+mathematics that the dotproduct of two
+ 
+
+ align:start position:0%
+mathematics that the dotproduct of two
+vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you know what this this it's
+
+ align:start position:0%
+what do you know what this this it's
+ 
+
+ align:start position:0%
+what do you know what this this it's
+called the Schwarz
+
+ align:start position:0%
+called the Schwarz
+ 
+
+ align:start position:0%
+called the Schwarz
+inequality several people uh found it
+
+ align:start position:0%
+inequality several people uh found it
+ 
+
+ align:start position:0%
+inequality several people uh found it
+independantly Schwarz had had uh is is
+
+ align:start position:0%
+independantly Schwarz had had uh is is
+ 
+
+ align:start position:0%
+independantly Schwarz had had uh is is
+is the single name most often
+
+ align:start position:0%
+is the single name most often
+ 
+
+ align:start position:0%
+is the single name most often
+used what do you know about the
+
+ align:start position:0%
+used what do you know about the
+ 
+
+ align:start position:0%
+used what do you know about the
+dotproduct of two
+
+ align:start position:0%
+dotproduct of two
+ 
+
+ align:start position:0%
+dotproduct of two
+vectors somehow it tells you the angle
+
+ align:start position:0%
+vectors somehow it tells you the angle
+ 
+
+ align:start position:0%
+vectors somehow it tells you the angle
+between them right somehow the the dot
+
+ align:start position:0%
+between them right somehow the the dot
+ 
+
+ align:start position:0%
+between them right somehow the the dot
+product of two
+
+ align:start position:0%
+product of two
+ 
+
+ align:start position:0%
+product of two
+vectors is if I divide by the length of
+
+ align:start position:0%
+vectors is if I divide by the length of
+ 
+
+ align:start position:0%
+vectors is if I divide by the length of
+the vectors so the dotproduct of vectors
+
+ align:start position:0%
+the vectors so the dotproduct of vectors
+ 
+
+ align:start position:0%
+the vectors so the dotproduct of vectors
+divided by the length do you know what
+
+ align:start position:0%
+divided by the length do you know what
+ 
+
+ align:start position:0%
+divided by the length do you know what
+this is in in
+
+ align:start position:0%
+this is in in
+ 
+
+ align:start position:0%
+this is in in
+Geometry it's a coine it's the coine of
+
+ align:start position:0%
+Geometry it's a coine it's the coine of
+ 
+
+ align:start position:0%
+Geometry it's a coine it's the coine of
+the angle between
+
+ align:start position:0%
+the angle between
+ 
+
+ align:start position:0%
+the angle between
+them and cosiness are never larger than
+
+ align:start position:0%
+them and cosiness are never larger than
+ 
+
+ align:start position:0%
+them and cosiness are never larger than
+one so this quantity here is never
+
+ align:start position:0%
+one so this quantity here is never
+ 
+
+ align:start position:0%
+one so this quantity here is never
+larger than one in other words this is
+
+ align:start position:0%
+larger than one in other words this is
+ 
+
+ align:start position:0%
+larger than one in other words this is
+never larger than the length of one
+
+ align:start position:0%
+never larger than the length of one
+ 
+
+ align:start position:0%
+never larger than the length of one
+vector times the length of the other
+
+ align:start position:0%
+vector times the length of the other
+ 
+
+ align:start position:0%
+vector times the length of the other
+Vector right I could do an example let V
+
+ align:start position:0%
+Vector right I could do an example let V
+ 
+
+ align:start position:0%
+Vector right I could do an example let V
+be uh
+
+ align:start position:0%
+be uh
+ 
+
+ align:start position:0%
+be uh
+13 and let
+
+ align:start position:0%
+13 and let
+ 
+
+ align:start position:0%
+13 and let
+WB six I don't know how this is going to
+
+ align:start position:0%
+WB six I don't know how this is going to
+ 
+
+ align:start position:0%
+WB six I don't know how this is going to
+work what's the dotproduct of those two
+
+ align:start position:0%
+work what's the dotproduct of those two
+ 
+
+ align:start position:0%
+work what's the dotproduct of those two
+vectors oh it's 19 sorry about that
+
+ align:start position:0%
+vectors oh it's 19 sorry about that
+ 
+
+ align:start position:0%
+vectors oh it's 19 sorry about that
+let's change this to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I want I'd like a nice number here
+
+ align:start position:0%
+what I want I'd like a nice number here
+ 
+
+ align:start position:0%
+what I want I'd like a nice number here
+what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggest make a five somewhere here oh
+
+ align:start position:0%
+suggest make a five somewhere here oh
+ 
+
+ align:start position:0%
+suggest make a five somewhere here oh
+yeah five wouldn't be bad five wouldn't
+
+ align:start position:0%
+yeah five wouldn't be bad five wouldn't
+ 
+
+ align:start position:0%
+yeah five wouldn't be bad five wouldn't
+be bad well it wouldn't be too good
+
+ align:start position:0%
+be bad well it wouldn't be too good
+ 
+
+ align:start position:0%
+be bad well it wouldn't be too good
+either but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah ah let's do it okay what's the
+
+ align:start position:0%
+um yeah ah let's do it okay what's the
+ 
+
+ align:start position:0%
+um yeah ah let's do it okay what's the
+dot product of those 16 and now what am
+
+ align:start position:0%
+dot product of those 16 and now what am
+ 
+
+ align:start position:0%
+dot product of those 16 and now what am
+I claiming that that's length less than
+
+ align:start position:0%
+I claiming that that's length less than
+ 
+
+ align:start position:0%
+I claiming that that's length less than
+the length of this Vector which is what
+
+ align:start position:0%
+the length of this Vector which is what
+ 
+
+ align:start position:0%
+the length of this Vector which is what
+what's the length of
+
+ align:start position:0%
+what's the length of
+ 
+
+ align:start position:0%
+what's the length of
+13 square otk of 10 it's good to do
+
+ align:start position:0%
+13 square otk of 10 it's good to do
+ 
+
+ align:start position:0%
+13 square otk of 10 it's good to do
+these small ones just to remember the
+
+ align:start position:0%
+these small ones just to remember the
+ 
+
+ align:start position:0%
+these small ones just to remember the
+length of that Vector is the sum of
+
+ align:start position:0%
+length of that Vector is the sum of
+ 
+
+ align:start position:0%
+length of that Vector is the sum of
+square root of the sum of the square
+
+ align:start position:0%
+square root of the sum of the square
+ 
+
+ align:start position:0%
+square root of the sum of the square
+square root of 10 and the length of this
+
+ align:start position:0%
+square root of 10 and the length of this
+ 
+
+ align:start position:0%
+square root of 10 and the length of this
+guy is the square root of
+
+ align:start position:0%
+guy is the square root of
+ 
+
+ align:start position:0%
+guy is the square root of
+26 and so I hope and Schwarz hopes that
+
+ align:start position:0%
+26 and so I hope and Schwarz hopes that
+ 
+
+ align:start position:0%
+26 and so I hope and Schwarz hopes that
+16 is less than that square root can we
+
+ align:start position:0%
+16 is less than that square root can we
+ 
+
+ align:start position:0%
+16 is less than that square root can we
+check it um well let's Square both sides
+
+ align:start position:0%
+check it um well let's Square both sides
+ 
+
+ align:start position:0%
+check it um well let's Square both sides
+that would make it easier uh so the
+
+ align:start position:0%
+that would make it easier uh so the
+ 
+
+ align:start position:0%
+that would make it easier uh so the
+right hand side when I Square both sides
+
+ align:start position:0%
+right hand side when I Square both sides
+ 
+
+ align:start position:0%
+right hand side when I Square both sides
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+260 when I Square both sides and what's
+
+ align:start position:0%
+260 when I Square both sides and what's
+ 
+
+ align:start position:0%
+260 when I Square both sides and what's
+the square of
+
+ align:start position:0%
+the square of
+ 
+
+ align:start position:0%
+the square of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+256 that was
+
+ align:start position:0%
+256 that was
+ 
+
+ align:start position:0%
+256 that was
+close
+
+ align:start position:0%
+close
+ 
+
+ align:start position:0%
+close
+but it worked right
+
+ align:start position:0%
+but it worked right
+ 
+
+ align:start position:0%
+but it worked right
+right I'll admit to you my whoops not
+
+ align:start position:0%
+right I'll admit to you my whoops not
+ 
+
+ align:start position:0%
+right I'll admit to you my whoops not
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+ah less or equal Schwarz would say and
+
+ align:start position:0%
+ah less or equal Schwarz would say and
+ 
+
+ align:start position:0%
+ah less or equal Schwarz would say and
+uh and uh it's actually less than
+
+ align:start position:0%
+uh and uh it's actually less than
+ 
+
+ align:start position:0%
+uh and uh it's actually less than
+because these vectors are not in the
+
+ align:start position:0%
+because these vectors are not in the
+ 
+
+ align:start position:0%
+because these vectors are not in the
+same direction if they were exactly in
+
+ align:start position:0%
+same direction if they were exactly in
+ 
+
+ align:start position:0%
+same direction if they were exactly in
+the same direction or opposite
+
+ align:start position:0%
+the same direction or opposite
+ 
+
+ align:start position:0%
+the same direction or opposite
+directions the cosine would be one and
+
+ align:start position:0%
+directions the cosine would be one and
+ 
+
+ align:start position:0%
+directions the cosine would be one and
+we would have equals but since the angle
+
+ align:start position:0%
+we would have equals but since the angle
+ 
+
+ align:start position:0%
+we would have equals but since the angle
+you see the angle between those two
+
+ align:start position:0%
+you see the angle between those two
+ 
+
+ align:start position:0%
+you see the angle between those two
+vectors is is is uh you know it's it's
+
+ align:start position:0%
+vectors is is is uh you know it's it's
+ 
+
+ align:start position:0%
+vectors is is is uh you know it's it's
+pretty small angle the cosine is quite
+
+ align:start position:0%
+pretty small angle the cosine is quite
+ 
+
+ align:start position:0%
+pretty small angle the cosine is quite
+near one but it's not exactly one yeah
+
+ align:start position:0%
+near one but it's not exactly one yeah
+ 
+
+ align:start position:0%
+near one but it's not exactly one yeah
+yeah so I'm glad somebody knew 16
+
+ align:start position:0%
+yeah so I'm glad somebody knew 16
+ 
+
+ align:start position:0%
+yeah so I'm glad somebody knew 16
+squared does anybody know 99
+
+ align:start position:0%
+squared does anybody know 99
+ 
+
+ align:start position:0%
+squared does anybody know 99
+squared it was I the reason I asked that
+
+ align:start position:0%
+squared it was I the reason I asked that
+ 
+
+ align:start position:0%
+squared it was I the reason I asked that
+is or 999 I'll make it sound harder uh
+
+ align:start position:0%
+is or 999 I'll make it sound harder uh
+ 
+
+ align:start position:0%
+is or 999 I'll make it sound harder uh
+the was the hope when I was a about 11
+
+ align:start position:0%
+the was the hope when I was a about 11
+ 
+
+ align:start position:0%
+the was the hope when I was a about 11
+or something I was always hoping
+
+ align:start position:0%
+or something I was always hoping
+ 
+
+ align:start position:0%
+or something I was always hoping
+somebody would ask me 999 squared
+
+ align:start position:0%
+somebody would ask me 999 squared
+ 
+
+ align:start position:0%
+somebody would ask me 999 squared
+because I was already ready with the
+
+ align:start position:0%
+because I was already ready with the
+ 
+
+ align:start position:0%
+because I was already ready with the
+answer nobody ever asked anyway but vast
+
+ align:start position:0%
+answer nobody ever asked anyway but vast
+ 
+
+ align:start position:0%
+answer nobody ever asked anyway but vast
+I think uh so 998,199
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
\ No newline at end of file
diff --git a/AYisLr9e0y4.txt b/AYisLr9e0y4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9a32a3b570821946d7642a57e05fcd4bbe438b08
--- /dev/null
+++ b/AYisLr9e0y4.txt
@@ -0,0 +1,1307 @@
+align:start position:0%
+ 
+welcome back to recitation what I'd like
+
+ align:start position:0%
+welcome back to recitation what I'd like
+ 
+
+ align:start position:0%
+welcome back to recitation what I'd like
+us to do in this in these two problems
+
+ align:start position:0%
+us to do in this in these two problems
+ 
+
+ align:start position:0%
+us to do in this in these two problems
+is to understand how to compute the flux
+
+ align:start position:0%
+is to understand how to compute the flux
+ 
+
+ align:start position:0%
+is to understand how to compute the flux
+in three dimensions the flux of a vector
+
+ align:start position:0%
+in three dimensions the flux of a vector
+ 
+
+ align:start position:0%
+in three dimensions the flux of a vector
+in three dimensions across a surface
+
+ align:start position:0%
+in three dimensions across a surface
+ 
+
+ align:start position:0%
+in three dimensions across a surface
+without maybe doing a lot of calculation
+
+ align:start position:0%
+without maybe doing a lot of calculation
+ 
+
+ align:start position:0%
+without maybe doing a lot of calculation
+so we're going to see if we can figure
+
+ align:start position:0%
+so we're going to see if we can figure
+ 
+
+ align:start position:0%
+so we're going to see if we can figure
+out how to do the these problems without
+
+ align:start position:0%
+out how to do the these problems without
+ 
+
+ align:start position:0%
+out how to do the these problems without
+doing a lot of computation so the first
+
+ align:start position:0%
+doing a lot of computation so the first
+ 
+
+ align:start position:0%
+doing a lot of computation so the first
+one is to find the V sorry find the flux
+
+ align:start position:0%
+one is to find the V sorry find the flux
+ 
+
+ align:start position:0%
+one is to find the V sorry find the flux
+of the vector k through the infinite
+
+ align:start position:0%
+of the vector k through the infinite
+ 
+
+ align:start position:0%
+of the vector k through the infinite
+cylinder x^2 + y^2 equal 1 so notice
+
+ align:start position:0%
+cylinder x^2 + y^2 equal 1 so notice
+ 
+
+ align:start position:0%
+cylinder x^2 + y^2 equal 1 so notice
+this is doesn't depend on Z but in fact
+
+ align:start position:0%
+this is doesn't depend on Z but in fact
+ 
+
+ align:start position:0%
+this is doesn't depend on Z but in fact
+at every height it is it is a unit
+
+ align:start position:0%
+at every height it is it is a unit
+ 
+
+ align:start position:0%
+at every height it is it is a unit
+circle so it's an infinite cylinder and
+
+ align:start position:0%
+circle so it's an infinite cylinder and
+ 
+
+ align:start position:0%
+circle so it's an infinite cylinder and
+then the second problem I'd like you to
+
+ align:start position:0%
+then the second problem I'd like you to
+ 
+
+ align:start position:0%
+then the second problem I'd like you to
+think about and to try is to find the
+
+ align:start position:0%
+think about and to try is to find the
+ 
+
+ align:start position:0%
+think about and to try is to find the
+flux of the vector J through one square
+
+ align:start position:0%
+flux of the vector J through one square
+ 
+
+ align:start position:0%
+flux of the vector J through one square
+that has side length one in the XZ plane
+
+ align:start position:0%
+that has side length one in the XZ plane
+ 
+
+ align:start position:0%
+that has side length one in the XZ plane
+so you pick any Square in the X plane of
+
+ align:start position:0%
+so you pick any Square in the X plane of
+ 
+
+ align:start position:0%
+so you pick any Square in the X plane of
+side length one and find the flux of J
+
+ align:start position:0%
+side length one and find the flux of J
+ 
+
+ align:start position:0%
+side length one and find the flux of J
+through that square and so I think think
+
+ align:start position:0%
+through that square and so I think think
+ 
+
+ align:start position:0%
+through that square and so I think think
+that that's enough information so why
+
+ align:start position:0%
+that that's enough information so why
+ 
+
+ align:start position:0%
+that that's enough information so why
+don't you try both those problems pause
+
+ align:start position:0%
+don't you try both those problems pause
+ 
+
+ align:start position:0%
+don't you try both those problems pause
+the video and then when you're ready to
+
+ align:start position:0%
+the video and then when you're ready to
+ 
+
+ align:start position:0%
+the video and then when you're ready to
+see my explanation of of how they work
+
+ align:start position:0%
+see my explanation of of how they work
+ 
+
+ align:start position:0%
+see my explanation of of how they work
+bring the video back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up okay welcome back again what we're
+
+ align:start position:0%
+up okay welcome back again what we're
+ 
+
+ align:start position:0%
+up okay welcome back again what we're
+trying to do is to understand the flux
+
+ align:start position:0%
+trying to do is to understand the flux
+ 
+
+ align:start position:0%
+trying to do is to understand the flux
+of a vector field across a surface and
+
+ align:start position:0%
+of a vector field across a surface and
+ 
+
+ align:start position:0%
+of a vector field across a surface and
+we're hoping to do it with the least
+
+ align:start position:0%
+we're hoping to do it with the least
+ 
+
+ align:start position:0%
+we're hoping to do it with the least
+amount of calculation possible for these
+
+ align:start position:0%
+amount of calculation possible for these
+ 
+
+ align:start position:0%
+amount of calculation possible for these
+particular problems so obviously it's
+
+ align:start position:0%
+particular problems so obviously it's
+ 
+
+ align:start position:0%
+particular problems so obviously it's
+going going to be helpful if you can
+
+ align:start position:0%
+going going to be helpful if you can
+ 
+
+ align:start position:0%
+going going to be helpful if you can
+draw a picture to draw a picture so I'm
+
+ align:start position:0%
+draw a picture to draw a picture so I'm
+ 
+
+ align:start position:0%
+draw a picture to draw a picture so I'm
+going to draw the surface that is the
+
+ align:start position:0%
+going to draw the surface that is the
+ 
+
+ align:start position:0%
+going to draw the surface that is the
+infinite cylinder first and then I'm
+
+ align:start position:0%
+infinite cylinder first and then I'm
+ 
+
+ align:start position:0%
+infinite cylinder first and then I'm
+going to look at the vector field uh K
+
+ align:start position:0%
+going to look at the vector field uh K
+ 
+
+ align:start position:0%
+going to look at the vector field uh K
+so let me draw my picture first if these
+
+ align:start position:0%
+so let me draw my picture first if these
+ 
+
+ align:start position:0%
+so let me draw my picture first if these
+are my coordinate axes I get uh I think
+
+ align:start position:0%
+are my coordinate axes I get uh I think
+ 
+
+ align:start position:0%
+are my coordinate axes I get uh I think
+you have something usually like this
+
+ align:start position:0%
+you have something usually like this
+ 
+
+ align:start position:0%
+you have something usually like this
+this is X this is y and this is z this
+
+ align:start position:0%
+this is X this is y and this is z this
+ 
+
+ align:start position:0%
+this is X this is y and this is z this
+is how you do them in your class and so
+
+ align:start position:0%
+is how you do them in your class and so
+ 
+
+ align:start position:0%
+is how you do them in your class and so
+it's not going to be a great picture but
+
+ align:start position:0%
+it's not going to be a great picture but
+ 
+
+ align:start position:0%
+it's not going to be a great picture but
+I'm going to try and make it look like a
+
+ align:start position:0%
+I'm going to try and make it look like a
+ 
+
+ align:start position:0%
+I'm going to try and make it look like a
+cylinder a
+
+ align:start position:0%
+cylinder a
+ 
+
+ align:start position:0%
+cylinder a
+here coming down so this is in fact it's
+
+ align:start position:0%
+here coming down so this is in fact it's
+ 
+
+ align:start position:0%
+here coming down so this is in fact it's
+going to be infinitely long going down
+
+ align:start position:0%
+going to be infinitely long going down
+ 
+
+ align:start position:0%
+going to be infinitely long going down
+forever but I'll stop it somewhere down
+
+ align:start position:0%
+forever but I'll stop it somewhere down
+ 
+
+ align:start position:0%
+forever but I'll stop it somewhere down
+here and then so every slice in the Z at
+
+ align:start position:0%
+here and then so every slice in the Z at
+ 
+
+ align:start position:0%
+here and then so every slice in the Z at
+a fixed height for Z is going to be a
+
+ align:start position:0%
+a fixed height for Z is going to be a
+ 
+
+ align:start position:0%
+a fixed height for Z is going to be a
+circle so that's I should think about
+
+ align:start position:0%
+circle so that's I should think about
+ 
+
+ align:start position:0%
+circle so that's I should think about
+these are intersecting the X and Y axis
+
+ align:start position:0%
+these are intersecting the X and Y axis
+ 
+
+ align:start position:0%
+these are intersecting the X and Y axis
+at 1 0 and 01 so there's actually a sort
+
+ align:start position:0%
+at 1 0 and 01 so there's actually a sort
+ 
+
+ align:start position:0%
+at 1 0 and 01 so there's actually a sort
+of unit circle down here as well now
+
+ align:start position:0%
+of unit circle down here as well now
+ 
+
+ align:start position:0%
+of unit circle down here as well now
+that's the surface
+
+ align:start position:0%
+that's the surface
+ 
+
+ align:start position:0%
+that's the surface
+now what does the vector field look like
+
+ align:start position:0%
+now what does the vector field look like
+ 
+
+ align:start position:0%
+now what does the vector field look like
+well in general what does the vector
+
+ align:start position:0%
+well in general what does the vector
+ 
+
+ align:start position:0%
+well in general what does the vector
+field look like K is just a constant
+
+ align:start position:0%
+field look like K is just a constant
+ 
+
+ align:start position:0%
+field look like K is just a constant
+Vector field that points in this
+
+ align:start position:0%
+Vector field that points in this
+ 
+
+ align:start position:0%
+Vector field that points in this
+direction this is K so k at every point
+
+ align:start position:0%
+direction this is K so k at every point
+ 
+
+ align:start position:0%
+direction this is K so k at every point
+on the surface is just the vector that's
+
+ align:start position:0%
+on the surface is just the vector that's
+ 
+
+ align:start position:0%
+on the surface is just the vector that's
+pointing straight up in this direction
+
+ align:start position:0%
+pointing straight up in this direction
+ 
+
+ align:start position:0%
+pointing straight up in this direction
+and the normal to the surface if you
+
+ align:start position:0%
+and the normal to the surface if you
+ 
+
+ align:start position:0%
+and the normal to the surface if you
+think about it the normal to the surface
+
+ align:start position:0%
+think about it the normal to the surface
+ 
+
+ align:start position:0%
+think about it the normal to the surface
+is independent of Z it doesn't depend on
+
+ align:start position:0%
+is independent of Z it doesn't depend on
+ 
+
+ align:start position:0%
+is independent of Z it doesn't depend on
+Z at all it is always going to be a
+
+ align:start position:0%
+Z at all it is always going to be a
+ 
+
+ align:start position:0%
+Z at all it is always going to be a
+vector that is in the XY Direction only
+
+ align:start position:0%
+vector that is in the XY Direction only
+ 
+
+ align:start position:0%
+vector that is in the XY Direction only
+it's going to be essentially at every
+
+ align:start position:0%
+it's going to be essentially at every
+ 
+
+ align:start position:0%
+it's going to be essentially at every
+point it's going to be be sitting in the
+
+ align:start position:0%
+point it's going to be be sitting in the
+ 
+
+ align:start position:0%
+point it's going to be be sitting in the
+the plane Z equals a constant because if
+
+ align:start position:0%
+the plane Z equals a constant because if
+ 
+
+ align:start position:0%
+the plane Z equals a constant because if
+you think about what you have you have a
+
+ align:start position:0%
+you think about what you have you have a
+ 
+
+ align:start position:0%
+you think about what you have you have a
+unit circle at every height and it
+
+ align:start position:0%
+unit circle at every height and it
+ 
+
+ align:start position:0%
+unit circle at every height and it
+doesn't vary in the Z Direction at all
+
+ align:start position:0%
+doesn't vary in the Z Direction at all
+ 
+
+ align:start position:0%
+doesn't vary in the Z Direction at all
+with that the bending of that unit
+
+ align:start position:0%
+with that the bending of that unit
+ 
+
+ align:start position:0%
+with that the bending of that unit
+circle so in fact the normal is always
+
+ align:start position:0%
+circle so in fact the normal is always
+ 
+
+ align:start position:0%
+circle so in fact the normal is always
+going to point straight out from the
+
+ align:start position:0%
+going to point straight out from the
+ 
+
+ align:start position:0%
+going to point straight out from the
+unit circle there's going to be no Z
+
+ align:start position:0%
+unit circle there's going to be no Z
+ 
+
+ align:start position:0%
+unit circle there's going to be no Z
+component or I should say the Z
+
+ align:start position:0%
+component or I should say the Z
+ 
+
+ align:start position:0%
+component or I should say the Z
+component zero maybe that's the best way
+
+ align:start position:0%
+component zero maybe that's the best way
+ 
+
+ align:start position:0%
+component zero maybe that's the best way
+to say it so that means that the normal
+
+ align:start position:0%
+to say it so that means that the normal
+ 
+
+ align:start position:0%
+to say it so that means that the normal
+dotted with K is going to be zero and so
+
+ align:start position:0%
+dotted with K is going to be zero and so
+ 
+
+ align:start position:0%
+dotted with K is going to be zero and so
+the answer to the first question is the
+
+ align:start position:0%
+the answer to the first question is the
+ 
+
+ align:start position:0%
+the answer to the first question is the
+flux of K through the infinite cylinder
+
+ align:start position:0%
+flux of K through the infinite cylinder
+ 
+
+ align:start position:0%
+flux of K through the infinite cylinder
+is actually
+
+ align:start position:0%
+is actually
+ 
+
+ align:start position:0%
+is actually
+zero okay so the answer to part
+
+ align:start position:0%
+zero okay so the answer to part
+ 
+
+ align:start position:0%
+zero okay so the answer to part
+A is zero been getting a lot of zeros in
+
+ align:start position:0%
+A is zero been getting a lot of zeros in
+ 
+
+ align:start position:0%
+A is zero been getting a lot of zeros in
+my videos so far okay the next one is
+
+ align:start position:0%
+my videos so far okay the next one is
+ 
+
+ align:start position:0%
+my videos so far okay the next one is
+Def find the flux of the vector J
+
+ align:start position:0%
+Def find the flux of the vector J
+ 
+
+ align:start position:0%
+Def find the flux of the vector J
+through one square in the XZ plane where
+
+ align:start position:0%
+through one square in the XZ plane where
+ 
+
+ align:start position:0%
+through one square in the XZ plane where
+the squares have side length one so I
+
+ align:start position:0%
+the squares have side length one so I
+ 
+
+ align:start position:0%
+the squares have side length one so I
+can draw any Square I want that seems to
+
+ align:start position:0%
+can draw any Square I want that seems to
+ 
+
+ align:start position:0%
+can draw any Square I want that seems to
+imply that maybe it'll be the same
+
+ align:start position:0%
+imply that maybe it'll be the same
+ 
+
+ align:start position:0%
+imply that maybe it'll be the same
+answer everywhere so let's see what we
+
+ align:start position:0%
+answer everywhere so let's see what we
+ 
+
+ align:start position:0%
+answer everywhere so let's see what we
+get let me draw a picture for Part B
+
+ align:start position:0%
+get let me draw a picture for Part B
+ 
+
+ align:start position:0%
+get let me draw a picture for Part B
+should label this first Maybe
+
+ align:start position:0%
+should label this first Maybe
+ 
+
+ align:start position:0%
+should label this first Maybe
+okay let me label my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axes and I'm going to draw the simplest
+
+ align:start position:0%
+axes and I'm going to draw the simplest
+ 
+
+ align:start position:0%
+axes and I'm going to draw the simplest
+one I can that does not look like a
+
+ align:start position:0%
+one I can that does not look like a
+ 
+
+ align:start position:0%
+one I can that does not look like a
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+but I'm not great at this there we go
+
+ align:start position:0%
+but I'm not great at this there we go
+ 
+
+ align:start position:0%
+but I'm not great at this there we go
+okay so this is my Surface sitting in
+
+ align:start position:0%
+okay so this is my Surface sitting in
+ 
+
+ align:start position:0%
+okay so this is my Surface sitting in
+the XZ plane this side length is one and
+
+ align:start position:0%
+the XZ plane this side length is one and
+ 
+
+ align:start position:0%
+the XZ plane this side length is one and
+this side length is one all right so
+
+ align:start position:0%
+this side length is one all right so
+ 
+
+ align:start position:0%
+this side length is one all right so
+what is the normal to that surface well
+
+ align:start position:0%
+what is the normal to that surface well
+ 
+
+ align:start position:0%
+what is the normal to that surface well
+we have two choices and so we will
+
+ align:start position:0%
+we have two choices and so we will
+ 
+
+ align:start position:0%
+we have two choices and so we will
+actually have a possibility of two
+
+ align:start position:0%
+actually have a possibility of two
+ 
+
+ align:start position:0%
+actually have a possibility of two
+answers so let me point out that the
+
+ align:start position:0%
+answers so let me point out that the
+ 
+
+ align:start position:0%
+answers so let me point out that the
+normal to the surface well what
+
+ align:start position:0%
+normal to the surface well what
+ 
+
+ align:start position:0%
+normal to the surface well what
+direction does it point in because this
+
+ align:start position:0%
+direction does it point in because this
+ 
+
+ align:start position:0%
+direction does it point in because this
+plane is in the XZ plane the normal to
+
+ align:start position:0%
+plane is in the XZ plane the normal to
+ 
+
+ align:start position:0%
+plane is in the XZ plane the normal to
+the surface is either J or it's minus J
+
+ align:start position:0%
+the surface is either J or it's minus J
+ 
+
+ align:start position:0%
+the surface is either J or it's minus J
+right and so if I'm integrating J dotted
+
+ align:start position:0%
+right and so if I'm integrating J dotted
+ 
+
+ align:start position:0%
+right and so if I'm integrating J dotted
+with the normal over the
+
+ align:start position:0%
+with the normal over the
+ 
+
+ align:start position:0%
+with the normal over the
+surface I I'll just call this surface
+
+ align:start position:0%
+surface I I'll just call this surface
+ 
+
+ align:start position:0%
+surface I I'll just call this surface
+capital r if I'm integrating over r j
+
+ align:start position:0%
+capital r if I'm integrating over r j
+ 
+
+ align:start position:0%
+capital r if I'm integrating over r j
+dotted with the normal DS right J dotted
+
+ align:start position:0%
+dotted with the normal DS right J dotted
+ 
+
+ align:start position:0%
+dotted with the normal DS right J dotted
+with the normal is going to be either
+
+ align:start position:0%
+with the normal is going to be either
+ 
+
+ align:start position:0%
+with the normal is going to be either
+one or minus one and hopefully that
+
+ align:start position:0%
+one or minus one and hopefully that
+ 
+
+ align:start position:0%
+one or minus one and hopefully that
+makes sense because J let me draw this J
+
+ align:start position:0%
+makes sense because J let me draw this J
+ 
+
+ align:start position:0%
+makes sense because J let me draw this J
+is pointing exactly in the y direction
+
+ align:start position:0%
+is pointing exactly in the y direction
+ 
+
+ align:start position:0%
+is pointing exactly in the y direction
+right and the normal is either in this
+
+ align:start position:0%
+right and the normal is either in this
+ 
+
+ align:start position:0%
+right and the normal is either in this
+direction or in the opposite direction
+
+ align:start position:0%
+direction or in the opposite direction
+ 
+
+ align:start position:0%
+direction or in the opposite direction
+up to how I choose to orient the surface
+
+ align:start position:0%
+up to how I choose to orient the surface
+ 
+
+ align:start position:0%
+up to how I choose to orient the surface
+and so J down with n is either plus or
+
+ align:start position:0%
+and so J down with n is either plus or
+ 
+
+ align:start position:0%
+and so J down with n is either plus or
+minus one and so I just get the area of
+
+ align:start position:0%
+minus one and so I just get the area of
+ 
+
+ align:start position:0%
+minus one and so I just get the area of
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+r as a with a plus or minus and oh that
+
+ align:start position:0%
+r as a with a plus or minus and oh that
+ 
+
+ align:start position:0%
+r as a with a plus or minus and oh that
+doesn't look like a plus or minus with a
+
+ align:start position:0%
+doesn't look like a plus or minus with a
+ 
+
+ align:start position:0%
+doesn't look like a plus or minus with a
+plus or minus in
+
+ align:start position:0%
+plus or minus in
+ 
+
+ align:start position:0%
+plus or minus in
+front Okay depending on whether J dotted
+
+ align:start position:0%
+front Okay depending on whether J dotted
+ 
+
+ align:start position:0%
+front Okay depending on whether J dotted
+with n is one or whether J dotted with n
+
+ align:start position:0%
+with n is one or whether J dotted with n
+ 
+
+ align:start position:0%
+with n is one or whether J dotted with n
+is minus one so the solution for for
+
+ align:start position:0%
+is minus one so the solution for for
+ 
+
+ align:start position:0%
+is minus one so the solution for for
+this computation is just the area of r
+
+ align:start position:0%
+this computation is just the area of r
+ 
+
+ align:start position:0%
+this computation is just the area of r
+or minus the area of R well what's the
+
+ align:start position:0%
+or minus the area of R well what's the
+ 
+
+ align:start position:0%
+or minus the area of R well what's the
+area of the region the area it's a
+
+ align:start position:0%
+area of the region the area it's a
+ 
+
+ align:start position:0%
+area of the region the area it's a
+square of side length one so it has area
+
+ align:start position:0%
+square of side length one so it has area
+ 
+
+ align:start position:0%
+square of side length one so it has area
+one so the final answer is just plus or
+
+ align:start position:0%
+one so the final answer is just plus or
+ 
+
+ align:start position:0%
+one so the final answer is just plus or
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one so again let me remind you what
+
+ align:start position:0%
+one so again let me remind you what
+ 
+
+ align:start position:0%
+one so again let me remind you what
+we're trying to do we're trying to do
+
+ align:start position:0%
+we're trying to do we're trying to do
+ 
+
+ align:start position:0%
+we're trying to do we're trying to do
+determine these some fluxes of vector
+
+ align:start position:0%
+determine these some fluxes of vector
+ 
+
+ align:start position:0%
+determine these some fluxes of vector
+Fields across surfaces without doing a
+
+ align:start position:0%
+Fields across surfaces without doing a
+ 
+
+ align:start position:0%
+Fields across surfaces without doing a
+lot of calculation
+
+ align:start position:0%
+lot of calculation
+ 
+
+ align:start position:0%
+lot of calculation
+and in the first case we had a vector
+
+ align:start position:0%
+and in the first case we had a vector
+ 
+
+ align:start position:0%
+and in the first case we had a vector
+field that pointed in the Z Direction
+
+ align:start position:0%
+field that pointed in the Z Direction
+ 
+
+ align:start position:0%
+field that pointed in the Z Direction
+only and the normal was only in the X
+
+ align:start position:0%
+only and the normal was only in the X
+ 
+
+ align:start position:0%
+only and the normal was only in the X
+and Y Direction and so the flux was zero
+
+ align:start position:0%
+and Y Direction and so the flux was zero
+ 
+
+ align:start position:0%
+and Y Direction and so the flux was zero
+even though it was a vector field on an
+
+ align:start position:0%
+even though it was a vector field on an
+ 
+
+ align:start position:0%
+even though it was a vector field on an
+infinite cylinder the flux was still
+
+ align:start position:0%
+infinite cylinder the flux was still
+ 
+
+ align:start position:0%
+infinite cylinder the flux was still
+zero and in the other case I had
+
+ align:start position:0%
+zero and in the other case I had
+ 
+
+ align:start position:0%
+zero and in the other case I had
+actually here I had some I had a surface
+
+ align:start position:0%
+actually here I had some I had a surface
+ 
+
+ align:start position:0%
+actually here I had some I had a surface
+that was exactly in the XZ plane and so
+
+ align:start position:0%
+that was exactly in the XZ plane and so
+ 
+
+ align:start position:0%
+that was exactly in the XZ plane and so
+its normal was exactly either in the
+
+ align:start position:0%
+its normal was exactly either in the
+ 
+
+ align:start position:0%
+its normal was exactly either in the
+same direction as J or 180° around from
+
+ align:start position:0%
+same direction as J or 180° around from
+ 
+
+ align:start position:0%
+same direction as J or 180° around from
+J so J dotted with the normal was either
+
+ align:start position:0%
+J so J dotted with the normal was either
+ 
+
+ align:start position:0%
+J so J dotted with the normal was either
+plus or minus one and so I only had to
+
+ align:start position:0%
+plus or minus one and so I only had to
+ 
+
+ align:start position:0%
+plus or minus one and so I only had to
+know the area of the region which is why
+
+ align:start position:0%
+know the area of the region which is why
+ 
+
+ align:start position:0%
+know the area of the region which is why
+it didn't matter where I moved this unit
+
+ align:start position:0%
+it didn't matter where I moved this unit
+ 
+
+ align:start position:0%
+it didn't matter where I moved this unit
+Square I didn't tell you where the unit
+
+ align:start position:0%
+Square I didn't tell you where the unit
+ 
+
+ align:start position:0%
+Square I didn't tell you where the unit
+Square had to sit so that's where you
+
+ align:start position:0%
+Square had to sit so that's where you
+ 
+
+ align:start position:0%
+Square had to sit so that's where you
+can see why it didn't matter because
+
+ align:start position:0%
+can see why it didn't matter because
+ 
+
+ align:start position:0%
+can see why it didn't matter because
+it's just the area okay I think that's
+
+ align:start position:0%
+it's just the area okay I think that's
+ 
+
+ align:start position:0%
+it's just the area okay I think that's
+where I'll stop
\ No newline at end of file
diff --git a/CWkh5kb4TGc.txt b/CWkh5kb4TGc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6eb7d148adfcc997dd104eb708d9b9b9eba7e7e6
--- /dev/null
+++ b/CWkh5kb4TGc.txt
@@ -0,0 +1,1643 @@
+align:start position:0%
+ 
+the issue of the approximate rate at
+
+ align:start position:0%
+the issue of the approximate rate at
+ 
+
+ align:start position:0%
+the issue of the approximate rate at
+which things happen
+
+ align:start position:0%
+which things happen
+ 
+
+ align:start position:0%
+which things happen
+is common in a lot of science is the
+
+ align:start position:0%
+is common in a lot of science is the
+ 
+
+ align:start position:0%
+is common in a lot of science is the
+rate at which things fall
+
+ align:start position:0%
+rate at which things fall
+ 
+
+ align:start position:0%
+rate at which things fall
+the rate at which reactions occur and in
+
+ align:start position:0%
+the rate at which reactions occur and in
+ 
+
+ align:start position:0%
+the rate at which reactions occur and in
+computer science
+
+ align:start position:0%
+computer science
+ 
+
+ align:start position:0%
+computer science
+typical concern about growth rates comes
+
+ align:start position:0%
+typical concern about growth rates comes
+ 
+
+ align:start position:0%
+typical concern about growth rates comes
+up in
+
+ align:start position:0%
+up in
+ 
+
+ align:start position:0%
+up in
+looking at the efficiency of algorithms
+
+ align:start position:0%
+looking at the efficiency of algorithms
+ 
+
+ align:start position:0%
+looking at the efficiency of algorithms
+and whether they're growing linearly or
+
+ align:start position:0%
+and whether they're growing linearly or
+ 
+
+ align:start position:0%
+and whether they're growing linearly or
+quadratically
+
+ align:start position:0%
+quadratically
+ 
+
+ align:start position:0%
+quadratically
+or more and we're going to look
+
+ align:start position:0%
+or more and we're going to look
+ 
+
+ align:start position:0%
+or more and we're going to look
+today at four notations that describe
+
+ align:start position:0%
+today at four notations that describe
+ 
+
+ align:start position:0%
+today at four notations that describe
+relations between the growth rates of
+
+ align:start position:0%
+relations between the growth rates of
+ 
+
+ align:start position:0%
+relations between the growth rates of
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+the first of these relations is the
+
+ align:start position:0%
+the first of these relations is the
+ 
+
+ align:start position:0%
+the first of these relations is the
+simplest one it's called asymptotic
+
+ align:start position:0%
+simplest one it's called asymptotic
+ 
+
+ align:start position:0%
+simplest one it's called asymptotic
+equivalence or asymptotic equality so
+
+ align:start position:0%
+equivalence or asymptotic equality so
+ 
+
+ align:start position:0%
+equivalence or asymptotic equality so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+uh tilde symbol is read as
+
+ align:start position:0%
+uh tilde symbol is read as
+ 
+
+ align:start position:0%
+uh tilde symbol is read as
+asymptotically equal to so f of n is
+
+ align:start position:0%
+asymptotically equal to so f of n is
+ 
+
+ align:start position:0%
+asymptotically equal to so f of n is
+asymptotically equal to g of n if and
+
+ align:start position:0%
+asymptotically equal to g of n if and
+ 
+
+ align:start position:0%
+asymptotically equal to g of n if and
+only if
+
+ align:start position:0%
+only if
+ 
+
+ align:start position:0%
+only if
+the limit of the quotient of f of n over
+
+ align:start position:0%
+the limit of the quotient of f of n over
+ 
+
+ align:start position:0%
+the limit of the quotient of f of n over
+g of n
+
+ align:start position:0%
+g of n
+ 
+
+ align:start position:0%
+g of n
+is one let's look at an example
+
+ align:start position:0%
+is one let's look at an example
+ 
+
+ align:start position:0%
+is one let's look at an example
+um n squared is asymptotically equal to
+
+ align:start position:0%
+um n squared is asymptotically equal to
+ 
+
+ align:start position:0%
+um n squared is asymptotically equal to
+n squared plus
+
+ align:start position:0%
+n squared plus
+ 
+
+ align:start position:0%
+n squared plus
+n why is that well it follows trivially
+
+ align:start position:0%
+n why is that well it follows trivially
+ 
+
+ align:start position:0%
+n why is that well it follows trivially
+by manipulating
+
+ align:start position:0%
+by manipulating
+ 
+
+ align:start position:0%
+by manipulating
+the algebra uh the limit of n squared
+
+ align:start position:0%
+the algebra uh the limit of n squared
+ 
+
+ align:start position:0%
+the algebra uh the limit of n squared
+plus n
+
+ align:start position:0%
+plus n
+ 
+
+ align:start position:0%
+plus n
+over n squared simplifying is just the
+
+ align:start position:0%
+over n squared simplifying is just the
+ 
+
+ align:start position:0%
+over n squared simplifying is just the
+same as the limit of 1
+
+ align:start position:0%
+same as the limit of 1
+ 
+
+ align:start position:0%
+same as the limit of 1
+plus 1 over n but as n goes to infinity
+
+ align:start position:0%
+plus 1 over n but as n goes to infinity
+ 
+
+ align:start position:0%
+plus 1 over n but as n goes to infinity
+1 over n goes to 0 so the limit is 1
+
+ align:start position:0%
+1 over n goes to 0 so the limit is 1
+ 
+
+ align:start position:0%
+1 over n goes to 0 so the limit is 1
+as claimed those two expressions
+
+ align:start position:0%
+as claimed those two expressions
+ 
+
+ align:start position:0%
+as claimed those two expressions
+or the functions they define n squared
+
+ align:start position:0%
+or the functions they define n squared
+ 
+
+ align:start position:0%
+or the functions they define n squared
+and n squared plus 1 are asymptotically
+
+ align:start position:0%
+and n squared plus 1 are asymptotically
+ 
+
+ align:start position:0%
+and n squared plus 1 are asymptotically
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+some there are some easy properties of
+
+ align:start position:0%
+some there are some easy properties of
+ 
+
+ align:start position:0%
+some there are some easy properties of
+asymptotic equality that follow
+
+ align:start position:0%
+asymptotic equality that follow
+ 
+
+ align:start position:0%
+asymptotic equality that follow
+immediately from the definition
+
+ align:start position:0%
+immediately from the definition
+ 
+
+ align:start position:0%
+immediately from the definition
+one of them is that it's symmetric
+
+ align:start position:0%
+one of them is that it's symmetric
+ 
+
+ align:start position:0%
+one of them is that it's symmetric
+namely suppose that f is asymptotically
+
+ align:start position:0%
+namely suppose that f is asymptotically
+ 
+
+ align:start position:0%
+namely suppose that f is asymptotically
+equal to g
+
+ align:start position:0%
+equal to g
+ 
+
+ align:start position:0%
+equal to g
+i want to prove that g is asymptotically
+
+ align:start position:0%
+i want to prove that g is asymptotically
+ 
+
+ align:start position:0%
+i want to prove that g is asymptotically
+equal to f well what's going on here
+
+ align:start position:0%
+equal to f well what's going on here
+ 
+
+ align:start position:0%
+equal to f well what's going on here
+let's look at the limit of g over f
+
+ align:start position:0%
+let's look at the limit of g over f
+ 
+
+ align:start position:0%
+let's look at the limit of g over f
+which is what i'd like to prove is one
+
+ align:start position:0%
+which is what i'd like to prove is one
+ 
+
+ align:start position:0%
+which is what i'd like to prove is one
+well the limit of g over f by algebra g
+
+ align:start position:0%
+well the limit of g over f by algebra g
+ 
+
+ align:start position:0%
+well the limit of g over f by algebra g
+over f is the same as one over
+
+ align:start position:0%
+over f is the same as one over
+ 
+
+ align:start position:0%
+over f is the same as one over
+f over g so just moving the limit
+
+ align:start position:0%
+f over g so just moving the limit
+ 
+
+ align:start position:0%
+f over g so just moving the limit
+across the division that's the same as
+
+ align:start position:0%
+across the division that's the same as
+ 
+
+ align:start position:0%
+across the division that's the same as
+one over the limit of f over g
+
+ align:start position:0%
+one over the limit of f over g
+ 
+
+ align:start position:0%
+one over the limit of f over g
+which is one over one and we've proved
+
+ align:start position:0%
+which is one over one and we've proved
+ 
+
+ align:start position:0%
+which is one over one and we've proved
+in other words that g
+
+ align:start position:0%
+in other words that g
+ 
+
+ align:start position:0%
+in other words that g
+is asymptotically equal to f given that
+
+ align:start position:0%
+is asymptotically equal to f given that
+ 
+
+ align:start position:0%
+is asymptotically equal to f given that
+f is asymptotically equal to g
+
+ align:start position:0%
+f is asymptotically equal to g
+ 
+
+ align:start position:0%
+f is asymptotically equal to g
+it's symmetric there's a similar
+
+ align:start position:0%
+it's symmetric there's a similar
+ 
+
+ align:start position:0%
+it's symmetric there's a similar
+argument for transitivity let's just
+
+ align:start position:0%
+argument for transitivity let's just
+ 
+
+ align:start position:0%
+argument for transitivity let's just
+crank through it for practice on the
+
+ align:start position:0%
+crank through it for practice on the
+ 
+
+ align:start position:0%
+crank through it for practice on the
+definition suppose that f
+
+ align:start position:0%
+definition suppose that f
+ 
+
+ align:start position:0%
+definition suppose that f
+is asymptotically equal to g and g is
+
+ align:start position:0%
+is asymptotically equal to g and g is
+ 
+
+ align:start position:0%
+is asymptotically equal to g and g is
+asymptotically equal to h i'd like to
+
+ align:start position:0%
+asymptotically equal to h i'd like to
+ 
+
+ align:start position:0%
+asymptotically equal to h i'd like to
+prove that
+
+ align:start position:0%
+prove that
+ 
+
+ align:start position:0%
+prove that
+f is asymptotically equal to h
+
+ align:start position:0%
+f is asymptotically equal to h
+ 
+
+ align:start position:0%
+f is asymptotically equal to h
+well again we just plug into the
+
+ align:start position:0%
+well again we just plug into the
+ 
+
+ align:start position:0%
+well again we just plug into the
+algebra and distribute limits let's just
+
+ align:start position:0%
+algebra and distribute limits let's just
+ 
+
+ align:start position:0%
+algebra and distribute limits let's just
+look at this we're given that one
+
+ align:start position:0%
+look at this we're given that one
+ 
+
+ align:start position:0%
+look at this we're given that one
+is the limit of f over g because f is
+
+ align:start position:0%
+is the limit of f over g because f is
+ 
+
+ align:start position:0%
+is the limit of f over g because f is
+asymptotic to g
+
+ align:start position:0%
+asymptotic to g
+ 
+
+ align:start position:0%
+asymptotic to g
+but f over g can be expressed as f over
+
+ align:start position:0%
+but f over g can be expressed as f over
+ 
+
+ align:start position:0%
+but f over g can be expressed as f over
+h divided by g
+
+ align:start position:0%
+h divided by g
+ 
+
+ align:start position:0%
+h divided by g
+over h that's just algebra the h's
+
+ align:start position:0%
+over h that's just algebra the h's
+ 
+
+ align:start position:0%
+over h that's just algebra the h's
+cancel
+
+ align:start position:0%
+cancel
+ 
+
+ align:start position:0%
+cancel
+so this limit now i can distribute the
+
+ align:start position:0%
+so this limit now i can distribute the
+ 
+
+ align:start position:0%
+so this limit now i can distribute the
+limits to the numerator and denominator
+
+ align:start position:0%
+limits to the numerator and denominator
+ 
+
+ align:start position:0%
+limits to the numerator and denominator
+assuming both exist and the numerator
+
+ align:start position:0%
+assuming both exist and the numerator
+ 
+
+ align:start position:0%
+assuming both exist and the numerator
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+is what i'm interested in the
+
+ align:start position:0%
+is what i'm interested in the
+ 
+
+ align:start position:0%
+is what i'm interested in the
+denominator limit is going to be
+
+ align:start position:0%
+denominator limit is going to be
+ 
+
+ align:start position:0%
+denominator limit is going to be
+1 because the limit of g over h is one
+
+ align:start position:0%
+1 because the limit of g over h is one
+ 
+
+ align:start position:0%
+1 because the limit of g over h is one
+since g is asymptotically equal to h the
+
+ align:start position:0%
+since g is asymptotically equal to h the
+ 
+
+ align:start position:0%
+since g is asymptotically equal to h the
+conclusion is indeed
+
+ align:start position:0%
+conclusion is indeed
+ 
+
+ align:start position:0%
+conclusion is indeed
+that the limit of f over h is equal to
+
+ align:start position:0%
+that the limit of f over h is equal to
+ 
+
+ align:start position:0%
+that the limit of f over h is equal to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+this is not really very interesting
+
+ align:start position:0%
+this is not really very interesting
+ 
+
+ align:start position:0%
+this is not really very interesting
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+and the top level message is that many
+
+ align:start position:0%
+and the top level message is that many
+ 
+
+ align:start position:0%
+and the top level message is that many
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+elementary properties of asymptotic
+
+ align:start position:0%
+elementary properties of asymptotic
+ 
+
+ align:start position:0%
+elementary properties of asymptotic
+equality
+
+ align:start position:0%
+equality
+ 
+
+ align:start position:0%
+equality
+and the other asymptotic relations that
+
+ align:start position:0%
+and the other asymptotic relations that
+ 
+
+ align:start position:0%
+and the other asymptotic relations that
+we're going to see
+
+ align:start position:0%
+we're going to see
+ 
+
+ align:start position:0%
+we're going to see
+follow by this kind of elementary
+
+ align:start position:0%
+follow by this kind of elementary
+ 
+
+ align:start position:0%
+follow by this kind of elementary
+algebra and distributing
+
+ align:start position:0%
+algebra and distributing
+ 
+
+ align:start position:0%
+algebra and distributing
+the limits over sub-expressions
+
+ align:start position:0%
+the limits over sub-expressions
+ 
+
+ align:start position:0%
+the limits over sub-expressions
+anyway uh the corollary of this is that
+
+ align:start position:0%
+anyway uh the corollary of this is that
+ 
+
+ align:start position:0%
+anyway uh the corollary of this is that
+asymptotic equality
+
+ align:start position:0%
+asymptotic equality
+ 
+
+ align:start position:0%
+asymptotic equality
+is in fact an equivalence relation we've
+
+ align:start position:0%
+is in fact an equivalence relation we've
+ 
+
+ align:start position:0%
+is in fact an equivalence relation we've
+proved it's symmetric and transitive and
+
+ align:start position:0%
+proved it's symmetric and transitive and
+ 
+
+ align:start position:0%
+proved it's symmetric and transitive and
+it's trivially
+
+ align:start position:0%
+it's trivially
+ 
+
+ align:start position:0%
+it's trivially
+reflexive it's an equivalence relation
+
+ align:start position:0%
+reflexive it's an equivalence relation
+ 
+
+ align:start position:0%
+reflexive it's an equivalence relation
+by the way it's worth noting that it's
+
+ align:start position:0%
+by the way it's worth noting that it's
+ 
+
+ align:start position:0%
+by the way it's worth noting that it's
+an equivalence relation on
+
+ align:start position:0%
+an equivalence relation on
+ 
+
+ align:start position:0%
+an equivalence relation on
+functions of one variable when we write
+
+ align:start position:0%
+functions of one variable when we write
+ 
+
+ align:start position:0%
+functions of one variable when we write
+sometimes that
+
+ align:start position:0%
+sometimes that
+ 
+
+ align:start position:0%
+sometimes that
+f of n is asymptotically equal to g of n
+
+ align:start position:0%
+f of n is asymptotically equal to g of n
+ 
+
+ align:start position:0%
+f of n is asymptotically equal to g of n
+but we mean that f of n is the
+
+ align:start position:0%
+but we mean that f of n is the
+ 
+
+ align:start position:0%
+but we mean that f of n is the
+description of a function
+
+ align:start position:0%
+description of a function
+ 
+
+ align:start position:0%
+description of a function
+f we're not talking about the number
+
+ align:start position:0%
+f we're not talking about the number
+ 
+
+ align:start position:0%
+f we're not talking about the number
+that f n happens to have for some
+
+ align:start position:0%
+that f n happens to have for some
+ 
+
+ align:start position:0%
+that f n happens to have for some
+particular value of f
+
+ align:start position:0%
+particular value of f
+ 
+
+ align:start position:0%
+particular value of f
+so while we'll sometimes write f of n is
+
+ align:start position:0%
+so while we'll sometimes write f of n is
+ 
+
+ align:start position:0%
+so while we'll sometimes write f of n is
+asymptotically equal to g
+
+ align:start position:0%
+asymptotically equal to g
+ 
+
+ align:start position:0%
+asymptotically equal to g
+of n for descriptive purposes the proper
+
+ align:start position:0%
+of n for descriptive purposes the proper
+ 
+
+ align:start position:0%
+of n for descriptive purposes the proper
+thing we should be writing is that f is
+
+ align:start position:0%
+thing we should be writing is that f is
+ 
+
+ align:start position:0%
+thing we should be writing is that f is
+asymptotically equal to g
+
+ align:start position:0%
+asymptotically equal to g
+ 
+
+ align:start position:0%
+asymptotically equal to g
+asymptotic equality is a relation
+
+ align:start position:0%
+asymptotic equality is a relation
+ 
+
+ align:start position:0%
+asymptotic equality is a relation
+between functions
+
+ align:start position:0%
+between functions
+ 
+
+ align:start position:0%
+between functions
+okay the next asymptotic relation we're
+
+ align:start position:0%
+okay the next asymptotic relation we're
+ 
+
+ align:start position:0%
+okay the next asymptotic relation we're
+going to look at is called
+
+ align:start position:0%
+going to look at is called
+ 
+
+ align:start position:0%
+going to look at is called
+asymptotically smaller than
+
+ align:start position:0%
+asymptotically smaller than
+ 
+
+ align:start position:0%
+asymptotically smaller than
+and it's the notation for it is this
+
+ align:start position:0%
+and it's the notation for it is this
+ 
+
+ align:start position:0%
+and it's the notation for it is this
+little o notation so you'd write
+
+ align:start position:0%
+little o notation so you'd write
+ 
+
+ align:start position:0%
+little o notation so you'd write
+that f of n is equal to little o of g of
+
+ align:start position:0%
+that f of n is equal to little o of g of
+ 
+
+ align:start position:0%
+that f of n is equal to little o of g of
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+if and only if the limit of f of n
+
+ align:start position:0%
+if and only if the limit of f of n
+ 
+
+ align:start position:0%
+if and only if the limit of f of n
+over g of n goes to zero as n approaches
+
+ align:start position:0%
+over g of n goes to zero as n approaches
+ 
+
+ align:start position:0%
+over g of n goes to zero as n approaches
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+so let's look at an example of that n
+
+ align:start position:0%
+so let's look at an example of that n
+ 
+
+ align:start position:0%
+so let's look at an example of that n
+squared is little o of n
+
+ align:start position:0%
+squared is little o of n
+ 
+
+ align:start position:0%
+squared is little o of n
+cubed because trivially the limit of n
+
+ align:start position:0%
+cubed because trivially the limit of n
+ 
+
+ align:start position:0%
+cubed because trivially the limit of n
+squared over n cubed is the same as the
+
+ align:start position:0%
+squared over n cubed is the same as the
+ 
+
+ align:start position:0%
+squared over n cubed is the same as the
+limit of one over n it's equal to zero
+
+ align:start position:0%
+limit of one over n it's equal to zero
+ 
+
+ align:start position:0%
+limit of one over n it's equal to zero
+and by similar kind of reasoning that we
+
+ align:start position:0%
+and by similar kind of reasoning that we
+ 
+
+ align:start position:0%
+and by similar kind of reasoning that we
+did for asymptotic equality being an
+
+ align:start position:0%
+did for asymptotic equality being an
+ 
+
+ align:start position:0%
+did for asymptotic equality being an
+equivalence relation it's not very hard
+
+ align:start position:0%
+equivalence relation it's not very hard
+ 
+
+ align:start position:0%
+equivalence relation it's not very hard
+to prove
+
+ align:start position:0%
+to prove
+ 
+
+ align:start position:0%
+to prove
+that uh that little o defines a strict
+
+ align:start position:0%
+that uh that little o defines a strict
+ 
+
+ align:start position:0%
+that uh that little o defines a strict
+partial order
+
+ align:start position:0%
+partial order
+ 
+
+ align:start position:0%
+partial order
+on functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the third relation asymptotic
+
+ align:start position:0%
+so the third relation asymptotic
+ 
+
+ align:start position:0%
+so the third relation asymptotic
+relation is the most
+
+ align:start position:0%
+relation is the most
+ 
+
+ align:start position:0%
+relation is the most
+complicated of the three although it's
+
+ align:start position:0%
+complicated of the three although it's
+ 
+
+ align:start position:0%
+complicated of the three although it's
+arguably the most important in computer
+
+ align:start position:0%
+arguably the most important in computer
+ 
+
+ align:start position:0%
+arguably the most important in computer
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+it's called the asymptotic order of
+
+ align:start position:0%
+it's called the asymptotic order of
+ 
+
+ align:start position:0%
+it's called the asymptotic order of
+growth big o
+
+ align:start position:0%
+growth big o
+ 
+
+ align:start position:0%
+growth big o
+and the definition is that a function f
+
+ align:start position:0%
+and the definition is that a function f
+ 
+
+ align:start position:0%
+and the definition is that a function f
+is big o
+
+ align:start position:0%
+is big o
+ 
+
+ align:start position:0%
+is big o
+of a function g what it means is
+
+ align:start position:0%
+of a function g what it means is
+ 
+
+ align:start position:0%
+of a function g what it means is
+that the limit of f over g is finite
+
+ align:start position:0%
+that the limit of f over g is finite
+ 
+
+ align:start position:0%
+that the limit of f over g is finite
+so it's it might be other than zero or
+
+ align:start position:0%
+so it's it might be other than zero or
+ 
+
+ align:start position:0%
+so it's it might be other than zero or
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+but it's finite and that means that f
+
+ align:start position:0%
+but it's finite and that means that f
+ 
+
+ align:start position:0%
+but it's finite and that means that f
+is big o of g now there's a technicality
+
+ align:start position:0%
+is big o of g now there's a technicality
+ 
+
+ align:start position:0%
+is big o of g now there's a technicality
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+where the expression actually says the
+
+ align:start position:0%
+where the expression actually says the
+ 
+
+ align:start position:0%
+where the expression actually says the
+limb soup
+
+ align:start position:0%
+limb soup
+ 
+
+ align:start position:0%
+limb soup
+of f of n over g of n let's just ignore
+
+ align:start position:0%
+of f of n over g of n let's just ignore
+ 
+
+ align:start position:0%
+of f of n over g of n let's just ignore
+that for now and we'll look at it
+
+ align:start position:0%
+that for now and we'll look at it
+ 
+
+ align:start position:0%
+that for now and we'll look at it
+uh uh and explain why the limb soup is
+
+ align:start position:0%
+uh uh and explain why the limb soup is
+ 
+
+ align:start position:0%
+uh uh and explain why the limb soup is
+there a little later
+
+ align:start position:0%
+there a little later
+ 
+
+ align:start position:0%
+there a little later
+so as an example 3n
+
+ align:start position:0%
+so as an example 3n
+ 
+
+ align:start position:0%
+so as an example 3n
+squared is big o of n squared
+
+ align:start position:0%
+squared is big o of n squared
+ 
+
+ align:start position:0%
+squared is big o of n squared
+because the quotient of 3n squared over
+
+ align:start position:0%
+because the quotient of 3n squared over
+ 
+
+ align:start position:0%
+because the quotient of 3n squared over
+n squared is 3
+
+ align:start position:0%
+n squared is 3
+ 
+
+ align:start position:0%
+n squared is 3
+which is less than infinity so what big
+
+ align:start position:0%
+which is less than infinity so what big
+ 
+
+ align:start position:0%
+which is less than infinity so what big
+o is doing is kind of saying that
+
+ align:start position:0%
+o is doing is kind of saying that
+ 
+
+ align:start position:0%
+o is doing is kind of saying that
+constant factors don't matter
+
+ align:start position:0%
+constant factors don't matter
+ 
+
+ align:start position:0%
+constant factors don't matter
+and that turns out to be particularly
+
+ align:start position:0%
+and that turns out to be particularly
+ 
+
+ align:start position:0%
+and that turns out to be particularly
+useful in computer science where
+
+ align:start position:0%
+useful in computer science where
+ 
+
+ align:start position:0%
+useful in computer science where
+you can't really talk about the time
+
+ align:start position:0%
+you can't really talk about the time
+ 
+
+ align:start position:0%
+you can't really talk about the time
+that a procedure takes because that's
+
+ align:start position:0%
+that a procedure takes because that's
+ 
+
+ align:start position:0%
+that a procedure takes because that's
+going to depend on the hardware
+
+ align:start position:0%
+going to depend on the hardware
+ 
+
+ align:start position:0%
+going to depend on the hardware
+so when you implement it on faster
+
+ align:start position:0%
+so when you implement it on faster
+ 
+
+ align:start position:0%
+so when you implement it on faster
+hardware
+
+ align:start position:0%
+hardware
+ 
+
+ align:start position:0%
+hardware
+it may grow at the same rate but the
+
+ align:start position:0%
+it may grow at the same rate but the
+ 
+
+ align:start position:0%
+it may grow at the same rate but the
+time will actually change
+
+ align:start position:0%
+time will actually change
+ 
+
+ align:start position:0%
+time will actually change
+and that's why big o plays a prominent
+
+ align:start position:0%
+and that's why big o plays a prominent
+ 
+
+ align:start position:0%
+and that's why big o plays a prominent
+role
+
+ align:start position:0%
+role
+ 
+
+ align:start position:0%
+role
+the final relation of the four is called
+
+ align:start position:0%
+the final relation of the four is called
+ 
+
+ align:start position:0%
+the final relation of the four is called
+theta or same order of growth the
+
+ align:start position:0%
+theta or same order of growth the
+ 
+
+ align:start position:0%
+theta or same order of growth the
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+of f is theta of g is simply
+
+ align:start position:0%
+of f is theta of g is simply
+ 
+
+ align:start position:0%
+of f is theta of g is simply
+that f is o of g and g is o of
+
+ align:start position:0%
+that f is o of g and g is o of
+ 
+
+ align:start position:0%
+that f is o of g and g is o of
+f and it's easy to show from the
+
+ align:start position:0%
+f and it's easy to show from the
+ 
+
+ align:start position:0%
+f and it's easy to show from the
+definition that theta
+
+ align:start position:0%
+definition that theta
+ 
+
+ align:start position:0%
+definition that theta
+is an equivalence relation so to
+
+ align:start position:0%
+is an equivalence relation so to
+ 
+
+ align:start position:0%
+is an equivalence relation so to
+summarize
+
+ align:start position:0%
+summarize
+ 
+
+ align:start position:0%
+summarize
+there are these four relations um
+
+ align:start position:0%
+there are these four relations um
+ 
+
+ align:start position:0%
+there are these four relations um
+f asymptotically equal to g means that
+
+ align:start position:0%
+f asymptotically equal to g means that
+ 
+
+ align:start position:0%
+f asymptotically equal to g means that
+informally that f and g are nearly equal
+
+ align:start position:0%
+informally that f and g are nearly equal
+ 
+
+ align:start position:0%
+informally that f and g are nearly equal
+um f equals little o of j informally
+
+ align:start position:0%
+um f equals little o of j informally
+ 
+
+ align:start position:0%
+um f equals little o of j informally
+means that f is much less than g
+
+ align:start position:0%
+means that f is much less than g
+ 
+
+ align:start position:0%
+means that f is much less than g
+f equals o of g means that f is roughly
+
+ align:start position:0%
+f equals o of g means that f is roughly
+ 
+
+ align:start position:0%
+f equals o of g means that f is roughly
+less than or equal to g where roughly
+
+ align:start position:0%
+less than or equal to g where roughly
+ 
+
+ align:start position:0%
+less than or equal to g where roughly
+means that we're not concerned about
+
+ align:start position:0%
+means that we're not concerned about
+ 
+
+ align:start position:0%
+means that we're not concerned about
+constant factors
+
+ align:start position:0%
+constant factors
+ 
+
+ align:start position:0%
+constant factors
+and f equals theta of g means that f is
+
+ align:start position:0%
+and f equals theta of g means that f is
+ 
+
+ align:start position:0%
+and f equals theta of g means that f is
+roughly
+
+ align:start position:0%
+roughly
+ 
+
+ align:start position:0%
+roughly
+equal to g and we'll examine these
+
+ align:start position:0%
+equal to g and we'll examine these
+ 
+
+ align:start position:0%
+equal to g and we'll examine these
+properties in more detail in the next
+
+ align:start position:0%
+properties in more detail in the next
+ 
+
+ align:start position:0%
+properties in more detail in the next
+segment
\ No newline at end of file
diff --git a/DdnXB0Fa3gQ.txt b/DdnXB0Fa3gQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..09edfad5f4db8f7cbea8ffa6e30e67a569d603f0
--- /dev/null
+++ b/DdnXB0Fa3gQ.txt
@@ -0,0 +1,13339 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so where were
+
+ align:start position:0%
+ocw.mit.edu so where were
+ 
+
+ align:start position:0%
+ocw.mit.edu so where were
+we so last time we were talking about
+
+ align:start position:0%
+we so last time we were talking about
+ 
+
+ align:start position:0%
+we so last time we were talking about
+MSR scheme and
+
+ align:start position:0%
+MSR scheme and
+ 
+
+ align:start position:0%
+MSR scheme and
+renormalons and so we talked about the
+
+ align:start position:0%
+renormalons and so we talked about the
+ 
+
+ align:start position:0%
+renormalons and so we talked about the
+msar scheme we talked about renormalons
+
+ align:start position:0%
+msar scheme we talked about renormalons
+ 
+
+ align:start position:0%
+msar scheme we talked about renormalons
+and we said that we could introduce a
+
+ align:start position:0%
+and we said that we could introduce a
+ 
+
+ align:start position:0%
+and we said that we could introduce a
+mass scheme that has an arbitrary power
+
+ align:start position:0%
+mass scheme that has an arbitrary power
+ 
+
+ align:start position:0%
+mass scheme that has an arbitrary power
+law cut off which we called R to
+
+ align:start position:0%
+law cut off which we called R to
+ 
+
+ align:start position:0%
+law cut off which we called R to
+distinguish it from mu or Lambda or some
+
+ align:start position:0%
+distinguish it from mu or Lambda or some
+ 
+
+ align:start position:0%
+distinguish it from mu or Lambda or some
+other cut
+
+ align:start position:0%
+other cut
+ 
+
+ align:start position:0%
+other cut
+off and so the idea of
+
+ align:start position:0%
+off and so the idea of
+ 
+
+ align:start position:0%
+off and so the idea of
+this scheme right here was to go was to
+
+ align:start position:0%
+this scheme right here was to go was to
+ 
+
+ align:start position:0%
+this scheme right here was to go was to
+have a way of perturbing away from Ms
+
+ align:start position:0%
+have a way of perturbing away from Ms
+ 
+
+ align:start position:0%
+have a way of perturbing away from Ms
+bar to get rid of this renormalon
+
+ align:start position:0%
+bar to get rid of this renormalon
+ 
+
+ align:start position:0%
+bar to get rid of this renormalon
+problem that msar has but retain all the
+
+ align:start position:0%
+problem that msar has but retain all the
+ 
+
+ align:start position:0%
+problem that msar has but retain all the
+nice features of
+
+ align:start position:0%
+nice features of
+ 
+
+ align:start position:0%
+nice features of
+msar in particular we don't really want
+
+ align:start position:0%
+msar in particular we don't really want
+ 
+
+ align:start position:0%
+msar in particular we don't really want
+to calculate anything new if we can
+
+ align:start position:0%
+to calculate anything new if we can
+ 
+
+ align:start position:0%
+to calculate anything new if we can
+avoid it and that's what this scheme
+
+ align:start position:0%
+avoid it and that's what this scheme
+ 
+
+ align:start position:0%
+avoid it and that's what this scheme
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+because really what it does is it uses
+
+ align:start position:0%
+because really what it does is it uses
+ 
+
+ align:start position:0%
+because really what it does is it uses
+the fact that we know that the msar
+
+ align:start position:0%
+the fact that we know that the msar
+ 
+
+ align:start position:0%
+the fact that we know that the msar
+scheme has this
+
+ align:start position:0%
+scheme has this
+ 
+
+ align:start position:0%
+scheme has this
+renormalon so this series here has a
+
+ align:start position:0%
+renormalon so this series here has a
+ 
+
+ align:start position:0%
+renormalon so this series here has a
+renormalon and it just takes that series
+
+ align:start position:0%
+renormalon and it just takes that series
+ 
+
+ align:start position:0%
+renormalon and it just takes that series
+over from msar puts it in with a cut off
+
+ align:start position:0%
+over from msar puts it in with a cut off
+ 
+
+ align:start position:0%
+over from msar puts it in with a cut off
+which is this R and defines a new Mass
+
+ align:start position:0%
+which is this R and defines a new Mass
+ 
+
+ align:start position:0%
+which is this R and defines a new Mass
+scheme using that
+
+ align:start position:0%
+scheme using that
+ 
+
+ align:start position:0%
+scheme using that
+formula uh so this is like a mass scheme
+
+ align:start position:0%
+formula uh so this is like a mass scheme
+ 
+
+ align:start position:0%
+formula uh so this is like a mass scheme
+that has an adjust trustable cut off
+
+ align:start position:0%
+that has an adjust trustable cut off
+ 
+
+ align:start position:0%
+that has an adjust trustable cut off
+which we can take to be at whatever
+
+ align:start position:0%
+which we can take to be at whatever
+ 
+
+ align:start position:0%
+which we can take to be at whatever
+scale we want and in particular in HQ
+
+ align:start position:0%
+scale we want and in particular in HQ
+ 
+
+ align:start position:0%
+scale we want and in particular in HQ
+you'd want to take that R to be
+
+ align:start position:0%
+you'd want to take that R to be
+ 
+
+ align:start position:0%
+you'd want to take that R to be
+something like a GV type scale because
+
+ align:start position:0%
+something like a GV type scale because
+ 
+
+ align:start position:0%
+something like a GV type scale because
+that wouldn't spoil your power
+
+ align:start position:0%
+that wouldn't spoil your power
+ 
+
+ align:start position:0%
+that wouldn't spoil your power
+counting so recall in HQ that this Delta
+
+ align:start position:0%
+counting so recall in HQ that this Delta
+ 
+
+ align:start position:0%
+counting so recall in HQ that this Delta
+M should be by power countings of Border
+
+ align:start position:0%
+M should be by power countings of Border
+ 
+
+ align:start position:0%
+M should be by power countings of Border
+Lambda qcd
+
+ align:start position:0%
+Lambda qcd
+ 
+
+ align:start position:0%
+Lambda qcd
+so typically you would take R somewhat
+
+ align:start position:0%
+so typically you would take R somewhat
+ 
+
+ align:start position:0%
+so typically you would take R somewhat
+greater than Lambda qcd bit of order
+
+ align:start position:0%
+greater than Lambda qcd bit of order
+ 
+
+ align:start position:0%
+greater than Lambda qcd bit of order
+Lambda qcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we have this extra cut off
+
+ align:start position:0%
+okay so now we have this extra cut off
+ 
+
+ align:start position:0%
+okay so now we have this extra cut off
+so when we have a cut off we have a
+
+ align:start position:0%
+so when we have a cut off we have a
+ 
+
+ align:start position:0%
+so when we have a cut off we have a
+renormalization group and if you think
+
+ align:start position:0%
+renormalization group and if you think
+ 
+
+ align:start position:0%
+renormalization group and if you think
+about the renormalization group for Ms
+
+ align:start position:0%
+about the renormalization group for Ms
+ 
+
+ align:start position:0%
+about the renormalization group for Ms
+bar Mass it would be something like mu D
+
+ align:start position:0%
+bar Mass it would be something like mu D
+ 
+
+ align:start position:0%
+bar Mass it would be something like mu D
+byd mu of M of mu is equal to anomalous
+
+ align:start position:0%
+byd mu of M of mu is equal to anomalous
+ 
+
+ align:start position:0%
+byd mu of M of mu is equal to anomalous
+Dimension time M of mu back again this
+
+ align:start position:0%
+Dimension time M of mu back again this
+ 
+
+ align:start position:0%
+Dimension time M of mu back again this
+one's a little different it's r d byd r
+
+ align:start position:0%
+one's a little different it's r d byd r
+ 
+
+ align:start position:0%
+one's a little different it's r d byd r
+of M of R and then there's no M on the
+
+ align:start position:0%
+of M of R and then there's no M on the
+ 
+
+ align:start position:0%
+of M of R and then there's no M on the
+right hand side it's an additive
+
+ align:start position:0%
+right hand side it's an additive
+ 
+
+ align:start position:0%
+right hand side it's an additive
+normalization to get rid of the r normal
+
+ align:start position:0%
+normalization to get rid of the r normal
+ 
+
+ align:start position:0%
+normalization to get rid of the r normal
+on and there's a power also of R here
+
+ align:start position:0%
+on and there's a power also of R here
+ 
+
+ align:start position:0%
+on and there's a power also of R here
+okay so it's not just it's not just
+
+ align:start position:0%
+okay so it's not just it's not just
+ 
+
+ align:start position:0%
+okay so it's not just it's not just
+summing log logs it's it is summing some
+
+ align:start position:0%
+summing log logs it's it is summing some
+ 
+
+ align:start position:0%
+summing log logs it's it is summing some
+logs related to the running of alpha but
+
+ align:start position:0%
+logs related to the running of alpha but
+ 
+
+ align:start position:0%
+logs related to the running of alpha but
+it's also got this power and when you
+
+ align:start position:0%
+it's also got this power and when you
+ 
+
+ align:start position:0%
+it's also got this power and when you
+solve this anom almost Dimension
+
+ align:start position:0%
+solve this anom almost Dimension
+ 
+
+ align:start position:0%
+solve this anom almost Dimension
+equation which we talked about last time
+
+ align:start position:0%
+equation which we talked about last time
+ 
+
+ align:start position:0%
+equation which we talked about last time
+you get an integral like this in this T
+
+ align:start position:0%
+you get an integral like this in this T
+ 
+
+ align:start position:0%
+you get an integral like this in this T
+variable and at leading log order it
+
+ align:start position:0%
+variable and at leading log order it
+ 
+
+ align:start position:0%
+variable and at leading log order it
+looks like this difference of two
+
+ align:start position:0%
+looks like this difference of two
+ 
+
+ align:start position:0%
+looks like this difference of two
+incomplete gamma functions because of
+
+ align:start position:0%
+incomplete gamma functions because of
+ 
+
+ align:start position:0%
+incomplete gamma functions because of
+the mass Dimensions it has to be made up
+
+ align:start position:0%
+the mass Dimensions it has to be made up
+ 
+
+ align:start position:0%
+the mass Dimensions it has to be made up
+by mass dimensions on the right hand
+
+ align:start position:0%
+by mass dimensions on the right hand
+ 
+
+ align:start position:0%
+by mass dimensions on the right hand
+side coupling is dimensionless the only
+
+ align:start position:0%
+side coupling is dimensionless the only
+ 
+
+ align:start position:0%
+side coupling is dimensionless the only
+thing that has Dimensions is Lambda qcd
+
+ align:start position:0%
+thing that has Dimensions is Lambda qcd
+ 
+
+ align:start position:0%
+thing that has Dimensions is Lambda qcd
+and that's exactly what pops out of
+
+ align:start position:0%
+and that's exactly what pops out of
+ 
+
+ align:start position:0%
+and that's exactly what pops out of
+solving this equation the r gets
+
+ align:start position:0%
+solving this equation the r gets
+ 
+
+ align:start position:0%
+solving this equation the r gets
+converted to a Lambda qcd by this
+
+ align:start position:0%
+converted to a Lambda qcd by this
+ 
+
+ align:start position:0%
+converted to a Lambda qcd by this
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+here this G of T was just T at lowest
+
+ align:start position:0%
+here this G of T was just T at lowest
+ 
+
+ align:start position:0%
+here this G of T was just T at lowest
+order so this is an all order form here
+
+ align:start position:0%
+order so this is an all order form here
+ 
+
+ align:start position:0%
+order so this is an all order form here
+and this is the leading log solution
+
+ align:start position:0%
+and this is the leading log solution
+ 
+
+ align:start position:0%
+and this is the leading log solution
+there so if we look at that leading log
+
+ align:start position:0%
+there so if we look at that leading log
+ 
+
+ align:start position:0%
+there so if we look at that leading log
+and what is the T t0 and the T1 that's
+
+ align:start position:0%
+and what is the T t0 and the T1 that's
+ 
+
+ align:start position:0%
+and what is the T t0 and the T1 that's
+just the the same formula here but with
+
+ align:start position:0%
+just the the same formula here but with
+ 
+
+ align:start position:0%
+just the the same formula here but with
+Alpha at R1 and r0 the boundary
+
+ align:start position:0%
+Alpha at R1 and r0 the boundary
+ 
+
+ align:start position:0%
+Alpha at R1 and r0 the boundary
+conditions we want to run from r0 to R1
+
+ align:start position:0%
+conditions we want to run from r0 to R1
+ 
+
+ align:start position:0%
+conditions we want to run from r0 to R1
+and this formula tells us how to do that
+
+ align:start position:0%
+and this formula tells us how to do that
+ 
+
+ align:start position:0%
+and this formula tells us how to do that
+and and we get a result here that has
+
+ align:start position:0%
+and and we get a result here that has
+ 
+
+ align:start position:0%
+and and we get a result here that has
+the coupling at r0 and the coupling at
+
+ align:start position:0%
+the coupling at r0 and the coupling at
+ 
+
+ align:start position:0%
+the coupling at r0 and the coupling at
+R1 okay so if we look at that result
+
+ align:start position:0%
+R1 okay so if we look at that result
+ 
+
+ align:start position:0%
+R1 okay so if we look at that result
+it's interesting because if we just had
+
+ align:start position:0%
+it's interesting because if we just had
+ 
+
+ align:start position:0%
+it's interesting because if we just had
+one of these gamma functions these
+
+ align:start position:0%
+one of these gamma functions these
+ 
+
+ align:start position:0%
+one of these gamma functions these
+incomplete gamma functions then we would
+
+ align:start position:0%
+incomplete gamma functions then we would
+ 
+
+ align:start position:0%
+incomplete gamma functions then we would
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+renormalon that's where I stopped last
+
+ align:start position:0%
+renormalon that's where I stopped last
+ 
+
+ align:start position:0%
+renormalon that's where I stopped last
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+so just looking at this Lambda qcd times
+
+ align:start position:0%
+so just looking at this Lambda qcd times
+ 
+
+ align:start position:0%
+so just looking at this Lambda qcd times
+gamma and expanding about the in a
+
+ align:start position:0%
+gamma and expanding about the in a
+ 
+
+ align:start position:0%
+gamma and expanding about the in a
+series of about zero which is expanding
+
+ align:start position:0%
+series of about zero which is expanding
+ 
+
+ align:start position:0%
+series of about zero which is expanding
+in in the coupling at
+
+ align:start position:0%
+in in the coupling at
+ 
+
+ align:start position:0%
+in in the coupling at
+Infinity uh you get this series which
+
+ align:start position:0%
+Infinity uh you get this series which
+ 
+
+ align:start position:0%
+Infinity uh you get this series which
+has a 2 the n and factorial it's an ASM
+
+ align:start position:0%
+has a 2 the n and factorial it's an ASM
+ 
+
+ align:start position:0%
+has a 2 the n and factorial it's an ASM
+totic Series this is a classic example
+
+ align:start position:0%
+totic Series this is a classic example
+ 
+
+ align:start position:0%
+totic Series this is a classic example
+of a function that has an ASM totic
+
+ align:start position:0%
+of a function that has an ASM totic
+ 
+
+ align:start position:0%
+of a function that has an ASM totic
+Series this incomplete gamma function
+
+ align:start position:0%
+Series this incomplete gamma function
+ 
+
+ align:start position:0%
+Series this incomplete gamma function
+there's some exponential that combines
+
+ align:start position:0%
+there's some exponential that combines
+ 
+
+ align:start position:0%
+there's some exponential that combines
+together with the Lambda qcd to give an
+
+ align:start position:0%
+together with the Lambda qcd to give an
+ 
+
+ align:start position:0%
+together with the Lambda qcd to give an
+R so I've pulled that out front and then
+
+ align:start position:0%
+R so I've pulled that out front and then
+ 
+
+ align:start position:0%
+R so I've pulled that out front and then
+we have this series which is exactly U
+
+ align:start position:0%
+we have this series which is exactly U
+ 
+
+ align:start position:0%
+we have this series which is exactly U
+equals a half or a normal on and the U
+
+ align:start position:0%
+equals a half or a normal on and the U
+ 
+
+ align:start position:0%
+equals a half or a normal on and the U
+equals a half had to do with this power
+
+ align:start position:0%
+equals a half had to do with this power
+ 
+
+ align:start position:0%
+equals a half had to do with this power
+two to the N here the fact that it's two
+
+ align:start position:0%
+two to the N here the fact that it's two
+ 
+
+ align:start position:0%
+two to the N here the fact that it's two
+to the n and not some other
+
+ align:start position:0%
+to the n and not some other
+ 
+
+ align:start position:0%
+to the n and not some other
+number but if we take the difference
+
+ align:start position:0%
+number but if we take the difference
+ 
+
+ align:start position:0%
+number but if we take the difference
+here and this is what I said in words
+
+ align:start position:0%
+here and this is what I said in words
+ 
+
+ align:start position:0%
+here and this is what I said in words
+last time but now I'll write it down in
+
+ align:start position:0%
+last time but now I'll write it down in
+ 
+
+ align:start position:0%
+last time but now I'll write it down in
+equations we take the difference there
+
+ align:start position:0%
+equations we take the difference there
+ 
+
+ align:start position:0%
+equations we take the difference there
+that actually doesn't have this for
+
+ align:start position:0%
+that actually doesn't have this for
+ 
+
+ align:start position:0%
+that actually doesn't have this for
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the difference of two series
+
+ align:start position:0%
+so this is the difference of two series
+ 
+
+ align:start position:0%
+so this is the difference of two series
+Each of which is Asm totic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we want to compare those series we
+
+ align:start position:0%
+if we want to compare those series we
+ 
+
+ align:start position:0%
+if we want to compare those series we
+should expand
+
+ align:start position:0%
+should expand
+ 
+
+ align:start position:0%
+should expand
+them in the same coupling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant so let me do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I take the difference of those two
+
+ align:start position:0%
+so if I take the difference of those two
+ 
+
+ align:start position:0%
+so if I take the difference of those two
+series taking this using this formula
+
+ align:start position:0%
+series taking this using this formula
+ 
+
+ align:start position:0%
+series taking this using this formula
+but now I re-expand all these Alphas in
+
+ align:start position:0%
+but now I re-expand all these Alphas in
+ 
+
+ align:start position:0%
+but now I re-expand all these Alphas in
+terms of Alphas at the R1 scale so when
+
+ align:start position:0%
+terms of Alphas at the R1 scale so when
+ 
+
+ align:start position:0%
+terms of Alphas at the R1 scale so when
+they're at the r zero scale I re-expand
+
+ align:start position:0%
+they're at the r zero scale I re-expand
+ 
+
+ align:start position:0%
+they're at the r zero scale I re-expand
+them in terms of alpha the R1 scale do
+
+ align:start position:0%
+them in terms of alpha the R1 scale do
+ 
+
+ align:start position:0%
+them in terms of alpha the R1 scale do
+some rearranging I can write the result
+
+ align:start position:0%
+some rearranging I can write the result
+ 
+
+ align:start position:0%
+some rearranging I can write the result
+in this form as this so the key thing is
+
+ align:start position:0%
+in this form as this so the key thing is
+ 
+
+ align:start position:0%
+in this form as this so the key thing is
+that difference
+
+ align:start position:0%
+that difference
+ 
+
+ align:start position:0%
+that difference
+there and if you thought think about
+
+ align:start position:0%
+there and if you thought think about
+ 
+
+ align:start position:0%
+there and if you thought think about
+what this sum here is this is like kind
+
+ align:start position:0%
+what this sum here is this is like kind
+ 
+
+ align:start position:0%
+what this sum here is this is like kind
+of like an exponential right something
+
+ align:start position:0%
+of like an exponential right something
+ 
+
+ align:start position:0%
+of like an exponential right something
+to a power K factorial except it's
+
+ align:start position:0%
+to a power K factorial except it's
+ 
+
+ align:start position:0%
+to a power K factorial except it's
+limited to n so if I really went all the
+
+ align:start position:0%
+limited to n so if I really went all the
+ 
+
+ align:start position:0%
+limited to n so if I really went all the
+way up to n equals infinity this would
+
+ align:start position:0%
+way up to n equals infinity this would
+ 
+
+ align:start position:0%
+way up to n equals infinity this would
+be just giving actually exponential of
+
+ align:start position:0%
+be just giving actually exponential of
+ 
+
+ align:start position:0%
+be just giving actually exponential of
+R1 over r0 would cancel the r0 over R1
+
+ align:start position:0%
+R1 over r0 would cancel the r0 over R1
+ 
+
+ align:start position:0%
+R1 over r0 would cancel the r0 over R1
+which would then cancel the
+
+ align:start position:0%
+which would then cancel the
+ 
+
+ align:start position:0%
+which would then cancel the
+one you can rearrange the series a
+
+ align:start position:0%
+one you can rearrange the series a
+ 
+
+ align:start position:0%
+one you can rearrange the series a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+bit to make it more obvious that it's
+
+ align:start position:0%
+bit to make it more obvious that it's
+ 
+
+ align:start position:0%
+bit to make it more obvious that it's
+convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because there is this n factorial here
+
+ align:start position:0%
+because there is this n factorial here
+ 
+
+ align:start position:0%
+because there is this n factorial here
+you might worry well this thing here has
+
+ align:start position:0%
+you might worry well this thing here has
+ 
+
+ align:start position:0%
+you might worry well this thing here has
+to fall fast enough to get rid of that n
+
+ align:start position:0%
+to fall fast enough to get rid of that n
+ 
+
+ align:start position:0%
+to fall fast enough to get rid of that n
+factorial so write this thing out this
+
+ align:start position:0%
+factorial so write this thing out this
+ 
+
+ align:start position:0%
+factorial so write this thing out this
+one as an infinite series of terms from
+
+ align:start position:0%
+one as an infinite series of terms from
+ 
+
+ align:start position:0%
+one as an infinite series of terms from
+0 to Infinity of this same form as this
+
+ align:start position:0%
+0 to Infinity of this same form as this
+ 
+
+ align:start position:0%
+0 to Infinity of this same form as this
+and then what you're left with is the
+
+ align:start position:0%
+and then what you're left with is the
+ 
+
+ align:start position:0%
+and then what you're left with is the
+following thing all the terms from 0 to
+
+ align:start position:0%
+following thing all the terms from 0 to
+ 
+
+ align:start position:0%
+following thing all the terms from 0 to
+n cancel and then you're just left with
+
+ align:start position:0%
+n cancel and then you're just left with
+ 
+
+ align:start position:0%
+n cancel and then you're just left with
+the terms from n plus 1 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity and then you can see that the N
+
+ align:start position:0%
+infinity and then you can see that the N
+ 
+
+ align:start position:0%
+infinity and then you can see that the N
+factorial is being tamed by another
+
+ align:start position:0%
+factorial is being tamed by another
+ 
+
+ align:start position:0%
+factorial is being tamed by another
+factorial growth which is always of a
+
+ align:start position:0%
+factorial growth which is always of a
+ 
+
+ align:start position:0%
+factorial growth which is always of a
+greater power n plus one
+
+ align:start position:0%
+greater power n plus one
+ 
+
+ align:start position:0%
+greater power n plus one
+okay so this is number less than one and
+
+ align:start position:0%
+okay so this is number less than one and
+ 
+
+ align:start position:0%
+okay so this is number less than one and
+this thing here beta Alpha over 2 pi *
+
+ align:start position:0%
+this thing here beta Alpha over 2 pi *
+ 
+
+ align:start position:0%
+this thing here beta Alpha over 2 pi *
+the log is also something that's less
+
+ align:start position:0%
+the log is also something that's less
+ 
+
+ align:start position:0%
+the log is also something that's less
+than one it's a it's exactly the thing
+
+ align:start position:0%
+than one it's a it's exactly the thing
+ 
+
+ align:start position:0%
+than one it's a it's exactly the thing
+that you sum up when you're running the
+
+ align:start position:0%
+that you sum up when you're running the
+ 
+
+ align:start position:0%
+that you sum up when you're running the
+coupling so this is a convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series and
+
+ align:start position:0%
+series and
+ 
+
+ align:start position:0%
+series and
+it's basically the physics of it is we
+
+ align:start position:0%
+it's basically the physics of it is we
+ 
+
+ align:start position:0%
+it's basically the physics of it is we
+had this Mass
+
+ align:start position:0%
+had this Mass
+ 
+
+ align:start position:0%
+had this Mass
+that didn't have a renormalon but it had
+
+ align:start position:0%
+that didn't have a renormalon but it had
+ 
+
+ align:start position:0%
+that didn't have a renormalon but it had
+an arbitrary scale and what the
+
+ align:start position:0%
+an arbitrary scale and what the
+ 
+
+ align:start position:0%
+an arbitrary scale and what the
+renormalization group allows us to do is
+
+ align:start position:0%
+renormalization group allows us to do is
+ 
+
+ align:start position:0%
+renormalization group allows us to do is
+move to another scale when we move to
+
+ align:start position:0%
+move to another scale when we move to
+ 
+
+ align:start position:0%
+move to another scale when we move to
+another scale it better be that we don't
+
+ align:start position:0%
+another scale it better be that we don't
+ 
+
+ align:start position:0%
+another scale it better be that we don't
+reintroduce the ralon and the fact that
+
+ align:start position:0%
+reintroduce the ralon and the fact that
+ 
+
+ align:start position:0%
+reintroduce the ralon and the fact that
+I can write this as a convergence series
+
+ align:start position:0%
+I can write this as a convergence series
+ 
+
+ align:start position:0%
+I can write this as a convergence series
+shows very explicitly that I'm not
+
+ align:start position:0%
+shows very explicitly that I'm not
+ 
+
+ align:start position:0%
+shows very explicitly that I'm not
+having that problem in the difference
+
+ align:start position:0%
+having that problem in the difference
+ 
+
+ align:start position:0%
+having that problem in the difference
+between these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so it's re normalized
+
+ align:start position:0%
+two so it's re normalized
+ 
+
+ align:start position:0%
+two so it's re normalized
+free and it remains normal on free when
+
+ align:start position:0%
+free and it remains normal on free when
+ 
+
+ align:start position:0%
+free and it remains normal on free when
+we change the
+
+ align:start position:0%
+we change the
+ 
+
+ align:start position:0%
+we change the
+scale and we can sum up these logarithms
+
+ align:start position:0%
+scale and we can sum up these logarithms
+ 
+
+ align:start position:0%
+scale and we can sum up these logarithms
+that have to do with changing the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale so if you were why would you care
+
+ align:start position:0%
+scale so if you were why would you care
+ 
+
+ align:start position:0%
+scale so if you were why would you care
+about that well imagine that you extract
+
+ align:start position:0%
+about that well imagine that you extract
+ 
+
+ align:start position:0%
+about that well imagine that you extract
+this ma Mass from some B physics so you
+
+ align:start position:0%
+this ma Mass from some B physics so you
+ 
+
+ align:start position:0%
+this ma Mass from some B physics so you
+take an R that's of order of GV and then
+
+ align:start position:0%
+take an R that's of order of GV and then
+ 
+
+ align:start position:0%
+take an R that's of order of GV and then
+you say well that's a very precise
+
+ align:start position:0%
+you say well that's a very precise
+ 
+
+ align:start position:0%
+you say well that's a very precise
+number but how do I use it for say LHC
+
+ align:start position:0%
+number but how do I use it for say LHC
+ 
+
+ align:start position:0%
+number but how do I use it for say LHC
+phenomenology well if I want to connect
+
+ align:start position:0%
+phenomenology well if I want to connect
+ 
+
+ align:start position:0%
+phenomenology well if I want to connect
+it to LHC phenomenology I probably want
+
+ align:start position:0%
+it to LHC phenomenology I probably want
+ 
+
+ align:start position:0%
+it to LHC phenomenology I probably want
+to convert to the msar
+
+ align:start position:0%
+to convert to the msar
+ 
+
+ align:start position:0%
+to convert to the msar
+scheme because LC is high energy maybe
+
+ align:start position:0%
+scheme because LC is high energy maybe
+ 
+
+ align:start position:0%
+scheme because LC is high energy maybe
+I'm doing higs to BB bar BB bar very
+
+ align:start position:0%
+I'm doing higs to BB bar BB bar very
+ 
+
+ align:start position:0%
+I'm doing higs to BB bar BB bar very
+energetic so we want to use the MS
+
+ align:start position:0%
+energetic so we want to use the MS
+ 
+
+ align:start position:0%
+energetic so we want to use the MS
+scheme but I've got this mass at a very
+
+ align:start position:0%
+scheme but I've got this mass at a very
+ 
+
+ align:start position:0%
+scheme but I've got this mass at a very
+low scale what you would want to do is
+
+ align:start position:0%
+low scale what you would want to do is
+ 
+
+ align:start position:0%
+low scale what you would want to do is
+you'd want to use the renormalization
+
+ align:start position:0%
+you'd want to use the renormalization
+ 
+
+ align:start position:0%
+you'd want to use the renormalization
+group run it up to the mass scale MB
+
+ align:start position:0%
+group run it up to the mass scale MB
+ 
+
+ align:start position:0%
+group run it up to the mass scale MB
+match switch schemes from this scheme
+
+ align:start position:0%
+match switch schemes from this scheme
+ 
+
+ align:start position:0%
+match switch schemes from this scheme
+there you extracted the mass to msar
+
+ align:start position:0%
+there you extracted the mass to msar
+ 
+
+ align:start position:0%
+there you extracted the mass to msar
+you'd get a correspondingly precise
+
+ align:start position:0%
+you'd get a correspondingly precise
+ 
+
+ align:start position:0%
+you'd get a correspondingly precise
+value of msar because the series between
+
+ align:start position:0%
+value of msar because the series between
+ 
+
+ align:start position:0%
+value of msar because the series between
+this mass and the msar mass is again at
+
+ align:start position:0%
+this mass and the msar mass is again at
+ 
+
+ align:start position:0%
+this mass and the msar mass is again at
+R normal on free series and then you
+
+ align:start position:0%
+R normal on free series and then you
+ 
+
+ align:start position:0%
+R normal on free series and then you
+could take that mass at the MB scale run
+
+ align:start position:0%
+could take that mass at the MB scale run
+ 
+
+ align:start position:0%
+could take that mass at the MB scale run
+it up to say the Hig scale and use it
+
+ align:start position:0%
+it up to say the Hig scale and use it
+ 
+
+ align:start position:0%
+it up to say the Hig scale and use it
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+phenomenology so you always want to be
+
+ align:start position:0%
+phenomenology so you always want to be
+ 
+
+ align:start position:0%
+phenomenology so you always want to be
+able to go back and forth between
+
+ align:start position:0%
+able to go back and forth between
+ 
+
+ align:start position:0%
+able to go back and forth between
+schemes and if different schemes have
+
+ align:start position:0%
+schemes and if different schemes have
+ 
+
+ align:start position:0%
+schemes and if different schemes have
+different scales Associated to them then
+
+ align:start position:0%
+different scales Associated to them then
+ 
+
+ align:start position:0%
+different scales Associated to them then
+you need the renormalization group to in
+
+ align:start position:0%
+you need the renormalization group to in
+ 
+
+ align:start position:0%
+you need the renormalization group to in
+order to put them at the same scale when
+
+ align:start position:0%
+order to put them at the same scale when
+ 
+
+ align:start position:0%
+order to put them at the same scale when
+where you want to do the conversion
+
+ align:start position:0%
+where you want to do the conversion
+ 
+
+ align:start position:0%
+where you want to do the conversion
+okay so that's why being able to sum up
+
+ align:start position:0%
+okay so that's why being able to sum up
+ 
+
+ align:start position:0%
+okay so that's why being able to sum up
+these logarithms without reintroducing
+
+ align:start position:0%
+these logarithms without reintroducing
+ 
+
+ align:start position:0%
+these logarithms without reintroducing
+any ralon problems is is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important and in general if you were to
+
+ align:start position:0%
+important and in general if you were to
+ 
+
+ align:start position:0%
+important and in general if you were to
+try to do this with
+
+ align:start position:0%
+try to do this with
+ 
+
+ align:start position:0%
+try to do this with
+msar um it wouldn't work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you don't really have a way of
+
+ align:start position:0%
+uh you don't really have a way of
+ 
+
+ align:start position:0%
+uh you don't really have a way of
+treating the normal on in m in the msar
+
+ align:start position:0%
+treating the normal on in m in the msar
+ 
+
+ align:start position:0%
+treating the normal on in m in the msar
+scheme when you're talking about physics
+
+ align:start position:0%
+scheme when you're talking about physics
+ 
+
+ align:start position:0%
+scheme when you're talking about physics
+below the mass of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle okay so we can generalize this
+
+ align:start position:0%
+particle okay so we can generalize this
+ 
+
+ align:start position:0%
+particle okay so we can generalize this
+little discussion here which was a fixed
+
+ align:start position:0%
+little discussion here which was a fixed
+ 
+
+ align:start position:0%
+little discussion here which was a fixed
+order leading log discussion and I can
+
+ align:start position:0%
+order leading log discussion and I can
+ 
+
+ align:start position:0%
+order leading log discussion and I can
+write down for you just how what would
+
+ align:start position:0%
+write down for you just how what would
+ 
+
+ align:start position:0%
+write down for you just how what would
+happen if I were to formally integrate
+
+ align:start position:0%
+happen if I were to formally integrate
+ 
+
+ align:start position:0%
+happen if I were to formally integrate
+this integral here without making any
+
+ align:start position:0%
+this integral here without making any
+ 
+
+ align:start position:0%
+this integral here without making any
+expansion in alpha
+
+ align:start position:0%
+expansion in alpha
+ 
+
+ align:start position:0%
+expansion in alpha
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Express gamma R of t as an infinite
+
+ align:start position:0%
+so Express gamma R of t as an infinite
+ 
+
+ align:start position:0%
+so Express gamma R of t as an infinite
+Series in it's an infinite Series in
+
+ align:start position:0%
+Series in it's an infinite Series in
+ 
+
+ align:start position:0%
+Series in it's an infinite Series in
+alpha s that means it's an infinite
+
+ align:start position:0%
+alpha s that means it's an infinite
+ 
+
+ align:start position:0%
+alpha s that means it's an infinite
+Series in one over T we had an
+
+ align:start position:0%
+Series in one over T we had an
+ 
+
+ align:start position:0%
+Series in one over T we had an
+expression for this capital G of T last
+
+ align:start position:0%
+expression for this capital G of T last
+ 
+
+ align:start position:0%
+expression for this capital G of T last
+time which again was a infinite series
+
+ align:start position:0%
+time which again was a infinite series
+ 
+
+ align:start position:0%
+time which again was a infinite series
+just plug in those infinite series do
+
+ align:start position:0%
+just plug in those infinite series do
+ 
+
+ align:start position:0%
+just plug in those infinite series do
+all the integrals they all turned out to
+
+ align:start position:0%
+all the integrals they all turned out to
+ 
+
+ align:start position:0%
+all the integrals they all turned out to
+be incomplete gamma
+
+ align:start position:0%
+be incomplete gamma
+ 
+
+ align:start position:0%
+be incomplete gamma
+functions okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can make write down a formula an
+
+ align:start position:0%
+so we can make write down a formula an
+ 
+
+ align:start position:0%
+so we can make write down a formula an
+all order generalization of that result
+
+ align:start position:0%
+all order generalization of that result
+ 
+
+ align:start position:0%
+all order generalization of that result
+just to see what happens at higher
+
+ align:start position:0%
+just to see what happens at higher
+ 
+
+ align:start position:0%
+just to see what happens at higher
+orders so basically we'd have something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like if I look back at what G of T was
+
+ align:start position:0%
+like if I look back at what G of T was
+ 
+
+ align:start position:0%
+like if I look back at what G of T was
+we'd have something like this and then
+
+ align:start position:0%
+we'd have something like this and then
+ 
+
+ align:start position:0%
+we'd have something like this and then
+all the rest of the terms we can expand
+
+ align:start position:0%
+all the rest of the terms we can expand
+ 
+
+ align:start position:0%
+all the rest of the terms we can expand
+out in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse tailor tailor Series in one over
+
+ align:start position:0%
+inverse tailor tailor Series in one over
+ 
+
+ align:start position:0%
+inverse tailor tailor Series in one over
+t Okay so just there's two terms in G of
+
+ align:start position:0%
+t Okay so just there's two terms in G of
+ 
+
+ align:start position:0%
+t Okay so just there's two terms in G of
+T why I want to keep in the exponential
+
+ align:start position:0%
+T why I want to keep in the exponential
+ 
+
+ align:start position:0%
+T why I want to keep in the exponential
+and then the rest of them I can expand
+
+ align:start position:0%
+and then the rest of them I can expand
+ 
+
+ align:start position:0%
+and then the rest of them I can expand
+out and combine with these terms and
+
+ align:start position:0%
+out and combine with these terms and
+ 
+
+ align:start position:0%
+out and combine with these terms and
+that just gives me some series and I can
+
+ align:start position:0%
+that just gives me some series and I can
+ 
+
+ align:start position:0%
+that just gives me some series and I can
+do these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integrals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so writing the integrand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out we can just establish some notation
+
+ align:start position:0%
+out we can just establish some notation
+ 
+
+ align:start position:0%
+out we can just establish some notation
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it for that infinite series of one over
+
+ align:start position:0%
+it for that infinite series of one over
+ 
+
+ align:start position:0%
+it for that infinite series of one over
+T's and we'll just call the coefficients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SJ there's a one overt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the so this gamma bar starts as a one
+
+ align:start position:0%
+the so this gamma bar starts as a one
+ 
+
+ align:start position:0%
+the so this gamma bar starts as a one
+overt so really should so that there's a
+
+ align:start position:0%
+overt so really should so that there's a
+ 
+
+ align:start position:0%
+overt so really should so that there's a
+one t
+
+ align:start position:0%
+one t
+ 
+
+ align:start position:0%
+one t
+here that's where this one overt came
+
+ align:start position:0%
+here that's where this one overt came
+ 
+
+ align:start position:0%
+here that's where this one overt came
+from so then integrate that and that
+
+ align:start position:0%
+from so then integrate that and that
+ 
+
+ align:start position:0%
+from so then integrate that and that
+gives us a generalization of this
+
+ align:start position:0%
+gives us a generalization of this
+ 
+
+ align:start position:0%
+gives us a generalization of this
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+here where we say that M of
+
+ align:start position:0%
+here where we say that M of
+ 
+
+ align:start position:0%
+here where we say that M of
+R1 minus m of r0 which we work where we
+
+ align:start position:0%
+R1 minus m of r0 which we work where we
+ 
+
+ align:start position:0%
+R1 minus m of r0 which we work where we
+work at some order in the
+
+ align:start position:0%
+work at some order in the
+ 
+
+ align:start position:0%
+work at some order in the
+resummation which you would say is n the
+
+ align:start position:0%
+resummation which you would say is n the
+ 
+
+ align:start position:0%
+resummation which you would say is n the
+k l so you have leading log next leading
+
+ align:start position:0%
+k l so you have leading log next leading
+ 
+
+ align:start position:0%
+k l so you have leading log next leading
+log next to next leading log and then
+
+ align:start position:0%
+log next to next leading log and then
+ 
+
+ align:start position:0%
+log next to next leading log and then
+and when you have n when you have K of
+
+ align:start position:0%
+and when you have n when you have K of
+ 
+
+ align:start position:0%
+and when you have n when you have K of
+them you say NK
+
+ align:start position:0%
+them you say NK
+ 
+
+ align:start position:0%
+them you say NK
+L and the solution of that
+
+ align:start position:0%
+L and the solution of that
+ 
+
+ align:start position:0%
+L and the solution of that
+equation would be the Cod or Lambda qcd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series and instead of just the zero
+
+ align:start position:0%
+series and instead of just the zero
+ 
+
+ align:start position:0%
+series and instead of just the zero
+incomplete gamma function we get some
+
+ align:start position:0%
+incomplete gamma function we get some
+ 
+
+ align:start position:0%
+incomplete gamma function we get some
+slightly different one but it's got the
+
+ align:start position:0%
+slightly different one but it's got the
+ 
+
+ align:start position:0%
+slightly different one but it's got the
+same kind of structure where we get the
+
+ align:start position:0%
+same kind of structure where we get the
+ 
+
+ align:start position:0%
+same kind of structure where we get the
+difference of gamma functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these s's are just whatever you get
+
+ align:start position:0%
+and these s's are just whatever you get
+ 
+
+ align:start position:0%
+and these s's are just whatever you get
+from the anous dimension
+
+ align:start position:0%
+from the anous dimension
+ 
+
+ align:start position:0%
+from the anous dimension
+so kind of a simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation ET so they're just some
+
+ align:start position:0%
+notation ET so they're just some
+ 
+
+ align:start position:0%
+notation ET so they're just some
+combination of numbers and the twiddles
+
+ align:start position:0%
+combination of numbers and the twiddles
+ 
+
+ align:start position:0%
+combination of numbers and the twiddles
+here is just my short hand
+
+ align:start position:0%
+here is just my short hand
+ 
+
+ align:start position:0%
+here is just my short hand
+for accounting for a fact that there's
+
+ align:start position:0%
+for accounting for a fact that there's
+ 
+
+ align:start position:0%
+for accounting for a fact that there's
+some beta knots floating
+
+ align:start position:0%
+some beta knots floating
+ 
+
+ align:start position:0%
+some beta knots floating
+around okay so this is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algebra and these B1 hats and B2 hats
+
+ align:start position:0%
+algebra and these B1 hats and B2 hats
+ 
+
+ align:start position:0%
+algebra and these B1 hats and B2 hats
+were things that showed up in the beta
+
+ align:start position:0%
+were things that showed up in the beta
+ 
+
+ align:start position:0%
+were things that showed up in the beta
+function of qcd which we also talked
+
+ align:start position:0%
+function of qcd which we also talked
+ 
+
+ align:start position:0%
+function of qcd which we also talked
+talked about last time so so we defined
+
+ align:start position:0%
+talked about last time so so we defined
+ 
+
+ align:start position:0%
+talked about last time so so we defined
+those last time the B1 hat and B2 hat
+
+ align:start position:0%
+those last time the B1 hat and B2 hat
+ 
+
+ align:start position:0%
+those last time the B1 hat and B2 hat
+were just combinations of the beta beta
+
+ align:start position:0%
+were just combinations of the beta beta
+ 
+
+ align:start position:0%
+were just combinations of the beta beta
+1 and beta
+
+ align:start position:0%
+1 and beta
+ 
+
+ align:start position:0%
+1 and beta
+2 and beta
+
+ align:start position:0%
+2 and beta
+ 
+
+ align:start position:0%
+2 and beta
+0o okay so these are some numbers that
+
+ align:start position:0%
+0o okay so these are some numbers that
+ 
+
+ align:start position:0%
+0o okay so these are some numbers that
+you can calculate given the enous
+
+ align:start position:0%
+you can calculate given the enous
+ 
+
+ align:start position:0%
+you can calculate given the enous
+dimensions given those numbers you can
+
+ align:start position:0%
+dimensions given those numbers you can
+ 
+
+ align:start position:0%
+dimensions given those numbers you can
+plug it into this formula and then you
+
+ align:start position:0%
+plug it into this formula and then you
+ 
+
+ align:start position:0%
+plug it into this formula and then you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+a generalization of the previous result
+
+ align:start position:0%
+a generalization of the previous result
+ 
+
+ align:start position:0%
+a generalization of the previous result
+so whatever order you know the enal
+
+ align:start position:0%
+so whatever order you know the enal
+ 
+
+ align:start position:0%
+so whatever order you know the enal
+dimension to you can use that solution
+
+ align:start position:0%
+dimension to you can use that solution
+ 
+
+ align:start position:0%
+dimension to you can use that solution
+and we'll use it a little later when I
+
+ align:start position:0%
+and we'll use it a little later when I
+ 
+
+ align:start position:0%
+and we'll use it a little later when I
+talk about some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers all right so any questions so
+
+ align:start position:0%
+numbers all right so any questions so
+ 
+
+ align:start position:0%
+numbers all right so any questions so
+far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a similar thing for msar Mass if
+
+ align:start position:0%
+there's a similar thing for msar Mass if
+ 
+
+ align:start position:0%
+there's a similar thing for msar Mass if
+you were summing logs of the MS bar Mass
+
+ align:start position:0%
+you were summing logs of the MS bar Mass
+ 
+
+ align:start position:0%
+you were summing logs of the MS bar Mass
+there's an all orders formula you can
+
+ align:start position:0%
+there's an all orders formula you can
+ 
+
+ align:start position:0%
+there's an all orders formula you can
+write down and use once you know the
+
+ align:start position:0%
+write down and use once you know the
+ 
+
+ align:start position:0%
+write down and use once you know the
+normal dimensions you could find it in
+
+ align:start position:0%
+normal dimensions you could find it in
+ 
+
+ align:start position:0%
+normal dimensions you could find it in
+the particle Data Book I
+
+ align:start position:0%
+the particle Data Book I
+ 
+
+ align:start position:0%
+the particle Data Book I
+think all right
+
+ align:start position:0%
+think all right
+ 
+
+ align:start position:0%
+think all right
+so just coming back to this comment
+
+ align:start position:0%
+so just coming back to this comment
+ 
+
+ align:start position:0%
+so just coming back to this comment
+about the fact that the anomalous
+
+ align:start position:0%
+about the fact that the anomalous
+ 
+
+ align:start position:0%
+about the fact that the anomalous
+Dimension is R normal on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free so the fact the fact that the
+
+ align:start position:0%
+free so the fact the fact that the
+ 
+
+ align:start position:0%
+free so the fact the fact that the
+solution here was romal on free that the
+
+ align:start position:0%
+solution here was romal on free that the
+ 
+
+ align:start position:0%
+solution here was romal on free that the
+difference here was aalon free was
+
+ align:start position:0%
+difference here was aalon free was
+ 
+
+ align:start position:0%
+difference here was aalon free was
+because there was no ralon on the right
+
+ align:start position:0%
+because there was no ralon on the right
+ 
+
+ align:start position:0%
+because there was no ralon on the right
+hand side here and that the anomalous
+
+ align:start position:0%
+hand side here and that the anomalous
+ 
+
+ align:start position:0%
+hand side here and that the anomalous
+Dimension was ralon
+
+ align:start position:0%
+Dimension was ralon
+ 
+
+ align:start position:0%
+Dimension was ralon
+free and it was constructed from
+
+ align:start position:0%
+free and it was constructed from
+ 
+
+ align:start position:0%
+free and it was constructed from
+something that had a
+
+ align:start position:0%
+something that had a
+ 
+
+ align:start position:0%
+something that had a
+renormalon which is this Delta
+
+ align:start position:0%
+renormalon which is this Delta
+ 
+
+ align:start position:0%
+renormalon which is this Delta
+M but it was a derivative of that Delta
+
+ align:start position:0%
+M but it was a derivative of that Delta
+ 
+
+ align:start position:0%
+M but it was a derivative of that Delta
+M and
+
+ align:start position:0%
+M and
+ 
+
+ align:start position:0%
+M and
+so the derivative kills the re normal
+
+ align:start position:0%
+so the derivative kills the re normal
+ 
+
+ align:start position:0%
+so the derivative kills the re normal
+on so this thing is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free of the delta to M of order Lambda
+
+ align:start position:0%
+free of the delta to M of order Lambda
+ 
+
+ align:start position:0%
+free of the delta to M of order Lambda
+qcd
+
+ align:start position:0%
+qcd
+ 
+
+ align:start position:0%
+qcd
+renormalon because that renormalon is a
+
+ align:start position:0%
+renormalon because that renormalon is a
+ 
+
+ align:start position:0%
+renormalon because that renormalon is a
+constant and when you take the
+
+ align:start position:0%
+constant and when you take the
+ 
+
+ align:start position:0%
+constant and when you take the
+derivative you kill the constant that's
+
+ align:start position:0%
+derivative you kill the constant that's
+ 
+
+ align:start position:0%
+derivative you kill the constant that's
+how you can think of
+
+ align:start position:0%
+how you can think of
+ 
+
+ align:start position:0%
+how you can think of
+it if you start writing out the gamma
+
+ align:start position:0%
+it if you start writing out the gamma
+ 
+
+ align:start position:0%
+it if you start writing out the gamma
+functions then you see that it looks
+
+ align:start position:0%
+functions then you see that it looks
+ 
+
+ align:start position:0%
+functions then you see that it looks
+like you're finding the r normal on but
+
+ align:start position:0%
+like you're finding the r normal on but
+ 
+
+ align:start position:0%
+like you're finding the r normal on but
+then there's some differences that show
+
+ align:start position:0%
+then there's some differences that show
+ 
+
+ align:start position:0%
+then there's some differences that show
+up and and cancel it off so the way that
+
+ align:start position:0%
+up and and cancel it off so the way that
+ 
+
+ align:start position:0%
+up and and cancel it off so the way that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+works it's kind of like this where you
+
+ align:start position:0%
+works it's kind of like this where you
+ 
+
+ align:start position:0%
+works it's kind of like this where you
+see sort of think that you have the re
+
+ align:start position:0%
+see sort of think that you have the re
+ 
+
+ align:start position:0%
+see sort of think that you have the re
+normal on but then you realize there's
+
+ align:start position:0%
+normal on but then you realize there's
+ 
+
+ align:start position:0%
+normal on but then you realize there's
+another term in cancels it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off so if
+
+ align:start position:0%
+off so if
+ 
+
+ align:start position:0%
+off so if
+we if we look back at our formula for
+
+ align:start position:0%
+we if we look back at our formula for
+ 
+
+ align:start position:0%
+we if we look back at our formula for
+Delta M this had an infinite series of
+
+ align:start position:0%
+Delta M this had an infinite series of
+ 
+
+ align:start position:0%
+Delta M this had an infinite series of
+A's so was like a sum over some a ends
+
+ align:start position:0%
+A's so was like a sum over some a ends
+ 
+
+ align:start position:0%
+A's so was like a sum over some a ends
+and some Alpha to the N some other
+
+ align:start position:0%
+and some Alpha to the N some other
+ 
+
+ align:start position:0%
+and some Alpha to the N some other
+factors and these gamas are just related
+
+ align:start position:0%
+factors and these gamas are just related
+ 
+
+ align:start position:0%
+factors and these gamas are just related
+to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A's but they're not just related to the
+
+ align:start position:0%
+A's but they're not just related to the
+ 
+
+ align:start position:0%
+A's but they're not just related to the
+A's they're also factors of the beta
+
+ align:start position:0%
+A's they're also factors of the beta
+ 
+
+ align:start position:0%
+A's they're also factors of the beta
+function that come
+
+ align:start position:0%
+function that come
+ 
+
+ align:start position:0%
+function that come
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+so just to give you an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea so once you know the scheme
+
+ align:start position:0%
+idea so once you know the scheme
+ 
+
+ align:start position:0%
+idea so once you know the scheme
+conversion to the scheme
+
+ align:start position:0%
+conversion to the scheme
+ 
+
+ align:start position:0%
+conversion to the scheme
+then you know the anomalous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dimension and if you look at this series
+
+ align:start position:0%
+Dimension and if you look at this series
+ 
+
+ align:start position:0%
+Dimension and if you look at this series
+and you think about whether the series
+
+ align:start position:0%
+and you think about whether the series
+ 
+
+ align:start position:0%
+and you think about whether the series
+for the Nal Dimension is convergent or
+
+ align:start position:0%
+for the Nal Dimension is convergent or
+ 
+
+ align:start position:0%
+for the Nal Dimension is convergent or
+ASM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+totic you can sort of identify the
+
+ align:start position:0%
+totic you can sort of identify the
+ 
+
+ align:start position:0%
+totic you can sort of identify the
+pattern of how these coefficients look
+
+ align:start position:0%
+pattern of how these coefficients look
+ 
+
+ align:start position:0%
+pattern of how these coefficients look
+and basically if you for example look at
+
+ align:start position:0%
+and basically if you for example look at
+ 
+
+ align:start position:0%
+and basically if you for example look at
+the bubble sum this a n + one would be
+
+ align:start position:0%
+the bubble sum this a n + one would be
+ 
+
+ align:start position:0%
+the bubble sum this a n + one would be
+something that has an N Factor factorial
+
+ align:start position:0%
+something that has an N Factor factorial
+ 
+
+ align:start position:0%
+something that has an N Factor factorial
+2 Beta KN to the n +
+
+ align:start position:0%
+2 Beta KN to the n +
+ 
+
+ align:start position:0%
+2 Beta KN to the n +
+one oh sorry to the N
+
+ align:start position:0%
+one oh sorry to the N
+ 
+
+ align:start position:0%
+one oh sorry to the N
+growth and then this thing here is n
+
+ align:start position:0%
+growth and then this thing here is n
+ 
+
+ align:start position:0%
+growth and then this thing here is n
+minus1
+
+ align:start position:0%
+minus1
+ 
+
+ align:start position:0%
+minus1
+factorial to Beta to the N minus
+
+ align:start position:0%
+factorial to Beta to the N minus
+ 
+
+ align:start position:0%
+factorial to Beta to the N minus
+one and then there's this exra 2N beta
+
+ align:start position:0%
+one and then there's this exra 2N beta
+ 
+
+ align:start position:0%
+one and then there's this exra 2N beta
+KN that multiplies it and you can see
+
+ align:start position:0%
+KN that multiplies it and you can see
+ 
+
+ align:start position:0%
+KN that multiplies it and you can see
+that there there's an exact cancellation
+
+ align:start position:0%
+that there there's an exact cancellation
+ 
+
+ align:start position:0%
+that there there's an exact cancellation
+so that's how the bubble sum you know
+
+ align:start position:0%
+so that's how the bubble sum you know
+ 
+
+ align:start position:0%
+so that's how the bubble sum you know
+one way of probing the normalan is just
+
+ align:start position:0%
+one way of probing the normalan is just
+ 
+
+ align:start position:0%
+one way of probing the normalan is just
+to look at the bubble sum and the bubble
+
+ align:start position:0%
+to look at the bubble sum and the bubble
+ 
+
+ align:start position:0%
+to look at the bubble sum and the bubble
+sum gave us a particular value of these
+
+ align:start position:0%
+sum gave us a particular value of these
+ 
+
+ align:start position:0%
+sum gave us a particular value of these
+A's and you can see that the bubble sum
+
+ align:start position:0%
+A's and you can see that the bubble sum
+ 
+
+ align:start position:0%
+A's and you can see that the bubble sum
+R normalan is canceling out between the
+
+ align:start position:0%
+R normalan is canceling out between the
+ 
+
+ align:start position:0%
+R normalan is canceling out between the
+terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so that's just a expression of
+
+ align:start position:0%
+here okay so that's just a expression of
+ 
+
+ align:start position:0%
+here okay so that's just a expression of
+what I said over here that's kind of
+
+ align:start position:0%
+what I said over here that's kind of
+ 
+
+ align:start position:0%
+what I said over here that's kind of
+more definite expression of the fact
+
+ align:start position:0%
+more definite expression of the fact
+ 
+
+ align:start position:0%
+more definite expression of the fact
+that this thing is actually free of the
+
+ align:start position:0%
+that this thing is actually free of the
+ 
+
+ align:start position:0%
+that this thing is actually free of the
+normal on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm going to put this aside for a
+
+ align:start position:0%
+so I'm going to put this aside for a
+ 
+
+ align:start position:0%
+so I'm going to put this aside for a
+minute and we'll come back and use this
+
+ align:start position:0%
+minute and we'll come back and use this
+ 
+
+ align:start position:0%
+minute and we'll come back and use this
+formula a little later in today's
+
+ align:start position:0%
+formula a little later in today's
+ 
+
+ align:start position:0%
+formula a little later in today's
+lecture um and I want to so there's sort
+
+ align:start position:0%
+lecture um and I want to so there's sort
+ 
+
+ align:start position:0%
+lecture um and I want to so there's sort
+of two ways that you can use this
+
+ align:start position:0%
+of two ways that you can use this
+ 
+
+ align:start position:0%
+of two ways that you can use this
+technology you can use it as a means of
+
+ align:start position:0%
+technology you can use it as a means of
+ 
+
+ align:start position:0%
+technology you can use it as a means of
+doing what I said of connecting masses
+
+ align:start position:0%
+doing what I said of connecting masses
+ 
+
+ align:start position:0%
+doing what I said of connecting masses
+at different scales and doing
+
+ align:start position:0%
+at different scales and doing
+ 
+
+ align:start position:0%
+at different scales and doing
+phenomenology and we'll come back to
+
+ align:start position:0%
+phenomenology and we'll come back to
+ 
+
+ align:start position:0%
+phenomenology and we'll come back to
+that a little bit later but you could
+
+ align:start position:0%
+that a little bit later but you could
+ 
+
+ align:start position:0%
+that a little bit later but you could
+also use it as a probe of the renormalon
+
+ align:start position:0%
+also use it as a probe of the renormalon
+ 
+
+ align:start position:0%
+also use it as a probe of the renormalon
+so one thing that you might complain
+
+ align:start position:0%
+so one thing that you might complain
+ 
+
+ align:start position:0%
+so one thing that you might complain
+about with the bubble sum is it's just
+
+ align:start position:0%
+about with the bubble sum is it's just
+ 
+
+ align:start position:0%
+about with the bubble sum is it's just
+some arbitrarily chosen way of probing
+
+ align:start position:0%
+some arbitrarily chosen way of probing
+ 
+
+ align:start position:0%
+some arbitrarily chosen way of probing
+the renormalon and maybe there's some
+
+ align:start position:0%
+the renormalon and maybe there's some
+ 
+
+ align:start position:0%
+the renormalon and maybe there's some
+problem where you don't have like Fons
+
+ align:start position:0%
+problem where you don't have like Fons
+ 
+
+ align:start position:0%
+problem where you don't have like Fons
+around maybe you only have gluons and
+
+ align:start position:0%
+around maybe you only have gluons and
+ 
+
+ align:start position:0%
+around maybe you only have gluons and
+there could still be a renormalon in
+
+ align:start position:0%
+there could still be a renormalon in
+ 
+
+ align:start position:0%
+there could still be a renormalon in
+those problems so how would you deal
+
+ align:start position:0%
+those problems so how would you deal
+ 
+
+ align:start position:0%
+those problems so how would you deal
+with that if you didn't have the light
+
+ align:start position:0%
+with that if you didn't have the light
+ 
+
+ align:start position:0%
+with that if you didn't have the light
+quarks available to make up this bubble
+
+ align:start position:0%
+quarks available to make up this bubble
+ 
+
+ align:start position:0%
+quarks available to make up this bubble
+sum or maybe there's some renormalon
+
+ align:start position:0%
+sum or maybe there's some renormalon
+ 
+
+ align:start position:0%
+sum or maybe there's some renormalon
+that just so happens you don't see it
+
+ align:start position:0%
+that just so happens you don't see it
+ 
+
+ align:start position:0%
+that just so happens you don't see it
+with the quirks there's no guarantee of
+
+ align:start position:0%
+with the quirks there's no guarantee of
+ 
+
+ align:start position:0%
+with the quirks there's no guarantee of
+that so you'd like to have some other
+
+ align:start position:0%
+that so you'd like to have some other
+ 
+
+ align:start position:0%
+that so you'd like to have some other
+mechanism for looking for renormalons
+
+ align:start position:0%
+mechanism for looking for renormalons
+ 
+
+ align:start position:0%
+mechanism for looking for renormalons
+and you can actually use the
+
+ align:start position:0%
+and you can actually use the
+ 
+
+ align:start position:0%
+and you can actually use the
+renormalization group to do that which
+
+ align:start position:0%
+renormalization group to do that which
+ 
+
+ align:start position:0%
+renormalization group to do that which
+is kind of interesting so I'll show you
+
+ align:start position:0%
+is kind of interesting so I'll show you
+ 
+
+ align:start position:0%
+is kind of interesting so I'll show you
+how that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works it also makes it nice thing about
+
+ align:start position:0%
+works it also makes it nice thing about
+ 
+
+ align:start position:0%
+works it also makes it nice thing about
+this is it also makes it clear how the
+
+ align:start position:0%
+this is it also makes it clear how the
+ 
+
+ align:start position:0%
+this is it also makes it clear how the
+renormalon relates to the landow pole so
+
+ align:start position:0%
+renormalon relates to the landow pole so
+ 
+
+ align:start position:0%
+renormalon relates to the landow pole so
+we'll see that as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so take our solution for the RG
+
+ align:start position:0%
+well so take our solution for the RG
+ 
+
+ align:start position:0%
+well so take our solution for the RG
+we could write in terms of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intergral and let's consider what this
+
+ align:start position:0%
+intergral and let's consider what this
+ 
+
+ align:start position:0%
+intergral and let's consider what this
+integral actually is doing in the
+
+ align:start position:0%
+integral actually is doing in the
+ 
+
+ align:start position:0%
+integral actually is doing in the
+complex T
+
+ align:start position:0%
+complex T
+ 
+
+ align:start position:0%
+complex T
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the t's are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative and so they look like this the
+
+ align:start position:0%
+negative and so they look like this the
+ 
+
+ align:start position:0%
+negative and so they look like this the
+land
+
+ align:start position:0%
+land
+ 
+
+ align:start position:0%
+land
+Pole where the coupling blows up is
+
+ align:start position:0%
+Pole where the coupling blows up is
+ 
+
+ align:start position:0%
+Pole where the coupling blows up is
+where the T goes to zero so the land out
+
+ align:start position:0%
+where the T goes to zero so the land out
+ 
+
+ align:start position:0%
+where the T goes to zero so the land out
+pole is at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+origin okay so this is what the complex
+
+ align:start position:0%
+origin okay so this is what the complex
+ 
+
+ align:start position:0%
+origin okay so this is what the complex
+T plane looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like and what we're doing when we do the
+
+ align:start position:0%
+like and what we're doing when we do the
+ 
+
+ align:start position:0%
+like and what we're doing when we do the
+integral is we're just doing an integral
+
+ align:start position:0%
+integral is we're just doing an integral
+ 
+
+ align:start position:0%
+integral is we're just doing an integral
+over that little range here right so
+
+ align:start position:0%
+over that little range here right so
+ 
+
+ align:start position:0%
+over that little range here right so
+we're far away from the L up hole and
+
+ align:start position:0%
+we're far away from the L up hole and
+ 
+
+ align:start position:0%
+we're far away from the L up hole and
+that's why everything was nicely
+
+ align:start position:0%
+that's why everything was nicely
+ 
+
+ align:start position:0%
+that's why everything was nicely
+convergent and you could connect one
+
+ align:start position:0%
+convergent and you could connect one
+ 
+
+ align:start position:0%
+convergent and you could connect one
+Mass to
+
+ align:start position:0%
+Mass to
+ 
+
+ align:start position:0%
+Mass to
+another but you you could ask what
+
+ align:start position:0%
+another but you you could ask what
+ 
+
+ align:start position:0%
+another but you you could ask what
+happens if I take this t0 and I move it
+
+ align:start position:0%
+happens if I take this t0 and I move it
+ 
+
+ align:start position:0%
+happens if I take this t0 and I move it
+somewhere else in this in this picture
+
+ align:start position:0%
+somewhere else in this in this picture
+ 
+
+ align:start position:0%
+somewhere else in this in this picture
+and that's what we're going to
+
+ align:start position:0%
+and that's what we're going to
+ 
+
+ align:start position:0%
+and that's what we're going to
+do so let's consider the limit where r0
+
+ align:start position:0%
+do so let's consider the limit where r0
+ 
+
+ align:start position:0%
+do so let's consider the limit where r0
+goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero if R goes to zero and you look back
+
+ align:start position:0%
+zero if R goes to zero and you look back
+ 
+
+ align:start position:0%
+zero if R goes to zero and you look back
+at the formula that we had that converts
+
+ align:start position:0%
+at the formula that we had that converts
+ 
+
+ align:start position:0%
+at the formula that we had that converts
+between the msar mass and this m of
+
+ align:start position:0%
+between the msar mass and this m of
+ 
+
+ align:start position:0%
+between the msar mass and this m of
+R you'll see that M of
+
+ align:start position:0%
+R you'll see that M of
+ 
+
+ align:start position:0%
+R you'll see that M of
+r0 goes to M Pole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we had a power of R times a
+
+ align:start position:0%
+because we had a power of R times a
+ 
+
+ align:start position:0%
+because we had a power of R times a
+series of alpha of RS which are just
+
+ align:start position:0%
+series of alpha of RS which are just
+ 
+
+ align:start position:0%
+series of alpha of RS which are just
+logs of R the power always wins and so
+
+ align:start position:0%
+logs of R the power always wins and so
+ 
+
+ align:start position:0%
+logs of R the power always wins and so
+the mass goes to the pole mass and that
+
+ align:start position:0%
+the mass goes to the pole mass and that
+ 
+
+ align:start position:0%
+the mass goes to the pole mass and that
+limit that r0 goes to
+
+ align:start position:0%
+limit that r0 goes to
+ 
+
+ align:start position:0%
+limit that r0 goes to
+zero and if you look at what t0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is t0 is related to the coupling which I
+
+ align:start position:0%
+is t0 is related to the coupling which I
+ 
+
+ align:start position:0%
+is t0 is related to the coupling which I
+could write in terms of a log of Lambda
+
+ align:start position:0%
+could write in terms of a log of Lambda
+ 
+
+ align:start position:0%
+could write in terms of a log of Lambda
+qcd and t0 is basically in this limit
+
+ align:start position:0%
+qcd and t0 is basically in this limit
+ 
+
+ align:start position:0%
+qcd and t0 is basically in this limit
+going to Plus
+
+ align:start position:0%
+going to Plus
+ 
+
+ align:start position:0%
+going to Plus
+inity so what happens is if I want to
+
+ align:start position:0%
+inity so what happens is if I want to
+ 
+
+ align:start position:0%
+inity so what happens is if I want to
+get back to the pole Mass from one of
+
+ align:start position:0%
+get back to the pole Mass from one of
+ 
+
+ align:start position:0%
+get back to the pole Mass from one of
+these masses I basically have to take
+
+ align:start position:0%
+these masses I basically have to take
+ 
+
+ align:start position:0%
+these masses I basically have to take
+this guy and move out to Infinity which
+
+ align:start position:0%
+this guy and move out to Infinity which
+ 
+
+ align:start position:0%
+this guy and move out to Infinity which
+means I have to make a choice about
+
+ align:start position:0%
+means I have to make a choice about
+ 
+
+ align:start position:0%
+means I have to make a choice about
+going around that Lando Pole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically you're taking your rge and
+
+ align:start position:0%
+so basically you're taking your rge and
+ 
+
+ align:start position:0%
+so basically you're taking your rge and
+you're pushing it into a region that's
+
+ align:start position:0%
+you're pushing it into a region that's
+ 
+
+ align:start position:0%
+you're pushing it into a region that's
+where you're no longer completely
+
+ align:start position:0%
+where you're no longer completely
+ 
+
+ align:start position:0%
+where you're no longer completely
+perturbative and that you're forced to
+
+ align:start position:0%
+perturbative and that you're forced to
+ 
+
+ align:start position:0%
+perturbative and that you're forced to
+continue by the L out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pole now you can actually avoid the land
+
+ align:start position:0%
+Pole now you can actually avoid the land
+ 
+
+ align:start position:0%
+Pole now you can actually avoid the land
+out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pole by going far you know it's true
+
+ align:start position:0%
+pole by going far you know it's true
+ 
+
+ align:start position:0%
+pole by going far you know it's true
+that the series becomes non-perturbative
+
+ align:start position:0%
+that the series becomes non-perturbative
+ 
+
+ align:start position:0%
+that the series becomes non-perturbative
+in this region but you you could go way
+
+ align:start position:0%
+in this region but you you could go way
+ 
+
+ align:start position:0%
+in this region but you you could go way
+up here and come back over there so you
+
+ align:start position:0%
+up here and come back over there so you
+ 
+
+ align:start position:0%
+up here and come back over there so you
+can actually AO you can actually
+
+ align:start position:0%
+can actually AO you can actually
+ 
+
+ align:start position:0%
+can actually AO you can actually
+formally stay in a region in the complex
+
+ align:start position:0%
+formally stay in a region in the complex
+ 
+
+ align:start position:0%
+formally stay in a region in the complex
+plane where your perturbation theory is
+
+ align:start position:0%
+plane where your perturbation theory is
+ 
+
+ align:start position:0%
+plane where your perturbation theory is
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+applicable but you still have to decide
+
+ align:start position:0%
+applicable but you still have to decide
+ 
+
+ align:start position:0%
+applicable but you still have to decide
+which way you go going to go around
+
+ align:start position:0%
+which way you go going to go around
+ 
+
+ align:start position:0%
+which way you go going to go around
+it and so that introduces it an
+
+ align:start position:0%
+it and so that introduces it an
+ 
+
+ align:start position:0%
+it and so that introduces it an
+ambiguity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that say we go above or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something and if you plug in in this
+
+ align:start position:0%
+something and if you plug in in this
+ 
+
+ align:start position:0%
+something and if you plug in in this
+result the lowest order meeing log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result you get this
+
+ align:start position:0%
+result you get this
+ 
+
+ align:start position:0%
+result you get this
+integral and this integral you know you
+
+ align:start position:0%
+integral and this integral you know you
+ 
+
+ align:start position:0%
+integral and this integral you know you
+have to go around the t equal Z pole
+
+ align:start position:0%
+have to go around the t equal Z pole
+ 
+
+ align:start position:0%
+have to go around the t equal Z pole
+because T1 is
+
+ align:start position:0%
+because T1 is
+ 
+
+ align:start position:0%
+because T1 is
+negative so it turns out that you can
+
+ align:start position:0%
+negative so it turns out that you can
+ 
+
+ align:start position:0%
+negative so it turns out that you can
+actually take this interval and I'm
+
+ align:start position:0%
+actually take this interval and I'm
+ 
+
+ align:start position:0%
+actually take this interval and I'm
+going to leave this for your problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set and write it in the form of a barel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intergral with an
+
+ align:start position:0%
+intergral with an
+ 
+
+ align:start position:0%
+intergral with an
+exponential that's exactly the Burell
+
+ align:start position:0%
+exponential that's exactly the Burell
+ 
+
+ align:start position:0%
+exponential that's exactly the Burell
+transform
+
+ align:start position:0%
+transform
+ 
+
+ align:start position:0%
+transform
+variable I just change variable from T
+
+ align:start position:0%
+variable I just change variable from T
+ 
+
+ align:start position:0%
+variable I just change variable from T
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+U so I get this
+
+ align:start position:0%
+U so I get this
+ 
+
+ align:start position:0%
+U so I get this
+integral and if you do that what you
+
+ align:start position:0%
+integral and if you do that what you
+ 
+
+ align:start position:0%
+integral and if you do that what you
+find is that F of U is
+
+ align:start position:0%
+find is that F of U is
+ 
+
+ align:start position:0%
+find is that F of U is
+proportional to 1 over uus a
+
+ align:start position:0%
+proportional to 1 over uus a
+ 
+
+ align:start position:0%
+proportional to 1 over uus a
+half what's the L
+
+ align:start position:0%
+half what's the L
+ 
+
+ align:start position:0%
+half what's the L
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so you can actually see that
+
+ align:start position:0%
+yeah okay so you can actually see that
+ 
+
+ align:start position:0%
+yeah okay so you can actually see that
+the rge and what was the Lando pole here
+
+ align:start position:0%
+the rge and what was the Lando pole here
+ 
+
+ align:start position:0%
+the rge and what was the Lando pole here
+is effectively in this inter here
+
+ align:start position:0%
+is effectively in this inter here
+ 
+
+ align:start position:0%
+is effectively in this inter here
+becoming this baral pole at U equal a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half and that makes a little more
+
+ align:start position:0%
+half and that makes a little more
+ 
+
+ align:start position:0%
+half and that makes a little more
+clear the fact that these poles are
+
+ align:start position:0%
+clear the fact that these poles are
+ 
+
+ align:start position:0%
+clear the fact that these poles are
+related to the non-perturbative physics
+
+ align:start position:0%
+related to the non-perturbative physics
+ 
+
+ align:start position:0%
+related to the non-perturbative physics
+that's in the coupling in the the
+
+ align:start position:0%
+that's in the coupling in the the
+ 
+
+ align:start position:0%
+that's in the coupling in the the
+infrared
+
+ align:start position:0%
+infrared
+ 
+
+ align:start position:0%
+infrared
+physics so formally this actually allows
+
+ align:start position:0%
+physics so formally this actually allows
+ 
+
+ align:start position:0%
+physics so formally this actually allows
+you to set up a method of trying to find
+
+ align:start position:0%
+you to set up a method of trying to find
+ 
+
+ align:start position:0%
+you to set up a method of trying to find
+the normal on because you can just do
+
+ align:start position:0%
+the normal on because you can just do
+ 
+
+ align:start position:0%
+the normal on because you can just do
+this Contin you can ask given some
+
+ align:start position:0%
+this Contin you can ask given some
+ 
+
+ align:start position:0%
+this Contin you can ask given some
+series if I if I sort of construct this
+
+ align:start position:0%
+series if I if I sort of construct this
+ 
+
+ align:start position:0%
+series if I if I sort of construct this
+thing what if I just I had this attitude
+
+ align:start position:0%
+thing what if I just I had this attitude
+ 
+
+ align:start position:0%
+thing what if I just I had this attitude
+that we want to pick that series to
+
+ align:start position:0%
+that we want to pick that series to
+ 
+
+ align:start position:0%
+that we want to pick that series to
+cancel R normal on now take the attitude
+
+ align:start position:0%
+cancel R normal on now take the attitude
+ 
+
+ align:start position:0%
+cancel R normal on now take the attitude
+what if we didn't know that that series
+
+ align:start position:0%
+what if we didn't know that that series
+ 
+
+ align:start position:0%
+what if we didn't know that that series
+had a r normal on I could still throw it
+
+ align:start position:0%
+had a r normal on I could still throw it
+ 
+
+ align:start position:0%
+had a r normal on I could still throw it
+in make a change of variable to some
+
+ align:start position:0%
+in make a change of variable to some
+ 
+
+ align:start position:0%
+in make a change of variable to some
+Mass if it's a convergent series then
+
+ align:start position:0%
+Mass if it's a convergent series then
+ 
+
+ align:start position:0%
+Mass if it's a convergent series then
+I'm just defining some new mass and I
+
+ align:start position:0%
+I'm just defining some new mass and I
+ 
+
+ align:start position:0%
+I'm just defining some new mass and I
+could go through this technology and it
+
+ align:start position:0%
+could go through this technology and it
+ 
+
+ align:start position:0%
+could go through this technology and it
+would turn it should turn out that if uh
+
+ align:start position:0%
+would turn it should turn out that if uh
+ 
+
+ align:start position:0%
+would turn it should turn out that if uh
+if the series was okay so to speak then
+
+ align:start position:0%
+if the series was okay so to speak then
+ 
+
+ align:start position:0%
+if the series was okay so to speak then
+you wouldn't find this normal
+
+ align:start position:0%
+you wouldn't find this normal
+ 
+
+ align:start position:0%
+you wouldn't find this normal
+on you wouldn't find a a pole
+
+ align:start position:0%
+on you wouldn't find a a pole
+ 
+
+ align:start position:0%
+on you wouldn't find a a pole
+there and that can be I won't go through
+
+ align:start position:0%
+there and that can be I won't go through
+ 
+
+ align:start position:0%
+there and that can be I won't go through
+this in detail because it does it is a
+
+ align:start position:0%
+this in detail because it does it is a
+ 
+
+ align:start position:0%
+this in detail because it does it is a
+bit tricky to
+
+ align:start position:0%
+bit tricky to
+ 
+
+ align:start position:0%
+bit tricky to
+derive but you can derive what's called
+
+ align:start position:0%
+derive but you can derive what's called
+ 
+
+ align:start position:0%
+derive but you can derive what's called
+a sum rule for the renormalon which is
+
+ align:start position:0%
+a sum rule for the renormalon which is
+ 
+
+ align:start position:0%
+a sum rule for the renormalon which is
+another way of probing
+
+ align:start position:0%
+another way of probing
+ 
+
+ align:start position:0%
+another way of probing
+it by basically taking our all order
+
+ align:start position:0%
+it by basically taking our all order
+ 
+
+ align:start position:0%
+it by basically taking our all order
+solution so I took our leading log
+
+ align:start position:0%
+solution so I took our leading log
+ 
+
+ align:start position:0%
+solution so I took our leading log
+solution here
+
+ align:start position:0%
+solution here
+ 
+
+ align:start position:0%
+solution here
+right if I did the same thing with the
+
+ align:start position:0%
+right if I did the same thing with the
+ 
+
+ align:start position:0%
+right if I did the same thing with the
+all orders
+
+ align:start position:0%
+all orders
+ 
+
+ align:start position:0%
+all orders
+solution I could also take the baral
+
+ align:start position:0%
+solution I could also take the baral
+ 
+
+ align:start position:0%
+solution I could also take the baral
+transform of that and that if I do that
+
+ align:start position:0%
+transform of that and that if I do that
+ 
+
+ align:start position:0%
+transform of that and that if I do that
+gives me this thing called a sum rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's just manipulating infinite
+
+ align:start position:0%
+so it's just manipulating infinite
+ 
+
+ align:start position:0%
+so it's just manipulating infinite
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+and Mathematica can sum some of them up
+
+ align:start position:0%
+and Mathematica can sum some of them up
+ 
+
+ align:start position:0%
+and Mathematica can sum some of them up
+for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tedious and what you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find is a
+
+ align:start position:0%
+find is a
+ 
+
+ align:start position:0%
+find is a
+formula for the residue
+
+ align:start position:0%
+formula for the residue
+ 
+
+ align:start position:0%
+formula for the residue
+of the barell
+
+ align:start position:0%
+of the barell
+ 
+
+ align:start position:0%
+of the barell
+pole so let me call that residue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p12 and the the answer is actually
+
+ align:start position:0%
+p12 and the the answer is actually
+ 
+
+ align:start position:0%
+p12 and the the answer is actually
+pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simple so these s's were these
+
+ align:start position:0%
+simple so these s's were these
+ 
+
+ align:start position:0%
+simple so these s's were these
+coefficients that were showing up in our
+
+ align:start position:0%
+coefficients that were showing up in our
+ 
+
+ align:start position:0%
+coefficients that were showing up in our
+solution for the all ERS
+
+ align:start position:0%
+solution for the all ERS
+ 
+
+ align:start position:0%
+solution for the all ERS
+rge p12 is a series which will tell me
+
+ align:start position:0%
+rge p12 is a series which will tell me
+ 
+
+ align:start position:0%
+rge p12 is a series which will tell me
+the residue of the
+
+ align:start position:0%
+the residue of the
+ 
+
+ align:start position:0%
+the residue of the
+pole so that means that if p12 is not
+
+ align:start position:0%
+pole so that means that if p12 is not
+ 
+
+ align:start position:0%
+pole so that means that if p12 is not
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+zero then you have a u equals a half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pole and if P of P2 is equal zero
+
+ align:start position:0%
+pole and if P of P2 is equal zero
+ 
+
+ align:start position:0%
+pole and if P of P2 is equal zero
+then you have no U equals a half
+
+ align:start position:0%
+then you have no U equals a half
+ 
+
+ align:start position:0%
+then you have no U equals a half
+Pole now in practice you don't have an
+
+ align:start position:0%
+Pole now in practice you don't have an
+ 
+
+ align:start position:0%
+Pole now in practice you don't have an
+all orders result you only know a not
+
+ align:start position:0%
+all orders result you only know a not
+ 
+
+ align:start position:0%
+all orders result you only know a not
+finite number of these s's so what you
+
+ align:start position:0%
+finite number of these s's so what you
+ 
+
+ align:start position:0%
+finite number of these s's so what you
+actually do is you look at this series
+
+ align:start position:0%
+actually do is you look at this series
+ 
+
+ align:start position:0%
+actually do is you look at this series
+and you try to figure out where it's
+
+ align:start position:0%
+and you try to figure out where it's
+ 
+
+ align:start position:0%
+and you try to figure out where it's
+converging
+
+ align:start position:0%
+converging
+ 
+
+ align:start position:0%
+converging
+to okay but actually even with the
+
+ align:start position:0%
+to okay but actually even with the
+ 
+
+ align:start position:0%
+to okay but actually even with the
+knowledge that we have of the of the
+
+ align:start position:0%
+knowledge that we have of the of the
+ 
+
+ align:start position:0%
+knowledge that we have of the of the
+series for example for the bork Mass you
+
+ align:start position:0%
+series for example for the bork Mass you
+ 
+
+ align:start position:0%
+series for example for the bork Mass you
+can very quickly see that has a u equals
+
+ align:start position:0%
+can very quickly see that has a u equals
+ 
+
+ align:start position:0%
+can very quickly see that has a u equals
+a half pole and you can even do some air
+
+ align:start position:0%
+a half pole and you can even do some air
+ 
+
+ align:start position:0%
+a half pole and you can even do some air
+analysis by varying some things and
+
+ align:start position:0%
+analysis by varying some things and
+ 
+
+ align:start position:0%
+analysis by varying some things and
+you're get some kind of idea of the
+
+ align:start position:0%
+you're get some kind of idea of the
+ 
+
+ align:start position:0%
+you're get some kind of idea of the
+theoretical uncertainty from higher
+
+ align:start position:0%
+theoretical uncertainty from higher
+ 
+
+ align:start position:0%
+theoretical uncertainty from higher
+order terms in the series if you just
+
+ align:start position:0%
+order terms in the series if you just
+ 
+
+ align:start position:0%
+order terms in the series if you just
+formally say take a series that's
+
+ align:start position:0%
+formally say take a series that's
+ 
+
+ align:start position:0%
+formally say take a series that's
+convergent you could calculate if I hand
+
+ align:start position:0%
+convergent you could calculate if I hand
+ 
+
+ align:start position:0%
+convergent you could calculate if I hand
+you a series that's convergent you can
+
+ align:start position:0%
+you a series that's convergent you can
+ 
+
+ align:start position:0%
+you a series that's convergent you can
+calculate all these
+
+ align:start position:0%
+calculate all these
+ 
+
+ align:start position:0%
+calculate all these
+SKS and then you can very easily see
+
+ align:start position:0%
+SKS and then you can very easily see
+ 
+
+ align:start position:0%
+SKS and then you can very easily see
+that actually there's no equals a half
+
+ align:start position:0%
+that actually there's no equals a half
+ 
+
+ align:start position:0%
+that actually there's no equals a half
+pole what happens is all the terms are
+
+ align:start position:0%
+pole what happens is all the terms are
+ 
+
+ align:start position:0%
+pole what happens is all the terms are
+cancelling in this series and you just
+
+ align:start position:0%
+cancelling in this series and you just
+ 
+
+ align:start position:0%
+cancelling in this series and you just
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+zero okay so it's kind of like the
+
+ align:start position:0%
+zero okay so it's kind of like the
+ 
+
+ align:start position:0%
+zero okay so it's kind of like the
+cancellations I was talking about where
+
+ align:start position:0%
+cancellations I was talking about where
+ 
+
+ align:start position:0%
+cancellations I was talking about where
+I was cancelling a pole in the in the
+
+ align:start position:0%
+I was cancelling a pole in the in the
+ 
+
+ align:start position:0%
+I was cancelling a pole in the in the
+anomal dimension but here it's happening
+
+ align:start position:0%
+anomal dimension but here it's happening
+ 
+
+ align:start position:0%
+anomal dimension but here it's happening
+this thing if I have a convergent Series
+
+ align:start position:0%
+this thing if I have a convergent Series
+ 
+
+ align:start position:0%
+this thing if I have a convergent Series
+so this is a way of probing for normal
+
+ align:start position:0%
+so this is a way of probing for normal
+ 
+
+ align:start position:0%
+so this is a way of probing for normal
+on which doesn't rely on the bubble sum
+
+ align:start position:0%
+on which doesn't rely on the bubble sum
+ 
+
+ align:start position:0%
+on which doesn't rely on the bubble sum
+and basically uses the perturbative
+
+ align:start position:0%
+and basically uses the perturbative
+ 
+
+ align:start position:0%
+and basically uses the perturbative
+information that you have available
+
+ align:start position:0%
+information that you have available
+ 
+
+ align:start position:0%
+information that you have available
+whether it's non ailan or
+
+ align:start position:0%
+whether it's non ailan or
+ 
+
+ align:start position:0%
+whether it's non ailan or
+ailon
+
+ align:start position:0%
+ailon
+ 
+
+ align:start position:0%
+ailon
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+yep so when you did the um well this
+
+ align:start position:0%
+yep so when you did the um well this
+ 
+
+ align:start position:0%
+yep so when you did the um well this
+calculation here that capital F is it
+
+ align:start position:0%
+calculation here that capital F is it
+ 
+
+ align:start position:0%
+calculation here that capital F is it
+the same result as we found like we or
+
+ align:start position:0%
+the same result as we found like we or
+ 
+
+ align:start position:0%
+the same result as we found like we or
+something that has like
+
+ align:start position:0%
+something that has like
+ 
+
+ align:start position:0%
+something that has like
+theal one and all that stuff as well um
+
+ align:start position:0%
+theal one and all that stuff as well um
+ 
+
+ align:start position:0%
+theal one and all that stuff as well um
+no it's just the U equals the half pole
+
+ align:start position:0%
+no it's just the U equals the half pole
+ 
+
+ align:start position:0%
+no it's just the U equals the half pole
+yeah so right so what we've done here
+
+ align:start position:0%
+yeah so right so what we've done here
+ 
+
+ align:start position:0%
+yeah so right so what we've done here
+and actually just going to come to this
+
+ align:start position:0%
+and actually just going to come to this
+ 
+
+ align:start position:0%
+and actually just going to come to this
+but I'll foreshadow so what we've done
+
+ align:start position:0%
+but I'll foreshadow so what we've done
+ 
+
+ align:start position:0%
+but I'll foreshadow so what we've done
+here is we set up a construction to
+
+ align:start position:0%
+here is we set up a construction to
+ 
+
+ align:start position:0%
+here is we set up a construction to
+remove the U equals a half pole and we
+
+ align:start position:0%
+remove the U equals a half pole and we
+ 
+
+ align:start position:0%
+remove the U equals a half pole and we
+did not remove any higher poles so you
+
+ align:start position:0%
+did not remove any higher poles so you
+ 
+
+ align:start position:0%
+did not remove any higher poles so you
+could we said the U equal a half is the
+
+ align:start position:0%
+could we said the U equal a half is the
+ 
+
+ align:start position:0%
+could we said the U equal a half is the
+most important let's get rid of that one
+
+ align:start position:0%
+most important let's get rid of that one
+ 
+
+ align:start position:0%
+most important let's get rid of that one
+from the msar mass there would be in
+
+ align:start position:0%
+from the msar mass there would be in
+ 
+
+ align:start position:0%
+from the msar mass there would be in
+principle higher ones and higher ones
+
+ align:start position:0%
+principle higher ones and higher ones
+ 
+
+ align:start position:0%
+principle higher ones and higher ones
+would basically we we had a some
+
+ align:start position:0%
+would basically we we had a some
+ 
+
+ align:start position:0%
+would basically we we had a some
+something that was proportional to R if
+
+ align:start position:0%
+something that was proportional to R if
+ 
+
+ align:start position:0%
+something that was proportional to R if
+you wanted to remove for that's for U
+
+ align:start position:0%
+you wanted to remove for that's for U
+ 
+
+ align:start position:0%
+you wanted to remove for that's for U
+equal a half if you wanted to remove
+
+ align:start position:0%
+equal a half if you wanted to remove
+ 
+
+ align:start position:0%
+equal a half if you wanted to remove
+higher ones you'd need terms
+
+ align:start position:0%
+higher ones you'd need terms
+ 
+
+ align:start position:0%
+higher ones you'd need terms
+proportional to R2 for example for = 1
+
+ align:start position:0%
+proportional to R2 for example for = 1
+ 
+
+ align:start position:0%
+proportional to R2 for example for = 1
+Etc so we could have added more terms to
+
+ align:start position:0%
+Etc so we could have added more terms to
+ 
+
+ align:start position:0%
+Etc so we could have added more terms to
+do more but we didn't we just sort of
+
+ align:start position:0%
+do more but we didn't we just sort of
+ 
+
+ align:start position:0%
+do more but we didn't we just sort of
+removed the problem at U equals a half
+
+ align:start position:0%
+removed the problem at U equals a half
+ 
+
+ align:start position:0%
+removed the problem at U equals a half
+and that's why when we go through this
+
+ align:start position:0%
+and that's why when we go through this
+ 
+
+ align:start position:0%
+and that's why when we go through this
+you only see a u equals a half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pole something you have to change the
+
+ align:start position:0%
+pole something you have to change the
+ 
+
+ align:start position:0%
+pole something you have to change the
+result of this yeah so the way you
+
+ align:start position:0%
+result of this yeah so the way you
+ 
+
+ align:start position:0%
+result of this yeah so the way you
+should think about it is that basically
+
+ align:start position:0%
+should think about it is that basically
+ 
+
+ align:start position:0%
+should think about it is that basically
+what you're doing is you're setting up a
+
+ align:start position:0%
+what you're doing is you're setting up a
+ 
+
+ align:start position:0%
+what you're doing is you're setting up a
+scheme change that perturbatively takes
+
+ align:start position:0%
+scheme change that perturbatively takes
+ 
+
+ align:start position:0%
+scheme change that perturbatively takes
+you out of msar towards something else
+
+ align:start position:0%
+you out of msar towards something else
+ 
+
+ align:start position:0%
+you out of msar towards something else
+you you remove the U equals a half and
+
+ align:start position:0%
+you you remove the U equals a half and
+ 
+
+ align:start position:0%
+you you remove the U equals a half and
+you get rid of that problem if you
+
+ align:start position:0%
+you get rid of that problem if you
+ 
+
+ align:start position:0%
+you get rid of that problem if you
+thought you had enough perturbative
+
+ align:start position:0%
+thought you had enough perturbative
+ 
+
+ align:start position:0%
+thought you had enough perturbative
+accuracy that you were seeing problems
+
+ align:start position:0%
+accuracy that you were seeing problems
+ 
+
+ align:start position:0%
+accuracy that you were seeing problems
+related to U equals 1 then you could
+
+ align:start position:0%
+related to U equals 1 then you could
+ 
+
+ align:start position:0%
+related to U equals 1 then you could
+make further scheme change with another
+
+ align:start position:0%
+make further scheme change with another
+ 
+
+ align:start position:0%
+make further scheme change with another
+series that's proportional to R 2 to get
+
+ align:start position:0%
+series that's proportional to R 2 to get
+ 
+
+ align:start position:0%
+series that's proportional to R 2 to get
+rid of that
+
+ align:start position:0%
+rid of that
+ 
+
+ align:start position:0%
+rid of that
+one so the would tell you about all the
+
+ align:start position:0%
+one so the would tell you about all the
+ 
+
+ align:start position:0%
+one so the would tell you about all the
+it would tell you about these ones too
+
+ align:start position:0%
+it would tell you about these ones too
+ 
+
+ align:start position:0%
+it would tell you about these ones too
+yeah absolutely
+
+ align:start position:0%
+yeah absolutely
+ 
+
+ align:start position:0%
+yeah absolutely
+so you can actually generalize this for
+
+ align:start position:0%
+so you can actually generalize this for
+ 
+
+ align:start position:0%
+so you can actually generalize this for
+arbit you know for R to the p and you
+
+ align:start position:0%
+arbit you know for R to the p and you
+ 
+
+ align:start position:0%
+arbit you know for R to the p and you
+can derive a sum rule for R to the p and
+
+ align:start position:0%
+can derive a sum rule for R to the p and
+ 
+
+ align:start position:0%
+can derive a sum rule for R to the p and
+it's a slightly more complicated formula
+
+ align:start position:0%
+it's a slightly more complicated formula
+ 
+
+ align:start position:0%
+it's a slightly more complicated formula
+here and then you'd have the P to P
+
+ align:start position:0%
+here and then you'd have the P to P
+ 
+
+ align:start position:0%
+here and then you'd have the P to P
+over2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pole all
+
+ align:start position:0%
+pole all
+ 
+
+ align:start position:0%
+pole all
+right okay so
+
+ align:start position:0%
+right okay so
+ 
+
+ align:start position:0%
+right okay so
+the sum
+
+ align:start position:0%
+the sum
+ 
+
+ align:start position:0%
+the sum
+rule is a
+
+ align:start position:0%
+rule is a
+ 
+
+ align:start position:0%
+rule is a
+probe alternate
+
+ align:start position:0%
+probe alternate
+ 
+
+ align:start position:0%
+probe alternate
+probe for the re normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the NF bubbles are the classic one
+
+ align:start position:0%
+on the NF bubbles are the classic one
+ 
+
+ align:start position:0%
+on the NF bubbles are the classic one
+that people know
+
+ align:start position:0%
+that people know
+ 
+
+ align:start position:0%
+that people know
+about and this provides an
+
+ align:start position:0%
+about and this provides an
+ 
+
+ align:start position:0%
+about and this provides an
+alternate the nice thing about this is
+
+ align:start position:0%
+alternate the nice thing about this is
+ 
+
+ align:start position:0%
+alternate the nice thing about this is
+it also provides a series that con that
+
+ align:start position:0%
+it also provides a series that con that
+ 
+
+ align:start position:0%
+it also provides a series that con that
+you can look at the convergence where
+
+ align:start position:0%
+you can look at the convergence where
+ 
+
+ align:start position:0%
+you can look at the convergence where
+the NF bubbles just get a result see NF
+
+ align:start position:0%
+the NF bubbles just get a result see NF
+ 
+
+ align:start position:0%
+the NF bubbles just get a result see NF
+bubbles are good for finding out whether
+
+ align:start position:0%
+bubbles are good for finding out whether
+ 
+
+ align:start position:0%
+bubbles are good for finding out whether
+or not this thing has a r Alon if you
+
+ align:start position:0%
+or not this thing has a r Alon if you
+ 
+
+ align:start position:0%
+or not this thing has a r Alon if you
+get some non zero result then you expect
+
+ align:start position:0%
+get some non zero result then you expect
+ 
+
+ align:start position:0%
+get some non zero result then you expect
+that it does this way you could actually
+
+ align:start position:0%
+that it does this way you could actually
+ 
+
+ align:start position:0%
+that it does this way you could actually
+calculate the
+
+ align:start position:0%
+calculate the
+ 
+
+ align:start position:0%
+calculate the
+residue if you thought if you wanted to
+
+ align:start position:0%
+residue if you thought if you wanted to
+ 
+
+ align:start position:0%
+residue if you thought if you wanted to
+know that value for some
+
+ align:start position:0%
+know that value for some
+ 
+
+ align:start position:0%
+know that value for some
+reason
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that actually might be useful
+
+ align:start position:0%
+okay and that actually might be useful
+ 
+
+ align:start position:0%
+okay and that actually might be useful
+for example if you wanted to think about
+
+ align:start position:0%
+for example if you wanted to think about
+ 
+
+ align:start position:0%
+for example if you wanted to think about
+higher normal on PS because you might
+
+ align:start position:0%
+higher normal on PS because you might
+ 
+
+ align:start position:0%
+higher normal on PS because you might
+want to say well let me get rid of the
+
+ align:start position:0%
+want to say well let me get rid of the
+ 
+
+ align:start position:0%
+want to say well let me get rid of the
+first one Whatever residue I can best
+
+ align:start position:0%
+first one Whatever residue I can best
+ 
+
+ align:start position:0%
+first one Whatever residue I can best
+approximate it for and see if there's
+
+ align:start position:0%
+approximate it for and see if there's
+ 
+
+ align:start position:0%
+approximate it for and see if there's
+another one
+
+ align:start position:0%
+another one
+ 
+
+ align:start position:0%
+another one
+underneath there's not really enough
+
+ align:start position:0%
+underneath there's not really enough
+ 
+
+ align:start position:0%
+underneath there's not really enough
+perturbative information that we have
+
+ align:start position:0%
+perturbative information that we have
+ 
+
+ align:start position:0%
+perturbative information that we have
+about qcd to be able to do that type of
+
+ align:start position:0%
+about qcd to be able to do that type of
+ 
+
+ align:start position:0%
+about qcd to be able to do that type of
+thing there's a few cases where U equals
+
+ align:start position:0%
+thing there's a few cases where U equals
+ 
+
+ align:start position:0%
+thing there's a few cases where U equals
+half is absent and then you can do that
+
+ align:start position:0%
+half is absent and then you can do that
+ 
+
+ align:start position:0%
+half is absent and then you can do that
+kind of thing I mean there's actually
+
+ align:start position:0%
+kind of thing I mean there's actually
+ 
+
+ align:start position:0%
+kind of thing I mean there's actually
+many cases where U equal a half is
+
+ align:start position:0%
+many cases where U equal a half is
+ 
+
+ align:start position:0%
+many cases where U equal a half is
+absent you can look for U equals 1 but
+
+ align:start position:0%
+absent you can look for U equals 1 but
+ 
+
+ align:start position:0%
+absent you can look for U equals 1 but
+looking for a subleading r normal one is
+
+ align:start position:0%
+looking for a subleading r normal one is
+ 
+
+ align:start position:0%
+looking for a subleading r normal one is
+something that nobody's found
+
+ align:start position:0%
+something that nobody's found
+ 
+
+ align:start position:0%
+something that nobody's found
+one people sometimes speculate about
+
+ align:start position:0%
+one people sometimes speculate about
+ 
+
+ align:start position:0%
+one people sometimes speculate about
+them because maybe the residue of the
+
+ align:start position:0%
+them because maybe the residue of the
+ 
+
+ align:start position:0%
+them because maybe the residue of the
+first one happens to be
+
+ align:start position:0%
+first one happens to be
+ 
+
+ align:start position:0%
+first one happens to be
+small this would allow you to test for
+
+ align:start position:0%
+small this would allow you to test for
+ 
+
+ align:start position:0%
+small this would allow you to test for
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in to Decay people talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so let's come back and
+
+ align:start position:0%
+that okay so let's come back and
+ 
+
+ align:start position:0%
+that okay so let's come back and
+actually show you how you can use this
+
+ align:start position:0%
+actually show you how you can use this
+ 
+
+ align:start position:0%
+actually show you how you can use this
+technology for some phenomenological
+
+ align:start position:0%
+technology for some phenomenological
+ 
+
+ align:start position:0%
+technology for some phenomenological
+stuff and I want to do that by
+
+ align:start position:0%
+stuff and I want to do that by
+ 
+
+ align:start position:0%
+stuff and I want to do that by
+generalizing our discussion slightly
+
+ align:start position:0%
+generalizing our discussion slightly
+ 
+
+ align:start position:0%
+generalizing our discussion slightly
+away from masses towards just a general
+
+ align:start position:0%
+away from masses towards just a general
+ 
+
+ align:start position:0%
+away from masses towards just a general
+operator product
+
+ align:start position:0%
+operator product
+ 
+
+ align:start position:0%
+operator product
+expansion so everything that we've said
+
+ align:start position:0%
+expansion so everything that we've said
+ 
+
+ align:start position:0%
+expansion so everything that we've said
+here for masses can be applied more
+
+ align:start position:0%
+here for masses can be applied more
+ 
+
+ align:start position:0%
+here for masses can be applied more
+generally
+
+ align:start position:0%
+generally
+ 
+
+ align:start position:0%
+generally
+to an operator product
+
+ align:start position:0%
+to an operator product
+ 
+
+ align:start position:0%
+to an operator product
+expansion so let me show you why how
+
+ align:start position:0%
+expansion so let me show you why how
+ 
+
+ align:start position:0%
+expansion so let me show you why how
+what I
+
+ align:start position:0%
+what I
+ 
+
+ align:start position:0%
+what I
+mean so let's first consider what I mean
+
+ align:start position:0%
+mean so let's first consider what I mean
+ 
+
+ align:start position:0%
+mean so let's first consider what I mean
+by an operator product expansion in
+
+ align:start position:0%
+by an operator product expansion in
+ 
+
+ align:start position:0%
+by an operator product expansion in
+msar so you can think of this like maybe
+
+ align:start position:0%
+msar so you can think of this like maybe
+ 
+
+ align:start position:0%
+msar so you can think of this like maybe
+I'm integrating out a heavy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle and I'm writing a formula down
+
+ align:start position:0%
+particle and I'm writing a formula down
+ 
+
+ align:start position:0%
+particle and I'm writing a formula down
+and has some wison coefficients it has
+
+ align:start position:0%
+and has some wison coefficients it has
+ 
+
+ align:start position:0%
+and has some wison coefficients it has
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+operators and it's a TA it's a tailor
+
+ align:start position:0%
+operators and it's a TA it's a tailor
+ 
+
+ align:start position:0%
+operators and it's a TA it's a tailor
+Series in this parameter Q which is the
+
+ align:start position:0%
+Series in this parameter Q which is the
+ 
+
+ align:start position:0%
+Series in this parameter Q which is the
+hard scale high energy
+
+ align:start position:0%
+hard scale high energy
+ 
+
+ align:start position:0%
+hard scale high energy
+scale and I'm basically just expanding
+
+ align:start position:0%
+scale and I'm basically just expanding
+ 
+
+ align:start position:0%
+scale and I'm basically just expanding
+if you like in Lambda qcd over
+
+ align:start position:0%
+if you like in Lambda qcd over
+ 
+
+ align:start position:0%
+if you like in Lambda qcd over
+Q and The Operators are they're set by
+
+ align:start position:0%
+Q and The Operators are they're set by
+ 
+
+ align:start position:0%
+Q and The Operators are they're set by
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+qcd so I'm going to take this guy to be
+
+ align:start position:0%
+qcd so I'm going to take this guy to be
+ 
+
+ align:start position:0%
+qcd so I'm going to take this guy to be
+dimensionless this is some dimensionless
+
+ align:start position:0%
+dimensionless this is some dimensionless
+ 
+
+ align:start position:0%
+dimensionless this is some dimensionless
+observable okay can always make it
+
+ align:start position:0%
+observable okay can always make it
+ 
+
+ align:start position:0%
+observable okay can always make it
+dimensionless by suitably
+
+ align:start position:0%
+dimensionless by suitably
+ 
+
+ align:start position:0%
+dimensionless by suitably
+choosing multiplying by appropriate Mass
+
+ align:start position:0%
+choosing multiplying by appropriate Mass
+ 
+
+ align:start position:0%
+choosing multiplying by appropriate Mass
+scales so then this is this here will be
+
+ align:start position:0%
+scales so then this is this here will be
+ 
+
+ align:start position:0%
+scales so then this is this here will be
+a dimensional Wilson
+
+ align:start position:0%
+a dimensional Wilson
+ 
+
+ align:start position:0%
+a dimensional Wilson
+coefficient and it's a Wilson
+
+ align:start position:0%
+coefficient and it's a Wilson
+ 
+
+ align:start position:0%
+coefficient and it's a Wilson
+coefficient in
+
+ align:start position:0%
+coefficient in
+ 
+
+ align:start position:0%
+coefficient in
+msar that's what the bar
+
+ align:start position:0%
+msar that's what the bar
+ 
+
+ align:start position:0%
+msar that's what the bar
+means and so this is an msar operator
+
+ align:start position:0%
+means and so this is an msar operator
+ 
+
+ align:start position:0%
+means and so this is an msar operator
+msar Matrix element of some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator and it's also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimensionless so this guy will be
+
+ align:start position:0%
+dimensionless so this guy will be
+ 
+
+ align:start position:0%
+dimensionless so this guy will be
+dimensionless
+
+ align:start position:0%
+dimensionless
+ 
+
+ align:start position:0%
+dimensionless
+too and finally this guy will have
+
+ align:start position:0%
+too and finally this guy will have
+ 
+
+ align:start position:0%
+too and finally this guy will have
+Dimension equals 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now in msar what's beautiful about msar
+
+ align:start position:0%
+now in msar what's beautiful about msar
+ 
+
+ align:start position:0%
+now in msar what's beautiful about msar
+is that the series for these
+
+ align:start position:0%
+is that the series for these
+ 
+
+ align:start position:0%
+is that the series for these
+coefficients are very
+
+ align:start position:0%
+coefficients are very
+ 
+
+ align:start position:0%
+coefficients are very
+simple that's why people like
+
+ align:start position:0%
+simple that's why people like
+ 
+
+ align:start position:0%
+simple that's why people like
+to compute an MS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar so if you look at what the series C
+
+ align:start position:0%
+bar so if you look at what the series C
+ 
+
+ align:start position:0%
+bar so if you look at what the series C
+bar looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like the form of it this as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follows it's got dependence on mu over
+
+ align:start position:0%
+follows it's got dependence on mu over
+ 
+
+ align:start position:0%
+follows it's got dependence on mu over
+q and then alpha s of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu and these guys here are not an
+
+ align:start position:0%
+mu and these guys here are not an
+ 
+
+ align:start position:0%
+mu and these guys here are not an
+arbitrary function of mu over q but
+
+ align:start position:0%
+arbitrary function of mu over q but
+ 
+
+ align:start position:0%
+arbitrary function of mu over q but
+they're really just some
+
+ align:start position:0%
+they're really just some
+ 
+
+ align:start position:0%
+they're really just some
+logs so this looks like a series of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+logs so in mpar you're only seeing these
+
+ align:start position:0%
+logs so in mpar you're only seeing these
+ 
+
+ align:start position:0%
+logs so in mpar you're only seeing these
+log
+
+ align:start position:0%
+log
+ 
+
+ align:start position:0%
+log
+Ms so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's good from a computational point
+
+ align:start position:0%
+that's good from a computational point
+ 
+
+ align:start position:0%
+that's good from a computational point
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+view but we also know that in
+
+ align:start position:0%
+view but we also know that in
+ 
+
+ align:start position:0%
+view but we also know that in
+generically in this msar approach you
+
+ align:start position:0%
+generically in this msar approach you
+ 
+
+ align:start position:0%
+generically in this msar approach you
+may get sensitivity to re normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on it's also another thing we like about
+
+ align:start position:0%
+on it's also another thing we like about
+ 
+
+ align:start position:0%
+on it's also another thing we like about
+MSR is that it satisfies all the
+
+ align:start position:0%
+MSR is that it satisfies all the
+ 
+
+ align:start position:0%
+MSR is that it satisfies all the
+symmetries we want to keep doesn't mess
+
+ align:start position:0%
+symmetries we want to keep doesn't mess
+ 
+
+ align:start position:0%
+symmetries we want to keep doesn't mess
+them up so it's luren engaging
+
+ align:start position:0%
+them up so it's luren engaging
+ 
+
+ align:start position:0%
+them up so it's luren engaging
+arean which is always a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing and not only is it simple for
+
+ align:start position:0%
+thing and not only is it simple for
+ 
+
+ align:start position:0%
+thing and not only is it simple for
+multi-loop computations but multi-loop
+
+ align:start position:0%
+multi-loop computations but multi-loop
+ 
+
+ align:start position:0%
+multi-loop computations but multi-loop
+computations are not even done in other
+
+ align:start position:0%
+computations are not even done in other
+ 
+
+ align:start position:0%
+computations are not even done in other
+schemes because they're just too
+
+ align:start position:0%
+schemes because they're just too
+ 
+
+ align:start position:0%
+schemes because they're just too
+difficult so it really makes multi-op
+
+ align:start position:0%
+difficult so it really makes multi-op
+ 
+
+ align:start position:0%
+difficult so it really makes multi-op
+computations possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the bot there's only really this one
+
+ align:start position:0%
+and the bot there's only really this one
+ 
+
+ align:start position:0%
+and the bot there's only really this one
+bot that that has this R normal
+
+ align:start position:0%
+bot that that has this R normal
+ 
+
+ align:start position:0%
+bot that that has this R normal
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+issue so we talked about re normal on
+
+ align:start position:0%
+issue so we talked about re normal on
+ 
+
+ align:start position:0%
+issue so we talked about re normal on
+for a mass and I just showed you what it
+
+ align:start position:0%
+for a mass and I just showed you what it
+ 
+
+ align:start position:0%
+for a mass and I just showed you what it
+was and then we explored it here let me
+
+ align:start position:0%
+was and then we explored it here let me
+ 
+
+ align:start position:0%
+was and then we explored it here let me
+tell you what the renormalon would
+
+ align:start position:0%
+tell you what the renormalon would
+ 
+
+ align:start position:0%
+tell you what the renormalon would
+be so generically what the ralon would
+
+ align:start position:0%
+be so generically what the ralon would
+ 
+
+ align:start position:0%
+be so generically what the ralon would
+be is the following you would have an
+
+ align:start position:0%
+be is the following you would have an
+ 
+
+ align:start position:0%
+be is the following you would have an
+ambiguity in the coefficient see c0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar it's of the size Lambda qcd over M
+
+ align:start position:0%
+bar it's of the size Lambda qcd over M
+ 
+
+ align:start position:0%
+bar it's of the size Lambda qcd over M
+over whatever the scale Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is and you would have a the same
+
+ align:start position:0%
+is and you would have a the same
+ 
+
+ align:start position:0%
+is and you would have a the same
+ambiguity in this Theta 1
+
+ align:start position:0%
+ambiguity in this Theta 1
+ 
+
+ align:start position:0%
+ambiguity in this Theta 1
+bar so this Theta 1 bar which is an msar
+
+ align:start position:0%
+bar so this Theta 1 bar which is an msar
+ 
+
+ align:start position:0%
+bar so this Theta 1 bar which is an msar
+Matrix element has an
+
+ align:start position:0%
+Matrix element has an
+ 
+
+ align:start position:0%
+Matrix element has an
+ambiguity is a border Lambda
+
+ align:start position:0%
+ambiguity is a border Lambda
+ 
+
+ align:start position:0%
+ambiguity is a border Lambda
+qcd this guy has an ambiguity and those
+
+ align:start position:0%
+qcd this guy has an ambiguity and those
+ 
+
+ align:start position:0%
+qcd this guy has an ambiguity and those
+ambiguities cancel so you're dividing up
+
+ align:start position:0%
+ambiguities cancel so you're dividing up
+ 
+
+ align:start position:0%
+ambiguities cancel so you're dividing up
+the physics again in msar into short
+
+ align:start position:0%
+the physics again in msar into short
+ 
+
+ align:start position:0%
+the physics again in msar into short
+distance physics and longdistance
+
+ align:start position:0%
+distance physics and longdistance
+ 
+
+ align:start position:0%
+distance physics and longdistance
+physics and the interesting thing is
+
+ align:start position:0%
+physics and the interesting thing is
+ 
+
+ align:start position:0%
+physics and the interesting thing is
+that it's there's a piece of short
+
+ align:start position:0%
+that it's there's a piece of short
+ 
+
+ align:start position:0%
+that it's there's a piece of short
+there's a piece of longdistance physics
+
+ align:start position:0%
+there's a piece of longdistance physics
+ 
+
+ align:start position:0%
+there's a piece of longdistance physics
+trapped in the c0 that should be if you
+
+ align:start position:0%
+trapped in the c0 that should be if you
+ 
+
+ align:start position:0%
+trapped in the c0 that should be if you
+really wanted it should be physically in
+
+ align:start position:0%
+really wanted it should be physically in
+ 
+
+ align:start position:0%
+really wanted it should be physically in
+the Theta one bar and vice versa so um
+
+ align:start position:0%
+the Theta one bar and vice versa so um
+ 
+
+ align:start position:0%
+the Theta one bar and vice versa so um
+so really what's the problem with Ms bar
+
+ align:start position:0%
+so really what's the problem with Ms bar
+ 
+
+ align:start position:0%
+so really what's the problem with Ms bar
+is that there's a piece of something
+
+ align:start position:0%
+is that there's a piece of something
+ 
+
+ align:start position:0%
+is that there's a piece of something
+that you want in Theta 1 bar but ends up
+
+ align:start position:0%
+that you want in Theta 1 bar but ends up
+ 
+
+ align:start position:0%
+that you want in Theta 1 bar but ends up
+just being in the c0 bar and that's what
+
+ align:start position:0%
+just being in the c0 bar and that's what
+ 
+
+ align:start position:0%
+just being in the c0 bar and that's what
+I mean by this that there's something
+
+ align:start position:0%
+I mean by this that there's something
+ 
+
+ align:start position:0%
+I mean by this that there's something
+here which is infrared sensitive
+
+ align:start position:0%
+here which is infrared sensitive
+ 
+
+ align:start position:0%
+here which is infrared sensitive
+correspondingly there's kind of a
+
+ align:start position:0%
+correspondingly there's kind of a
+ 
+
+ align:start position:0%
+correspondingly there's kind of a
+ultraviolet sensitivity in this Theta 1
+
+ align:start position:0%
+ultraviolet sensitivity in this Theta 1
+ 
+
+ align:start position:0%
+ultraviolet sensitivity in this Theta 1
+bar and you'd like to get that
+
+ align:start position:0%
+bar and you'd like to get that
+ 
+
+ align:start position:0%
+bar and you'd like to get that
+rearranged in an appropriate way and
+
+ align:start position:0%
+rearranged in an appropriate way and
+ 
+
+ align:start position:0%
+rearranged in an appropriate way and
+that's like this kind of rearrangement
+
+ align:start position:0%
+that's like this kind of rearrangement
+ 
+
+ align:start position:0%
+that's like this kind of rearrangement
+we were making by changing schemes for
+
+ align:start position:0%
+we were making by changing schemes for
+ 
+
+ align:start position:0%
+we were making by changing schemes for
+masses except here it's going to be
+
+ align:start position:0%
+masses except here it's going to be
+ 
+
+ align:start position:0%
+masses except here it's going to be
+changing schemes for Wilson
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coefficients so this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is it what we would call a u equal
+
+ align:start position:0%
+here is it what we would call a u equal
+ 
+
+ align:start position:0%
+here is it what we would call a u equal
+1un
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so what happens with u equal 1 is
+
+ align:start position:0%
+one so what happens with u equal 1 is
+ 
+
+ align:start position:0%
+one so what happens with u equal 1 is
+that you make a connection between the
+
+ align:start position:0%
+that you make a connection between the
+ 
+
+ align:start position:0%
+that you make a connection between the
+leading order term and the power
+
+ align:start position:0%
+leading order term and the power
+ 
+
+ align:start position:0%
+leading order term and the power
+suppressed
+
+ align:start position:0%
+suppressed
+ 
+
+ align:start position:0%
+suppressed
+term that's what happens with the Delta
+
+ align:start position:0%
+term that's what happens with the Delta
+ 
+
+ align:start position:0%
+term that's what happens with the Delta
+c0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar so in order to flesh out a little
+
+ align:start position:0%
+bar so in order to flesh out a little
+ 
+
+ align:start position:0%
+bar so in order to flesh out a little
+bit better what I just said in words
+
+ align:start position:0%
+bit better what I just said in words
+ 
+
+ align:start position:0%
+bit better what I just said in words
+let's pretend that we understand what
+
+ align:start position:0%
+let's pretend that we understand what
+ 
+
+ align:start position:0%
+let's pretend that we understand what
+the theory is and let's just pretend
+
+ align:start position:0%
+the theory is and let's just pretend
+ 
+
+ align:start position:0%
+the theory is and let's just pretend
+it's some integral
+
+ align:start position:0%
+it's some integral
+ 
+
+ align:start position:0%
+it's some integral
+and I'll just show you what is going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so let's imagine that our
+
+ align:start position:0%
+here so let's imagine that our
+ 
+
+ align:start position:0%
+here so let's imagine that our
+theory is an integral instead of a
+
+ align:start position:0%
+theory is an integral instead of a
+ 
+
+ align:start position:0%
+theory is an integral instead of a
+Quantum the theory it's a one
+
+ align:start position:0%
+Quantum the theory it's a one
+ 
+
+ align:start position:0%
+Quantum the theory it's a one
+dimensional integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it has two
+
+ align:start position:0%
+and it has two
+ 
+
+ align:start position:0%
+and it has two
+scales one which I'll call Lambda qcd
+
+ align:start position:0%
+scales one which I'll call Lambda qcd
+ 
+
+ align:start position:0%
+scales one which I'll call Lambda qcd
+which is some low scale and one which
+
+ align:start position:0%
+which is some low scale and one which
+ 
+
+ align:start position:0%
+which is some low scale and one which
+I'll call
+
+ align:start position:0%
+I'll call
+ 
+
+ align:start position:0%
+I'll call
+Q which is some high
+
+ align:start position:0%
+Q which is some high
+ 
+
+ align:start position:0%
+Q which is some high
+scale and I'm using a notation where the
+
+ align:start position:0%
+scale and I'm using a notation where the
+ 
+
+ align:start position:0%
+scale and I'm using a notation where the
+integral could diverge and i' regulate
+
+ align:start position:0%
+integral could diverge and i' regulate
+ 
+
+ align:start position:0%
+integral could diverge and i' regulate
+it with a dimensional regularization
+
+ align:start position:0%
+it with a dimensional regularization
+ 
+
+ align:start position:0%
+it with a dimensional regularization
+type uh parameter so I'm doing a
+
+ align:start position:0%
+type uh parameter so I'm doing a
+ 
+
+ align:start position:0%
+type uh parameter so I'm doing a
+one-dimensional integral but continua
+
+ align:start position:0%
+one-dimensional integral but continua
+ 
+
+ align:start position:0%
+one-dimensional integral but continua
+into Epsilon Dimensions to regulate any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divergences so what msar does with this
+
+ align:start position:0%
+divergences so what msar does with this
+ 
+
+ align:start position:0%
+divergences so what msar does with this
+integral is it just says well I'm not
+
+ align:start position:0%
+integral is it just says well I'm not
+ 
+
+ align:start position:0%
+integral is it just says well I'm not
+going to change the limits of the
+
+ align:start position:0%
+going to change the limits of the
+ 
+
+ align:start position:0%
+going to change the limits of the
+integral I'm just going to either expand
+
+ align:start position:0%
+integral I'm just going to either expand
+ 
+
+ align:start position:0%
+integral I'm just going to either expand
+out this F or expand out this
+
+ align:start position:0%
+out this F or expand out this
+ 
+
+ align:start position:0%
+out this F or expand out this
+denominator I'll do two different tailor
+
+ align:start position:0%
+denominator I'll do two different tailor
+ 
+
+ align:start position:0%
+denominator I'll do two different tailor
+series and then I'll put them together
+
+ align:start position:0%
+series and then I'll put them together
+ 
+
+ align:start position:0%
+series and then I'll put them together
+and that's basically well how I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identifying the terms in my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+op so msar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I sort of associate there being a
+
+ align:start position:0%
+so I sort of associate there being a
+ 
+
+ align:start position:0%
+so I sort of associate there being a
+high energy piece where K is of order
+
+ align:start position:0%
+high energy piece where K is of order
+ 
+
+ align:start position:0%
+high energy piece where K is of order
+q and then there's some low energy
+
+ align:start position:0%
+q and then there's some low energy
+ 
+
+ align:start position:0%
+q and then there's some low energy
+piece I don't change the limits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the low energy piece I keep the
+
+ align:start position:0%
+so in the low energy piece I keep the
+ 
+
+ align:start position:0%
+so in the low energy piece I keep the
+full function
+
+ align:start position:0%
+full function
+ 
+
+ align:start position:0%
+full function
+f and then I expand
+
+ align:start position:0%
+f and then I expand
+ 
+
+ align:start position:0%
+f and then I expand
+out the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing and if I drop the dots in this
+
+ align:start position:0%
+thing and if I drop the dots in this
+ 
+
+ align:start position:0%
+thing and if I drop the dots in this
+formula I can identify these integrals
+
+ align:start position:0%
+formula I can identify these integrals
+ 
+
+ align:start position:0%
+formula I can identify these integrals
+as toy models for the things that are
+
+ align:start position:0%
+as toy models for the things that are
+ 
+
+ align:start position:0%
+as toy models for the things that are
+appearing in my
+
+ align:start position:0%
+appearing in my
+ 
+
+ align:start position:0%
+appearing in my
+op let me write that op again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here these things are one this
+
+ align:start position:0%
+so here these things are one this
+ 
+
+ align:start position:0%
+so here these things are one this
+example this integral here which is over
+
+ align:start position:0%
+example this integral here which is over
+ 
+
+ align:start position:0%
+example this integral here which is over
+high energy scales K dominated by Q is
+
+ align:start position:0%
+high energy scales K dominated by Q is
+ 
+
+ align:start position:0%
+high energy scales K dominated by Q is
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy and this integral here where K is of
+
+ align:start position:0%
+guy and this integral here where K is of
+ 
+
+ align:start position:0%
+guy and this integral here where K is of
+order Lambda qcd effectively there's a
+
+ align:start position:0%
+order Lambda qcd effectively there's a
+ 
+
+ align:start position:0%
+order Lambda qcd effectively there's a
+one over Q which is this one over Q
+
+ align:start position:0%
+one over Q which is this one over Q
+ 
+
+ align:start position:0%
+one over Q which is this one over Q
+that's giving me the operator Theta 1
+
+ align:start position:0%
+that's giving me the operator Theta 1
+ 
+
+ align:start position:0%
+that's giving me the operator Theta 1
+bar okay so Wilson coefficient is the
+
+ align:start position:0%
+bar okay so Wilson coefficient is the
+ 
+
+ align:start position:0%
+bar okay so Wilson coefficient is the
+high energy piece of the original thing
+
+ align:start position:0%
+high energy piece of the original thing
+ 
+
+ align:start position:0%
+high energy piece of the original thing
+Matrix element here is the low energy
+
+ align:start position:0%
+Matrix element here is the low energy
+ 
+
+ align:start position:0%
+Matrix element here is the low energy
+piece which is suppressed by one over
+
+ align:start position:0%
+piece which is suppressed by one over
+ 
+
+ align:start position:0%
+piece which is suppressed by one over
+Q
+
+ align:start position:0%
+Q
+ 
+
+ align:start position:0%
+Q
+okay but they both came from the same
+
+ align:start position:0%
+okay but they both came from the same
+ 
+
+ align:start position:0%
+okay but they both came from the same
+physics in the
+
+ align:start position:0%
+physics in the
+ 
+
+ align:start position:0%
+physics in the
+beginning and I just was expanding it
+
+ align:start position:0%
+beginning and I just was expanding it
+ 
+
+ align:start position:0%
+beginning and I just was expanding it
+because that's how I wanted to organize
+
+ align:start position:0%
+because that's how I wanted to organize
+ 
+
+ align:start position:0%
+because that's how I wanted to organize
+it now the thing about msar is that you
+
+ align:start position:0%
+it now the thing about msar is that you
+ 
+
+ align:start position:0%
+it now the thing about msar is that you
+integrate all the way down to zero there
+
+ align:start position:0%
+integrate all the way down to zero there
+ 
+
+ align:start position:0%
+integrate all the way down to zero there
+and you integrate all the way up to
+
+ align:start position:0%
+and you integrate all the way up to
+ 
+
+ align:start position:0%
+and you integrate all the way up to
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+here okay and that's where the ralon
+
+ align:start position:0%
+here okay and that's where the ralon
+ 
+
+ align:start position:0%
+here okay and that's where the ralon
+problems come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this little procedure here separates
+
+ align:start position:0%
+so this little procedure here separates
+ 
+
+ align:start position:0%
+so this little procedure here separates
+the long and short distance
+
+ align:start position:0%
+the long and short distance
+ 
+
+ align:start position:0%
+the long and short distance
+physics to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+logs it does that
+
+ align:start position:0%
+logs it does that
+ 
+
+ align:start position:0%
+logs it does that
+correctly but for
+
+ align:start position:0%
+correctly but for
+ 
+
+ align:start position:0%
+correctly but for
+Powers we effectively rely on the fact
+
+ align:start position:0%
+Powers we effectively rely on the fact
+ 
+
+ align:start position:0%
+Powers we effectively rely on the fact
+that it set scal as integrals to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what's forced Upon Us by the
+
+ align:start position:0%
+that's what's forced Upon Us by the
+ 
+
+ align:start position:0%
+that's what's forced Upon Us by the
+definition of msar and dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regularization and what goes wrong is
+
+ align:start position:0%
+regularization and what goes wrong is
+ 
+
+ align:start position:0%
+regularization and what goes wrong is
+basically that physically we're still
+
+ align:start position:0%
+basically that physically we're still
+ 
+
+ align:start position:0%
+basically that physically we're still
+integrating over regions of those
+
+ align:start position:0%
+integrating over regions of those
+ 
+
+ align:start position:0%
+integrating over regions of those
+integrals which are not associated to
+
+ align:start position:0%
+integrals which are not associated to
+ 
+
+ align:start position:0%
+integrals which are not associated to
+the to the physics that should be in
+
+ align:start position:0%
+the to the physics that should be in
+ 
+
+ align:start position:0%
+the to the physics that should be in
+those parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now this is a toy toy example
+
+ align:start position:0%
+okay so now this is a toy toy example
+ 
+
+ align:start position:0%
+okay so now this is a toy toy example
+but the same thing is happening in the
+
+ align:start position:0%
+but the same thing is happening in the
+ 
+
+ align:start position:0%
+but the same thing is happening in the
+quantum field Theory when you think
+
+ align:start position:0%
+quantum field Theory when you think
+ 
+
+ align:start position:0%
+quantum field Theory when you think
+about what you're doing when you write
+
+ align:start position:0%
+about what you're doing when you write
+ 
+
+ align:start position:0%
+about what you're doing when you write
+down fan diagrams and you construct a
+
+ align:start position:0%
+down fan diagrams and you construct a
+ 
+
+ align:start position:0%
+down fan diagrams and you construct a
+Wilson coefficient it's effectively the
+
+ align:start position:0%
+Wilson coefficient it's effectively the
+ 
+
+ align:start position:0%
+Wilson coefficient it's effectively the
+same thing in dimentional regularization
+
+ align:start position:0%
+same thing in dimentional regularization
+ 
+
+ align:start position:0%
+same thing in dimentional regularization
+you're integrating all our all values of
+
+ align:start position:0%
+you're integrating all our all values of
+ 
+
+ align:start position:0%
+you're integrating all our all values of
+the momentum and this little kind of toy
+
+ align:start position:0%
+the momentum and this little kind of toy
+ 
+
+ align:start position:0%
+the momentum and this little kind of toy
+analogy is actually apt for what's going
+
+ align:start position:0%
+analogy is actually apt for what's going
+ 
+
+ align:start position:0%
+analogy is actually apt for what's going
+on in a true operator product
+
+ align:start position:0%
+on in a true operator product
+ 
+
+ align:start position:0%
+on in a true operator product
+expansion what would happen if you did a
+
+ align:start position:0%
+expansion what would happen if you did a
+ 
+
+ align:start position:0%
+expansion what would happen if you did a
+wilsonian picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in our toy
+
+ align:start position:0%
+in our toy
+ 
+
+ align:start position:0%
+in our toy
+model well then you would cut off the
+
+ align:start position:0%
+model well then you would cut off the
+ 
+
+ align:start position:0%
+model well then you would cut off the
+integrals explicitly say let's introduce
+
+ align:start position:0%
+integrals explicitly say let's introduce
+ 
+
+ align:start position:0%
+integrals explicitly say let's introduce
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+scale Lambda
+
+ align:start position:0%
+scale Lambda
+ 
+
+ align:start position:0%
+scale Lambda
+F I could still think of expanding in
+
+ align:start position:0%
+F I could still think of expanding in
+ 
+
+ align:start position:0%
+F I could still think of expanding in
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way I don't need the dimensional
+
+ align:start position:0%
+way I don't need the dimensional
+ 
+
+ align:start position:0%
+way I don't need the dimensional
+regularization anymore so I'll set that
+
+ align:start position:0%
+regularization anymore so I'll set that
+ 
+
+ align:start position:0%
+regularization anymore so I'll set that
+get rid of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I think of breaking the integral
+
+ align:start position:0%
+that I think of breaking the integral
+ 
+
+ align:start position:0%
+that I think of breaking the integral
+into two pieces the low energy and high
+
+ align:start position:0%
+into two pieces the low energy and high
+ 
+
+ align:start position:0%
+into two pieces the low energy and high
+energy pieces and in each of those
+
+ align:start position:0%
+energy pieces and in each of those
+ 
+
+ align:start position:0%
+energy pieces and in each of those
+pieces I expand the integral in
+
+ align:start position:0%
+pieces I expand the integral in
+ 
+
+ align:start position:0%
+pieces I expand the integral in
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways so same type of expansion I'm just
+
+ align:start position:0%
+ways so same type of expansion I'm just
+ 
+
+ align:start position:0%
+ways so same type of expansion I'm just
+regulating it
+
+ align:start position:0%
+regulating it
+ 
+
+ align:start position:0%
+regulating it
+differently now I'm guaranteed that this
+
+ align:start position:0%
+differently now I'm guaranteed that this
+ 
+
+ align:start position:0%
+differently now I'm guaranteed that this
+is high energy and this is low
+
+ align:start position:0%
+is high energy and this is low
+ 
+
+ align:start position:0%
+is high energy and this is low
+energy and you could write down sort of
+
+ align:start position:0%
+energy and you could write down sort of
+ 
+
+ align:start position:0%
+energy and you could write down sort of
+what this is appr proxy for is a
+
+ align:start position:0%
+what this is appr proxy for is a
+ 
+
+ align:start position:0%
+what this is appr proxy for is a
+wilsonian op
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu gets replaced by this scale LDA
+
+ align:start position:0%
+mu gets replaced by this scale LDA
+ 
+
+ align:start position:0%
+mu gets replaced by this scale LDA
+f everything gets a W for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wilsonian so again this is one with our
+
+ align:start position:0%
+wilsonian so again this is one with our
+ 
+
+ align:start position:0%
+wilsonian so again this is one with our
+toy model this guy is this guy now this
+
+ align:start position:0%
+toy model this guy is this guy now this
+ 
+
+ align:start position:0%
+toy model this guy is this guy now this
+guy is this guy
+
+ align:start position:0%
+guy is this guy
+ 
+
+ align:start position:0%
+guy is this guy
+now so it's a very similar kind of
+
+ align:start position:0%
+now so it's a very similar kind of
+ 
+
+ align:start position:0%
+now so it's a very similar kind of
+Association but just the way that we're
+
+ align:start position:0%
+Association but just the way that we're
+ 
+
+ align:start position:0%
+Association but just the way that we're
+treating the integral is
+
+ align:start position:0%
+treating the integral is
+ 
+
+ align:start position:0%
+treating the integral is
+different and this way of doing things
+
+ align:start position:0%
+different and this way of doing things
+ 
+
+ align:start position:0%
+different and this way of doing things
+you don't have any problem with the
+
+ align:start position:0%
+you don't have any problem with the
+ 
+
+ align:start position:0%
+you don't have any problem with the
+normal one you just have an explicit cut
+
+ align:start position:0%
+normal one you just have an explicit cut
+ 
+
+ align:start position:0%
+normal one you just have an explicit cut
+off which says there's no low energy
+
+ align:start position:0%
+off which says there's no low energy
+ 
+
+ align:start position:0%
+off which says there's no low energy
+thing part of this and there's no high
+
+ align:start position:0%
+thing part of this and there's no high
+ 
+
+ align:start position:0%
+thing part of this and there's no high
+energy part of
+
+ align:start position:0%
+energy part of
+ 
+
+ align:start position:0%
+energy part of
+that I'm not
+
+ align:start position:0%
+that I'm not
+ 
+
+ align:start position:0%
+that I'm not
+integrating not integrating all the way
+
+ align:start position:0%
+integrating not integrating all the way
+ 
+
+ align:start position:0%
+integrating not integrating all the way
+down to zero in the first integral so I
+
+ align:start position:0%
+down to zero in the first integral so I
+ 
+
+ align:start position:0%
+down to zero in the first integral so I
+don't have any problems with the
+
+ align:start position:0%
+don't have any problems with the
+ 
+
+ align:start position:0%
+don't have any problems with the
+renormalon the renormalon came from
+
+ align:start position:0%
+renormalon the renormalon came from
+ 
+
+ align:start position:0%
+renormalon the renormalon came from
+infrared physics that was happening near
+
+ align:start position:0%
+infrared physics that was happening near
+ 
+
+ align:start position:0%
+infrared physics that was happening near
+k equal Z
+
+ align:start position:0%
+k equal Z
+ 
+
+ align:start position:0%
+k equal Z
+and in this one there's no sort of
+
+ align:start position:0%
+and in this one there's no sort of
+ 
+
+ align:start position:0%
+and in this one there's no sort of
+problem which would come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+so in some sense this is what we'd like
+
+ align:start position:0%
+so in some sense this is what we'd like
+ 
+
+ align:start position:0%
+so in some sense this is what we'd like
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do and the butt
+
+ align:start position:0%
+do and the butt
+ 
+
+ align:start position:0%
+do and the butt
+here is that it causes difficulties with
+
+ align:start position:0%
+here is that it causes difficulties with
+ 
+
+ align:start position:0%
+here is that it causes difficulties with
+symmetries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in particular it generically breaks
+
+ align:start position:0%
+in particular it generically breaks
+ 
+
+ align:start position:0%
+in particular it generically breaks
+gauging
+
+ align:start position:0%
+gauging
+ 
+
+ align:start position:0%
+gauging
+variance and Loren and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variance let's get
+
+ align:start position:0%
+variance let's get
+ 
+
+ align:start position:0%
+variance let's get
+broken and the calculations that you
+
+ align:start position:0%
+broken and the calculations that you
+ 
+
+ align:start position:0%
+broken and the calculations that you
+would like to do are just too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difficult I don't know of anybody that's
+
+ align:start position:0%
+difficult I don't know of anybody that's
+ 
+
+ align:start position:0%
+difficult I don't know of anybody that's
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+maybe somebody's done two Loops in the
+
+ align:start position:0%
+maybe somebody's done two Loops in the
+ 
+
+ align:start position:0%
+maybe somebody's done two Loops in the
+wilsonian picture but nobody's ever done
+
+ align:start position:0%
+wilsonian picture but nobody's ever done
+ 
+
+ align:start position:0%
+wilsonian picture but nobody's ever done
+three okay so you have in some sense you
+
+ align:start position:0%
+three okay so you have in some sense you
+ 
+
+ align:start position:0%
+three okay so you have in some sense you
+have some nice things here you have some
+
+ align:start position:0%
+have some nice things here you have some
+ 
+
+ align:start position:0%
+have some nice things here you have some
+nice things here but they're not the
+
+ align:start position:0%
+nice things here but they're not the
+ 
+
+ align:start position:0%
+nice things here but they're not the
+same nice things and you'd like to have
+
+ align:start position:0%
+same nice things and you'd like to have
+ 
+
+ align:start position:0%
+same nice things and you'd like to have
+something that does the best of both and
+
+ align:start position:0%
+something that does the best of both and
+ 
+
+ align:start position:0%
+something that does the best of both and
+that's effectively what we're doing when
+
+ align:start position:0%
+that's effectively what we're doing when
+ 
+
+ align:start position:0%
+that's effectively what we're doing when
+we construct these R schemes what we're
+
+ align:start position:0%
+we construct these R schemes what we're
+ 
+
+ align:start position:0%
+we construct these R schemes what we're
+doing is we're saying well let's take
+
+ align:start position:0%
+doing is we're saying well let's take
+ 
+
+ align:start position:0%
+doing is we're saying well let's take
+msar as a starting point and try to get
+
+ align:start position:0%
+msar as a starting point and try to get
+ 
+
+ align:start position:0%
+msar as a starting point and try to get
+rid of the problem that it has by
+
+ align:start position:0%
+rid of the problem that it has by
+ 
+
+ align:start position:0%
+rid of the problem that it has by
+perturbing towards a wilsonian picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what would an R scheme op look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like start with
+
+ align:start position:0%
+like start with
+ 
+
+ align:start position:0%
+like start with
+msar and make a scheme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change I make a scheme change here both
+
+ align:start position:0%
+change I make a scheme change here both
+ 
+
+ align:start position:0%
+change I make a scheme change here both
+to The Operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the I make the same scheme change to
+
+ align:start position:0%
+and the I make the same scheme change to
+ 
+
+ align:start position:0%
+and the I make the same scheme change to
+the coefficient so I'm just really
+
+ align:start position:0%
+the coefficient so I'm just really
+ 
+
+ align:start position:0%
+the coefficient so I'm just really
+moving things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around so let me just formally write
+
+ align:start position:0%
+around so let me just formally write
+ 
+
+ align:start position:0%
+around so let me just formally write
+down what such a scheme change would
+
+ align:start position:0%
+down what such a scheme change would
+ 
+
+ align:start position:0%
+down what such a scheme change would
+look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I set up some coefficients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DN and I make the same I do a
+
+ align:start position:0%
+DN and I make the same I do a
+ 
+
+ align:start position:0%
+DN and I make the same I do a
+subtraction on The Operators and an
+
+ align:start position:0%
+subtraction on The Operators and an
+ 
+
+ align:start position:0%
+subtraction on The Operators and an
+addition on the coefficients in the way
+
+ align:start position:0%
+addition on the coefficients in the way
+ 
+
+ align:start position:0%
+addition on the coefficients in the way
+I've written
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so that's just a rearrangement of the
+
+ align:start position:0%
+it so that's just a rearrangement of the
+ 
+
+ align:start position:0%
+it so that's just a rearrangement of the
+physics and we've set it up so so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the result of that looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this I took in this
+
+ align:start position:0%
+this I took in this
+ 
+
+ align:start position:0%
+this I took in this
+example C1 equal to one for
+
+ align:start position:0%
+example C1 equal to one for
+ 
+
+ align:start position:0%
+example C1 equal to one for
+Simplicity a little more complicated if
+
+ align:start position:0%
+Simplicity a little more complicated if
+ 
+
+ align:start position:0%
+Simplicity a little more complicated if
+I want to keep it but we could keep it
+
+ align:start position:0%
+I want to keep it but we could keep it
+ 
+
+ align:start position:0%
+I want to keep it but we could keep it
+if we needed to so basically I've made a
+
+ align:start position:0%
+if we needed to so basically I've made a
+ 
+
+ align:start position:0%
+if we needed to so basically I've made a
+re a rearrangement to some equivalent op
+
+ align:start position:0%
+re a rearrangement to some equivalent op
+ 
+
+ align:start position:0%
+re a rearrangement to some equivalent op
+by just changing the thing the the
+
+ align:start position:0%
+by just changing the thing the the
+ 
+
+ align:start position:0%
+by just changing the thing the the
+definitions here but I have now the
+
+ align:start position:0%
+definitions here but I have now the
+ 
+
+ align:start position:0%
+definitions here but I have now the
+freedom to pick these D's and what I can
+
+ align:start position:0%
+freedom to pick these D's and what I can
+ 
+
+ align:start position:0%
+freedom to pick these D's and what I can
+do is I can pick the D's to have the
+
+ align:start position:0%
+do is I can pick the D's to have the
+ 
+
+ align:start position:0%
+do is I can pick the D's to have the
+same renormalon as the msar scheme and
+
+ align:start position:0%
+same renormalon as the msar scheme and
+ 
+
+ align:start position:0%
+same renormalon as the msar scheme and
+therefore I can iteratively again remove
+
+ align:start position:0%
+therefore I can iteratively again remove
+ 
+
+ align:start position:0%
+therefore I can iteratively again remove
+you know the first problematic term of
+
+ align:start position:0%
+you know the first problematic term of
+ 
+
+ align:start position:0%
+you know the first problematic term of
+this to get a better better defined
+
+ align:start position:0%
+this to get a better better defined
+ 
+
+ align:start position:0%
+this to get a better better defined
+Theta one and c0 just like we were doing
+
+ align:start position:0%
+Theta one and c0 just like we were doing
+ 
+
+ align:start position:0%
+Theta one and c0 just like we were doing
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+masses so you can remove the U = 1 for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example you can remove the U equal 1
+
+ align:start position:0%
+example you can remove the U equal 1
+ 
+
+ align:start position:0%
+example you can remove the U equal 1
+Normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on by choose choosing the
+
+ align:start position:0%
+on by choose choosing the
+ 
+
+ align:start position:0%
+on by choose choosing the
+D and that's exactly what the wilsonian
+
+ align:start position:0%
+D and that's exactly what the wilsonian
+ 
+
+ align:start position:0%
+D and that's exactly what the wilsonian
+was trying to do for you and that's what
+
+ align:start position:0%
+was trying to do for you and that's what
+ 
+
+ align:start position:0%
+was trying to do for you and that's what
+it was doing for you with putting this
+
+ align:start position:0%
+it was doing for you with putting this
+ 
+
+ align:start position:0%
+it was doing for you with putting this
+cut off Ms bar was having problems at
+
+ align:start position:0%
+cut off Ms bar was having problems at
+ 
+
+ align:start position:0%
+cut off Ms bar was having problems at
+zero and we're sort of perturbatively
+
+ align:start position:0%
+zero and we're sort of perturbatively
+ 
+
+ align:start position:0%
+zero and we're sort of perturbatively
+removing those
+
+ align:start position:0%
+removing those
+ 
+
+ align:start position:0%
+removing those
+problems ctively going towards the
+
+ align:start position:0%
+problems ctively going towards the
+ 
+
+ align:start position:0%
+problems ctively going towards the
+wilsonian picture and the nice thing
+
+ align:start position:0%
+wilsonian picture and the nice thing
+ 
+
+ align:start position:0%
+wilsonian picture and the nice thing
+about this is that we can maintain the
+
+ align:start position:0%
+about this is that we can maintain the
+ 
+
+ align:start position:0%
+about this is that we can maintain the
+symmetries still Gage and variant still
+
+ align:start position:0%
+symmetries still Gage and variant still
+ 
+
+ align:start position:0%
+symmetries still Gage and variant still
+Loren and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variant and we don't get the full sort
+
+ align:start position:0%
+variant and we don't get the full sort
+ 
+
+ align:start position:0%
+variant and we don't get the full sort
+of power of the wilsonian but we get
+
+ align:start position:0%
+of power of the wilsonian but we get
+ 
+
+ align:start position:0%
+of power of the wilsonian but we get
+closer to it and can in some sense get
+
+ align:start position:0%
+closer to it and can in some sense get
+ 
+
+ align:start position:0%
+closer to it and can in some sense get
+as close as we want Again by sort of
+
+ align:start position:0%
+as close as we want Again by sort of
+ 
+
+ align:start position:0%
+as close as we want Again by sort of
+perturbing us
+
+ align:start position:0%
+perturbing us
+ 
+
+ align:start position:0%
+perturbing us
+from order by
+
+ align:start position:0%
+from order by
+ 
+
+ align:start position:0%
+from order by
+order so what we introduce is power law
+
+ align:start position:0%
+order so what we introduce is power law
+ 
+
+ align:start position:0%
+order so what we introduce is power law
+dependence in
+
+ align:start position:0%
+dependence in
+ 
+
+ align:start position:0%
+dependence in
+R and that power law dependence is like
+
+ align:start position:0%
+R and that power law dependence is like
+ 
+
+ align:start position:0%
+R and that power law dependence is like
+the power law it's the analog of the
+
+ align:start position:0%
+the power law it's the analog of the
+ 
+
+ align:start position:0%
+the power law it's the analog of the
+power law dependence that would be in
+
+ align:start position:0%
+power law dependence that would be in
+ 
+
+ align:start position:0%
+power law dependence that would be in
+the Willian scheme so when you have
+
+ align:start position:0%
+the Willian scheme so when you have
+ 
+
+ align:start position:0%
+the Willian scheme so when you have
+integrals like this you would have
+
+ align:start position:0%
+integrals like this you would have
+ 
+
+ align:start position:0%
+integrals like this you would have
+powers there's nothing that stops you
+
+ align:start position:0%
+powers there's nothing that stops you
+ 
+
+ align:start position:0%
+powers there's nothing that stops you
+from having a complicated function of Q
+
+ align:start position:0%
+from having a complicated function of Q
+ 
+
+ align:start position:0%
+from having a complicated function of Q
+over Lambda and what we're saying is
+
+ align:start position:0%
+over Lambda and what we're saying is
+ 
+
+ align:start position:0%
+over Lambda and what we're saying is
+that the dominant kind of uh Power law
+
+ align:start position:0%
+that the dominant kind of uh Power law
+ 
+
+ align:start position:0%
+that the dominant kind of uh Power law
+sensitive terms here and here are
+
+ align:start position:0%
+sensitive terms here and here are
+ 
+
+ align:start position:0%
+sensitive terms here and here are
+captured by making this scheme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change so we decide that we like msar
+
+ align:start position:0%
+change so we decide that we like msar
+ 
+
+ align:start position:0%
+change so we decide that we like msar
+because we have calculations that other
+
+ align:start position:0%
+because we have calculations that other
+ 
+
+ align:start position:0%
+because we have calculations that other
+people have done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully after three Loop order you
+
+ align:start position:0%
+hopefully after three Loop order you
+ 
+
+ align:start position:0%
+hopefully after three Loop order you
+certainly hope that someone else spent
+
+ align:start position:0%
+certainly hope that someone else spent
+ 
+
+ align:start position:0%
+certainly hope that someone else spent
+two years of their life on it rather
+
+ align:start position:0%
+two years of their life on it rather
+ 
+
+ align:start position:0%
+two years of their life on it rather
+than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you and you can take and perturb your
+
+ align:start position:0%
+you and you can take and perturb your
+ 
+
+ align:start position:0%
+you and you can take and perturb your
+results from
+
+ align:start position:0%
+results from
+ 
+
+ align:start position:0%
+results from
+msbar towards a gage inv variant Loren
+
+ align:start position:0%
+msbar towards a gage inv variant Loren
+ 
+
+ align:start position:0%
+msbar towards a gage inv variant Loren
+inv variant version of wilsonian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the wilsonian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture so let me give you one example
+
+ align:start position:0%
+picture so let me give you one example
+ 
+
+ align:start position:0%
+picture so let me give you one example
+of that to show you in
+
+ align:start position:0%
+of that to show you in
+ 
+
+ align:start position:0%
+of that to show you in
+practice putting in some
+
+ align:start position:0%
+practice putting in some
+ 
+
+ align:start position:0%
+practice putting in some
+numbers oh I'm not quite there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yet okay so let me give you a well-
+
+ align:start position:0%
+yet okay so let me give you a well-
+ 
+
+ align:start position:0%
+yet okay so let me give you a well-
+defined scheme which is analogous to the
+
+ align:start position:0%
+defined scheme which is analogous to the
+ 
+
+ align:start position:0%
+defined scheme which is analogous to the
+scheme that we just talked about with
+
+ align:start position:0%
+scheme that we just talked about with
+ 
+
+ align:start position:0%
+scheme that we just talked about with
+which was MSR scheme for the mass
+
+ align:start position:0%
+which was MSR scheme for the mass
+ 
+
+ align:start position:0%
+which was MSR scheme for the mass
+there's also an MSR scheme for the
+
+ align:start position:0%
+there's also an MSR scheme for the
+ 
+
+ align:start position:0%
+there's also an MSR scheme for the
+op and again the attitude is let's not
+
+ align:start position:0%
+op and again the attitude is let's not
+ 
+
+ align:start position:0%
+op and again the attitude is let's not
+calculate anything new that we don't
+
+ align:start position:0%
+calculate anything new that we don't
+ 
+
+ align:start position:0%
+calculate anything new that we don't
+have to so we'll reuse the coefficients
+
+ align:start position:0%
+have to so we'll reuse the coefficients
+ 
+
+ align:start position:0%
+have to so we'll reuse the coefficients
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+msar those coefficients had the
+
+ align:start position:0%
+msar those coefficients had the
+ 
+
+ align:start position:0%
+msar those coefficients had the
+renormalon so if those coefficients were
+
+ align:start position:0%
+renormalon so if those coefficients were
+ 
+
+ align:start position:0%
+renormalon so if those coefficients were
+we called them a few minutes ago BN mu
+
+ align:start position:0%
+we called them a few minutes ago BN mu
+ 
+
+ align:start position:0%
+we called them a few minutes ago BN mu
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+Q we just reuse these at a different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale so what we do is we say DN of mu /
+
+ align:start position:0%
+scale so what we do is we say DN of mu /
+ 
+
+ align:start position:0%
+scale so what we do is we say DN of mu /
+R is defined to be the BN of mu
+
+ align:start position:0%
+R is defined to be the BN of mu
+ 
+
+ align:start position:0%
+R is defined to be the BN of mu
+R so these guys were the MSR
+
+ align:start position:0%
+R so these guys were the MSR
+ 
+
+ align:start position:0%
+R so these guys were the MSR
+coefficients these guys are whatever we
+
+ align:start position:0%
+coefficients these guys are whatever we
+ 
+
+ align:start position:0%
+coefficients these guys are whatever we
+decide to put into the series over there
+
+ align:start position:0%
+decide to put into the series over there
+ 
+
+ align:start position:0%
+decide to put into the series over there
+just take them to be equal that's the
+
+ align:start position:0%
+just take them to be equal that's the
+ 
+
+ align:start position:0%
+just take them to be equal that's the
+MSR
+
+ align:start position:0%
+MSR
+ 
+
+ align:start position:0%
+MSR
+scheme and then if you look at what the
+
+ align:start position:0%
+scheme and then if you look at what the
+ 
+
+ align:start position:0%
+scheme and then if you look at what the
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+is if we just write out explicitly what
+
+ align:start position:0%
+is if we just write out explicitly what
+ 
+
+ align:start position:0%
+is if we just write out explicitly what
+the coefficient is by plugging in the
+
+ align:start position:0%
+the coefficient is by plugging in the
+ 
+
+ align:start position:0%
+the coefficient is by plugging in the
+series you can again see the kind
+
+ align:start position:0%
+series you can again see the kind
+ 
+
+ align:start position:0%
+series you can again see the kind
+of how it's provided a cut
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off so this was our original msar series
+
+ align:start position:0%
+off so this was our original msar series
+ 
+
+ align:start position:0%
+off so this was our original msar series
+BN of mu over Q we introduce a
+
+ align:start position:0%
+BN of mu over Q we introduce a
+ 
+
+ align:start position:0%
+BN of mu over Q we introduce a
+subtraction which is suppressed by R
+
+ align:start position:0%
+subtraction which is suppressed by R
+ 
+
+ align:start position:0%
+subtraction which is suppressed by R
+over Q times the same series
+
+ align:start position:0%
+over Q times the same series
+ 
+
+ align:start position:0%
+over Q times the same series
+BN and this R is providing kind of like
+
+ align:start position:0%
+BN and this R is providing kind of like
+ 
+
+ align:start position:0%
+BN and this R is providing kind of like
+a power law cut off on a problem that
+
+ align:start position:0%
+a power law cut off on a problem that
+ 
+
+ align:start position:0%
+a power law cut off on a problem that
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+had exactly a power LW cut off so again
+
+ align:start position:0%
+had exactly a power LW cut off so again
+ 
+
+ align:start position:0%
+had exactly a power LW cut off so again
+if you look at the renormalon in this
+
+ align:start position:0%
+if you look at the renormalon in this
+ 
+
+ align:start position:0%
+if you look at the renormalon in this
+thing this combined thing the re normal
+
+ align:start position:0%
+thing this combined thing the re normal
+ 
+
+ align:start position:0%
+thing this combined thing the re normal
+L is independent of R and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you so to look say you would just plug
+
+ align:start position:0%
+you so to look say you would just plug
+ 
+
+ align:start position:0%
+you so to look say you would just plug
+in the Bubble Series result you'd find
+
+ align:start position:0%
+in the Bubble Series result you'd find
+ 
+
+ align:start position:0%
+in the Bubble Series result you'd find
+actually that the r over Q here would
+
+ align:start position:0%
+actually that the r over Q here would
+ 
+
+ align:start position:0%
+actually that the r over Q here would
+cancel out and so that these would just
+
+ align:start position:0%
+cancel out and so that these would just
+ 
+
+ align:start position:0%
+cancel out and so that these would just
+exactly cancel each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+= 1 re normal
+
+ align:start position:0%
+= 1 re normal
+ 
+
+ align:start position:0%
+= 1 re normal
+one and again if I wanted to probe other
+
+ align:start position:0%
+one and again if I wanted to probe other
+ 
+
+ align:start position:0%
+one and again if I wanted to probe other
+re normal lines I'd have to consider
+
+ align:start position:0%
+re normal lines I'd have to consider
+ 
+
+ align:start position:0%
+re normal lines I'd have to consider
+other powers besides R over q but those
+
+ align:start position:0%
+other powers besides R over q but those
+ 
+
+ align:start position:0%
+other powers besides R over q but those
+actually in this op would be connected
+
+ align:start position:0%
+actually in this op would be connected
+ 
+
+ align:start position:0%
+actually in this op would be connected
+to other operators so there was there's
+
+ align:start position:0%
+to other operators so there was there's
+ 
+
+ align:start position:0%
+to other operators so there was there's
+other subleading normal lines here which
+
+ align:start position:0%
+other subleading normal lines here which
+ 
+
+ align:start position:0%
+other subleading normal lines here which
+could be connected to 1 over q^2 etc
+
+ align:start position:0%
+could be connected to 1 over q^2 etc
+ 
+
+ align:start position:0%
+could be connected to 1 over q^2 etc
+etc and an MS bar that generically will
+
+ align:start position:0%
+etc and an MS bar that generically will
+ 
+
+ align:start position:0%
+etc and an MS bar that generically will
+happen but usually it suffices just to
+
+ align:start position:0%
+happen but usually it suffices just to
+ 
+
+ align:start position:0%
+happen but usually it suffices just to
+worry about the first one since many
+
+ align:start position:0%
+worry about the first one since many
+ 
+
+ align:start position:0%
+worry about the first one since many
+people in the community that do these
+
+ align:start position:0%
+people in the community that do these
+ 
+
+ align:start position:0%
+people in the community that do these
+multi-loop calculations don't even worry
+
+ align:start position:0%
+multi-loop calculations don't even worry
+ 
+
+ align:start position:0%
+multi-loop calculations don't even worry
+about the first
+
+ align:start position:0%
+about the first
+ 
+
+ align:start position:0%
+about the first
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway okay so you can again after youve
+
+ align:start position:0%
+anyway okay so you can again after youve
+ 
+
+ align:start position:0%
+anyway okay so you can again after youve
+got this
+
+ align:start position:0%
+got this
+ 
+
+ align:start position:0%
+got this
+definition uh you could actually
+
+ align:start position:0%
+definition uh you could actually
+ 
+
+ align:start position:0%
+definition uh you could actually
+formally write this as c0
+
+ align:start position:0%
+formally write this as c0
+ 
+
+ align:start position:0%
+formally write this as c0
+bar of Q comma mu if you want to think
+
+ align:start position:0%
+bar of Q comma mu if you want to think
+ 
+
+ align:start position:0%
+bar of Q comma mu if you want to think
+about what it
+
+ align:start position:0%
+about what it
+ 
+
+ align:start position:0%
+about what it
+is minus r over Q same Wilson
+
+ align:start position:0%
+is minus r over Q same Wilson
+ 
+
+ align:start position:0%
+is minus r over Q same Wilson
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+replacing all the RS by all the q's by R
+
+ align:start position:0%
+replacing all the RS by all the q's by R
+ 
+
+ align:start position:0%
+replacing all the RS by all the q's by R
+okay so that's another way of saying
+
+ align:start position:0%
+okay so that's another way of saying
+ 
+
+ align:start position:0%
+okay so that's another way of saying
+what the scheme change is from msar
+
+ align:start position:0%
+what the scheme change is from msar
+ 
+
+ align:start position:0%
+what the scheme change is from msar
+results to to this
+
+ align:start position:0%
+results to to this
+ 
+
+ align:start position:0%
+results to to this
+result and this R is acting like an IR
+
+ align:start position:0%
+result and this R is acting like an IR
+ 
+
+ align:start position:0%
+result and this R is acting like an IR
+cut
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off to get rid of the bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem and again we have a a
+
+ align:start position:0%
+problem and again we have a a
+ 
+
+ align:start position:0%
+problem and again we have a a
+normalization group so r d byd
+
+ align:start position:0%
+normalization group so r d byd
+ 
+
+ align:start position:0%
+normalization group so r d byd
+r of this this Wilson
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coefficient it's convenient to think
+
+ align:start position:0%
+coefficient it's convenient to think
+ 
+
+ align:start position:0%
+coefficient it's convenient to think
+about that renormalization group with
+
+ align:start position:0%
+about that renormalization group with
+ 
+
+ align:start position:0%
+about that renormalization group with
+the log cut off mu set equal to the
+
+ align:start position:0%
+the log cut off mu set equal to the
+ 
+
+ align:start position:0%
+the log cut off mu set equal to the
+Power log cut off
+
+ align:start position:0%
+Power log cut off
+ 
+
+ align:start position:0%
+Power log cut off
+R and it's very much like our masses
+
+ align:start position:0%
+R and it's very much like our masses
+ 
+
+ align:start position:0%
+R and it's very much like our masses
+there's some
+
+ align:start position:0%
+there's some
+ 
+
+ align:start position:0%
+there's some
+function with an r in front and we could
+
+ align:start position:0%
+function with an r in front and we could
+ 
+
+ align:start position:0%
+function with an r in front and we could
+formally write down solutions to
+
+ align:start position:0%
+formally write down solutions to
+ 
+
+ align:start position:0%
+formally write down solutions to
+it and we can explicitly plug in results
+
+ align:start position:0%
+it and we can explicitly plug in results
+ 
+
+ align:start position:0%
+it and we can explicitly plug in results
+given how many terms in the series we
+
+ align:start position:0%
+given how many terms in the series we
+ 
+
+ align:start position:0%
+given how many terms in the series we
+know in the MS barar series
+
+ align:start position:0%
+know in the MS barar series
+ 
+
+ align:start position:0%
+know in the MS barar series
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so all the anomalous dimensions of this
+
+ align:start position:0%
+so all the anomalous dimensions of this
+ 
+
+ align:start position:0%
+so all the anomalous dimensions of this
+Wilson coefficient would be determined
+
+ align:start position:0%
+Wilson coefficient would be determined
+ 
+
+ align:start position:0%
+Wilson coefficient would be determined
+by the msar series the original one
+
+ align:start position:0%
+by the msar series the original one
+ 
+
+ align:start position:0%
+by the msar series the original one
+because the scheme that we're defining
+
+ align:start position:0%
+because the scheme that we're defining
+ 
+
+ align:start position:0%
+because the scheme that we're defining
+is set up so that it uses those msar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coefficients so what would the RG look
+
+ align:start position:0%
+coefficients so what would the RG look
+ 
+
+ align:start position:0%
+coefficients so what would the RG look
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the same kind of structure as
+
+ align:start position:0%
+that's the same kind of structure as
+ 
+
+ align:start position:0%
+that's the same kind of structure as
+what we had for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+masses some gamma functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can think of this as some
+
+ align:start position:0%
+and you can think of this as some
+ 
+
+ align:start position:0%
+and you can think of this as some
+c0 if you want kind of to have a more
+
+ align:start position:0%
+c0 if you want kind of to have a more
+ 
+
+ align:start position:0%
+c0 if you want kind of to have a more
+standard notation you would say that
+
+ align:start position:0%
+standard notation you would say that
+ 
+
+ align:start position:0%
+standard notation you would say that
+this is some U
+
+ align:start position:0%
+this is some U
+ 
+
+ align:start position:0%
+this is some U
+function and this is a bit of abusive
+
+ align:start position:0%
+function and this is a bit of abusive
+ 
+
+ align:start position:0%
+function and this is a bit of abusive
+notation actually here
+
+ align:start position:0%
+notation actually here
+ 
+
+ align:start position:0%
+notation actually here
+because it's additive not
+
+ align:start position:0%
+because it's additive not
+ 
+
+ align:start position:0%
+because it's additive not
+multiplicative but if you allow me to
+
+ align:start position:0%
+multiplicative but if you allow me to
+ 
+
+ align:start position:0%
+multiplicative but if you allow me to
+put this guy into here then I can always
+
+ align:start position:0%
+put this guy into here then I can always
+ 
+
+ align:start position:0%
+put this guy into here then I can always
+write it this way and I'll just do that
+
+ align:start position:0%
+write it this way and I'll just do that
+ 
+
+ align:start position:0%
+write it this way and I'll just do that
+for convenience so I want to show you
+
+ align:start position:0%
+for convenience so I want to show you
+ 
+
+ align:start position:0%
+for convenience so I want to show you
+one example of how this plays out in
+
+ align:start position:0%
+one example of how this plays out in
+ 
+
+ align:start position:0%
+one example of how this plays out in
+practice this so and it's related to our
+
+ align:start position:0%
+practice this so and it's related to our
+ 
+
+ align:start position:0%
+practice this so and it's related to our
+discussion of
+
+ align:start position:0%
+discussion of
+ 
+
+ align:start position:0%
+discussion of
+HQ so one thing that we said about hqet
+
+ align:start position:0%
+HQ so one thing that we said about hqet
+ 
+
+ align:start position:0%
+HQ so one thing that we said about hqet
+is that you could calculate the
+
+ align:start position:0%
+is that you could calculate the
+ 
+
+ align:start position:0%
+is that you could calculate the
+following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantity so hqt makes some predictions
+
+ align:start position:0%
+quantity so hqt makes some predictions
+ 
+
+ align:start position:0%
+quantity so hqt makes some predictions
+about the B star and the B they were
+
+ align:start position:0%
+about the B star and the B they were
+ 
+
+ align:start position:0%
+about the B star and the B they were
+connected they were in a symmetry
+
+ align:start position:0%
+connected they were in a symmetry
+ 
+
+ align:start position:0%
+connected they were in a symmetry
+multiplet and when you took the
+
+ align:start position:0%
+multiplet and when you took the
+ 
+
+ align:start position:0%
+multiplet and when you took the
+difference of B Star and B and you took
+
+ align:start position:0%
+difference of B Star and B and you took
+ 
+
+ align:start position:0%
+difference of B Star and B and you took
+this combination it actually is purely
+
+ align:start position:0%
+this combination it actually is purely
+ 
+
+ align:start position:0%
+this combination it actually is purely
+perturbative because there's a
+
+ align:start position:0%
+perturbative because there's a
+ 
+
+ align:start position:0%
+perturbative because there's a
+non-perturbative parameter but it's
+
+ align:start position:0%
+non-perturbative parameter but it's
+ 
+
+ align:start position:0%
+non-perturbative parameter but it's
+actually if you treat the charm cork as
+
+ align:start position:0%
+actually if you treat the charm cork as
+ 
+
+ align:start position:0%
+actually if you treat the charm cork as
+heavy it's the same for charm and bottom
+
+ align:start position:0%
+heavy it's the same for charm and bottom
+ 
+
+ align:start position:0%
+heavy it's the same for charm and bottom
+and it cancels
+
+ align:start position:0%
+and it cancels
+ 
+
+ align:start position:0%
+and it cancels
+out so you can actually write down an MS
+
+ align:start position:0%
+out so you can actually write down an MS
+ 
+
+ align:start position:0%
+out so you can actually write down an MS
+bar operator product
+
+ align:start position:0%
+bar operator product
+ 
+
+ align:start position:0%
+bar operator product
+expansion which is technically defined
+
+ align:start position:0%
+expansion which is technically defined
+ 
+
+ align:start position:0%
+expansion which is technically defined
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+HQ and what it looks like is the first
+
+ align:start position:0%
+HQ and what it looks like is the first
+ 
+
+ align:start position:0%
+HQ and what it looks like is the first
+thing is just a ratio of Wilson
+
+ align:start position:0%
+thing is just a ratio of Wilson
+ 
+
+ align:start position:0%
+thing is just a ratio of Wilson
+coefficients so we talked about this and
+
+ align:start position:0%
+coefficients so we talked about this and
+ 
+
+ align:start position:0%
+coefficients so we talked about this and
+we plugged in the sort of leading log
+
+ align:start position:0%
+we plugged in the sort of leading log
+ 
+
+ align:start position:0%
+we plugged in the sort of leading log
+result and we saw that it was working
+
+ align:start position:0%
+result and we saw that it was working
+ 
+
+ align:start position:0%
+result and we saw that it was working
+actually pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well and if you were to kind of look at
+
+ align:start position:0%
+well and if you were to kind of look at
+ 
+
+ align:start position:0%
+well and if you were to kind of look at
+higher order terms in that op there
+
+ align:start position:0%
+higher order terms in that op there
+ 
+
+ align:start position:0%
+higher order terms in that op there
+would be some power corrections to
+
+ align:start position:0%
+would be some power corrections to
+ 
+
+ align:start position:0%
+would be some power corrections to
+that they've got some traditional names
+
+ align:start position:0%
+that they've got some traditional names
+ 
+
+ align:start position:0%
+that they've got some traditional names
+the names are not too
+
+ align:start position:0%
+the names are not too
+ 
+
+ align:start position:0%
+the names are not too
+important but this is like the one the
+
+ align:start position:0%
+important but this is like the one the
+ 
+
+ align:start position:0%
+important but this is like the one the
+analog of the one over Q term okay this
+
+ align:start position:0%
+analog of the one over Q term okay this
+ 
+
+ align:start position:0%
+analog of the one over Q term okay this
+is the one/ Q term this is the leading
+
+ align:start position:0%
+is the one/ Q term this is the leading
+ 
+
+ align:start position:0%
+is the one/ Q term this is the leading
+order term which is purely perturbative
+
+ align:start position:0%
+order term which is purely perturbative
+ 
+
+ align:start position:0%
+order term which is purely perturbative
+there's no Matrix element here it's just
+
+ align:start position:0%
+there's no Matrix element here it's just
+ 
+
+ align:start position:0%
+there's no Matrix element here it's just
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+this is a higher Dimension operator this
+
+ align:start position:0%
+this is a higher Dimension operator this
+ 
+
+ align:start position:0%
+this is a higher Dimension operator this
+guy scales like Lambda qcd cubed over
+
+ align:start position:0%
+guy scales like Lambda qcd cubed over
+ 
+
+ align:start position:0%
+guy scales like Lambda qcd cubed over
+Lambda qcd
+
+ align:start position:0%
+Lambda qcd
+ 
+
+ align:start position:0%
+Lambda qcd
+s which is just Lambda
+
+ align:start position:0%
+s which is just Lambda
+ 
+
+ align:start position:0%
+s which is just Lambda
+qcd so that's like the Lambda qcd or Q
+
+ align:start position:0%
+qcd so that's like the Lambda qcd or Q
+ 
+
+ align:start position:0%
+qcd so that's like the Lambda qcd or Q
+term and this is the formula you would
+
+ align:start position:0%
+term and this is the formula you would
+ 
+
+ align:start position:0%
+term and this is the formula you would
+write down if you wanted to make a
+
+ align:start position:0%
+write down if you wanted to make a
+ 
+
+ align:start position:0%
+write down if you wanted to make a
+prediction for this thing at higher
+
+ align:start position:0%
+prediction for this thing at higher
+ 
+
+ align:start position:0%
+prediction for this thing at higher
+Precision in
+
+ align:start position:0%
+Precision in
+ 
+
+ align:start position:0%
+Precision in
+msar so what happens if I think about
+
+ align:start position:0%
+msar so what happens if I think about
+ 
+
+ align:start position:0%
+msar so what happens if I think about
+this perturbative result at higher
+
+ align:start position:0%
+this perturbative result at higher
+ 
+
+ align:start position:0%
+this perturbative result at higher
+orders so people have actually
+
+ align:start position:0%
+orders so people have actually
+ 
+
+ align:start position:0%
+orders so people have actually
+calculated that coefficient into three
+
+ align:start position:0%
+calculated that coefficient into three
+ 
+
+ align:start position:0%
+calculated that coefficient into three
+Loop order and here's what it looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so at order Alpha you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+-113 at order Alpha
+
+ align:start position:0%
+-113 at order Alpha
+ 
+
+ align:start position:0%
+-113 at order Alpha
+squar getus
+
+ align:start position:0%
+squar getus
+ 
+
+ align:start position:0%
+squar getus
+078 and then you get
+
+ align:start position:0%
+078 and then you get
+ 
+
+ align:start position:0%
+078 and then you get
+anotherus
+
+ align:start position:0%
+anotherus
+ 
+
+ align:start position:0%
+anotherus
+0755 at Alpha
+
+ align:start position:0%
+0755 at Alpha
+ 
+
+ align:start position:0%
+0755 at Alpha
+cubed doesn't look so
+
+ align:start position:0%
+cubed doesn't look so
+ 
+
+ align:start position:0%
+cubed doesn't look so
+pretty all right so each order that you
+
+ align:start position:0%
+pretty all right so each order that you
+ 
+
+ align:start position:0%
+pretty all right so each order that you
+calculate is giving you a Corrections is
+
+ align:start position:0%
+calculate is giving you a Corrections is
+ 
+
+ align:start position:0%
+calculate is giving you a Corrections is
+about the same size as the previous
+
+ align:start position:0%
+about the same size as the previous
+ 
+
+ align:start position:0%
+about the same size as the previous
+order well you might say of course
+
+ align:start position:0%
+order well you might say of course
+ 
+
+ align:start position:0%
+order well you might say of course
+there's logs so I should resum the logs
+
+ align:start position:0%
+there's logs so I should resum the logs
+ 
+
+ align:start position:0%
+there's logs so I should resum the logs
+so let's resum the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+logs so leading
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+log and then I get since I have higher
+
+ align:start position:0%
+log and then I get since I have higher
+ 
+
+ align:start position:0%
+log and then I get since I have higher
+order in almost Dimensions let me put in
+
+ align:start position:0%
+order in almost Dimensions let me put in
+ 
+
+ align:start position:0%
+order in almost Dimensions let me put in
+next deleting
+
+ align:start position:0%
+next deleting
+ 
+
+ align:start position:0%
+next deleting
+log and actually I have one more order
+
+ align:start position:0%
+log and actually I have one more order
+ 
+
+ align:start position:0%
+log and actually I have one more order
+so let me put that in
+
+ align:start position:0%
+so let me put that in
+ 
+
+ align:start position:0%
+so let me put that in
+too 908
+
+ align:start position:0%
+too 908
+ 
+
+ align:start position:0%
+too 908
+next for next leading
+
+ align:start position:0%
+next for next leading
+ 
+
+ align:start position:0%
+next for next leading
+log uh
+
+ align:start position:0%
+log uh
+ 
+
+ align:start position:0%
+log uh
+oh all right so this is the one that we
+
+ align:start position:0%
+oh all right so this is the one that we
+ 
+
+ align:start position:0%
+oh all right so this is the one that we
+actually talked about earlier and that
+
+ align:start position:0%
+actually talked about earlier and that
+ 
+
+ align:start position:0%
+actually talked about earlier and that
+one is actually close to the
+
+ align:start position:0%
+one is actually close to the
+ 
+
+ align:start position:0%
+one is actually close to the
+data the leading log result was sort of
+
+ align:start position:0%
+data the leading log result was sort of
+ 
+
+ align:start position:0%
+data the leading log result was sort of
+close to what the data
+
+ align:start position:0%
+close to what the data
+ 
+
+ align:start position:0%
+close to what the data
+was but when you think about whether
+
+ align:start position:0%
+was but when you think about whether
+ 
+
+ align:start position:0%
+was but when you think about whether
+that's actually right and you calculate
+
+ align:start position:0%
+that's actually right and you calculate
+ 
+
+ align:start position:0%
+that's actually right and you calculate
+the higher order Corrections you find
+
+ align:start position:0%
+the higher order Corrections you find
+ 
+
+ align:start position:0%
+the higher order Corrections you find
+that you're moving away from the data
+
+ align:start position:0%
+that you're moving away from the data
+ 
+
+ align:start position:0%
+that you're moving away from the data
+right and again it's not convergent
+
+ align:start position:0%
+right and again it's not convergent
+ 
+
+ align:start position:0%
+right and again it's not convergent
+soing the logs has not helped you and
+
+ align:start position:0%
+soing the logs has not helped you and
+ 
+
+ align:start position:0%
+soing the logs has not helped you and
+that's because what we're talking about
+
+ align:start position:0%
+that's because what we're talking about
+ 
+
+ align:start position:0%
+that's because what we're talking about
+here has nothing to do with logs has to
+
+ align:start position:0%
+here has nothing to do with logs has to
+ 
+
+ align:start position:0%
+here has nothing to do with logs has to
+do with powers it's the normal on that's
+
+ align:start position:0%
+do with powers it's the normal on that's
+ 
+
+ align:start position:0%
+do with powers it's the normal on that's
+causing this
+
+ align:start position:0%
+causing this
+ 
+
+ align:start position:0%
+causing this
+problem okay so we could throw up our
+
+ align:start position:0%
+problem okay so we could throw up our
+ 
+
+ align:start position:0%
+problem okay so we could throw up our
+hands and say oh doesn't work or we
+
+ align:start position:0%
+hands and say oh doesn't work or we
+ 
+
+ align:start position:0%
+hands and say oh doesn't work or we
+could try to do something
+
+ align:start position:0%
+could try to do something
+ 
+
+ align:start position:0%
+could try to do something
+better so let me show you what happens
+
+ align:start position:0%
+better so let me show you what happens
+ 
+
+ align:start position:0%
+better so let me show you what happens
+if we do some of this stuff that I've
+
+ align:start position:0%
+if we do some of this stuff that I've
+ 
+
+ align:start position:0%
+if we do some of this stuff that I've
+been telling you
+
+ align:start position:0%
+been telling you
+ 
+
+ align:start position:0%
+been telling you
+about so this guy
+
+ align:start position:0%
+about so this guy
+ 
+
+ align:start position:0%
+about so this guy
+has a = one or normal on you can check
+
+ align:start position:0%
+has a = one or normal on you can check
+ 
+
+ align:start position:0%
+has a = one or normal on you can check
+that very easily by doing a bubble sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switch to the MSR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scheme so we reuse our perturbative
+
+ align:start position:0%
+scheme so we reuse our perturbative
+ 
+
+ align:start position:0%
+scheme so we reuse our perturbative
+information in msar but just organizing
+
+ align:start position:0%
+information in msar but just organizing
+ 
+
+ align:start position:0%
+information in msar but just organizing
+a more intelligent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fashion we Define a coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+above saying that this problem must have
+
+ align:start position:0%
+above saying that this problem must have
+ 
+
+ align:start position:0%
+above saying that this problem must have
+to do with that normal on and then if we
+
+ align:start position:0%
+to do with that normal on and then if we
+ 
+
+ align:start position:0%
+to do with that normal on and then if we
+write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down what the op looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like we have again an
+
+ align:start position:0%
+like we have again an
+ 
+
+ align:start position:0%
+like we have again an
+op and we've changed Matrix element
+
+ align:start position:0%
+op and we've changed Matrix element
+ 
+
+ align:start position:0%
+op and we've changed Matrix element
+definitions as well as Wilson
+
+ align:start position:0%
+definitions as well as Wilson
+ 
+
+ align:start position:0%
+definitions as well as Wilson
+coefficients def definitions so I'm
+
+ align:start position:0%
+coefficients def definitions so I'm
+ 
+
+ align:start position:0%
+coefficients def definitions so I'm
+putting everything this scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r0o so that's just the rewriting the op
+
+ align:start position:0%
+r0o so that's just the rewriting the op
+ 
+
+ align:start position:0%
+r0o so that's just the rewriting the op
+in this new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scheme when we look at this scheme and
+
+ align:start position:0%
+scheme when we look at this scheme and
+ 
+
+ align:start position:0%
+scheme when we look at this scheme and
+we think about what's going on we want
+
+ align:start position:0%
+we think about what's going on we want
+ 
+
+ align:start position:0%
+we think about what's going on we want
+to choose the r0o to be a void Lambda
+
+ align:start position:0%
+to choose the r0o to be a void Lambda
+ 
+
+ align:start position:0%
+to choose the r0o to be a void Lambda
+qcd or a bit bigger and the reason we
+
+ align:start position:0%
+qcd or a bit bigger and the reason we
+ 
+
+ align:start position:0%
+qcd or a bit bigger and the reason we
+want to do that is to preserve power
+
+ align:start position:0%
+want to do that is to preserve power
+ 
+
+ align:start position:0%
+want to do that is to preserve power
+power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+counting so power counting is
+
+ align:start position:0%
+counting so power counting is
+ 
+
+ align:start position:0%
+counting so power counting is
+important when we're making expansions
+
+ align:start position:0%
+important when we're making expansions
+ 
+
+ align:start position:0%
+important when we're making expansions
+in some sense it's
+
+ align:start position:0%
+in some sense it's
+ 
+
+ align:start position:0%
+in some sense it's
+key and if we
+
+ align:start position:0%
+key and if we
+ 
+
+ align:start position:0%
+key and if we
+thought that the original msar Matrix
+
+ align:start position:0%
+thought that the original msar Matrix
+ 
+
+ align:start position:0%
+thought that the original msar Matrix
+element was dominated by the scale
+
+ align:start position:0%
+element was dominated by the scale
+ 
+
+ align:start position:0%
+element was dominated by the scale
+Lambda qcd we better not screw that
+
+ align:start position:0%
+Lambda qcd we better not screw that
+ 
+
+ align:start position:0%
+Lambda qcd we better not screw that
+up when we make a change of
+
+ align:start position:0%
+up when we make a change of
+ 
+
+ align:start position:0%
+up when we make a change of
+variable and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the kind of change of variable you're
+
+ align:start position:0%
+the kind of change of variable you're
+ 
+
+ align:start position:0%
+the kind of change of variable you're
+making is you're taking the original
+
+ align:start position:0%
+making is you're taking the original
+ 
+
+ align:start position:0%
+making is you're taking the original
+Matrix element you're subtracting a
+
+ align:start position:0%
+Matrix element you're subtracting a
+ 
+
+ align:start position:0%
+Matrix element you're subtracting a
+series with the proportionality constant
+
+ align:start position:0%
+series with the proportionality constant
+ 
+
+ align:start position:0%
+series with the proportionality constant
+R zero this guy was Lambda qcd s and you
+
+ align:start position:0%
+R zero this guy was Lambda qcd s and you
+ 
+
+ align:start position:0%
+R zero this guy was Lambda qcd s and you
+you want this to be not too far
+
+ align:start position:0%
+you want this to be not too far
+ 
+
+ align:start position:0%
+you want this to be not too far
+different than Lambda qcd so that this
+
+ align:start position:0%
+different than Lambda qcd so that this
+ 
+
+ align:start position:0%
+different than Lambda qcd so that this
+whole thing here is Lambda qcd Cub just
+
+ align:start position:0%
+whole thing here is Lambda qcd Cub just
+ 
+
+ align:start position:0%
+whole thing here is Lambda qcd Cub just
+like this so that this
+
+ align:start position:0%
+like this so that this
+ 
+
+ align:start position:0%
+like this so that this
+thing is still of order Lambda qcd cubed
+
+ align:start position:0%
+thing is still of order Lambda qcd cubed
+ 
+
+ align:start position:0%
+thing is still of order Lambda qcd cubed
+so you don't want to do something like
+
+ align:start position:0%
+so you don't want to do something like
+ 
+
+ align:start position:0%
+so you don't want to do something like
+choose the r0 to be you know MB or
+
+ align:start position:0%
+choose the r0 to be you know MB or
+ 
+
+ align:start position:0%
+choose the r0 to be you know MB or
+something because then you'd be making a
+
+ align:start position:0%
+something because then you'd be making a
+ 
+
+ align:start position:0%
+something because then you'd be making a
+huge change in the value of this Matrix
+
+ align:start position:0%
+huge change in the value of this Matrix
+ 
+
+ align:start position:0%
+huge change in the value of this Matrix
+element you really want to take the r0o
+
+ align:start position:0%
+element you really want to take the r0o
+ 
+
+ align:start position:0%
+element you really want to take the r0o
+cut off to be of order say a GV or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something so you can use the RG to sum
+
+ align:start position:0%
+something so you can use the RG to sum
+ 
+
+ align:start position:0%
+something so you can use the RG to sum
+up logs from that scale R zero up to the
+
+ align:start position:0%
+up logs from that scale R zero up to the
+ 
+
+ align:start position:0%
+up logs from that scale R zero up to the
+scale of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mq so again we can sum up logs and have
+
+ align:start position:0%
+mq so again we can sum up logs and have
+ 
+
+ align:start position:0%
+mq so again we can sum up logs and have
+a logarithmically
+
+ align:start position:0%
+a logarithmically
+ 
+
+ align:start position:0%
+a logarithmically
+improved result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but actually the most important thing
+
+ align:start position:0%
+but actually the most important thing
+ 
+
+ align:start position:0%
+but actually the most important thing
+here is getting rid of the normal on I
+
+ align:start position:0%
+here is getting rid of the normal on I
+ 
+
+ align:start position:0%
+here is getting rid of the normal on I
+still I want just wanted to kind of show
+
+ align:start position:0%
+still I want just wanted to kind of show
+ 
+
+ align:start position:0%
+still I want just wanted to kind of show
+you what the result would look like with
+
+ align:start position:0%
+you what the result would look like with
+ 
+
+ align:start position:0%
+you what the result would look like with
+both the RG
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Improvement just sort of using the full
+
+ align:start position:0%
+Improvement just sort of using the full
+ 
+
+ align:start position:0%
+Improvement just sort of using the full
+set of tools that we
+
+ align:start position:0%
+set of tools that we
+ 
+
+ align:start position:0%
+set of tools that we
+have so here's the scales you have three
+
+ align:start position:0%
+have so here's the scales you have three
+ 
+
+ align:start position:0%
+have so here's the scales you have three
+physical scales bork Mass charm Mass
+
+ align:start position:0%
+physical scales bork Mass charm Mass
+ 
+
+ align:start position:0%
+physical scales bork Mass charm Mass
+Lambda qcd you have two cut offs you
+
+ align:start position:0%
+Lambda qcd you have two cut offs you
+ 
+
+ align:start position:0%
+Lambda qcd you have two cut offs you
+have r0 which I just told you you should
+
+ align:start position:0%
+have r0 which I just told you you should
+ 
+
+ align:start position:0%
+have r0 which I just told you you should
+pick to be close to Lambda Q CD and then
+
+ align:start position:0%
+pick to be close to Lambda Q CD and then
+ 
+
+ align:start position:0%
+pick to be close to Lambda Q CD and then
+you could think that you that there's
+
+ align:start position:0%
+you could think that you that there's
+ 
+
+ align:start position:0%
+you could think that you that there's
+these other scales MB and M charm and
+
+ align:start position:0%
+these other scales MB and M charm and
+ 
+
+ align:start position:0%
+these other scales MB and M charm and
+you'd like to if this is some low scale
+
+ align:start position:0%
+you'd like to if this is some low scale
+ 
+
+ align:start position:0%
+you'd like to if this is some low scale
+and that's some high scale I'd like to
+
+ align:start position:0%
+and that's some high scale I'd like to
+ 
+
+ align:start position:0%
+and that's some high scale I'd like to
+sum logs and I can do that by running up
+
+ align:start position:0%
+sum logs and I can do that by running up
+ 
+
+ align:start position:0%
+sum logs and I can do that by running up
+from r0 to
+
+ align:start position:0%
+from r0 to
+ 
+
+ align:start position:0%
+from r0 to
+R1 which in this case I'll just pick
+
+ align:start position:0%
+R1 which in this case I'll just pick
+ 
+
+ align:start position:0%
+R1 which in this case I'll just pick
+between MB andm
+
+ align:start position:0%
+between MB andm
+ 
+
+ align:start position:0%
+between MB andm
+charm so if you did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that you'd get some result that looks
+
+ align:start position:0%
+that you'd get some result that looks
+ 
+
+ align:start position:0%
+that you'd get some result that looks
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just putting in some notation for the
+
+ align:start position:0%
+just putting in some notation for the
+ 
+
+ align:start position:0%
+just putting in some notation for the
+resummation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and then this guy is at the low
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale okay so now everybody's happy the
+
+ align:start position:0%
+scale okay so now everybody's happy the
+ 
+
+ align:start position:0%
+scale okay so now everybody's happy the
+Wilson coefficients here can be expanded
+
+ align:start position:0%
+Wilson coefficients here can be expanded
+ 
+
+ align:start position:0%
+Wilson coefficients here can be expanded
+in privation theory we don't think
+
+ align:start position:0%
+in privation theory we don't think
+ 
+
+ align:start position:0%
+in privation theory we don't think
+there's any large logs
+
+ align:start position:0%
+there's any large logs
+ 
+
+ align:start position:0%
+there's any large logs
+this U sums up any large logs between
+
+ align:start position:0%
+this U sums up any large logs between
+ 
+
+ align:start position:0%
+this U sums up any large logs between
+the low scales and the high scales and
+
+ align:start position:0%
+the low scales and the high scales and
+ 
+
+ align:start position:0%
+the low scales and the high scales and
+this guy's living at a scale that he
+
+ align:start position:0%
+this guy's living at a scale that he
+ 
+
+ align:start position:0%
+this guy's living at a scale that he
+likes to live at okay and there's no re
+
+ align:start position:0%
+likes to live at okay and there's no re
+ 
+
+ align:start position:0%
+likes to live at okay and there's no re
+normal one no U equals one R normal one
+
+ align:start position:0%
+normal one no U equals one R normal one
+ 
+
+ align:start position:0%
+normal one no U equals one R normal one
+so what does it look like if I write
+
+ align:start position:0%
+so what does it look like if I write
+ 
+
+ align:start position:0%
+so what does it look like if I write
+down this
+
+ align:start position:0%
+down this
+ 
+
+ align:start position:0%
+down this
+guy so first of all if I look at this
+
+ align:start position:0%
+guy so first of all if I look at this
+ 
+
+ align:start position:0%
+guy so first of all if I look at this
+thing order by order this is how the
+
+ align:start position:0%
+thing order by order this is how the
+ 
+
+ align:start position:0%
+thing order by order this is how the
+convergent convergence looks you get a
+
+ align:start position:0%
+convergent convergence looks you get a
+ 
+
+ align:start position:0%
+convergent convergence looks you get a
+downward shift by about the same amount
+
+ align:start position:0%
+downward shift by about the same amount
+ 
+
+ align:start position:0%
+downward shift by about the same amount
+as before but the next shifts are small
+
+ align:start position:0%
+as before but the next shifts are small
+ 
+
+ align:start position:0%
+as before but the next shifts are small
+so the series actually looks like it's
+
+ align:start position:0%
+so the series actually looks like it's
+ 
+
+ align:start position:0%
+so the series actually looks like it's
+converging to
+
+ align:start position:0%
+converging to
+ 
+
+ align:start position:0%
+converging to
+something so that's the first three
+
+ align:start position:0%
+something so that's the first three
+ 
+
+ align:start position:0%
+something so that's the first three
+orders if you use this
+
+ align:start position:0%
+orders if you use this
+ 
+
+ align:start position:0%
+orders if you use this
+approach and if you use the complete
+
+ align:start position:0%
+approach and if you use the complete
+ 
+
+ align:start position:0%
+approach and if you use the complete
+power of this at the highest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order you can write
+
+ align:start position:0%
+order you can write
+ 
+
+ align:start position:0%
+order you can write
+down that you get this 860 from the
+
+ align:start position:0%
+down that you get this 860 from the
+ 
+
+ align:start position:0%
+down that you get this 860 from the
+perative part which is not too far from
+
+ align:start position:0%
+perative part which is not too far from
+ 
+
+ align:start position:0%
+perative part which is not too far from
+the 088 or the 8517 which I said was
+
+ align:start position:0%
+the 088 or the 8517 which I said was
+ 
+
+ align:start position:0%
+the 088 or the 8517 which I said was
+close to the data okay so this actually
+
+ align:start position:0%
+close to the data okay so this actually
+ 
+
+ align:start position:0%
+close to the data okay so this actually
+is pretty good
+
+ align:start position:0%
+is pretty good
+ 
+
+ align:start position:0%
+is pretty good
+you can make some air estimate for how
+
+ align:start position:0%
+you can make some air estimate for how
+ 
+
+ align:start position:0%
+you can make some air estimate for how
+big this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is and you can make some error estimate
+
+ align:start position:0%
+is and you can make some error estimate
+ 
+
+ align:start position:0%
+is and you can make some error estimate
+for the perturbative uncertainty from
+
+ align:start position:0%
+for the perturbative uncertainty from
+ 
+
+ align:start position:0%
+for the perturbative uncertainty from
+higher orders by varying
+
+ align:start position:0%
+higher orders by varying
+ 
+
+ align:start position:0%
+higher orders by varying
+scales and you get with a prediction
+
+ align:start position:0%
+scales and you get with a prediction
+ 
+
+ align:start position:0%
+scales and you get with a prediction
+that looks like
+
+ align:start position:0%
+that looks like
+ 
+
+ align:start position:0%
+that looks like
+that so when you want to estimate
+
+ align:start position:0%
+that so when you want to estimate
+ 
+
+ align:start position:0%
+that so when you want to estimate
+uncertainties what you typically do with
+
+ align:start position:0%
+uncertainties what you typically do with
+ 
+
+ align:start position:0%
+uncertainties what you typically do with
+your cut off is you vary them you say
+
+ align:start position:0%
+your cut off is you vary them you say
+ 
+
+ align:start position:0%
+your cut off is you vary them you say
+Well it has to be up here but I don't
+
+ align:start position:0%
+Well it has to be up here but I don't
+ 
+
+ align:start position:0%
+Well it has to be up here but I don't
+have to take take it exactly there I
+
+ align:start position:0%
+have to take take it exactly there I
+ 
+
+ align:start position:0%
+have to take take it exactly there I
+could take it up here take it a little
+
+ align:start position:0%
+could take it up here take it a little
+ 
+
+ align:start position:0%
+could take it up here take it a little
+lower move this guy around that gives
+
+ align:start position:0%
+lower move this guy around that gives
+ 
+
+ align:start position:0%
+lower move this guy around that gives
+you some idea of higher order
+
+ align:start position:0%
+you some idea of higher order
+ 
+
+ align:start position:0%
+you some idea of higher order
+uncertainties because the dependence on
+
+ align:start position:0%
+uncertainties because the dependence on
+ 
+
+ align:start position:0%
+uncertainties because the dependence on
+these scales cancels out order by order
+
+ align:start position:0%
+these scales cancels out order by order
+ 
+
+ align:start position:0%
+these scales cancels out order by order
+and peration theory and so varying it um
+
+ align:start position:0%
+and peration theory and so varying it um
+ 
+
+ align:start position:0%
+and peration theory and so varying it um
+is a way of getting an idea of higher
+
+ align:start position:0%
+is a way of getting an idea of higher
+ 
+
+ align:start position:0%
+is a way of getting an idea of higher
+order uncertainties from peration Theory
+
+ align:start position:0%
+order uncertainties from peration Theory
+ 
+
+ align:start position:0%
+order uncertainties from peration Theory
+and that's what I've done for example
+
+ align:start position:0%
+and that's what I've done for example
+ 
+
+ align:start position:0%
+and that's what I've done for example
+for this perative term here this is
+
+ align:start position:0%
+for this perative term here this is
+ 
+
+ align:start position:0%
+for this perative term here this is
+varying
+
+ align:start position:0%
+varying
+ 
+
+ align:start position:0%
+varying
+R1 up and down by a factor of two and
+
+ align:start position:0%
+R1 up and down by a factor of two and
+ 
+
+ align:start position:0%
+R1 up and down by a factor of two and
+just see kind of what residual
+
+ align:start position:0%
+just see kind of what residual
+ 
+
+ align:start position:0%
+just see kind of what residual
+uncertainty you have this one's more
+
+ align:start position:0%
+uncertainty you have this one's more
+ 
+
+ align:start position:0%
+uncertainty you have this one's more
+interesting so one's like mu variation
+
+ align:start position:0%
+interesting so one's like mu variation
+ 
+
+ align:start position:0%
+interesting so one's like mu variation
+this one's more interesting and that's
+
+ align:start position:0%
+this one's more interesting and that's
+ 
+
+ align:start position:0%
+this one's more interesting and that's
+because we have this other cut off r0
+
+ align:start position:0%
+because we have this other cut off r0
+ 
+
+ align:start position:0%
+because we have this other cut off r0
+but what r0 does is it connects a
+
+ align:start position:0%
+but what r0 does is it connects a
+ 
+
+ align:start position:0%
+but what r0 does is it connects a
+leading order term to a subleading power
+
+ align:start position:0%
+leading order term to a subleading power
+ 
+
+ align:start position:0%
+leading order term to a subleading power
+term the r0o dependence cancels between
+
+ align:start position:0%
+term the r0o dependence cancels between
+ 
+
+ align:start position:0%
+term the r0o dependence cancels between
+something that's order one in the power
+
+ align:start position:0%
+something that's order one in the power
+ 
+
+ align:start position:0%
+something that's order one in the power
+counting something that's higher order
+
+ align:start position:0%
+counting something that's higher order
+ 
+
+ align:start position:0%
+counting something that's higher order
+in the power
+
+ align:start position:0%
+in the power
+ 
+
+ align:start position:0%
+in the power
+counting but when I vary r0o it still
+
+ align:start position:0%
+counting but when I vary r0o it still
+ 
+
+ align:start position:0%
+counting but when I vary r0o it still
+cancels between these two pieces because
+
+ align:start position:0%
+cancels between these two pieces because
+ 
+
+ align:start position:0%
+cancels between these two pieces because
+remember I've included in if you look at
+
+ align:start position:0%
+remember I've included in if you look at
+ 
+
+ align:start position:0%
+remember I've included in if you look at
+the top of the board I've included
+
+ align:start position:0%
+the top of the board I've included
+ 
+
+ align:start position:0%
+the top of the board I've included
+higher power terms in my Wilson
+
+ align:start position:0%
+higher power terms in my Wilson
+ 
+
+ align:start position:0%
+higher power terms in my Wilson
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+and so varying the r0 you can actually
+
+ align:start position:0%
+and so varying the r0 you can actually
+ 
+
+ align:start position:0%
+and so varying the r0 you can actually
+get an idea of how big this thing is
+
+ align:start position:0%
+get an idea of how big this thing is
+ 
+
+ align:start position:0%
+get an idea of how big this thing is
+kind of in a naive dimensional analysis
+
+ align:start position:0%
+kind of in a naive dimensional analysis
+ 
+
+ align:start position:0%
+kind of in a naive dimensional analysis
+type way and that gives this number
+
+ align:start position:0%
+type way and that gives this number
+ 
+
+ align:start position:0%
+type way and that gives this number
+here so r0o variation actually allows
+
+ align:start position:0%
+here so r0o variation actually allows
+ 
+
+ align:start position:0%
+here so r0o variation actually allows
+you to test for the size of power
+
+ align:start position:0%
+you to test for the size of power
+ 
+
+ align:start position:0%
+you to test for the size of power
+Corrections if you don't know
+
+ align:start position:0%
+Corrections if you don't know
+ 
+
+ align:start position:0%
+Corrections if you don't know
+them and in this case it turns out that
+
+ align:start position:0%
+them and in this case it turns out that
+ 
+
+ align:start position:0%
+them and in this case it turns out that
+the power correction is kind of small in
+
+ align:start position:0%
+the power correction is kind of small in
+ 
+
+ align:start position:0%
+the power correction is kind of small in
+this scheme but didn't have to be that
+
+ align:start position:0%
+this scheme but didn't have to be that
+ 
+
+ align:start position:0%
+this scheme but didn't have to be that
+small it could have been 165
+
+ align:start position:0%
+small it could have been 165
+ 
+
+ align:start position:0%
+small it could have been 165
+265 happens to be
+
+ align:start position:0%
+265 happens to be
+ 
+
+ align:start position:0%
+265 happens to be
+0065 okay so everything looks much nicer
+
+ align:start position:0%
+0065 okay so everything looks much nicer
+ 
+
+ align:start position:0%
+0065 okay so everything looks much nicer
+after we get just get rid of the re
+
+ align:start position:0%
+after we get just get rid of the re
+ 
+
+ align:start position:0%
+after we get just get rid of the re
+normal one someone else did the
+
+ align:start position:0%
+normal one someone else did the
+ 
+
+ align:start position:0%
+normal one someone else did the
+three-loop calculation you made the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prediction just true in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so the moral of the story is that if you
+
+ align:start position:0%
+so the moral of the story is that if you
+ 
+
+ align:start position:0%
+so the moral of the story is that if you
+really want to use calculations that are
+
+ align:start position:0%
+really want to use calculations that are
+ 
+
+ align:start position:0%
+really want to use calculations that are
+out there and you you have to think
+
+ align:start position:0%
+out there and you you have to think
+ 
+
+ align:start position:0%
+out there and you you have to think
+about the physics you can't just
+
+ align:start position:0%
+about the physics you can't just
+ 
+
+ align:start position:0%
+about the physics you can't just
+calculate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry okay so these were normal lines
+
+ align:start position:0%
+sorry okay so these were normal lines
+ 
+
+ align:start position:0%
+sorry okay so these were normal lines
+when you have kind of order alpha squ or
+
+ align:start position:0%
+when you have kind of order alpha squ or
+ 
+
+ align:start position:0%
+when you have kind of order alpha squ or
+Alpha cubed information then you have to
+
+ align:start position:0%
+Alpha cubed information then you have to
+ 
+
+ align:start position:0%
+Alpha cubed information then you have to
+worry about things like this and if you
+
+ align:start position:0%
+worry about things like this and if you
+ 
+
+ align:start position:0%
+worry about things like this and if you
+didn't what looked like was working
+
+ align:start position:0%
+didn't what looked like was working
+ 
+
+ align:start position:0%
+didn't what looked like was working
+beautifully at leading log order might
+
+ align:start position:0%
+beautifully at leading log order might
+ 
+
+ align:start position:0%
+beautifully at leading log order might
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+spoiled your leading log might be the
+
+ align:start position:0%
+spoiled your leading log might be the
+ 
+
+ align:start position:0%
+spoiled your leading log might be the
+best prediction unless you think about
+
+ align:start position:0%
+best prediction unless you think about
+ 
+
+ align:start position:0%
+best prediction unless you think about
+this that you can make because you're
+
+ align:start position:0%
+this that you can make because you're
+ 
+
+ align:start position:0%
+this that you can make because you're
+just higher orders you're getting
+
+ align:start position:0%
+just higher orders you're getting
+ 
+
+ align:start position:0%
+just higher orders you're getting
+sensitive to this normal on problem
+
+ align:start position:0%
+sensitive to this normal on problem
+ 
+
+ align:start position:0%
+sensitive to this normal on problem
+and that what that means is
+
+ align:start position:0%
+and that what that means is
+ 
+
+ align:start position:0%
+and that what that means is
+generically this is changing and this is
+
+ align:start position:0%
+generically this is changing and this is
+ 
+
+ align:start position:0%
+generically this is changing and this is
+changing the power correction is
+
+ align:start position:0%
+changing the power correction is
+ 
+
+ align:start position:0%
+changing the power correction is
+changing and so at each order that this
+
+ align:start position:0%
+changing and so at each order that this
+ 
+
+ align:start position:0%
+changing and so at each order that this
+changes I could compensate by changing
+
+ align:start position:0%
+changes I could compensate by changing
+ 
+
+ align:start position:0%
+changes I could compensate by changing
+this but it would have to be a pretty
+
+ align:start position:0%
+this but it would have to be a pretty
+ 
+
+ align:start position:0%
+this but it would have to be a pretty
+big change right I change this guy by
+
+ align:start position:0%
+big change right I change this guy by
+ 
+
+ align:start position:0%
+big change right I change this guy by
+this amount then I have to compensate by
+
+ align:start position:0%
+this amount then I have to compensate by
+ 
+
+ align:start position:0%
+this amount then I have to compensate by
+that oop now it even changes by a larger
+
+ align:start position:0%
+that oop now it even changes by a larger
+ 
+
+ align:start position:0%
+that oop now it even changes by a larger
+amount well compensate by changing this
+
+ align:start position:0%
+amount well compensate by changing this
+ 
+
+ align:start position:0%
+amount well compensate by changing this
+by order one amount that's exactly this
+
+ align:start position:0%
+by order one amount that's exactly this
+ 
+
+ align:start position:0%
+by order one amount that's exactly this
+this fact that both things have this
+
+ align:start position:0%
+this fact that both things have this
+ 
+
+ align:start position:0%
+this fact that both things have this
+problem order by order I can cancel out
+
+ align:start position:0%
+problem order by order I can cancel out
+ 
+
+ align:start position:0%
+problem order by order I can cancel out
+the problem by but I don't want but then
+
+ align:start position:0%
+the problem by but I don't want but then
+ 
+
+ align:start position:0%
+the problem by but I don't want but then
+I can never really assign a number to
+
+ align:start position:0%
+I can never really assign a number to
+ 
+
+ align:start position:0%
+I can never really assign a number to
+this it's an order dependent number each
+
+ align:start position:0%
+this it's an order dependent number each
+ 
+
+ align:start position:0%
+this it's an order dependent number each
+order in peration theory that I use here
+
+ align:start position:0%
+order in peration theory that I use here
+ 
+
+ align:start position:0%
+order in peration theory that I use here
+this number changes and that's not
+
+ align:start position:0%
+this number changes and that's not
+ 
+
+ align:start position:0%
+this number changes and that's not
+really what you think of for a physical
+
+ align:start position:0%
+really what you think of for a physical
+ 
+
+ align:start position:0%
+really what you think of for a physical
+concept that this Matrix element should
+
+ align:start position:0%
+concept that this Matrix element should
+ 
+
+ align:start position:0%
+concept that this Matrix element should
+have a meaning that it it shouldn't be
+
+ align:start position:0%
+have a meaning that it it shouldn't be
+ 
+
+ align:start position:0%
+have a meaning that it it shouldn't be
+changing by order one depending on the
+
+ align:start position:0%
+changing by order one depending on the
+ 
+
+ align:start position:0%
+changing by order one depending on the
+perturbative order that you're working
+
+ align:start position:0%
+perturbative order that you're working
+ 
+
+ align:start position:0%
+perturbative order that you're working
+in this way of thinking this thing is
+
+ align:start position:0%
+in this way of thinking this thing is
+ 
+
+ align:start position:0%
+in this way of thinking this thing is
+stable much more stable anyway and you
+
+ align:start position:0%
+stable much more stable anyway and you
+ 
+
+ align:start position:0%
+stable much more stable anyway and you
+can assign a number to
+
+ align:start position:0%
+can assign a number to
+ 
+
+ align:start position:0%
+can assign a number to
+it that's kind of the
+
+ align:start position:0%
+it that's kind of the
+ 
+
+ align:start position:0%
+it that's kind of the
+moral all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so the thing is that the
+
+ align:start position:0%
+yeah so the thing is that the
+ 
+
+ align:start position:0%
+yeah so the thing is that the
+convergence it's not about the Precision
+
+ align:start position:0%
+convergence it's not about the Precision
+ 
+
+ align:start position:0%
+convergence it's not about the Precision
+it's about the
+
+ align:start position:0%
+it's about the
+ 
+
+ align:start position:0%
+it's about the
+convergence right so you would be fine
+
+ align:start position:0%
+convergence right so you would be fine
+ 
+
+ align:start position:0%
+convergence right so you would be fine
+in some sense it would not be
+
+ align:start position:0%
+in some sense it would not be
+ 
+
+ align:start position:0%
+in some sense it would not be
+technically a problem if this was
+
+ align:start position:0%
+technically a problem if this was
+ 
+
+ align:start position:0%
+technically a problem if this was
+zero right if this guy was that much of
+
+ align:start position:0%
+zero right if this guy was that much of
+ 
+
+ align:start position:0%
+zero right if this guy was that much of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+shift and well this this was a 15 shift
+
+ align:start position:0%
+shift and well this this was a 15 shift
+ 
+
+ align:start position:0%
+shift and well this this was a 15 shift
+this is a seven shift if this guy was
+
+ align:start position:0%
+this is a seven shift if this guy was
+ 
+
+ align:start position:0%
+this is a seven shift if this guy was
+like small again you'd be fine
+
+ align:start position:0%
+like small again you'd be fine
+ 
+
+ align:start position:0%
+like small again you'd be fine
+right because then you'd say okay well I
+
+ align:start position:0%
+right because then you'd say okay well I
+ 
+
+ align:start position:0%
+right because then you'd say okay well I
+extract this thing in the same order
+
+ align:start position:0%
+extract this thing in the same order
+ 
+
+ align:start position:0%
+extract this thing in the same order
+that I include that and you know and
+
+ align:start position:0%
+that I include that and you know and
+ 
+
+ align:start position:0%
+that I include that and you know and
+maybe this thing gives a plus 07 and
+
+ align:start position:0%
+maybe this thing gives a plus 07 and
+ 
+
+ align:start position:0%
+maybe this thing gives a plus 07 and
+this guy gives Aus 07 and then I'm close
+
+ align:start position:0%
+this guy gives Aus 07 and then I'm close
+ 
+
+ align:start position:0%
+this guy gives Aus 07 and then I'm close
+to the data and you're happy the issue
+
+ align:start position:0%
+to the data and you're happy the issue
+ 
+
+ align:start position:0%
+to the data and you're happy the issue
+is that you go to a higher order and you
+
+ align:start position:0%
+is that you go to a higher order and you
+ 
+
+ align:start position:0%
+is that you go to a higher order and you
+get even bigger shift that's the real
+
+ align:start position:0%
+get even bigger shift that's the real
+ 
+
+ align:start position:0%
+get even bigger shift that's the real
+real problem that you don't in the
+
+ align:start position:0%
+real problem that you don't in the
+ 
+
+ align:start position:0%
+real problem that you don't in the
+perturbative part alone have any sign of
+
+ align:start position:0%
+perturbative part alone have any sign of
+ 
+
+ align:start position:0%
+perturbative part alone have any sign of
+convergence that's the issue it's not so
+
+ align:start position:0%
+convergence that's the issue it's not so
+ 
+
+ align:start position:0%
+convergence that's the issue it's not so
+the fact that this number is sort of
+
+ align:start position:0%
+the fact that this number is sort of
+ 
+
+ align:start position:0%
+the fact that this number is sort of
+close to that number is you know in some
+
+ align:start position:0%
+close to that number is you know in some
+ 
+
+ align:start position:0%
+close to that number is you know in some
+sense okay because you think that this
+
+ align:start position:0%
+sense okay because you think that this
+ 
+
+ align:start position:0%
+sense okay because you think that this
+thing should generically be of that size
+
+ align:start position:0%
+thing should generically be of that size
+ 
+
+ align:start position:0%
+thing should generically be of that size
+that's what dimensional analysis would
+
+ align:start position:0%
+that's what dimensional analysis would
+ 
+
+ align:start position:0%
+that's what dimensional analysis would
+say dimensional analysis might even say
+
+ align:start position:0%
+say dimensional analysis might even say
+ 
+
+ align:start position:0%
+say dimensional analysis might even say
+it's a little
+
+ align:start position:0%
+it's a little
+ 
+
+ align:start position:0%
+it's a little
+bigger um so the real issue is that you
+
+ align:start position:0%
+bigger um so the real issue is that you
+ 
+
+ align:start position:0%
+bigger um so the real issue is that you
+want your predictions to be
+
+ align:start position:0%
+want your predictions to be
+ 
+
+ align:start position:0%
+want your predictions to be
+stable and
+
+ align:start position:0%
+stable and
+ 
+
+ align:start position:0%
+stable and
+yeah be higher than so this now this
+
+ align:start position:0%
+yeah be higher than so this now this
+ 
+
+ align:start position:0%
+yeah be higher than so this now this
+this actually here is connected to that
+
+ align:start position:0%
+this actually here is connected to that
+ 
+
+ align:start position:0%
+this actually here is connected to that
+term I'm saying even if I leave this
+
+ align:start position:0%
+term I'm saying even if I leave this
+ 
+
+ align:start position:0%
+term I'm saying even if I leave this
+term out I actually get something that
+
+ align:start position:0%
+term out I actually get something that
+ 
+
+ align:start position:0%
+term out I actually get something that
+agrees with the data
+
+ align:start position:0%
+agrees with the data
+ 
+
+ align:start position:0%
+agrees with the data
+and that's because it turns out that the
+
+ align:start position:0%
+and that's because it turns out that the
+ 
+
+ align:start position:0%
+and that's because it turns out that the
+power correction here is you know of
+
+ align:start position:0%
+power correction here is you know of
+ 
+
+ align:start position:0%
+power correction here is you know of
+this size and I can get an idea of how
+
+ align:start position:0%
+this size and I can get an idea of how
+ 
+
+ align:start position:0%
+this size and I can get an idea of how
+big it is by varying the r0o in this
+
+ align:start position:0%
+big it is by varying the r0o in this
+ 
+
+ align:start position:0%
+big it is by varying the r0o in this
+prediction and that changes this number
+
+ align:start position:0%
+prediction and that changes this number
+ 
+
+ align:start position:0%
+prediction and that changes this number
+by that amount and that's I and since
+
+ align:start position:0%
+by that amount and that's I and since
+ 
+
+ align:start position:0%
+by that amount and that's I and since
+this thing is also changing in exactly a
+
+ align:start position:0%
+this thing is also changing in exactly a
+ 
+
+ align:start position:0%
+this thing is also changing in exactly a
+way that compensates that R zero
+
+ align:start position:0%
+way that compensates that R zero
+ 
+
+ align:start position:0%
+way that compensates that R zero
+dependence I'm getting an estimate for
+
+ align:start position:0%
+dependence I'm getting an estimate for
+ 
+
+ align:start position:0%
+dependence I'm getting an estimate for
+this thing that's what I did there so if
+
+ align:start position:0%
+this thing that's what I did there so if
+ 
+
+ align:start position:0%
+this thing that's what I did there so if
+I were to put this thing in I'd have a
+
+ align:start position:0%
+I were to put this thing in I'd have a
+ 
+
+ align:start position:0%
+I were to put this thing in I'd have a
+new parameter and I could exactly fit
+
+ align:start position:0%
+new parameter and I could exactly fit
+ 
+
+ align:start position:0%
+new parameter and I could exactly fit
+the data right but I did it I wrote what
+
+ align:start position:0%
+the data right but I did it I wrote what
+ 
+
+ align:start position:0%
+the data right but I did it I wrote what
+I wrote was a little different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I kind of went over that
+
+ align:start position:0%
+yeah I kind of went over that
+ 
+
+ align:start position:0%
+yeah I kind of went over that
+quickly all right
+
+ align:start position:0%
+quickly all right
+ 
+
+ align:start position:0%
+quickly all right
+so that's actually it for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+HQ so before we get to se which is
+
+ align:start position:0%
+HQ so before we get to se which is
+ 
+
+ align:start position:0%
+HQ so before we get to se which is
+coming up after spring
+
+ align:start position:0%
+coming up after spring
+ 
+
+ align:start position:0%
+coming up after spring
+break we're going to talk about one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topic which I'll just basically
+
+ align:start position:0%
+topic which I'll just basically
+ 
+
+ align:start position:0%
+topic which I'll just basically
+introduce and then we'll stop and
+
+ align:start position:0%
+introduce and then we'll stop and
+ 
+
+ align:start position:0%
+introduce and then we'll stop and
+continue on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thursday so there's going to be one more
+
+ align:start position:0%
+Thursday so there's going to be one more
+ 
+
+ align:start position:0%
+Thursday so there's going to be one more
+example of an effective field
+
+ align:start position:0%
+example of an effective field
+ 
+
+ align:start position:0%
+example of an effective field
+Theory and this is going to be an
+
+ align:start position:0%
+Theory and this is going to be an
+ 
+
+ align:start position:0%
+Theory and this is going to be an
+example of an effective field Theory
+
+ align:start position:0%
+example of an effective field Theory
+ 
+
+ align:start position:0%
+example of an effective field Theory
+with what looks like a problem it's got
+
+ align:start position:0%
+with what looks like a problem it's got
+ 
+
+ align:start position:0%
+with what looks like a problem it's got
+a fine
+
+ align:start position:0%
+a fine
+ 
+
+ align:start position:0%
+a fine
+tuning so usually the whole notion of
+
+ align:start position:0%
+tuning so usually the whole notion of
+ 
+
+ align:start position:0%
+tuning so usually the whole notion of
+effective field theory is against the
+
+ align:start position:0%
+effective field theory is against the
+ 
+
+ align:start position:0%
+effective field theory is against the
+idea that there should be a fine tuning
+
+ align:start position:0%
+idea that there should be a fine tuning
+ 
+
+ align:start position:0%
+idea that there should be a fine tuning
+because you're making an dimensional
+
+ align:start position:0%
+because you're making an dimensional
+ 
+
+ align:start position:0%
+because you're making an dimensional
+analysis estimates of things if there's
+
+ align:start position:0%
+analysis estimates of things if there's
+ 
+
+ align:start position:0%
+analysis estimates of things if there's
+a fine tuning that means you're
+
+ align:start position:0%
+a fine tuning that means you're
+ 
+
+ align:start position:0%
+a fine tuning that means you're
+dimensional analysis failed in this
+
+ align:start position:0%
+dimensional analysis failed in this
+ 
+
+ align:start position:0%
+dimensional analysis failed in this
+example we'll see that you can make one
+
+ align:start position:0%
+example we'll see that you can make one
+ 
+
+ align:start position:0%
+example we'll see that you can make one
+fine tuning and you can understand
+
+ align:start position:0%
+fine tuning and you can understand
+ 
+
+ align:start position:0%
+fine tuning and you can understand
+what's going on with that fine tuning
+
+ align:start position:0%
+what's going on with that fine tuning
+ 
+
+ align:start position:0%
+what's going on with that fine tuning
+and actually propagate it to change your
+
+ align:start position:0%
+and actually propagate it to change your
+ 
+
+ align:start position:0%
+and actually propagate it to change your
+power counting to change your power
+
+ align:start position:0%
+power counting to change your power
+ 
+
+ align:start position:0%
+power counting to change your power
+counting such that it takes into account
+
+ align:start position:0%
+counting such that it takes into account
+ 
+
+ align:start position:0%
+counting such that it takes into account
+the existence of that fine tuning builds
+
+ align:start position:0%
+the existence of that fine tuning builds
+ 
+
+ align:start position:0%
+the existence of that fine tuning builds
+the whole defective theory around the
+
+ align:start position:0%
+the whole defective theory around the
+ 
+
+ align:start position:0%
+the whole defective theory around the
+idea that there was this fine tuning
+
+ align:start position:0%
+idea that there was this fine tuning
+ 
+
+ align:start position:0%
+idea that there was this fine tuning
+from an original perhaps Dimension
+
+ align:start position:0%
+from an original perhaps Dimension
+ 
+
+ align:start position:0%
+from an original perhaps Dimension
+counting point of view but that we can
+
+ align:start position:0%
+counting point of view but that we can
+ 
+
+ align:start position:0%
+counting point of view but that we can
+adopt a different Power counting that
+
+ align:start position:0%
+adopt a different Power counting that
+ 
+
+ align:start position:0%
+adopt a different Power counting that
+actually organizes the physics in
+
+ align:start position:0%
+actually organizes the physics in
+ 
+
+ align:start position:0%
+actually organizes the physics in
+exactly the right way that we want to
+
+ align:start position:0%
+exactly the right way that we want to
+ 
+
+ align:start position:0%
+exactly the right way that we want to
+and in fact it's going to be such an
+
+ align:start position:0%
+and in fact it's going to be such an
+ 
+
+ align:start position:0%
+and in fact it's going to be such an
+easy example where we we can just
+
+ align:start position:0%
+easy example where we we can just
+ 
+
+ align:start position:0%
+easy example where we we can just
+basically calculate all the fan diagrams
+
+ align:start position:0%
+basically calculate all the fan diagrams
+ 
+
+ align:start position:0%
+basically calculate all the fan diagrams
+like very simply one line um so that's
+
+ align:start position:0%
+like very simply one line um so that's
+ 
+
+ align:start position:0%
+like very simply one line um so that's
+what we'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do it'll be a very simple example of an
+
+ align:start position:0%
+do it'll be a very simple example of an
+ 
+
+ align:start position:0%
+do it'll be a very simple example of an
+effective the field
+
+ align:start position:0%
+effective the field
+ 
+
+ align:start position:0%
+effective the field
+Theory and we'll prove some things about
+
+ align:start position:0%
+Theory and we'll prove some things about
+ 
+
+ align:start position:0%
+Theory and we'll prove some things about
+quantum mechanics that would be very
+
+ align:start position:0%
+quantum mechanics that would be very
+ 
+
+ align:start position:0%
+quantum mechanics that would be very
+difficult if we weren't
+
+ align:start position:0%
+difficult if we weren't
+ 
+
+ align:start position:0%
+difficult if we weren't
+using effective field Theory along the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so we'll investigate an effective
+
+ align:start position:0%
+way so we'll investigate an effective
+ 
+
+ align:start position:0%
+way so we'll investigate an effective
+theory that has a naively irrelevant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator that must be
+
+ align:start position:0%
+operator that must be
+ 
+
+ align:start position:0%
+operator that must be
+promoted to being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relevant so by dimensional analysis it
+
+ align:start position:0%
+relevant so by dimensional analysis it
+ 
+
+ align:start position:0%
+relevant so by dimensional analysis it
+would be irrelevant and one way of
+
+ align:start position:0%
+would be irrelevant and one way of
+ 
+
+ align:start position:0%
+would be irrelevant and one way of
+thinking about it is that it just has
+
+ align:start position:0%
+thinking about it is that it just has
+ 
+
+ align:start position:0%
+thinking about it is that it just has
+such a large anomalous Dimension that it
+
+ align:start position:0%
+such a large anomalous Dimension that it
+ 
+
+ align:start position:0%
+such a large anomalous Dimension that it
+actually ends up being totally
+
+ align:start position:0%
+actually ends up being totally
+ 
+
+ align:start position:0%
+actually ends up being totally
+relevant and that is actually not a bad
+
+ align:start position:0%
+relevant and that is actually not a bad
+ 
+
+ align:start position:0%
+relevant and that is actually not a bad
+way of thinking about
+
+ align:start position:0%
+way of thinking about
+ 
+
+ align:start position:0%
+way of thinking about
+it so the example we'll talk
+
+ align:start position:0%
+it so the example we'll talk
+ 
+
+ align:start position:0%
+it so the example we'll talk
+about is something called two
+
+ align:start position:0%
+about is something called two
+ 
+
+ align:start position:0%
+about is something called two
+nucleon non-relativistic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effective field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory so you have two nucleons a
+
+ align:start position:0%
+Theory so you have two nucleons a
+ 
+
+ align:start position:0%
+Theory so you have two nucleons a
+neutron and a proton for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a bottomup effective
+
+ align:start position:0%
+it's a bottomup effective
+ 
+
+ align:start position:0%
+it's a bottomup effective
+Theory we're not going to be thinking
+
+ align:start position:0%
+Theory we're not going to be thinking
+ 
+
+ align:start position:0%
+Theory we're not going to be thinking
+about calculating nucleons in qcd we're
+
+ align:start position:0%
+about calculating nucleons in qcd we're
+ 
+
+ align:start position:0%
+about calculating nucleons in qcd we're
+going to work at momenta that are so
+
+ align:start position:0%
+going to work at momenta that are so
+ 
+
+ align:start position:0%
+going to work at momenta that are so
+small that we actually integrate out the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pon so all exchange particles are
+
+ align:start position:0%
+pon so all exchange particles are
+ 
+
+ align:start position:0%
+pon so all exchange particles are
+integrated out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's nothing to exchange and
+
+ align:start position:0%
+so there's nothing to exchange and
+ 
+
+ align:start position:0%
+so there's nothing to exchange and
+really just have contact type
+
+ align:start position:0%
+really just have contact type
+ 
+
+ align:start position:0%
+really just have contact type
+interactions so something that you might
+
+ align:start position:0%
+interactions so something that you might
+ 
+
+ align:start position:0%
+interactions so something that you might
+think of as like a pine exchange between
+
+ align:start position:0%
+think of as like a pine exchange between
+ 
+
+ align:start position:0%
+think of as like a pine exchange between
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleons that's represented by some
+
+ align:start position:0%
+nucleons that's represented by some
+ 
+
+ align:start position:0%
+nucleons that's represented by some
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+operators between the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleons all right so let me stop there
+
+ align:start position:0%
+nucleons all right so let me stop there
+ 
+
+ align:start position:0%
+nucleons all right so let me stop there
+and we'll come back and talk more about
+
+ align:start position:0%
+and we'll come back and talk more about
+ 
+
+ align:start position:0%
+and we'll come back and talk more about
+this Theory next time and we'll see that
+
+ align:start position:0%
+this Theory next time and we'll see that
+ 
+
+ align:start position:0%
+this Theory next time and we'll see that
+we can first that these operators of
+
+ align:start position:0%
+we can first that these operators of
+ 
+
+ align:start position:0%
+we can first that these operators of
+this type actually can organize some
+
+ align:start position:0%
+this type actually can organize some
+ 
+
+ align:start position:0%
+this type actually can organize some
+facts about quantum mechanics in a very
+
+ align:start position:0%
+facts about quantum mechanics in a very
+ 
+
+ align:start position:0%
+facts about quantum mechanics in a very
+nice way and then we'll see how to think
+
+ align:start position:0%
+nice way and then we'll see how to think
+ 
+
+ align:start position:0%
+nice way and then we'll see how to think
+about fine-tuning from this contact
+
+ align:start position:0%
+about fine-tuning from this contact
+ 
+
+ align:start position:0%
+about fine-tuning from this contact
+interaction
+
+ align:start position:0%
+interaction
+ 
+
+ align:start position:0%
+interaction
+Theory and also how to think about sort
+
+ align:start position:0%
+Theory and also how to think about sort
+ 
+
+ align:start position:0%
+Theory and also how to think about sort
+of how we want to organize the power
+
+ align:start position:0%
+of how we want to organize the power
+ 
+
+ align:start position:0%
+of how we want to organize the power
+counting what's msar say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Etc okay it's kind of a fun thing very
\ No newline at end of file
diff --git a/FCFpaKcpuXQ.txt b/FCFpaKcpuXQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5421c00b660c96da8037db15e3cd3ccc61e5f373
--- /dev/null
+++ b/FCFpaKcpuXQ.txt
@@ -0,0 +1,9827 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license
+
+ align:start position:0%
+a Creative Commons license
+ 
+
+ align:start position:0%
+a Creative Commons license
+your support will help MIT
+
+ align:start position:0%
+your support will help MIT
+ 
+
+ align:start position:0%
+your support will help MIT
+OpenCourseWare continue to offer high
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+ 
+
+ align:start position:0%
+OpenCourseWare continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so welcome back everybody happy to
+
+ align:start position:0%
+okay so welcome back everybody happy to
+ 
+
+ align:start position:0%
+okay so welcome back everybody happy to
+see you again so today we are going to
+
+ align:start position:0%
+see you again so today we are going to
+ 
+
+ align:start position:0%
+see you again so today we are going to
+continue our exploration and understand
+
+ align:start position:0%
+continue our exploration and understand
+ 
+
+ align:start position:0%
+continue our exploration and understand
+a single harmonic oscillator and this is
+
+ align:start position:0%
+a single harmonic oscillator and this is
+ 
+
+ align:start position:0%
+a single harmonic oscillator and this is
+actually our list of our goals and we
+
+ align:start position:0%
+actually our list of our goals and we
+ 
+
+ align:start position:0%
+actually our list of our goals and we
+would like to learn how to translate
+
+ align:start position:0%
+would like to learn how to translate
+ 
+
+ align:start position:0%
+would like to learn how to translate
+physical situations into mathematics so
+
+ align:start position:0%
+physical situations into mathematics so
+ 
+
+ align:start position:0%
+physical situations into mathematics so
+that we can actually solve the physical
+
+ align:start position:0%
+that we can actually solve the physical
+ 
+
+ align:start position:0%
+that we can actually solve the physical
+problems we actually have and predict
+
+ align:start position:0%
+problems we actually have and predict
+ 
+
+ align:start position:0%
+problems we actually have and predict
+what is going to happen up to work and
+
+ align:start position:0%
+what is going to happen up to work and
+ 
+
+ align:start position:0%
+what is going to happen up to work and
+we also sort of started to this course
+
+ align:start position:0%
+we also sort of started to this course
+ 
+
+ align:start position:0%
+we also sort of started to this course
+by solving really simple examples single
+
+ align:start position:0%
+by solving really simple examples single
+ 
+
+ align:start position:0%
+by solving really simple examples single
+harmonic oscillators and as a function
+
+ align:start position:0%
+harmonic oscillators and as a function
+ 
+
+ align:start position:0%
+harmonic oscillators and as a function
+of time you will see that from next
+
+ align:start position:0%
+of time you will see that from next
+ 
+
+ align:start position:0%
+of time you will see that from next
+class the next lecture we are going to
+
+ align:start position:0%
+class the next lecture we are going to
+ 
+
+ align:start position:0%
+class the next lecture we are going to
+bring in more and more objects and of
+
+ align:start position:0%
+bring in more and more objects and of
+ 
+
+ align:start position:0%
+bring in more and more objects and of
+course more of just means more
+
+ align:start position:0%
+course more of just means more
+ 
+
+ align:start position:0%
+course more of just means more
+excitement also in terms of phenomena
+
+ align:start position:0%
+excitement also in terms of phenomena
+ 
+
+ align:start position:0%
+excitement also in terms of phenomena
+were also more complication on the
+
+ align:start position:0%
+were also more complication on the
+ 
+
+ align:start position:0%
+were also more complication on the
+mathematics so so we will see what how
+
+ align:start position:0%
+mathematics so so we will see what how
+ 
+
+ align:start position:0%
+mathematics so so we will see what how
+things goes and then after that we are
+
+ align:start position:0%
+things goes and then after that we are
+ 
+
+ align:start position:0%
+things goes and then after that we are
+going to go to infinite number of
+
+ align:start position:0%
+going to go to infinite number of
+ 
+
+ align:start position:0%
+going to go to infinite number of
+oscillators and to see what happen of
+
+ align:start position:0%
+oscillators and to see what happen of
+ 
+
+ align:start position:0%
+oscillators and to see what happen of
+course we will produce waves that's very
+
+ align:start position:0%
+course we will produce waves that's very
+ 
+
+ align:start position:0%
+course we will produce waves that's very
+exciting then we'll do all kinds of
+
+ align:start position:0%
+exciting then we'll do all kinds of
+ 
+
+ align:start position:0%
+exciting then we'll do all kinds of
+different tricks to to those waves okay
+
+ align:start position:0%
+different tricks to to those waves okay
+ 
+
+ align:start position:0%
+different tricks to to those waves okay
+so what we have we learned last time so
+
+ align:start position:0%
+so what we have we learned last time so
+ 
+
+ align:start position:0%
+so what we have we learned last time so
+last time we hang over example a simple
+
+ align:start position:0%
+last time we hang over example a simple
+ 
+
+ align:start position:0%
+last time we hang over example a simple
+harmonic oscillator it says your rod
+
+ align:start position:0%
+harmonic oscillator it says your rod
+ 
+
+ align:start position:0%
+harmonic oscillator it says your rod
+fixed on the wall and you can actually
+
+ align:start position:0%
+fixed on the wall and you can actually
+ 
+
+ align:start position:0%
+fixed on the wall and you can actually
+go back and forth and we also introduced
+
+ align:start position:0%
+go back and forth and we also introduced
+ 
+
+ align:start position:0%
+go back and forth and we also introduced
+a model of the drag force or track
+
+ align:start position:0%
+a model of the drag force or track
+ 
+
+ align:start position:0%
+a model of the drag force or track
+torque and this is actually proportional
+
+ align:start position:0%
+torque and this is actually proportional
+ 
+
+ align:start position:0%
+torque and this is actually proportional
+to the velocity of the motion of the
+
+ align:start position:0%
+to the velocity of the motion of the
+ 
+
+ align:start position:0%
+to the velocity of the motion of the
+single particle and the interesting
+
+ align:start position:0%
+single particle and the interesting
+ 
+
+ align:start position:0%
+single particle and the interesting
+thing we learned last time is that we
+
+ align:start position:0%
+thing we learned last time is that we
+ 
+
+ align:start position:0%
+thing we learned last time is that we
+have three
+
+ align:start position:0%
+have three
+ 
+
+ align:start position:0%
+have three
+completely different behaviors if we
+
+ align:start position:0%
+completely different behaviors if we
+ 
+
+ align:start position:0%
+completely different behaviors if we
+actually turn on the track force the
+
+ align:start position:0%
+actually turn on the track force the
+ 
+
+ align:start position:0%
+actually turn on the track force the
+first one is under damped the temp temp
+
+ align:start position:0%
+first one is under damped the temp temp
+ 
+
+ align:start position:0%
+first one is under damped the temp temp
+in usage is very small then we have the
+
+ align:start position:0%
+in usage is very small then we have the
+ 
+
+ align:start position:0%
+in usage is very small then we have the
+solution in this form is oscillating the
+
+ align:start position:0%
+solution in this form is oscillating the
+ 
+
+ align:start position:0%
+solution in this form is oscillating the
+amplitude is decaying exponentially and
+
+ align:start position:0%
+amplitude is decaying exponentially and
+ 
+
+ align:start position:0%
+amplitude is decaying exponentially and
+we as we increase and greet as we make
+
+ align:start position:0%
+we as we increase and greet as we make
+ 
+
+ align:start position:0%
+we as we increase and greet as we make
+the drag force larger and larger you
+
+ align:start position:0%
+the drag force larger and larger you
+ 
+
+ align:start position:0%
+the drag force larger and larger you
+will pass a critical point which
+
+ align:start position:0%
+will pass a critical point which
+ 
+
+ align:start position:0%
+will pass a critical point which
+actually give you a solution which you
+
+ align:start position:0%
+actually give you a solution which you
+ 
+
+ align:start position:0%
+actually give you a solution which you
+don't have oscillation anymore the
+
+ align:start position:0%
+don't have oscillation anymore the
+ 
+
+ align:start position:0%
+don't have oscillation anymore the
+cosine disappeared finally if you use
+
+ align:start position:0%
+cosine disappeared finally if you use
+ 
+
+ align:start position:0%
+cosine disappeared finally if you use
+you actually put a whole system into
+
+ align:start position:0%
+you actually put a whole system into
+ 
+
+ align:start position:0%
+you actually put a whole system into
+water or introduce something really
+
+ align:start position:0%
+water or introduce something really
+ 
+
+ align:start position:0%
+water or introduce something really
+dramatic very big drag force then you
+
+ align:start position:0%
+dramatic very big drag force then you
+ 
+
+ align:start position:0%
+dramatic very big drag force then you
+have over temp situation and you see
+
+ align:start position:0%
+have over temp situation and you see
+ 
+
+ align:start position:0%
+have over temp situation and you see
+that the solution is actually a sum of
+
+ align:start position:0%
+that the solution is actually a sum of
+ 
+
+ align:start position:0%
+that the solution is actually a sum of
+two exponential function so this is
+
+ align:start position:0%
+two exponential function so this is
+ 
+
+ align:start position:0%
+two exponential function so this is
+actually the one equation which actually
+
+ align:start position:0%
+actually the one equation which actually
+ 
+
+ align:start position:0%
+actually the one equation which actually
+works for all the tempte system we
+
+ align:start position:0%
+works for all the tempte system we
+ 
+
+ align:start position:0%
+works for all the tempte system we
+discuss up to now and that is actually
+
+ align:start position:0%
+discuss up to now and that is actually
+ 
+
+ align:start position:0%
+discuss up to now and that is actually
+the map basically if gamma goes to zero
+
+ align:start position:0%
+the map basically if gamma goes to zero
+ 
+
+ align:start position:0%
+the map basically if gamma goes to zero
+gamma Z should control the size of the
+
+ align:start position:0%
+gamma Z should control the size of the
+ 
+
+ align:start position:0%
+gamma Z should control the size of the
+drag force then we got no tamping then
+
+ align:start position:0%
+drag force then we got no tamping then
+ 
+
+ align:start position:0%
+drag force then we got no tamping then
+you have a pure simple harmonic motion
+
+ align:start position:0%
+you have a pure simple harmonic motion
+ 
+
+ align:start position:0%
+you have a pure simple harmonic motion
+and as we increase the gamma then you
+
+ align:start position:0%
+and as we increase the gamma then you
+ 
+
+ align:start position:0%
+and as we increase the gamma then you
+can see that the behavior is changing as
+
+ align:start position:0%
+can see that the behavior is changing as
+ 
+
+ align:start position:0%
+can see that the behavior is changing as
+we increase the gamma so you can see
+
+ align:start position:0%
+we increase the gamma so you can see
+ 
+
+ align:start position:0%
+we increase the gamma so you can see
+that we can use a quat quantity which is
+
+ align:start position:0%
+that we can use a quat quantity which is
+ 
+
+ align:start position:0%
+that we can use a quat quantity which is
+called Q q is actually defined as a
+
+ align:start position:0%
+called Q q is actually defined as a
+ 
+
+ align:start position:0%
+called Q q is actually defined as a
+ratio of Omega zero which is actually
+
+ align:start position:0%
+ratio of Omega zero which is actually
+ 
+
+ align:start position:0%
+ratio of Omega zero which is actually
+the natural frequency angular frequency
+
+ align:start position:0%
+the natural frequency angular frequency
+ 
+
+ align:start position:0%
+the natural frequency angular frequency
+of the system okay
+
+ align:start position:0%
+of the system okay
+ 
+
+ align:start position:0%
+of the system okay
+and gamma is actually a measure of how
+
+ align:start position:0%
+and gamma is actually a measure of how
+ 
+
+ align:start position:0%
+and gamma is actually a measure of how
+big the track force is if we make a
+
+ align:start position:0%
+big the track force is if we make a
+ 
+
+ align:start position:0%
+big the track force is if we make a
+ratio of these two quantity then you
+
+ align:start position:0%
+ratio of these two quantity then you
+ 
+
+ align:start position:0%
+ratio of these two quantity then you
+will see that at Q equal to point five
+
+ align:start position:0%
+will see that at Q equal to point five
+ 
+
+ align:start position:0%
+will see that at Q equal to point five
+it reach a critical point which actually
+
+ align:start position:0%
+it reach a critical point which actually
+ 
+
+ align:start position:0%
+it reach a critical point which actually
+hold the behavior ball whole system
+
+ align:start position:0%
+hold the behavior ball whole system
+ 
+
+ align:start position:0%
+hold the behavior ball whole system
+changed and you can see that the
+
+ align:start position:0%
+changed and you can see that the
+ 
+
+ align:start position:0%
+changed and you can see that the
+oscillation completely disappeared
+
+ align:start position:0%
+oscillation completely disappeared
+ 
+
+ align:start position:0%
+oscillation completely disappeared
+okay so that is actually what we have
+
+ align:start position:0%
+okay so that is actually what we have
+ 
+
+ align:start position:0%
+okay so that is actually what we have
+learned last time so what are we going
+
+ align:start position:0%
+learned last time so what are we going
+ 
+
+ align:start position:0%
+learned last time so what are we going
+to do today we have been really doing
+
+ align:start position:0%
+to do today we have been really doing
+ 
+
+ align:start position:0%
+to do today we have been really doing
+experiment really without our hands and
+
+ align:start position:0%
+experiment really without our hands and
+ 
+
+ align:start position:0%
+experiment really without our hands and
+Sun right so basically we we prepare the
+
+ align:start position:0%
+Sun right so basically we we prepare the
+ 
+
+ align:start position:0%
+Sun right so basically we we prepare the
+system then we release it then we don't
+
+ align:start position:0%
+system then we release it then we don't
+ 
+
+ align:start position:0%
+system then we release it then we don't
+touch it again and see how this system
+
+ align:start position:0%
+touch it again and see how this system
+ 
+
+ align:start position:0%
+touch it again and see how this system
+actually evolve as a function of time
+
+ align:start position:0%
+actually evolve as a function of time
+ 
+
+ align:start position:0%
+actually evolve as a function of time
+all right so that's actually what we
+
+ align:start position:0%
+all right so that's actually what we
+ 
+
+ align:start position:0%
+all right so that's actually what we
+have been doing so today what we are
+
+ align:start position:0%
+have been doing so today what we are
+ 
+
+ align:start position:0%
+have been doing so today what we are
+going to do is to start to drive this
+
+ align:start position:0%
+going to do is to start to drive this
+ 
+
+ align:start position:0%
+going to do is to start to drive this
+system okay we can introduce some some
+
+ align:start position:0%
+system okay we can introduce some some
+ 
+
+ align:start position:0%
+system okay we can introduce some some
+kind of driving force and see what how
+
+ align:start position:0%
+kind of driving force and see what how
+ 
+
+ align:start position:0%
+kind of driving force and see what how
+this system will respond to this
+
+ align:start position:0%
+this system will respond to this
+ 
+
+ align:start position:0%
+this system will respond to this
+external force okay so that is actually
+
+ align:start position:0%
+external force okay so that is actually
+ 
+
+ align:start position:0%
+external force okay so that is actually
+what we are going to do and that now
+
+ align:start position:0%
+what we are going to do and that now
+ 
+
+ align:start position:0%
+what we are going to do and that now
+will bring us to the situation of tempt
+
+ align:start position:0%
+will bring us to the situation of tempt
+ 
+
+ align:start position:0%
+will bring us to the situation of tempt
+driven harmonic oscillator okay so
+
+ align:start position:0%
+driven harmonic oscillator okay so
+ 
+
+ align:start position:0%
+driven harmonic oscillator okay so
+that's immediately get started so we
+
+ align:start position:0%
+that's immediately get started so we
+ 
+
+ align:start position:0%
+that's immediately get started so we
+will use the example which we went
+
+ align:start position:0%
+will use the example which we went
+ 
+
+ align:start position:0%
+will use the example which we went
+through last time as a starting point
+
+ align:start position:0%
+through last time as a starting point
+ 
+
+ align:start position:0%
+through last time as a starting point
+so it's a example from the last lecture
+
+ align:start position:0%
+so it's a example from the last lecture
+ 
+
+ align:start position:0%
+so it's a example from the last lecture
+is a lot which is a fix on the wall and
+
+ align:start position:0%
+is a lot which is a fix on the wall and
+ 
+
+ align:start position:0%
+is a lot which is a fix on the wall and
+the length of this rod is a over two and
+
+ align:start position:0%
+the length of this rod is a over two and
+ 
+
+ align:start position:0%
+the length of this rod is a over two and
+I define a contact hunter clockwise
+
+ align:start position:0%
+I define a contact hunter clockwise
+ 
+
+ align:start position:0%
+I define a contact hunter clockwise
+direction to be positive and I measure
+
+ align:start position:0%
+direction to be positive and I measure
+ 
+
+ align:start position:0%
+direction to be positive and I measure
+the position of the rod by this Seeta
+
+ align:start position:0%
+the position of the rod by this Seeta
+ 
+
+ align:start position:0%
+the position of the rod by this Seeta
+which is the angle between the vertical
+
+ align:start position:0%
+which is the angle between the vertical
+ 
+
+ align:start position:0%
+which is the angle between the vertical
+direction and the pointing direction of
+
+ align:start position:0%
+direction and the pointing direction of
+ 
+
+ align:start position:0%
+direction and the pointing direction of
+the rod okay and we have went through
+
+ align:start position:0%
+the rod okay and we have went through
+ 
+
+ align:start position:0%
+the rod okay and we have went through
+the mass and we got the equation of
+
+ align:start position:0%
+the mass and we got the equation of
+ 
+
+ align:start position:0%
+the mass and we got the equation of
+motion without external force which is
+
+ align:start position:0%
+motion without external force which is
+ 
+
+ align:start position:0%
+motion without external force which is
+already show another blackboard so now
+
+ align:start position:0%
+already show another blackboard so now
+ 
+
+ align:start position:0%
+already show another blackboard so now
+as I mentioned in the beginning I would
+
+ align:start position:0%
+as I mentioned in the beginning I would
+ 
+
+ align:start position:0%
+as I mentioned in the beginning I would
+like to add a driving force or stator
+
+ align:start position:0%
+like to add a driving force or stator
+ 
+
+ align:start position:0%
+like to add a driving force or stator
+driving torque power drive okay this is
+
+ align:start position:0%
+driving torque power drive okay this is
+ 
+
+ align:start position:0%
+driving torque power drive okay this is
+equal to the zero cosine Omega T key
+
+ align:start position:0%
+equal to the zero cosine Omega T key
+ 
+
+ align:start position:0%
+equal to the zero cosine Omega T key
+okay so I'm adding a driving force with
+
+ align:start position:0%
+okay so I'm adding a driving force with
+ 
+
+ align:start position:0%
+okay so I'm adding a driving force with
+driving power
+
+ align:start position:0%
+driving power
+ 
+
+ align:start position:0%
+driving power
+the amplitude with the torque is
+
+ align:start position:0%
+the amplitude with the torque is
+ 
+
+ align:start position:0%
+the amplitude with the torque is
+actually d0 okay and it's actually also
+
+ align:start position:0%
+actually d0 okay and it's actually also
+ 
+
+ align:start position:0%
+actually d0 okay and it's actually also
+a harmonic oscillator force or fork and
+
+ align:start position:0%
+a harmonic oscillator force or fork and
+ 
+
+ align:start position:0%
+a harmonic oscillator force or fork and
+the frequency the angular frequency of
+
+ align:start position:0%
+the frequency the angular frequency of
+ 
+
+ align:start position:0%
+the frequency the angular frequency of
+this torque is only omega D okay and
+
+ align:start position:0%
+this torque is only omega D okay and
+ 
+
+ align:start position:0%
+this torque is only omega D okay and
+that means our total torque tau of T
+
+ align:start position:0%
+that means our total torque tau of T
+ 
+
+ align:start position:0%
+that means our total torque tau of T
+will be equal to tau G T this is
+
+ align:start position:0%
+will be equal to tau G T this is
+ 
+
+ align:start position:0%
+will be equal to tau G T this is
+actually coming from the gravitational
+
+ align:start position:0%
+actually coming from the gravitational
+ 
+
+ align:start position:0%
+actually coming from the gravitational
+force plus tau drag which is a song for
+
+ align:start position:0%
+force plus tau drag which is a song for
+ 
+
+ align:start position:0%
+force plus tau drag which is a song for
+the drag force and and also this time I
+
+ align:start position:0%
+the drag force and and also this time I
+ 
+
+ align:start position:0%
+the drag force and and also this time I
+we are adding in at outdrive okay so I'm
+
+ align:start position:0%
+we are adding in at outdrive okay so I'm
+ 
+
+ align:start position:0%
+we are adding in at outdrive okay so I'm
+not going to go over all the calculation
+
+ align:start position:0%
+not going to go over all the calculation
+ 
+
+ align:start position:0%
+not going to go over all the calculation
+how to derive from the beginning to the
+
+ align:start position:0%
+how to derive from the beginning to the
+ 
+
+ align:start position:0%
+how to derive from the beginning to the
+end but I will just continue from what
+
+ align:start position:0%
+end but I will just continue from what
+ 
+
+ align:start position:0%
+end but I will just continue from what
+we actually start the last time so if I
+
+ align:start position:0%
+we actually start the last time so if I
+ 
+
+ align:start position:0%
+we actually start the last time so if I
+have additional driving torque there
+
+ align:start position:0%
+have additional driving torque there
+ 
+
+ align:start position:0%
+have additional driving torque there
+that means my equation of motion will be
+
+ align:start position:0%
+that means my equation of motion will be
+ 
+
+ align:start position:0%
+that means my equation of motion will be
+slightly modified this time my equation
+
+ align:start position:0%
+slightly modified this time my equation
+ 
+
+ align:start position:0%
+slightly modified this time my equation
+of motion will become theta double dot
+
+ align:start position:0%
+of motion will become theta double dot
+ 
+
+ align:start position:0%
+of motion will become theta double dot
+plus gamma theta dot plus Omega 0 square
+
+ align:start position:0%
+plus gamma theta dot plus Omega 0 square
+ 
+
+ align:start position:0%
+plus gamma theta dot plus Omega 0 square
+theta and that is equal to t0 divided by
+
+ align:start position:0%
+theta and that is equal to t0 divided by
+ 
+
+ align:start position:0%
+theta and that is equal to t0 divided by
+I okay this is actually divided by I
+
+ align:start position:0%
+I okay this is actually divided by I
+ 
+
+ align:start position:0%
+I okay this is actually divided by I
+because in order to get a serration I
+
+ align:start position:0%
+because in order to get a serration I
+ 
+
+ align:start position:0%
+because in order to get a serration I
+need to divide my torque by a moment of
+
+ align:start position:0%
+need to divide my torque by a moment of
+ 
+
+ align:start position:0%
+need to divide my torque by a moment of
+inertia of this system and cosine Omega
+
+ align:start position:0%
+inertia of this system and cosine Omega
+ 
+
+ align:start position:0%
+inertia of this system and cosine Omega
+T this is actually the oscillating
+
+ align:start position:0%
+T this is actually the oscillating
+ 
+
+ align:start position:0%
+T this is actually the oscillating
+frequency of the driving torque okay
+
+ align:start position:0%
+frequency of the driving torque okay
+ 
+
+ align:start position:0%
+frequency of the driving torque okay
+and the just a reminder gamma is equal
+
+ align:start position:0%
+and the just a reminder gamma is equal
+ 
+
+ align:start position:0%
+and the just a reminder gamma is equal
+to find two to be equal to 3b over and L
+
+ align:start position:0%
+to find two to be equal to 3b over and L
+ 
+
+ align:start position:0%
+to find two to be equal to 3b over and L
+square and the Omega zero is actually
+
+ align:start position:0%
+square and the Omega zero is actually
+ 
+
+ align:start position:0%
+square and the Omega zero is actually
+defined to be square root of 3G or but
+
+ align:start position:0%
+defined to be square root of 3G or but
+ 
+
+ align:start position:0%
+defined to be square root of 3G or but
+well okay so as I mentioned in the
+
+ align:start position:0%
+well okay so as I mentioned in the
+ 
+
+ align:start position:0%
+well okay so as I mentioned in the
+beginning this is actually giving you a
+
+ align:start position:0%
+beginning this is actually giving you a
+ 
+
+ align:start position:0%
+beginning this is actually giving you a
+sense of the size of the drag force
+
+ align:start position:0%
+sense of the size of the drag force
+ 
+
+ align:start position:0%
+sense of the size of the drag force
+and the right hand side oh my god did ro
+
+ align:start position:0%
+and the right hand side oh my god did ro
+ 
+
+ align:start position:0%
+and the right hand side oh my god did ro
+is actually the nature and group
+
+ align:start position:0%
+is actually the nature and group
+ 
+
+ align:start position:0%
+is actually the nature and group
+frequency okay so of course we can
+
+ align:start position:0%
+frequency okay so of course we can
+ 
+
+ align:start position:0%
+frequency okay so of course we can
+actually simplify this by replacing this
+
+ align:start position:0%
+actually simplify this by replacing this
+ 
+
+ align:start position:0%
+actually simplify this by replacing this
+turn at this constant by a pink bow so
+
+ align:start position:0%
+turn at this constant by a pink bow so
+ 
+
+ align:start position:0%
+turn at this constant by a pink bow so
+the simple I'm choosing is f0 okay and
+
+ align:start position:0%
+the simple I'm choosing is f0 okay and
+ 
+
+ align:start position:0%
+the simple I'm choosing is f0 okay and
+this is defined would be a t0 divided by
+
+ align:start position:0%
+this is defined would be a t0 divided by
+ 
+
+ align:start position:0%
+this is defined would be a t0 divided by
+I okay
+
+ align:start position:0%
+I okay
+ 
+
+ align:start position:0%
+I okay
+therefore I arrive my final equation of
+
+ align:start position:0%
+therefore I arrive my final equation of
+ 
+
+ align:start position:0%
+therefore I arrive my final equation of
+motion Sita double dot plus gamma theta
+
+ align:start position:0%
+motion Sita double dot plus gamma theta
+ 
+
+ align:start position:0%
+motion Sita double dot plus gamma theta
+dot plus Omega 0 square Sita and that is
+
+ align:start position:0%
+dot plus Omega 0 square Sita and that is
+ 
+
+ align:start position:0%
+dot plus Omega 0 square Sita and that is
+equal to f0 cosine Omega T P okay so I
+
+ align:start position:0%
+equal to f0 cosine Omega T P okay so I
+ 
+
+ align:start position:0%
+equal to f0 cosine Omega T P okay so I
+hope this looks pretty straightforward
+
+ align:start position:0%
+hope this looks pretty straightforward
+ 
+
+ align:start position:0%
+hope this looks pretty straightforward
+to you so this is our equation of motion
+
+ align:start position:0%
+to you so this is our equation of motion
+ 
+
+ align:start position:0%
+to you so this is our equation of motion
+you can see from this slide so we have
+
+ align:start position:0%
+you can see from this slide so we have
+ 
+
+ align:start position:0%
+you can see from this slide so we have
+three turns in addition to the theta
+
+ align:start position:0%
+three turns in addition to the theta
+ 
+
+ align:start position:0%
+three turns in addition to the theta
+double dot the first one is actually
+
+ align:start position:0%
+double dot the first one is actually
+ 
+
+ align:start position:0%
+double dot the first one is actually
+related to drag force or drag torque the
+
+ align:start position:0%
+related to drag force or drag torque the
+ 
+
+ align:start position:0%
+related to drag force or drag torque the
+second one is actually related to
+
+ align:start position:0%
+second one is actually related to
+ 
+
+ align:start position:0%
+second one is actually related to
+so-called spring force right so that is
+
+ align:start position:0%
+so-called spring force right so that is
+ 
+
+ align:start position:0%
+so-called spring force right so that is
+actually related to the spring constant
+
+ align:start position:0%
+actually related to the spring constant
+ 
+
+ align:start position:0%
+actually related to the spring constant
+or you know because of the restoring
+
+ align:start position:0%
+or you know because of the restoring
+ 
+
+ align:start position:0%
+or you know because of the restoring
+force of the occupational force okay the
+
+ align:start position:0%
+force of the occupational force okay the
+ 
+
+ align:start position:0%
+force of the occupational force okay the
+third one is actually what we just
+
+ align:start position:0%
+third one is actually what we just
+ 
+
+ align:start position:0%
+third one is actually what we just
+adding is a driving force okay
+
+ align:start position:0%
+adding is a driving force okay
+ 
+
+ align:start position:0%
+adding is a driving force okay
+so one question which I would like to
+
+ align:start position:0%
+so one question which I would like to
+ 
+
+ align:start position:0%
+so one question which I would like to
+ask you is okay so now I bring one more
+
+ align:start position:0%
+ask you is okay so now I bring one more
+ 
+
+ align:start position:0%
+ask you is okay so now I bring one more
+complication to this system so now I'm
+
+ align:start position:0%
+complication to this system so now I'm
+ 
+
+ align:start position:0%
+complication to this system so now I'm
+out driving this system with a different
+
+ align:start position:0%
+out driving this system with a different
+ 
+
+ align:start position:0%
+out driving this system with a different
+frequency which is omega D the question
+
+ align:start position:0%
+frequency which is omega D the question
+ 
+
+ align:start position:0%
+frequency which is omega D the question
+is what would be the rerouting
+
+ align:start position:0%
+is what would be the rerouting
+ 
+
+ align:start position:0%
+is what would be the rerouting
+oscillation frequency of this driven
+
+ align:start position:0%
+oscillation frequency of this driven
+ 
+
+ align:start position:0%
+oscillation frequency of this driven
+harmonic oscillator what is going to
+
+ align:start position:0%
+harmonic oscillator what is going to
+ 
+
+ align:start position:0%
+harmonic oscillator what is going to
+happen well this system actually follow
+
+ align:start position:0%
+happen well this system actually follow
+ 
+
+ align:start position:0%
+happen well this system actually follow
+the original tempt oscillator frequency
+
+ align:start position:0%
+the original tempt oscillator frequency
+ 
+
+ align:start position:0%
+the original tempt oscillator frequency
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+which is actually close to Omega zero or
+
+ align:start position:0%
+which is actually close to Omega zero or
+ 
+
+ align:start position:0%
+which is actually close to Omega zero or
+where this system as we follow that try
+
+ align:start position:0%
+where this system as we follow that try
+ 
+
+ align:start position:0%
+where this system as we follow that try
+to enforce frequency finally maybe this
+
+ align:start position:0%
+to enforce frequency finally maybe this
+ 
+
+ align:start position:0%
+to enforce frequency finally maybe this
+system choose to do something in between
+
+ align:start position:0%
+system choose to do something in between
+ 
+
+ align:start position:0%
+system choose to do something in between
+we don't know what is going to happen
+
+ align:start position:0%
+we don't know what is going to happen
+ 
+
+ align:start position:0%
+we don't know what is going to happen
+okay so our job today is to solve this
+
+ align:start position:0%
+okay so our job today is to solve this
+ 
+
+ align:start position:0%
+okay so our job today is to solve this
+equation of motion and see what we can
+
+ align:start position:0%
+equation of motion and see what we can
+ 
+
+ align:start position:0%
+equation of motion and see what we can
+learn from the mathematics then actually
+
+ align:start position:0%
+learn from the mathematics then actually
+ 
+
+ align:start position:0%
+learn from the mathematics then actually
+we can actually care for the check or
+
+ align:start position:0%
+we can actually care for the check or
+ 
+
+ align:start position:0%
+we can actually care for the check or
+those results to see if that agrees with
+
+ align:start position:0%
+those results to see if that agrees with
+ 
+
+ align:start position:0%
+those results to see if that agrees with
+the experimental result which through
+
+ align:start position:0%
+the experimental result which through
+ 
+
+ align:start position:0%
+the experimental result which through
+those pay demos okay so as usual I have
+
+ align:start position:0%
+those pay demos okay so as usual I have
+ 
+
+ align:start position:0%
+those pay demos okay so as usual I have
+this equation of motion here so one
+
+ align:start position:0%
+this equation of motion here so one
+ 
+
+ align:start position:0%
+this equation of motion here so one
+trick which I have been using is to come
+
+ align:start position:0%
+trick which I have been using is to come
+ 
+
+ align:start position:0%
+trick which I have been using is to come
+go to complex notation right therefore I
+
+ align:start position:0%
+go to complex notation right therefore I
+ 
+
+ align:start position:0%
+go to complex notation right therefore I
+can now rewrite this thing to be Z
+
+ align:start position:0%
+can now rewrite this thing to be Z
+ 
+
+ align:start position:0%
+can now rewrite this thing to be Z
+double dot plus gamma Z dot plus Omega 0
+
+ align:start position:0%
+double dot plus gamma Z dot plus Omega 0
+ 
+
+ align:start position:0%
+double dot plus gamma Z dot plus Omega 0
+square 3 and that is equal to f0
+
+ align:start position:0%
+square 3 and that is equal to f0
+ 
+
+ align:start position:0%
+square 3 and that is equal to f0
+exponential I Omega T T okay so
+
+ align:start position:0%
+exponential I Omega T T okay so
+ 
+
+ align:start position:0%
+exponential I Omega T T okay so
+basically I just go to the complex
+
+ align:start position:0%
+basically I just go to the complex
+ 
+
+ align:start position:0%
+basically I just go to the complex
+notation and we would like to solve this
+
+ align:start position:0%
+notation and we would like to solve this
+ 
+
+ align:start position:0%
+notation and we would like to solve this
+equation so in order to solve this
+
+ align:start position:0%
+equation so in order to solve this
+ 
+
+ align:start position:0%
+equation so in order to solve this
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+I make cast a test function I guess Z of
+
+ align:start position:0%
+I make cast a test function I guess Z of
+ 
+
+ align:start position:0%
+I make cast a test function I guess Z of
+T have this functional form this is
+
+ align:start position:0%
+T have this functional form this is
+ 
+
+ align:start position:0%
+T have this functional form this is
+equal to a some kind of amplitude ok
+
+ align:start position:0%
+equal to a some kind of amplitude ok
+ 
+
+ align:start position:0%
+equal to a some kind of amplitude ok
+exponential I Omega DT minus Delta Delta
+
+ align:start position:0%
+exponential I Omega DT minus Delta Delta
+ 
+
+ align:start position:0%
+exponential I Omega DT minus Delta Delta
+is actually some kind of angle which is
+
+ align:start position:0%
+is actually some kind of angle which is
+ 
+
+ align:start position:0%
+is actually some kind of angle which is
+actually to account for the possible
+
+ align:start position:0%
+actually to account for the possible
+ 
+
+ align:start position:0%
+actually to account for the possible
+delay of the system okay so so if I
+
+ align:start position:0%
+delay of the system okay so so if I
+ 
+
+ align:start position:0%
+delay of the system okay so so if I
+start to type for example this is a
+
+ align:start position:0%
+start to type for example this is a
+ 
+
+ align:start position:0%
+start to type for example this is a
+system which I'm interested I start to
+
+ align:start position:0%
+system which I'm interested I start to
+ 
+
+ align:start position:0%
+system which I'm interested I start to
+drive this system it may take some time
+
+ align:start position:0%
+drive this system it may take some time
+ 
+
+ align:start position:0%
+drive this system it may take some time
+for the system to react to your driving
+
+ align:start position:0%
+for the system to react to your driving
+ 
+
+ align:start position:0%
+for the system to react to your driving
+force right so that's actually accounted
+
+ align:start position:0%
+force right so that's actually accounted
+ 
+
+ align:start position:0%
+force right so that's actually accounted
+for by this Delta constant okay
+
+ align:start position:0%
+for by this Delta constant okay
+ 
+
+ align:start position:0%
+for by this Delta constant okay
+and the amplitude is actually what we
+
+ align:start position:0%
+and the amplitude is actually what we
+ 
+
+ align:start position:0%
+and the amplitude is actually what we
+were wondering what will be the
+
+ align:start position:0%
+were wondering what will be the
+ 
+
+ align:start position:0%
+were wondering what will be the
+amplitude therefore you have some kind
+
+ align:start position:0%
+amplitude therefore you have some kind
+ 
+
+ align:start position:0%
+amplitude therefore you have some kind
+of constant in front of the exponential
+
+ align:start position:0%
+of constant in front of the exponential
+ 
+
+ align:start position:0%
+of constant in front of the exponential
+function and you can see that this
+
+ align:start position:0%
+function and you can see that this
+ 
+
+ align:start position:0%
+function and you can see that this
+exponential is actually having angular
+
+ align:start position:0%
+exponential is actually having angular
+ 
+
+ align:start position:0%
+exponential is actually having angular
+frequency Omega T and that is actually
+
+ align:start position:0%
+frequency Omega T and that is actually
+ 
+
+ align:start position:0%
+frequency Omega T and that is actually
+designed to actually to cancel this
+
+ align:start position:0%
+designed to actually to cancel this
+ 
+
+ align:start position:0%
+designed to actually to cancel this
+exponential I Omega DT here in new track
+
+ align:start position:0%
+exponential I Omega DT here in new track
+ 
+
+ align:start position:0%
+exponential I Omega DT here in new track
+force okay so now we can actually
+
+ align:start position:0%
+force okay so now we can actually
+ 
+
+ align:start position:0%
+force okay so now we can actually
+calculate what the dot of T will be
+
+ align:start position:0%
+calculate what the dot of T will be
+ 
+
+ align:start position:0%
+calculate what the dot of T will be
+equal to I Omega D Z Z double dot T will
+
+ align:start position:0%
+equal to I Omega D Z Z double dot T will
+ 
+
+ align:start position:0%
+equal to I Omega D Z Z double dot T will
+be equal to minus Omega T squared C okay
+
+ align:start position:0%
+be equal to minus Omega T squared C okay
+ 
+
+ align:start position:0%
+be equal to minus Omega T squared C okay
+it's DOS we can now plug the back into
+
+ align:start position:0%
+it's DOS we can now plug the back into
+ 
+
+ align:start position:0%
+it's DOS we can now plug the back into
+this equation of motion and I see what
+
+ align:start position:0%
+this equation of motion and I see what
+ 
+
+ align:start position:0%
+this equation of motion and I see what
+we can as you learn from there okay so
+
+ align:start position:0%
+we can as you learn from there okay so
+ 
+
+ align:start position:0%
+we can as you learn from there okay so
+basically what I'm going to is to insert
+
+ align:start position:0%
+basically what I'm going to is to insert
+ 
+
+ align:start position:0%
+basically what I'm going to is to insert
+all those things back into the equation
+
+ align:start position:0%
+all those things back into the equation
+ 
+
+ align:start position:0%
+all those things back into the equation
+of motion and that is actually going to
+
+ align:start position:0%
+of motion and that is actually going to
+ 
+
+ align:start position:0%
+of motion and that is actually going to
+be like this basically the first time
+
+ align:start position:0%
+be like this basically the first time
+ 
+
+ align:start position:0%
+be like this basically the first time
+the double dot you get a minus Omega T
+
+ align:start position:0%
+the double dot you get a minus Omega T
+ 
+
+ align:start position:0%
+the double dot you get a minus Omega T
+Square out of it the second term gamma Z
+
+ align:start position:0%
+Square out of it the second term gamma Z
+ 
+
+ align:start position:0%
+Square out of it the second term gamma Z
+dot I have the g'tok here basically I
+
+ align:start position:0%
+dot I have the g'tok here basically I
+ 
+
+ align:start position:0%
+dot I have the g'tok here basically I
+will get plus I Omega D gamma out of
+
+ align:start position:0%
+will get plus I Omega D gamma out of
+ 
+
+ align:start position:0%
+will get plus I Omega D gamma out of
+this the second turn the certain I get
+
+ align:start position:0%
+this the second turn the certain I get
+ 
+
+ align:start position:0%
+this the second turn the certain I get
+omega 0 square out of it and that is
+
+ align:start position:0%
+omega 0 square out of it and that is
+ 
+
+ align:start position:0%
+omega 0 square out of it and that is
+actually multiplied by Z and this is
+
+ align:start position:0%
+actually multiplied by Z and this is
+ 
+
+ align:start position:0%
+actually multiplied by Z and this is
+equal to f0 exponential I Omega DT okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and we also know from this
+
+ align:start position:0%
+all right and we also know from this
+ 
+
+ align:start position:0%
+all right and we also know from this
+expression okay Z is equal to a
+
+ align:start position:0%
+expression okay Z is equal to a
+ 
+
+ align:start position:0%
+expression okay Z is equal to a
+exponential I Omega DT minus Delta
+
+ align:start position:0%
+exponential I Omega DT minus Delta
+ 
+
+ align:start position:0%
+exponential I Omega DT minus Delta
+that's the tester function so this is
+
+ align:start position:0%
+that's the tester function so this is
+ 
+
+ align:start position:0%
+that's the tester function so this is
+actually equal to a exponential I Omega
+
+ align:start position:0%
+actually equal to a exponential I Omega
+ 
+
+ align:start position:0%
+actually equal to a exponential I Omega
+DT minus Delta okay so now what I can do
+
+ align:start position:0%
+DT minus Delta okay so now what I can do
+ 
+
+ align:start position:0%
+DT minus Delta okay so now what I can do
+you say huh I have some kind of some
+
+ align:start position:0%
+you say huh I have some kind of some
+ 
+
+ align:start position:0%
+you say huh I have some kind of some
+constant in the front multiplied by
+
+ align:start position:0%
+constant in the front multiplied by
+ 
+
+ align:start position:0%
+constant in the front multiplied by
+exponential I Omega DT and now I can
+
+ align:start position:0%
+exponential I Omega DT and now I can
+ 
+
+ align:start position:0%
+exponential I Omega DT and now I can
+actually cancel this exponential I Omega
+
+ align:start position:0%
+actually cancel this exponential I Omega
+ 
+
+ align:start position:0%
+actually cancel this exponential I Omega
+DT with the right hand side turn very
+
+ align:start position:0%
+DT with the right hand side turn very
+ 
+
+ align:start position:0%
+DT with the right hand side turn very
+good the whole system is actually the
+
+ align:start position:0%
+good the whole system is actually the
+ 
+
+ align:start position:0%
+good the whole system is actually the
+whole equation is actually exponential
+
+ align:start position:0%
+whole equation is actually exponential
+ 
+
+ align:start position:0%
+whole equation is actually exponential
+free right okay now I don't have any
+
+ align:start position:0%
+free right okay now I don't have any
+ 
+
+ align:start position:0%
+free right okay now I don't have any
+exponential function left and
+
+ align:start position:0%
+exponential function left and
+ 
+
+ align:start position:0%
+exponential function left and
+exponential I Delta si should be just a
+
+ align:start position:0%
+exponential I Delta si should be just a
+ 
+
+ align:start position:0%
+exponential I Delta si should be just a
+constant so it's actually now this
+
+ align:start position:0%
+constant so it's actually now this
+ 
+
+ align:start position:0%
+constant so it's actually now this
+equation is actually independent of time
+
+ align:start position:0%
+equation is actually independent of time
+ 
+
+ align:start position:0%
+equation is actually independent of time
+okay so what I'm getting is like this
+
+ align:start position:0%
+okay so what I'm getting is like this
+ 
+
+ align:start position:0%
+okay so what I'm getting is like this
+specially if I multiply both side by
+
+ align:start position:0%
+specially if I multiply both side by
+ 
+
+ align:start position:0%
+specially if I multiply both side by
+exponential I Delta then I get minus
+
+ align:start position:0%
+exponential I Delta then I get minus
+ 
+
+ align:start position:0%
+exponential I Delta then I get minus
+Omega T squared plus I Omega DT plus
+
+ align:start position:0%
+Omega T squared plus I Omega DT plus
+ 
+
+ align:start position:0%
+Omega T squared plus I Omega DT plus
+Omega 0 square a and this is going to be
+
+ align:start position:0%
+Omega 0 square a and this is going to be
+ 
+
+ align:start position:0%
+Omega 0 square a and this is going to be
+equal to F exponential I Delta because I
+
+ align:start position:0%
+equal to F exponential I Delta because I
+ 
+
+ align:start position:0%
+equal to F exponential I Delta because I
+multiply both side by exponential I
+
+ align:start position:0%
+multiply both side by exponential I
+ 
+
+ align:start position:0%
+multiply both side by exponential I
+Delta okay and this is equal to F cosine
+
+ align:start position:0%
+Delta okay and this is equal to F cosine
+ 
+
+ align:start position:0%
+Delta okay and this is equal to F cosine
+theta plus I sine Delta just use the
+
+ align:start position:0%
+theta plus I sine Delta just use the
+ 
+
+ align:start position:0%
+theta plus I sine Delta just use the
+Euler's equation okay any questions so
+
+ align:start position:0%
+Euler's equation okay any questions so
+ 
+
+ align:start position:0%
+Euler's equation okay any questions so
+far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so look at what I have been doing
+
+ align:start position:0%
+okay so look at what I have been doing
+ 
+
+ align:start position:0%
+okay so look at what I have been doing
+so I have this equation of motion a
+
+ align:start position:0%
+so I have this equation of motion a
+ 
+
+ align:start position:0%
+so I have this equation of motion a
+studio I go to complex notation then I
+
+ align:start position:0%
+studio I go to complex notation then I
+ 
+
+ align:start position:0%
+studio I go to complex notation then I
+guess Z equal to a exponential I Omega
+
+ align:start position:0%
+guess Z equal to a exponential I Omega
+ 
+
+ align:start position:0%
+guess Z equal to a exponential I Omega
+DT minus Delta because my friends from
+
+ align:start position:0%
+DT minus Delta because my friends from
+ 
+
+ align:start position:0%
+DT minus Delta because my friends from
+the math department already stopped this
+
+ align:start position:0%
+the math department already stopped this
+ 
+
+ align:start position:0%
+the math department already stopped this
+and I'm just following it okay then I
+
+ align:start position:0%
+and I'm just following it okay then I
+ 
+
+ align:start position:0%
+and I'm just following it okay then I
+can calculate all those turns plug them
+
+ align:start position:0%
+can calculate all those turns plug them
+ 
+
+ align:start position:0%
+can calculate all those turns plug them
+in and the end the basically you will
+
+ align:start position:0%
+in and the end the basically you will
+ 
+
+ align:start position:0%
+in and the end the basically you will
+arrive this equation okay
+
+ align:start position:0%
+arrive this equation okay
+ 
+
+ align:start position:0%
+arrive this equation okay
+this equation is a complex equation
+
+ align:start position:0%
+this equation is a complex equation
+ 
+
+ align:start position:0%
+this equation is a complex equation
+right so what does that mean
+
+ align:start position:0%
+right so what does that mean
+ 
+
+ align:start position:0%
+right so what does that mean
+that means one equation is equal to two
+
+ align:start position:0%
+that means one equation is equal to two
+ 
+
+ align:start position:0%
+that means one equation is equal to two
+equation right because you have the real
+
+ align:start position:0%
+equation right because you have the real
+ 
+
+ align:start position:0%
+equation right because you have the real
+part you have the imagery part okay
+
+ align:start position:0%
+part you have the imagery part okay
+ 
+
+ align:start position:0%
+part you have the imagery part okay
+therefore that's very nice because I
+
+ align:start position:0%
+therefore that's very nice because I
+ 
+
+ align:start position:0%
+therefore that's very nice because I
+have two unknown the first one is a
+
+ align:start position:0%
+have two unknown the first one is a
+ 
+
+ align:start position:0%
+have two unknown the first one is a
+constant and the second one is Delta now
+
+ align:start position:0%
+constant and the second one is Delta now
+ 
+
+ align:start position:0%
+constant and the second one is Delta now
+I have two equations I can solve what
+
+ align:start position:0%
+I have two equations I can solve what
+ 
+
+ align:start position:0%
+I have two equations I can solve what
+would be the functional form for a and
+
+ align:start position:0%
+would be the functional form for a and
+ 
+
+ align:start position:0%
+would be the functional form for a and
+the tota and let me go immediately solve
+
+ align:start position:0%
+the tota and let me go immediately solve
+ 
+
+ align:start position:0%
+the tota and let me go immediately solve
+this equation so if I take the real part
+
+ align:start position:0%
+this equation so if I take the real part
+ 
+
+ align:start position:0%
+this equation so if I take the real part
+a real part front from this equation
+
+ align:start position:0%
+a real part front from this equation
+ 
+
+ align:start position:0%
+a real part front from this equation
+basically what I'm going to get is Omega
+
+ align:start position:0%
+basically what I'm going to get is Omega
+ 
+
+ align:start position:0%
+basically what I'm going to get is Omega
+0 Square this is the this video minus
+
+ align:start position:0%
+0 Square this is the this video minus
+ 
+
+ align:start position:0%
+0 Square this is the this video minus
+Omega T squared okay this is real
+
+ align:start position:0%
+Omega T squared okay this is real
+ 
+
+ align:start position:0%
+Omega T squared okay this is real
+times a is HD sound real number okay
+
+ align:start position:0%
+times a is HD sound real number okay
+ 
+
+ align:start position:0%
+times a is HD sound real number okay
+this is a should equal to F cosine f0 so
+
+ align:start position:0%
+this is a should equal to F cosine f0 so
+ 
+
+ align:start position:0%
+this is a should equal to F cosine f0 so
+I missed a 0 here okay so there are 0 I
+
+ align:start position:0%
+I missed a 0 here okay so there are 0 I
+ 
+
+ align:start position:0%
+I missed a 0 here okay so there are 0 I
+missed okay
+
+ align:start position:0%
+missed okay
+ 
+
+ align:start position:0%
+missed okay
+he should be F 0 ok f0 cosine Delta ok
+
+ align:start position:0%
+he should be F 0 ok f0 cosine Delta ok
+ 
+
+ align:start position:0%
+he should be F 0 ok f0 cosine Delta ok
+and I can also call that all the turns
+
+ align:start position:0%
+and I can also call that all the turns
+ 
+
+ align:start position:0%
+and I can also call that all the turns
+which is imaginary turns then I get only
+
+ align:start position:0%
+which is imaginary turns then I get only
+ 
+
+ align:start position:0%
+which is imaginary turns then I get only
+the second turn from the left hand side
+
+ align:start position:0%
+the second turn from the left hand side
+ 
+
+ align:start position:0%
+the second turn from the left hand side
+is with the I in front of it right
+
+ align:start position:0%
+is with the I in front of it right
+ 
+
+ align:start position:0%
+is with the I in front of it right
+therefore I get Omega T gamma a ok
+
+ align:start position:0%
+therefore I get Omega T gamma a ok
+ 
+
+ align:start position:0%
+therefore I get Omega T gamma a ok
+follow
+
+ align:start position:0%
+follow
+ 
+
+ align:start position:0%
+follow
+up and lap inside and the from the
+
+ align:start position:0%
+up and lap inside and the from the
+ 
+
+ align:start position:0%
+up and lap inside and the from the
+right-hand side is only one imaginary
+
+ align:start position:0%
+right-hand side is only one imaginary
+ 
+
+ align:start position:0%
+right-hand side is only one imaginary
+turn therefore I get this is equal to f0
+
+ align:start position:0%
+turn therefore I get this is equal to f0
+ 
+
+ align:start position:0%
+turn therefore I get this is equal to f0
+sine Delta okay so now I have two
+
+ align:start position:0%
+sine Delta okay so now I have two
+ 
+
+ align:start position:0%
+sine Delta okay so now I have two
+equations I have two unknowns therefore
+
+ align:start position:0%
+equations I have two unknowns therefore
+ 
+
+ align:start position:0%
+equations I have two unknowns therefore
+I can easily solve a and the Delta okay
+
+ align:start position:0%
+I can easily solve a and the Delta okay
+ 
+
+ align:start position:0%
+I can easily solve a and the Delta okay
+so I call this equation number one I
+
+ align:start position:0%
+so I call this equation number one I
+ 
+
+ align:start position:0%
+so I call this equation number one I
+call this equation number two so now I
+
+ align:start position:0%
+call this equation number two so now I
+ 
+
+ align:start position:0%
+call this equation number two so now I
+can sound them in quadrature the two
+
+ align:start position:0%
+can sound them in quadrature the two
+ 
+
+ align:start position:0%
+can sound them in quadrature the two
+equation in portraiture a Latins I will
+
+ align:start position:0%
+equation in portraiture a Latins I will
+ 
+
+ align:start position:0%
+equation in portraiture a Latins I will
+give you a square Omega 0 square minus
+
+ align:start position:0%
+give you a square Omega 0 square minus
+ 
+
+ align:start position:0%
+give you a square Omega 0 square minus
+Omega T squared squared plus Omega t
+
+ align:start position:0%
+Omega T squared squared plus Omega t
+ 
+
+ align:start position:0%
+Omega T squared squared plus Omega t
+square gamma square that essentially
+
+ align:start position:0%
+square gamma square that essentially
+ 
+
+ align:start position:0%
+square gamma square that essentially
+coming from on the second equation okay
+
+ align:start position:0%
+coming from on the second equation okay
+ 
+
+ align:start position:0%
+coming from on the second equation okay
+now give you the lapin side is just a
+
+ align:start position:0%
+now give you the lapin side is just a
+ 
+
+ align:start position:0%
+now give you the lapin side is just a
+square root a square Sun a square the
+
+ align:start position:0%
+square root a square Sun a square the
+ 
+
+ align:start position:0%
+square root a square Sun a square the
+sound of the first day and second
+
+ align:start position:0%
+sound of the first day and second
+ 
+
+ align:start position:0%
+sound of the first day and second
+equation ok and the right hand side will
+
+ align:start position:0%
+equation ok and the right hand side will
+ 
+
+ align:start position:0%
+equation ok and the right hand side will
+become F 0 square cosine Delta cosine
+
+ align:start position:0%
+become F 0 square cosine Delta cosine
+ 
+
+ align:start position:0%
+become F 0 square cosine Delta cosine
+squared theta plus sine squared Delta
+
+ align:start position:0%
+squared theta plus sine squared Delta
+ 
+
+ align:start position:0%
+squared theta plus sine squared Delta
+okay and this is actually equal to 1
+
+ align:start position:0%
+okay and this is actually equal to 1
+ 
+
+ align:start position:0%
+okay and this is actually equal to 1
+alright so that's actually the trick to
+
+ align:start position:0%
+alright so that's actually the trick to
+ 
+
+ align:start position:0%
+alright so that's actually the trick to
+get rid of Delta okay
+
+ align:start position:0%
+get rid of Delta okay
+ 
+
+ align:start position:0%
+get rid of Delta okay
+then I can get what will be the
+
+ align:start position:0%
+then I can get what will be the
+ 
+
+ align:start position:0%
+then I can get what will be the
+resulting a a should be a function of
+
+ align:start position:0%
+resulting a a should be a function of
+ 
+
+ align:start position:0%
+resulting a a should be a function of
+Omega T ok Omega T is given okay to you
+
+ align:start position:0%
+Omega T ok Omega T is given okay to you
+ 
+
+ align:start position:0%
+Omega T ok Omega T is given okay to you
+it's actually determined by you right
+
+ align:start position:0%
+it's actually determined by you right
+ 
+
+ align:start position:0%
+it's actually determined by you right
+how how free as you want to oscillate
+
+ align:start position:0%
+how how free as you want to oscillate
+ 
+
+ align:start position:0%
+how how free as you want to oscillate
+this system ok and this is equal to f0
+
+ align:start position:0%
+this system ok and this is equal to f0
+ 
+
+ align:start position:0%
+this system ok and this is equal to f0
+divided by square root of this whole
+
+ align:start position:0%
+divided by square root of this whole
+ 
+
+ align:start position:0%
+divided by square root of this whole
+thing right so this will give you Omega
+
+ align:start position:0%
+thing right so this will give you Omega
+ 
+
+ align:start position:0%
+thing right so this will give you Omega
+0 square minus Omega T Square
+
+ align:start position:0%
+0 square minus Omega T Square
+ 
+
+ align:start position:0%
+0 square minus Omega T Square
+squared plus Omega P square gamma square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then we can also calculate what
+
+ align:start position:0%
+okay then we can also calculate what
+ 
+
+ align:start position:0%
+okay then we can also calculate what
+will be the Delta the trick is to take a
+
+ align:start position:0%
+will be the Delta the trick is to take a
+ 
+
+ align:start position:0%
+will be the Delta the trick is to take a
+ratio between equation number two and
+
+ align:start position:0%
+ratio between equation number two and
+ 
+
+ align:start position:0%
+ratio between equation number two and
+the equation number one 2/1 basically
+
+ align:start position:0%
+the equation number one 2/1 basically
+ 
+
+ align:start position:0%
+the equation number one 2/1 basically
+you will get tangent
+
+ align:start position:0%
+you will get tangent
+ 
+
+ align:start position:0%
+you will get tangent
+dorota right this is scientific if I
+
+ align:start position:0%
+dorota right this is scientific if I
+ 
+
+ align:start position:0%
+dorota right this is scientific if I
+cosign right f zero actually cancel
+
+ align:start position:0%
+cosign right f zero actually cancel
+ 
+
+ align:start position:0%
+cosign right f zero actually cancel
+right and this is equal to what equal to
+
+ align:start position:0%
+right and this is equal to what equal to
+ 
+
+ align:start position:0%
+right and this is equal to what equal to
+the ratio of these two strands right
+
+ align:start position:0%
+the ratio of these two strands right
+ 
+
+ align:start position:0%
+the ratio of these two strands right
+after you take the ratio eight job oh
+
+ align:start position:0%
+after you take the ratio eight job oh
+ 
+
+ align:start position:0%
+after you take the ratio eight job oh
+right basically what you get is gamma
+
+ align:start position:0%
+right basically what you get is gamma
+ 
+
+ align:start position:0%
+right basically what you get is gamma
+Omega T divided by Omega zero squared
+
+ align:start position:0%
+Omega T divided by Omega zero squared
+ 
+
+ align:start position:0%
+Omega T divided by Omega zero squared
+minus Omega T squared okay so we have
+
+ align:start position:0%
+minus Omega T squared okay so we have
+ 
+
+ align:start position:0%
+minus Omega T squared okay so we have
+solved a and Delta through this exercise
+
+ align:start position:0%
+solved a and Delta through this exercise
+ 
+
+ align:start position:0%
+solved a and Delta through this exercise
+okay so what does that mean originally I
+
+ align:start position:0%
+okay so what does that mean originally I
+ 
+
+ align:start position:0%
+okay so what does that mean originally I
+assumed my solution to be a exponential
+
+ align:start position:0%
+assumed my solution to be a exponential
+ 
+
+ align:start position:0%
+assumed my solution to be a exponential
+I Omega DT minus Delta right therefore I
+
+ align:start position:0%
+I Omega DT minus Delta right therefore I
+ 
+
+ align:start position:0%
+I Omega DT minus Delta right therefore I
+would like to go back to the the real
+
+ align:start position:0%
+would like to go back to the the real
+ 
+
+ align:start position:0%
+would like to go back to the the real
+world which is a theta right so
+
+ align:start position:0%
+world which is a theta right so
+ 
+
+ align:start position:0%
+world which is a theta right so
+basically if I take the real part I will
+
+ align:start position:0%
+basically if I take the real part I will
+ 
+
+ align:start position:0%
+basically if I take the real part I will
+get theta of T which is actually the
+
+ align:start position:0%
+get theta of T which is actually the
+ 
+
+ align:start position:0%
+get theta of T which is actually the
+real part of Z okay and that will give
+
+ align:start position:0%
+real part of Z okay and that will give
+ 
+
+ align:start position:0%
+real part of Z okay and that will give
+you a Omega T cosine Omega T t minus
+
+ align:start position:0%
+you a Omega T cosine Omega T t minus
+ 
+
+ align:start position:0%
+you a Omega T cosine Omega T t minus
+theta is also a function of Omega T okay
+
+ align:start position:0%
+theta is also a function of Omega T okay
+ 
+
+ align:start position:0%
+theta is also a function of Omega T okay
+so we have done this exercise and you
+
+ align:start position:0%
+so we have done this exercise and you
+ 
+
+ align:start position:0%
+so we have done this exercise and you
+can see that the first thing which we
+
+ align:start position:0%
+can see that the first thing which we
+ 
+
+ align:start position:0%
+can see that the first thing which we
+see here is that there's no free
+
+ align:start position:0%
+see here is that there's no free
+ 
+
+ align:start position:0%
+see here is that there's no free
+parameter from this solution
+
+ align:start position:0%
+parameter from this solution
+ 
+
+ align:start position:0%
+parameter from this solution
+right a is decided by Omega T and Delta
+
+ align:start position:0%
+right a is decided by Omega T and Delta
+ 
+
+ align:start position:0%
+right a is decided by Omega T and Delta
+is also decided by Omega T there's a lot
+
+ align:start position:0%
+is also decided by Omega T there's a lot
+ 
+
+ align:start position:0%
+is also decided by Omega T there's a lot
+of mass but actually we have over condos
+
+ align:start position:0%
+of mass but actually we have over condos
+ 
+
+ align:start position:0%
+of mass but actually we have over condos
+and we have the solution
+
+ align:start position:0%
+and we have the solution
+ 
+
+ align:start position:0%
+and we have the solution
+but the ad says you clear to you that
+
+ align:start position:0%
+but the ad says you clear to you that
+ 
+
+ align:start position:0%
+but the ad says you clear to you that
+this cannot be the full story right
+
+ align:start position:0%
+this cannot be the full story right
+ 
+
+ align:start position:0%
+this cannot be the full story right
+because you have a second order
+
+ align:start position:0%
+because you have a second order
+ 
+
+ align:start position:0%
+because you have a second order
+differential equation you need to have
+
+ align:start position:0%
+differential equation you need to have
+ 
+
+ align:start position:0%
+differential equation you need to have
+two free parameters in the solution okay
+
+ align:start position:0%
+two free parameters in the solution okay
+ 
+
+ align:start position:0%
+two free parameters in the solution okay
+what is actually missing anybody can
+
+ align:start position:0%
+what is actually missing anybody can
+ 
+
+ align:start position:0%
+what is actually missing anybody can
+tell me what is missing is very good the
+
+ align:start position:0%
+tell me what is missing is very good the
+ 
+
+ align:start position:0%
+tell me what is missing is very good the
+homogeneous solution is missing okay so
+
+ align:start position:0%
+homogeneous solution is missing okay so
+ 
+
+ align:start position:0%
+homogeneous solution is missing okay so
+that's issue why we actually have no pre
+
+ align:start position:0%
+that's issue why we actually have no pre
+ 
+
+ align:start position:0%
+that's issue why we actually have no pre
+parameter here once the Omega T is
+
+ align:start position:0%
+parameter here once the Omega T is
+ 
+
+ align:start position:0%
+parameter here once the Omega T is
+determined once the f0 is given then you
+
+ align:start position:0%
+determined once the f0 is given then you
+ 
+
+ align:start position:0%
+determined once the f0 is given then you
+have the functional form which decide
+
+ align:start position:0%
+have the functional form which decide
+ 
+
+ align:start position:0%
+have the functional form which decide
+what is actually C okay so what
+
+ align:start position:0%
+what is actually C okay so what
+ 
+
+ align:start position:0%
+what is actually C okay so what
+essentially the for solution for full
+
+ align:start position:0%
+essentially the for solution for full
+ 
+
+ align:start position:0%
+essentially the for solution for full
+solution should be as you said a
+
+ align:start position:0%
+solution should be as you said a
+ 
+
+ align:start position:0%
+solution should be as you said a
+combination of homogeneous solution and
+
+ align:start position:0%
+combination of homogeneous solution and
+ 
+
+ align:start position:0%
+combination of homogeneous solution and
+the particular solution which we as we
+
+ align:start position:0%
+the particular solution which we as we
+ 
+
+ align:start position:0%
+the particular solution which we as we
+got here so if I prepare the system to
+
+ align:start position:0%
+got here so if I prepare the system to
+ 
+
+ align:start position:0%
+got here so if I prepare the system to
+be in a situation of for example under
+
+ align:start position:0%
+be in a situation of for example under
+ 
+
+ align:start position:0%
+be in a situation of for example under
+damped situation okay then what I'm
+
+ align:start position:0%
+damped situation okay then what I'm
+ 
+
+ align:start position:0%
+damped situation okay then what I'm
+going to do is actually pretty simple
+
+ align:start position:0%
+going to do is actually pretty simple
+ 
+
+ align:start position:0%
+going to do is actually pretty simple
+what I am going to do is to just to copy
+
+ align:start position:0%
+what I am going to do is to just to copy
+ 
+
+ align:start position:0%
+what I am going to do is to just to copy
+the under damped as a solution from last
+
+ align:start position:0%
+the under damped as a solution from last
+ 
+
+ align:start position:0%
+the under damped as a solution from last
+lecture and combine that with my
+
+ align:start position:0%
+lecture and combine that with my
+ 
+
+ align:start position:0%
+lecture and combine that with my
+particular solution which are obtained
+
+ align:start position:0%
+particular solution which are obtained
+ 
+
+ align:start position:0%
+particular solution which are obtained
+here okay so that's actually see what is
+
+ align:start position:0%
+here okay so that's actually see what is
+ 
+
+ align:start position:0%
+here okay so that's actually see what is
+issue the full solution looks like so I
+
+ align:start position:0%
+issue the full solution looks like so I
+ 
+
+ align:start position:0%
+issue the full solution looks like so I
+have a Omega D cosine Omega DT minus
+
+ align:start position:0%
+have a Omega D cosine Omega DT minus
+ 
+
+ align:start position:0%
+have a Omega D cosine Omega DT minus
+delta is omega T it's a function of
+
+ align:start position:0%
+delta is omega T it's a function of
+ 
+
+ align:start position:0%
+delta is omega T it's a function of
+Omega T okay this is actually does
+
+ align:start position:0%
+Omega T okay this is actually does
+ 
+
+ align:start position:0%
+Omega T okay this is actually does
+so-called a steady stay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution okay and of course as you
+
+ align:start position:0%
+solution okay and of course as you
+ 
+
+ align:start position:0%
+solution okay and of course as you
+mentioned I need to also add the
+
+ align:start position:0%
+mentioned I need to also add the
+ 
+
+ align:start position:0%
+mentioned I need to also add the
+homogeneous solution and basically that
+
+ align:start position:0%
+homogeneous solution and basically that
+ 
+
+ align:start position:0%
+homogeneous solution and basically that
+decision according to what I wrote there
+
+ align:start position:0%
+decision according to what I wrote there
+ 
+
+ align:start position:0%
+decision according to what I wrote there
+have a functional form of exponential a
+
+ align:start position:0%
+have a functional form of exponential a
+ 
+
+ align:start position:0%
+have a functional form of exponential a
+exponential minus gamma over 2t cosine
+
+ align:start position:0%
+exponential minus gamma over 2t cosine
+ 
+
+ align:start position:0%
+exponential minus gamma over 2t cosine
+Omega T plus alpha so I change a to be
+
+ align:start position:0%
+Omega T plus alpha so I change a to be
+ 
+
+ align:start position:0%
+Omega T plus alpha so I change a to be
+because I already have the a there just
+
+ align:start position:0%
+because I already have the a there just
+ 
+
+ align:start position:0%
+because I already have the a there just
+to avoid confusion okay the basis you
+
+ align:start position:0%
+to avoid confusion okay the basis you
+ 
+
+ align:start position:0%
+to avoid confusion okay the basis you
+get P exponential minus gamma over 2t
+
+ align:start position:0%
+get P exponential minus gamma over 2t
+ 
+
+ align:start position:0%
+get P exponential minus gamma over 2t
+cosine Omega T plus alpha
+
+ align:start position:0%
+cosine Omega T plus alpha
+ 
+
+ align:start position:0%
+cosine Omega T plus alpha
+okay crazy D there are two three
+
+ align:start position:0%
+okay crazy D there are two three
+ 
+
+ align:start position:0%
+okay crazy D there are two three
+parameters a B and alpha those two three
+
+ align:start position:0%
+parameters a B and alpha those two three
+ 
+
+ align:start position:0%
+parameters a B and alpha those two three
+parameters can be determined by initial
+
+ align:start position:0%
+parameters can be determined by initial
+ 
+
+ align:start position:0%
+parameters can be determined by initial
+conditions okay so for example initially
+
+ align:start position:0%
+conditions okay so for example initially
+ 
+
+ align:start position:0%
+conditions okay so for example initially
+I I actually release the rod and some
+
+ align:start position:0%
+I I actually release the rod and some
+ 
+
+ align:start position:0%
+I I actually release the rod and some
+fixed angle of Sita initial and also the
+
+ align:start position:0%
+fixed angle of Sita initial and also the
+ 
+
+ align:start position:0%
+fixed angle of Sita initial and also the
+initial velocity is zero then I can
+
+ align:start position:0%
+initial velocity is zero then I can
+ 
+
+ align:start position:0%
+initial velocity is zero then I can
+actually practice solution in using
+
+ align:start position:0%
+actually practice solution in using
+ 
+
+ align:start position:0%
+actually practice solution in using
+those initial conditions to solve P and
+
+ align:start position:0%
+those initial conditions to solve P and
+ 
+
+ align:start position:0%
+those initial conditions to solve P and
+alpha okay any questions so far
+
+ align:start position:0%
+alpha okay any questions so far
+ 
+
+ align:start position:0%
+alpha okay any questions so far
+yes yeah iein assuming it's under damp
+
+ align:start position:0%
+yes yeah iein assuming it's under damp
+ 
+
+ align:start position:0%
+yes yeah iein assuming it's under damp
+to situation okay so that's an
+
+ align:start position:0%
+to situation okay so that's an
+ 
+
+ align:start position:0%
+to situation okay so that's an
+assumption so if if the it depends on
+
+ align:start position:0%
+assumption so if if the it depends on
+ 
+
+ align:start position:0%
+assumption so if if the it depends on
+the size of gamma and Omega zero right
+
+ align:start position:0%
+the size of gamma and Omega zero right
+ 
+
+ align:start position:0%
+the size of gamma and Omega zero right
+then you actually have actually four
+
+ align:start position:0%
+then you actually have actually four
+ 
+
+ align:start position:0%
+then you actually have actually four
+different kinds of solution right if
+
+ align:start position:0%
+different kinds of solution right if
+ 
+
+ align:start position:0%
+different kinds of solution right if
+gamma is equal to zero then what you are
+
+ align:start position:0%
+gamma is equal to zero then what you are
+ 
+
+ align:start position:0%
+gamma is equal to zero then what you are
+going to plug in is the solution from no
+
+ align:start position:0%
+going to plug in is the solution from no
+ 
+
+ align:start position:0%
+going to plug in is the solution from no
+damping as you were homogeneous solution
+
+ align:start position:0%
+damping as you were homogeneous solution
+ 
+
+ align:start position:0%
+damping as you were homogeneous solution
+okay and then you if you prepare this
+
+ align:start position:0%
+okay and then you if you prepare this
+ 
+
+ align:start position:0%
+okay and then you if you prepare this
+system under water
+
+ align:start position:0%
+system under water
+ 
+
+ align:start position:0%
+system under water
+you know damping's color so it is huge
+
+ align:start position:0%
+you know damping's color so it is huge
+ 
+
+ align:start position:0%
+you know damping's color so it is huge
+then you actually plug in the over
+
+ align:start position:0%
+then you actually plug in the over
+ 
+
+ align:start position:0%
+then you actually plug in the over
+damped solution to be your homogeneous
+
+ align:start position:0%
+damped solution to be your homogeneous
+ 
+
+ align:start position:0%
+damped solution to be your homogeneous
+part of the solution
+
+ align:start position:0%
+part of the solution
+ 
+
+ align:start position:0%
+part of the solution
+okay any other questions very good
+
+ align:start position:0%
+okay any other questions very good
+ 
+
+ align:start position:0%
+okay any other questions very good
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+okay so now maybe you got confused a bit
+
+ align:start position:0%
+okay so now maybe you got confused a bit
+ 
+
+ align:start position:0%
+okay so now maybe you got confused a bit
+right I have now Omega T I have also
+
+ align:start position:0%
+right I have now Omega T I have also
+ 
+
+ align:start position:0%
+right I have now Omega T I have also
+Omega and these are another one we just
+
+ align:start position:0%
+Omega and these are another one we just
+ 
+
+ align:start position:0%
+Omega and these are another one we just
+called Omega zero what are they what are
+
+ align:start position:0%
+called Omega zero what are they what are
+ 
+
+ align:start position:0%
+called Omega zero what are they what are
+those right
+
+ align:start position:0%
+those right
+ 
+
+ align:start position:0%
+those right
+so Omega zero is the nature angular
+
+ align:start position:0%
+so Omega zero is the nature angular
+ 
+
+ align:start position:0%
+so Omega zero is the nature angular
+frequency without even the track force
+
+ align:start position:0%
+frequency without even the track force
+ 
+
+ align:start position:0%
+frequency without even the track force
+okay if you remove everything just like
+
+ align:start position:0%
+okay if you remove everything just like
+ 
+
+ align:start position:0%
+okay if you remove everything just like
+you know without considering any drag
+
+ align:start position:0%
+you know without considering any drag
+ 
+
+ align:start position:0%
+you know without considering any drag
+force as a child and naturally the
+
+ align:start position:0%
+force as a child and naturally the
+ 
+
+ align:start position:0%
+force as a child and naturally the
+natural frequency of the system and what
+
+ align:start position:0%
+natural frequency of the system and what
+ 
+
+ align:start position:0%
+natural frequency of the system and what
+is Omega Omega according to that
+
+ align:start position:0%
+is Omega Omega according to that
+ 
+
+ align:start position:0%
+is Omega Omega according to that
+function okay Omega is defined to be
+
+ align:start position:0%
+function okay Omega is defined to be
+ 
+
+ align:start position:0%
+function okay Omega is defined to be
+Omega square minus gamma square over
+
+ align:start position:0%
+Omega square minus gamma square over
+ 
+
+ align:start position:0%
+Omega square minus gamma square over
+fourth square do though that that
+
+ align:start position:0%
+fourth square do though that that
+ 
+
+ align:start position:0%
+fourth square do though that that
+essentially the oscillation frequency
+
+ align:start position:0%
+essentially the oscillation frequency
+ 
+
+ align:start position:0%
+essentially the oscillation frequency
+which way I should discuss last lecture
+
+ align:start position:0%
+which way I should discuss last lecture
+ 
+
+ align:start position:0%
+which way I should discuss last lecture
+after you add drag force into the gap
+
+ align:start position:0%
+after you add drag force into the gap
+ 
+
+ align:start position:0%
+after you add drag force into the gap
+okay finally Omega T is how fast you
+
+ align:start position:0%
+okay finally Omega T is how fast you
+ 
+
+ align:start position:0%
+okay finally Omega T is how fast you
+actually type this system okay so that
+
+ align:start position:0%
+actually type this system okay so that
+ 
+
+ align:start position:0%
+actually type this system okay so that
+is actually the definition of these
+
+ align:start position:0%
+is actually the definition of these
+ 
+
+ align:start position:0%
+is actually the definition of these
+three omegas okay so you can see that if
+
+ align:start position:0%
+three omegas okay so you can see that if
+ 
+
+ align:start position:0%
+three omegas okay so you can see that if
+I prepare my solution to be in under
+
+ align:start position:0%
+I prepare my solution to be in under
+ 
+
+ align:start position:0%
+I prepare my solution to be in under
+template situation then basically you
+
+ align:start position:0%
+template situation then basically you
+ 
+
+ align:start position:0%
+template situation then basically you
+see that this is actually so-called
+
+ align:start position:0%
+see that this is actually so-called
+ 
+
+ align:start position:0%
+see that this is actually so-called
+steady state solution because the a
+
+ align:start position:0%
+steady state solution because the a
+ 
+
+ align:start position:0%
+steady state solution because the a
+Omega D is a constant so it's going to
+
+ align:start position:0%
+Omega D is a constant so it's going to
+ 
+
+ align:start position:0%
+Omega D is a constant so it's going to
+be there forever right and the second
+
+ align:start position:0%
+be there forever right and the second
+ 
+
+ align:start position:0%
+be there forever right and the second
+second time is actually P exponential
+
+ align:start position:0%
+second time is actually P exponential
+ 
+
+ align:start position:0%
+second time is actually P exponential
+minus gamma over 2t it's decaying as a
+
+ align:start position:0%
+minus gamma over 2t it's decaying as a
+ 
+
+ align:start position:0%
+minus gamma over 2t it's decaying as a
+function of time so if you are patient
+
+ align:start position:0%
+function of time so if you are patient
+ 
+
+ align:start position:0%
+function of time so if you are patient
+enough you wait then this will be gone
+
+ align:start position:0%
+enough you wait then this will be gone
+ 
+
+ align:start position:0%
+enough you wait then this will be gone
+right okay so that is actually how we
+
+ align:start position:0%
+right okay so that is actually how we
+ 
+
+ align:start position:0%
+right okay so that is actually how we
+actually understand this mathematical
+
+ align:start position:0%
+actually understand this mathematical
+ 
+
+ align:start position:0%
+actually understand this mathematical
+result and then of course you can
+
+ align:start position:0%
+result and then of course you can
+ 
+
+ align:start position:0%
+result and then of course you can
+actually take a look at this this is
+
+ align:start position:0%
+actually take a look at this this is
+ 
+
+ align:start position:0%
+actually take a look at this this is
+actually just assuming some kind of
+
+ align:start position:0%
+actually just assuming some kind of
+ 
+
+ align:start position:0%
+actually just assuming some kind of
+initial condition and Prague in the
+
+ align:start position:0%
+initial condition and Prague in the
+ 
+
+ align:start position:0%
+initial condition and Prague in the
+solution and profit as a function of
+
+ align:start position:0%
+solution and profit as a function of
+ 
+
+ align:start position:0%
+solution and profit as a function of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay and you can see that this function
+
+ align:start position:0%
+okay and you can see that this function
+ 
+
+ align:start position:0%
+okay and you can see that this function
+looks really weird look a bit surprising
+
+ align:start position:0%
+looks really weird look a bit surprising
+ 
+
+ align:start position:0%
+looks really weird look a bit surprising
+what does that mean right looks really
+
+ align:start position:0%
+what does that mean right looks really
+ 
+
+ align:start position:0%
+what does that mean right looks really
+strange but at some point this
+
+ align:start position:0%
+strange but at some point this
+ 
+
+ align:start position:0%
+strange but at some point this
+superposition of this to function
+
+ align:start position:0%
+superposition of this to function
+ 
+
+ align:start position:0%
+superposition of this to function
+because one of the function H Street
+
+ align:start position:0%
+because one of the function H Street
+ 
+
+ align:start position:0%
+because one of the function H Street
+dies out disappear
+
+ align:start position:0%
+dies out disappear
+ 
+
+ align:start position:0%
+dies out disappear
+then you will see that huh if you wait
+
+ align:start position:0%
+then you will see that huh if you wait
+ 
+
+ align:start position:0%
+then you will see that huh if you wait
+long enough then you actually only see a
+
+ align:start position:0%
+long enough then you actually only see a
+ 
+
+ align:start position:0%
+long enough then you actually only see a
+very simple structure which is
+
+ align:start position:0%
+very simple structure which is
+ 
+
+ align:start position:0%
+very simple structure which is
+oscillation frequency of Omega T and
+
+ align:start position:0%
+oscillation frequency of Omega T and
+ 
+
+ align:start position:0%
+oscillation frequency of Omega T and
+that means at large T okay the in the
+
+ align:start position:0%
+that means at large T okay the in the
+ 
+
+ align:start position:0%
+that means at large T okay the in the
+beginning the system will not like it
+
+ align:start position:0%
+beginning the system will not like it
+ 
+
+ align:start position:0%
+beginning the system will not like it
+you drive it and little system turn like
+
+ align:start position:0%
+you drive it and little system turn like
+ 
+
+ align:start position:0%
+you drive it and little system turn like
+it like if I go and strike you in the
+
+ align:start position:0%
+it like if I go and strike you in the
+ 
+
+ align:start position:0%
+it like if I go and strike you in the
+beginning you would not like it right
+
+ align:start position:0%
+beginning you would not like it right
+ 
+
+ align:start position:0%
+beginning you would not like it right
+maybe and if I shake it long enough and
+
+ align:start position:0%
+maybe and if I shake it long enough and
+ 
+
+ align:start position:0%
+maybe and if I shake it long enough and
+come on okay fine I accept that okay so
+
+ align:start position:0%
+come on okay fine I accept that okay so
+ 
+
+ align:start position:0%
+come on okay fine I accept that okay so
+that is actually what is going to happen
+
+ align:start position:0%
+that is actually what is going to happen
+ 
+
+ align:start position:0%
+that is actually what is going to happen
+to the system okay so now I would like
+
+ align:start position:0%
+to the system okay so now I would like
+ 
+
+ align:start position:0%
+to the system okay so now I would like
+to go through a short demonstration
+
+ align:start position:0%
+to go through a short demonstration
+ 
+
+ align:start position:0%
+to go through a short demonstration
+which is actually the Elkhart which you
+
+ align:start position:0%
+which is actually the Elkhart which you
+ 
+
+ align:start position:0%
+which is actually the Elkhart which you
+see before there's a mass and there are
+
+ align:start position:0%
+see before there's a mass and there are
+ 
+
+ align:start position:0%
+see before there's a mass and there are
+two springs in the near front and the
+
+ align:start position:0%
+two springs in the near front and the
+ 
+
+ align:start position:0%
+two springs in the near front and the
+back of this cart and of course judo I
+
+ align:start position:0%
+back of this cart and of course judo I
+ 
+
+ align:start position:0%
+back of this cart and of course judo I
+will turn on the air so that I make the
+
+ align:start position:0%
+will turn on the air so that I make the
+ 
+
+ align:start position:0%
+will turn on the air so that I make the
+friction smolder but actually still
+
+ align:start position:0%
+friction smolder but actually still
+ 
+
+ align:start position:0%
+friction smolder but actually still
+there are some still some residual
+
+ align:start position:0%
+there are some still some residual
+ 
+
+ align:start position:0%
+there are some still some residual
+friction okay and you will see that this
+
+ align:start position:0%
+friction okay and you will see that this
+ 
+
+ align:start position:0%
+friction okay and you will see that this
+this mass is actually oscillating back
+
+ align:start position:0%
+this mass is actually oscillating back
+ 
+
+ align:start position:0%
+this mass is actually oscillating back
+and forth okay and the the amplitude can
+
+ align:start position:0%
+and forth okay and the the amplitude can
+ 
+
+ align:start position:0%
+and forth okay and the the amplitude can
+become smaller and smaller as a function
+
+ align:start position:0%
+become smaller and smaller as a function
+ 
+
+ align:start position:0%
+become smaller and smaller as a function
+of time okay now in the right hand side
+
+ align:start position:0%
+of time okay now in the right hand side
+ 
+
+ align:start position:0%
+of time okay now in the right hand side
+I have a motor which is actually can
+
+ align:start position:0%
+I have a motor which is actually can
+ 
+
+ align:start position:0%
+I have a motor which is actually can
+drive this I can actually shorten over
+
+ align:start position:0%
+drive this I can actually shorten over
+ 
+
+ align:start position:0%
+drive this I can actually shorten over
+or increase the length of the right hand
+
+ align:start position:0%
+or increase the length of the right hand
+ 
+
+ align:start position:0%
+or increase the length of the right hand
+side string then actually I actually
+
+ align:start position:0%
+side string then actually I actually
+ 
+
+ align:start position:0%
+side string then actually I actually
+introduce a driving force by the right
+
+ align:start position:0%
+introduce a driving force by the right
+ 
+
+ align:start position:0%
+introduce a driving force by the right
+hand side motor if I turn it down this
+
+ align:start position:0%
+hand side motor if I turn it down this
+ 
+
+ align:start position:0%
+hand side motor if I turn it down this
+is what what is going to happen okay so
+
+ align:start position:0%
+is what what is going to happen okay so
+ 
+
+ align:start position:0%
+is what what is going to happen okay so
+you can see now this motor is actually
+
+ align:start position:0%
+you can see now this motor is actually
+ 
+
+ align:start position:0%
+you can see now this motor is actually
+going back and forth right and it has a
+
+ align:start position:0%
+going back and forth right and it has a
+ 
+
+ align:start position:0%
+going back and forth right and it has a
+slightly higher frequency
+
+ align:start position:0%
+slightly higher frequency
+ 
+
+ align:start position:0%
+slightly higher frequency
+compared to the natural frequency right
+
+ align:start position:0%
+compared to the natural frequency right
+ 
+
+ align:start position:0%
+compared to the natural frequency right
+so they the frequency of the motor is
+
+ align:start position:0%
+so they the frequency of the motor is
+ 
+
+ align:start position:0%
+so they the frequency of the motor is
+higher okay then you can see that huh
+
+ align:start position:0%
+higher okay then you can see that huh
+ 
+
+ align:start position:0%
+higher okay then you can see that huh
+this mode this this cart is actually
+
+ align:start position:0%
+this mode this this cart is actually
+ 
+
+ align:start position:0%
+this mode this this cart is actually
+oscillating but you can see that
+
+ align:start position:0%
+oscillating but you can see that
+ 
+
+ align:start position:0%
+oscillating but you can see that
+sometimes it pause and sometimes it
+
+ align:start position:0%
+sometimes it pause and sometimes it
+ 
+
+ align:start position:0%
+sometimes it pause and sometimes it
+moves faster right it's actually not you
+
+ align:start position:0%
+moves faster right it's actually not you
+ 
+
+ align:start position:0%
+moves faster right it's actually not you
+see so you can see that it's actually
+
+ align:start position:0%
+see so you can see that it's actually
+ 
+
+ align:start position:0%
+see so you can see that it's actually
+moving and it stopped a little bit and
+
+ align:start position:0%
+moving and it stopped a little bit and
+ 
+
+ align:start position:0%
+moving and it stopped a little bit and
+because there are a superposition of two
+
+ align:start position:0%
+because there are a superposition of two
+ 
+
+ align:start position:0%
+because there are a superposition of two
+different kinds of oscillation
+
+ align:start position:0%
+different kinds of oscillation
+ 
+
+ align:start position:0%
+different kinds of oscillation
+oscillating functions hang interpret you
+
+ align:start position:0%
+oscillating functions hang interpret you
+ 
+
+ align:start position:0%
+oscillating functions hang interpret you
+can see that now it got slowed down and
+
+ align:start position:0%
+can see that now it got slowed down and
+ 
+
+ align:start position:0%
+can see that now it got slowed down and
+it becomes faster and the slower and
+
+ align:start position:0%
+it becomes faster and the slower and
+ 
+
+ align:start position:0%
+it becomes faster and the slower and
+faster but eventually if we wait long
+
+ align:start position:0%
+faster but eventually if we wait long
+ 
+
+ align:start position:0%
+faster but eventually if we wait long
+enough okay if we were only now what is
+
+ align:start position:0%
+enough okay if we were only now what is
+ 
+
+ align:start position:0%
+enough okay if we were only now what is
+going to happen what is going to happen
+
+ align:start position:0%
+going to happen what is going to happen
+ 
+
+ align:start position:0%
+going to happen what is going to happen
+if we wait long enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly so basically if you wait long
+
+ align:start position:0%
+exactly so basically if you wait long
+ 
+
+ align:start position:0%
+exactly so basically if you wait long
+enough as you said you were actually
+
+ align:start position:0%
+enough as you said you were actually
+ 
+
+ align:start position:0%
+enough as you said you were actually
+just oscillate at the frequency of the
+
+ align:start position:0%
+just oscillate at the frequency of the
+ 
+
+ align:start position:0%
+just oscillate at the frequency of the
+driving force you can see that this this
+
+ align:start position:0%
+driving force you can see that this this
+ 
+
+ align:start position:0%
+driving force you can see that this this
+motion is really look 3d peas are right
+
+ align:start position:0%
+motion is really look 3d peas are right
+ 
+
+ align:start position:0%
+motion is really look 3d peas are right
+sometimes they stop and sometimes they
+
+ align:start position:0%
+sometimes they stop and sometimes they
+ 
+
+ align:start position:0%
+sometimes they stop and sometimes they
+actually continue to move and are you
+
+ align:start position:0%
+actually continue to move and are you
+ 
+
+ align:start position:0%
+actually continue to move and are you
+surprised
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probably you are not surprised anymore
+
+ align:start position:0%
+probably you are not surprised anymore
+ 
+
+ align:start position:0%
+probably you are not surprised anymore
+right because we know mass is the
+
+ align:start position:0%
+right because we know mass is the
+ 
+
+ align:start position:0%
+right because we know mass is the
+language to describe the nature right
+
+ align:start position:0%
+language to describe the nature right
+ 
+
+ align:start position:0%
+language to describe the nature right
+and indeed ypres did this kind of
+
+ align:start position:0%
+and indeed ypres did this kind of
+ 
+
+ align:start position:0%
+and indeed ypres did this kind of
+behavior that's really pretty cool okay
+
+ align:start position:0%
+behavior that's really pretty cool okay
+ 
+
+ align:start position:0%
+behavior that's really pretty cool okay
+in order to help you to learn a bit how
+
+ align:start position:0%
+in order to help you to learn a bit how
+ 
+
+ align:start position:0%
+in order to help you to learn a bit how
+to actually translate a physical
+
+ align:start position:0%
+to actually translate a physical
+ 
+
+ align:start position:0%
+to actually translate a physical
+situation into mathematics what I am
+
+ align:start position:0%
+situation into mathematics what I am
+ 
+
+ align:start position:0%
+situation into mathematics what I am
+going to do is to introduce you another
+
+ align:start position:0%
+going to do is to introduce you another
+ 
+
+ align:start position:0%
+going to do is to introduce you another
+example so that actually we can actually
+
+ align:start position:0%
+example so that actually we can actually
+ 
+
+ align:start position:0%
+example so that actually we can actually
+solve it together so now I would like to
+
+ align:start position:0%
+solve it together so now I would like to
+ 
+
+ align:start position:0%
+solve it together so now I would like to
+drive a pendulum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I prepare at a pendulum at time
+
+ align:start position:0%
+okay so I prepare at a pendulum at time
+ 
+
+ align:start position:0%
+okay so I prepare at a pendulum at time
+equal to zero okay
+
+ align:start position:0%
+equal to zero okay
+ 
+
+ align:start position:0%
+equal to zero okay
+this is a string attached to a ball with
+
+ align:start position:0%
+this is a string attached to a ball with
+ 
+
+ align:start position:0%
+this is a string attached to a ball with
+mass equal to M okay and the length of
+
+ align:start position:0%
+mass equal to M okay and the length of
+ 
+
+ align:start position:0%
+mass equal to M okay and the length of
+the string says should L and the angle
+
+ align:start position:0%
+the string says should L and the angle
+ 
+
+ align:start position:0%
+the string says should L and the angle
+between the vertical direction and the
+
+ align:start position:0%
+between the vertical direction and the
+ 
+
+ align:start position:0%
+between the vertical direction and the
+string the direction of the string is
+
+ align:start position:0%
+string the direction of the string is
+ 
+
+ align:start position:0%
+string the direction of the string is
+Sita okay and of course I can actually
+
+ align:start position:0%
+Sita okay and of course I can actually
+ 
+
+ align:start position:0%
+Sita okay and of course I can actually
+give you an initial condition X initial
+
+ align:start position:0%
+give you an initial condition X initial
+ 
+
+ align:start position:0%
+give you an initial condition X initial
+which is actually measured which is fed
+
+ align:start position:0%
+which is actually measured which is fed
+ 
+
+ align:start position:0%
+which is actually measured which is fed
+to the vertical direction okay and at
+
+ align:start position:0%
+to the vertical direction okay and at
+ 
+
+ align:start position:0%
+to the vertical direction okay and at
+time equal to T okay this is actually
+
+ align:start position:0%
+time equal to T okay this is actually
+ 
+
+ align:start position:0%
+time equal to T okay this is actually
+the original vertical direction the
+
+ align:start position:0%
+the original vertical direction the
+ 
+
+ align:start position:0%
+the original vertical direction the
+original vertical direction the same as
+
+ align:start position:0%
+original vertical direction the same as
+ 
+
+ align:start position:0%
+original vertical direction the same as
+this dash line okay and I can actually
+
+ align:start position:0%
+this dash line okay and I can actually
+ 
+
+ align:start position:0%
+this dash line okay and I can actually
+move this the the top of this stream
+
+ align:start position:0%
+move this the the top of this stream
+ 
+
+ align:start position:0%
+move this the the top of this stream
+back and forth to some position and of
+
+ align:start position:0%
+back and forth to some position and of
+ 
+
+ align:start position:0%
+back and forth to some position and of
+course the string is still connect is
+
+ align:start position:0%
+course the string is still connect is
+ 
+
+ align:start position:0%
+course the string is still connect is
+connected to the ball and and this
+
+ align:start position:0%
+connected to the ball and and this
+ 
+
+ align:start position:0%
+connected to the ball and and this
+system is they should be driven from the
+
+ align:start position:0%
+system is they should be driven from the
+ 
+
+ align:start position:0%
+system is they should be driven from the
+top by Yun Jie's Han so Yoon ji says
+
+ align:start position:0%
+top by Yun Jie's Han so Yoon ji says
+ 
+
+ align:start position:0%
+top by Yun Jie's Han so Yoon ji says
+she's shaking this assistant from the
+
+ align:start position:0%
+she's shaking this assistant from the
+ 
+
+ align:start position:0%
+she's shaking this assistant from the
+top okay and I do it really nicely so
+
+ align:start position:0%
+top okay and I do it really nicely so
+ 
+
+ align:start position:0%
+top okay and I do it really nicely so
+basically I define that the displacement
+
+ align:start position:0%
+basically I define that the displacement
+ 
+
+ align:start position:0%
+basically I define that the displacement
+T as a function of time is equal to
+
+ align:start position:0%
+T as a function of time is equal to
+ 
+
+ align:start position:0%
+T as a function of time is equal to
+Delta sine Omega DT okay so that is
+
+ align:start position:0%
+Delta sine Omega DT okay so that is
+ 
+
+ align:start position:0%
+Delta sine Omega DT okay so that is
+actually what I'm going to do okay and I
+
+ align:start position:0%
+actually what I'm going to do okay and I
+ 
+
+ align:start position:0%
+actually what I'm going to do okay and I
+would like to see what is going to
+
+ align:start position:0%
+would like to see what is going to
+ 
+
+ align:start position:0%
+would like to see what is going to
+happen to this pendulum okay so a pseudo
+
+ align:start position:0%
+happen to this pendulum okay so a pseudo
+ 
+
+ align:start position:0%
+happen to this pendulum okay so a pseudo
+the first step okay towards solving this
+
+ align:start position:0%
+the first step okay towards solving this
+ 
+
+ align:start position:0%
+the first step okay towards solving this
+problem is to define a coordinate system
+
+ align:start position:0%
+problem is to define a coordinate system
+ 
+
+ align:start position:0%
+problem is to define a coordinate system
+right so what is actually the coordinate
+
+ align:start position:0%
+right so what is actually the coordinate
+ 
+
+ align:start position:0%
+right so what is actually the coordinate
+system I am going to use so now I define
+
+ align:start position:0%
+system I am going to use so now I define
+ 
+
+ align:start position:0%
+system I am going to use so now I define
+pointing upward to be Y I define the
+
+ align:start position:0%
+pointing upward to be Y I define the
+ 
+
+ align:start position:0%
+pointing upward to be Y I define the
+vertical horizontal direction pointing
+
+ align:start position:0%
+vertical horizontal direction pointing
+ 
+
+ align:start position:0%
+vertical horizontal direction pointing
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+right hand side with the port to be X
+
+ align:start position:0%
+right hand side with the port to be X
+ 
+
+ align:start position:0%
+right hand side with the port to be X
+okay so that's not good enough I still
+
+ align:start position:0%
+okay so that's not good enough I still
+ 
+
+ align:start position:0%
+okay so that's not good enough I still
+need the origin right so now I also
+
+ align:start position:0%
+need the origin right so now I also
+ 
+
+ align:start position:0%
+need the origin right so now I also
+define my origin to be the original
+
+ align:start position:0%
+define my origin to be the original
+ 
+
+ align:start position:0%
+define my origin to be the original
+position of the ball when this is
+
+ align:start position:0%
+position of the ball when this is
+ 
+
+ align:start position:0%
+position of the ball when this is
+actually temperate the vertical which is
+
+ align:start position:0%
+actually temperate the vertical which is
+ 
+
+ align:start position:0%
+actually temperate the vertical which is
+actually completely at rest before I do
+
+ align:start position:0%
+actually completely at rest before I do
+ 
+
+ align:start position:0%
+actually completely at rest before I do
+the experiment right so that is actually
+
+ align:start position:0%
+the experiment right so that is actually
+ 
+
+ align:start position:0%
+the experiment right so that is actually
+the equilibrium position of this system
+
+ align:start position:0%
+the equilibrium position of this system
+ 
+
+ align:start position:0%
+the equilibrium position of this system
+actually okay then I define here to be
+
+ align:start position:0%
+actually okay then I define here to be
+ 
+
+ align:start position:0%
+actually okay then I define here to be
+zero zero okay so once I have not
+
+ align:start position:0%
+zero zero okay so once I have not
+ 
+
+ align:start position:0%
+zero zero okay so once I have not
+defined I can now express the position
+
+ align:start position:0%
+defined I can now express the position
+ 
+
+ align:start position:0%
+defined I can now express the position
+of this math mess or dispo to be X T and
+
+ align:start position:0%
+of this math mess or dispo to be X T and
+ 
+
+ align:start position:0%
+of this math mess or dispo to be X T and
+Y T okay and see what we are going to
+
+ align:start position:0%
+Y T okay and see what we are going to
+ 
+
+ align:start position:0%
+Y T okay and see what we are going to
+get of course as usual we are going to
+
+ align:start position:0%
+get of course as usual we are going to
+ 
+
+ align:start position:0%
+get of course as usual we are going to
+analyze the force acting forces as we
+
+ align:start position:0%
+analyze the force acting forces as we
+ 
+
+ align:start position:0%
+analyze the force acting forces as we
+are getting under on this board right so
+
+ align:start position:0%
+are getting under on this board right so
+ 
+
+ align:start position:0%
+are getting under on this board right so
+therefore as usual we will draw a force
+
+ align:start position:0%
+therefore as usual we will draw a force
+ 
+
+ align:start position:0%
+therefore as usual we will draw a force
+diagram okay so basically you have the
+
+ align:start position:0%
+diagram okay so basically you have the
+ 
+
+ align:start position:0%
+diagram okay so basically you have the
+magneto mass here and that you have I
+
+ align:start position:0%
+magneto mass here and that you have I
+ 
+
+ align:start position:0%
+magneto mass here and that you have I
+should be a swift actually two force
+
+ align:start position:0%
+should be a swift actually two force
+ 
+
+ align:start position:0%
+should be a swift actually two force
+acting on this bit of mass or a little
+
+ align:start position:0%
+acting on this bit of mass or a little
+ 
+
+ align:start position:0%
+acting on this bit of mass or a little
+ball this is FG pointing down where is
+
+ align:start position:0%
+ball this is FG pointing down where is
+ 
+
+ align:start position:0%
+ball this is FG pointing down where is
+the gravitational force and not
+
+ align:start position:0%
+the gravitational force and not
+ 
+
+ align:start position:0%
+the gravitational force and not
+essentially equal to minus mg Y okay and
+
+ align:start position:0%
+essentially equal to minus mg Y okay and
+ 
+
+ align:start position:0%
+essentially equal to minus mg Y okay and
+there's also a string tension T okay
+
+ align:start position:0%
+there's also a string tension T okay
+ 
+
+ align:start position:0%
+there's also a string tension T okay
+since we have this definition of Sita
+
+ align:start position:0%
+since we have this definition of Sita
+ 
+
+ align:start position:0%
+since we have this definition of Sita
+here basically I have the T which is
+
+ align:start position:0%
+here basically I have the T which is
+ 
+
+ align:start position:0%
+here basically I have the T which is
+actually pointing to the upper left
+
+ align:start position:0%
+actually pointing to the upper left
+ 
+
+ align:start position:0%
+actually pointing to the upper left
+direction of the board okay and of
+
+ align:start position:0%
+direction of the board okay and of
+ 
+
+ align:start position:0%
+direction of the board okay and of
+course don't forget issue there there is
+
+ align:start position:0%
+course don't forget issue there there is
+ 
+
+ align:start position:0%
+course don't forget issue there there is
+a third force which is actually F track
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay f track is actually equal to minus
+
+ align:start position:0%
+okay f track is actually equal to minus
+ 
+
+ align:start position:0%
+okay f track is actually equal to minus
+B X dot in the x-direction
+
+ align:start position:0%
+B X dot in the x-direction
+ 
+
+ align:start position:0%
+B X dot in the x-direction
+okay now I would like to write down the
+
+ align:start position:0%
+okay now I would like to write down the
+ 
+
+ align:start position:0%
+okay now I would like to write down the
+expression for also the string tension P
+
+ align:start position:0%
+expression for also the string tension P
+ 
+
+ align:start position:0%
+expression for also the string tension P
+the P is actually equal to minus T sine
+
+ align:start position:0%
+the P is actually equal to minus T sine
+ 
+
+ align:start position:0%
+the P is actually equal to minus T sine
+theta in the X direction right because
+
+ align:start position:0%
+theta in the X direction right because
+ 
+
+ align:start position:0%
+theta in the X direction right because
+the T is pointing to upper lapped
+
+ align:start position:0%
+the T is pointing to upper lapped
+ 
+
+ align:start position:0%
+the T is pointing to upper lapped
+direction right so therefore the
+
+ align:start position:0%
+direction right so therefore the
+ 
+
+ align:start position:0%
+direction right so therefore the
+position to X direction will be minus
+
+ align:start position:0%
+position to X direction will be minus
+ 
+
+ align:start position:0%
+position to X direction will be minus
+sine theta and the price T cosine theta
+
+ align:start position:0%
+sine theta and the price T cosine theta
+ 
+
+ align:start position:0%
+sine theta and the price T cosine theta
+in the Y direction right because the
+
+ align:start position:0%
+in the Y direction right because the
+ 
+
+ align:start position:0%
+in the Y direction right because the
+tension is actually pointing up that
+
+ align:start position:0%
+tension is actually pointing up that
+ 
+
+ align:start position:0%
+tension is actually pointing up that
+okay as usual this is actually pretty
+
+ align:start position:0%
+okay as usual this is actually pretty
+ 
+
+ align:start position:0%
+okay as usual this is actually pretty
+complicated to solve I have this cosine
+
+ align:start position:0%
+complicated to solve I have this cosine
+ 
+
+ align:start position:0%
+complicated to solve I have this cosine
+I have this sign there right so what I'm
+
+ align:start position:0%
+I have this sign there right so what I'm
+ 
+
+ align:start position:0%
+I have this sign there right so what I'm
+going to do is to assume that the this
+
+ align:start position:0%
+going to do is to assume that the this
+ 
+
+ align:start position:0%
+going to do is to assume that the this
+angle theta is very small okay as usual
+
+ align:start position:0%
+angle theta is very small okay as usual
+ 
+
+ align:start position:0%
+angle theta is very small okay as usual
+okay so I will take small angle
+
+ align:start position:0%
+okay so I will take small angle
+ 
+
+ align:start position:0%
+okay so I will take small angle
+approximation then basically you have
+
+ align:start position:0%
+approximation then basically you have
+ 
+
+ align:start position:0%
+approximation then basically you have
+sine theta roughly to be equal to theta
+
+ align:start position:0%
+sine theta roughly to be equal to theta
+ 
+
+ align:start position:0%
+sine theta roughly to be equal to theta
+and that is actually equal to what equal
+
+ align:start position:0%
+and that is actually equal to what equal
+ 
+
+ align:start position:0%
+and that is actually equal to what equal
+to here basically you can actually
+
+ align:start position:0%
+to here basically you can actually
+ 
+
+ align:start position:0%
+to here basically you can actually
+calculate what will be the theta right
+
+ align:start position:0%
+calculate what will be the theta right
+ 
+
+ align:start position:0%
+calculate what will be the theta right
+okay the CETA the sine theta or theta
+
+ align:start position:0%
+okay the CETA the sine theta or theta
+ 
+
+ align:start position:0%
+okay the CETA the sine theta or theta
+will be equal to X minus P divided by L
+
+ align:start position:0%
+will be equal to X minus P divided by L
+ 
+
+ align:start position:0%
+will be equal to X minus P divided by L
+right and of course taking a small angle
+
+ align:start position:0%
+right and of course taking a small angle
+ 
+
+ align:start position:0%
+right and of course taking a small angle
+approximation will bring cosine theta to
+
+ align:start position:0%
+approximation will bring cosine theta to
+ 
+
+ align:start position:0%
+approximation will bring cosine theta to
+be 1 okay then after this approximation
+
+ align:start position:0%
+be 1 okay then after this approximation
+ 
+
+ align:start position:0%
+be 1 okay then after this approximation
+my T will become minus T X minus D
+
+ align:start position:0%
+my T will become minus T X minus D
+ 
+
+ align:start position:0%
+my T will become minus T X minus D
+divided by L in the X direction
+
+ align:start position:0%
+divided by L in the X direction
+ 
+
+ align:start position:0%
+divided by L in the X direction
+press T in the y-direction okay because
+
+ align:start position:0%
+press T in the y-direction okay because
+ 
+
+ align:start position:0%
+press T in the y-direction okay because
+sine theta is replaced by this
+
+ align:start position:0%
+sine theta is replaced by this
+ 
+
+ align:start position:0%
+sine theta is replaced by this
+approximated value cosine theta is a
+
+ align:start position:0%
+approximated value cosine theta is a
+ 
+
+ align:start position:0%
+approximated value cosine theta is a
+should be pressed by what okay
+
+ align:start position:0%
+should be pressed by what okay
+ 
+
+ align:start position:0%
+should be pressed by what okay
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I can ah
+
+ align:start position:0%
+so I can ah
+ 
+
+ align:start position:0%
+so I can ah
+this theater ah is a constant yeah I was
+
+ align:start position:0%
+this theater ah is a constant yeah I was
+ 
+
+ align:start position:0%
+this theater ah is a constant yeah I was
+going too fast so this is a constant I
+
+ align:start position:0%
+going too fast so this is a constant I
+ 
+
+ align:start position:0%
+going too fast so this is a constant I
+hope my other MP - okay yes it's only in
+
+ align:start position:0%
+hope my other MP - okay yes it's only in
+ 
+
+ align:start position:0%
+hope my other MP - okay yes it's only in
+the director X direction so I'm only
+
+ align:start position:0%
+the director X direction so I'm only
+ 
+
+ align:start position:0%
+the director X direction so I'm only
+trying to actually move this point back
+
+ align:start position:0%
+trying to actually move this point back
+ 
+
+ align:start position:0%
+trying to actually move this point back
+and forth horizontally okay okay so now
+
+ align:start position:0%
+and forth horizontally okay okay so now
+ 
+
+ align:start position:0%
+and forth horizontally okay okay so now
+I have all the components t FG f Jack
+
+ align:start position:0%
+I have all the components t FG f Jack
+ 
+
+ align:start position:0%
+I have all the components t FG f Jack
+okay and of course you can see that I
+
+ align:start position:0%
+okay and of course you can see that I
+ 
+
+ align:start position:0%
+okay and of course you can see that I
+already ignore the drag force in the
+
+ align:start position:0%
+already ignore the drag force in the
+ 
+
+ align:start position:0%
+already ignore the drag force in the
+y-direction right from that formula okay
+
+ align:start position:0%
+y-direction right from that formula okay
+ 
+
+ align:start position:0%
+y-direction right from that formula okay
+because I'm only considering the system
+
+ align:start position:0%
+because I'm only considering the system
+ 
+
+ align:start position:0%
+because I'm only considering the system
+to be moving in the X direction okay
+
+ align:start position:0%
+to be moving in the X direction okay
+ 
+
+ align:start position:0%
+to be moving in the X direction okay
+therefore I can now collect all the
+
+ align:start position:0%
+therefore I can now collect all the
+ 
+
+ align:start position:0%
+therefore I can now collect all the
+turns in the X direction okay basically
+
+ align:start position:0%
+turns in the X direction okay basically
+ 
+
+ align:start position:0%
+turns in the X direction okay basically
+you will have em X double dot this is
+
+ align:start position:0%
+you will have em X double dot this is
+ 
+
+ align:start position:0%
+you will have em X double dot this is
+equal to minus P X dot okay which is
+
+ align:start position:0%
+equal to minus P X dot okay which is
+ 
+
+ align:start position:0%
+equal to minus P X dot okay which is
+actually I'm in front the drag force
+
+ align:start position:0%
+actually I'm in front the drag force
+ 
+
+ align:start position:0%
+actually I'm in front the drag force
+okay - T X minus T divided by L this is
+
+ align:start position:0%
+okay - T X minus T divided by L this is
+ 
+
+ align:start position:0%
+okay - T X minus T divided by L this is
+actually coming from this term in the X
+
+ align:start position:0%
+actually coming from this term in the X
+ 
+
+ align:start position:0%
+actually coming from this term in the X
+direction let's look at also the Y
+
+ align:start position:0%
+direction let's look at also the Y
+ 
+
+ align:start position:0%
+direction let's look at also the Y
+direction and y double dot will be equal
+
+ align:start position:0%
+direction and y double dot will be equal
+ 
+
+ align:start position:0%
+direction and y double dot will be equal
+to minus mg plus T right the minus mg is
+
+ align:start position:0%
+to minus mg plus T right the minus mg is
+ 
+
+ align:start position:0%
+to minus mg plus T right the minus mg is
+from the publication of force and this T
+
+ align:start position:0%
+from the publication of force and this T
+ 
+
+ align:start position:0%
+from the publication of force and this T
+is coming from the Y component of the
+
+ align:start position:0%
+is coming from the Y component of the
+ 
+
+ align:start position:0%
+is coming from the Y component of the
+stream tension okay
+
+ align:start position:0%
+stream tension okay
+ 
+
+ align:start position:0%
+stream tension okay
+and of course since we are taking as
+
+ align:start position:0%
+and of course since we are taking as
+ 
+
+ align:start position:0%
+and of course since we are taking as
+very small angle approximation there
+
+ align:start position:0%
+very small angle approximation there
+ 
+
+ align:start position:0%
+very small angle approximation there
+will be no vertical motion right yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so so actually in this case they
+
+ align:start position:0%
+yeah so so actually in this case they
+ 
+
+ align:start position:0%
+yeah so so actually in this case they
+happen to be exactly the same and and
+
+ align:start position:0%
+happen to be exactly the same and and
+ 
+
+ align:start position:0%
+happen to be exactly the same and and
+what I care is actually the cosine theta
+
+ align:start position:0%
+what I care is actually the cosine theta
+ 
+
+ align:start position:0%
+what I care is actually the cosine theta
+otherwise I would have to deal with
+
+ align:start position:0%
+otherwise I would have to deal with
+ 
+
+ align:start position:0%
+otherwise I would have to deal with
+cosine theta and also this white upper
+
+ align:start position:0%
+cosine theta and also this white upper
+ 
+
+ align:start position:0%
+cosine theta and also this white upper
+dog will not be equal to zero right
+
+ align:start position:0%
+dog will not be equal to zero right
+ 
+
+ align:start position:0%
+dog will not be equal to zero right
+which is what I'm going to assume here
+
+ align:start position:0%
+which is what I'm going to assume here
+ 
+
+ align:start position:0%
+which is what I'm going to assume here
+okay good question so the question was
+
+ align:start position:0%
+okay good question so the question was
+ 
+
+ align:start position:0%
+okay good question so the question was
+why do I need to take a person because I
+
+ align:start position:0%
+why do I need to take a person because I
+ 
+
+ align:start position:0%
+why do I need to take a person because I
+want to get rid of cause I see okay so
+
+ align:start position:0%
+want to get rid of cause I see okay so
+ 
+
+ align:start position:0%
+want to get rid of cause I see okay so
+now I from this y direction I can solve
+
+ align:start position:0%
+now I from this y direction I can solve
+ 
+
+ align:start position:0%
+now I from this y direction I can solve
+T will be equal to and G right because
+
+ align:start position:0%
+T will be equal to and G right because
+ 
+
+ align:start position:0%
+T will be equal to and G right because
+there's I assume that there's no y
+
+ align:start position:0%
+there's I assume that there's no y
+ 
+
+ align:start position:0%
+there's I assume that there's no y
+direction motion then I can conclude
+
+ align:start position:0%
+direction motion then I can conclude
+ 
+
+ align:start position:0%
+direction motion then I can conclude
+that okay originally I don't know what
+
+ align:start position:0%
+that okay originally I don't know what
+ 
+
+ align:start position:0%
+that okay originally I don't know what
+this is you the string tension right
+
+ align:start position:0%
+this is you the string tension right
+ 
+
+ align:start position:0%
+this is you the string tension right
+it's denoted by T now from this second
+
+ align:start position:0%
+it's denoted by T now from this second
+ 
+
+ align:start position:0%
+it's denoted by T now from this second
+equation I can conclude that T will be
+
+ align:start position:0%
+equation I can conclude that T will be
+ 
+
+ align:start position:0%
+equation I can conclude that T will be
+equal to ng okay which is the
+
+ align:start position:0%
+equal to ng okay which is the
+ 
+
+ align:start position:0%
+equal to ng okay which is the
+gravitational force okay then once I
+
+ align:start position:0%
+gravitational force okay then once I
+ 
+
+ align:start position:0%
+gravitational force okay then once I
+have that I can go back to to X
+
+ align:start position:0%
+have that I can go back to to X
+ 
+
+ align:start position:0%
+have that I can go back to to X
+direction okay basically I get an X
+
+ align:start position:0%
+direction okay basically I get an X
+ 
+
+ align:start position:0%
+direction okay basically I get an X
+double dot this is equal to minus P X
+
+ align:start position:0%
+double dot this is equal to minus P X
+ 
+
+ align:start position:0%
+double dot this is equal to minus P X
+dot minus n G over L X minus T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything is working very well and I
+
+ align:start position:0%
+everything is working very well and I
+ 
+
+ align:start position:0%
+everything is working very well and I
+just have to read it write down the T
+
+ align:start position:0%
+just have to read it write down the T
+ 
+
+ align:start position:0%
+just have to read it write down the T
+and the X explicitly okay the team
+
+ align:start position:0%
+and the X explicitly okay the team
+ 
+
+ align:start position:0%
+and the X explicitly okay the team
+function explicitly what is d D is just
+
+ align:start position:0%
+function explicitly what is d D is just
+ 
+
+ align:start position:0%
+function explicitly what is d D is just
+a reminder Delta sine Omega DT right
+
+ align:start position:0%
+a reminder Delta sine Omega DT right
+ 
+
+ align:start position:0%
+a reminder Delta sine Omega DT right
+okay so I will product that into that
+
+ align:start position:0%
+okay so I will product that into that
+ 
+
+ align:start position:0%
+okay so I will product that into that
+equation and also I will bring all the
+
+ align:start position:0%
+equation and also I will bring all the
+ 
+
+ align:start position:0%
+equation and also I will bring all the
+turns I will bring all the terms with
+
+ align:start position:0%
+turns I will bring all the terms with
+ 
+
+ align:start position:0%
+turns I will bring all the terms with
+82x Toula laugh and sigh okay just to
+
+ align:start position:0%
+82x Toula laugh and sigh okay just to
+ 
+
+ align:start position:0%
+82x Toula laugh and sigh okay just to
+match my my convention okay all right so
+
+ align:start position:0%
+match my my convention okay all right so
+ 
+
+ align:start position:0%
+match my my convention okay all right so
+now I will be able to get a visa and X
+
+ align:start position:0%
+now I will be able to get a visa and X
+ 
+
+ align:start position:0%
+now I will be able to get a visa and X
+double dot plus P X dot
+
+ align:start position:0%
+double dot plus P X dot
+ 
+
+ align:start position:0%
+double dot plus P X dot
+pass and G over L X and that is actually
+
+ align:start position:0%
+pass and G over L X and that is actually
+ 
+
+ align:start position:0%
+pass and G over L X and that is actually
+equal to n G over L T okay and this is
+
+ align:start position:0%
+equal to n G over L T okay and this is
+ 
+
+ align:start position:0%
+equal to n G over L T okay and this is
+equal to n G over L Delta sine Omega T
+
+ align:start position:0%
+equal to n G over L Delta sine Omega T
+ 
+
+ align:start position:0%
+equal to n G over L Delta sine Omega T
+right so basically I collect all the
+
+ align:start position:0%
+right so basically I collect all the
+ 
+
+ align:start position:0%
+right so basically I collect all the
+turns put it to a lap inside and I write
+
+ align:start position:0%
+turns put it to a lap inside and I write
+ 
+
+ align:start position:0%
+turns put it to a lap inside and I write
+down T explicitly okay which is this
+
+ align:start position:0%
+down T explicitly okay which is this
+ 
+
+ align:start position:0%
+down T explicitly okay which is this
+okay then I can divide everything by an
+
+ align:start position:0%
+okay then I can divide everything by an
+ 
+
+ align:start position:0%
+okay then I can divide everything by an
+end then I get n X double dot plus P
+
+ align:start position:0%
+end then I get n X double dot plus P
+ 
+
+ align:start position:0%
+end then I get n X double dot plus P
+over N X dot plus G over L X and that
+
+ align:start position:0%
+over N X dot plus G over L X and that
+ 
+
+ align:start position:0%
+over N X dot plus G over L X and that
+will be equal to G over L Delta sine
+
+ align:start position:0%
+will be equal to G over L Delta sine
+ 
+
+ align:start position:0%
+will be equal to G over L Delta sine
+Omega T now course as usual I would
+
+ align:start position:0%
+Omega T now course as usual I would
+ 
+
+ align:start position:0%
+Omega T now course as usual I would
+define this to be comma define this to
+
+ align:start position:0%
+define this to be comma define this to
+ 
+
+ align:start position:0%
+define this to be comma define this to
+be Omega 0 square I will define this to
+
+ align:start position:0%
+be Omega 0 square I will define this to
+ 
+
+ align:start position:0%
+be Omega 0 square I will define this to
+pf0
+
+ align:start position:0%
+pf0
+ 
+
+ align:start position:0%
+pf0
+and which is equal to Omega 0 square
+
+ align:start position:0%
+and which is equal to Omega 0 square
+ 
+
+ align:start position:0%
+and which is equal to Omega 0 square
+Delta ok happen to be good like that and
+
+ align:start position:0%
+Delta ok happen to be good like that and
+ 
+
+ align:start position:0%
+Delta ok happen to be good like that and
+then this HDPE can X double dot plus
+
+ align:start position:0%
+then this HDPE can X double dot plus
+ 
+
+ align:start position:0%
+then this HDPE can X double dot plus
+gamma X dot plus Omega 0 square X equal
+
+ align:start position:0%
+gamma X dot plus Omega 0 square X equal
+ 
+
+ align:start position:0%
+gamma X dot plus Omega 0 square X equal
+to F 0 sine Omega T T are going too fast
+
+ align:start position:0%
+to F 0 sine Omega T T are going too fast
+ 
+
+ align:start position:0%
+to F 0 sine Omega T T are going too fast
+okay everybody is following so we see
+
+ align:start position:0%
+okay everybody is following so we see
+ 
+
+ align:start position:0%
+okay everybody is following so we see
+the half this equation I know that I
+
+ align:start position:0%
+the half this equation I know that I
+ 
+
+ align:start position:0%
+the half this equation I know that I
+know this equation right because we have
+
+ align:start position:0%
+know this equation right because we have
+ 
+
+ align:start position:0%
+know this equation right because we have
+just solved that a few minutes ago right
+
+ align:start position:0%
+just solved that a few minutes ago right
+ 
+
+ align:start position:0%
+just solved that a few minutes ago right
+therefore I know immediately what would
+
+ align:start position:0%
+therefore I know immediately what would
+ 
+
+ align:start position:0%
+therefore I know immediately what would
+be the solution the solution is here
+
+ align:start position:0%
+be the solution the solution is here
+ 
+
+ align:start position:0%
+be the solution the solution is here
+already right I have a Omega D and the
+
+ align:start position:0%
+already right I have a Omega D and the
+ 
+
+ align:start position:0%
+already right I have a Omega D and the
+10 tangents Delta the functional points
+
+ align:start position:0%
+10 tangents Delta the functional points
+ 
+
+ align:start position:0%
+10 tangents Delta the functional points
+there therefore I can now write down
+
+ align:start position:0%
+there therefore I can now write down
+ 
+
+ align:start position:0%
+there therefore I can now write down
+what would be the a ok so a is actually
+
+ align:start position:0%
+what would be the a ok so a is actually
+ 
+
+ align:start position:0%
+what would be the a ok so a is actually
+just equal to F 0 divided by square root
+
+ align:start position:0%
+just equal to F 0 divided by square root
+ 
+
+ align:start position:0%
+just equal to F 0 divided by square root
+of Omega 0 square minus or me
+
+ align:start position:0%
+of Omega 0 square minus or me
+ 
+
+ align:start position:0%
+of Omega 0 square minus or me
+d square squared plus Omega P square
+
+ align:start position:0%
+d square squared plus Omega P square
+ 
+
+ align:start position:0%
+d square squared plus Omega P square
+gamma square okay okay so now the
+
+ align:start position:0%
+gamma square okay okay so now the
+ 
+
+ align:start position:0%
+gamma square okay okay so now the
+question is what does the result should
+
+ align:start position:0%
+question is what does the result should
+ 
+
+ align:start position:0%
+question is what does the result should
+be me I have this function okay I have
+
+ align:start position:0%
+be me I have this function okay I have
+ 
+
+ align:start position:0%
+be me I have this function okay I have
+that function tangent is soft it's
+
+ align:start position:0%
+that function tangent is soft it's
+ 
+
+ align:start position:0%
+that function tangent is soft it's
+actually the amplitude of the steady
+
+ align:start position:0%
+actually the amplitude of the steady
+ 
+
+ align:start position:0%
+actually the amplitude of the steady
+state solution and also the phase
+
+ align:start position:0%
+state solution and also the phase
+ 
+
+ align:start position:0%
+state solution and also the phase
+difference between the drag force phase
+
+ align:start position:0%
+difference between the drag force phase
+ 
+
+ align:start position:0%
+difference between the drag force phase
+and the steady state oscillation phase
+
+ align:start position:0%
+and the steady state oscillation phase
+ 
+
+ align:start position:0%
+and the steady state oscillation phase
+right so that issue that the among of
+
+ align:start position:0%
+right so that issue that the among of
+ 
+
+ align:start position:0%
+right so that issue that the among of
+lag and the size of the amplitude right
+
+ align:start position:0%
+lag and the size of the amplitude right
+ 
+
+ align:start position:0%
+lag and the size of the amplitude right
+but I but through this equation is very
+
+ align:start position:0%
+but I but through this equation is very
+ 
+
+ align:start position:0%
+but I but through this equation is very
+difficult to understand right so what
+
+ align:start position:0%
+difficult to understand right so what
+ 
+
+ align:start position:0%
+difficult to understand right so what
+I'm going to do is to take some limit so
+
+ align:start position:0%
+I'm going to do is to take some limit so
+ 
+
+ align:start position:0%
+I'm going to do is to take some limit so
+that actually we can help you to
+
+ align:start position:0%
+that actually we can help you to
+ 
+
+ align:start position:0%
+that actually we can help you to
+understand what is going down so suppose
+
+ align:start position:0%
+understand what is going down so suppose
+ 
+
+ align:start position:0%
+understand what is going down so suppose
+I assume that Omega T goes to zero okay
+
+ align:start position:0%
+I assume that Omega T goes to zero okay
+ 
+
+ align:start position:0%
+I assume that Omega T goes to zero okay
+so what does I mean this is Yun Jie's
+
+ align:start position:0%
+so what does I mean this is Yun Jie's
+ 
+
+ align:start position:0%
+so what does I mean this is Yun Jie's
+hand and eyes moving really slowly and
+
+ align:start position:0%
+hand and eyes moving really slowly and
+ 
+
+ align:start position:0%
+hand and eyes moving really slowly and
+see what is going to happen okay
+
+ align:start position:0%
+see what is going to happen okay
+ 
+
+ align:start position:0%
+see what is going to happen okay
+if I do this okay then you will find
+
+ align:start position:0%
+if I do this okay then you will find
+ 
+
+ align:start position:0%
+if I do this okay then you will find
+that a Omega D okay since Omega T goes
+
+ align:start position:0%
+that a Omega D okay since Omega T goes
+ 
+
+ align:start position:0%
+that a Omega D okay since Omega T goes
+to zero right this is gone this is gone
+
+ align:start position:0%
+to zero right this is gone this is gone
+ 
+
+ align:start position:0%
+to zero right this is gone this is gone
+right therefore you will see that Omega
+
+ align:start position:0%
+right therefore you will see that Omega
+ 
+
+ align:start position:0%
+right therefore you will see that Omega
+a will be equal to Omega zero divided by
+
+ align:start position:0%
+a will be equal to Omega zero divided by
+ 
+
+ align:start position:0%
+a will be equal to Omega zero divided by
+the way of the F zero divided by Omega 0
+
+ align:start position:0%
+the way of the F zero divided by Omega 0
+ 
+
+ align:start position:0%
+the way of the F zero divided by Omega 0
+square and that is actually equal to G
+
+ align:start position:0%
+square and that is actually equal to G
+ 
+
+ align:start position:0%
+square and that is actually equal to G
+Delta over L divided by G over L and now
+
+ align:start position:0%
+Delta over L divided by G over L and now
+ 
+
+ align:start position:0%
+Delta over L divided by G over L and now
+will give you Delta so what does that
+
+ align:start position:0%
+will give you Delta so what does that
+ 
+
+ align:start position:0%
+will give you Delta so what does that
+mean this means that if I move this
+
+ align:start position:0%
+mean this means that if I move this
+ 
+
+ align:start position:0%
+mean this means that if I move this
+thing drive this thing really slowly
+
+ align:start position:0%
+thing drive this thing really slowly
+ 
+
+ align:start position:0%
+thing drive this thing really slowly
+then the amplitude of the mass will be
+
+ align:start position:0%
+then the amplitude of the mass will be
+ 
+
+ align:start position:0%
+then the amplitude of the mass will be
+equal to how much I as you move which is
+
+ align:start position:0%
+equal to how much I as you move which is
+ 
+
+ align:start position:0%
+equal to how much I as you move which is
+total
+
+ align:start position:0%
+total
+ 
+
+ align:start position:0%
+total
+okay do get it in additional to that
+
+ align:start position:0%
+okay do get it in additional to that
+ 
+
+ align:start position:0%
+okay do get it in additional to that
+okay tangent do that since I'm taking
+
+ align:start position:0%
+okay tangent do that since I'm taking
+ 
+
+ align:start position:0%
+okay tangent do that since I'm taking
+the limit of Omega T goes to 0 therefore
+
+ align:start position:0%
+the limit of Omega T goes to 0 therefore
+ 
+
+ align:start position:0%
+the limit of Omega T goes to 0 therefore
+tangent theta will be equal to 0 and na
+
+ align:start position:0%
+tangent theta will be equal to 0 and na
+ 
+
+ align:start position:0%
+tangent theta will be equal to 0 and na
+means Delta will be equal to 0
+
+ align:start position:0%
+means Delta will be equal to 0
+ 
+
+ align:start position:0%
+means Delta will be equal to 0
+any questions so that means there will
+
+ align:start position:0%
+any questions so that means there will
+ 
+
+ align:start position:0%
+any questions so that means there will
+be no phase difference that cistern have
+
+ align:start position:0%
+be no phase difference that cistern have
+ 
+
+ align:start position:0%
+be no phase difference that cistern have
+enough time to keep up with my speed ok
+
+ align:start position:0%
+enough time to keep up with my speed ok
+ 
+
+ align:start position:0%
+enough time to keep up with my speed ok
+the second limit obviously Omega T goes
+
+ align:start position:0%
+the second limit obviously Omega T goes
+ 
+
+ align:start position:0%
+the second limit obviously Omega T goes
+to infinity okay what does I mean that
+
+ align:start position:0%
+to infinity okay what does I mean that
+ 
+
+ align:start position:0%
+to infinity okay what does I mean that
+means I am going to hold this string
+
+ align:start position:0%
+means I am going to hold this string
+ 
+
+ align:start position:0%
+means I am going to hold this string
+shaking like crazy really fast okay and
+
+ align:start position:0%
+shaking like crazy really fast okay and
+ 
+
+ align:start position:0%
+shaking like crazy really fast okay and
+see what what happened okay so in that
+
+ align:start position:0%
+see what what happened okay so in that
+ 
+
+ align:start position:0%
+see what what happened okay so in that
+case you will get a Omega D and that
+
+ align:start position:0%
+case you will get a Omega D and that
+ 
+
+ align:start position:0%
+case you will get a Omega D and that
+goes to 0 because Omega T goes to
+
+ align:start position:0%
+goes to 0 because Omega T goes to
+ 
+
+ align:start position:0%
+goes to 0 because Omega T goes to
+infinity right this goes to 0 and also
+
+ align:start position:0%
+infinity right this goes to 0 and also
+ 
+
+ align:start position:0%
+infinity right this goes to 0 and also
+tangent Delta goes to infinity therefore
+
+ align:start position:0%
+tangent Delta goes to infinity therefore
+ 
+
+ align:start position:0%
+tangent Delta goes to infinity therefore
+Delta what goes to PI so that means
+
+ align:start position:0%
+Delta what goes to PI so that means
+ 
+
+ align:start position:0%
+Delta what goes to PI so that means
+there will be out of phase okay any
+
+ align:start position:0%
+there will be out of phase okay any
+ 
+
+ align:start position:0%
+there will be out of phase okay any
+questions so far in these two limits ok
+
+ align:start position:0%
+questions so far in these two limits ok
+ 
+
+ align:start position:0%
+questions so far in these two limits ok
+so what I'm going to do now is to take a
+
+ align:start position:0%
+so what I'm going to do now is to take a
+ 
+
+ align:start position:0%
+so what I'm going to do now is to take a
+small toy which I made for my son with
+
+ align:start position:0%
+small toy which I made for my son with
+ 
+
+ align:start position:0%
+small toy which I made for my son with
+one year oh now because I would like to
+
+ align:start position:0%
+one year oh now because I would like to
+ 
+
+ align:start position:0%
+one year oh now because I would like to
+him to learn waves and vibration before
+
+ align:start position:0%
+him to learn waves and vibration before
+ 
+
+ align:start position:0%
+him to learn waves and vibration before
+he goes to content right alright so I
+
+ align:start position:0%
+he goes to content right alright so I
+ 
+
+ align:start position:0%
+he goes to content right alright so I
+made this toy and he so don't get it
+
+ align:start position:0%
+made this toy and he so don't get it
+ 
+
+ align:start position:0%
+made this toy and he so don't get it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so you can see now I can
+
+ align:start position:0%
+all right so you can see now I can
+ 
+
+ align:start position:0%
+all right so you can see now I can
+demonstrate what is going to happen when
+
+ align:start position:0%
+demonstrate what is going to happen when
+ 
+
+ align:start position:0%
+demonstrate what is going to happen when
+Omega is approaching to zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm ready to win it can you see it no
+
+ align:start position:0%
+I'm ready to win it can you see it no
+ 
+
+ align:start position:0%
+I'm ready to win it can you see it no
+it's a very exciting experiment can you
+
+ align:start position:0%
+it's a very exciting experiment can you
+ 
+
+ align:start position:0%
+it's a very exciting experiment can you
+see that you see that this is original
+
+ align:start position:0%
+see that you see that this is original
+ 
+
+ align:start position:0%
+see that you see that this is original
+vertical direction if I do it really
+
+ align:start position:0%
+vertical direction if I do it really
+ 
+
+ align:start position:0%
+vertical direction if I do it really
+really slowly okay you can see that the
+
+ align:start position:0%
+really slowly okay you can see that the
+ 
+
+ align:start position:0%
+really slowly okay you can see that the
+amplitude of the ball is actually
+
+ align:start position:0%
+amplitude of the ball is actually
+ 
+
+ align:start position:0%
+amplitude of the ball is actually
+exactly the same as the displacement I
+
+ align:start position:0%
+exactly the same as the displacement I
+ 
+
+ align:start position:0%
+exactly the same as the displacement I
+introduced right so that's actually kind
+
+ align:start position:0%
+introduced right so that's actually kind
+ 
+
+ align:start position:0%
+introduced right so that's actually kind
+of a bit obvious right okay so now let's
+
+ align:start position:0%
+of a bit obvious right okay so now let's
+ 
+
+ align:start position:0%
+of a bit obvious right okay so now let's
+see what is going to happen if I type
+
+ align:start position:0%
+see what is going to happen if I type
+ 
+
+ align:start position:0%
+see what is going to happen if I type
+this system like crazy
+
+ align:start position:0%
+this system like crazy
+ 
+
+ align:start position:0%
+this system like crazy
+okay not going up and down that's what
+
+ align:start position:0%
+okay not going up and down that's what
+ 
+
+ align:start position:0%
+okay not going up and down that's what
+makes it must be I can do maybe you can
+
+ align:start position:0%
+makes it must be I can do maybe you can
+ 
+
+ align:start position:0%
+makes it must be I can do maybe you can
+do it better faster but you can see that
+
+ align:start position:0%
+do it better faster but you can see that
+ 
+
+ align:start position:0%
+do it better faster but you can see that
+nothing happened right
+
+ align:start position:0%
+nothing happened right
+ 
+
+ align:start position:0%
+nothing happened right
+so mp2 is close to zero because what you
+
+ align:start position:0%
+so mp2 is close to zero because what you
+ 
+
+ align:start position:0%
+so mp2 is close to zero because what you
+have been doing so what you know
+
+ align:start position:0%
+have been doing so what you know
+ 
+
+ align:start position:0%
+have been doing so what you know
+disappear I mean you call cancel to each
+
+ align:start position:0%
+disappear I mean you call cancel to each
+ 
+
+ align:start position:0%
+disappear I mean you call cancel to each
+other cancelling each other right and
+
+ align:start position:0%
+other cancelling each other right and
+ 
+
+ align:start position:0%
+other cancelling each other right and
+it's actually not going to contribute to
+
+ align:start position:0%
+it's actually not going to contribute to
+ 
+
+ align:start position:0%
+it's actually not going to contribute to
+the motion of this this ball okay so now
+
+ align:start position:0%
+the motion of this this ball okay so now
+ 
+
+ align:start position:0%
+the motion of this this ball okay so now
+you can see that I can also test what is
+
+ align:start position:0%
+you can see that I can also test what is
+ 
+
+ align:start position:0%
+you can see that I can also test what is
+actually the natural frequency and what
+
+ align:start position:0%
+actually the natural frequency and what
+ 
+
+ align:start position:0%
+actually the natural frequency and what
+I'm going to do is to oscillate around
+
+ align:start position:0%
+I'm going to do is to oscillate around
+ 
+
+ align:start position:0%
+I'm going to do is to oscillate around
+the nature of frequency to see what is
+
+ align:start position:0%
+the nature of frequency to see what is
+ 
+
+ align:start position:0%
+the nature of frequency to see what is
+going to happen okay let's see what is
+
+ align:start position:0%
+going to happen okay let's see what is
+ 
+
+ align:start position:0%
+going to happen okay let's see what is
+going to happen you can see that the
+
+ align:start position:0%
+going to happen you can see that the
+ 
+
+ align:start position:0%
+going to happen you can see that the
+Delta is really small right can you see
+
+ align:start position:0%
+Delta is really small right can you see
+ 
+
+ align:start position:0%
+Delta is really small right can you see
+the tilde it's really small very small
+
+ align:start position:0%
+the tilde it's really small very small
+ 
+
+ align:start position:0%
+the tilde it's really small very small
+very small but you can see that the
+
+ align:start position:0%
+very small but you can see that the
+ 
+
+ align:start position:0%
+very small but you can see that the
+amplitude the a is huge what does that
+
+ align:start position:0%
+amplitude the a is huge what does that
+ 
+
+ align:start position:0%
+amplitude the a is huge what does that
+tell us what does that tell us
+
+ align:start position:0%
+tell us what does that tell us
+ 
+
+ align:start position:0%
+tell us what does that tell us
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yes we are experiencing resonance and
+
+ align:start position:0%
+yes we are experiencing resonance and
+ 
+
+ align:start position:0%
+yes we are experiencing resonance and
+also that also tells you that the system
+
+ align:start position:0%
+also that also tells you that the system
+ 
+
+ align:start position:0%
+also that also tells you that the system
+is under damped very much the Q value is
+
+ align:start position:0%
+is under damped very much the Q value is
+ 
+
+ align:start position:0%
+is under damped very much the Q value is
+very big okay so if I calculate the
+
+ align:start position:0%
+very big okay so if I calculate the
+ 
+
+ align:start position:0%
+very big okay so if I calculate the
+amplitude a okay now I can calculate the
+
+ align:start position:0%
+amplitude a okay now I can calculate the
+ 
+
+ align:start position:0%
+amplitude a okay now I can calculate the
+MP to a at natural frequency okay what
+
+ align:start position:0%
+MP to a at natural frequency okay what
+ 
+
+ align:start position:0%
+MP to a at natural frequency okay what
+I'm going to get is now I can as you
+
+ align:start position:0%
+I'm going to get is now I can as you
+ 
+
+ align:start position:0%
+I'm going to get is now I can as you
+plug in Omega T equal to omega0 okay so
+
+ align:start position:0%
+plug in Omega T equal to omega0 okay so
+ 
+
+ align:start position:0%
+plug in Omega T equal to omega0 okay so
+if I plug in Omega T Omega T equal to
+
+ align:start position:0%
+if I plug in Omega T Omega T equal to
+ 
+
+ align:start position:0%
+if I plug in Omega T Omega T equal to
+Omega 0 then what is going to happen so
+
+ align:start position:0%
+Omega 0 then what is going to happen so
+ 
+
+ align:start position:0%
+Omega 0 then what is going to happen so
+this term will cancel right so you have
+
+ align:start position:0%
+this term will cancel right so you have
+ 
+
+ align:start position:0%
+this term will cancel right so you have
+a will equal to f0 divided by Omega 0
+
+ align:start position:0%
+a will equal to f0 divided by Omega 0
+ 
+
+ align:start position:0%
+a will equal to f0 divided by Omega 0
+squared Omega 0 comma right Omega T is
+
+ align:start position:0%
+squared Omega 0 comma right Omega T is
+ 
+
+ align:start position:0%
+squared Omega 0 comma right Omega T is
+now equal to Omega 0 okay and that is
+
+ align:start position:0%
+now equal to Omega 0 okay and that is
+ 
+
+ align:start position:0%
+now equal to Omega 0 okay and that is
+going to keep keep you okay so f0 is
+
+ align:start position:0%
+going to keep keep you okay so f0 is
+ 
+
+ align:start position:0%
+going to keep keep you okay so f0 is
+they should be Omega 0 square Delta
+
+ align:start position:0%
+they should be Omega 0 square Delta
+ 
+
+ align:start position:0%
+they should be Omega 0 square Delta
+divided by Omega 0 okay and 1 Omega 0
+
+ align:start position:0%
+divided by Omega 0 okay and 1 Omega 0
+ 
+
+ align:start position:0%
+divided by Omega 0 okay and 1 Omega 0
+has to cancel then basically you will
+
+ align:start position:0%
+has to cancel then basically you will
+ 
+
+ align:start position:0%
+has to cancel then basically you will
+get Q times Delta okay what is Q just a
+
+ align:start position:0%
+get Q times Delta okay what is Q just a
+ 
+
+ align:start position:0%
+get Q times Delta okay what is Q just a
+reminder it's actually the ratio of
+
+ align:start position:0%
+reminder it's actually the ratio of
+ 
+
+ align:start position:0%
+reminder it's actually the ratio of
+Omega 0 and the gamma when the Q is very
+
+ align:start position:0%
+Omega 0 and the gamma when the Q is very
+ 
+
+ align:start position:0%
+Omega 0 and the gamma when the Q is very
+large what does that mean that means is
+
+ align:start position:0%
+large what does that mean that means is
+ 
+
+ align:start position:0%
+large what does that mean that means is
+so close to idealize the situation the
+
+ align:start position:0%
+so close to idealize the situation the
+ 
+
+ align:start position:0%
+so close to idealize the situation the
+drag force is very small okay
+
+ align:start position:0%
+drag force is very small okay
+ 
+
+ align:start position:0%
+drag force is very small okay
+you can see that in the example at which
+
+ align:start position:0%
+you can see that in the example at which
+ 
+
+ align:start position:0%
+you can see that in the example at which
+I have been doing right so you can see
+
+ align:start position:0%
+I have been doing right so you can see
+ 
+
+ align:start position:0%
+I have been doing right so you can see
+that ah it is really the case right so
+
+ align:start position:0%
+that ah it is really the case right so
+ 
+
+ align:start position:0%
+that ah it is really the case right so
+you can see that if my Delta is
+
+ align:start position:0%
+you can see that if my Delta is
+ 
+
+ align:start position:0%
+you can see that if my Delta is
+something like 1 centimeter right for
+
+ align:start position:0%
+something like 1 centimeter right for
+ 
+
+ align:start position:0%
+something like 1 centimeter right for
+the amplitude
+
+ align:start position:0%
+the amplitude
+ 
+
+ align:start position:0%
+the amplitude
+essentially at the order of 1 meter
+
+ align:start position:0%
+essentially at the order of 1 meter
+ 
+
+ align:start position:0%
+essentially at the order of 1 meter
+maybe what does that mean that means the
+
+ align:start position:0%
+maybe what does that mean that means the
+ 
+
+ align:start position:0%
+maybe what does that mean that means the
+queue is actually roughly 100 okay so
+
+ align:start position:0%
+queue is actually roughly 100 okay so
+ 
+
+ align:start position:0%
+queue is actually roughly 100 okay so
+you can easily even get a queue out of
+
+ align:start position:0%
+you can easily even get a queue out of
+ 
+
+ align:start position:0%
+you can easily even get a queue out of
+this experiment okay any questions so
+
+ align:start position:0%
+this experiment okay any questions so
+ 
+
+ align:start position:0%
+this experiment okay any questions so
+far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's very good so now we can go
+
+ align:start position:0%
+okay that's very good so now we can go
+ 
+
+ align:start position:0%
+okay that's very good so now we can go
+ahead and take a look at the structure
+
+ align:start position:0%
+ahead and take a look at the structure
+ 
+
+ align:start position:0%
+ahead and take a look at the structure
+of a and the Delta okay as we
+
+ align:start position:0%
+of a and the Delta okay as we
+ 
+
+ align:start position:0%
+of a and the Delta okay as we
+demonstrate it before we make sense of
+
+ align:start position:0%
+demonstrate it before we make sense of
+ 
+
+ align:start position:0%
+demonstrate it before we make sense of
+the three different kinds of situation
+
+ align:start position:0%
+the three different kinds of situation
+ 
+
+ align:start position:0%
+the three different kinds of situation
+Omega T cos of 0 Omega T goes to
+
+ align:start position:0%
+Omega T cos of 0 Omega T goes to
+ 
+
+ align:start position:0%
+Omega T cos of 0 Omega T goes to
+infinity and of course I would like to
+
+ align:start position:0%
+infinity and of course I would like to
+ 
+
+ align:start position:0%
+infinity and of course I would like to
+know the full structure of those a and
+
+ align:start position:0%
+know the full structure of those a and
+ 
+
+ align:start position:0%
+know the full structure of those a and
+Delta therefore what I'm going to do is
+
+ align:start position:0%
+Delta therefore what I'm going to do is
+ 
+
+ align:start position:0%
+Delta therefore what I'm going to do is
+to plot a Omega T ok that's a function
+
+ align:start position:0%
+to plot a Omega T ok that's a function
+ 
+
+ align:start position:0%
+to plot a Omega T ok that's a function
+of Omega T ok so what I'm going to do
+
+ align:start position:0%
+of Omega T ok so what I'm going to do
+ 
+
+ align:start position:0%
+of Omega T ok so what I'm going to do
+what I can I'm going to get is this will
+
+ align:start position:0%
+what I can I'm going to get is this will
+ 
+
+ align:start position:0%
+what I can I'm going to get is this will
+be equal to theta when Omega T goes to
+
+ align:start position:0%
+be equal to theta when Omega T goes to
+ 
+
+ align:start position:0%
+be equal to theta when Omega T goes to
+zero right we just demonstrated that
+
+ align:start position:0%
+zero right we just demonstrated that
+ 
+
+ align:start position:0%
+zero right we just demonstrated that
+right and this will increase to a large
+
+ align:start position:0%
+right and this will increase to a large
+ 
+
+ align:start position:0%
+right and this will increase to a large
+value and drop down to some two to zero
+
+ align:start position:0%
+value and drop down to some two to zero
+ 
+
+ align:start position:0%
+value and drop down to some two to zero
+when you when Omega T goes to infinity
+
+ align:start position:0%
+when you when Omega T goes to infinity
+ 
+
+ align:start position:0%
+when you when Omega T goes to infinity
+okay and you can see that this is around
+
+ align:start position:0%
+okay and you can see that this is around
+ 
+
+ align:start position:0%
+okay and you can see that this is around
+Omega zero and that you are going to get
+
+ align:start position:0%
+Omega zero and that you are going to get
+ 
+
+ align:start position:0%
+Omega zero and that you are going to get
+a huge amplitude okay at run Omega zero
+
+ align:start position:0%
+a huge amplitude okay at run Omega zero
+ 
+
+ align:start position:0%
+a huge amplitude okay at run Omega zero
+but not quite that maximises should be
+
+ align:start position:0%
+but not quite that maximises should be
+ 
+
+ align:start position:0%
+but not quite that maximises should be
+slightly smaller than Omega zero you can
+
+ align:start position:0%
+slightly smaller than Omega zero you can
+ 
+
+ align:start position:0%
+slightly smaller than Omega zero you can
+actually calculate that as a part of the
+
+ align:start position:0%
+actually calculate that as a part of the
+ 
+
+ align:start position:0%
+actually calculate that as a part of the
+homework okay so that makes sense now I
+
+ align:start position:0%
+homework okay so that makes sense now I
+ 
+
+ align:start position:0%
+homework okay so that makes sense now I
+can also press the the Delta which is
+
+ align:start position:0%
+can also press the the Delta which is
+ 
+
+ align:start position:0%
+can also press the the Delta which is
+the phase difference okay and you can
+
+ align:start position:0%
+the phase difference okay and you can
+ 
+
+ align:start position:0%
+the phase difference okay and you can
+see that this phase difference will be
+
+ align:start position:0%
+see that this phase difference will be
+ 
+
+ align:start position:0%
+see that this phase difference will be
+originally zero when the Omega T is very
+
+ align:start position:0%
+originally zero when the Omega T is very
+ 
+
+ align:start position:0%
+originally zero when the Omega T is very
+small and this is actually Omega zero I
+
+ align:start position:0%
+small and this is actually Omega zero I
+ 
+
+ align:start position:0%
+small and this is actually Omega zero I
+hope you can see it okay and this will
+
+ align:start position:0%
+hope you can see it okay and this will
+ 
+
+ align:start position:0%
+hope you can see it okay and this will
+be increasing rapidly here and
+
+ align:start position:0%
+be increasing rapidly here and
+ 
+
+ align:start position:0%
+be increasing rapidly here and
+approaching to two pi okay so that
+
+ align:start position:0%
+approaching to two pi okay so that
+ 
+
+ align:start position:0%
+approaching to two pi okay so that
+means when you are shaking this system
+
+ align:start position:0%
+means when you are shaking this system
+ 
+
+ align:start position:0%
+means when you are shaking this system
+like crazy very high frequency then the
+
+ align:start position:0%
+like crazy very high frequency then the
+ 
+
+ align:start position:0%
+like crazy very high frequency then the
+system cannot keep up with the lip speed
+
+ align:start position:0%
+system cannot keep up with the lip speed
+ 
+
+ align:start position:0%
+system cannot keep up with the lip speed
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the amplitude will be very small and
+
+ align:start position:0%
+the amplitude will be very small and
+ 
+
+ align:start position:0%
+the amplitude will be very small and
+also the amplitude will be out of phase
+
+ align:start position:0%
+also the amplitude will be out of phase
+ 
+
+ align:start position:0%
+also the amplitude will be out of phase
+completely okay so that's actually to us
+
+ align:start position:0%
+completely okay so that's actually to us
+ 
+
+ align:start position:0%
+completely okay so that's actually to us
+another demonstration you've seen this
+
+ align:start position:0%
+another demonstration you've seen this
+ 
+
+ align:start position:0%
+another demonstration you've seen this
+little device here this is actually what
+
+ align:start position:0%
+little device here this is actually what
+ 
+
+ align:start position:0%
+little device here this is actually what
+you see before the LeBeau with a Mexican
+
+ align:start position:0%
+you see before the LeBeau with a Mexican
+ 
+
+ align:start position:0%
+you see before the LeBeau with a Mexican
+head okay and you can see that there is
+
+ align:start position:0%
+head okay and you can see that there is
+ 
+
+ align:start position:0%
+head okay and you can see that there is
+a spring attached to this system and on
+
+ align:start position:0%
+a spring attached to this system and on
+ 
+
+ align:start position:0%
+a spring attached to this system and on
+the top what I'm going to do is to use
+
+ align:start position:0%
+the top what I'm going to do is to use
+ 
+
+ align:start position:0%
+the top what I'm going to do is to use
+this motor to drive this system up and
+
+ align:start position:0%
+this motor to drive this system up and
+ 
+
+ align:start position:0%
+this motor to drive this system up and
+down okay where's drag force okay so now
+
+ align:start position:0%
+down okay where's drag force okay so now
+ 
+
+ align:start position:0%
+down okay where's drag force okay so now
+what I'm going to do is to come from a
+
+ align:start position:0%
+what I'm going to do is to come from a
+ 
+
+ align:start position:0%
+what I'm going to do is to come from a
+very low frequency oscillation so you
+
+ align:start position:0%
+very low frequency oscillation so you
+ 
+
+ align:start position:0%
+very low frequency oscillation so you
+can see that the natural frequency is
+
+ align:start position:0%
+can see that the natural frequency is
+ 
+
+ align:start position:0%
+can see that the natural frequency is
+sort of like this
+
+ align:start position:0%
+sort of like this
+ 
+
+ align:start position:0%
+sort of like this
+okay and you can see that okay now i'm
+
+ align:start position:0%
+okay and you can see that okay now i'm
+ 
+
+ align:start position:0%
+okay and you can see that okay now i'm
+tribe in this system really slowly you
+
+ align:start position:0%
+tribe in this system really slowly you
+ 
+
+ align:start position:0%
+tribe in this system really slowly you
+can see this is actually going up and
+
+ align:start position:0%
+can see this is actually going up and
+ 
+
+ align:start position:0%
+can see this is actually going up and
+down reduce slowly okay and you see that
+
+ align:start position:0%
+down reduce slowly okay and you see that
+ 
+
+ align:start position:0%
+down reduce slowly okay and you see that
+huh the amplitude is actually pretty
+
+ align:start position:0%
+huh the amplitude is actually pretty
+ 
+
+ align:start position:0%
+huh the amplitude is actually pretty
+small right there's no excitement for
+
+ align:start position:0%
+small right there's no excitement for
+ 
+
+ align:start position:0%
+small right there's no excitement for
+the moment okay alright so what I'm
+
+ align:start position:0%
+the moment okay alright so what I'm
+ 
+
+ align:start position:0%
+the moment okay alright so what I'm
+going to do is now I increase the speed
+
+ align:start position:0%
+going to do is now I increase the speed
+ 
+
+ align:start position:0%
+going to do is now I increase the speed
+of the motor and see what happened so
+
+ align:start position:0%
+of the motor and see what happened so
+ 
+
+ align:start position:0%
+of the motor and see what happened so
+you can see now this is also essentially
+
+ align:start position:0%
+you can see now this is also essentially
+ 
+
+ align:start position:0%
+you can see now this is also essentially
+driving it with higher and higher
+
+ align:start position:0%
+driving it with higher and higher
+ 
+
+ align:start position:0%
+driving it with higher and higher
+frequency you see that something is
+
+ align:start position:0%
+frequency you see that something is
+ 
+
+ align:start position:0%
+frequency you see that something is
+happening you can see the amplitude is
+
+ align:start position:0%
+happening you can see the amplitude is
+ 
+
+ align:start position:0%
+happening you can see the amplitude is
+getting larger and larger and still
+
+ align:start position:0%
+getting larger and larger and still
+ 
+
+ align:start position:0%
+getting larger and larger and still
+increasing the time the frequency
+
+ align:start position:0%
+increasing the time the frequency
+ 
+
+ align:start position:0%
+increasing the time the frequency
+increasing increasing until something
+
+ align:start position:0%
+increasing increasing until something
+ 
+
+ align:start position:0%
+increasing increasing until something
+something happened right did you see
+
+ align:start position:0%
+something happened right did you see
+ 
+
+ align:start position:0%
+something happened right did you see
+that start to oscillate
+
+ align:start position:0%
+that start to oscillate
+ 
+
+ align:start position:0%
+that start to oscillate
+benda right because right now you can
+
+ align:start position:0%
+benda right because right now you can
+ 
+
+ align:start position:0%
+benda right because right now you can
+see that look at the top okay
+
+ align:start position:0%
+see that look at the top okay
+ 
+
+ align:start position:0%
+see that look at the top okay
+the frequency of the motor is now really
+
+ align:start position:0%
+the frequency of the motor is now really
+ 
+
+ align:start position:0%
+the frequency of the motor is now really
+close to the frequency the natural
+
+ align:start position:0%
+close to the frequency the natural
+ 
+
+ align:start position:0%
+close to the frequency the natural
+frequency of this system okay so so a
+
+ align:start position:0%
+frequency of this system okay so so a
+ 
+
+ align:start position:0%
+frequency of this system okay so so a
+resonance behaviour will happen and what
+
+ align:start position:0%
+resonance behaviour will happen and what
+ 
+
+ align:start position:0%
+resonance behaviour will happen and what
+do you what you are going to get is that
+
+ align:start position:0%
+do you what you are going to get is that
+ 
+
+ align:start position:0%
+do you what you are going to get is that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+Omega Omega D around Omega zero then you
+
+ align:start position:0%
+Omega Omega D around Omega zero then you
+ 
+
+ align:start position:0%
+Omega Omega D around Omega zero then you
+are going to get large time every two
+
+ align:start position:0%
+are going to get large time every two
+ 
+
+ align:start position:0%
+are going to get large time every two
+okay so now what I'm going to do is to
+
+ align:start position:0%
+okay so now what I'm going to do is to
+ 
+
+ align:start position:0%
+okay so now what I'm going to do is to
+continue to increase the driving
+
+ align:start position:0%
+continue to increase the driving
+ 
+
+ align:start position:0%
+continue to increase the driving
+frequency to a very large value okay now
+
+ align:start position:0%
+frequency to a very large value okay now
+ 
+
+ align:start position:0%
+frequency to a very large value okay now
+it's actually doing the mmm doing this
+
+ align:start position:0%
+it's actually doing the mmm doing this
+ 
+
+ align:start position:0%
+it's actually doing the mmm doing this
+really fast you can see top very fast I
+
+ align:start position:0%
+really fast you can see top very fast I
+ 
+
+ align:start position:0%
+really fast you can see top very fast I
+can even kill even faster you see that
+
+ align:start position:0%
+can even kill even faster you see that
+ 
+
+ align:start position:0%
+can even kill even faster you see that
+ha indeed this system is now oscillating
+
+ align:start position:0%
+ha indeed this system is now oscillating
+ 
+
+ align:start position:0%
+ha indeed this system is now oscillating
+at a larger frequency right is trying to
+
+ align:start position:0%
+at a larger frequency right is trying to
+ 
+
+ align:start position:0%
+at a larger frequency right is trying to
+keep up with the driving force but you
+
+ align:start position:0%
+keep up with the driving force but you
+ 
+
+ align:start position:0%
+keep up with the driving force but you
+can see that the amplitude is actually
+
+ align:start position:0%
+can see that the amplitude is actually
+ 
+
+ align:start position:0%
+can see that the amplitude is actually
+much smaller than what had happened
+
+ align:start position:0%
+much smaller than what had happened
+ 
+
+ align:start position:0%
+much smaller than what had happened
+before so so you before the class you
+
+ align:start position:0%
+before so so you before the class you
+ 
+
+ align:start position:0%
+before so so you before the class you
+may actually think that okay try be
+
+ align:start position:0%
+may actually think that okay try be
+ 
+
+ align:start position:0%
+may actually think that okay try be
+really fast maybe we'll increase the
+
+ align:start position:0%
+really fast maybe we'll increase the
+ 
+
+ align:start position:0%
+really fast maybe we'll increase the
+amplitude but in reality actually you
+
+ align:start position:0%
+amplitude but in reality actually you
+ 
+
+ align:start position:0%
+amplitude but in reality actually you
+will give you a very small amplitude
+
+ align:start position:0%
+will give you a very small amplitude
+ 
+
+ align:start position:0%
+will give you a very small amplitude
+okay another thing which is interesting
+
+ align:start position:0%
+okay another thing which is interesting
+ 
+
+ align:start position:0%
+okay another thing which is interesting
+to know is that you can see that when
+
+ align:start position:0%
+to know is that you can see that when
+ 
+
+ align:start position:0%
+to know is that you can see that when
+the tribe is that when the driving force
+
+ align:start position:0%
+the tribe is that when the driving force
+ 
+
+ align:start position:0%
+the tribe is that when the driving force
+is actually at the Maxima okay and
+
+ align:start position:0%
+is actually at the Maxima okay and
+ 
+
+ align:start position:0%
+is actually at the Maxima okay and
+actually this the position of this mass
+
+ align:start position:0%
+actually this the position of this mass
+ 
+
+ align:start position:0%
+actually this the position of this mass
+is a atom at a minimum right so they are
+
+ align:start position:0%
+is a atom at a minimum right so they are
+ 
+
+ align:start position:0%
+is a atom at a minimum right so they are
+actually out of phase okay I hope you
+
+ align:start position:0%
+actually out of phase okay I hope you
+ 
+
+ align:start position:0%
+actually out of phase okay I hope you
+can see it right beside this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what you can see is that when I
+
+ align:start position:0%
+okay so what you can see is that when I
+ 
+
+ align:start position:0%
+okay so what you can see is that when I
+understand this system and I try to
+
+ align:start position:0%
+understand this system and I try to
+ 
+
+ align:start position:0%
+understand this system and I try to
+drive it with the natural frequency what
+
+ align:start position:0%
+drive it with the natural frequency what
+ 
+
+ align:start position:0%
+drive it with the natural frequency what
+is going to happen is that I am exciting
+
+ align:start position:0%
+is going to happen is that I am exciting
+ 
+
+ align:start position:0%
+is going to happen is that I am exciting
+this system to a stay of resonance right
+
+ align:start position:0%
+this system to a stay of resonance right
+ 
+
+ align:start position:0%
+this system to a stay of resonance right
+so basically your case on resonance
+
+ align:start position:0%
+so basically your case on resonance
+ 
+
+ align:start position:0%
+so basically your case on resonance
+behavior so I have shown you that this
+
+ align:start position:0%
+behavior so I have shown you that this
+ 
+
+ align:start position:0%
+behavior so I have shown you that this
+works for driven couple mechanical
+
+ align:start position:0%
+works for driven couple mechanical
+ 
+
+ align:start position:0%
+works for driven couple mechanical
+oscillator he also works for the spring
+
+ align:start position:0%
+oscillator he also works for the spring
+ 
+
+ align:start position:0%
+oscillator he also works for the spring
+mass system right and there are many
+
+ align:start position:0%
+mass system right and there are many
+ 
+
+ align:start position:0%
+mass system right and there are many
+other things which also works which is
+
+ align:start position:0%
+other things which also works which is
+ 
+
+ align:start position:0%
+other things which also works which is
+around you right for example if you
+
+ align:start position:0%
+around you right for example if you
+ 
+
+ align:start position:0%
+around you right for example if you
+happen to be in my office hour okay you
+
+ align:start position:0%
+happen to be in my office hour okay you
+ 
+
+ align:start position:0%
+happen to be in my office hour okay you
+will notice that the air condition in my
+
+ align:start position:0%
+will notice that the air condition in my
+ 
+
+ align:start position:0%
+will notice that the air condition in my
+office is actually creating a resonance
+
+ align:start position:0%
+office is actually creating a resonance
+ 
+
+ align:start position:0%
+office is actually creating a resonance
+behavior you see low frequencies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something is like something like that
+
+ align:start position:0%
+something is like something like that
+ 
+
+ align:start position:0%
+something is like something like that
+and that is because the pipe is actually
+
+ align:start position:0%
+and that is because the pipe is actually
+ 
+
+ align:start position:0%
+and that is because the pipe is actually
+having happened to have the frequency
+
+ align:start position:0%
+having happened to have the frequency
+ 
+
+ align:start position:0%
+having happened to have the frequency
+match with the resonance frequency okay
+
+ align:start position:0%
+match with the resonance frequency okay
+ 
+
+ align:start position:0%
+match with the resonance frequency okay
+the airflow issue happened to excite the
+
+ align:start position:0%
+the airflow issue happened to excite the
+ 
+
+ align:start position:0%
+the airflow issue happened to excite the
+the pipe so that is we essentially other
+
+ align:start position:0%
+the pipe so that is we essentially other
+ 
+
+ align:start position:0%
+the pipe so that is we essentially other
+than yumping dam at a frequency so what
+
+ align:start position:0%
+than yumping dam at a frequency so what
+ 
+
+ align:start position:0%
+than yumping dam at a frequency so what
+I did was I try to turn it down to low
+
+ align:start position:0%
+I did was I try to turn it down to low
+ 
+
+ align:start position:0%
+I did was I try to turn it down to low
+and see what happened but unfortunately
+
+ align:start position:0%
+and see what happened but unfortunately
+ 
+
+ align:start position:0%
+and see what happened but unfortunately
+yes you excite another resonance okay I
+
+ align:start position:0%
+yes you excite another resonance okay I
+ 
+
+ align:start position:0%
+yes you excite another resonance okay I
+see now another low frequency sound but
+
+ align:start position:0%
+see now another low frequency sound but
+ 
+
+ align:start position:0%
+see now another low frequency sound but
+a very high frequency sound I will post
+
+ align:start position:0%
+a very high frequency sound I will post
+ 
+
+ align:start position:0%
+a very high frequency sound I will post
+a video it should be online so my life
+
+ align:start position:0%
+a video it should be online so my life
+ 
+
+ align:start position:0%
+a video it should be online so my life
+is hard right so but I mean I never
+
+ align:start position:0%
+is hard right so but I mean I never
+ 
+
+ align:start position:0%
+is hard right so but I mean I never
+physicist so I choose to use the median
+
+ align:start position:0%
+physicist so I choose to use the median
+ 
+
+ align:start position:0%
+physicist so I choose to use the median
+then I actually stay between the two
+
+ align:start position:0%
+then I actually stay between the two
+ 
+
+ align:start position:0%
+then I actually stay between the two
+resonance then I don't see like the
+
+ align:start position:0%
+resonance then I don't see like the
+ 
+
+ align:start position:0%
+resonance then I don't see like the
+night on here the additional song which
+
+ align:start position:0%
+night on here the additional song which
+ 
+
+ align:start position:0%
+night on here the additional song which
+passes me okay another example is that
+
+ align:start position:0%
+passes me okay another example is that
+ 
+
+ align:start position:0%
+passes me okay another example is that
+when I was in Taiwan as an undergrad I
+
+ align:start position:0%
+when I was in Taiwan as an undergrad I
+ 
+
+ align:start position:0%
+when I was in Taiwan as an undergrad I
+was living outside you know apartment
+
+ align:start position:0%
+was living outside you know apartment
+ 
+
+ align:start position:0%
+was living outside you know apartment
+and with my fret mate we owned a very
+
+ align:start position:0%
+and with my fret mate we owned a very
+ 
+
+ align:start position:0%
+and with my fret mate we owned a very
+old washing machine ok so in the middle
+
+ align:start position:0%
+old washing machine ok so in the middle
+ 
+
+ align:start position:0%
+old washing machine ok so in the middle
+of night the washing machine will start
+
+ align:start position:0%
+of night the washing machine will start
+ 
+
+ align:start position:0%
+of night the washing machine will start
+to walk around like my frat may okay and
+
+ align:start position:0%
+to walk around like my frat may okay and
+ 
+
+ align:start position:0%
+to walk around like my frat may okay and
+we were not scared because that is
+
+ align:start position:0%
+we were not scared because that is
+ 
+
+ align:start position:0%
+we were not scared because that is
+because the oscillation frequency
+
+ align:start position:0%
+because the oscillation frequency
+ 
+
+ align:start position:0%
+because the oscillation frequency
+actually the rotation it should happen
+
+ align:start position:0%
+actually the rotation it should happen
+ 
+
+ align:start position:0%
+actually the rotation it should happen
+to match with the frequency of the
+
+ align:start position:0%
+to match with the frequency of the
+ 
+
+ align:start position:0%
+to match with the frequency of the
+washing machine therefore when we start
+
+ align:start position:0%
+washing machine therefore when we start
+ 
+
+ align:start position:0%
+washing machine therefore when we start
+to wash our clothes they start to walk
+
+ align:start position:0%
+to wash our clothes they start to walk
+ 
+
+ align:start position:0%
+to wash our clothes they start to walk
+around in the room so as a physicist
+
+ align:start position:0%
+around in the room so as a physicist
+ 
+
+ align:start position:0%
+around in the room so as a physicist
+what we have decided is to make the spin
+
+ align:start position:0%
+what we have decided is to make the spin
+ 
+
+ align:start position:0%
+what we have decided is to make the spin
+slightly slower then as you can see that
+
+ align:start position:0%
+slightly slower then as you can see that
+ 
+
+ align:start position:0%
+slightly slower then as you can see that
+or even faster then issue you can see
+
+ align:start position:0%
+or even faster then issue you can see
+ 
+
+ align:start position:0%
+or even faster then issue you can see
+that when you do that then you get rid
+
+ align:start position:0%
+that when you do that then you get rid
+ 
+
+ align:start position:0%
+that when you do that then you get rid
+of the Restless behavior so it's not
+
+ align:start position:0%
+of the Restless behavior so it's not
+ 
+
+ align:start position:0%
+of the Restless behavior so it's not
+working around anymore
+
+ align:start position:0%
+working around anymore
+ 
+
+ align:start position:0%
+working around anymore
+we can control it okay another thing
+
+ align:start position:0%
+we can control it okay another thing
+ 
+
+ align:start position:0%
+we can control it okay another thing
+which is interesting is that the
+
+ align:start position:0%
+which is interesting is that the
+ 
+
+ align:start position:0%
+which is interesting is that the
+resonance behavior is not only in the
+
+ align:start position:0%
+resonance behavior is not only in the
+ 
+
+ align:start position:0%
+resonance behavior is not only in the
+physical object which we actually deal
+
+ align:start position:0%
+physical object which we actually deal
+ 
+
+ align:start position:0%
+physical object which we actually deal
+with these days also but after you learn
+
+ align:start position:0%
+with these days also but after you learn
+ 
+
+ align:start position:0%
+with these days also but after you learn
+quantum
+
+ align:start position:0%
+quantum
+ 
+
+ align:start position:0%
+quantum
+quantum field theory you'll find that
+
+ align:start position:0%
+quantum field theory you'll find that
+ 
+
+ align:start position:0%
+quantum field theory you'll find that
+there are resonance also in mass a wave
+
+ align:start position:0%
+there are resonance also in mass a wave
+ 
+
+ align:start position:0%
+there are resonance also in mass a wave
+function okay so basically you can see
+
+ align:start position:0%
+function okay so basically you can see
+ 
+
+ align:start position:0%
+function okay so basically you can see
+that these are example of the Z boson
+
+ align:start position:0%
+that these are example of the Z boson
+ 
+
+ align:start position:0%
+that these are example of the Z boson
+resonance peak so if you scatter in
+
+ align:start position:0%
+resonance peak so if you scatter in
+ 
+
+ align:start position:0%
+resonance peak so if you scatter in
+electron and positron then basically you
+
+ align:start position:0%
+electron and positron then basically you
+ 
+
+ align:start position:0%
+electron and positron then basically you
+see that the cross section have
+
+ align:start position:0%
+see that the cross section have
+ 
+
+ align:start position:0%
+see that the cross section have
+resonance peak at around 90 GeV okay and
+
+ align:start position:0%
+resonance peak at around 90 GeV okay and
+ 
+
+ align:start position:0%
+resonance peak at around 90 GeV okay and
+that is actually another very
+
+ align:start position:0%
+that is actually another very
+ 
+
+ align:start position:0%
+that is actually another very
+interesting example about resonance in
+
+ align:start position:0%
+interesting example about resonance in
+ 
+
+ align:start position:0%
+interesting example about resonance in
+particle physics finally the last
+
+ align:start position:0%
+particle physics finally the last
+ 
+
+ align:start position:0%
+particle physics finally the last
+example which I am going to go through
+
+ align:start position:0%
+example which I am going to go through
+ 
+
+ align:start position:0%
+example which I am going to go through
+is a example involving a glass okay we
+
+ align:start position:0%
+is a example involving a glass okay we
+ 
+
+ align:start position:0%
+is a example involving a glass okay we
+have prepared a very high-quality glass
+
+ align:start position:0%
+have prepared a very high-quality glass
+ 
+
+ align:start position:0%
+have prepared a very high-quality glass
+here okay maybe you have seen this class
+
+ align:start position:0%
+here okay maybe you have seen this class
+ 
+
+ align:start position:0%
+here okay maybe you have seen this class
+before they are very nice and I usually
+
+ align:start position:0%
+before they are very nice and I usually
+ 
+
+ align:start position:0%
+before they are very nice and I usually
+use it to enjoy my red wines which you
+
+ align:start position:0%
+use it to enjoy my red wines which you
+ 
+
+ align:start position:0%
+use it to enjoy my red wines which you
+can I enjoy pop it now so you can see
+
+ align:start position:0%
+can I enjoy pop it now so you can see
+ 
+
+ align:start position:0%
+can I enjoy pop it now so you can see
+that if this is the glass and if I put a
+
+ align:start position:0%
+that if this is the glass and if I put a
+ 
+
+ align:start position:0%
+that if this is the glass and if I put a
+little water on my hand and I rub it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carefully I can actually excite one of
+
+ align:start position:0%
+carefully I can actually excite one of
+ 
+
+ align:start position:0%
+carefully I can actually excite one of
+the resonance frequency okay so so you
+
+ align:start position:0%
+the resonance frequency okay so so you
+ 
+
+ align:start position:0%
+the resonance frequency okay so so you
+can see that we have always been working
+
+ align:start position:0%
+can see that we have always been working
+ 
+
+ align:start position:0%
+can see that we have always been working
+on a single particle okay and that will
+
+ align:start position:0%
+on a single particle okay and that will
+ 
+
+ align:start position:0%
+on a single particle okay and that will
+give you one resonance frequency if I
+
+ align:start position:0%
+give you one resonance frequency if I
+ 
+
+ align:start position:0%
+give you one resonance frequency if I
+work on two particles which we will see
+
+ align:start position:0%
+work on two particles which we will see
+ 
+
+ align:start position:0%
+work on two particles which we will see
+that in the next lecture I were to get
+
+ align:start position:0%
+that in the next lecture I were to get
+ 
+
+ align:start position:0%
+that in the next lecture I were to get
+two resonance frequency and this glass
+
+ align:start position:0%
+two resonance frequency and this glass
+ 
+
+ align:start position:0%
+two resonance frequency and this glass
+is made of infinite number of particles
+
+ align:start position:0%
+is made of infinite number of particles
+ 
+
+ align:start position:0%
+is made of infinite number of particles
+therefore I will have infinite number of
+
+ align:start position:0%
+therefore I will have infinite number of
+ 
+
+ align:start position:0%
+therefore I will have infinite number of
+resonance frequency okay when I am
+
+ align:start position:0%
+resonance frequency okay when I am
+ 
+
+ align:start position:0%
+resonance frequency okay when I am
+rubbing it
+
+ align:start position:0%
+rubbing it
+ 
+
+ align:start position:0%
+rubbing it
+I'm actually giving input of all kinds
+
+ align:start position:0%
+I'm actually giving input of all kinds
+ 
+
+ align:start position:0%
+I'm actually giving input of all kinds
+of different frequencies but the the
+
+ align:start position:0%
+of different frequencies but the the
+ 
+
+ align:start position:0%
+of different frequencies but the the
+class will be smart enough so that you
+
+ align:start position:0%
+class will be smart enough so that you
+ 
+
+ align:start position:0%
+class will be smart enough so that you
+will pick up the one he likes the most
+
+ align:start position:0%
+will pick up the one he likes the most
+ 
+
+ align:start position:0%
+will pick up the one he likes the most
+which is the resonance frequency so you
+
+ align:start position:0%
+which is the resonance frequency so you
+ 
+
+ align:start position:0%
+which is the resonance frequency so you
+can see that the sound he says should be
+
+ align:start position:0%
+can see that the sound he says should be
+ 
+
+ align:start position:0%
+can see that the sound he says should be
+roughly 683 hurt okay and you can
+
+ align:start position:0%
+roughly 683 hurt okay and you can
+ 
+
+ align:start position:0%
+roughly 683 hurt okay and you can
+actually measure it with your phone
+
+ align:start position:0%
+actually measure it with your phone
+ 
+
+ align:start position:0%
+actually measure it with your phone
+right okay so on the TV commercial you
+
+ align:start position:0%
+right okay so on the TV commercial you
+ 
+
+ align:start position:0%
+right okay so on the TV commercial you
+may have seen that there's a lady
+
+ align:start position:0%
+may have seen that there's a lady
+ 
+
+ align:start position:0%
+may have seen that there's a lady
+singing you know he seemed so louder D
+
+ align:start position:0%
+singing you know he seemed so louder D
+ 
+
+ align:start position:0%
+singing you know he seemed so louder D
+such that the glass breaks right can we
+
+ align:start position:0%
+such that the glass breaks right can we
+ 
+
+ align:start position:0%
+such that the glass breaks right can we
+get that volunteer today to sing in
+
+ align:start position:0%
+get that volunteer today to sing in
+ 
+
+ align:start position:0%
+get that volunteer today to sing in
+front of oh I see can you sing it high
+
+ align:start position:0%
+front of oh I see can you sing it high
+ 
+
+ align:start position:0%
+front of oh I see can you sing it high
+high frequencies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good try but didn't work okay okay
+
+ align:start position:0%
+very good try but didn't work okay okay
+ 
+
+ align:start position:0%
+very good try but didn't work okay okay
+I think I guess it's really difficult to
+
+ align:start position:0%
+I think I guess it's really difficult to
+ 
+
+ align:start position:0%
+I think I guess it's really difficult to
+perform that in front of so many people
+
+ align:start position:0%
+perform that in front of so many people
+ 
+
+ align:start position:0%
+perform that in front of so many people
+unprepared but fortunately we are an IT
+
+ align:start position:0%
+unprepared but fortunately we are an IT
+ 
+
+ align:start position:0%
+unprepared but fortunately we are an IT
+so we have designed that is a device
+
+ align:start position:0%
+so we have designed that is a device
+ 
+
+ align:start position:0%
+so we have designed that is a device
+which actually can help us to achieve
+
+ align:start position:0%
+which actually can help us to achieve
+ 
+
+ align:start position:0%
+which actually can help us to achieve
+this okay so this device is actually
+
+ align:start position:0%
+this okay so this device is actually
+ 
+
+ align:start position:0%
+this okay so this device is actually
+content amplifier here and I can now
+
+ align:start position:0%
+content amplifier here and I can now
+ 
+
+ align:start position:0%
+content amplifier here and I can now
+control the frequency of the sound
+
+ align:start position:0%
+control the frequency of the sound
+ 
+
+ align:start position:0%
+control the frequency of the sound
+through this scope and this amplifier
+
+ align:start position:0%
+through this scope and this amplifier
+ 
+
+ align:start position:0%
+through this scope and this amplifier
+will actually amplify the signal and the
+
+ align:start position:0%
+will actually amplify the signal and the
+ 
+
+ align:start position:0%
+will actually amplify the signal and the
+producer Soundwave and try to actually
+
+ align:start position:0%
+producer Soundwave and try to actually
+ 
+
+ align:start position:0%
+producer Soundwave and try to actually
+oscillate this class okay so we are
+
+ align:start position:0%
+oscillate this class okay so we are
+ 
+
+ align:start position:0%
+oscillate this class okay so we are
+going to do this experiment so we will
+
+ align:start position:0%
+going to do this experiment so we will
+ 
+
+ align:start position:0%
+going to do this experiment so we will
+need to change the light set in a bit
+
+ align:start position:0%
+need to change the light set in a bit
+ 
+
+ align:start position:0%
+need to change the light set in a bit
+because the Sun is going to be probably
+
+ align:start position:0%
+because the Sun is going to be probably
+ 
+
+ align:start position:0%
+because the Sun is going to be probably
+too loud just for safety some of you may
+
+ align:start position:0%
+too loud just for safety some of you may
+ 
+
+ align:start position:0%
+too loud just for safety some of you may
+not survive
+
+ align:start position:0%
+not survive
+ 
+
+ align:start position:0%
+not survive
+so I'm handing out this okay who is
+
+ align:start position:0%
+so I'm handing out this okay who is
+ 
+
+ align:start position:0%
+so I'm handing out this okay who is
+closer okay
+
+ align:start position:0%
+closer okay
+ 
+
+ align:start position:0%
+closer okay
+oh oh sorry I'm so sorry
+
+ align:start position:0%
+oh oh sorry I'm so sorry
+ 
+
+ align:start position:0%
+oh oh sorry I'm so sorry
+what I don't need that okay so so just
+
+ align:start position:0%
+what I don't need that okay so so just
+ 
+
+ align:start position:0%
+what I don't need that okay so so just
+for safety I will put this on and what
+
+ align:start position:0%
+for safety I will put this on and what
+ 
+
+ align:start position:0%
+for safety I will put this on and what
+I'm going to do is also put this curse
+
+ align:start position:0%
+I'm going to do is also put this curse
+ 
+
+ align:start position:0%
+I'm going to do is also put this curse
+on right okay to this first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what I'm going to do now is to
+
+ align:start position:0%
+okay so what I'm going to do now is to
+ 
+
+ align:start position:0%
+okay so what I'm going to do now is to
+start producing Soundwave so through the
+
+ align:start position:0%
+start producing Soundwave so through the
+ 
+
+ align:start position:0%
+start producing Soundwave so through the
+camera you should be able to see what
+
+ align:start position:0%
+camera you should be able to see what
+ 
+
+ align:start position:0%
+camera you should be able to see what
+this issue is showing in on the spring
+
+ align:start position:0%
+this issue is showing in on the spring
+ 
+
+ align:start position:0%
+this issue is showing in on the spring
+so you can see this you can even see
+
+ align:start position:0%
+so you can see this you can even see
+ 
+
+ align:start position:0%
+so you can see this you can even see
+that if if this class is actually moving
+
+ align:start position:0%
+that if if this class is actually moving
+ 
+
+ align:start position:0%
+that if if this class is actually moving
+the wood inside will also vibrate okay
+
+ align:start position:0%
+the wood inside will also vibrate okay
+ 
+
+ align:start position:0%
+the wood inside will also vibrate okay
+so you can see that clearly we don't
+
+ align:start position:0%
+so you can see that clearly we don't
+ 
+
+ align:start position:0%
+so you can see that clearly we don't
+have rest on us yet so what I am going
+
+ align:start position:0%
+have rest on us yet so what I am going
+ 
+
+ align:start position:0%
+have rest on us yet so what I am going
+to do is to increase the frequency and
+
+ align:start position:0%
+to do is to increase the frequency and
+ 
+
+ align:start position:0%
+to do is to increase the frequency and
+see what happens so now it's so now it's
+
+ align:start position:0%
+see what happens so now it's so now it's
+ 
+
+ align:start position:0%
+see what happens so now it's so now it's
+actually the 643 say she's Filipino the
+
+ align:start position:0%
+actually the 643 say she's Filipino the
+ 
+
+ align:start position:0%
+actually the 643 say she's Filipino the
+resonance frequency now I have measure
+
+ align:start position:0%
+resonance frequency now I have measure
+ 
+
+ align:start position:0%
+resonance frequency now I have measure
+the frequency should be 684 so now it's
+
+ align:start position:0%
+the frequency should be 684 so now it's
+ 
+
+ align:start position:0%
+the frequency should be 684 so now it's
+a c6 53
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+6:63 hurt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+673 Hertz can you see the movement you
+
+ align:start position:0%
+673 Hertz can you see the movement you
+ 
+
+ align:start position:0%
+673 Hertz can you see the movement you
+cannot see the movement still yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+683 you see you see now the frequency of
+
+ align:start position:0%
+683 you see you see now the frequency of
+ 
+
+ align:start position:0%
+683 you see you see now the frequency of
+the sound is actually matching with the
+
+ align:start position:0%
+the sound is actually matching with the
+ 
+
+ align:start position:0%
+the sound is actually matching with the
+nature of one of the natural frequency
+
+ align:start position:0%
+nature of one of the natural frequency
+ 
+
+ align:start position:0%
+nature of one of the natural frequency
+of the class ok apparently the class
+
+ align:start position:0%
+of the class ok apparently the class
+ 
+
+ align:start position:0%
+of the class ok apparently the class
+like it ok and now you can see that we
+
+ align:start position:0%
+like it ok and now you can see that we
+ 
+
+ align:start position:0%
+like it ok and now you can see that we
+still start vibrating and the next step
+
+ align:start position:0%
+still start vibrating and the next step
+ 
+
+ align:start position:0%
+still start vibrating and the next step
+which we are going to do is to try to
+
+ align:start position:0%
+which we are going to do is to try to
+ 
+
+ align:start position:0%
+which we are going to do is to try to
+increase the amplitude increase the
+
+ align:start position:0%
+increase the amplitude increase the
+ 
+
+ align:start position:0%
+increase the amplitude increase the
+volume of the sound and see what
+
+ align:start position:0%
+volume of the sound and see what
+ 
+
+ align:start position:0%
+volume of the sound and see what
+happened maybe you want to cover you a
+
+ align:start position:0%
+happened maybe you want to cover you a
+ 
+
+ align:start position:0%
+happened maybe you want to cover you a
+year just for safety
+
+ align:start position:0%
+year just for safety
+ 
+
+ align:start position:0%
+year just for safety
+okay then the then the the glass may
+
+ align:start position:0%
+okay then the then the the glass may
+ 
+
+ align:start position:0%
+okay then the then the the glass may
+break if we are lucky okay should I see
+
+ align:start position:0%
+break if we are lucky okay should I see
+ 
+
+ align:start position:0%
+break if we are lucky okay should I see
+what is going to happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah thank you very much thank you gasps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can see the power of resonance
+
+ align:start position:0%
+so you can see the power of resonance
+ 
+
+ align:start position:0%
+so you can see the power of resonance
+right so if I tune down the frequency
+
+ align:start position:0%
+right so if I tune down the frequency
+ 
+
+ align:start position:0%
+right so if I tune down the frequency
+slightly more then it will be where
+
+ align:start position:0%
+slightly more then it will be where
+ 
+
+ align:start position:0%
+slightly more then it will be where
+you'll be here right then you will not
+
+ align:start position:0%
+you'll be here right then you will not
+ 
+
+ align:start position:0%
+you'll be here right then you will not
+have enough amplitude to break the glass
+
+ align:start position:0%
+have enough amplitude to break the glass
+ 
+
+ align:start position:0%
+have enough amplitude to break the glass
+and also the clip we discussed before
+
+ align:start position:0%
+and also the clip we discussed before
+ 
+
+ align:start position:0%
+and also the clip we discussed before
+the quality of the glass should be
+
+ align:start position:0%
+the quality of the glass should be
+ 
+
+ align:start position:0%
+the quality of the glass should be
+really really high such that the
+
+ align:start position:0%
+really really high such that the
+ 
+
+ align:start position:0%
+really really high such that the
+resulting amplitude will be very large
+
+ align:start position:0%
+resulting amplitude will be very large
+ 
+
+ align:start position:0%
+resulting amplitude will be very large
+then you can actually break it with
+
+ align:start position:0%
+then you can actually break it with
+ 
+
+ align:start position:0%
+then you can actually break it with
+external song wave and if we go above
+
+ align:start position:0%
+external song wave and if we go above
+ 
+
+ align:start position:0%
+external song wave and if we go above
+the resonance frequency then you will
+
+ align:start position:0%
+the resonance frequency then you will
+ 
+
+ align:start position:0%
+the resonance frequency then you will
+not also move a bit because you know
+
+ align:start position:0%
+not also move a bit because you know
+ 
+
+ align:start position:0%
+not also move a bit because you know
+because if you go to very large Omega D
+
+ align:start position:0%
+because if you go to very large Omega D
+ 
+
+ align:start position:0%
+because if you go to very large Omega D
+then every two will be pretty small okay
+
+ align:start position:0%
+then every two will be pretty small okay
+ 
+
+ align:start position:0%
+then every two will be pretty small okay
+let me try to switch back to my
+
+ align:start position:0%
+let me try to switch back to my
+ 
+
+ align:start position:0%
+let me try to switch back to my
+presentation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is as you what we have
+
+ align:start position:0%
+okay so this is as you what we have
+ 
+
+ align:start position:0%
+okay so this is as you what we have
+learned today we have learned that
+
+ align:start position:0%
+learned today we have learned that
+ 
+
+ align:start position:0%
+learned today we have learned that
+behavior of attempted ribbon oscillator
+
+ align:start position:0%
+behavior of attempted ribbon oscillator
+ 
+
+ align:start position:0%
+behavior of attempted ribbon oscillator
+okay we have learned the transom
+
+ align:start position:0%
+okay we have learned the transom
+ 
+
+ align:start position:0%
+okay we have learned the transom
+transient behavior so what is actually
+
+ align:start position:0%
+transient behavior so what is actually
+ 
+
+ align:start position:0%
+transient behavior so what is actually
+transient behavior is actually a mixture
+
+ align:start position:0%
+transient behavior is actually a mixture
+ 
+
+ align:start position:0%
+transient behavior is actually a mixture
+or it's a mixture of steady-state
+
+ align:start position:0%
+or it's a mixture of steady-state
+ 
+
+ align:start position:0%
+or it's a mixture of steady-state
+solution which is coming from the tribe
+
+ align:start position:0%
+solution which is coming from the tribe
+ 
+
+ align:start position:0%
+solution which is coming from the tribe
+in force and the homogeneous solution
+
+ align:start position:0%
+in force and the homogeneous solution
+ 
+
+ align:start position:0%
+in force and the homogeneous solution
+okay if you wait long enough this will
+
+ align:start position:0%
+okay if you wait long enough this will
+ 
+
+ align:start position:0%
+okay if you wait long enough this will
+decay and the disappear okay and we have
+
+ align:start position:0%
+decay and the disappear okay and we have
+ 
+
+ align:start position:0%
+decay and the disappear okay and we have
+learned resonance right so in IOC
+
+ align:start position:0%
+learned resonance right so in IOC
+ 
+
+ align:start position:0%
+learned resonance right so in IOC
+circuit which you actually solved that
+
+ align:start position:0%
+circuit which you actually solved that
+ 
+
+ align:start position:0%
+circuit which you actually solved that
+in your pset in pendulum which way I
+
+ align:start position:0%
+in your pset in pendulum which way I
+ 
+
+ align:start position:0%
+in your pset in pendulum which way I
+just show you which helped me my son to
+
+ align:start position:0%
+just show you which helped me my son to
+ 
+
+ align:start position:0%
+just show you which helped me my son to
+learn waves and vibrations and a
+
+ align:start position:0%
+learn waves and vibrations and a
+ 
+
+ align:start position:0%
+learn waves and vibrations and a
+condition washing machine class particle
+
+ align:start position:0%
+condition washing machine class particle
+ 
+
+ align:start position:0%
+condition washing machine class particle
+physics we can see templars driven
+
+ align:start position:0%
+physics we can see templars driven
+ 
+
+ align:start position:0%
+physics we can see templars driven
+oscillator or resonance almost
+
+ align:start position:0%
+oscillator or resonance almost
+ 
+
+ align:start position:0%
+oscillator or resonance almost
+everywhere okay so I hope that you enjoy
+
+ align:start position:0%
+everywhere okay so I hope that you enjoy
+ 
+
+ align:start position:0%
+everywhere okay so I hope that you enjoy
+the lecture today and what we are going
+
+ align:start position:0%
+the lecture today and what we are going
+ 
+
+ align:start position:0%
+the lecture today and what we are going
+to do next time is to put multiple
+
+ align:start position:0%
+to do next time is to put multiple
+ 
+
+ align:start position:0%
+to do next time is to put multiple
+object together so that you will see the
+
+ align:start position:0%
+object together so that you will see the
+ 
+
+ align:start position:0%
+object together so that you will see the
+interaction between one particle to the
+
+ align:start position:0%
+interaction between one particle to the
+ 
+
+ align:start position:0%
+interaction between one particle to the
+other particle and see how we can
+
+ align:start position:0%
+other particle and see how we can
+ 
+
+ align:start position:0%
+other particle and see how we can
+actually make sense of this kind of
+
+ align:start position:0%
+actually make sense of this kind of
+ 
+
+ align:start position:0%
+actually make sense of this kind of
+system thank you very much
+
+ align:start position:0%
+system thank you very much
+ 
+
+ align:start position:0%
+system thank you very much
+and when I will be here if you have
+
+ align:start position:0%
+and when I will be here if you have
+ 
+
+ align:start position:0%
+and when I will be here if you have
+additional questions to relate it to a
+
+ align:start position:0%
+additional questions to relate it to a
+ 
+
+ align:start position:0%
+additional questions to relate it to a
+lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/Fixc8hVo_cY.txt b/Fixc8hVo_cY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ef0b5a732f52fad45d8dceca8045ec0e085a2c5f
--- /dev/null
+++ b/Fixc8hVo_cY.txt
@@ -0,0 +1,2106 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So let's start.
+
+I mean for the first question
+you can answer what is tuple.
+
+You can go to that later.
+
+Can a tuple contain a list?
+
+What do you think?
+
+Can a tuple contain a list?
+
+AUDIENCE: Yes.
+
+PROFESSOR: Yes, it can.
+
+So we'll go through the
+examples later.
+
+And let's see this
+first example.
+
+We have two tuples.
+
+The tuple B contains tuple
+A, as well as a list.
+
+So it can't populate.
+
+Let's bring those lists, too.
+
+So for the first example we try
+to access the elements 0
+
+and 2 of the tuple A. And
+let me use minus 1 to
+
+access which element?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: OK.
+
+And 0 is the first element,
+of course.
+
+And remember now we
+are using 0, 1.
+
+OK, what is tuple B?
+
+It's a two-dimensional tuple.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah, exactly.
+
+It has a list and
+a tuple inside.
+
+So the first element is
+a tuple, and the last
+
+element is the list.
+
+So now it's sort of like
+two-dimensional.
+
+But if you look at the first
+element of it, the MIT word,
+
+that doesn't have
+any dimension.
+
+Does it?
+
+It's a string.
+
+So you can again access,
+but not this way.
+
+But still you can access.
+
+And we are using this notation
+to access a portion of the
+
+list, a part of the tuple,
+actually, here.
+
+It's called slicing.
+
+So here 0 to 1 gives
+you which element?
+
+Just one element right?
+
+It's the first element.
+
+0 to 2 gives you 1 and 2 OK?
+
+This is an interesting
+usage of the slicing.
+
+This is used to access
+the whole tuple.
+
+Now you might wonder
+why we need them.
+
+We could just--
+
+the handouts are here.
+
+So why we need to copy or why
+we need to access the list
+
+through the column operator
+like this?
+
+We'll look at that later.
+
+It's very essential when
+we have lists.
+
+For the timing it's OK when
+tuples are immutable.
+
+So it doesn't have
+a special usage.
+
+But later on we'll
+be using it.
+
+Then if you look at this
+part, this is the
+
+most interesting part.
+
+How do iterate through
+a tuple?
+
+You use a FOR loop and you call
+like item in tuple, the
+
+element in tuple.
+
+The element is initialized with
+every element when it
+
+goes through iteration.
+
+At every iteration it will
+be instantiated with the
+
+corresponding element
+in the tuple.
+
+But you're using the
+same name anyway.
+
+It's item.
+
+This is equivalent to accessing
+the tuple like this.
+
+Going one-by-one in the range
+and accessing their
+
+corresponding element
+in the tuple.
+
+So this is the simpler
+way to access that.
+
+Do you have any questions
+in that part?
+
+Yeah?
+
+AUDIENCE: For that part, don't,
+usually if you have a
+
+range you have to [INAUDIBLE]
+
+name because is not--
+
+PROFESSOR: OK, that's correct.
+
+.
+
+OK.
+
+Suppose a tuple has 3 elements,
+or for example in
+
+this case tuple A, how many
+elements are in the tuple A?
+
+3 elements.
+
+So what would be the
+length of tuple A?
+
+AUDIENCE: 3.
+
+PROFESSOR: 3.
+
+But what would be the range?
+
+0, 1, 2, right?
+
+So you have to type 0 to 3.
+
+So that's why I put that, OK?
+
+That is 3, OK?
+
+PROFESSOR: You.
+
+AUDIENCE: So you just say a
+range like the tuple is, it
+
+seems like the first one--
+
+PROFESSOR: First the 0 if you
+don't specify it the same way.
+
+OK.
+
+Now let's go through the list.
+
+So if you go through the
+questions, what is the
+
+difference between a
+list and a tuple?
+
+What is the difference between
+a list and a tuple?
+
+Anyone?
+
+Yeah?
+
+AUDIENCE: Tuples
+are immutable.
+
+PROFESSOR: OK.
+
+Lists are mutable.
+
+And because it's mutable it
+takes special functions to
+
+access the elements,
+add elements, and
+
+modify the list itself.
+
+How would you add an
+element to a list?
+
+Suppose you have list A. How
+would you add 3 to this list?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: OK.
+
+Let's start our print.
+
+OK.
+
+That's good.
+
+OK?
+
+How would you remove
+the element from
+
+the top of the list?
+
+Or the last element, how
+would you remove
+
+this 3 from the list?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: This one?
+
+Let's see.
+
+You know how to check
+the specification
+
+of a function, right?
+
+Sorry.
+
+So it's not the right
+function, right?
+
+Because it says it removes
+the first occurrence of a
+
+particular value you are parsing
+to that function.
+
+OK, there's another function.
+
+It's called list.pop.
+
+That removes the last inserted
+value, so it
+
+pops from the top.
+
+So remove can be used to remove
+a particular element.
+
+So here suppose we
+want to remove 1.
+
+So we could say list
+A, remove 1.
+
+OK.
+
+So in this example,
+actually, I have
+
+commented out this line.
+
+This will be an error
+if I execute.
+
+Why?
+
+Why will it give you an error?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: It doesn't exit.
+
+Great.
+
+So the problem here is we can't
+access an element in the
+
+list unless we explicitly
+assign
+
+something or create something.
+
+But suppose we want to pass
+a list of 10 elements to a
+
+program so that it can assign
+values on the fly.
+
+And it can modify.
+
+OK?
+
+So how would you pass an empty
+list of 10 elements?
+
+OK.
+
+The problem is if you're passing
+something like this,
+
+you need to know how this list
+should be instantiated.
+
+So you should know what
+are the initial
+
+values of these elements.
+
+Suppose you want to create
+a list of ten 0's.
+
+Then the easiest way to
+create the list is--
+
+So you would create a list
+with ten elements.
+
+But If you don't want to waste
+memory, or if you don't want
+
+to keep anything particular,
+you could do
+
+something like this.
+
+Now this will create a
+list of empty list.
+
+And there'll be ten
+such empty lists.
+
+OK?
+
+And you could pass this list to
+a program so that it will
+
+assign the elements.
+
+OK?
+
+You can iterate to the
+list the same way.
+
+But lists are interesting.
+
+Why?
+
+They are mutable.
+
+So they can be actually used
+to create interesting
+
+mathematical objects.
+
+For example, like matrix.
+
+So how would you create
+a matrix using lists?
+
+Any ideas?
+
+How would you create,
+say a 2 by 2 matrix?
+
+If you consider this example,
+this creates a matrix 4 by 2.
+
+So that would be like 4
+rows and 2 columns.
+
+But how can you go and
+access the inner
+
+element or inner matrix?
+
+So if you suppose you want
+access 2, 3, that is the third
+
+row, then how would
+you access?
+
+How would you call M?
+
+AUDIENCE: M3?
+
+PROFESSOR: M3.
+
+M3 gives you 2, 3.
+
+Suppose you want to access
+the 3 and the 2, 3.
+
+Then we--
+
+[INTERPOSING VOICES]
+
+PROFESSOR: Sorry.
+
+AUDIENCE: Why does a 3
+give you [INAUDIBLE]?
+
+PROFESSOR: Oh, sorry.
+
+My bad.
+
+Yeah.
+
+OK.
+
+This is computer science,
+not maths.
+
+You got it right, why
+it's not 3, it's 2?
+
+AUDIENCE: Yeah.
+
+I thought you were talking
+about 3 and 4.
+
+PROFESSOR: OK.
+
+That's fine.
+
+So I'm asking now how
+would you access the
+
+3 in the 2, 3 box?
+
+AUDIENCE: So I need to do
+another parentheses?
+
+PROFESSOR: Not a bracket.
+
+AUDIENCE: OK.
+
+PROFESSOR: OK.
+
+That is all.
+
+So you can access matrices
+like this.
+
+OK.
+
+Great.
+
+We are on time.
+
+So this actually gives you
+a summary of functions.
+
+Associated functions.
+
+For example the pop I
+explained earlier.
+
+Remove removes a particular
+element.
+
+Extent, that's interesting.
+
+Can you tell me what
+it does here, the
+
+method extent on list?
+
+What does that method take?
+
+It takes another list.
+
+So which means it's going to
+merge the list you are passing
+
+with the list you're calling
+the method on, that is
+
+[UNINTELLIGIBLE].
+
+So it's going to combine
+those lists.
+
+Let's see.
+
+So this corresponds to this.
+
+So two lists are combined.
+
+So this method is actually
+useful, right, because you
+
+don't have to write yourself.
+
+Most of things you
+can easily do.
+
+Now the question is, why tuple
+didn't have these methods?
+
+Why?
+
+Why we didn't have these
+methods for tuples?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: They're immutable.
+
+So you can't extent, you
+can't [UNINTELLIGIBLE].
+
+So even if you extent,
+what would happen?
+
+It's going to create
+a new tuple.
+
+Actually, you can do that.
+
+But like this.
+
+For example, you have tuple
+A which is 1, 2.
+
+And suppose you have
+tuple B --
+
+3, 4.
+
+If you want to combine them,
+how would you do it?
+
+Tuple A plus tuple B. OK?
+
+That concatenates.
+
+This operator is all
+loaded for tuples.
+
+OK?
+
+So lists are mutable so you can
+do all of these things.
+
+Let's look at a few other
+examples, too.
+
+OK.
+
+There's an interesting
+part here.
+
+Lists are mutable.
+
+That we understand.
+
+But how these lists are actually
+stored in the memory,
+
+For example, suppose you
+have a list lst,
+
+sorry, 0, 1, apple.
+
+How do you think it's stored
+in the memory?
+
+So you have 3 elements.
+
+But these elements are actually
+not stored in the
+
+list itself.
+
+They actually in the memory.
+
+0, 1, apple.
+
+But you have the pointers
+to those lists.
+
+Sorry, to those elements.
+
+So actually you can modify these
+values without changing
+
+the list itself, because the
+list actually points to this
+
+part, the container.
+
+So in this example you have list
+A and B. But the list B
+
+actually contains list A. OK?
+
+Since list A is mutable you
+can go and change it.
+
+So here first you print list A
+and B, but you're going to
+
+change list A's 0th element.
+
+After changing the element
+the list A becomes first.
+
+Its first element
+changed to 88.
+
+OK.
+
+Fine.
+
+What do you think the
+list B would be?
+
+OK, let's print.
+
+It contains the 88, right,
+the modified value.
+
+Why?
+
+Because list B actually had a
+pointer to list A. Which again
+
+had pointers to other
+elements.
+
+And we modified this
+value to 88.
+
+So you're still accessing
+list B. OK?
+
+The pointers are not changed.
+
+That we can see here, in
+the second example,
+
+the problem of aliasing.
+
+So we have list X. And we call
+it by list Y as well.
+
+And we are now changing
+the list Y. Sorry.
+
+We are changing the list X. But
+it's going to affect list
+
+X as well as list Y. See?
+
+Because it's just a reference.
+
+The actual object is this.
+
+You can call it by two
+different names.
+
+It doesn't matter.
+
+But the actual object is here.
+
+That's where we need
+this operator.
+
+So if you just point, OK, for
+example we had list X, if you
+
+just assign list Y to list X,
+it's not going to copy the
+
+elements, just going to
+copy the reference.
+
+Which means list X and list Y,
+both would be pointing to the
+
+same object.
+
+If you want to copy these
+elements and put in a new one,
+
+say, list Z, then we need to
+copy one-by-one every element.
+
+For that we can use
+this operator.
+
+It's called full slicing.
+
+It's not going to
+modify elements.
+
+It's going to copy the whole
+list of elements.
+
+And in the same line, just
+another small example that
+
+tells you how to cast a
+list into tuple, and
+
+a tuple into list.
+
+So you had a tuple, one for
+apple [UNINTELLIGIBLE]
+
+and you cast into list.
+
+Now the type is list.
+
+It's a very simple operation.
+
+Can you do that yourself?
+
+How would you do it if you want
+to write a function to
+
+cast, how would you do that?
+
+You go through element by
+element and add it to a tuple.
+
+And then concatentae
+two tuples.
+
+Right?
+
+So I guess you can write
+probably as a
+
+homework, try that.
+
+Try how to convert a list to
+a tuple without explicitly
+
+calling the casting function.
+
+OK.
+
+Similarly you can convert
+a tuple back into list.
+
+So it's pretty straightforward.
+
+And suppose you're getting
+an input from
+
+the user as a tuple.
+
+then suppose you want
+to make it a list.
+
+You don't have to write
+your function.
+
+You can just call this
+casting operator.
+
+So it'll be--
+
+it will save some time.
+
+OK.
+
+Great.
+
+Let's go to our dictionaries
+now.
+
+So we have a third data
+type, dictionaries.
+
+Oh, you didn't get
+the second one?
+
+So we have another data
+type, dictionaries.
+
+And why do we need dictionaries
+
+in the first place?
+
+Do we need another data type?
+
+Can we just get away with
+tuple and list?
+
+Yes.
+
+Because you can actually make
+a dictionary out of lists.
+
+And Professor Grimson went
+through that in the lecture.
+
+If you want, you can come and
+ask in the office hours.
+
+But first try whether you
+can do it yourself.
+
+But the problem is, actually not
+just the dictionaries, but
+
+the high-level data structures
+are actually available in
+
+Python as building data
+structures or as classes.
+
+Just because they will have
+these methods on these data
+
+structures implemented.
+
+So it would say some
+time for us.
+
+Plus those methods are
+guaranteed to be state of art.
+
+For example, if you want to go
+through all the lists, then
+
+the search function or the
+lookup function that you write
+
+may not be that efficient,
+right?
+
+But they might use those
+efficient algorithms in the
+
+standard implementation.
+
+So it's why you should
+always look for the
+
+standard data types.
+
+If you can't you can
+write yourself one.
+
+But it's good to use the
+available data types so that
+
+they would have this efficient
+method implemented.
+
+OK.
+
+So in this dictionary,
+we have two elements.
+
+One is key, one is value.
+
+OK?
+
+So these keys actually have
+a special property.
+
+What is that?
+
+The keys should be an
+immutable object.
+
+So you can actually have
+a tuple as a key.
+
+You can have a string as a key,
+but not a list as a key.
+
+So you need an immutable
+object for the keys.
+
+What about the values?
+
+They can be anything.
+
+Values can be even
+a dictionary.
+
+It can be a list.
+
+But the keys must be mutable.
+
+Do these keys need
+to be unique?
+
+Yes.
+
+No?
+
+OK.
+
+The problem is this.
+
+Dictionaries have the same
+type, I mean structure.
+
+This is a key.
+
+And this key points to a
+place in the memory.
+
+Suppose you call it key A. OK?
+
+If you assign another value to
+key A, that will actually
+
+replace the content in
+the memory, right?
+
+So that's why keys are going
+to be unique, It's by
+
+construction, by the
+construction of the dictionary
+
+the keys are going
+to be unique.
+
+Because if you want to assign
+something different, you have
+
+to call it by a different key,
+call it by a different name.
+
+Say key B.
+
+What about the values.
+
+Do they need to be unique?
+
+No, of course.
+
+Otherwise no use of key, and no
+use of dictionaries, right?
+
+What is the order of the items
+stored in the dictionary?
+
+Can you give a guarantee
+like in lists?
+
+In lists items are stored from
+zero to the left, right?
+
+Length minus 1, actually.
+
+What about dictionaries?
+
+Surely can't guarantee
+the order, but you
+
+can modify the order.
+
+OK.
+
+So the thing is first, if you
+look at this example, first we
+
+have the staff dictionary.
+
+And when I pin the length
+it gives me 3, fine.
+
+Then I'm doing three things.
+
+First I change the address
+by calling its key.
+
+And dictionaries are
+mutable so you can
+
+change their values.
+
+Then also we are adding
+a new element.
+
+Fine.
+
+If you wanted a new element you
+call it by the key that
+
+you already assigned.
+
+If the key already exists you
+will just modify the value.
+
+Otherwise it will create a new
+key and add that value.
+
+You can also check whether this
+particular element is in
+
+the dictionary.
+
+But this must be the key.
+
+Whatever you are calling
+here should be the
+
+key, not the value.
+
+It won't search for the value.
+
+It will search only for the
+key, [UNINTELLIGIBLE]
+
+for that particular key because
+you access the values
+
+through keys.
+
+Again here if it is not
+in the list, actually
+
+I'm adding an element--
+
+OK.
+
+OK.
+
+To compare in the list, suppose
+I have a list 0, 1, 2.
+
+If I want to check whether
+1 is in the
+
+list, how would I check?
+
+Do you have to go through
+element by element?
+
+No, there's a shortcut.
+
+If 1 in list, right?
+
+If I want to check whether 1 is
+not in the list, if I want
+
+to negate this, I would write
+it 1 not in list.
+
+We just ignore the words.
+
+It's pretty much like English.
+
+OK?
+
+We just remove the words.
+
+OK.
+
+In the dictionary we do the
+same thing through keys.
+
+If key A and, OK I'll
+call it, say, D1.
+
+OK?
+
+And you actually call or you'd
+search for the key,
+
+not the other way.
+
+OK.
+
+There is an interesting
+part here.
+
+If you want to modify
+the order--
+
+actually I tell you that the
+order C earlier, we couldn't
+
+guarantee the order, right?
+
+It was not the order we typed
+because it starts at
+
+[UNINTELLIGIBLE]
+
+because we added at the
+end actually, right?
+
+So actually you can't
+guarantee the order.
+
+But we can sort it.
+
+But how do you sort it?
+
+We call the keys and
+we sort the keys.
+
+Because remember,
+every values--
+
+if you want to access a
+particular value, you access
+
+it through key.
+
+Actually, if you call the
+dictionary, it doesn't know
+
+where these values are.
+
+Just you have to go to the
+key to access the value.
+
+So if you want to do something
+in the dictionary itself, you
+
+can do that only on keys.
+
+So if you want to sort
+the dictionary,
+
+you sort it by keys.
+
+So you call the keys method
+for the dictionary--
+
+so it returns the list of
+keys and you sort them.
+
+This is called chaining
+methods.
+
+So I have chained the methods.
+
+I would have like two
+methods, right?
+
+I call the keys.
+
+This first part actually returns
+to this top key.
+
+Then you sort them.
+
+Yes?
+
+AUDIENCE: It doesn't look like
+they're in alphabetical order?
+
+PROFESSOR: Oh, on this?
+
+Sorry.
+
+Let's see.
+
+OK.
+
+Let's see.
+
+Ooops.
+
+OK.
+
+Now they're sorted.
+
+OK.
+
+What was the problem?
+
+What was the problem there?
+
+Why it wasn't sorted?
+
+AUDIENCE: You have to
+do it in two lines.
+
+PROFESSOR: Sorry?
+
+AUDIENCE: You have to call up
+the keys and then sort it in a
+
+separate line?
+
+PROFESSOR: OK.
+
+The problem is in the logic.
+
+Actually, when you call this
+function, method, you're
+
+actually sorting the keys
+returned by this method.
+
+You're not actually going to
+sort of the dictionary itself.
+
+You're sorting only the list
+that was returned, right?
+
+The list of keys.
+
+Although the dictionary is
+mutable, it wasn't sorted.
+
+Do you see the problem?
+
+So that's why when they called
+keys equal to staff.keys I'm
+
+getting a list of keys.
+
+Then I'm sorting that list.
+
+And I'm printing that list.
+
+But if you want to go in a
+particular order, if you want
+
+to access the dictionary in a
+particular order, what could
+
+you do is you could do something
+like keys is equal
+
+to staff.keys.
+
+Then you can store keys.
+
+Then for k in keys you can go
+and iterate now, right?
+
+So you can say print
+k and staff k.
+
+OK?
+
+So you can do this.
+
+But actually, Python provides a
+way to iterate what keys and
+
+value pairs.
+
+That you do by calling
+both elements?
+
+All the method items.
+
+The items return a list
+of key-value pairs.
+
+If you call D1.items you get
+a list of key-value pairs.
+
+You see that?
+
+And we are going to iterate
+through individual elements.
+
+So first we start with this
+and then second this.
+
+So that's a simpler way to
+access every elements in the
+
+dictionary.
+
+Great.
+
+OK.
+
+Now we have an interesting
+part, recursion.
+
+What's the principle
+behind recursion?
+
+Anyone?
+
+What's the idea of recursion?
+
+Yes?
+
+AUDIENCE: The cause itself
+is [INAUDIBLE]
+
+base case.
+
+And it saves a lot of money.
+
+PROFESSOR: Yes.
+
+The idea of recursion is, if
+you have a problem, try to
+
+express the problem
+in a simpler
+
+version of the same problem.
+
+So if you want to find factorial
+n, try to express it
+
+in terms of factorial
+n minus 1.
+
+So you could keep on doing
+this till you come to
+
+factorial 1 for which you know
+the explicit answer.
+
+Right?
+
+So you try to express the
+problem in its simpler form.
+
+It would be useful
+in many cases.
+
+Actually, in your next piece
+you do have the problem.
+
+But be mindful.
+
+What's --
+
+what makes it possible for
+you to use the recursion?
+
+Only if you can express in terms
+of the simpler version.
+
+Otherwise you can't.
+
+This is probably quite like the
+induction you might have
+
+studied, mathematical
+induction.
+
+I don't know whether you studied
+it in high school, but
+
+it's quite like that.
+
+OK.
+
+So there are two parts
+in recursion.
+
+The first one is
+the base case.
+
+So for a factorial problem we
+can express the factorial, say
+
+nth factorial, as any n in
+to n minus 1 factorial.
+
+OK?
+
+So this would be our
+recursive case.
+
+So what is a recursive case?
+
+Suppose we want to define a
+function factorial A. OK?
+
+So what will be our
+recursive case?
+
+AUDIENCE: A is greater than 0?
+
+PROFESSOR: I'm asking the
+recursive function.
+
+What would be that?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: n into 2.
+
+Factorial n minus 1 right?
+
+And you just return this.
+
+What would be your base case?
+
+If n is equal to 0, we know
+factorial 0 is 1, right?
+
+What is factorial of 1?
+
+1.
+
+OK?
+
+But why in this program
+we didn't have
+
+that particular line.
+
+Why we didn't have n equals 1?
+
+Why we didn't have that?
+
+AUDIENCE: Because it
+always goes to 0?
+
+PROFESSOR: It always
+goes 0, right?
+
+Because you can express 1 in
+terms of 0 as well, right?
+
+So you don't need to actually
+write this explicitly.
+
+Why?
+
+Because your recursive function
+only depends on its
+
+previous value.
+
+So you need only one value in
+advance Which means you need
+
+only one value for
+your base case.
+
+So you can understand
+this program, right?
+
+I'm not going to go
+through that.
+
+But anyway when you write
+a program always
+
+check its base case.
+
+So you have to start with
+factorial 0 for this case.
+
+OK?
+
+And check one by one.
+
+Then you would know whether
+the program is running
+
+correctly or not.
+
+So always start with
+a simpler case.
+
+But remember in Fibonacci
+series.
+
+OK. for Fibonacci series
+can you give me
+
+the recursive function.?
+
+Yes.
+
+What is Fibonacci series?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: OK.
+
+Yeah.
+
+That's great.
+
+So return say F of n minus
+1 plus F of n minus 2.
+
+What is the Fibonacci series?
+
+You start from 0, you
+add these elements.
+
+So 1.
+
+You add last two elements, 2.
+
+You add last two elements, 3.
+
+You add last two elements, 5.
+
+So you add last two elements.
+
+So if you want to find F of n,
+you return F of n minus 1 and
+
+plus F of n minus 2.
+
+But here since you have two
+elements, or you need to
+
+access two previous elements,
+you need to define you base
+
+case accordingly.
+
+So for your base case,
+F of 0, is what?
+
+Actually, that depends
+on whether you
+
+start here or here.
+
+OK?
+
+You could do this.
+
+I'll go through an interesting
+recursive example.
+
+OK.
+
+It's called a recursive
+exponentiation.
+
+So I actually you can do an
+exponentiation through
+
+recursive multiplication.
+
+Suppose you want to find 3
+to the power, say, of 10.
+
+Then how would you do that?
+
+You start by expressing
+it in terms of its
+
+simpler version, right?
+
+So it will be 3 into
+3 to the power 9.
+
+Sorry, 3 to the power 9.
+
+OK?
+
+So if you want to find that
+nth power of number M, you
+
+would say M into M to
+the power n minus 1.
+
+So now you have your
+recursive case.
+
+What is the base case?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yes, if
+n is equal to 0.
+
+In Python you would test this
+by two equal signs.
+
+If n is equal to 0, then what?
+
+AUDIENCE: Return 1.
+
+PROFESSOR: Return 1.
+
+OK?
+
+Why we have only one
+base case here?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Sorry?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yes.
+
+And because you're accessing
+only one
+
+previous series, right?
+
+Fibonacci series.
+
+Similarly, if you want to
+multiply something--
+
+OK, here what we did is we
+replaced this operator by
+
+recursively using
+this operator.
+
+OK?
+
+Can you do the multiplication
+by recursive addition?
+
+So can you replace this operator
+by this operator?
+
+Yes.
+
+So how would you do this, for
+example say 3 into 5?
+
+So how would you do it here?
+
+Tell me.
+
+What would this?
+
+AUDIENCE: 3 plus 3 times 4.
+
+PROFESSOR: 3 plus?
+
+AUDIENCE: 3 times 4.
+
+PROFESSOR: 3 times 4.
+
+Here?
+
+Come on, it's simple, right?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: I'm insulting you.
+
+OK.
+
+What's the base case?
+
+That is interesting.
+
+What is the base case
+if n is equal to 0?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: OK.
+
+If n is equal to 0, that is 0.
+
+But that's fine.
+
+But there's another problem.
+
+The problem is you don't know
+whether these values are
+
+positive or negative.
+
+So you can't just keep
+on adding like this.
+
+This will work if
+it's positive.
+
+But if it's negative, actually
+you have to check.
+
+Which is sort of tricky
+if you want to use the
+
+same recursive function.
+
+Otherwise you could have
+an if condition here.
+
+If say n is greater
+than 0, do this.
+
+Else-if you multiply n by minus
+1 you negate that so it
+
+becomes positive.
+
+And do it the same way and
+then that's the answer.
+
+So you could do that.
+
+But if you want to do it in the
+same recursive case, then
+
+you had to follow this.
+
+If you have any questions,
+come to the
+
+office hours on that.
+
+The final question is, final
+example is, the Hanoi example.
+
+OK.
+
+This is very interesting.
+
+So here we have three towers;
+source, target, and buffer.
+
+Suppose you have three disks.
+
+You want to move them from
+source to target.
+
+And you can always have a
+smaller disk on top of a
+
+bigger disk.
+
+Then how would you move?
+
+OK?
+
+So can you express this problem
+in a simpler version?
+
+So now we have three disks.
+
+You want to move
+them to target.
+
+So can you express it in
+a simpler version?
+
+Come on.
+
+Just in plain English,
+how would you do it?
+
+Without looking at
+the program.
+
+Because Python is very robust.
+
+So if you read the program
+you get it in English.
+
+So any ideas?
+
+OK.
+
+We have to here move the last
+disk to target, right?
+
+But that's the hardest part.
+
+So before doing that you have
+to move this somewhere else.
+
+So let's move it to buffer.
+
+Done.
+
+How would you move this?
+
+Now you can move it to target.
+
+OK.
+
+Now what would you do?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: OK.
+
+Sorry.
+
+Yeah, OK?
+
+No.
+
+What would you do?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: You can only move
+this to the buffer, right?
+
+AUDIENCE: [INAUDIBLE]
+
+[?
+
+PROFESSOR: Not the target.
+
+OK.
+
+So we made some mistake
+earlier.
+
+Remember?
+
+The problem is because we didn't
+think recursively.
+
+OK.
+
+Let's think recursively.
+
+Source, target, buffer.
+
+Sorry.
+
+Suppose we have only one disk.
+
+Then you can simply
+move to target.
+
+OK?
+
+So a condition is if there's
+only one disk, just move it to
+
+the target.
+
+So if n is equal to 1
+we always move from
+
+move source to target.
+
+OK?
+
+Suppose you have two.
+
+Then what would you do?
+
+You move the top
+one to buffer.
+
+OK?
+
+So move source to buffer.
+
+Then you move the next disk
+from source to target.
+
+So now it's source to target.
+
+And finally you move
+it from the buffer.
+
+All right?
+
+Now we have a very nice
+recursive case.
+
+If you have two, we move from
+source to buffer, then source
+
+to target, then from
+buffer to target.
+
+So if you look at this example
+I'm checking if
+
+n is equal to 1.
+
+If it is 1, just I'm moving
+from source to target.
+
+If it is greater than
+n, what would I do?
+
+And that first assert statement
+is just there to
+
+make sure that n is
+greater than 0.
+
+Otherwise it's meaningless,
+right?
+
+You need to have this.
+
+You can't have negative this.
+
+So what would be the next
+step if you have
+
+more than one disk?
+
+Suppose you have two disks.
+
+Then what would you do?
+
+You move the top disk
+or whatever on
+
+the top to the buffer.
+
+For this simple example
+it was just one disk.
+
+But suppose you had more disks
+on top of the last disk?
+
+So you would have moved
+all of them to buffer.
+
+You don't have to worry
+how you move it.
+
+But you have to move
+it anyway.
+
+After moving that, you can
+leisurely move this big disk
+
+to the top, to the target.
+
+OK?
+
+Finally, you bring back all
+of them here, right?
+
+For you first operation, for
+your first operation, from
+
+source to target, you have
+to move all of them, the
+
+[UNINTELLIGIBLE].
+
+You could have used target
+as your buffer.
+
+OK?
+
+So that's why in this line I'm
+using source as source.
+
+But the second argument, which
+should have been the target,
+
+is now buffer because my current
+target is buffer for
+
+the top n minus 1 disk.
+
+But my buffer is
+now the target.
+
+OK.
+
+Because I can use the target
+as buffer for the movement.
+
+Then I moved from source to the
+target, the last big disk.
+
+OK?
+
+For that I can use buffer
+as my buffer.
+
+Then finally I bring back from
+buffer to target using source
+
+as my buffer.
+
+OK?
+
+So the thing is if you want to
+have a recursive problem you
+
+can do it in two ways.
+
+One thing, you can start
+thinking how to express this
+
+problem in its simpler version
+like how you thought about the
+
+Fibonacci series,
+for instance.
+
+Or else, you can start from
+its base case, the most
+
+fundamental situation.
+
+So here it's n equal to
+1, but this doesn't
+
+give you enough context.
+
+So you go to the next level, n
+is equal to 2, and you have
+
+the answer.
+
+Right?
\ No newline at end of file
diff --git a/Fq0mvAbzUrY.txt b/Fq0mvAbzUrY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6b3c2cd1cacb0b4e254135a8da079b658e6b79f0
--- /dev/null
+++ b/Fq0mvAbzUrY.txt
@@ -0,0 +1,9563 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu our topic today
+
+ align:start position:0%
+ocw.mit.edu our topic today
+ 
+
+ align:start position:0%
+ocw.mit.edu our topic today
+is the influential movement called
+
+ align:start position:0%
+is the influential movement called
+ 
+
+ align:start position:0%
+is the influential movement called
+Italian
+
+ align:start position:0%
+Italian
+ 
+
+ align:start position:0%
+Italian
+neorealism a um a movement of uh
+
+ align:start position:0%
+neorealism a um a movement of uh
+ 
+
+ align:start position:0%
+neorealism a um a movement of uh
+filmmakers that arose in Italy at the
+
+ align:start position:0%
+filmmakers that arose in Italy at the
+ 
+
+ align:start position:0%
+filmmakers that arose in Italy at the
+end of the second world war and had
+
+ align:start position:0%
+end of the second world war and had
+ 
+
+ align:start position:0%
+end of the second world war and had
+although it was a very short lived
+
+ align:start position:0%
+although it was a very short lived
+ 
+
+ align:start position:0%
+although it was a very short lived
+movement lasted only six or seven years
+
+ align:start position:0%
+movement lasted only six or seven years
+ 
+
+ align:start position:0%
+movement lasted only six or seven years
+uh before it kind of uh dissolved of its
+
+ align:start position:0%
+uh before it kind of uh dissolved of its
+ 
+
+ align:start position:0%
+uh before it kind of uh dissolved of its
+own of its own way uh in part
+
+ align:start position:0%
+own of its own way uh in part
+ 
+
+ align:start position:0%
+own of its own way uh in part
+incidentally because although the films
+
+ align:start position:0%
+incidentally because although the films
+ 
+
+ align:start position:0%
+incidentally because although the films
+were very successful with critics and
+
+ align:start position:0%
+were very successful with critics and
+ 
+
+ align:start position:0%
+were very successful with critics and
+several of the neorealist films won
+
+ align:start position:0%
+several of the neorealist films won
+ 
+
+ align:start position:0%
+several of the neorealist films won
+Academy Awards as the best foreign film
+
+ align:start position:0%
+Academy Awards as the best foreign film
+ 
+
+ align:start position:0%
+Academy Awards as the best foreign film
+of the year in uh 1946 and then again in
+
+ align:start position:0%
+of the year in uh 1946 and then again in
+ 
+
+ align:start position:0%
+of the year in uh 1946 and then again in
+1948 when when the film you're going to
+
+ align:start position:0%
+1948 when when the film you're going to
+ 
+
+ align:start position:0%
+1948 when when the film you're going to
+see tonight bicycle thieves won the
+
+ align:start position:0%
+see tonight bicycle thieves won the
+ 
+
+ align:start position:0%
+see tonight bicycle thieves won the
+award despite that Acclaim and even
+
+ align:start position:0%
+award despite that Acclaim and even
+ 
+
+ align:start position:0%
+award despite that Acclaim and even
+Global success uh the the movement sort
+
+ align:start position:0%
+Global success uh the the movement sort
+ 
+
+ align:start position:0%
+Global success uh the the movement sort
+of petered out although its influence as
+
+ align:start position:0%
+of petered out although its influence as
+ 
+
+ align:start position:0%
+of petered out although its influence as
+I've suggested was very great one reason
+
+ align:start position:0%
+I've suggested was very great one reason
+ 
+
+ align:start position:0%
+I've suggested was very great one reason
+the movement petered out was that uh
+
+ align:start position:0%
+the movement petered out was that uh
+ 
+
+ align:start position:0%
+the movement petered out was that uh
+forces in Italian Society Chambers of
+
+ align:start position:0%
+forces in Italian Society Chambers of
+ 
+
+ align:start position:0%
+forces in Italian Society Chambers of
+Commerce types uh people who were
+
+ align:start position:0%
+Commerce types uh people who were
+ 
+
+ align:start position:0%
+Commerce types uh people who were
+interested in encouraging the rebuilding
+
+ align:start position:0%
+interested in encouraging the rebuilding
+ 
+
+ align:start position:0%
+interested in encouraging the rebuilding
+of a devastate of the devastated uh uh
+
+ align:start position:0%
+of a devastate of the devastated uh uh
+ 
+
+ align:start position:0%
+of a devastate of the devastated uh uh
+cities of Italy function a consequence
+
+ align:start position:0%
+cities of Italy function a consequence
+ 
+
+ align:start position:0%
+cities of Italy function a consequence
+of the of the second world war those
+
+ align:start position:0%
+of the of the second world war those
+ 
+
+ align:start position:0%
+of the of the second world war those
+folks began to feel that the messages
+
+ align:start position:0%
+folks began to feel that the messages
+ 
+
+ align:start position:0%
+folks began to feel that the messages
+coming from neorealist films were too
+
+ align:start position:0%
+coming from neorealist films were too
+ 
+
+ align:start position:0%
+coming from neorealist films were too
+negative uh and were discouraging
+
+ align:start position:0%
+negative uh and were discouraging
+ 
+
+ align:start position:0%
+negative uh and were discouraging
+foreign investors uh uh so although it
+
+ align:start position:0%
+foreign investors uh uh so although it
+ 
+
+ align:start position:0%
+foreign investors uh uh so although it
+was a very remarkable movement it it it
+
+ align:start position:0%
+was a very remarkable movement it it it
+ 
+
+ align:start position:0%
+was a very remarkable movement it it it
+lasted only as I say a short time but
+
+ align:start position:0%
+lasted only as I say a short time but
+ 
+
+ align:start position:0%
+lasted only as I say a short time but
+its influence ramified very very very
+
+ align:start position:0%
+its influence ramified very very very
+ 
+
+ align:start position:0%
+its influence ramified very very very
+broadly uh we can trace its influence uh
+
+ align:start position:0%
+broadly uh we can trace its influence uh
+ 
+
+ align:start position:0%
+broadly uh we can trace its influence uh
+to virtually every National Cinema uh
+
+ align:start position:0%
+to virtually every National Cinema uh
+ 
+
+ align:start position:0%
+to virtually every National Cinema uh
+that that came after it and there are
+
+ align:start position:0%
+that that came after it and there are
+ 
+
+ align:start position:0%
+that that came after it and there are
+there are certain very particular
+
+ align:start position:0%
+there are certain very particular
+ 
+
+ align:start position:0%
+there are certain very particular
+influences that one can trace from the
+
+ align:start position:0%
+influences that one can trace from the
+ 
+
+ align:start position:0%
+influences that one can trace from the
+neorealist movement to certain American
+
+ align:start position:0%
+neorealist movement to certain American
+ 
+
+ align:start position:0%
+neorealist movement to certain American
+directors of film Noir in the 40s and
+
+ align:start position:0%
+directors of film Noir in the 40s and
+ 
+
+ align:start position:0%
+directors of film Noir in the 40s and
+early 50s to certain very interesting
+
+ align:start position:0%
+early 50s to certain very interesting
+ 
+
+ align:start position:0%
+early 50s to certain very interesting
+and historically curious forms of
+
+ align:start position:0%
+and historically curious forms of
+ 
+
+ align:start position:0%
+and historically curious forms of
+Television that emerged in the early
+
+ align:start position:0%
+Television that emerged in the early
+ 
+
+ align:start position:0%
+Television that emerged in the early
+years of American television that were
+
+ align:start position:0%
+years of American television that were
+ 
+
+ align:start position:0%
+years of American television that were
+deeply imitative of and influenced by
+
+ align:start position:0%
+deeply imitative of and influenced by
+ 
+
+ align:start position:0%
+deeply imitative of and influenced by
+Italian neorealist
+
+ align:start position:0%
+Italian neorealist
+ 
+
+ align:start position:0%
+Italian neorealist
+movies there was the man that many would
+
+ align:start position:0%
+movies there was the man that many would
+ 
+
+ align:start position:0%
+movies there was the man that many would
+identify as the greatest of all Indian
+
+ align:start position:0%
+identify as the greatest of all Indian
+ 
+
+ align:start position:0%
+identify as the greatest of all Indian
+directors Sagi Ray uh was directly
+
+ align:start position:0%
+directors Sagi Ray uh was directly
+ 
+
+ align:start position:0%
+directors Sagi Ray uh was directly
+inspired to make movies by The Bicycle
+
+ align:start position:0%
+inspired to make movies by The Bicycle
+ 
+
+ align:start position:0%
+inspired to make movies by The Bicycle
+Thief and he made a a a series of three
+
+ align:start position:0%
+Thief and he made a a a series of three
+ 
+
+ align:start position:0%
+Thief and he made a a a series of three
+films that are essentially a form of
+
+ align:start position:0%
+films that are essentially a form of
+ 
+
+ align:start position:0%
+films that are essentially a form of
+Italian neorealism moved to India uh
+
+ align:start position:0%
+Italian neorealism moved to India uh
+ 
+
+ align:start position:0%
+Italian neorealism moved to India uh
+wonderful Trilogy of of uh films some of
+
+ align:start position:0%
+wonderful Trilogy of of uh films some of
+ 
+
+ align:start position:0%
+wonderful Trilogy of of uh films some of
+them actually about the Untouchable
+
+ align:start position:0%
+them actually about the Untouchable
+ 
+
+ align:start position:0%
+them actually about the Untouchable
+classes in in India called the Apu
+
+ align:start position:0%
+classes in in India called the Apu
+ 
+
+ align:start position:0%
+classes in in India called the Apu
+Trilogy and they are they remain among
+
+ align:start position:0%
+Trilogy and they are they remain among
+ 
+
+ align:start position:0%
+Trilogy and they are they remain among
+the the most treasured uh forms of
+
+ align:start position:0%
+the the most treasured uh forms of
+ 
+
+ align:start position:0%
+the the most treasured uh forms of
+Indian of Indian film uh the Italian
+
+ align:start position:0%
+Indian of Indian film uh the Italian
+ 
+
+ align:start position:0%
+Indian of Indian film uh the Italian
+neorealist had had a profound influence
+
+ align:start position:0%
+neorealist had had a profound influence
+ 
+
+ align:start position:0%
+neorealist had had a profound influence
+on other European cinemas as well uh and
+
+ align:start position:0%
+on other European cinemas as well uh and
+ 
+
+ align:start position:0%
+on other European cinemas as well uh and
+most particularly can be said to be the
+
+ align:start position:0%
+most particularly can be said to be the
+ 
+
+ align:start position:0%
+most particularly can be said to be the
+originating movement behind the French
+
+ align:start position:0%
+originating movement behind the French
+ 
+
+ align:start position:0%
+originating movement behind the French
+Nel new velv vag the new wave movement
+
+ align:start position:0%
+Nel new velv vag the new wave movement
+ 
+
+ align:start position:0%
+Nel new velv vag the new wave movement
+that uh in France that emerges at the
+
+ align:start position:0%
+that uh in France that emerges at the
+ 
+
+ align:start position:0%
+that uh in France that emerges at the
+end of the 50s and the early 60s and uh
+
+ align:start position:0%
+end of the 50s and the early 60s and uh
+ 
+
+ align:start position:0%
+end of the 50s and the early 60s and uh
+in involved such now
+
+ align:start position:0%
+in involved such now
+ 
+
+ align:start position:0%
+in involved such now
+recognized uh such directors uh now
+
+ align:start position:0%
+recognized uh such directors uh now
+ 
+
+ align:start position:0%
+recognized uh such directors uh now
+recognized as major figures in the
+
+ align:start position:0%
+recognized as major figures in the
+ 
+
+ align:start position:0%
+recognized as major figures in the
+history of film as Jean L Godard and
+
+ align:start position:0%
+history of film as Jean L Godard and
+ 
+
+ align:start position:0%
+history of film as Jean L Godard and
+Fran
+
+ align:start position:0%
+Fran
+ 
+
+ align:start position:0%
+Fran
+trufo so it was although a short live
+
+ align:start position:0%
+trufo so it was although a short live
+ 
+
+ align:start position:0%
+trufo so it was although a short live
+movement a profoundly influential one
+
+ align:start position:0%
+movement a profoundly influential one
+ 
+
+ align:start position:0%
+movement a profoundly influential one
+and it produced some enduring and
+
+ align:start position:0%
+and it produced some enduring and
+ 
+
+ align:start position:0%
+and it produced some enduring and
+beautiful and I guess I would say
+
+ align:start position:0%
+beautiful and I guess I would say
+ 
+
+ align:start position:0%
+beautiful and I guess I would say
+Immortal films the most famous and
+
+ align:start position:0%
+Immortal films the most famous and
+ 
+
+ align:start position:0%
+Immortal films the most famous and
+perhaps in some ways the most perfect of
+
+ align:start position:0%
+perhaps in some ways the most perfect of
+ 
+
+ align:start position:0%
+perhaps in some ways the most perfect of
+those films is the one you're going to
+
+ align:start position:0%
+those films is the one you're going to
+ 
+
+ align:start position:0%
+those films is the one you're going to
+see tonight bicycle thieves and I'll
+
+ align:start position:0%
+see tonight bicycle thieves and I'll
+ 
+
+ align:start position:0%
+see tonight bicycle thieves and I'll
+talk a bit about that film in my
+
+ align:start position:0%
+talk a bit about that film in my
+ 
+
+ align:start position:0%
+talk a bit about that film in my
+introduction to the lecture this evening
+
+ align:start position:0%
+introduction to the lecture this evening
+ 
+
+ align:start position:0%
+introduction to the lecture this evening
+I want to begin though by giving you a
+
+ align:start position:0%
+I want to begin though by giving you a
+ 
+
+ align:start position:0%
+I want to begin though by giving you a
+sense of how neorealism feels a kind of
+
+ align:start position:0%
+sense of how neorealism feels a kind of
+ 
+
+ align:start position:0%
+sense of how neorealism feels a kind of
+a kind of a kind of distilled version of
+
+ align:start position:0%
+a kind of a kind of distilled version of
+ 
+
+ align:start position:0%
+a kind of a kind of distilled version of
+or distilled embodiment of many of the
+
+ align:start position:0%
+or distilled embodiment of many of the
+ 
+
+ align:start position:0%
+or distilled embodiment of many of the
+deepest principles of neorealism uh and
+
+ align:start position:0%
+deepest principles of neorealism uh and
+ 
+
+ align:start position:0%
+deepest principles of neorealism uh and
+uh in order to do that I want to show
+
+ align:start position:0%
+uh in order to do that I want to show
+ 
+
+ align:start position:0%
+uh in order to do that I want to show
+you a clip from the very beginning of
+
+ align:start position:0%
+you a clip from the very beginning of
+ 
+
+ align:start position:0%
+you a clip from the very beginning of
+the film you're going to see tonight so
+
+ align:start position:0%
+the film you're going to see tonight so
+ 
+
+ align:start position:0%
+the film you're going to see tonight so
+you'll see this beginning twice
+
+ align:start position:0%
+you'll see this beginning twice
+ 
+
+ align:start position:0%
+you'll see this beginning twice
+hopefully the second time you see it
+
+ align:start position:0%
+hopefully the second time you see it
+ 
+
+ align:start position:0%
+hopefully the second time you see it
+you'll be alive to More Alive to some of
+
+ align:start position:0%
+you'll be alive to More Alive to some of
+ 
+
+ align:start position:0%
+you'll be alive to More Alive to some of
+its implications so here is the very
+
+ align:start position:0%
+its implications so here is the very
+ 
+
+ align:start position:0%
+its implications so here is the very
+opening of bicycle thieves and one of
+
+ align:start position:0%
+opening of bicycle thieves and one of
+ 
+
+ align:start position:0%
+opening of bicycle thieves and one of
+the things I want to ask you to watch
+
+ align:start position:0%
+the things I want to ask you to watch
+ 
+
+ align:start position:0%
+the things I want to ask you to watch
+for is first how much information how
+
+ align:start position:0%
+for is first how much information how
+ 
+
+ align:start position:0%
+for is first how much information how
+much visual information dramatic
+
+ align:start position:0%
+much visual information dramatic
+ 
+
+ align:start position:0%
+much visual information dramatic
+information becomes available to you
+
+ align:start position:0%
+information becomes available to you
+ 
+
+ align:start position:0%
+information becomes available to you
+under the titles uh and then how
+
+ align:start position:0%
+under the titles uh and then how
+ 
+
+ align:start position:0%
+under the titles uh and then how
+fluently and fluidly the film moves out
+
+ align:start position:0%
+fluently and fluidly the film moves out
+ 
+
+ align:start position:0%
+fluently and fluidly the film moves out
+of the title sequence into a kind of
+
+ align:start position:0%
+of the title sequence into a kind of
+ 
+
+ align:start position:0%
+of the title sequence into a kind of
+continuation of the drama that's
+
+ align:start position:0%
+continuation of the drama that's
+ 
+
+ align:start position:0%
+continuation of the drama that's
+articulated in that title sequence on
+
+ align:start position:0%
+articulated in that title sequence on
+ 
+
+ align:start position:0%
+articulated in that title sequence on
+the surface this little anecdote at the
+
+ align:start position:0%
+the surface this little anecdote at the
+ 
+
+ align:start position:0%
+the surface this little anecdote at the
+very beginning of the film seems very
+
+ align:start position:0%
+very beginning of the film seems very
+ 
+
+ align:start position:0%
+very beginning of the film seems very
+modest and uh one might even think of it
+
+ align:start position:0%
+modest and uh one might even think of it
+ 
+
+ align:start position:0%
+modest and uh one might even think of it
+as simply expository that is to
+
+ align:start position:0%
+as simply expository that is to
+ 
+
+ align:start position:0%
+as simply expository that is to
+providing information to the audience so
+
+ align:start position:0%
+providing information to the audience so
+ 
+
+ align:start position:0%
+providing information to the audience so
+that they can get on with the story uh
+
+ align:start position:0%
+that they can get on with the story uh
+ 
+
+ align:start position:0%
+that they can get on with the story uh
+as I hope you'll recognize and as I'll
+
+ align:start position:0%
+as I hope you'll recognize and as I'll
+ 
+
+ align:start position:0%
+as I hope you'll recognize and as I'll
+try to show you briefly after I've shown
+
+ align:start position:0%
+try to show you briefly after I've shown
+ 
+
+ align:start position:0%
+try to show you briefly after I've shown
+you the clip much more is going on than
+
+ align:start position:0%
+you the clip much more is going on than
+ 
+
+ align:start position:0%
+you the clip much more is going on than
+that and it's a particularly uh
+
+ align:start position:0%
+that and it's a particularly uh
+ 
+
+ align:start position:0%
+that and it's a particularly uh
+wonderful example of the way in which
+
+ align:start position:0%
+wonderful example of the way in which
+ 
+
+ align:start position:0%
+wonderful example of the way in which
+the best neorealist films generate a
+
+ align:start position:0%
+the best neorealist films generate a
+ 
+
+ align:start position:0%
+the best neorealist films generate a
+kind of texture a kind of density what
+
+ align:start position:0%
+kind of texture a kind of density what
+ 
+
+ align:start position:0%
+kind of texture a kind of density what
+I've sometimes called a multiplicity
+
+ align:start position:0%
+I've sometimes called a multiplicity
+ 
+
+ align:start position:0%
+I've sometimes called a multiplicity
+that we have suggested in this course is
+
+ align:start position:0%
+that we have suggested in this course is
+ 
+
+ align:start position:0%
+that we have suggested in this course is
+one of the fundamental ways in which you
+
+ align:start position:0%
+one of the fundamental ways in which you
+ 
+
+ align:start position:0%
+one of the fundamental ways in which you
+can distinguish between entertainment
+
+ align:start position:0%
+can distinguish between entertainment
+ 
+
+ align:start position:0%
+can distinguish between entertainment
+and serious entertainment or between
+
+ align:start position:0%
+and serious entertainment or between
+ 
+
+ align:start position:0%
+and serious entertainment or between
+entertainment and art when items and
+
+ align:start position:0%
+entertainment and art when items and
+ 
+
+ align:start position:0%
+entertainment and art when items and
+objects begin to have this multiplicity
+
+ align:start position:0%
+objects begin to have this multiplicity
+ 
+
+ align:start position:0%
+objects begin to have this multiplicity
+when they begin to serve Ser multiple
+
+ align:start position:0%
+when they begin to serve Ser multiple
+ 
+
+ align:start position:0%
+when they begin to serve Ser multiple
+functions not just a single function
+
+ align:start position:0%
+functions not just a single function
+ 
+
+ align:start position:0%
+functions not just a single function
+you're in the presence of something not
+
+ align:start position:0%
+you're in the presence of something not
+ 
+
+ align:start position:0%
+you're in the presence of something not
+only complex but something that
+
+ align:start position:0%
+only complex but something that
+ 
+
+ align:start position:0%
+only complex but something that
+acknowledges the complexity of the world
+
+ align:start position:0%
+acknowledges the complexity of the world
+ 
+
+ align:start position:0%
+acknowledges the complexity of the world
+in some in some respects and this
+
+ align:start position:0%
+in some in some respects and this
+ 
+
+ align:start position:0%
+in some in some respects and this
+opening sequence of bicycle thieves does
+
+ align:start position:0%
+opening sequence of bicycle thieves does
+ 
+
+ align:start position:0%
+opening sequence of bicycle thieves does
+this with remarkable economy so here's
+
+ align:start position:0%
+this with remarkable economy so here's
+ 
+
+ align:start position:0%
+this with remarkable economy so here's
+the beginning of the film
+
+ align:start position:0%
+the beginning of the film
+ 
+
+ align:start position:0%
+the beginning of the film
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rich rich
+
+ align:start position:0%
+rich rich
+ 
+
+ align:start position:0%
+rich rich
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Greg can you freeze it for a
+
+ align:start position:0%
+Greg can you freeze it for a
+ 
+
+ align:start position:0%
+Greg can you freeze it for a
+second one thing I should mention while
+
+ align:start position:0%
+second one thing I should mention while
+ 
+
+ align:start position:0%
+second one thing I should mention while
+you're watching this to interrupt the
+
+ align:start position:0%
+you're watching this to interrupt the
+ 
+
+ align:start position:0%
+you're watching this to interrupt the
+sequence for a moment
+
+ align:start position:0%
+sequence for a moment
+ 
+
+ align:start position:0%
+sequence for a moment
+the activity that you see taking place
+
+ align:start position:0%
+the activity that you see taking place
+ 
+
+ align:start position:0%
+the activity that you see taking place
+under the titles is supposed to be
+
+ align:start position:0%
+under the titles is supposed to be
+ 
+
+ align:start position:0%
+under the titles is supposed to be
+confusing at first although after a
+
+ align:start position:0%
+confusing at first although after a
+ 
+
+ align:start position:0%
+confusing at first although after a
+while it begins to clarify perhaps
+
+ align:start position:0%
+while it begins to clarify perhaps
+ 
+
+ align:start position:0%
+while it begins to clarify perhaps
+you're not fully clear what is going on
+
+ align:start position:0%
+you're not fully clear what is going on
+ 
+
+ align:start position:0%
+you're not fully clear what is going on
+until the titles appear and you see
+
+ align:start position:0%
+until the titles appear and you see
+ 
+
+ align:start position:0%
+until the titles appear and you see
+these men assembling around that
+
+ align:start position:0%
+these men assembling around that
+ 
+
+ align:start position:0%
+these men assembling around that
+staircase there where a man with a A
+
+ align:start position:0%
+staircase there where a man with a A
+ 
+
+ align:start position:0%
+staircase there where a man with a A
+list is speaking to them what is going
+
+ align:start position:0%
+list is speaking to them what is going
+ 
+
+ align:start position:0%
+list is speaking to them what is going
+on here is what in in in in the United
+
+ align:start position:0%
+on here is what in in in in the United
+ 
+
+ align:start position:0%
+on here is what in in in in the United
+States in the in the 40s and 50s on the
+
+ align:start position:0%
+States in the in the 40s and 50s on the
+ 
+
+ align:start position:0%
+States in the in the 40s and 50s on the
+on the docks in New York they called The
+
+ align:start position:0%
+on the docks in New York they called The
+ 
+
+ align:start position:0%
+on the docks in New York they called The
+Shape Up and a shape up is a place where
+
+ align:start position:0%
+Shape Up and a shape up is a place where
+ 
+
+ align:start position:0%
+Shape Up and a shape up is a place where
+men who are eager for work sort of come
+
+ align:start position:0%
+men who are eager for work sort of come
+ 
+
+ align:start position:0%
+men who are eager for work sort of come
+and hang around and wait for the boss
+
+ align:start position:0%
+and hang around and wait for the boss
+ 
+
+ align:start position:0%
+and hang around and wait for the boss
+the the the foreman or the or the hiring
+
+ align:start position:0%
+the the the foreman or the or the hiring
+ 
+
+ align:start position:0%
+the the the foreman or the or the hiring
+boss to pick them out of the crowd shape
+
+ align:start position:0%
+boss to pick them out of the crowd shape
+ 
+
+ align:start position:0%
+boss to pick them out of the crowd shape
+ups are always unpleasant experiences
+
+ align:start position:0%
+ups are always unpleasant experiences
+ 
+
+ align:start position:0%
+ups are always unpleasant experiences
+because there are many people who are
+
+ align:start position:0%
+because there are many people who are
+ 
+
+ align:start position:0%
+because there are many people who are
+excluded and the people who are chosen
+
+ align:start position:0%
+excluded and the people who are chosen
+ 
+
+ align:start position:0%
+excluded and the people who are chosen
+are often this was especially true on
+
+ align:start position:0%
+are often this was especially true on
+ 
+
+ align:start position:0%
+are often this was especially true on
+the New York Waterfront in the days when
+
+ align:start position:0%
+the New York Waterfront in the days when
+ 
+
+ align:start position:0%
+the New York Waterfront in the days when
+which I know about because my father was
+
+ align:start position:0%
+which I know about because my father was
+ 
+
+ align:start position:0%
+which I know about because my father was
+a long shoreman for a while it was a
+
+ align:start position:0%
+a long shoreman for a while it was a
+ 
+
+ align:start position:0%
+a long shoreman for a while it was a
+particularly bad thing in the New York
+
+ align:start position:0%
+particularly bad thing in the New York
+ 
+
+ align:start position:0%
+particularly bad thing in the New York
+Waterfront because you had to know
+
+ align:start position:0%
+Waterfront because you had to know
+ 
+
+ align:start position:0%
+Waterfront because you had to know
+somebody to get work I don't know if
+
+ align:start position:0%
+somebody to get work I don't know if
+ 
+
+ align:start position:0%
+somebody to get work I don't know if
+that's an implication here or not
+
+ align:start position:0%
+that's an implication here or not
+ 
+
+ align:start position:0%
+that's an implication here or not
+although you'll see as the men complain
+
+ align:start position:0%
+although you'll see as the men complain
+ 
+
+ align:start position:0%
+although you'll see as the men complain
+that some of them have that suspicion in
+
+ align:start position:0%
+that some of them have that suspicion in
+ 
+
+ align:start position:0%
+that some of them have that suspicion in
+any case what's going on here is what is
+
+ align:start position:0%
+any case what's going on here is what is
+ 
+
+ align:start position:0%
+any case what's going on here is what is
+called a shape up men are gathered
+
+ align:start position:0%
+called a shape up men are gathered
+ 
+
+ align:start position:0%
+called a shape up men are gathered
+around men who are unemployed looking
+
+ align:start position:0%
+around men who are unemployed looking
+ 
+
+ align:start position:0%
+around men who are unemployed looking
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speee fore
+
+ align:start position:0%
+speee fore
+ 
+
+ align:start position:0%
+speee fore
+spe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+speee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speee
+
+ align:start position:0%
+speee
+ 
+
+ align:start position:0%
+speee
+fore
+
+ align:start position:0%
+fore
+ 
+
+ align:start position:0%
+fore
+spee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+for GU for
+
+ align:start position:0%
+for GU for
+ 
+
+ align:start position:0%
+for GU for
+spe fore spe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speee spe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I wish I could let the scene run on but
+
+ align:start position:0%
+I wish I could let the scene run on but
+ 
+
+ align:start position:0%
+I wish I could let the scene run on but
+I hope you I hope you I can tell some of
+
+ align:start position:0%
+I hope you I hope you I can tell some of
+ 
+
+ align:start position:0%
+I hope you I hope you I can tell some of
+you are responding to what you saw there
+
+ align:start position:0%
+you are responding to what you saw there
+ 
+
+ align:start position:0%
+you are responding to what you saw there
+make some observations about what you
+
+ align:start position:0%
+make some observations about what you
+ 
+
+ align:start position:0%
+make some observations about what you
+saw there what that in that introduction
+
+ align:start position:0%
+saw there what that in that introduction
+ 
+
+ align:start position:0%
+saw there what that in that introduction
+what do we learn as an
+
+ align:start position:0%
+what do we learn as an
+ 
+
+ align:start position:0%
+what do we learn as an
+audience you have to be fast I only have
+
+ align:start position:0%
+audience you have to be fast I only have
+ 
+
+ align:start position:0%
+audience you have to be fast I only have
+a few minutes here yes for all right one
+
+ align:start position:0%
+a few minutes here yes for all right one
+ 
+
+ align:start position:0%
+a few minutes here yes for all right one
+thing we know is that there's a lot of
+
+ align:start position:0%
+thing we know is that there's a lot of
+ 
+
+ align:start position:0%
+thing we know is that there's a lot of
+unemployment in this a lot right and
+
+ align:start position:0%
+unemployment in this a lot right and
+ 
+
+ align:start position:0%
+unemployment in this a lot right and
+there's a lot of discontent and then the
+
+ align:start position:0%
+there's a lot of discontent and then the
+ 
+
+ align:start position:0%
+there's a lot of discontent and then the
+minute he says I don't have a bicycle
+
+ align:start position:0%
+minute he says I don't have a bicycle
+ 
+
+ align:start position:0%
+minute he says I don't have a bicycle
+virtually everyone else in the crowd
+
+ align:start position:0%
+virtually everyone else in the crowd
+ 
+
+ align:start position:0%
+virtually everyone else in the crowd
+says I have a bicycle everyone is
+
+ align:start position:0%
+says I have a bicycle everyone is
+ 
+
+ align:start position:0%
+says I have a bicycle everyone is
+desperate for a job not just Richi
+
+ align:start position:0%
+desperate for a job not just Richi
+ 
+
+ align:start position:0%
+desperate for a job not just Richi
+that's right uh so there and he he we we
+
+ align:start position:0%
+that's right uh so there and he he we we
+ 
+
+ align:start position:0%
+that's right uh so there and he he we we
+learn how grateful he is but also how
+
+ align:start position:0%
+learn how grateful he is but also how
+ 
+
+ align:start position:0%
+learn how grateful he is but also how
+troubled he is what is what's the
+
+ align:start position:0%
+troubled he is what is what's the
+ 
+
+ align:start position:0%
+troubled he is what is what's the
+evidence in the film that he is really
+
+ align:start position:0%
+evidence in the film that he is really
+ 
+
+ align:start position:0%
+evidence in the film that he is really
+very unha very very troubled by the fact
+
+ align:start position:0%
+very unha very very troubled by the fact
+ 
+
+ align:start position:0%
+very unha very very troubled by the fact
+that he doesn't have a bicycle to get
+
+ align:start position:0%
+that he doesn't have a bicycle to get
+ 
+
+ align:start position:0%
+that he doesn't have a bicycle to get
+this job after so long what's the most
+
+ align:start position:0%
+this job after so long what's the most
+ 
+
+ align:start position:0%
+this job after so long what's the most
+dramatic piece of evidence we see that
+
+ align:start position:0%
+dramatic piece of evidence we see that
+ 
+
+ align:start position:0%
+dramatic piece of evidence we see that
+he's distracted by his anxiety
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H he doesn't help her with the water he
+
+ align:start position:0%
+H he doesn't help her with the water he
+ 
+
+ align:start position:0%
+H he doesn't help her with the water he
+doesn't help his wife with the water yes
+
+ align:start position:0%
+doesn't help his wife with the water yes
+ 
+
+ align:start position:0%
+doesn't help his wife with the water yes
+it's a very dramatic scene isn't it uh
+
+ align:start position:0%
+it's a very dramatic scene isn't it uh
+ 
+
+ align:start position:0%
+it's a very dramatic scene isn't it uh
+she she's walking behind him carrying
+
+ align:start position:0%
+she she's walking behind him carrying
+ 
+
+ align:start position:0%
+she she's walking behind him carrying
+these two heavy and he doesn't ignore
+
+ align:start position:0%
+these two heavy and he doesn't ignore
+ 
+
+ align:start position:0%
+these two heavy and he doesn't ignore
+her because he's a a nasty patriarch who
+
+ align:start position:0%
+her because he's a a nasty patriarch who
+ 
+
+ align:start position:0%
+her because he's a a nasty patriarch who
+thinks that women should carry water uh
+
+ align:start position:0%
+thinks that women should carry water uh
+ 
+
+ align:start position:0%
+thinks that women should carry water uh
+he he's so distracted he doesn't notice
+
+ align:start position:0%
+he he's so distracted he doesn't notice
+ 
+
+ align:start position:0%
+he he's so distracted he doesn't notice
+it and in fact what he walks down that
+
+ align:start position:0%
+it and in fact what he walks down that
+ 
+
+ align:start position:0%
+it and in fact what he walks down that
+that little incline and looks back and
+
+ align:start position:0%
+that little incline and looks back and
+ 
+
+ align:start position:0%
+that little incline and looks back and
+sees her struggling goes back and as
+
+ align:start position:0%
+sees her struggling goes back and as
+ 
+
+ align:start position:0%
+sees her struggling goes back and as
+soon as he recognizes it he takes one
+
+ align:start position:0%
+soon as he recognizes it he takes one
+ 
+
+ align:start position:0%
+soon as he recognizes it he takes one
+from her and it's significant isn't it
+
+ align:start position:0%
+from her and it's significant isn't it
+ 
+
+ align:start position:0%
+from her and it's significant isn't it
+that he takes only one from her is if
+
+ align:start position:0%
+that he takes only one from her is if
+ 
+
+ align:start position:0%
+that he takes only one from her is if
+they're really Partners I mean and it's
+
+ align:start position:0%
+they're really Partners I mean and it's
+ 
+
+ align:start position:0%
+they're really Partners I mean and it's
+also what else is significant she
+
+ align:start position:0%
+also what else is significant she
+ 
+
+ align:start position:0%
+also what else is significant she
+doesn't yell at him she doesn't say my
+
+ align:start position:0%
+doesn't yell at him she doesn't say my
+ 
+
+ align:start position:0%
+doesn't yell at him she doesn't say my
+God Richi what kind of a pig are you
+
+ align:start position:0%
+God Richi what kind of a pig are you
+ 
+
+ align:start position:0%
+God Richi what kind of a pig are you
+making me carry all this stuff by myself
+
+ align:start position:0%
+making me carry all this stuff by myself
+ 
+
+ align:start position:0%
+making me carry all this stuff by myself
+right because she shares his his uh
+
+ align:start position:0%
+right because she shares his his uh
+ 
+
+ align:start position:0%
+right because she shares his his uh
+anxiety and his concern doesn't she U
+
+ align:start position:0%
+anxiety and his concern doesn't she U
+ 
+
+ align:start position:0%
+anxiety and his concern doesn't she U
+so on the surface what the the the SE
+
+ align:start position:0%
+so on the surface what the the the SE
+ 
+
+ align:start position:0%
+so on the surface what the the the SE
+the scene certainly dramatizes richi's
+
+ align:start position:0%
+the scene certainly dramatizes richi's
+ 
+
+ align:start position:0%
+the scene certainly dramatizes richi's
+desperate need for for for a job and the
+
+ align:start position:0%
+desperate need for for for a job and the
+ 
+
+ align:start position:0%
+desperate need for for for a job and the
+fact that he's one of many people in a
+
+ align:start position:0%
+fact that he's one of many people in a
+ 
+
+ align:start position:0%
+fact that he's one of many people in a
+similar situation but what does it tell
+
+ align:start position:0%
+similar situation but what does it tell
+ 
+
+ align:start position:0%
+similar situation but what does it tell
+us about his marriage on the basis of
+
+ align:start position:0%
+us about his marriage on the basis of
+ 
+
+ align:start position:0%
+us about his marriage on the basis of
+these detail what you just saw in this
+
+ align:start position:0%
+these detail what you just saw in this
+ 
+
+ align:start position:0%
+these detail what you just saw in this
+beginning do you think he has a good
+
+ align:start position:0%
+beginning do you think he has a good
+ 
+
+ align:start position:0%
+beginning do you think he has a good
+marriage that he has a good relationship
+
+ align:start position:0%
+marriage that he has a good relationship
+ 
+
+ align:start position:0%
+marriage that he has a good relationship
+with his wife that that that it's a
+
+ align:start position:0%
+with his wife that that that it's a
+ 
+
+ align:start position:0%
+with his wife that that that it's a
+mutually trusting relationship that they
+
+ align:start position:0%
+mutually trusting relationship that they
+ 
+
+ align:start position:0%
+mutually trusting relationship that they
+of course of course right and how do we
+
+ align:start position:0%
+of course of course right and how do we
+ 
+
+ align:start position:0%
+of course of course right and how do we
+know that we know that from that detail
+
+ align:start position:0%
+know that we know that from that detail
+ 
+
+ align:start position:0%
+know that we know that from that detail
+now the detail does not Advance the plot
+
+ align:start position:0%
+now the detail does not Advance the plot
+ 
+
+ align:start position:0%
+now the detail does not Advance the plot
+in the sense of telling us anything
+
+ align:start position:0%
+in the sense of telling us anything
+ 
+
+ align:start position:0%
+in the sense of telling us anything
+further about his need for the bicycle
+
+ align:start position:0%
+further about his need for the bicycle
+ 
+
+ align:start position:0%
+further about his need for the bicycle
+or his unemployment but it does reveal
+
+ align:start position:0%
+or his unemployment but it does reveal
+ 
+
+ align:start position:0%
+or his unemployment but it does reveal
+to us something about their marriage
+
+ align:start position:0%
+to us something about their marriage
+ 
+
+ align:start position:0%
+to us something about their marriage
+about the kind of man is about the kind
+
+ align:start position:0%
+about the kind of man is about the kind
+ 
+
+ align:start position:0%
+about the kind of man is about the kind
+of woman she is right uh so that it's a
+
+ align:start position:0%
+of woman she is right uh so that it's a
+ 
+
+ align:start position:0%
+of woman she is right uh so that it's a
+moment in which his anxiety about his
+
+ align:start position:0%
+moment in which his anxiety about his
+ 
+
+ align:start position:0%
+moment in which his anxiety about his
+job is maybe the primary thing we see
+
+ align:start position:0%
+job is maybe the primary thing we see
+ 
+
+ align:start position:0%
+job is maybe the primary thing we see
+but what is also dramatized for us is
+
+ align:start position:0%
+but what is also dramatized for us is
+ 
+
+ align:start position:0%
+but what is also dramatized for us is
+the nature of their relationship and
+
+ align:start position:0%
+the nature of their relationship and
+ 
+
+ align:start position:0%
+the nature of their relationship and
+it's dramatized for us without anyone
+
+ align:start position:0%
+it's dramatized for us without anyone
+ 
+
+ align:start position:0%
+it's dramatized for us without anyone
+coming out and saying let me show you a
+
+ align:start position:0%
+coming out and saying let me show you a
+ 
+
+ align:start position:0%
+coming out and saying let me show you a
+mutually engaged couple who depend on
+
+ align:start position:0%
+mutually engaged couple who depend on
+ 
+
+ align:start position:0%
+mutually engaged couple who depend on
+each other and who survive in part
+
+ align:start position:0%
+each other and who survive in part
+ 
+
+ align:start position:0%
+each other and who survive in part
+because they share each other's troubles
+
+ align:start position:0%
+because they share each other's troubles
+ 
+
+ align:start position:0%
+because they share each other's troubles
+people whose respect for each other is
+
+ align:start position:0%
+people whose respect for each other is
+ 
+
+ align:start position:0%
+people whose respect for each other is
+so total that even when one of them
+
+ align:start position:0%
+so total that even when one of them
+ 
+
+ align:start position:0%
+so total that even when one of them
+commits a a re a really uh uh mean or at
+
+ align:start position:0%
+commits a a re a really uh uh mean or at
+ 
+
+ align:start position:0%
+commits a a re a really uh uh mean or at
+least or or or at least unpleasant act
+
+ align:start position:0%
+least or or or at least unpleasant act
+ 
+
+ align:start position:0%
+least or or or at least unpleasant act
+By ignoring his wife's struggles she
+
+ align:start position:0%
+By ignoring his wife's struggles she
+ 
+
+ align:start position:0%
+By ignoring his wife's struggles she
+doesn't even think to complain to him
+
+ align:start position:0%
+doesn't even think to complain to him
+ 
+
+ align:start position:0%
+doesn't even think to complain to him
+about it because she shares his anxiety
+
+ align:start position:0%
+about it because she shares his anxiety
+ 
+
+ align:start position:0%
+about it because she shares his anxiety
+so that's it's an example of what I mean
+
+ align:start position:0%
+so that's it's an example of what I mean
+ 
+
+ align:start position:0%
+so that's it's an example of what I mean
+by a Moment of Multiplicity in which
+
+ align:start position:0%
+by a Moment of Multiplicity in which
+ 
+
+ align:start position:0%
+by a Moment of Multiplicity in which
+something about their relationship
+
+ align:start position:0%
+something about their relationship
+ 
+
+ align:start position:0%
+something about their relationship
+something about their marriage emerges
+
+ align:start position:0%
+something about their marriage emerges
+ 
+
+ align:start position:0%
+something about their marriage emerges
+even as we are also learning something
+
+ align:start position:0%
+even as we are also learning something
+ 
+
+ align:start position:0%
+even as we are also learning something
+about the economic circumstances in
+
+ align:start position:0%
+about the economic circumstances in
+ 
+
+ align:start position:0%
+about the economic circumstances in
+which these characters live say a little
+
+ align:start position:0%
+which these characters live say a little
+ 
+
+ align:start position:0%
+which these characters live say a little
+bit more about the scene that you saw
+
+ align:start position:0%
+bit more about the scene that you saw
+ 
+
+ align:start position:0%
+bit more about the scene that you saw
+how about the place where she's drawing
+
+ align:start position:0%
+how about the place where she's drawing
+ 
+
+ align:start position:0%
+how about the place where she's drawing
+War
+
+ align:start position:0%
+War
+ 
+
+ align:start position:0%
+War
+what about that why would they're in a
+
+ align:start position:0%
+what about that why would they're in a
+ 
+
+ align:start position:0%
+what about that why would they're in a
+city they're they're walking in fact to
+
+ align:start position:0%
+city they're they're walking in fact to
+ 
+
+ align:start position:0%
+city they're they're walking in fact to
+a high-rise apartment house in which
+
+ align:start position:0%
+a high-rise apartment house in which
+ 
+
+ align:start position:0%
+a high-rise apartment house in which
+they live what does it mean that she's
+
+ align:start position:0%
+they live what does it mean that she's
+ 
+
+ align:start position:0%
+they live what does it mean that she's
+carrying two buckets of water to an
+
+ align:start position:0%
+carrying two buckets of water to an
+ 
+
+ align:start position:0%
+carrying two buckets of water to an
+apartment and then she's going to climb
+
+ align:start position:0%
+apartment and then she's going to climb
+ 
+
+ align:start position:0%
+apartment and then she's going to climb
+up four flights or three flights to get
+
+ align:start position:0%
+up four flights or three flights to get
+ 
+
+ align:start position:0%
+up four flights or three flights to get
+to their apartment what does that tell
+
+ align:start position:0%
+to their apartment what does that tell
+ 
+
+ align:start position:0%
+to their apartment what does that tell
+us about melini's Italy there's no
+
+ align:start position:0%
+us about melini's Italy there's no
+ 
+
+ align:start position:0%
+us about melini's Italy there's no
+running water in the building in the in
+
+ align:start position:0%
+running water in the building in the in
+ 
+
+ align:start position:0%
+running water in the building in the in
+the high-rise apartments right uh and
+
+ align:start position:0%
+the high-rise apartments right uh and
+ 
+
+ align:start position:0%
+the high-rise apartments right uh and
+not just that is the water precious how
+
+ align:start position:0%
+not just that is the water precious how
+ 
+
+ align:start position:0%
+not just that is the water precious how
+do you know it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say yes but what else where do they get
+
+ align:start position:0%
+say yes but what else where do they get
+ 
+
+ align:start position:0%
+say yes but what else where do they get
+the water is the water do they go to a
+
+ align:start position:0%
+the water is the water do they go to a
+ 
+
+ align:start position:0%
+the water is the water do they go to a
+pump in the open Square no it's in a
+
+ align:start position:0%
+pump in the open Square no it's in a
+ 
+
+ align:start position:0%
+pump in the open Square no it's in a
+barbed wire compound right again these
+
+ align:start position:0%
+barbed wire compound right again these
+ 
+
+ align:start position:0%
+barbed wire compound right again these
+details may not register instantly as
+
+ align:start position:0%
+details may not register instantly as
+ 
+
+ align:start position:0%
+details may not register instantly as
+deeply significant but think what they
+
+ align:start position:0%
+deeply significant but think what they
+ 
+
+ align:start position:0%
+deeply significant but think what they
+tell us about the conditions of urban
+
+ align:start position:0%
+tell us about the conditions of urban
+ 
+
+ align:start position:0%
+tell us about the conditions of urban
+life in Rome in 1947 or 1948 when the
+
+ align:start position:0%
+life in Rome in 1947 or 1948 when the
+ 
+
+ align:start position:0%
+life in Rome in 1947 or 1948 when the
+film is when the film is set you have
+
+ align:start position:0%
+film is when the film is set you have
+ 
+
+ align:start position:0%
+film is when the film is set you have
+and and and you could even go further
+
+ align:start position:0%
+and and and you could even go further
+ 
+
+ align:start position:0%
+and and and you could even go further
+look more closely at the setting did
+
+ align:start position:0%
+look more closely at the setting did
+ 
+
+ align:start position:0%
+look more closely at the setting did
+anything grow there it looked like they
+
+ align:start position:0%
+anything grow there it looked like they
+ 
+
+ align:start position:0%
+anything grow there it looked like they
+were walking across across a wasteland
+
+ align:start position:0%
+were walking across across a wasteland
+ 
+
+ align:start position:0%
+were walking across across a wasteland
+of mud except for these high-rise
+
+ align:start position:0%
+of mud except for these high-rise
+ 
+
+ align:start position:0%
+of mud except for these high-rise
+tenement buildings so we have high-rise
+
+ align:start position:0%
+tenement buildings so we have high-rise
+ 
+
+ align:start position:0%
+tenement buildings so we have high-rise
+tenement buildings set down in a kind of
+
+ align:start position:0%
+tenement buildings set down in a kind of
+ 
+
+ align:start position:0%
+tenement buildings set down in a kind of
+desert right uh a place in uh buildings
+
+ align:start position:0%
+desert right uh a place in uh buildings
+ 
+
+ align:start position:0%
+desert right uh a place in uh buildings
+that don't even have running water uh in
+
+ align:start position:0%
+that don't even have running water uh in
+ 
+
+ align:start position:0%
+that don't even have running water uh in
+which in which the main water pump has
+
+ align:start position:0%
+which in which the main water pump has
+ 
+
+ align:start position:0%
+which in which the main water pump has
+to be protected by barbed wire right so
+
+ align:start position:0%
+to be protected by barbed wire right so
+ 
+
+ align:start position:0%
+to be protected by barbed wire right so
+that it's almost as if in this brief
+
+ align:start position:0%
+that it's almost as if in this brief
+ 
+
+ align:start position:0%
+that it's almost as if in this brief
+introduction to the film the whole
+
+ align:start position:0%
+introduction to the film the whole
+ 
+
+ align:start position:0%
+introduction to the film the whole
+socioeconomic environment of the story
+
+ align:start position:0%
+socioeconomic environment of the story
+ 
+
+ align:start position:0%
+socioeconomic environment of the story
+has been established for us without
+
+ align:start position:0%
+has been established for us without
+ 
+
+ align:start position:0%
+has been established for us without
+anyone giving us lectures about it or
+
+ align:start position:0%
+anyone giving us lectures about it or
+ 
+
+ align:start position:0%
+anyone giving us lectures about it or
+calling our attention to it that's what
+
+ align:start position:0%
+calling our attention to it that's what
+ 
+
+ align:start position:0%
+calling our attention to it that's what
+I by multiplicity when the details of
+
+ align:start position:0%
+I by multiplicity when the details of
+ 
+
+ align:start position:0%
+I by multiplicity when the details of
+the film serve character and serve plot
+
+ align:start position:0%
+the film serve character and serve plot
+ 
+
+ align:start position:0%
+the film serve character and serve plot
+and serve our sense of the environment
+
+ align:start position:0%
+and serve our sense of the environment
+ 
+
+ align:start position:0%
+and serve our sense of the environment
+right uh so it's a it's a rich moment
+
+ align:start position:0%
+right uh so it's a it's a rich moment
+ 
+
+ align:start position:0%
+right uh so it's a it's a rich moment
+it's a moment it's a moment of art it's
+
+ align:start position:0%
+it's a moment it's a moment of art it's
+ 
+
+ align:start position:0%
+it's a moment it's a moment of art it's
+a moment of complexity it's a moment of
+
+ align:start position:0%
+a moment of complexity it's a moment of
+ 
+
+ align:start position:0%
+a moment of complexity it's a moment of
+human
+
+ align:start position:0%
+human
+ 
+
+ align:start position:0%
+human
+truthfulness that that resonates for us
+
+ align:start position:0%
+truthfulness that that resonates for us
+ 
+
+ align:start position:0%
+truthfulness that that resonates for us
+as the as the film as the film goes on
+
+ align:start position:0%
+as the as the film as the film goes on
+ 
+
+ align:start position:0%
+as the as the film as the film goes on
+well there are many many moments like
+
+ align:start position:0%
+well there are many many moments like
+ 
+
+ align:start position:0%
+well there are many many moments like
+this virtually every moment uh in
+
+ align:start position:0%
+this virtually every moment uh in
+ 
+
+ align:start position:0%
+this virtually every moment uh in
+bicycle thieves has this kind of density
+
+ align:start position:0%
+bicycle thieves has this kind of density
+ 
+
+ align:start position:0%
+bicycle thieves has this kind of density
+or texture has this kind of uh uh
+
+ align:start position:0%
+or texture has this kind of uh uh
+ 
+
+ align:start position:0%
+or texture has this kind of uh uh
+implication built into the particular
+
+ align:start position:0%
+implication built into the particular
+ 
+
+ align:start position:0%
+implication built into the particular
+details I want to very quickly set the
+
+ align:start position:0%
+details I want to very quickly set the
+ 
+
+ align:start position:0%
+details I want to very quickly set the
+kind of the context for I've already
+
+ align:start position:0%
+kind of the context for I've already
+ 
+
+ align:start position:0%
+kind of the context for I've already
+implied the context for the neorealist
+
+ align:start position:0%
+implied the context for the neorealist
+ 
+
+ align:start position:0%
+implied the context for the neorealist
+movement the basic context is the end of
+
+ align:start position:0%
+movement the basic context is the end of
+ 
+
+ align:start position:0%
+movement the basic context is the end of
+World War II uh most historians trace
+
+ align:start position:0%
+World War II uh most historians trace
+ 
+
+ align:start position:0%
+World War II uh most historians trace
+the beginnings of the neorealist
+
+ align:start position:0%
+the beginnings of the neorealist
+ 
+
+ align:start position:0%
+the beginnings of the neorealist
+movement to to films that were made
+
+ align:start position:0%
+movement to to films that were made
+ 
+
+ align:start position:0%
+movement to to films that were made
+under melini while while while the war
+
+ align:start position:0%
+under melini while while while the war
+ 
+
+ align:start position:0%
+under melini while while while the war
+was still going on and some people
+
+ align:start position:0%
+was still going on and some people
+ 
+
+ align:start position:0%
+was still going on and some people
+actually date the very beginning of
+
+ align:start position:0%
+actually date the very beginning of
+ 
+
+ align:start position:0%
+actually date the very beginning of
+of um the movement to a film made in uh
+
+ align:start position:0%
+of um the movement to a film made in uh
+ 
+
+ align:start position:0%
+of um the movement to a film made in uh
+1942 by luchino Visconti called
+
+ align:start position:0%
+1942 by luchino Visconti called
+ 
+
+ align:start position:0%
+1942 by luchino Visconti called
+Obsession uh it's actually a an
+
+ align:start position:0%
+Obsession uh it's actually a an
+ 
+
+ align:start position:0%
+Obsession uh it's actually a an
+adaptation of a of a a very a popular
+
+ align:start position:0%
+adaptation of a of a a very a popular
+ 
+
+ align:start position:0%
+adaptation of a of a a very a popular
+American pulp novel called The Postman
+
+ align:start position:0%
+American pulp novel called The Postman
+ 
+
+ align:start position:0%
+American pulp novel called The Postman
+Always Rings Twice It's been made twice
+
+ align:start position:0%
+Always Rings Twice It's been made twice
+ 
+
+ align:start position:0%
+Always Rings Twice It's been made twice
+into an English Language American movie
+
+ align:start position:0%
+into an English Language American movie
+ 
+
+ align:start position:0%
+into an English Language American movie
+but most recently starring Jack
+
+ align:start position:0%
+but most recently starring Jack
+ 
+
+ align:start position:0%
+but most recently starring Jack
+Nicholson uh the but but but the the
+
+ align:start position:0%
+Nicholson uh the but but but the the
+ 
+
+ align:start position:0%
+Nicholson uh the but but but the the
+Italian version may be the most the most
+
+ align:start position:0%
+Italian version may be the most the most
+ 
+
+ align:start position:0%
+Italian version may be the most the most
+important and interesting of the uh
+
+ align:start position:0%
+important and interesting of the uh
+ 
+
+ align:start position:0%
+important and interesting of the uh
+films made from the book uh the the the
+
+ align:start position:0%
+films made from the book uh the the the
+ 
+
+ align:start position:0%
+films made from the book uh the the the
+book itself is a rather tody uh noirish
+
+ align:start position:0%
+book itself is a rather tody uh noirish
+ 
+
+ align:start position:0%
+book itself is a rather tody uh noirish
+story about about a uh the owner of a
+
+ align:start position:0%
+story about about a uh the owner of a
+ 
+
+ align:start position:0%
+story about about a uh the owner of a
+diner who's
+
+ align:start position:0%
+diner who's
+ 
+
+ align:start position:0%
+diner who's
+who an ugly middle-aged pug who's
+
+ align:start position:0%
+who an ugly middle-aged pug who's
+ 
+
+ align:start position:0%
+who an ugly middle-aged pug who's
+married to a beautiful and somewhat
+
+ align:start position:0%
+married to a beautiful and somewhat
+ 
+
+ align:start position:0%
+married to a beautiful and somewhat
+younger woman who very unhappy with her
+
+ align:start position:0%
+younger woman who very unhappy with her
+ 
+
+ align:start position:0%
+younger woman who very unhappy with her
+husband uh uh begins an affair with a
+
+ align:start position:0%
+husband uh uh begins an affair with a
+ 
+
+ align:start position:0%
+husband uh uh begins an affair with a
+Drifter who comes by and uh um
+
+ align:start position:0%
+Drifter who comes by and uh um
+ 
+
+ align:start position:0%
+Drifter who comes by and uh um
+ultimately encourages The Drifter to
+
+ align:start position:0%
+ultimately encourages The Drifter to
+ 
+
+ align:start position:0%
+ultimately encourages The Drifter to
+kill her husband uh and it's a it's
+
+ align:start position:0%
+kill her husband uh and it's a it's
+ 
+
+ align:start position:0%
+kill her husband uh and it's a it's
+actually a rather uh a rather
+
+ align:start position:0%
+actually a rather uh a rather
+ 
+
+ align:start position:0%
+actually a rather uh a rather
+heavy-handed uh male chauvinist fantasy
+
+ align:start position:0%
+heavy-handed uh male chauvinist fantasy
+ 
+
+ align:start position:0%
+heavy-handed uh male chauvinist fantasy
+about uh about the partly about about
+
+ align:start position:0%
+about uh about the partly about about
+ 
+
+ align:start position:0%
+about uh about the partly about about
+how cunning and dangerous women are the
+
+ align:start position:0%
+how cunning and dangerous women are the
+ 
+
+ align:start position:0%
+how cunning and dangerous women are the
+Italian version is much more interesting
+
+ align:start position:0%
+Italian version is much more interesting
+ 
+
+ align:start position:0%
+Italian version is much more interesting
+in part because the workingclass
+
+ align:start position:0%
+in part because the workingclass
+ 
+
+ align:start position:0%
+in part because the workingclass
+dimensions of the story are given much
+
+ align:start position:0%
+dimensions of the story are given much
+ 
+
+ align:start position:0%
+dimensions of the story are given much
+greater emphasis in Lino Visconti's
+
+ align:start position:0%
+greater emphasis in Lino Visconti's
+ 
+
+ align:start position:0%
+greater emphasis in Lino Visconti's
+version and the film partly becomes a
+
+ align:start position:0%
+version and the film partly becomes a
+ 
+
+ align:start position:0%
+version and the film partly becomes a
+kind of meditation on the fate of uh
+
+ align:start position:0%
+kind of meditation on the fate of uh
+ 
+
+ align:start position:0%
+kind of meditation on the fate of uh
+undocumented workers and non-union
+
+ align:start position:0%
+undocumented workers and non-union
+ 
+
+ align:start position:0%
+undocumented workers and non-union
+workers in in uh uh in in uh uh Italian
+
+ align:start position:0%
+workers in in uh uh in in uh uh Italian
+ 
+
+ align:start position:0%
+workers in in uh uh in in uh uh Italian
+Society uh in any case the emphasis on
+
+ align:start position:0%
+Society uh in any case the emphasis on
+ 
+
+ align:start position:0%
+Society uh in any case the emphasis on
+ordinary people and the emphasis on
+
+ align:start position:0%
+ordinary people and the emphasis on
+ 
+
+ align:start position:0%
+ordinary people and the emphasis on
+socioeconomic circumstances in that film
+
+ align:start position:0%
+socioeconomic circumstances in that film
+ 
+
+ align:start position:0%
+socioeconomic circumstances in that film
+by visanti came to be defining features
+
+ align:start position:0%
+by visanti came to be defining features
+ 
+
+ align:start position:0%
+by visanti came to be defining features
+among the defining features of Italian
+
+ align:start position:0%
+among the defining features of Italian
+ 
+
+ align:start position:0%
+among the defining features of Italian
+neorealist um uh film
+
+ align:start position:0%
+neorealist um uh film
+ 
+
+ align:start position:0%
+neorealist um uh film
+making but the movement really doesn't
+
+ align:start position:0%
+making but the movement really doesn't
+ 
+
+ align:start position:0%
+making but the movement really doesn't
+get going until after the war and the
+
+ align:start position:0%
+get going until after the war and the
+ 
+
+ align:start position:0%
+get going until after the war and the
+context of the war is very important we
+
+ align:start position:0%
+context of the war is very important we
+ 
+
+ align:start position:0%
+context of the war is very important we
+need to recognize that the film is
+
+ align:start position:0%
+need to recognize that the film is
+ 
+
+ align:start position:0%
+need to recognize that the film is
+really set in a devastated Society a
+
+ align:start position:0%
+really set in a devastated Society a
+ 
+
+ align:start position:0%
+really set in a devastated Society a
+society uh in which I'm talking now
+
+ align:start position:0%
+society uh in which I'm talking now
+ 
+
+ align:start position:0%
+society uh in which I'm talking now
+about all of Europe after the second
+
+ align:start position:0%
+about all of Europe after the second
+ 
+
+ align:start position:0%
+about all of Europe after the second
+world war unemployment reached at 25 or
+
+ align:start position:0%
+world war unemployment reached at 25 or
+ 
+
+ align:start position:0%
+world war unemployment reached at 25 or
+30% higher in some societies uh there
+
+ align:start position:0%
+30% higher in some societies uh there
+ 
+
+ align:start position:0%
+30% higher in some societies uh there
+was economic turmoil in virtually every
+
+ align:start position:0%
+was economic turmoil in virtually every
+ 
+
+ align:start position:0%
+was economic turmoil in virtually every
+European Society profound terrible
+
+ align:start position:0%
+European Society profound terrible
+ 
+
+ align:start position:0%
+European Society profound terrible
+pressures from Black Market um uh
+
+ align:start position:0%
+pressures from Black Market um uh
+ 
+
+ align:start position:0%
+pressures from Black Market um uh
+activities of all kinds the de the war
+
+ align:start position:0%
+activities of all kinds the de the war
+ 
+
+ align:start position:0%
+activities of all kinds the de the war
+was so devast stating that something on
+
+ align:start position:0%
+was so devast stating that something on
+ 
+
+ align:start position:0%
+was so devast stating that something on
+the order of 35% of all the permanent
+
+ align:start position:0%
+the order of 35% of all the permanent
+ 
+
+ align:start position:0%
+the order of 35% of all the permanent
+dwellings in Western Europe were
+
+ align:start position:0%
+dwellings in Western Europe were
+ 
+
+ align:start position:0%
+dwellings in Western Europe were
+destroyed during the War uh 25% of the
+
+ align:start position:0%
+destroyed during the War uh 25% of the
+ 
+
+ align:start position:0%
+destroyed during the War uh 25% of the
+Polish population was killed a
+
+ align:start position:0%
+Polish population was killed a
+ 
+
+ align:start position:0%
+Polish population was killed a
+tremendous proportion uh virtually every
+
+ align:start position:0%
+tremendous proportion uh virtually every
+ 
+
+ align:start position:0%
+tremendous proportion uh virtually every
+well a very large number of Italian
+
+ align:start position:0%
+well a very large number of Italian
+ 
+
+ align:start position:0%
+well a very large number of Italian
+cities were damaged very badly including
+
+ align:start position:0%
+cities were damaged very badly including
+ 
+
+ align:start position:0%
+cities were damaged very badly including
+of course Rome itself uh and and these
+
+ align:start position:0%
+of course Rome itself uh and and these
+ 
+
+ align:start position:0%
+of course Rome itself uh and and these
+these abject and terrifying economic
+
+ align:start position:0%
+these abject and terrifying economic
+ 
+
+ align:start position:0%
+these abject and terrifying economic
+conditions were were of course uh in in
+
+ align:start position:0%
+conditions were were of course uh in in
+ 
+
+ align:start position:0%
+conditions were were of course uh in in
+Italy doubled by the problem that Italy
+
+ align:start position:0%
+Italy doubled by the problem that Italy
+ 
+
+ align:start position:0%
+Italy doubled by the problem that Italy
+was on the losing side in the war and
+
+ align:start position:0%
+was on the losing side in the war and
+ 
+
+ align:start position:0%
+was on the losing side in the war and
+had and and uh
+
+ align:start position:0%
+had and and uh
+ 
+
+ align:start position:0%
+had and and uh
+therefore faced even more difficulties
+
+ align:start position:0%
+therefore faced even more difficulties
+ 
+
+ align:start position:0%
+therefore faced even more difficulties
+in in in a Rec in the recovery than than
+
+ align:start position:0%
+in in in a Rec in the recovery than than
+ 
+
+ align:start position:0%
+in in in a Rec in the recovery than than
+uh a culture like the French culture or
+
+ align:start position:0%
+uh a culture like the French culture or
+ 
+
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+uh a culture like the French culture or
+the or or or or English society so so
+
+ align:start position:0%
+the or or or or English society so so
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+
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+the or or or or English society so so
+the devastation of World War II and the
+
+ align:start position:0%
+the devastation of World War II and the
+ 
+
+ align:start position:0%
+the devastation of World War II and the
+turmoil and and and dislocation caused
+
+ align:start position:0%
+turmoil and and and dislocation caused
+ 
+
+ align:start position:0%
+turmoil and and and dislocation caused
+by World War II is the fundamental fact
+
+ align:start position:0%
+by World War II is the fundamental fact
+ 
+
+ align:start position:0%
+by World War II is the fundamental fact
+in words what what is still operative in
+
+ align:start position:0%
+in words what what is still operative in
+ 
+
+ align:start position:0%
+in words what what is still operative in
+Italian Society what institutions still
+
+ align:start position:0%
+Italian Society what institutions still
+ 
+
+ align:start position:0%
+Italian Society what institutions still
+work is one of the implicit questions
+
+ align:start position:0%
+work is one of the implicit questions
+ 
+
+ align:start position:0%
+work is one of the implicit questions
+that the film explores and the film
+
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+that the film explores and the film
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+
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+that the film explores and the film
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+
+ align:start position:0%
+suggests that a lot of the official
+ 
+
+ align:start position:0%
+suggests that a lot of the official
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+
+ align:start position:0%
+institutions like the police and the and
+ 
+
+ align:start position:0%
+institutions like the police and the and
+the and and especially the religious
+
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+the and and especially the religious
+ 
+
+ align:start position:0%
+the and and especially the religious
+institutions have broken down and are
+
+ align:start position:0%
+institutions have broken down and are
+ 
+
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+institutions have broken down and are
+not really helping people very much as
+
+ align:start position:0%
+not really helping people very much as
+ 
+
+ align:start position:0%
+not really helping people very much as
+you'll see when you when you watch
+
+ align:start position:0%
+you'll see when you when you watch
+ 
+
+ align:start position:0%
+you'll see when you when you watch
+tonight's film but that there there are
+
+ align:start position:0%
+tonight's film but that there there are
+ 
+
+ align:start position:0%
+tonight's film but that there there are
+other uh forms
+
+ align:start position:0%
+other uh forms
+ 
+
+ align:start position:0%
+other uh forms
+of help and Aid that people get mostly
+
+ align:start position:0%
+of help and Aid that people get mostly
+ 
+
+ align:start position:0%
+of help and Aid that people get mostly
+in some sense from their the film
+
+ align:start position:0%
+in some sense from their the film
+ 
+
+ align:start position:0%
+in some sense from their the film
+suggests from their local communities
+
+ align:start position:0%
+suggests from their local communities
+ 
+
+ align:start position:0%
+suggests from their local communities
+and from their and from and from their
+
+ align:start position:0%
+and from their and from and from their
+ 
+
+ align:start position:0%
+and from their and from and from their
+immediate families well to this basic
+
+ align:start position:0%
+immediate families well to this basic
+ 
+
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+immediate families well to this basic
+sort of setting of Devastation and
+
+ align:start position:0%
+sort of setting of Devastation and
+ 
+
+ align:start position:0%
+sort of setting of Devastation and
+turmoil and un and economic uncertainty
+
+ align:start position:0%
+turmoil and un and economic uncertainty
+ 
+
+ align:start position:0%
+turmoil and un and economic uncertainty
+we need we need to add two other
+
+ align:start position:0%
+we need we need to add two other
+ 
+
+ align:start position:0%
+we need we need to add two other
+contextual
+
+ align:start position:0%
+contextual
+ 
+
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+contextual
+factors both of them having to do with
+
+ align:start position:0%
+factors both of them having to do with
+ 
+
+ align:start position:0%
+factors both of them having to do with
+the film Traditions against which
+
+ align:start position:0%
+the film Traditions against which
+ 
+
+ align:start position:0%
+the film Traditions against which
+neorealism set itself against which it
+
+ align:start position:0%
+neorealism set itself against which it
+ 
+
+ align:start position:0%
+neorealism set itself against which it
+understood itself to be ar uh to be um
+
+ align:start position:0%
+understood itself to be ar uh to be um
+ 
+
+ align:start position:0%
+understood itself to be ar uh to be um
+uh in in in a in a kind of profound
+
+ align:start position:0%
+uh in in in a in a kind of profound
+ 
+
+ align:start position:0%
+uh in in in a in a kind of profound
+argument the first tradition was the
+
+ align:start position:0%
+argument the first tradition was the
+ 
+
+ align:start position:0%
+argument the first tradition was the
+tradition of of fascist film under
+
+ align:start position:0%
+tradition of of fascist film under
+ 
+
+ align:start position:0%
+tradition of of fascist film under
+melini
+
+ align:start position:0%
+melini
+ 
+
+ align:start position:0%
+melini
+these were very almost all Studio films
+
+ align:start position:0%
+these were very almost all Studio films
+ 
+
+ align:start position:0%
+these were very almost all Studio films
+they were shot inside Studios neorealist
+
+ align:start position:0%
+they were shot inside Studios neorealist
+ 
+
+ align:start position:0%
+they were shot inside Studios neorealist
+films are shot
+
+ align:start position:0%
+films are shot
+ 
+
+ align:start position:0%
+films are shot
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+
+ align:start position:0%
+outdoors and they all and they were
+ 
+
+ align:start position:0%
+outdoors and they all and they were
+largely Escapist uh they were largely
+
+ align:start position:0%
+largely Escapist uh they were largely
+ 
+
+ align:start position:0%
+largely Escapist uh they were largely
+Escapist Fair uh focusing more often
+
+ align:start position:0%
+Escapist Fair uh focusing more often
+ 
+
+ align:start position:0%
+Escapist Fair uh focusing more often
+than not on the upper social orders in
+
+ align:start position:0%
+than not on the upper social orders in
+ 
+
+ align:start position:0%
+than not on the upper social orders in
+fact there was a genre of film so
+
+ align:start position:0%
+fact there was a genre of film so
+ 
+
+ align:start position:0%
+fact there was a genre of film so
+devoted to the Romantic entanglements of
+
+ align:start position:0%
+devoted to the Romantic entanglements of
+ 
+
+ align:start position:0%
+devoted to the Romantic entanglements of
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+
+ align:start position:0%
+aristocrats that they came to be known
+ 
+
+ align:start position:0%
+aristocrats that they came to be known
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+
+ align:start position:0%
+as white telephone films the reason for
+ 
+
+ align:start position:0%
+as white telephone films the reason for
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+
+ align:start position:0%
+this is that in the old days before cell
+ 
+
+ align:start position:0%
+this is that in the old days before cell
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+
+ align:start position:0%
+phones uh and before multicolored phones
+ 
+
+ align:start position:0%
+phones uh and before multicolored phones
+all telephones were
+
+ align:start position:0%
+all telephones were
+ 
+
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+all telephones were
+black uh and uh it was a mark of
+
+ align:start position:0%
+black uh and uh it was a mark of
+ 
+
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+astonishing
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+astonishing
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+
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+aristocratic privilege that the people
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+
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+aristocratic privilege that the people
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+
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+in some of these films had white
+ 
+
+ align:start position:0%
+in some of these films had white
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+
+ align:start position:0%
+telephones they were such unusual
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+
+ align:start position:0%
+telephones they were such unusual
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+
+ align:start position:0%
+objects for the time that the films came
+ 
+
+ align:start position:0%
+objects for the time that the films came
+to be labeled as white telephone films
+
+ align:start position:0%
+to be labeled as white telephone films
+ 
+
+ align:start position:0%
+to be labeled as white telephone films
+and they were largely uh as I said
+
+ align:start position:0%
+and they were largely uh as I said
+ 
+
+ align:start position:0%
+and they were largely uh as I said
+Escapist movies with with beautifully
+
+ align:start position:0%
+Escapist movies with with beautifully
+ 
+
+ align:start position:0%
+Escapist movies with with beautifully
+made up uh actors and actresses in
+
+ align:start position:0%
+made up uh actors and actresses in
+ 
+
+ align:start position:0%
+made up uh actors and actresses in
+artificial light per forming what were
+
+ align:start position:0%
+artificial light per forming what were
+ 
+
+ align:start position:0%
+artificial light per forming what were
+essentially artificial Stories the
+
+ align:start position:0%
+essentially artificial Stories the
+ 
+
+ align:start position:0%
+essentially artificial Stories the
+second tradition against which the
+
+ align:start position:0%
+second tradition against which the
+ 
+
+ align:start position:0%
+second tradition against which the
+neorealists are responding against which
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+ align:start position:0%
+neorealists are responding against which
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+
+ align:start position:0%
+neorealists are responding against which
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+
+ align:start position:0%
+they are reacting is the tradition of
+ 
+
+ align:start position:0%
+they are reacting is the tradition of
+Hollywood glamour there's a wonderful
+
+ align:start position:0%
+Hollywood glamour there's a wonderful
+ 
+
+ align:start position:0%
+Hollywood glamour there's a wonderful
+moment in The Bicycle Thief and you'll
+
+ align:start position:0%
+moment in The Bicycle Thief and you'll
+ 
+
+ align:start position:0%
+moment in The Bicycle Thief and you'll
+as you'll see tonight when Richi finally
+
+ align:start position:0%
+as you'll see tonight when Richi finally
+ 
+
+ align:start position:0%
+as you'll see tonight when Richi finally
+goes off to get his job he recovers his
+
+ align:start position:0%
+goes off to get his job he recovers his
+ 
+
+ align:start position:0%
+goes off to get his job he recovers his
+bicycle from hackets he he's pawned it
+
+ align:start position:0%
+bicycle from hackets he he's pawned it
+ 
+
+ align:start position:0%
+bicycle from hackets he he's pawned it
+uh and that's why he's so nervous he
+
+ align:start position:0%
+uh and that's why he's so nervous he
+ 
+
+ align:start position:0%
+uh and that's why he's so nervous he
+knows where the bicycle is but he
+
+ align:start position:0%
+knows where the bicycle is but he
+ 
+
+ align:start position:0%
+knows where the bicycle is but he
+doesn't know how they're going to get it
+
+ align:start position:0%
+doesn't know how they're going to get it
+ 
+
+ align:start position:0%
+doesn't know how they're going to get it
+out of Pawn and you'll see how his wife
+
+ align:start position:0%
+out of Pawn and you'll see how his wife
+ 
+
+ align:start position:0%
+out of Pawn and you'll see how his wife
+solves that problem in the very next
+
+ align:start position:0%
+solves that problem in the very next
+ 
+
+ align:start position:0%
+solves that problem in the very next
+sequence is Bey uh beyond the one I've
+
+ align:start position:0%
+sequence is Bey uh beyond the one I've
+ 
+
+ align:start position:0%
+sequence is Bey uh beyond the one I've
+just shown to you um when Richi finally
+
+ align:start position:0%
+just shown to you um when Richi finally
+ 
+
+ align:start position:0%
+just shown to you um when Richi finally
+goes to work for the first time he has
+
+ align:start position:0%
+goes to work for the first time he has
+ 
+
+ align:start position:0%
+goes to work for the first time he has
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+
+ align:start position:0%
+someone with him giving him instructions
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+
+ align:start position:0%
+someone with him giving him instructions
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+
+ align:start position:0%
+and what he is is a bill sticker he puts
+ 
+
+ align:start position:0%
+and what he is is a bill sticker he puts
+up posters great Po in fact the poster
+
+ align:start position:0%
+up posters great Po in fact the poster
+ 
+
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+up posters great Po in fact the poster
+that he's putting up is a poster for an
+
+ align:start position:0%
+that he's putting up is a poster for an
+ 
+
+ align:start position:0%
+that he's putting up is a poster for an
+American movie and it has a great am
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+American movie and it has a great am
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+American movie and it has a great am
+famous American movie star of the 40s
+
+ align:start position:0%
+famous American movie star of the 40s
+ 
+
+ align:start position:0%
+famous American movie star of the 40s
+and 50s Rita Hayworth on the on it and
+
+ align:start position:0%
+and 50s Rita Hayworth on the on it and
+ 
+
+ align:start position:0%
+and 50s Rita Hayworth on the on it and
+as he's putting the picture up he uh you
+
+ align:start position:0%
+as he's putting the picture up he uh you
+ 
+
+ align:start position:0%
+as he's putting the picture up he uh you
+put paste on the board then you he's
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+ align:start position:0%
+put paste on the board then you he's
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+put paste on the board then you he's
+given the stupid instructions anyone
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+given the stupid instructions anyone
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+
+ align:start position:0%
+given the stupid instructions anyone
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+could do this job but the man giving him
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+could do this job but the man giving him
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+instructions acts as if he's explaining
+ 
+
+ align:start position:0%
+instructions acts as if he's explaining
+something really difficult
+
+ align:start position:0%
+something really difficult
+ 
+
+ align:start position:0%
+something really difficult
+like like rocket science uh when all
+
+ align:start position:0%
+like like rocket science uh when all
+ 
+
+ align:start position:0%
+like like rocket science uh when all
+he's doing is tell telling him how to
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+ align:start position:0%
+he's doing is tell telling him how to
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+
+ align:start position:0%
+he's doing is tell telling him how to
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+ align:start position:0%
+paste a a poster up on a board but his
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+paste a a poster up on a board but his
+but his instructions include a
+
+ align:start position:0%
+but his instructions include a
+ 
+
+ align:start position:0%
+but his instructions include a
+systematic uh remarks about being sure
+
+ align:start position:0%
+systematic uh remarks about being sure
+ 
+
+ align:start position:0%
+systematic uh remarks about being sure
+not to leave any wrinkles in it and I've
+
+ align:start position:0%
+not to leave any wrinkles in it and I've
+ 
+
+ align:start position:0%
+not to leave any wrinkles in it and I've
+taken that myself to be a kind of
+
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+taken that myself to be a kind of
+ 
+
+ align:start position:0%
+taken that myself to be a kind of
+implicit complaint against Hollywood
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+implicit complaint against Hollywood
+ 
+
+ align:start position:0%
+implicit complaint against Hollywood
+that say the Hollywood the Hollywood
+
+ align:start position:0%
+that say the Hollywood the Hollywood
+ 
+
+ align:start position:0%
+that say the Hollywood the Hollywood
+female has no wrinkles the Hollywood
+
+ align:start position:0%
+female has no wrinkles the Hollywood
+ 
+
+ align:start position:0%
+female has no wrinkles the Hollywood
+female uh the Hollywood star the
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+ align:start position:0%
+female uh the Hollywood star the
+ 
+
+ align:start position:0%
+female uh the Hollywood star the
+Hollywood movie is so glamorized that
+
+ align:start position:0%
+Hollywood movie is so glamorized that
+ 
+
+ align:start position:0%
+Hollywood movie is so glamorized that
+you never see wrinkles or defects and
+
+ align:start position:0%
+you never see wrinkles or defects and
+ 
+
+ align:start position:0%
+you never see wrinkles or defects and
+this couldn't contrast more sharply with
+
+ align:start position:0%
+this couldn't contrast more sharply with
+ 
+
+ align:start position:0%
+this couldn't contrast more sharply with
+the ordinary faces of the actors that we
+
+ align:start position:0%
+the ordinary faces of the actors that we
+ 
+
+ align:start position:0%
+the ordinary faces of the actors that we
+see in neorealist films so two
+
+ align:start position:0%
+see in neorealist films so two
+ 
+
+ align:start position:0%
+see in neorealist films so two
+traditions of Glamour and of and of
+
+ align:start position:0%
+traditions of Glamour and of and of
+ 
+
+ align:start position:0%
+traditions of Glamour and of and of
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+
+ align:start position:0%
+escapism are essentially uh the
+ 
+
+ align:start position:0%
+escapism are essentially uh the
+antagonists that that uh that that that
+
+ align:start position:0%
+antagonists that that uh that that that
+ 
+
+ align:start position:0%
+antagonists that that uh that that that
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+
+ align:start position:0%
+that that help to explain how neorealism
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+
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+that that help to explain how neorealism
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+defines itself uh uh and under and
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+defines itself uh uh and under and
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+understands itself it's worth briefly
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+
+ align:start position:0%
+understands itself it's worth briefly
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+
+ align:start position:0%
+mentioning that neorealism has
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+
+ align:start position:0%
+mentioning that neorealism has
+distinguished Origins uh in at least
+
+ align:start position:0%
+distinguished Origins uh in at least
+ 
+
+ align:start position:0%
+distinguished Origins uh in at least
+three different National Cinemas the
+
+ align:start position:0%
+three different National Cinemas the
+ 
+
+ align:start position:0%
+three different National Cinemas the
+first is in Italian Cinema itself um uh
+
+ align:start position:0%
+first is in Italian Cinema itself um uh
+ 
+
+ align:start position:0%
+first is in Italian Cinema itself um uh
+there was a movement in during the
+
+ align:start position:0%
+there was a movement in during the
+ 
+
+ align:start position:0%
+there was a movement in during the
+silent era a kind of documentary
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+ align:start position:0%
+silent era a kind of documentary
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+
+ align:start position:0%
+silent era a kind of documentary
+movement that wanted to talk a quazi
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+ align:start position:0%
+movement that wanted to talk a quazi
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+
+ align:start position:0%
+movement that wanted to talk a quazi
+documentary movement they were still
+
+ align:start position:0%
+documentary movement they were still
+ 
+
+ align:start position:0%
+documentary movement they were still
+fiction films but they wanted to talk
+
+ align:start position:0%
+fiction films but they wanted to talk
+ 
+
+ align:start position:0%
+fiction films but they wanted to talk
+more openly and honestly about
+
+ align:start position:0%
+more openly and honestly about
+ 
+
+ align:start position:0%
+more openly and honestly about
+contemporary events and contemporary
+
+ align:start position:0%
+contemporary events and contemporary
+ 
+
+ align:start position:0%
+contemporary events and contemporary
+Society and the movement was called the
+
+ align:start position:0%
+Society and the movement was called the
+ 
+
+ align:start position:0%
+Society and the movement was called the
+Verismo movement the truth movement
+
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+Verismo movement the truth movement
+ 
+
+ align:start position:0%
+Verismo movement the truth movement
+right and it occurred between 1914 and
+
+ align:start position:0%
+right and it occurred between 1914 and
+ 
+
+ align:start position:0%
+right and it occurred between 1914 and
+1916 in Italy and this and when the Neo
+
+ align:start position:0%
+1916 in Italy and this and when the Neo
+ 
+
+ align:start position:0%
+1916 in Italy and this and when the Neo
+when when the neorealists began to
+
+ align:start position:0%
+when when the neorealists began to
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+
+ align:start position:0%
+when when the neorealists began to
+articulate their own manifestos and to
+
+ align:start position:0%
+articulate their own manifestos and to
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+
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+articulate their own manifestos and to
+explain theoretically what they were up
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+explain theoretically what they were up
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+
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+
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+to they sometimes reached back to the
+ 
+
+ align:start position:0%
+to they sometimes reached back to the
+Verismo movement as a way of saying
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+Verismo movement as a way of saying
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+
+ align:start position:0%
+Verismo movement as a way of saying
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+we're we're actually traditional as well
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+
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+we're we're actually traditional as well
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+
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+as new a second fundamental influence on
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+
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+as new a second fundamental influence on
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+
+ align:start position:0%
+neorealism uh a kind of earlier version
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+
+ align:start position:0%
+neorealism uh a kind of earlier version
+of neorealism occurred in the German
+
+ align:start position:0%
+of neorealism occurred in the German
+ 
+
+ align:start position:0%
+of neorealism occurred in the German
+Tradition at the end of the silent era
+
+ align:start position:0%
+Tradition at the end of the silent era
+ 
+
+ align:start position:0%
+Tradition at the end of the silent era
+in a series of films made in the 1920s
+
+ align:start position:0%
+in a series of films made in the 1920s
+ 
+
+ align:start position:0%
+in a series of films made in the 1920s
+by the director GW Pap
+
+ align:start position:0%
+by the director GW Pap
+ 
+
+ align:start position:0%
+by the director GW Pap
+PST his the most famous of these films
+
+ align:start position:0%
+PST his the most famous of these films
+ 
+
+ align:start position:0%
+PST his the most famous of these films
+is a film produced in 1925 called the
+
+ align:start position:0%
+is a film produced in 1925 called the
+ 
+
+ align:start position:0%
+is a film produced in 1925 called the
+joyless street and partly deals with
+
+ align:start position:0%
+joyless street and partly deals with
+ 
+
+ align:start position:0%
+joyless street and partly deals with
+prostitutes and it and it and it talks
+
+ align:start position:0%
+prostitutes and it and it and it talks
+ 
+
+ align:start position:0%
+prostitutes and it and it and it talks
+in it tries to dramatize in realistic
+
+ align:start position:0%
+in it tries to dramatize in realistic
+ 
+
+ align:start position:0%
+in it tries to dramatize in realistic
+ways the conditions of the lower social
+
+ align:start position:0%
+ways the conditions of the lower social
+ 
+
+ align:start position:0%
+ways the conditions of the lower social
+orders uh and of course the final um
+
+ align:start position:0%
+orders uh and of course the final um
+ 
+
+ align:start position:0%
+orders uh and of course the final um
+originating Source this also so explains
+
+ align:start position:0%
+originating Source this also so explains
+ 
+
+ align:start position:0%
+originating Source this also so explains
+the richness of neorealism that there
+
+ align:start position:0%
+the richness of neorealism that there
+ 
+
+ align:start position:0%
+the richness of neorealism that there
+are these other film Traditions that are
+
+ align:start position:0%
+are these other film Traditions that are
+ 
+
+ align:start position:0%
+are these other film Traditions that are
+feeding into it and enriching it uh is
+
+ align:start position:0%
+feeding into it and enriching it uh is
+ 
+
+ align:start position:0%
+feeding into it and enriching it uh is
+French and it's the it's the kind of
+
+ align:start position:0%
+French and it's the it's the kind of
+ 
+
+ align:start position:0%
+French and it's the it's the kind of
+French film that we associate with Jean
+
+ align:start position:0%
+French film that we associate with Jean
+ 
+
+ align:start position:0%
+French film that we associate with Jean
+Renoir and with the traditions of poetic
+
+ align:start position:0%
+Renoir and with the traditions of poetic
+ 
+
+ align:start position:0%
+Renoir and with the traditions of poetic
+realism uh uh some of the neorealist one
+
+ align:start position:0%
+realism uh uh some of the neorealist one
+ 
+
+ align:start position:0%
+realism uh uh some of the neorealist one
+of at least one of the neorealist
+
+ align:start position:0%
+of at least one of the neorealist
+ 
+
+ align:start position:0%
+of at least one of the neorealist
+directors visconte had worked as an
+
+ align:start position:0%
+directors visconte had worked as an
+ 
+
+ align:start position:0%
+directors visconte had worked as an
+assistant director for Jean Renoir at
+
+ align:start position:0%
+assistant director for Jean Renoir at
+ 
+
+ align:start position:0%
+assistant director for Jean Renoir at
+one point in his career and uh I I
+
+ align:start position:0%
+one point in his career and uh I I
+ 
+
+ align:start position:0%
+one point in his career and uh I I
+believe I'm not sure this is accurate so
+
+ align:start position:0%
+believe I'm not sure this is accurate so
+ 
+
+ align:start position:0%
+believe I'm not sure this is accurate so
+don't take this as absolute fact but I
+
+ align:start position:0%
+don't take this as absolute fact but I
+ 
+
+ align:start position:0%
+don't take this as absolute fact but I
+believe that it was Renoir himself who
+
+ align:start position:0%
+believe that it was Renoir himself who
+ 
+
+ align:start position:0%
+believe that it was Renoir himself who
+gave a copy of The Postman Always Rings
+
+ align:start position:0%
+gave a copy of The Postman Always Rings
+ 
+
+ align:start position:0%
+gave a copy of The Postman Always Rings
+Twice to visconte uh to uh which led to
+
+ align:start position:0%
+Twice to visconte uh to uh which led to
+ 
+
+ align:start position:0%
+Twice to visconte uh to uh which led to
+the creation of what many people would
+
+ align:start position:0%
+the creation of what many people would
+ 
+
+ align:start position:0%
+the creation of what many people would
+identify as the very first
+
+ align:start position:0%
+identify as the very first
+ 
+
+ align:start position:0%
+identify as the very first
+neorealist neorealist film the Basic
+
+ align:start position:0%
+neorealist neorealist film the Basic
+ 
+
+ align:start position:0%
+neorealist neorealist film the Basic
+practices and traditions of poetic
+
+ align:start position:0%
+practices and traditions of poetic
+ 
+
+ align:start position:0%
+practices and traditions of poetic
+realism are carried over in neorealism
+
+ align:start position:0%
+realism are carried over in neorealism
+ 
+
+ align:start position:0%
+realism are carried over in neorealism
+and in one sense one can see neorealism
+
+ align:start position:0%
+and in one sense one can see neorealism
+ 
+
+ align:start position:0%
+and in one sense one can see neorealism
+as an extension of poetic realism the
+
+ align:start position:0%
+as an extension of poetic realism the
+ 
+
+ align:start position:0%
+as an extension of poetic realism the
+difference is that neorealism has a more
+
+ align:start position:0%
+difference is that neorealism has a more
+ 
+
+ align:start position:0%
+difference is that neorealism has a more
+political and social orientation it's
+
+ align:start position:0%
+political and social orientation it's
+ 
+
+ align:start position:0%
+political and social orientation it's
+more conscious of having a political and
+
+ align:start position:0%
+more conscious of having a political and
+ 
+
+ align:start position:0%
+more conscious of having a political and
+social ambition it wants to
+
+ align:start position:0%
+social ambition it wants to
+ 
+
+ align:start position:0%
+social ambition it wants to
+uh uh and and and sometimes neorealist
+
+ align:start position:0%
+uh uh and and and sometimes neorealist
+ 
+
+ align:start position:0%
+uh uh and and and sometimes neorealist
+films can seem a bit preachy because of
+
+ align:start position:0%
+films can seem a bit preachy because of
+ 
+
+ align:start position:0%
+films can seem a bit preachy because of
+that I mean there's a there's clearly a
+
+ align:start position:0%
+that I mean there's a there's clearly a
+ 
+
+ align:start position:0%
+that I mean there's a there's clearly a
+kind of a a sentiment uh de deeply
+
+ align:start position:0%
+kind of a a sentiment uh de deeply
+ 
+
+ align:start position:0%
+kind of a a sentiment uh de deeply
+sympathetic to the lower social orders
+
+ align:start position:0%
+sympathetic to the lower social orders
+ 
+
+ align:start position:0%
+sympathetic to the lower social orders
+deeply suspicious of the hierarchies of
+
+ align:start position:0%
+deeply suspicious of the hierarchies of
+ 
+
+ align:start position:0%
+deeply suspicious of the hierarchies of
+capitalism some some of the neorealists
+
+ align:start position:0%
+capitalism some some of the neorealists
+ 
+
+ align:start position:0%
+capitalism some some of the neorealists
+were marxists or Marxist sympathizers uh
+
+ align:start position:0%
+were marxists or Marxist sympathizers uh
+ 
+
+ align:start position:0%
+were marxists or Marxist sympathizers uh
+and that helps to explain the political
+
+ align:start position:0%
+and that helps to explain the political
+ 
+
+ align:start position:0%
+and that helps to explain the political
+orientation of neorealist films but the
+
+ align:start position:0%
+orientation of neorealist films but the
+ 
+
+ align:start position:0%
+orientation of neorealist films but the
+basic features of poetic realism the use
+
+ align:start position:0%
+basic features of poetic realism the use
+ 
+
+ align:start position:0%
+basic features of poetic realism the use
+of an outdoor camera the interest in
+
+ align:start position:0%
+of an outdoor camera the interest in
+ 
+
+ align:start position:0%
+of an outdoor camera the interest in
+aanen
+
+ align:start position:0%
+aanen
+ 
+
+ align:start position:0%
+aanen
+style uh and in a film made by which I
+
+ align:start position:0%
+style uh and in a film made by which I
+ 
+
+ align:start position:0%
+style uh and in a film made by which I
+mentioned I think last time made by
+
+ align:start position:0%
+mentioned I think last time made by
+ 
+
+ align:start position:0%
+mentioned I think last time made by
+Renoir in 1935 a film called Tony T we
+
+ align:start position:0%
+Renoir in 1935 a film called Tony T we
+ 
+
+ align:start position:0%
+Renoir in 1935 a film called Tony T we
+have a French version of neorealism
+
+ align:start position:0%
+have a French version of neorealism
+ 
+
+ align:start position:0%
+have a French version of neorealism
+because that film as I mentioned last
+
+ align:start position:0%
+because that film as I mentioned last
+ 
+
+ align:start position:0%
+because that film as I mentioned last
+time is about Italian Quarry workers in
+
+ align:start position:0%
+time is about Italian Quarry workers in
+ 
+
+ align:start position:0%
+time is about Italian Quarry workers in
+the south of France and it has a lot of
+
+ align:start position:0%
+the south of France and it has a lot of
+ 
+
+ align:start position:0%
+the south of France and it has a lot of
+nonprofessional actors in it something
+
+ align:start position:0%
+nonprofessional actors in it something
+ 
+
+ align:start position:0%
+nonprofessional actors in it something
+that became a key feature of neorealism
+
+ align:start position:0%
+that became a key feature of neorealism
+ 
+
+ align:start position:0%
+that became a key feature of neorealism
+so the neorealist movement then uh has
+
+ align:start position:0%
+so the neorealist movement then uh has
+ 
+
+ align:start position:0%
+so the neorealist movement then uh has
+this powerful context which creates a
+
+ align:start position:0%
+this powerful context which creates a
+ 
+
+ align:start position:0%
+this powerful context which creates a
+kind of moral and and and aesthetic
+
+ align:start position:0%
+kind of moral and and and aesthetic
+ 
+
+ align:start position:0%
+kind of moral and and and aesthetic
+energy that helps to explain the power
+
+ align:start position:0%
+energy that helps to explain the power
+ 
+
+ align:start position:0%
+energy that helps to explain the power
+and the excitement of these films uh it
+
+ align:start position:0%
+and the excitement of these films uh it
+ 
+
+ align:start position:0%
+and the excitement of these films uh it
+has two very clear antagonists the
+
+ align:start position:0%
+has two very clear antagonists the
+ 
+
+ align:start position:0%
+has two very clear antagonists the
+glamour of Hollywood and the the false
+
+ align:start position:0%
+glamour of Hollywood and the the false
+ 
+
+ align:start position:0%
+glamour of Hollywood and the the false
+and aristocratic glamour of the film
+
+ align:start position:0%
+and aristocratic glamour of the film
+ 
+
+ align:start position:0%
+and aristocratic glamour of the film
+under musolini uh and it also draws as
+
+ align:start position:0%
+under musolini uh and it also draws as
+ 
+
+ align:start position:0%
+under musolini uh and it also draws as
+well on older traditions of film in
+
+ align:start position:0%
+well on older traditions of film in
+ 
+
+ align:start position:0%
+well on older traditions of film in
+Italian in German and in French that set
+
+ align:start position:0%
+Italian in German and in French that set
+ 
+
+ align:start position:0%
+Italian in German and in French that set
+earlier examples for the kind of thing
+
+ align:start position:0%
+earlier examples for the kind of thing
+ 
+
+ align:start position:0%
+earlier examples for the kind of thing
+that the neorealists want to do I've
+
+ align:start position:0%
+that the neorealists want to do I've
+ 
+
+ align:start position:0%
+that the neorealists want to do I've
+already talked about the key features of
+
+ align:start position:0%
+already talked about the key features of
+ 
+
+ align:start position:0%
+already talked about the key features of
+neorealism when I uh uh just a second
+
+ align:start position:0%
+neorealism when I uh uh just a second
+ 
+
+ align:start position:0%
+neorealism when I uh uh just a second
+ago when I spoke about poetic realism
+
+ align:start position:0%
+ago when I spoke about poetic realism
+ 
+
+ align:start position:0%
+ago when I spoke about poetic realism
+but let me mention some of those key
+
+ align:start position:0%
+but let me mention some of those key
+ 
+
+ align:start position:0%
+but let me mention some of those key
+features in a little bit more detail one
+
+ align:start position:0%
+features in a little bit more detail one
+ 
+
+ align:start position:0%
+features in a little bit more detail one
+way to think about neorealist films is
+
+ align:start position:0%
+way to think about neorealist films is
+ 
+
+ align:start position:0%
+way to think about neorealist films is
+to recognize that their emphasis on
+
+ align:start position:0%
+to recognize that their emphasis on
+ 
+
+ align:start position:0%
+to recognize that their emphasis on
+reality is one which insists on trying
+
+ align:start position:0%
+reality is one which insists on trying
+ 
+
+ align:start position:0%
+reality is one which insists on trying
+to create uh an illusion of plaus of a
+
+ align:start position:0%
+to create uh an illusion of plaus of a
+ 
+
+ align:start position:0%
+to create uh an illusion of plaus of a
+plausible actuality and what this meant
+
+ align:start position:0%
+plausible actuality and what this meant
+ 
+
+ align:start position:0%
+plausible actuality and what this meant
+to them was listen people have warts on
+
+ align:start position:0%
+to them was listen people have warts on
+ 
+
+ align:start position:0%
+to them was listen people have warts on
+their noses people are not beautiful the
+
+ align:start position:0%
+their noses people are not beautiful the
+ 
+
+ align:start position:0%
+their noses people are not beautiful the
+way they are in Hollywood let so one
+
+ align:start position:0%
+way they are in Hollywood let so one
+ 
+
+ align:start position:0%
+way they are in Hollywood let so one
+thing we need to do is we need to
+
+ align:start position:0%
+thing we need to do is we need to
+ 
+
+ align:start position:0%
+thing we need to do is we need to
+roughen up the look of our performers
+
+ align:start position:0%
+roughen up the look of our performers
+ 
+
+ align:start position:0%
+roughen up the look of our performers
+and in fact professional actors it was
+
+ align:start position:0%
+and in fact professional actors it was
+ 
+
+ align:start position:0%
+and in fact professional actors it was
+felt often bring a kind of smoothness or
+
+ align:start position:0%
+felt often bring a kind of smoothness or
+ 
+
+ align:start position:0%
+felt often bring a kind of smoothness or
+a fluidity to their performance that is
+
+ align:start position:0%
+a fluidity to their performance that is
+ 
+
+ align:start position:0%
+a fluidity to their performance that is
+inherently artificial so many neorealist
+
+ align:start position:0%
+inherently artificial so many neorealist
+ 
+
+ align:start position:0%
+inherently artificial so many neorealist
+films have no or virtually no
+
+ align:start position:0%
+films have no or virtually no
+ 
+
+ align:start position:0%
+films have no or virtually no
+professional actors in them or sometimes
+
+ align:start position:0%
+professional actors in them or sometimes
+ 
+
+ align:start position:0%
+professional actors in them or sometimes
+only professional actors in the major
+
+ align:start position:0%
+only professional actors in the major
+ 
+
+ align:start position:0%
+only professional actors in the major
+roles in the film you're going to see
+
+ align:start position:0%
+roles in the film you're going to see
+ 
+
+ align:start position:0%
+roles in the film you're going to see
+tonight the star is a nonprofessional
+
+ align:start position:0%
+tonight the star is a nonprofessional
+ 
+
+ align:start position:0%
+tonight the star is a nonprofessional
+actor he actually ended up having a
+
+ align:start position:0%
+actor he actually ended up having a
+ 
+
+ align:start position:0%
+actor he actually ended up having a
+tragic life the film won the Academy
+
+ align:start position:0%
+tragic life the film won the Academy
+ 
+
+ align:start position:0%
+tragic life the film won the Academy
+Award is the best foreign film of the
+
+ align:start position:0%
+Award is the best foreign film of the
+ 
+
+ align:start position:0%
+Award is the best foreign film of the
+year in the America in 1948 uh and the
+
+ align:start position:0%
+year in the America in 1948 uh and the
+ 
+
+ align:start position:0%
+year in the America in 1948 uh and the
+man who played Richi was an inter became
+
+ align:start position:0%
+man who played Richi was an inter became
+ 
+
+ align:start position:0%
+man who played Richi was an inter became
+an international star but he he uh fell
+
+ align:start position:0%
+an international star but he he uh fell
+ 
+
+ align:start position:0%
+an international star but he he uh fell
+into hard times and and and and ended up
+
+ align:start position:0%
+into hard times and and and and ended up
+ 
+
+ align:start position:0%
+into hard times and and and and ended up
+not not really making making much uh
+
+ align:start position:0%
+not not really making making much uh
+ 
+
+ align:start position:0%
+not not really making making much uh
+money off his
+
+ align:start position:0%
+money off his
+ 
+
+ align:start position:0%
+money off his
+off from his from his very brief stardom
+
+ align:start position:0%
+off from his from his very brief stardom
+ 
+
+ align:start position:0%
+off from his from his very brief stardom
+and then and and and my understanding is
+
+ align:start position:0%
+and then and and and my understanding is
+ 
+
+ align:start position:0%
+and then and and and my understanding is
+that that he that he uh uh U never again
+
+ align:start position:0%
+that that he that he uh uh U never again
+ 
+
+ align:start position:0%
+that that he that he uh uh U never again
+made a film as remarkable as as The
+
+ align:start position:0%
+made a film as remarkable as as The
+ 
+
+ align:start position:0%
+made a film as remarkable as as The
+Bicycle Thief but one of the things that
+
+ align:start position:0%
+Bicycle Thief but one of the things that
+ 
+
+ align:start position:0%
+Bicycle Thief but one of the things that
+is absolutely astonishing about the
+
+ align:start position:0%
+is absolutely astonishing about the
+ 
+
+ align:start position:0%
+is absolutely astonishing about the
+performance is that this man is not an
+
+ align:start position:0%
+performance is that this man is not an
+ 
+
+ align:start position:0%
+performance is that this man is not an
+actor you would never guess it I mean
+
+ align:start position:0%
+actor you would never guess it I mean
+ 
+
+ align:start position:0%
+actor you would never guess it I mean
+it's an absolute well maybe you would
+
+ align:start position:0%
+it's an absolute well maybe you would
+ 
+
+ align:start position:0%
+it's an absolute well maybe you would
+but you would guess it only after having
+
+ align:start position:0%
+but you would guess it only after having
+ 
+
+ align:start position:0%
+but you would guess it only after having
+been told uh that because he he performs
+
+ align:start position:0%
+been told uh that because he he performs
+ 
+
+ align:start position:0%
+been told uh that because he he performs
+with such naturalness and such Grace uh
+
+ align:start position:0%
+with such naturalness and such Grace uh
+ 
+
+ align:start position:0%
+with such naturalness and such Grace uh
+so the use of nonprofessional actors is
+
+ align:start position:0%
+so the use of nonprofessional actors is
+ 
+
+ align:start position:0%
+so the use of nonprofessional actors is
+a is one of the key features of
+
+ align:start position:0%
+a is one of the key features of
+ 
+
+ align:start position:0%
+a is one of the key features of
+neorealism a second key feature is a
+
+ align:start position:0%
+neorealism a second key feature is a
+ 
+
+ align:start position:0%
+neorealism a second key feature is a
+rejection of Studio filming all
+
+ align:start position:0%
+rejection of Studio filming all
+ 
+
+ align:start position:0%
+rejection of Studio filming all
+neorealist films like almost all poetic
+
+ align:start position:0%
+neorealist films like almost all poetic
+ 
+
+ align:start position:0%
+neorealist films like almost all poetic
+realism films realist films were shot
+
+ align:start position:0%
+realism films realist films were shot
+ 
+
+ align:start position:0%
+realism films realist films were shot
+outdoors in natural light partly because
+
+ align:start position:0%
+outdoors in natural light partly because
+ 
+
+ align:start position:0%
+outdoors in natural light partly because
+they wanted natural light and partly
+
+ align:start position:0%
+they wanted natural light and partly
+ 
+
+ align:start position:0%
+they wanted natural light and partly
+because Studios lie about the texture of
+
+ align:start position:0%
+because Studios lie about the texture of
+ 
+
+ align:start position:0%
+because Studios lie about the texture of
+the world we want the texture of the
+
+ align:start position:0%
+the world we want the texture of the
+ 
+
+ align:start position:0%
+the world we want the texture of the
+world in our films the ne our films are
+
+ align:start position:0%
+world in our films the ne our films are
+ 
+
+ align:start position:0%
+world in our films the ne our films are
+really about reality so we can't shoot
+
+ align:start position:0%
+really about reality so we can't shoot
+ 
+
+ align:start position:0%
+really about reality so we can't shoot
+in we we we can't shoot indoors a third
+
+ align:start position:0%
+in we we we can't shoot indoors a third
+ 
+
+ align:start position:0%
+in we we we can't shoot indoors a third
+nonprofessional actors outdoor camera a
+
+ align:start position:0%
+nonprofessional actors outdoor camera a
+ 
+
+ align:start position:0%
+nonprofessional actors outdoor camera a
+third feature would be what we might
+
+ align:start position:0%
+third feature would be what we might
+ 
+
+ align:start position:0%
+third feature would be what we might
+call a fundamental misen style taken
+
+ align:start position:0%
+call a fundamental misen style taken
+ 
+
+ align:start position:0%
+call a fundamental misen style taken
+directly from the the uh stylistic
+
+ align:start position:0%
+directly from the the uh stylistic
+ 
+
+ align:start position:0%
+directly from the the uh stylistic
+habits established by Jean Renoir and
+
+ align:start position:0%
+habits established by Jean Renoir and
+ 
+
+ align:start position:0%
+habits established by Jean Renoir and
+other French directors who worked in the
+
+ align:start position:0%
+other French directors who worked in the
+ 
+
+ align:start position:0%
+other French directors who worked in the
+same style uh relatively modest forms of
+
+ align:start position:0%
+same style uh relatively modest forms of
+ 
+
+ align:start position:0%
+same style uh relatively modest forms of
+editing the forms of Montage that you
+
+ align:start position:0%
+editing the forms of Montage that you
+ 
+
+ align:start position:0%
+editing the forms of Montage that you
+see are are not disruptive you won't get
+
+ align:start position:0%
+see are are not disruptive you won't get
+ 
+
+ align:start position:0%
+see are are not disruptive you won't get
+jump Cuts or or or disorienting moments
+
+ align:start position:0%
+jump Cuts or or or disorienting moments
+ 
+
+ align:start position:0%
+jump Cuts or or or disorienting moments
+the camera the camera is as with Renoir
+
+ align:start position:0%
+the camera the camera is as with Renoir
+ 
+
+ align:start position:0%
+the camera the camera is as with Renoir
+constantly restless and in but often in
+
+ align:start position:0%
+constantly restless and in but often in
+ 
+
+ align:start position:0%
+constantly restless and in but often in
+very gentle ways there's a wonderful Mo
+
+ align:start position:0%
+very gentle ways there's a wonderful Mo
+ 
+
+ align:start position:0%
+very gentle ways there's a wonderful Mo
+moment in the scene I mentioned a moment
+
+ align:start position:0%
+moment in the scene I mentioned a moment
+ 
+
+ align:start position:0%
+moment in the scene I mentioned a moment
+ago where we see Richi putting up his
+
+ align:start position:0%
+ago where we see Richi putting up his
+ 
+
+ align:start position:0%
+ago where we see Richi putting up his
+first poster when the camera is watching
+
+ align:start position:0%
+first poster when the camera is watching
+ 
+
+ align:start position:0%
+first poster when the camera is watching
+them and and and he's getting these
+
+ align:start position:0%
+them and and and he's getting these
+ 
+
+ align:start position:0%
+them and and and he's getting these
+instructions from his comrade about how
+
+ align:start position:0%
+instructions from his comrade about how
+ 
+
+ align:start position:0%
+instructions from his comrade about how
+to put the thing up and it's really
+
+ align:start position:0%
+to put the thing up and it's really
+ 
+
+ align:start position:0%
+to put the thing up and it's really
+boring well the we one reason that you
+
+ align:start position:0%
+boring well the we one reason that you
+ 
+
+ align:start position:0%
+boring well the we one reason that you
+know it's boring obviously you as a
+
+ align:start position:0%
+know it's boring obviously you as a
+ 
+
+ align:start position:0%
+know it's boring obviously you as a
+viewer you begin to probably feel it
+
+ align:start position:0%
+viewer you begin to probably feel it
+ 
+
+ align:start position:0%
+viewer you begin to probably feel it
+without registering that it's boring but
+
+ align:start position:0%
+without registering that it's boring but
+ 
+
+ align:start position:0%
+without registering that it's boring but
+the way reason that you know it is is
+
+ align:start position:0%
+the way reason that you know it is is
+ 
+
+ align:start position:0%
+the way reason that you know it is is
+that the camera suddenly looks away what
+
+ align:start position:0%
+that the camera suddenly looks away what
+ 
+
+ align:start position:0%
+that the camera suddenly looks away what
+happens is the camera discovers
+
+ align:start position:0%
+happens is the camera discovers
+ 
+
+ align:start position:0%
+happens is the camera discovers
+something something interesting
+
+ align:start position:0%
+something something interesting
+ 
+
+ align:start position:0%
+something something interesting
+happening on the street and while the
+
+ align:start position:0%
+happening on the street and while the
+ 
+
+ align:start position:0%
+happening on the street and while the
+conversation continues on the soundtrack
+
+ align:start position:0%
+conversation continues on the soundtrack
+ 
+
+ align:start position:0%
+conversation continues on the soundtrack
+the camera shifts away from Richi and
+
+ align:start position:0%
+the camera shifts away from Richi and
+ 
+
+ align:start position:0%
+the camera shifts away from Richi and
+his instructor and follows uh a wealthy
+
+ align:start position:0%
+his instructor and follows uh a wealthy
+ 
+
+ align:start position:0%
+his instructor and follows uh a wealthy
+man and two children who are walking
+
+ align:start position:0%
+man and two children who are walking
+ 
+
+ align:start position:0%
+man and two children who are walking
+behind him and they're really Beggars
+
+ align:start position:0%
+behind him and they're really Beggars
+ 
+
+ align:start position:0%
+behind him and they're really Beggars
+trying to get money from him and the
+
+ align:start position:0%
+trying to get money from him and the
+ 
+
+ align:start position:0%
+trying to get money from him and the
+camera just just it found it interesting
+
+ align:start position:0%
+camera just just it found it interesting
+ 
+
+ align:start position:0%
+camera just just it found it interesting
+so it looked at it a very Jean Ren
+
+ align:start position:0%
+so it looked at it a very Jean Ren
+ 
+
+ align:start position:0%
+so it looked at it a very Jean Ren
+noirish move there are other moves like
+
+ align:start position:0%
+noirish move there are other moves like
+ 
+
+ align:start position:0%
+noirish move there are other moves like
+this so uh in the in the film as if the
+
+ align:start position:0%
+this so uh in the in the film as if the
+ 
+
+ align:start position:0%
+this so uh in the in the film as if the
+camera like je renoir's camera is uh so
+
+ align:start position:0%
+camera like je renoir's camera is uh so
+ 
+
+ align:start position:0%
+camera like je renoir's camera is uh so
+interested in the world that it's
+
+ align:start position:0%
+interested in the world that it's
+ 
+
+ align:start position:0%
+interested in the world that it's
+capable of being distracted there's a
+
+ align:start position:0%
+capable of being distracted there's a
+ 
+
+ align:start position:0%
+capable of being distracted there's a
+that the world's complexity is always
+
+ align:start position:0%
+that the world's complexity is always
+ 
+
+ align:start position:0%
+that the world's complexity is always
+threatening uh the the coherences and
+
+ align:start position:0%
+threatening uh the the coherences and
+ 
+
+ align:start position:0%
+threatening uh the the coherences and
+meanings that the film is releasing for
+
+ align:start position:0%
+meanings that the film is releasing for
+ 
+
+ align:start position:0%
+meanings that the film is releasing for
+us so nonprofessional actors outdoor
+
+ align:start position:0%
+us so nonprofessional actors outdoor
+ 
+
+ align:start position:0%
+us so nonprofessional actors outdoor
+filming a Misan a a profound serious
+
+ align:start position:0%
+filming a Misan a a profound serious
+ 
+
+ align:start position:0%
+filming a Misan a a profound serious
+Misan style influenced by deeply by Jean
+
+ align:start position:0%
+Misan style influenced by deeply by Jean
+ 
+
+ align:start position:0%
+Misan style influenced by deeply by Jean
+Renoir and finally we might maybe
+
+ align:start position:0%
+Renoir and finally we might maybe
+ 
+
+ align:start position:0%
+Renoir and finally we might maybe
+another not finally one more a fourth
+
+ align:start position:0%
+another not finally one more a fourth
+ 
+
+ align:start position:0%
+another not finally one more a fourth
+feature we might say is what what I what
+
+ align:start position:0%
+feature we might say is what what I what
+ 
+
+ align:start position:0%
+feature we might say is what what I what
+I was trying to indicate when I talked
+
+ align:start position:0%
+I was trying to indicate when I talked
+ 
+
+ align:start position:0%
+I was trying to indicate when I talked
+about the social or political bias of
+
+ align:start position:0%
+about the social or political bias of
+ 
+
+ align:start position:0%
+about the social or political bias of
+these films one might say that these
+
+ align:start position:0%
+these films one might say that these
+ 
+
+ align:start position:0%
+these films one might say that these
+films have a more profoundly documentary
+
+ align:start position:0%
+films have a more profoundly documentary
+ 
+
+ align:start position:0%
+films have a more profoundly documentary
+flavor I don't mean that we feel we're
+
+ align:start position:0%
+flavor I don't mean that we feel we're
+ 
+
+ align:start position:0%
+flavor I don't mean that we feel we're
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+
+ align:start position:0%
+watching documentaries but we watch we
+ 
+
+ align:start position:0%
+watching documentaries but we watch we
+do feel we're watching a slice of life
+
+ align:start position:0%
+do feel we're watching a slice of life
+ 
+
+ align:start position:0%
+do feel we're watching a slice of life
+that the uh economic and moral and
+
+ align:start position:0%
+that the uh economic and moral and
+ 
+
+ align:start position:0%
+that the uh economic and moral and
+social and personal circumstances of the
+
+ align:start position:0%
+social and personal circumstances of the
+ 
+
+ align:start position:0%
+social and personal circumstances of the
+characters we see in neorealist films
+
+ align:start position:0%
+characters we see in neorealist films
+ 
+
+ align:start position:0%
+characters we see in neorealist films
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+
+ align:start position:0%
+are a version of what we would find if
+ 
+
+ align:start position:0%
+are a version of what we would find if
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+
+ align:start position:0%
+we walked into Rome not in a movie and
+ 
+
+ align:start position:0%
+we walked into Rome not in a movie and
+just look for people of this class right
+
+ align:start position:0%
+just look for people of this class right
+ 
+
+ align:start position:0%
+just look for people of this class right
+a documentary flavor so that's four
+
+ align:start position:0%
+a documentary flavor so that's four
+ 
+
+ align:start position:0%
+a documentary flavor so that's four
+features and a final feature that I
+
+ align:start position:0%
+features and a final feature that I
+ 
+
+ align:start position:0%
+features and a final feature that I
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+
+ align:start position:0%
+suppose I would want to add has to do do
+ 
+
+ align:start position:0%
+suppose I would want to add has to do do
+with the relation between plot and
+
+ align:start position:0%
+with the relation between plot and
+ 
+
+ align:start position:0%
+with the relation between plot and
+character it's not quite true to say
+
+ align:start position:0%
+character it's not quite true to say
+ 
+
+ align:start position:0%
+character it's not quite true to say
+that these films are plotless they're
+
+ align:start position:0%
+that these films are plotless they're
+ 
+
+ align:start position:0%
+that these films are plotless they're
+not and one of the most magnificent
+
+ align:start position:0%
+not and one of the most magnificent
+ 
+
+ align:start position:0%
+not and one of the most magnificent
+things about The Bicycle Thief is the
+
+ align:start position:0%
+things about The Bicycle Thief is the
+ 
+
+ align:start position:0%
+things about The Bicycle Thief is the
+economy of its plot and I'll talk a bit
+
+ align:start position:0%
+economy of its plot and I'll talk a bit
+ 
+
+ align:start position:0%
+economy of its plot and I'll talk a bit
+about that tonight but it's nonetheless
+
+ align:start position:0%
+about that tonight but it's nonetheless
+ 
+
+ align:start position:0%
+about that tonight but it's nonetheless
+true that in neorealist films you do not
+
+ align:start position:0%
+true that in neorealist films you do not
+ 
+
+ align:start position:0%
+true that in neorealist films you do not
+feel that action drives events what you
+
+ align:start position:0%
+feel that action drives events what you
+ 
+
+ align:start position:0%
+feel that action drives events what you
+feel is that character drives events in
+
+ align:start position:0%
+feel is that character drives events in
+ 
+
+ align:start position:0%
+feel is that character drives events in
+some sense that the that the plot is a
+
+ align:start position:0%
+some sense that the that the plot is a
+ 
+
+ align:start position:0%
+some sense that the that the plot is a
+what the plot aims for is a natural
+
+ align:start position:0%
+what the plot aims for is a natural
+ 
+
+ align:start position:0%
+what the plot aims for is a natural
+unfolding you're never supposed to feel
+
+ align:start position:0%
+unfolding you're never supposed to feel
+ 
+
+ align:start position:0%
+unfolding you're never supposed to feel
+in a neorealist film uh that that up
+
+ align:start position:0%
+in a neorealist film uh that that up
+ 
+
+ align:start position:0%
+in a neorealist film uh that that up
+some event in the plot has been
+
+ align:start position:0%
+some event in the plot has been
+ 
+
+ align:start position:0%
+some event in the plot has been
+introduced arbitrarily you're never
+
+ align:start position:0%
+introduced arbitrarily you're never
+ 
+
+ align:start position:0%
+introduced arbitrarily you're never
+supposed to step back and say oh that
+
+ align:start position:0%
+supposed to step back and say oh that
+ 
+
+ align:start position:0%
+supposed to step back and say oh that
+could never happen that how implausible
+
+ align:start position:0%
+could never happen that how implausible
+ 
+
+ align:start position:0%
+could never happen that how implausible
+is that or I guess they did that because
+
+ align:start position:0%
+is that or I guess they did that because
+ 
+
+ align:start position:0%
+is that or I guess they did that because
+they wanted to show X right the kind of
+
+ align:start position:0%
+they wanted to show X right the kind of
+ 
+
+ align:start position:0%
+they wanted to show X right the kind of
+response you often have watching certain
+
+ align:start position:0%
+response you often have watching certain
+ 
+
+ align:start position:0%
+response you often have watching certain
+forms
+
+ align:start position:0%
+forms
+ 
+
+ align:start position:0%
+forms
+of Hollywood entertainment and and other
+
+ align:start position:0%
+of Hollywood entertainment and and other
+ 
+
+ align:start position:0%
+of Hollywood entertainment and and other
+other forms of merely Escapist uh uh
+
+ align:start position:0%
+other forms of merely Escapist uh uh
+ 
+
+ align:start position:0%
+other forms of merely Escapist uh uh
+entertainment fair but you don't ever
+
+ align:start position:0%
+entertainment fair but you don't ever
+ 
+
+ align:start position:0%
+entertainment fair but you don't ever
+have that feeling in a in a good real
+
+ align:start position:0%
+have that feeling in a in a good real
+ 
+
+ align:start position:0%
+have that feeling in a in a good real
+neorealist film what you feel is that
+
+ align:start position:0%
+neorealist film what you feel is that
+ 
+
+ align:start position:0%
+neorealist film what you feel is that
+the events of the plot unfold naturally
+
+ align:start position:0%
+the events of the plot unfold naturally
+ 
+
+ align:start position:0%
+the events of the plot unfold naturally
+out of the economic and social realities
+
+ align:start position:0%
+out of the economic and social realities
+ 
+
+ align:start position:0%
+out of the economic and social realities
+the characters live in and out of their
+
+ align:start position:0%
+the characters live in and out of their
+ 
+
+ align:start position:0%
+the characters live in and out of their
+characters you can test this
+
+ align:start position:0%
+characters you can test this
+ 
+
+ align:start position:0%
+characters you can test this
+generalization against tonight's film
+
+ align:start position:0%
+generalization against tonight's film
+ 
+
+ align:start position:0%
+generalization against tonight's film
+and I'm sure that you'll find that it's
+
+ align:start position:0%
+and I'm sure that you'll find that it's
+ 
+
+ align:start position:0%
+and I'm sure that you'll find that it's
+a compelling one that it really
+
+ align:start position:0%
+a compelling one that it really
+ 
+
+ align:start position:0%
+a compelling one that it really
+describes this
+
+ align:start position:0%
+describes this
+ 
+
+ align:start position:0%
+describes this
+movement's respect for the complexity of
+
+ align:start position:0%
+movement's respect for the complexity of
+ 
+
+ align:start position:0%
+movement's respect for the complexity of
+character over plot for for the
+
+ align:start position:0%
+character over plot for for the
+ 
+
+ align:start position:0%
+character over plot for for the
+complexity of character and therefore
+
+ align:start position:0%
+complexity of character and therefore
+ 
+
+ align:start position:0%
+complexity of character and therefore
+for its commitment to a kind of movie
+
+ align:start position:0%
+for its commitment to a kind of movie
+ 
+
+ align:start position:0%
+for its commitment to a kind of movie
+that is more interested in character
+
+ align:start position:0%
+that is more interested in character
+ 
+
+ align:start position:0%
+that is more interested in character
+than it is in in in story or event in a
+
+ align:start position:0%
+than it is in in in story or event in a
+ 
+
+ align:start position:0%
+than it is in in in story or event in a
+narrow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense the central figures of neorealism
+
+ align:start position:0%
+sense the central figures of neorealism
+ 
+
+ align:start position:0%
+sense the central figures of neorealism
+are important to mention and maybe
+
+ align:start position:0%
+are important to mention and maybe
+ 
+
+ align:start position:0%
+are important to mention and maybe
+especially the fellow that I have first
+
+ align:start position:0%
+especially the fellow that I have first
+ 
+
+ align:start position:0%
+especially the fellow that I have first
+on my list here um chz zaatini uh
+
+ align:start position:0%
+on my list here um chz zaatini uh
+ 
+
+ align:start position:0%
+on my list here um chz zaatini uh
+because he's the least well-known of the
+
+ align:start position:0%
+because he's the least well-known of the
+ 
+
+ align:start position:0%
+because he's the least well-known of the
+names I've listed there the other three
+
+ align:start position:0%
+names I've listed there the other three
+ 
+
+ align:start position:0%
+names I've listed there the other three
+names are all famous directors and of
+
+ align:start position:0%
+names are all famous directors and of
+ 
+
+ align:start position:0%
+names are all famous directors and of
+course Desa is the director of bicycle
+
+ align:start position:0%
+course Desa is the director of bicycle
+ 
+
+ align:start position:0%
+course Desa is the director of bicycle
+thieves and I'll talk about his career
+
+ align:start position:0%
+thieves and I'll talk about his career
+ 
+
+ align:start position:0%
+thieves and I'll talk about his career
+this evening but zaatini was the
+
+ align:start position:0%
+this evening but zaatini was the
+ 
+
+ align:start position:0%
+this evening but zaatini was the
+theoretical gen genus behind neorealism
+
+ align:start position:0%
+theoretical gen genus behind neorealism
+ 
+
+ align:start position:0%
+theoretical gen genus behind neorealism
+and a figure for whom I still retain a
+
+ align:start position:0%
+and a figure for whom I still retain a
+ 
+
+ align:start position:0%
+and a figure for whom I still retain a
+tremendous uh sympathy and affection uh
+
+ align:start position:0%
+tremendous uh sympathy and affection uh
+ 
+
+ align:start position:0%
+tremendous uh sympathy and affection uh
+he he was a novelist and a an essay
+
+ align:start position:0%
+he he was a novelist and a an essay
+ 
+
+ align:start position:0%
+he he was a novelist and a an essay
+writer uh uh as well as a uh screen
+
+ align:start position:0%
+writer uh uh as well as a uh screen
+ 
+
+ align:start position:0%
+writer uh uh as well as a uh screen
+screenwriter uh he collaborated
+
+ align:start position:0%
+screenwriter uh he collaborated
+ 
+
+ align:start position:0%
+screenwriter uh he collaborated
+with with um Victorio Desa on almost
+
+ align:start position:0%
+with with um Victorio Desa on almost
+ 
+
+ align:start position:0%
+with with um Victorio Desa on almost
+every one of desa's significant films
+
+ align:start position:0%
+every one of desa's significant films
+ 
+
+ align:start position:0%
+every one of desa's significant films
+not on everyone but on virtually
+
+ align:start position:0%
+not on everyone but on virtually
+ 
+
+ align:start position:0%
+not on everyone but on virtually
+everyone that is truly outstanding and
+
+ align:start position:0%
+everyone that is truly outstanding and
+ 
+
+ align:start position:0%
+everyone that is truly outstanding and
+there are a number of them he's a he's
+
+ align:start position:0%
+there are a number of them he's a he's
+ 
+
+ align:start position:0%
+there are a number of them he's a he's
+the the script writer on and he he had a
+
+ align:start position:0%
+the the script writer on and he he had a
+ 
+
+ align:start position:0%
+the the script writer on and he he had a
+particularly symbiotic relation to Desa
+
+ align:start position:0%
+particularly symbiotic relation to Desa
+ 
+
+ align:start position:0%
+particularly symbiotic relation to Desa
+zaatini also articulated what came to be
+
+ align:start position:0%
+zaatini also articulated what came to be
+ 
+
+ align:start position:0%
+zaatini also articulated what came to be
+understood as the manifesto of
+
+ align:start position:0%
+understood as the manifesto of
+ 
+
+ align:start position:0%
+understood as the manifesto of
+neorealism and in one such essay I don't
+
+ align:start position:0%
+neorealism and in one such essay I don't
+ 
+
+ align:start position:0%
+neorealism and in one such essay I don't
+know it was titled Manifesto of
+
+ align:start position:0%
+know it was titled Manifesto of
+ 
+
+ align:start position:0%
+know it was titled Manifesto of
+neorealism but that was its effect he
+
+ align:start position:0%
+neorealism but that was its effect he
+ 
+
+ align:start position:0%
+neorealism but that was its effect he
+said this to try to summarize what he
+
+ align:start position:0%
+said this to try to summarize what he
+ 
+
+ align:start position:0%
+said this to try to summarize what he
+thought the Ambitions of neorealism were
+
+ align:start position:0%
+thought the Ambitions of neorealism were
+ 
+
+ align:start position:0%
+thought the Ambitions of neorealism were
+he said a good film ought to be focused
+
+ align:start position:0%
+he said a good film ought to be focused
+ 
+
+ align:start position:0%
+he said a good film ought to be focused
+on if on the life of an ordinary man to
+
+ align:start position:0%
+on if on the life of an ordinary man to
+ 
+
+ align:start position:0%
+on if on the life of an ordinary man to
+whom nothing
+
+ align:start position:0%
+whom nothing
+ 
+
+ align:start position:0%
+whom nothing
+happens now he didn't really mean that
+
+ align:start position:0%
+happens now he didn't really mean that
+ 
+
+ align:start position:0%
+happens now he didn't really mean that
+nothing would happen right um it's not
+
+ align:start position:0%
+nothing would happen right um it's not
+ 
+
+ align:start position:0%
+nothing would happen right um it's not
+it's not an early version of the
+
+ align:start position:0%
+it's not an early version of the
+ 
+
+ align:start position:0%
+it's not an early version of the
+Seinfeld program uh what what what what
+
+ align:start position:0%
+Seinfeld program uh what what what what
+ 
+
+ align:start position:0%
+Seinfeld program uh what what what what
+what what he's trying to get at is this
+
+ align:start position:0%
+what what he's trying to get at is this
+ 
+
+ align:start position:0%
+what what he's trying to get at is this
+idea that plot does not dominate that
+
+ align:start position:0%
+idea that plot does not dominate that
+ 
+
+ align:start position:0%
+idea that plot does not dominate that
+character dominates that the events of
+
+ align:start position:0%
+character dominates that the events of
+ 
+
+ align:start position:0%
+character dominates that the events of
+the story grow organically out of the
+
+ align:start position:0%
+the story grow organically out of the
+ 
+
+ align:start position:0%
+the story grow organically out of the
+materials of the of the text both out of
+
+ align:start position:0%
+materials of the of the text both out of
+ 
+
+ align:start position:0%
+materials of the of the text both out of
+character and out of out of out out of
+
+ align:start position:0%
+character and out of out of out out of
+ 
+
+ align:start position:0%
+character and out of out of out out of
+social out of social
+
+ align:start position:0%
+social out of social
+ 
+
+ align:start position:0%
+social out of social
+realities um so
+
+ align:start position:0%
+realities um so
+ 
+
+ align:start position:0%
+realities um so
+uh zavi was in many ways a a Visionary
+
+ align:start position:0%
+uh zavi was in many ways a a Visionary
+ 
+
+ align:start position:0%
+uh zavi was in many ways a a Visionary
+figure
+
+ align:start position:0%
+figure
+ 
+
+ align:start position:0%
+figure
+um an overt Marxist for a good part for
+
+ align:start position:0%
+um an overt Marxist for a good part for
+ 
+
+ align:start position:0%
+um an overt Marxist for a good part for
+a good part of his life and probably the
+
+ align:start position:0%
+a good part of his life and probably the
+ 
+
+ align:start position:0%
+a good part of his life and probably the
+central
+
+ align:start position:0%
+central
+ 
+
+ align:start position:0%
+central
+intellectual influence on the neorealist
+
+ align:start position:0%
+intellectual influence on the neorealist
+ 
+
+ align:start position:0%
+intellectual influence on the neorealist
+movement Visconti the uh the director
+
+ align:start position:0%
+movement Visconti the uh the director
+ 
+
+ align:start position:0%
+movement Visconti the uh the director
+whose dates I've put there uh is
+
+ align:start position:0%
+whose dates I've put there uh is
+ 
+
+ align:start position:0%
+whose dates I've put there uh is
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+suggested it is often said that not all
+
+ align:start position:0%
+suggested it is often said that not all
+ 
+
+ align:start position:0%
+suggested it is often said that not all
+of this con's work fits neatly maybe
+
+ align:start position:0%
+of this con's work fits neatly maybe
+ 
+
+ align:start position:0%
+of this con's work fits neatly maybe
+none of it fits neatly into the category
+
+ align:start position:0%
+none of it fits neatly into the category
+ 
+
+ align:start position:0%
+none of it fits neatly into the category
+of neorealism uh this partly has to do
+
+ align:start position:0%
+of neorealism uh this partly has to do
+ 
+
+ align:start position:0%
+of neorealism uh this partly has to do
+with a with a a kind of flamboyance in
+
+ align:start position:0%
+with a with a a kind of flamboyance in
+ 
+
+ align:start position:0%
+with a with a a kind of flamboyance in
+in in in Vis country's visual style and
+
+ align:start position:0%
+in in in Vis country's visual style and
+ 
+
+ align:start position:0%
+in in in Vis country's visual style and
+maybe also a fness for decadence and for
+
+ align:start position:0%
+maybe also a fness for decadence and for
+ 
+
+ align:start position:0%
+maybe also a fness for decadence and for
+and for um elaboration that does
+
+ align:start position:0%
+and for um elaboration that does
+ 
+
+ align:start position:0%
+and for um elaboration that does
+not comport with the social meanings
+
+ align:start position:0%
+not comport with the social meanings
+ 
+
+ align:start position:0%
+not comport with the social meanings
+that are implicit in neorealism so he's
+
+ align:start position:0%
+that are implicit in neorealism so he's
+ 
+
+ align:start position:0%
+that are implicit in neorealism so he's
+the uh of the main neorealists he's the
+
+ align:start position:0%
+the uh of the main neorealists he's the
+ 
+
+ align:start position:0%
+the uh of the main neorealists he's the
+he's the one who fits least as well but
+
+ align:start position:0%
+he's the one who fits least as well but
+ 
+
+ align:start position:0%
+he's the one who fits least as well but
+he's often said to be the best of them
+
+ align:start position:0%
+he's often said to be the best of them
+ 
+
+ align:start position:0%
+he's often said to be the best of them
+and there are many uh uh historians of
+
+ align:start position:0%
+and there are many uh uh historians of
+ 
+
+ align:start position:0%
+and there are many uh uh historians of
+film and Scholars of film including
+
+ align:start position:0%
+film and Scholars of film including
+ 
+
+ align:start position:0%
+film and Scholars of film including
+David Cook who believed that the Earth
+
+ align:start position:0%
+David Cook who believed that the Earth
+ 
+
+ align:start position:0%
+David Cook who believed that the Earth
+trembles the film that he made in uh in
+
+ align:start position:0%
+trembles the film that he made in uh in
+ 
+
+ align:start position:0%
+trembles the film that he made in uh in
+1948 laa Tria the Earth trembles is the
+
+ align:start position:0%
+1948 laa Tria the Earth trembles is the
+ 
+
+ align:start position:0%
+1948 laa Tria the Earth trembles is the
+greatest of all neorealist movies I have
+
+ align:start position:0%
+greatest of all neorealist movies I have
+ 
+
+ align:start position:0%
+greatest of all neorealist movies I have
+sometimes been tempted to show it but
+
+ align:start position:0%
+sometimes been tempted to show it but
+ 
+
+ align:start position:0%
+sometimes been tempted to show it but
+it's less characteristic of neorealism
+
+ align:start position:0%
+it's less characteristic of neorealism
+ 
+
+ align:start position:0%
+it's less characteristic of neorealism
+so I don't show it but it is a very
+
+ align:start position:0%
+so I don't show it but it is a very
+ 
+
+ align:start position:0%
+so I don't show it but it is a very
+remarkable film and and uh Visconti is a
+
+ align:start position:0%
+remarkable film and and uh Visconti is a
+ 
+
+ align:start position:0%
+remarkable film and and uh Visconti is a
+very important figure in this in this
+
+ align:start position:0%
+very important figure in this in this
+ 
+
+ align:start position:0%
+very important figure in this in this
+movement even though he probably can be
+
+ align:start position:0%
+movement even though he probably can be
+ 
+
+ align:start position:0%
+movement even though he probably can be
+said in his later films to to move
+
+ align:start position:0%
+said in his later films to to move
+ 
+
+ align:start position:0%
+said in his later films to to move
+Beyond neorealist concerns Roberto
+
+ align:start position:0%
+Beyond neorealist concerns Roberto
+ 
+
+ align:start position:0%
+Beyond neorealist concerns Roberto
+rosolini who also had a very rich long
+
+ align:start position:0%
+rosolini who also had a very rich long
+ 
+
+ align:start position:0%
+rosolini who also had a very rich long
+career as a filmmaker and I've only
+
+ align:start position:0%
+career as a filmmaker and I've only
+ 
+
+ align:start position:0%
+career as a filmmaker and I've only
+listed his uh uh one film there because
+
+ align:start position:0%
+listed his uh uh one film there because
+ 
+
+ align:start position:0%
+listed his uh uh one film there because
+I want to show you a clip from it uh
+
+ align:start position:0%
+I want to show you a clip from it uh
+ 
+
+ align:start position:0%
+I want to show you a clip from it uh
+part of a Trilogy of films he made at
+
+ align:start position:0%
+part of a Trilogy of films he made at
+ 
+
+ align:start position:0%
+part of a Trilogy of films he made at
+the very end of the war called uh it was
+
+ align:start position:0%
+the very end of the war called uh it was
+ 
+
+ align:start position:0%
+the very end of the war called uh it was
+called his Roman Trilogy or his Rome
+
+ align:start position:0%
+called his Roman Trilogy or his Rome
+ 
+
+ align:start position:0%
+called his Roman Trilogy or his Rome
+Trilogy and the first one was or his
+
+ align:start position:0%
+Trilogy and the first one was or his
+ 
+
+ align:start position:0%
+Trilogy and the first one was or his
+World War II trilogy olog uh the first
+
+ align:start position:0%
+World War II trilogy olog uh the first
+ 
+
+ align:start position:0%
+World War II trilogy olog uh the first
+one was called Rome Open City and then
+
+ align:start position:0%
+one was called Rome Open City and then
+ 
+
+ align:start position:0%
+one was called Rome Open City and then
+there were two other uh the third one
+
+ align:start position:0%
+there were two other uh the third one
+ 
+
+ align:start position:0%
+there were two other uh the third one
+was called Germany year zero and they
+
+ align:start position:0%
+was called Germany year zero and they
+ 
+
+ align:start position:0%
+was called Germany year zero and they
+they all had sort of uh uh political and
+
+ align:start position:0%
+they all had sort of uh uh political and
+ 
+
+ align:start position:0%
+they all had sort of uh uh political and
+social Ambitions they wanted to
+
+ align:start position:0%
+social Ambitions they wanted to
+ 
+
+ align:start position:0%
+social Ambitions they wanted to
+dramatize the post-war conditions and
+
+ align:start position:0%
+dramatize the post-war conditions and
+ 
+
+ align:start position:0%
+dramatize the post-war conditions and
+show the devastation that followed uh
+
+ align:start position:0%
+show the devastation that followed uh
+ 
+
+ align:start position:0%
+show the devastation that followed uh
+the the aftermath that that was the
+
+ align:start position:0%
+the the aftermath that that was the
+ 
+
+ align:start position:0%
+the the aftermath that that was the
+aftermath of the second World War uh
+
+ align:start position:0%
+aftermath of the second World War uh
+ 
+
+ align:start position:0%
+aftermath of the second World War uh
+open
+
+ align:start position:0%
+open
+ 
+
+ align:start position:0%
+open
+city um had a tremendous impact when it
+
+ align:start position:0%
+city um had a tremendous impact when it
+ 
+
+ align:start position:0%
+city um had a tremendous impact when it
+was first uh uh released especially in
+
+ align:start position:0%
+was first uh uh released especially in
+ 
+
+ align:start position:0%
+was first uh uh released especially in
+Italy because it told an anti-fascist
+
+ align:start position:0%
+Italy because it told an anti-fascist
+ 
+
+ align:start position:0%
+Italy because it told an anti-fascist
+story uh it's a somewhat melodramatic
+
+ align:start position:0%
+story uh it's a somewhat melodramatic
+ 
+
+ align:start position:0%
+story uh it's a somewhat melodramatic
+film that that ends in a very uh in a
+
+ align:start position:0%
+film that that ends in a very uh in a
+ 
+
+ align:start position:0%
+film that that ends in a very uh in a
+very melodramatic uh death in a very
+
+ align:start position:0%
+very melodramatic uh death in a very
+ 
+
+ align:start position:0%
+very melodramatic uh death in a very
+melodramatic murder U or an accidental
+
+ align:start position:0%
+melodramatic murder U or an accidental
+ 
+
+ align:start position:0%
+melodramatic murder U or an accidental
+murder um uh and and and and partly for
+
+ align:start position:0%
+murder um uh and and and and partly for
+ 
+
+ align:start position:0%
+murder um uh and and and and partly for
+that reason it's it's a a less it's a
+
+ align:start position:0%
+that reason it's it's a a less it's a
+ 
+
+ align:start position:0%
+that reason it's it's a a less it's a
+less powerful and less compelling uh
+
+ align:start position:0%
+less powerful and less compelling uh
+ 
+
+ align:start position:0%
+less powerful and less compelling uh
+film totally than something like bicycle
+
+ align:start position:0%
+film totally than something like bicycle
+ 
+
+ align:start position:0%
+film totally than something like bicycle
+thieves uh but it but but its importance
+
+ align:start position:0%
+thieves uh but it but but its importance
+ 
+
+ align:start position:0%
+thieves uh but it but but its importance
+is can't be overestimated
+
+ align:start position:0%
+is can't be overestimated
+ 
+
+ align:start position:0%
+is can't be overestimated
+it it established the basic principles
+
+ align:start position:0%
+it it established the basic principles
+ 
+
+ align:start position:0%
+it it established the basic principles
+that I've been talking about it was
+
+ align:start position:0%
+that I've been talking about it was
+ 
+
+ align:start position:0%
+that I've been talking about it was
+actually begun before the war was over
+
+ align:start position:0%
+actually begun before the war was over
+ 
+
+ align:start position:0%
+actually begun before the war was over
+when it was illegal to when when the
+
+ align:start position:0%
+when it was illegal to when when the
+ 
+
+ align:start position:0%
+when it was illegal to when when the
+when the German authorities were fascist
+
+ align:start position:0%
+when the German authorities were fascist
+ 
+
+ align:start position:0%
+when the German authorities were fascist
+authorities were still controlling uh
+
+ align:start position:0%
+authorities were still controlling uh
+ 
+
+ align:start position:0%
+authorities were still controlling uh
+Rome and Italian society and you weren't
+
+ align:start position:0%
+Rome and Italian society and you weren't
+ 
+
+ align:start position:0%
+Rome and Italian society and you weren't
+supposed you couldn't film without a
+
+ align:start position:0%
+supposed you couldn't film without a
+ 
+
+ align:start position:0%
+supposed you couldn't film without a
+license and some of the early scenes
+
+ align:start position:0%
+license and some of the early scenes
+ 
+
+ align:start position:0%
+license and some of the early scenes
+from Rome Open City were actually shot
+
+ align:start position:0%
+from Rome Open City were actually shot
+ 
+
+ align:start position:0%
+from Rome Open City were actually shot
+illicitly on very bad film stock uh from
+
+ align:start position:0%
+illicitly on very bad film stock uh from
+ 
+
+ align:start position:0%
+illicitly on very bad film stock uh from
+behind doorways and around corners so
+
+ align:start position:0%
+behind doorways and around corners so
+ 
+
+ align:start position:0%
+behind doorways and around corners so
+the people uh the people behind the
+
+ align:start position:0%
+the people uh the people behind the
+ 
+
+ align:start position:0%
+the people uh the people behind the
+camera wouldn't be caught by the
+
+ align:start position:0%
+camera wouldn't be caught by the
+ 
+
+ align:start position:0%
+camera wouldn't be caught by the
+authorities and then the film was
+
+ align:start position:0%
+authorities and then the film was
+ 
+
+ align:start position:0%
+authorities and then the film was
+completed after peace came and after
+
+ align:start position:0%
+completed after peace came and after
+ 
+
+ align:start position:0%
+completed after peace came and after
+after the after the uh uh defeat of the
+
+ align:start position:0%
+after the after the uh uh defeat of the
+ 
+
+ align:start position:0%
+after the after the uh uh defeat of the
+axis forces um I'm going to show you a
+
+ align:start position:0%
+axis forces um I'm going to show you a
+ 
+
+ align:start position:0%
+axis forces um I'm going to show you a
+clip from that sequence from that film
+
+ align:start position:0%
+clip from that sequence from that film
+ 
+
+ align:start position:0%
+clip from that sequence from that film
+from the very beginning of that film to
+
+ align:start position:0%
+from the very beginning of that film to
+ 
+
+ align:start position:0%
+from the very beginning of that film to
+give you a feel for what that film was
+
+ align:start position:0%
+give you a feel for what that film was
+ 
+
+ align:start position:0%
+give you a feel for what that film was
+like as well and I think that that clip
+
+ align:start position:0%
+like as well and I think that that clip
+ 
+
+ align:start position:0%
+like as well and I think that that clip
+will also show you why the film was so
+
+ align:start position:0%
+will also show you why the film was so
+ 
+
+ align:start position:0%
+will also show you why the film was so
+successful but I'll partly explain it
+
+ align:start position:0%
+successful but I'll partly explain it
+ 
+
+ align:start position:0%
+successful but I'll partly explain it
+now I think the Italians loved this
+
+ align:start position:0%
+now I think the Italians loved this
+ 
+
+ align:start position:0%
+now I think the Italians loved this
+movie because it told a useful myth it
+
+ align:start position:0%
+movie because it told a useful myth it
+ 
+
+ align:start position:0%
+movie because it told a useful myth it
+made it made it appear that very few
+
+ align:start position:0%
+made it made it appear that very few
+ 
+
+ align:start position:0%
+made it made it appear that very few
+Italians collaborated with the Nazis and
+
+ align:start position:0%
+Italians collaborated with the Nazis and
+ 
+
+ align:start position:0%
+Italians collaborated with the Nazis and
+that most Italians were really on the
+
+ align:start position:0%
+that most Italians were really on the
+ 
+
+ align:start position:0%
+that most Italians were really on the
+side of the sabur who were trying to
+
+ align:start position:0%
+side of the sabur who were trying to
+ 
+
+ align:start position:0%
+side of the sabur who were trying to
+blow up fascist Waterworks and F this is
+
+ align:start position:0%
+blow up fascist Waterworks and F this is
+ 
+
+ align:start position:0%
+blow up fascist Waterworks and F this is
+probably not entirely historically
+
+ align:start position:0%
+probably not entirely historically
+ 
+
+ align:start position:0%
+probably not entirely historically
+accurate since melini was during much of
+
+ align:start position:0%
+accurate since melini was during much of
+ 
+
+ align:start position:0%
+accurate since melini was during much of
+his career a very popular figure in
+
+ align:start position:0%
+his career a very popular figure in
+ 
+
+ align:start position:0%
+his career a very popular figure in
+Italy but you can certainly understand
+
+ align:start position:0%
+Italy but you can certainly understand
+ 
+
+ align:start position:0%
+Italy but you can certainly understand
+why it would have uh U hit a sympathetic
+
+ align:start position:0%
+why it would have uh U hit a sympathetic
+ 
+
+ align:start position:0%
+why it would have uh U hit a sympathetic
+cord among Italians many of whom I'm
+
+ align:start position:0%
+cord among Italians many of whom I'm
+ 
+
+ align:start position:0%
+cord among Italians many of whom I'm
+sure felt terrible ambivalence and shame
+
+ align:start position:0%
+sure felt terrible ambivalence and shame
+ 
+
+ align:start position:0%
+sure felt terrible ambivalence and shame
+over the over the events of the of the
+
+ align:start position:0%
+over the over the events of the of the
+ 
+
+ align:start position:0%
+over the over the events of the of the
+second world war the Italians were
+
+ align:start position:0%
+second world war the Italians were
+ 
+
+ align:start position:0%
+second world war the Italians were
+always much more reluctant anti-semites
+
+ align:start position:0%
+always much more reluctant anti-semites
+ 
+
+ align:start position:0%
+always much more reluctant anti-semites
+than the Hitler fascists were and the
+
+ align:start position:0%
+than the Hitler fascists were and the
+ 
+
+ align:start position:0%
+than the Hitler fascists were and the
+story of Italian anti anti-Semitism is
+
+ align:start position:0%
+story of Italian anti anti-Semitism is
+ 
+
+ align:start position:0%
+story of Italian anti anti-Semitism is
+much more complicated than the story of
+
+ align:start position:0%
+much more complicated than the story of
+ 
+
+ align:start position:0%
+much more complicated than the story of
+of of German
+
+ align:start position:0%
+of of German
+ 
+
+ align:start position:0%
+of of German
+anti-Semitism uh in this in this period
+
+ align:start position:0%
+anti-Semitism uh in this in this period
+ 
+
+ align:start position:0%
+anti-Semitism uh in this in this period
+especially so I so I think that one
+
+ align:start position:0%
+especially so I so I think that one
+ 
+
+ align:start position:0%
+especially so I so I think that one
+reason for the success of the film had
+
+ align:start position:0%
+reason for the success of the film had
+ 
+
+ align:start position:0%
+reason for the success of the film had
+to do with the way it told a kind of
+
+ align:start position:0%
+to do with the way it told a kind of
+ 
+
+ align:start position:0%
+to do with the way it told a kind of
+anti-fascist fable that worked
+
+ align:start position:0%
+anti-fascist fable that worked
+ 
+
+ align:start position:0%
+anti-fascist fable that worked
+particularly well for this post-war
+
+ align:start position:0%
+particularly well for this post-war
+ 
+
+ align:start position:0%
+particularly well for this post-war
+society that wanted to put fascism
+
+ align:start position:0%
+society that wanted to put fascism
+ 
+
+ align:start position:0%
+society that wanted to put fascism
+behind it that wanted to repudiate that
+
+ align:start position:0%
+behind it that wanted to repudiate that
+ 
+
+ align:start position:0%
+behind it that wanted to repudiate that
+past that felt there were certainly
+
+ align:start position:0%
+past that felt there were certainly
+ 
+
+ align:start position:0%
+past that felt there were certainly
+segments of the population that had
+
+ align:start position:0%
+segments of the population that had
+ 
+
+ align:start position:0%
+segments of the population that had
+never gone along with that past anyway
+
+ align:start position:0%
+never gone along with that past anyway
+ 
+
+ align:start position:0%
+never gone along with that past anyway
+so the film sort of mobilized uh a feel
+
+ align:start position:0%
+so the film sort of mobilized uh a feel
+ 
+
+ align:start position:0%
+so the film sort of mobilized uh a feel
+a new kind of feeling of Italian
+
+ align:start position:0%
+a new kind of feeling of Italian
+ 
+
+ align:start position:0%
+a new kind of feeling of Italian
+patriotism and maybe even some in in
+
+ align:start position:0%
+patriotism and maybe even some in in
+ 
+
+ align:start position:0%
+patriotism and maybe even some in in
+some sense uh uh a kind of despite the
+
+ align:start position:0%
+some sense uh uh a kind of despite the
+ 
+
+ align:start position:0%
+some sense uh uh a kind of despite the
+catastrophe in which it ends a kind of
+
+ align:start position:0%
+catastrophe in which it ends a kind of
+ 
+
+ align:start position:0%
+catastrophe in which it ends a kind of
+hope for the future because the film
+
+ align:start position:0%
+hope for the future because the film
+ 
+
+ align:start position:0%
+hope for the future because the film
+takes place entirely within the period
+
+ align:start position:0%
+takes place entirely within the period
+ 
+
+ align:start position:0%
+takes place entirely within the period
+when the when when the fascists were
+
+ align:start position:0%
+when the when when the fascists were
+ 
+
+ align:start position:0%
+when the when when the fascists were
+still in control of of Italy and the
+
+ align:start position:0%
+still in control of of Italy and the
+ 
+
+ align:start position:0%
+still in control of of Italy and the
+catastrophe that occurs at the end is a
+
+ align:start position:0%
+catastrophe that occurs at the end is a
+ 
+
+ align:start position:0%
+catastrophe that occurs at the end is a
+is a is an is an act of fascist uh
+
+ align:start position:0%
+is a is an is an act of fascist uh
+ 
+
+ align:start position:0%
+is a is an is an act of fascist uh
+murder and
+
+ align:start position:0%
+murder and
+ 
+
+ align:start position:0%
+murder and
+assassin and indifference to humanity uh
+
+ align:start position:0%
+assassin and indifference to humanity uh
+ 
+
+ align:start position:0%
+assassin and indifference to humanity uh
+the so so so um uh Ros rosalini went on
+
+ align:start position:0%
+the so so so um uh Ros rosalini went on
+ 
+
+ align:start position:0%
+the so so so um uh Ros rosalini went on
+to make many many films and I I feel a
+
+ align:start position:0%
+to make many many films and I I feel a
+ 
+
+ align:start position:0%
+to make many many films and I I feel a
+little guilty only mentioning this one
+
+ align:start position:0%
+little guilty only mentioning this one
+ 
+
+ align:start position:0%
+little guilty only mentioning this one
+uh not totally characteristic film of
+
+ align:start position:0%
+uh not totally characteristic film of
+ 
+
+ align:start position:0%
+uh not totally characteristic film of
+his but it's important in the history of
+
+ align:start position:0%
+his but it's important in the history of
+ 
+
+ align:start position:0%
+his but it's important in the history of
+neorealism rosalini is a director I much
+
+ align:start position:0%
+neorealism rosalini is a director I much
+ 
+
+ align:start position:0%
+neorealism rosalini is a director I much
+admire partly because he moved away from
+
+ align:start position:0%
+admire partly because he moved away from
+ 
+
+ align:start position:0%
+admire partly because he moved away from
+fiction and at the end of his career he
+
+ align:start position:0%
+fiction and at the end of his career he
+ 
+
+ align:start position:0%
+fiction and at the end of his career he
+was he was making what he thought of as
+
+ align:start position:0%
+was he was making what he thought of as
+ 
+
+ align:start position:0%
+was he was making what he thought of as
+educational or instructional
+
+ align:start position:0%
+educational or instructional
+ 
+
+ align:start position:0%
+educational or instructional
+films but but but with the dazzling
+
+ align:start position:0%
+films but but but with the dazzling
+ 
+
+ align:start position:0%
+films but but but with the dazzling
+technique of a great fiction filmmaker
+
+ align:start position:0%
+technique of a great fiction filmmaker
+ 
+
+ align:start position:0%
+technique of a great fiction filmmaker
+so he's a very interesting figure to to
+
+ align:start position:0%
+so he's a very interesting figure to to
+ 
+
+ align:start position:0%
+so he's a very interesting figure to to
+study and to and I hope some of you will
+
+ align:start position:0%
+study and to and I hope some of you will
+ 
+
+ align:start position:0%
+study and to and I hope some of you will
+will look at more neorealist films and
+
+ align:start position:0%
+will look at more neorealist films and
+ 
+
+ align:start position:0%
+will look at more neorealist films and
+consider looking at
+
+ align:start position:0%
+consider looking at
+ 
+
+ align:start position:0%
+consider looking at
+rosolini Deek is the final figure uh
+
+ align:start position:0%
+rosolini Deek is the final figure uh
+ 
+
+ align:start position:0%
+rosolini Deek is the final figure uh
+that I want to mention as a as a
+
+ align:start position:0%
+that I want to mention as a as a
+ 
+
+ align:start position:0%
+that I want to mention as a as a
+fundamental uh uh energy in neorealism
+
+ align:start position:0%
+fundamental uh uh energy in neorealism
+ 
+
+ align:start position:0%
+fundamental uh uh energy in neorealism
+and I'll only say about him uh that he's
+
+ align:start position:0%
+and I'll only say about him uh that he's
+ 
+
+ align:start position:0%
+and I'll only say about him uh that he's
+probably the most various and gifted of
+
+ align:start position:0%
+probably the most various and gifted of
+ 
+
+ align:start position:0%
+probably the most various and gifted of
+all the of all the neorealist figures
+
+ align:start position:0%
+all the of all the neorealist figures
+ 
+
+ align:start position:0%
+all the of all the neorealist figures
+partly because he had been a very
+
+ align:start position:0%
+partly because he had been a very
+ 
+
+ align:start position:0%
+partly because he had been a very
+successful actor on uh before he became
+
+ align:start position:0%
+successful actor on uh before he became
+ 
+
+ align:start position:0%
+successful actor on uh before he became
+a director and I'll talk a bit more
+
+ align:start position:0%
+a director and I'll talk a bit more
+ 
+
+ align:start position:0%
+a director and I'll talk a bit more
+about Desa this evening what I want to
+
+ align:start position:0%
+about Desa this evening what I want to
+ 
+
+ align:start position:0%
+about Desa this evening what I want to
+illustrate now in the mo in the time we
+
+ align:start position:0%
+illustrate now in the mo in the time we
+ 
+
+ align:start position:0%
+illustrate now in the mo in the time we
+have left
+
+ align:start position:0%
+have left
+ 
+
+ align:start position:0%
+have left
+is an aspect of the neorealist aesthetic
+
+ align:start position:0%
+is an aspect of the neorealist aesthetic
+ 
+
+ align:start position:0%
+is an aspect of the neorealist aesthetic
+if we could use that term uh that I've
+
+ align:start position:0%
+if we could use that term uh that I've
+ 
+
+ align:start position:0%
+if we could use that term uh that I've
+talked about before when we discussed
+
+ align:start position:0%
+talked about before when we discussed
+ 
+
+ align:start position:0%
+talked about before when we discussed
+Renoir
+
+ align:start position:0%
+Renoir
+ 
+
+ align:start position:0%
+Renoir
+and that I implied in earlier comments
+
+ align:start position:0%
+and that I implied in earlier comments
+ 
+
+ align:start position:0%
+and that I implied in earlier comments
+that I made this afternoon it's what I
+
+ align:start position:0%
+that I made this afternoon it's what I
+ 
+
+ align:start position:0%
+that I made this afternoon it's what I
+call the neorealist
+
+ align:start position:0%
+call the neorealist
+ 
+
+ align:start position:0%
+call the neorealist
+counterplot and what by counterplot what
+
+ align:start position:0%
+counterplot and what by counterplot what
+ 
+
+ align:start position:0%
+counterplot and what by counterplot what
+I really want to call attention to are
+
+ align:start position:0%
+I really want to call attention to are
+ 
+
+ align:start position:0%
+I really want to call attention to are
+all those elements in the film that seem
+
+ align:start position:0%
+all those elements in the film that seem
+ 
+
+ align:start position:0%
+all those elements in the film that seem
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+to take part in the forward momentum of
+
+ align:start position:0%
+to take part in the forward momentum of
+ 
+
+ align:start position:0%
+to take part in the forward momentum of
+the story or what we might even think of
+
+ align:start position:0%
+the story or what we might even think of
+ 
+
+ align:start position:0%
+the story or what we might even think of
+them as retarding elements in which in
+
+ align:start position:0%
+them as retarding elements in which in
+ 
+
+ align:start position:0%
+them as retarding elements in which in
+which these films will sort of pause to
+
+ align:start position:0%
+which these films will sort of pause to
+ 
+
+ align:start position:0%
+which these films will sort of pause to
+smell the roses it's uh uh a version of
+
+ align:start position:0%
+smell the roses it's uh uh a version of
+ 
+
+ align:start position:0%
+smell the roses it's uh uh a version of
+what I mean of what I mean by this
+
+ align:start position:0%
+what I mean of what I mean by this
+ 
+
+ align:start position:0%
+what I mean of what I mean by this
+neorealist counterplot might be said to
+
+ align:start position:0%
+neorealist counterplot might be said to
+ 
+
+ align:start position:0%
+neorealist counterplot might be said to
+be embodied in that in that uh uh
+
+ align:start position:0%
+be embodied in that in that uh uh
+ 
+
+ align:start position:0%
+be embodied in that in that uh uh
+astonishing camera move we studied at
+
+ align:start position:0%
+astonishing camera move we studied at
+ 
+
+ align:start position:0%
+astonishing camera move we studied at
+the end of budoo save from drowning last
+
+ align:start position:0%
+the end of budoo save from drowning last
+ 
+
+ align:start position:0%
+the end of budoo save from drowning last
+week where the camera makes 180 degre
+
+ align:start position:0%
+week where the camera makes 180 degre
+ 
+
+ align:start position:0%
+week where the camera makes 180 degre
+swerve becomes interested in the beauty
+
+ align:start position:0%
+swerve becomes interested in the beauty
+ 
+
+ align:start position:0%
+swerve becomes interested in the beauty
+of the of the river becomes interested
+
+ align:start position:0%
+of the of the river becomes interested
+ 
+
+ align:start position:0%
+of the of the river becomes interested
+in the scenery almost as if it's
+
+ align:start position:0%
+in the scenery almost as if it's
+ 
+
+ align:start position:0%
+in the scenery almost as if it's
+forgotten its character right uh now
+
+ align:start position:0%
+forgotten its character right uh now
+ 
+
+ align:start position:0%
+forgotten its character right uh now
+what I mean by the counterplot is this
+
+ align:start position:0%
+what I mean by the counterplot is this
+ 
+
+ align:start position:0%
+what I mean by the counterplot is this
+impulse in these films and especially in
+
+ align:start position:0%
+impulse in these films and especially in
+ 
+
+ align:start position:0%
+impulse in these films and especially in
+these Italian films to uh to to
+
+ align:start position:0%
+these Italian films to uh to to
+ 
+
+ align:start position:0%
+these Italian films to uh to to
+uh complicate the social and political
+
+ align:start position:0%
+uh complicate the social and political
+ 
+
+ align:start position:0%
+uh complicate the social and political
+and even the psychological Pro processes
+
+ align:start position:0%
+and even the psychological Pro processes
+ 
+
+ align:start position:0%
+and even the psychological Pro processes
+of the story simply in order to give us
+
+ align:start position:0%
+of the story simply in order to give us
+ 
+
+ align:start position:0%
+of the story simply in order to give us
+a sense of what the experience it's
+
+ align:start position:0%
+a sense of what the experience it's
+ 
+
+ align:start position:0%
+a sense of what the experience it's
+describing is like as if it's a version
+
+ align:start position:0%
+describing is like as if it's a version
+ 
+
+ align:start position:0%
+describing is like as if it's a version
+of what I of what I'm interested in when
+
+ align:start position:0%
+of what I of what I'm interested in when
+ 
+
+ align:start position:0%
+of what I of what I'm interested in when
+I talk about how the camera can distract
+
+ align:start position:0%
+I talk about how the camera can distract
+ 
+
+ align:start position:0%
+I talk about how the camera can distract
+itself and one way I can illustrate what
+
+ align:start position:0%
+itself and one way I can illustrate what
+ 
+
+ align:start position:0%
+itself and one way I can illustrate what
+so so what I mean by counterplot then
+
+ align:start position:0%
+so so what I mean by counterplot then
+ 
+
+ align:start position:0%
+so so what I mean by counterplot then
+are energies that or slow down
+
+ align:start position:0%
+are energies that or slow down
+ 
+
+ align:start position:0%
+are energies that or slow down
+the basic the the basic story or that
+
+ align:start position:0%
+the basic the the basic story or that
+ 
+
+ align:start position:0%
+the basic the the basic story or that
+seem not to directly contribute to the
+
+ align:start position:0%
+seem not to directly contribute to the
+ 
+
+ align:start position:0%
+seem not to directly contribute to the
+basic story but are but but but remain
+
+ align:start position:0%
+basic story but are but but but remain
+ 
+
+ align:start position:0%
+basic story but are but but but remain
+part of the film's desire to represent
+
+ align:start position:0%
+part of the film's desire to represent
+ 
+
+ align:start position:0%
+part of the film's desire to represent
+the world to represent reality in
+
+ align:start position:0%
+the world to represent reality in
+ 
+
+ align:start position:0%
+the world to represent reality in
+something of its complexity in something
+
+ align:start position:0%
+something of its complexity in something
+ 
+
+ align:start position:0%
+something of its complexity in something
+of its Nuance even in something of its
+
+ align:start position:0%
+of its Nuance even in something of its
+ 
+
+ align:start position:0%
+of its Nuance even in something of its
+contradictory incoherence right in other
+
+ align:start position:0%
+contradictory incoherence right in other
+ 
+
+ align:start position:0%
+contradictory incoherence right in other
+words I don't really want to call these
+
+ align:start position:0%
+words I don't really want to call these
+ 
+
+ align:start position:0%
+words I don't really want to call these
+moments incoherent moments they're not
+
+ align:start position:0%
+moments incoherent moments they're not
+ 
+
+ align:start position:0%
+moments incoherent moments they're not
+because they build a much larger and
+
+ align:start position:0%
+because they build a much larger and
+ 
+
+ align:start position:0%
+because they build a much larger and
+more complete picture of the whole world
+
+ align:start position:0%
+more complete picture of the whole world
+ 
+
+ align:start position:0%
+more complete picture of the whole world
+you're looking at and in that sense
+
+ align:start position:0%
+you're looking at and in that sense
+ 
+
+ align:start position:0%
+you're looking at and in that sense
+they're not incoherent but but but they
+
+ align:start position:0%
+they're not incoherent but but but they
+ 
+
+ align:start position:0%
+they're not incoherent but but but they
+are a kind of counter to the ongoing
+
+ align:start position:0%
+are a kind of counter to the ongoing
+ 
+
+ align:start position:0%
+are a kind of counter to the ongoing
+pressure to find out what happens next
+
+ align:start position:0%
+pressure to find out what happens next
+ 
+
+ align:start position:0%
+pressure to find out what happens next
+what happens next what happens next well
+
+ align:start position:0%
+what happens next what happens next well
+ 
+
+ align:start position:0%
+what happens next what happens next well
+there are many many examples of this um
+
+ align:start position:0%
+there are many many examples of this um
+ 
+
+ align:start position:0%
+there are many many examples of this um
+uh principle in The Bicycle Thief and in
+
+ align:start position:0%
+uh principle in The Bicycle Thief and in
+ 
+
+ align:start position:0%
+uh principle in The Bicycle Thief and in
+other neorealist films but I want to
+
+ align:start position:0%
+other neorealist films but I want to
+ 
+
+ align:start position:0%
+other neorealist films but I want to
+show you one very dramatic one also to
+
+ align:start position:0%
+show you one very dramatic one also to
+ 
+
+ align:start position:0%
+show you one very dramatic one also to
+give you a a flavor for an earlier
+
+ align:start position:0%
+give you a a flavor for an earlier
+ 
+
+ align:start position:0%
+give you a a flavor for an earlier
+neorealist film other than the one
+
+ align:start position:0%
+neorealist film other than the one
+ 
+
+ align:start position:0%
+neorealist film other than the one
+you're going to see tonight this is from
+
+ align:start position:0%
+you're going to see tonight this is from
+ 
+
+ align:start position:0%
+you're going to see tonight this is from
+the very beginning of Open
+
+ align:start position:0%
+the very beginning of Open
+ 
+
+ align:start position:0%
+the very beginning of Open
+City
+
+ align:start position:0%
+City
+ 
+
+ align:start position:0%
+City
+great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for these are residents of Rome they've
+
+ align:start position:0%
+for these are residents of Rome they've
+ 
+
+ align:start position:0%
+for these are residents of Rome they've
+heard an explosion there's sabotage
+
+ align:start position:0%
+heard an explosion there's sabotage
+ 
+
+ align:start position:0%
+heard an explosion there's sabotage
+going on in Rome now it's near the end
+
+ align:start position:0%
+going on in Rome now it's near the end
+ 
+
+ align:start position:0%
+going on in Rome now it's near the end
+of the war where the war's not over and
+
+ align:start position:0%
+of the war where the war's not over and
+ 
+
+ align:start position:0%
+of the war where the war's not over and
+now the sabur return
+
+ align:start position:0%
+now the sabur return
+ 
+
+ align:start position:0%
+now the sabur return
+home and look who they turn out to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be and of course that's why Anna manani
+
+ align:start position:0%
+be and of course that's why Anna manani
+ 
+
+ align:start position:0%
+be and of course that's why Anna manani
+was the actress was worried about where
+
+ align:start position:0%
+was the actress was worried about where
+ 
+
+ align:start position:0%
+was the actress was worried about where
+the children were because they
+
+ align:start position:0%
+the children were because they
+ 
+
+ align:start position:0%
+the children were because they
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+suspected there's already a counterplot
+
+ align:start position:0%
+suspected there's already a counterplot
+ 
+
+ align:start position:0%
+suspected there's already a counterplot
+operating here I hope you see what look
+
+ align:start position:0%
+operating here I hope you see what look
+ 
+
+ align:start position:0%
+operating here I hope you see what look
+at these little innocent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+faces so these sabur have now come home
+
+ align:start position:0%
+faces so these sabur have now come home
+ 
+
+ align:start position:0%
+faces so these sabur have now come home
+watch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fore
+
+ align:start position:0%
+fore
+ 
+
+ align:start position:0%
+fore
+fore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+foree
+
+ align:start position:0%
+foree
+ 
+
+ align:start position:0%
+foree
+foree
+
+ align:start position:0%
+foree
+ 
+
+ align:start position:0%
+foree
+speee spee spee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speee foree
+
+ align:start position:0%
+speee foree
+ 
+
+ align:start position:0%
+speee foree
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right stop I'm stopping it a little
+
+ align:start position:0%
+all right stop I'm stopping it a little
+ 
+
+ align:start position:0%
+all right stop I'm stopping it a little
+early the scene continues you actually
+
+ align:start position:0%
+early the scene continues you actually
+ 
+
+ align:start position:0%
+early the scene continues you actually
+go into another room in a moment and you
+
+ align:start position:0%
+go into another room in a moment and you
+ 
+
+ align:start position:0%
+go into another room in a moment and you
+see children in a kind of dormatory like
+
+ align:start position:0%
+see children in a kind of dormatory like
+ 
+
+ align:start position:0%
+see children in a kind of dormatory like
+room in which there's one little child
+
+ align:start position:0%
+room in which there's one little child
+ 
+
+ align:start position:0%
+room in which there's one little child
+sitting on a potty and I think it's the
+
+ align:start position:0%
+sitting on a potty and I think it's the
+ 
+
+ align:start position:0%
+sitting on a potty and I think it's the
+first potty scene in Western film and
+
+ align:start position:0%
+first potty scene in Western film and
+ 
+
+ align:start position:0%
+first potty scene in Western film and
+they do something very disturbing too
+
+ align:start position:0%
+they do something very disturbing too
+ 
+
+ align:start position:0%
+they do something very disturbing too
+they pick him off the potty and put him
+
+ align:start position:0%
+they pick him off the potty and put him
+ 
+
+ align:start position:0%
+they pick him off the potty and put him
+back in bed without wiping him but leave
+
+ align:start position:0%
+back in bed without wiping him but leave
+ 
+
+ align:start position:0%
+back in bed without wiping him but leave
+the maybe there was no toilet paper in
+
+ align:start position:0%
+the maybe there was no toilet paper in
+ 
+
+ align:start position:0%
+the maybe there was no toilet paper in
+post-war Italy but uh I your laughter
+
+ align:start position:0%
+post-war Italy but uh I your laughter
+ 
+
+ align:start position:0%
+post-war Italy but uh I your laughter
+indicated to me that you sort of got the
+
+ align:start position:0%
+indicated to me that you sort of got the
+ 
+
+ align:start position:0%
+indicated to me that you sort of got the
+point but talk to me a little bit about
+
+ align:start position:0%
+point but talk to me a little bit about
+ 
+
+ align:start position:0%
+point but talk to me a little bit about
+what you see there I mean what it's a
+
+ align:start position:0%
+what you see there I mean what it's a
+ 
+
+ align:start position:0%
+what you see there I mean what it's a
+wonderful example of what I was trying
+
+ align:start position:0%
+wonderful example of what I was trying
+ 
+
+ align:start position:0%
+wonderful example of what I was trying
+to illustrate at the beginning as well
+
+ align:start position:0%
+to illustrate at the beginning as well
+ 
+
+ align:start position:0%
+to illustrate at the beginning as well
+this principle of Multiplicity what's
+
+ align:start position:0%
+this principle of Multiplicity what's
+ 
+
+ align:start position:0%
+this principle of Multiplicity what's
+happening in this sequence what what do
+
+ align:start position:0%
+happening in this sequence what what do
+ 
+
+ align:start position:0%
+happening in this sequence what what do
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+learn what about living conditions in
+
+ align:start position:0%
+learn what about living conditions in
+ 
+
+ align:start position:0%
+learn what about living conditions in
+what do we learn nobody gives a lecture
+
+ align:start position:0%
+what do we learn nobody gives a lecture
+ 
+
+ align:start position:0%
+what do we learn nobody gives a lecture
+about it what what you think there is a
+
+ align:start position:0%
+about it what what you think there is a
+ 
+
+ align:start position:0%
+about it what what you think there is a
+housing crisis in Rome seven families
+
+ align:start position:0%
+housing crisis in Rome seven families
+ 
+
+ align:start position:0%
+housing crisis in Rome seven families
+living together in the same room an old
+
+ align:start position:0%
+living together in the same room an old
+ 
+
+ align:start position:0%
+living together in the same room an old
+man in bed lying in a bed in the Parlor
+
+ align:start position:0%
+man in bed lying in a bed in the Parlor
+ 
+
+ align:start position:0%
+man in bed lying in a bed in the Parlor
+right in the in the space where the in
+
+ align:start position:0%
+right in the in the space where the in
+ 
+
+ align:start position:0%
+right in the in the space where the in
+the living space of the place right he's
+
+ align:start position:0%
+the living space of the place right he's
+ 
+
+ align:start position:0%
+the living space of the place right he's
+so that's clearly where he stays he's
+
+ align:start position:0%
+so that's clearly where he stays he's
+ 
+
+ align:start position:0%
+so that's clearly where he stays he's
+very ill right what
+
+ align:start position:0%
+very ill right what
+ 
+
+ align:start position:0%
+very ill right what
+else the deviation into comedy the
+
+ align:start position:0%
+else the deviation into comedy the
+ 
+
+ align:start position:0%
+else the deviation into comedy the
+extent right the mean the the extent to
+
+ align:start position:0%
+extent right the mean the the extent to
+ 
+
+ align:start position:0%
+extent right the mean the the extent to
+which a kind of a a kind of series of
+
+ align:start position:0%
+which a kind of a a kind of series of
+ 
+
+ align:start position:0%
+which a kind of a a kind of series of
+comic encounters occur after what after
+
+ align:start position:0%
+comic encounters occur after what after
+ 
+
+ align:start position:0%
+comic encounters occur after what after
+a moment of political sabotage right and
+
+ align:start position:0%
+a moment of political sabotage right and
+ 
+
+ align:start position:0%
+a moment of political sabotage right and
+the in congruity of these little
+
+ align:start position:0%
+the in congruity of these little
+ 
+
+ align:start position:0%
+the in congruity of these little
+children who are the ones who are the
+
+ align:start position:0%
+children who are the ones who are the
+ 
+
+ align:start position:0%
+children who are the ones who are the
+sabur is also part of the comedy even
+
+ align:start position:0%
+sabur is also part of the comedy even
+ 
+
+ align:start position:0%
+sabur is also part of the comedy even
+before we see them fully return to the
+
+ align:start position:0%
+before we see them fully return to the
+ 
+
+ align:start position:0%
+before we see them fully return to the
+condition of children when their parents
+
+ align:start position:0%
+condition of children when their parents
+ 
+
+ align:start position:0%
+condition of children when their parents
+start slapping them in there in the
+
+ align:start position:0%
+start slapping them in there in the
+ 
+
+ align:start position:0%
+start slapping them in there in the
+faces and saying how dare you stay out
+
+ align:start position:0%
+faces and saying how dare you stay out
+ 
+
+ align:start position:0%
+faces and saying how dare you stay out
+so late I didn't mean to suggest that
+
+ align:start position:0%
+so late I didn't mean to suggest that
+ 
+
+ align:start position:0%
+so late I didn't mean to suggest that
+the parents actually know that the
+
+ align:start position:0%
+the parents actually know that the
+ 
+
+ align:start position:0%
+the parents actually know that the
+children are sabur although although
+
+ align:start position:0%
+children are sabur although although
+ 
+
+ align:start position:0%
+children are sabur although although
+some may but I think the point is that
+
+ align:start position:0%
+some may but I think the point is that
+ 
+
+ align:start position:0%
+some may but I think the point is that
+being outside at night is very dangerous
+
+ align:start position:0%
+being outside at night is very dangerous
+ 
+
+ align:start position:0%
+being outside at night is very dangerous
+for little children children in this
+
+ align:start position:0%
+for little children children in this
+ 
+
+ align:start position:0%
+for little children children in this
+environment and that's why they're so
+
+ align:start position:0%
+environment and that's why they're so
+ 
+
+ align:start position:0%
+environment and that's why they're so
+concerned but they but but the fact that
+
+ align:start position:0%
+concerned but they but but the fact that
+ 
+
+ align:start position:0%
+concerned but they but but the fact that
+even the children are partisan
+
+ align:start position:0%
+even the children are partisan
+ 
+
+ align:start position:0%
+even the children are partisan
+anti-fascist Fighters becomes a part of
+
+ align:start position:0%
+anti-fascist Fighters becomes a part of
+ 
+
+ align:start position:0%
+anti-fascist Fighters becomes a part of
+what the film is about so the now you
+
+ align:start position:0%
+what the film is about so the now you
+ 
+
+ align:start position:0%
+what the film is about so the now you
+can't tell from the very beginning from
+
+ align:start position:0%
+can't tell from the very beginning from
+ 
+
+ align:start position:0%
+can't tell from the very beginning from
+this beginning what the real sort of uh
+
+ align:start position:0%
+this beginning what the real sort of uh
+ 
+
+ align:start position:0%
+this beginning what the real sort of uh
+plot energy of the film is yet can you
+
+ align:start position:0%
+plot energy of the film is yet can you
+ 
+
+ align:start position:0%
+plot energy of the film is yet can you
+uh and it will take a bit longer before
+
+ align:start position:0%
+uh and it will take a bit longer before
+ 
+
+ align:start position:0%
+uh and it will take a bit longer before
+it finally turns out the man that she's
+
+ align:start position:0%
+it finally turns out the man that she's
+ 
+
+ align:start position:0%
+it finally turns out the man that she's
+about to marry is a is a uh is a is a
+
+ align:start position:0%
+about to marry is a is a uh is a is a
+ 
+
+ align:start position:0%
+about to marry is a is a uh is a is a
+secret agent and he's been he's under
+
+ align:start position:0%
+secret agent and he's been he's under
+ 
+
+ align:start position:0%
+secret agent and he's been he's under
+he's he he's being he's being hunted by
+
+ align:start position:0%
+he's he he's being he's being hunted by
+ 
+
+ align:start position:0%
+he's he he's being he's being hunted by
+the fascist authorities and the film is
+
+ align:start position:0%
+the fascist authorities and the film is
+ 
+
+ align:start position:0%
+the fascist authorities and the film is
+about how he's how how the good Italians
+
+ align:start position:0%
+about how he's how how the good Italians
+ 
+
+ align:start position:0%
+about how he's how how the good Italians
+try to hide him uh uh but we don't learn
+
+ align:start position:0%
+try to hide him uh uh but we don't learn
+ 
+
+ align:start position:0%
+try to hide him uh uh but we don't learn
+that yet and I what what I want to
+
+ align:start position:0%
+that yet and I what what I want to
+ 
+
+ align:start position:0%
+that yet and I what what I want to
+suggest to you is something of life's
+
+ align:start position:0%
+suggest to you is something of life's
+ 
+
+ align:start position:0%
+suggest to you is something of life's
+variety something of life's comedy
+
+ align:start position:0%
+variety something of life's comedy
+ 
+
+ align:start position:0%
+variety something of life's comedy
+something of life's in congruity uh so
+
+ align:start position:0%
+something of life's in congruity uh so
+ 
+
+ align:start position:0%
+something of life's in congruity uh so
+uh emerges for us in those moments and
+
+ align:start position:0%
+uh emerges for us in those moments and
+ 
+
+ align:start position:0%
+uh emerges for us in those moments and
+it's what I want to call a counterplot
+
+ align:start position:0%
+it's what I want to call a counterplot
+ 
+
+ align:start position:0%
+it's what I want to call a counterplot
+because we take Delight in those moments
+
+ align:start position:0%
+because we take Delight in those moments
+ 
+
+ align:start position:0%
+because we take Delight in those moments
+we don't be impatient and say come on
+
+ align:start position:0%
+we don't be impatient and say come on
+ 
+
+ align:start position:0%
+we don't be impatient and say come on
+film tell me where you're going because
+
+ align:start position:0%
+film tell me where you're going because
+ 
+
+ align:start position:0%
+film tell me where you're going because
+what the film teaches us is that it's
+
+ align:start position:0%
+what the film teaches us is that it's
+ 
+
+ align:start position:0%
+what the film teaches us is that it's
+not in that narrow sense about plot at
+
+ align:start position:0%
+not in that narrow sense about plot at
+ 
+
+ align:start position:0%
+not in that narrow sense about plot at
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+but it's about life in its infinite
+
+ align:start position:0%
+but it's about life in its infinite
+ 
+
+ align:start position:0%
+but it's about life in its infinite
+complexity the greatest neorealist films
+
+ align:start position:0%
+complexity the greatest neorealist films
+ 
+
+ align:start position:0%
+complexity the greatest neorealist films
+Embrace this Principle as well as any
+
+ align:start position:0%
+Embrace this Principle as well as any
+ 
+
+ align:start position:0%
+Embrace this Principle as well as any
+films I've ever known and in addition
+
+ align:start position:0%
+films I've ever known and in addition
+ 
+
+ align:start position:0%
+films I've ever known and in addition
+they have a kind of moral Authority
+
+ align:start position:0%
+they have a kind of moral Authority
+ 
+
+ align:start position:0%
+they have a kind of moral Authority
+that's very rare I'm very jealous of
+
+ align:start position:0%
+that's very rare I'm very jealous of
+ 
+
+ align:start position:0%
+that's very rare I'm very jealous of
+those of you in this course who have
+
+ align:start position:0%
+those of you in this course who have
+ 
+
+ align:start position:0%
+those of you in this course who have
+never seen The Bicycle Thief because it
+
+ align:start position:0%
+never seen The Bicycle Thief because it
+ 
+
+ align:start position:0%
+never seen The Bicycle Thief because it
+is a remarkable film that I'm sure
+
+ align:start position:0%
+is a remarkable film that I'm sure
+ 
+
+ align:start position:0%
+is a remarkable film that I'm sure
+you'll remember for the rest of your
+
+ align:start position:0%
+you'll remember for the rest of your
+ 
+
+ align:start position:0%
+you'll remember for the rest of your
+lives I'll see you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tonight for
\ No newline at end of file
diff --git a/GFoYtA6TmRA.txt b/GFoYtA6TmRA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2505a803771ef8844ef63c86da5e3842b687dd1d
--- /dev/null
+++ b/GFoYtA6TmRA.txt
@@ -0,0 +1,2451 @@
+align:start position:0%
+ 
+when I explain to people what my job is
+
+ align:start position:0%
+when I explain to people what my job is
+ 
+
+ align:start position:0%
+when I explain to people what my job is
+like I always say that I'm somewhere in
+
+ align:start position:0%
+like I always say that I'm somewhere in
+ 
+
+ align:start position:0%
+like I always say that I'm somewhere in
+between a chief executive of uh edtech
+
+ align:start position:0%
+between a chief executive of uh edtech
+ 
+
+ align:start position:0%
+between a chief executive of uh edtech
+startup and the faculty adviser to a
+
+ align:start position:0%
+startup and the faculty adviser to a
+ 
+
+ align:start position:0%
+startup and the faculty adviser to a
+high school AV club that has grown out
+
+ align:start position:0%
+high school AV club that has grown out
+ 
+
+ align:start position:0%
+high school AV club that has grown out
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+control that's exactly what your job is
+
+ align:start position:0%
+control that's exactly what your job is
+ 
+
+ align:start position:0%
+control that's exactly what your job is
+yes so it's a really kind of remarkable
+
+ align:start position:0%
+yes so it's a really kind of remarkable
+ 
+
+ align:start position:0%
+yes so it's a really kind of remarkable
+and creative space in in that
+
+ align:start position:0%
+and creative space in in that
+ 
+
+ align:start position:0%
+and creative space in in that
+right today on Chalk radio I'm talking
+
+ align:start position:0%
+right today on Chalk radio I'm talking
+ 
+
+ align:start position:0%
+right today on Chalk radio I'm talking
+with Christopher capizola senior
+
+ align:start position:0%
+with Christopher capizola senior
+ 
+
+ align:start position:0%
+with Christopher capizola senior
+associate Dean for open learning at MIT
+
+ align:start position:0%
+associate Dean for open learning at MIT
+ 
+
+ align:start position:0%
+associate Dean for open learning at MIT
+part of his job is to provide strategic
+
+ align:start position:0%
+part of his job is to provide strategic
+ 
+
+ align:start position:0%
+part of his job is to provide strategic
+direction for MIT open courseware but
+
+ align:start position:0%
+direction for MIT open courseware but
+ 
+
+ align:start position:0%
+direction for MIT open courseware but
+that's not his only role here at MIT I'm
+
+ align:start position:0%
+that's not his only role here at MIT I'm
+ 
+
+ align:start position:0%
+that's not his only role here at MIT I'm
+also a professor of History so I've been
+
+ align:start position:0%
+also a professor of History so I've been
+ 
+
+ align:start position:0%
+also a professor of History so I've been
+teaching here for about 20 years and I
+
+ align:start position:0%
+teaching here for about 20 years and I
+ 
+
+ align:start position:0%
+teaching here for about 20 years and I
+teach American history so I teach
+
+ align:start position:0%
+teach American history so I teach
+ 
+
+ align:start position:0%
+teach American history so I teach
+everything from you know the American
+
+ align:start position:0%
+everything from you know the American
+ 
+
+ align:start position:0%
+everything from you know the American
+Revolution all the way to what's
+
+ align:start position:0%
+Revolution all the way to what's
+ 
+
+ align:start position:0%
+Revolution all the way to what's
+happening in the news this week Chris
+
+ align:start position:0%
+happening in the news this week Chris
+ 
+
+ align:start position:0%
+happening in the news this week Chris
+sees his role at the helm of open
+
+ align:start position:0%
+sees his role at the helm of open
+ 
+
+ align:start position:0%
+sees his role at the helm of open
+learning as very well connected to his
+
+ align:start position:0%
+learning as very well connected to his
+ 
+
+ align:start position:0%
+learning as very well connected to his
+background as a professor of history and
+
+ align:start position:0%
+background as a professor of history and
+ 
+
+ align:start position:0%
+background as a professor of history and
+I found it fascinating how his knowledge
+
+ align:start position:0%
+I found it fascinating how his knowledge
+ 
+
+ align:start position:0%
+I found it fascinating how his knowledge
+of American History informs his vision
+
+ align:start position:0%
+of American History informs his vision
+ 
+
+ align:start position:0%
+of American History informs his vision
+for OC's
+
+ align:start position:0%
+for OC's
+ 
+
+ align:start position:0%
+for OC's
+future I'd like to draw on your
+
+ align:start position:0%
+future I'd like to draw on your
+ 
+
+ align:start position:0%
+future I'd like to draw on your
+expertise as a historian to you know
+
+ align:start position:0%
+expertise as a historian to you know
+ 
+
+ align:start position:0%
+expertise as a historian to you know
+think about ocw when it started you
+
+ align:start position:0%
+think about ocw when it started you
+ 
+
+ align:start position:0%
+think about ocw when it started you
+mentioned earlier that it was like kind
+
+ align:start position:0%
+mentioned earlier that it was like kind
+ 
+
+ align:start position:0%
+mentioned earlier that it was like kind
+of an audacious move in the early
+
+ align:start position:0%
+of an audacious move in the early
+ 
+
+ align:start position:0%
+of an audacious move in the early
+2000s and I'm wondering if you could
+
+ align:start position:0%
+2000s and I'm wondering if you could
+ 
+
+ align:start position:0%
+2000s and I'm wondering if you could
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+
+ align:start position:0%
+draw a parallel pars to any other
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+
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+draw a parallel pars to any other
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+
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+movements in history where people tried
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+
+ align:start position:0%
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+ align:start position:0%
+to do something differently they weren't
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+
+ align:start position:0%
+to do something differently they weren't
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+
+ align:start position:0%
+sure what the outcome would be what they
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+
+ align:start position:0%
+sure what the outcome would be what they
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+
+ align:start position:0%
+learned that could inform where we take
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+
+ align:start position:0%
+learned that could inform where we take
+ocw in the
+
+ align:start position:0%
+ocw in the
+ 
+
+ align:start position:0%
+ocw in the
+future so about 150 years ago between
+
+ align:start position:0%
+future so about 150 years ago between
+ 
+
+ align:start position:0%
+future so about 150 years ago between
+the 1870s and
+
+ align:start position:0%
+the 1870s and
+ 
+
+ align:start position:0%
+the 1870s and
+1890s the United States and the rest of
+
+ align:start position:0%
+1890s the United States and the rest of
+ 
+
+ align:start position:0%
+1890s the United States and the rest of
+the world went through an information
+
+ align:start position:0%
+the world went through an information
+ 
+
+ align:start position:0%
+the world went through an information
+revolution transformations in
+
+ align:start position:0%
+revolution transformations in
+ 
+
+ align:start position:0%
+revolution transformations in
+communication technologies that gave us
+
+ align:start position:0%
+communication technologies that gave us
+ 
+
+ align:start position:0%
+communication technologies that gave us
+things like the telegraph the telephone
+
+ align:start position:0%
+things like the telegraph the telephone
+ 
+
+ align:start position:0%
+things like the telegraph the telephone
+and Transformations also in information
+
+ align:start position:0%
+and Transformations also in information
+ 
+
+ align:start position:0%
+and Transformations also in information
+and Publishing new inventions
+
+ align:start position:0%
+and Publishing new inventions
+ 
+
+ align:start position:0%
+and Publishing new inventions
+photography right Mass photography um
+
+ align:start position:0%
+photography right Mass photography um
+ 
+
+ align:start position:0%
+photography right Mass photography um
+printing of newspapers and images the
+
+ align:start position:0%
+printing of newspapers and images the
+ 
+
+ align:start position:0%
+printing of newspapers and images the
+mass circulation of books you know cheap
+
+ align:start position:0%
+mass circulation of books you know cheap
+ 
+
+ align:start position:0%
+mass circulation of books you know cheap
+paperback books other things like that
+
+ align:start position:0%
+paperback books other things like that
+ 
+
+ align:start position:0%
+paperback books other things like that
+that people in the 1870s and ' 80s also
+
+ align:start position:0%
+that people in the 1870s and ' 80s also
+ 
+
+ align:start position:0%
+that people in the 1870s and ' 80s also
+lived in a world in which there were new
+
+ align:start position:0%
+lived in a world in which there were new
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+
+ align:start position:0%
+lived in a world in which there were new
+possibilities for knowledge both its
+
+ align:start position:0%
+possibilities for knowledge both its
+ 
+
+ align:start position:0%
+possibilities for knowledge both its
+production and its dissemination and and
+
+ align:start position:0%
+production and its dissemination and and
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+
+ align:start position:0%
+production and its dissemination and and
+new questions about the trustworthiness
+
+ align:start position:0%
+new questions about the trustworthiness
+ 
+
+ align:start position:0%
+new questions about the trustworthiness
+of what they were seeing and
+
+ align:start position:0%
+of what they were seeing and
+ 
+
+ align:start position:0%
+of what they were seeing and
+reading and also I think another key
+
+ align:start position:0%
+reading and also I think another key
+ 
+
+ align:start position:0%
+reading and also I think another key
+element of this is new technologies for
+
+ align:start position:0%
+element of this is new technologies for
+ 
+
+ align:start position:0%
+element of this is new technologies for
+organizing that information right um so
+
+ align:start position:0%
+organizing that information right um so
+ 
+
+ align:start position:0%
+organizing that information right um so
+I warned you I'm a history nerd right
+
+ align:start position:0%
+I warned you I'm a history nerd right
+ 
+
+ align:start position:0%
+I warned you I'm a history nerd right
+and so I'm going to tell you about a
+
+ align:start position:0%
+and so I'm going to tell you about a
+ 
+
+ align:start position:0%
+and so I'm going to tell you about a
+very nerdy moment in American history
+
+ align:start position:0%
+very nerdy moment in American history
+ 
+
+ align:start position:0%
+very nerdy moment in American history
+great um which is the invention of the
+
+ align:start position:0%
+great um which is the invention of the
+ 
+
+ align:start position:0%
+great um which is the invention of the
+Dewey Decimal System I love it in 1876
+
+ align:start position:0%
+Dewey Decimal System I love it in 1876
+ 
+
+ align:start position:0%
+Dewey Decimal System I love it in 1876
+Melville Dewey who was a librarian at
+
+ align:start position:0%
+Melville Dewey who was a librarian at
+ 
+
+ align:start position:0%
+Melville Dewey who was a librarian at
+ammer College here in Massachusetts
+
+ align:start position:0%
+ammer College here in Massachusetts
+ 
+
+ align:start position:0%
+ammer College here in Massachusetts
+realized that the books in the library
+
+ align:start position:0%
+realized that the books in the library
+ 
+
+ align:start position:0%
+realized that the books in the library
+were just badly organized right and so
+
+ align:start position:0%
+were just badly organized right and so
+ 
+
+ align:start position:0%
+were just badly organized right and so
+he developed the Dewey Decimal System
+
+ align:start position:0%
+he developed the Dewey Decimal System
+ 
+
+ align:start position:0%
+he developed the Dewey Decimal System
+which many of us know from the
+
+ align:start position:0%
+which many of us know from the
+ 
+
+ align:start position:0%
+which many of us know from the
+elementary school library class but it's
+
+ align:start position:0%
+elementary school library class but it's
+ 
+
+ align:start position:0%
+elementary school library class but it's
+sort of the foundation of information
+
+ align:start position:0%
+sort of the foundation of information
+ 
+
+ align:start position:0%
+sort of the foundation of information
+science and it's a way of organizing
+
+ align:start position:0%
+science and it's a way of organizing
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+
+ align:start position:0%
+science and it's a way of organizing
+knowledge at the same time another
+
+ align:start position:0%
+knowledge at the same time another
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+
+ align:start position:0%
+knowledge at the same time another
+transformation is happening in libraries
+
+ align:start position:0%
+transformation is happening in libraries
+ 
+
+ align:start position:0%
+transformation is happening in libraries
+which is the Innovations of the carnegi
+
+ align:start position:0%
+which is the Innovations of the carnegi
+ 
+
+ align:start position:0%
+which is the Innovations of the carnegi
+library designed to bring books and
+
+ align:start position:0%
+library designed to bring books and
+ 
+
+ align:start position:0%
+library designed to bring books and
+knowledge to communities all around the
+
+ align:start position:0%
+knowledge to communities all around the
+ 
+
+ align:start position:0%
+knowledge to communities all around the
+country and so if we think about it we
+
+ align:start position:0%
+country and so if we think about it we
+ 
+
+ align:start position:0%
+country and so if we think about it we
+have technological innovation we have
+
+ align:start position:0%
+have technological innovation we have
+ 
+
+ align:start position:0%
+have technological innovation we have
+specific Innovations around information
+
+ align:start position:0%
+specific Innovations around information
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+
+ align:start position:0%
+specific Innovations around information
+and knowledge
+
+ align:start position:0%
+and knowledge
+ 
+
+ align:start position:0%
+and knowledge
+organization and we have a critical role
+
+ align:start position:0%
+organization and we have a critical role
+ 
+
+ align:start position:0%
+organization and we have a critical role
+of Foundations and other players in
+
+ align:start position:0%
+of Foundations and other players in
+ 
+
+ align:start position:0%
+of Foundations and other players in
+democratizing that information now in
+
+ align:start position:0%
+democratizing that information now in
+ 
+
+ align:start position:0%
+democratizing that information now in
+the 1870s and ' 80s you know that didn't
+
+ align:start position:0%
+the 1870s and ' 80s you know that didn't
+ 
+
+ align:start position:0%
+the 1870s and ' 80s you know that didn't
+go far enough libraries particularly in
+
+ align:start position:0%
+go far enough libraries particularly in
+ 
+
+ align:start position:0%
+go far enough libraries particularly in
+the South were racially segregated those
+
+ align:start position:0%
+the South were racially segregated those
+ 
+
+ align:start position:0%
+the South were racially segregated those
+Technologies of information could
+
+ align:start position:0%
+Technologies of information could
+ 
+
+ align:start position:0%
+Technologies of information could
+sometimes be used as much to organize
+
+ align:start position:0%
+sometimes be used as much to organize
+ 
+
+ align:start position:0%
+sometimes be used as much to organize
+and discipline workers and ethnic groups
+
+ align:start position:0%
+and discipline workers and ethnic groups
+ 
+
+ align:start position:0%
+and discipline workers and ethnic groups
+as to share that knowledge but you know
+
+ align:start position:0%
+as to share that knowledge but you know
+ 
+
+ align:start position:0%
+as to share that knowledge but you know
+everything that we're going through
+
+ align:start position:0%
+everything that we're going through
+ 
+
+ align:start position:0%
+everything that we're going through
+right now we've been there
+
+ align:start position:0%
+right now we've been there
+ 
+
+ align:start position:0%
+right now we've been there
+before the lessons are that you know as
+
+ align:start position:0%
+before the lessons are that you know as
+ 
+
+ align:start position:0%
+before the lessons are that you know as
+with many other sort of technological
+
+ align:start position:0%
+with many other sort of technological
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+
+ align:start position:0%
+with many other sort of technological
+innovations and also efforts to
+
+ align:start position:0%
+innovations and also efforts to
+ 
+
+ align:start position:0%
+innovations and also efforts to
+democratize
+
+ align:start position:0%
+democratize
+ 
+
+ align:start position:0%
+democratize
+Technologies is that we need to build in
+
+ align:start position:0%
+Technologies is that we need to build in
+ 
+
+ align:start position:0%
+Technologies is that we need to build in
+equity from the beginning that we need
+
+ align:start position:0%
+equity from the beginning that we need
+ 
+
+ align:start position:0%
+equity from the beginning that we need
+to be asking who are these for who are
+
+ align:start position:0%
+to be asking who are these for who are
+ 
+
+ align:start position:0%
+to be asking who are these for who are
+we trying to reach who are the users how
+
+ align:start position:0%
+we trying to reach who are the users how
+ 
+
+ align:start position:0%
+we trying to reach who are the users how
+do they guide us to share and preserve
+
+ align:start position:0%
+do they guide us to share and preserve
+ 
+
+ align:start position:0%
+do they guide us to share and preserve
+information in valuable and meaningful
+
+ align:start position:0%
+information in valuable and meaningful
+ 
+
+ align:start position:0%
+information in valuable and meaningful
+and Equitable ways so that's a lesson
+
+ align:start position:0%
+and Equitable ways so that's a lesson
+ 
+
+ align:start position:0%
+and Equitable ways so that's a lesson
+what this might tell us for where ocw
+
+ align:start position:0%
+what this might tell us for where ocw
+ 
+
+ align:start position:0%
+what this might tell us for where ocw
+should go next right is that we have
+
+ align:start position:0%
+should go next right is that we have
+ 
+
+ align:start position:0%
+should go next right is that we have
+challenges for how to preserve the
+
+ align:start position:0%
+challenges for how to preserve the
+ 
+
+ align:start position:0%
+challenges for how to preserve the
+massive amount of information that is
+
+ align:start position:0%
+massive amount of information that is
+ 
+
+ align:start position:0%
+massive amount of information that is
+generated on our campus every day
+
+ align:start position:0%
+generated on our campus every day
+ 
+
+ align:start position:0%
+generated on our campus every day
+thousands of hours of video thousands
+
+ align:start position:0%
+thousands of hours of video thousands
+ 
+
+ align:start position:0%
+thousands of hours of video thousands
+and thousands of pages of learning
+
+ align:start position:0%
+and thousands of pages of learning
+ 
+
+ align:start position:0%
+and thousands of pages of learning
+Beyond a lecture from a professor at the
+
+ align:start position:0%
+Beyond a lecture from a professor at the
+ 
+
+ align:start position:0%
+Beyond a lecture from a professor at the
+front of the room you know so much
+
+ align:start position:0%
+front of the room you know so much
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+
+ align:start position:0%
+front of the room you know so much
+learning is happening in chat it's
+
+ align:start position:0%
+learning is happening in chat it's
+ 
+
+ align:start position:0%
+learning is happening in chat it's
+happening on the sidebars of of a class
+
+ align:start position:0%
+happening on the sidebars of of a class
+ 
+
+ align:start position:0%
+happening on the sidebars of of a class
+but we have to make it discoverable you
+
+ align:start position:0%
+but we have to make it discoverable you
+ 
+
+ align:start position:0%
+but we have to make it discoverable you
+know it's one thing to put a th000 hours
+
+ align:start position:0%
+know it's one thing to put a th000 hours
+ 
+
+ align:start position:0%
+know it's one thing to put a th000 hours
+of video online but but how can you find
+
+ align:start position:0%
+of video online but but how can you find
+ 
+
+ align:start position:0%
+of video online but but how can you find
+the 5 minutes that that you're
+
+ align:start position:0%
+the 5 minutes that that you're
+ 
+
+ align:start position:0%
+the 5 minutes that that you're
+interested in and we have to make it
+
+ align:start position:0%
+interested in and we have to make it
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+
+ align:start position:0%
+interested in and we have to make it
+trustable we need not only to find the
+
+ align:start position:0%
+trustable we need not only to find the
+ 
+
+ align:start position:0%
+trustable we need not only to find the
+Andrew carnegies of today to support us
+
+ align:start position:0%
+Andrew carnegies of today to support us
+ 
+
+ align:start position:0%
+Andrew carnegies of today to support us
+to make it possible we need to find the
+
+ align:start position:0%
+to make it possible we need to find the
+ 
+
+ align:start position:0%
+to make it possible we need to find the
+Melville deys of today who can help us
+
+ align:start position:0%
+Melville deys of today who can help us
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+
+ align:start position:0%
+Melville deys of today who can help us
+come up with you know the version of the
+
+ align:start position:0%
+come up with you know the version of the
+ 
+
+ align:start position:0%
+come up with you know the version of the
+Dewey Decimal System but the special
+
+ align:start position:0%
+Dewey Decimal System but the special
+ 
+
+ align:start position:0%
+Dewey Decimal System but the special
+challenge we face today is to make it
+
+ align:start position:0%
+challenge we face today is to make it
+ 
+
+ align:start position:0%
+challenge we face today is to make it
+trustworthy as you a listener of this
+
+ align:start position:0%
+trustworthy as you a listener of this
+ 
+
+ align:start position:0%
+trustworthy as you a listener of this
+show are probably already aware the core
+
+ align:start position:0%
+show are probably already aware the core
+ 
+
+ align:start position:0%
+show are probably already aware the core
+of OC's mission is making education open
+
+ align:start position:0%
+of OC's mission is making education open
+ 
+
+ align:start position:0%
+of OC's mission is making education open
+Equitable and available to the world in
+
+ align:start position:0%
+Equitable and available to the world in
+ 
+
+ align:start position:0%
+Equitable and available to the world in
+the age of generative AI products like
+
+ align:start position:0%
+the age of generative AI products like
+ 
+
+ align:start position:0%
+the age of generative AI products like
+chat GPT are bringing into question both
+
+ align:start position:0%
+chat GPT are bringing into question both
+ 
+
+ align:start position:0%
+chat GPT are bringing into question both
+what the future of Education looks looks
+
+ align:start position:0%
+what the future of Education looks looks
+ 
+
+ align:start position:0%
+what the future of Education looks looks
+like and how equitably it can be
+
+ align:start position:0%
+like and how equitably it can be
+ 
+
+ align:start position:0%
+like and how equitably it can be
+disseminated as he looks to OC's future
+
+ align:start position:0%
+disseminated as he looks to OC's future
+ 
+
+ align:start position:0%
+disseminated as he looks to OC's future
+I was curious how Chris imagines
+
+ align:start position:0%
+I was curious how Chris imagines
+ 
+
+ align:start position:0%
+I was curious how Chris imagines
+generative AI impacting For Better or
+
+ align:start position:0%
+generative AI impacting For Better or
+ 
+
+ align:start position:0%
+generative AI impacting For Better or
+For Worse teaching and learning some of
+
+ align:start position:0%
+For Worse teaching and learning some of
+ 
+
+ align:start position:0%
+For Worse teaching and learning some of
+the very first responses from Educators
+
+ align:start position:0%
+the very first responses from Educators
+ 
+
+ align:start position:0%
+the very first responses from Educators
+were defensive how do we shut it down
+
+ align:start position:0%
+were defensive how do we shut it down
+ 
+
+ align:start position:0%
+were defensive how do we shut it down
+and also distrustful of Learners right
+
+ align:start position:0%
+and also distrustful of Learners right
+ 
+
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+and also distrustful of Learners right
+students are going to use it to cheat
+
+ align:start position:0%
+students are going to use it to cheat
+ 
+
+ align:start position:0%
+students are going to use it to cheat
+you know we all heard this right you
+
+ align:start position:0%
+you know we all heard this right you
+ 
+
+ align:start position:0%
+you know we all heard this right you
+know it's going to write the essays no
+
+ align:start position:0%
+know it's going to write the essays no
+ 
+
+ align:start position:0%
+know it's going to write the essays no
+one's ever going to write essay again
+
+ align:start position:0%
+one's ever going to write essay again
+ 
+
+ align:start position:0%
+one's ever going to write essay again
+Etc and being defensive and distrustful
+
+ align:start position:0%
+Etc and being defensive and distrustful
+ 
+
+ align:start position:0%
+Etc and being defensive and distrustful
+is usually not the best way to be a good
+
+ align:start position:0%
+is usually not the best way to be a good
+ 
+
+ align:start position:0%
+is usually not the best way to be a good
+teacher you know I feel like most
+
+ align:start position:0%
+teacher you know I feel like most
+ 
+
+ align:start position:0%
+teacher you know I feel like most
+instructors at MIT are in a sort of
+
+ align:start position:0%
+instructors at MIT are in a sort of
+ 
+
+ align:start position:0%
+instructors at MIT are in a sort of
+phase between trying to stop chat GPT
+
+ align:start position:0%
+phase between trying to stop chat GPT
+ 
+
+ align:start position:0%
+phase between trying to stop chat GPT
+and other tools um and completely
+
+ align:start position:0%
+and other tools um and completely
+ 
+
+ align:start position:0%
+and other tools um and completely
+embracing them right in between there's
+
+ align:start position:0%
+embracing them right in between there's
+ 
+
+ align:start position:0%
+embracing them right in between there's
+a a space of
+
+ align:start position:0%
+a a space of
+ 
+
+ align:start position:0%
+a a space of
+curiosity and that's I think where we'll
+
+ align:start position:0%
+curiosity and that's I think where we'll
+ 
+
+ align:start position:0%
+curiosity and that's I think where we'll
+be most productive obviously there are
+
+ align:start position:0%
+be most productive obviously there are
+ 
+
+ align:start position:0%
+be most productive obviously there are
+challenges us with academic Integrity
+
+ align:start position:0%
+challenges us with academic Integrity
+ 
+
+ align:start position:0%
+challenges us with academic Integrity
+that you know came up in the very first
+
+ align:start position:0%
+that you know came up in the very first
+ 
+
+ align:start position:0%
+that you know came up in the very first
+days after these products came to Market
+
+ align:start position:0%
+days after these products came to Market
+ 
+
+ align:start position:0%
+days after these products came to Market
+and for some of the other offerings we
+
+ align:start position:0%
+and for some of the other offerings we
+ 
+
+ align:start position:0%
+and for some of the other offerings we
+have in open learning the mitx courses
+
+ align:start position:0%
+have in open learning the mitx courses
+ 
+
+ align:start position:0%
+have in open learning the mitx courses
+and so forth um you know those
+
+ align:start position:0%
+and so forth um you know those
+ 
+
+ align:start position:0%
+and so forth um you know those
+conversations are are happening but
+
+ align:start position:0%
+conversations are are happening but
+ 
+
+ align:start position:0%
+conversations are are happening but
+those were already happening right and
+
+ align:start position:0%
+those were already happening right and
+ 
+
+ align:start position:0%
+those were already happening right and
+you know trying to figure out how
+
+ align:start position:0%
+you know trying to figure out how
+ 
+
+ align:start position:0%
+you know trying to figure out how
+to ensure that Learners use these tools
+
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+to ensure that Learners use these tools
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+shortcut it is it's not an enforcement
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+ align:start position:0%
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+
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+spend more time explaining why they are
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+ align:start position:0%
+spend more time explaining why they are
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+conversation with Chris was how
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+conversation with Chris was how
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+conversation with Chris was how
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+important it is in all of his work to
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+spend time in this middle space of
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+ align:start position:0%
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+curiosity and reflectiveness that he
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+talks about he explained how he creates
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+talks about he explained how he creates
+an environment in which his students can
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+an environment in which his students can
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+engage in reflection it starts the
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+ align:start position:0%
+engage in reflection it starts the
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+
+ align:start position:0%
+engage in reflection it starts the
+moment they walk in the door my students
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+ align:start position:0%
+moment they walk in the door my students
+ 
+
+ align:start position:0%
+moment they walk in the door my students
+find this very awkward at first right
+
+ align:start position:0%
+find this very awkward at first right
+ 
+
+ align:start position:0%
+find this very awkward at first right
+but you can't come into my class without
+
+ align:start position:0%
+but you can't come into my class without
+ 
+
+ align:start position:0%
+but you can't come into my class without
+saying
+
+ align:start position:0%
+saying
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+saying
+hello and I might even shake your hand
+
+ align:start position:0%
+hello and I might even shake your hand
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+
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+hello and I might even shake your hand
+and you you have to know the names of
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+and you you have to know the names of
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+and you you have to know the names of
+every other student in the room right
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+every other student in the room right
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+every other student in the room right
+and I actually give a quiz sometimes to
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+and I actually give a quiz sometimes to
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+and I actually give a quiz sometimes to
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+make sure that students know it right
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+make sure that students know it right
+and and you know that's really just
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+and and you know that's really just
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+
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+and and you know that's really just
+really basic
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+really basic
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+
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+really basic
+crucial step to understanding that this
+
+ align:start position:0%
+crucial step to understanding that this
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+
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+crucial step to understanding that this
+is a collective Enterprise and not a
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+is a collective Enterprise and not a
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+
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+is a collective Enterprise and not a
+spectator sport if you know the names of
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+spectator sport if you know the names of
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+
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+spectator sport if you know the names of
+of everyone else in the room and if
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+of everyone else in the room and if
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+
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+of everyone else in the room and if
+you've you know if you've said hello to
+
+ align:start position:0%
+you've you know if you've said hello to
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+
+ align:start position:0%
+you've you know if you've said hello to
+all of them the tone just changes
+
+ align:start position:0%
+all of them the tone just changes
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+
+ align:start position:0%
+all of them the tone just changes
+immediately you know I've have the Good
+
+ align:start position:0%
+immediately you know I've have the Good
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+
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+immediately you know I've have the Good
+Fortune at MIT of you know teaching
+
+ align:start position:0%
+Fortune at MIT of you know teaching
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+
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+Fortune at MIT of you know teaching
+small enough classes where we can do
+
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+small enough classes where we can do
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+small enough classes where we can do
+that Chris shared some strategies he
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+that Chris shared some strategies he
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+that Chris shared some strategies he
+uses to help students reflect on the
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+uses to help students reflect on the
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+uses to help students reflect on the
+complexities that have shaped decisions
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+complexities that have shaped decisions
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+complexities that have shaped decisions
+made throughout
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+made throughout
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+made throughout
+history I like to give them very sort
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+history I like to give them very sort
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+
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+history I like to give them very sort
+of real world puzzle-based sort of
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+of real world puzzle-based sort of
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+of real world puzzle-based sort of
+problem-based moments of the past right
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+problem-based moments of the past right
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+
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+problem-based moments of the past right
+where people were making decisions and
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+where people were making decisions and
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+where people were making decisions and
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+technology right they I generally don't
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+technology right they I generally don't
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+technology right they I generally don't
+teach that much about the history of
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+teach that much about the history of
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+teach that much about the history of
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+specific
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+specific
+Technologies um but where they might
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+Technologies um but where they might
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+a moment and then make them realize just
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+decades later when they're sort of
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+confronting choices in their profession
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+it's complicated yeah introducing
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+it's complicated yeah introducing
+complexity and recognizing that
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+complexity and recognizing that
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+acknowledging it I think that's really
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+important so especially in history like
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+important so especially in history like
+how do you create a classroom culture
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+how do you create a classroom culture
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+how do you create a classroom culture
+where people can express dissenting
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+where people can express dissenting
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+topics you know I can't
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+topics you know I can't
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+topics you know I can't
+say I've gotten it right every time and
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+say I've gotten it right every time and
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+say I've gotten it right every time and
+it's a moving Target as our culture
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+it's a moving Target as our culture
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+it's a moving Target as our culture
+shifts and as people come into class
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+shifts and as people come into class
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+shifts and as people come into class
+with different expectations um you know
+
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+with different expectations um you know
+ 
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+ align:start position:0%
+with different expectations um you know
+there's no one answer to these questions
+
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+there's no one answer to these questions
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+
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+there's no one answer to these questions
+I think part of it
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+I think part of it
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+I think part of it
+is the importance
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+is the importance
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+is the importance
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+of
+structured discussion which is to
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+structured discussion which is to
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+structured discussion which is to
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+say
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+say
+before you state a position it's
+
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+before you state a position it's
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+
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+before you state a position it's
+important to know what the what the
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+important to know what the what the
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+
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+important to know what the what the
+landscape of possible positions is and
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+landscape of possible positions is and
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+landscape of possible positions is and
+to articulate them right and so
+
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+to articulate them right and so
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+to articulate them right and so
+encouraging students not just to know
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+encouraging students not just to know
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+encouraging students not just to know
+that there is a counterargument but
+
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+that there is a counterargument but
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+
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+that there is a counterargument but
+actually to to state it and then they
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+actually to to state it and then they
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+actually to to state it and then they
+can navigate
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+can navigate
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+where they fit within
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+where they fit within
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+where they fit within
+that it was inspiring to hear how Chris
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+that it was inspiring to hear how Chris
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+that it was inspiring to hear how Chris
+infuses the values of reflectiveness and
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+infuses the values of reflectiveness and
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+infuses the values of reflectiveness and
+openness not just into his teaching but
+
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+openness not just into his teaching but
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+
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+openness not just into his teaching but
+also into our work here at MIT open
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+also into our work here at MIT open
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+
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+also into our work here at MIT open
+courseware there are plenty of
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+courseware there are plenty of
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+
+ align:start position:0%
+courseware there are plenty of
+researchers at MIT who would love if a
+
+ align:start position:0%
+researchers at MIT who would love if a
+ 
+
+ align:start position:0%
+researchers at MIT who would love if a
+few million more people understood what
+
+ align:start position:0%
+few million more people understood what
+ 
+
+ align:start position:0%
+few million more people understood what
+they did every day and you know open
+
+ align:start position:0%
+they did every day and you know open
+ 
+
+ align:start position:0%
+they did every day and you know open
+courseware can play a really kind of
+
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+courseware can play a really kind of
+ 
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+courseware can play a really kind of
+crucial role in making that possible we
+
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+crucial role in making that possible we
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+
+ align:start position:0%
+crucial role in making that possible we
+have a special role to play in in
+
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+have a special role to play in in
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+
+ align:start position:0%
+have a special role to play in in
+translating it and in part by feeding
+
+ align:start position:0%
+translating it and in part by feeding
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+
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+translating it and in part by feeding
+back to the MIT Community what Learners
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+back to the MIT Community what Learners
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+back to the MIT Community what Learners
+on open courseware are curious about
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+on open courseware are curious about
+ 
+
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+on open courseware are curious about
+what they're hungry to know about and at
+
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+what they're hungry to know about and at
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+
+ align:start position:0%
+what they're hungry to know about and at
+at what level of technical rigor and
+
+ align:start position:0%
+at what level of technical rigor and
+ 
+
+ align:start position:0%
+at what level of technical rigor and
+scientific Advance they can follow it
+
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+scientific Advance they can follow it
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+
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+scientific Advance they can follow it
+we've actually only begun to imagine
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+we've actually only begun to imagine
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+
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+we've actually only begun to imagine
+what's possible in those spaces and I
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+what's possible in those spaces and I
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+
+ align:start position:0%
+what's possible in those spaces and I
+think it's less in the delivery of
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+ align:start position:0%
+think it's less in the delivery of
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+
+ align:start position:0%
+think it's less in the delivery of
+content and more in the meaningfulness
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+content and more in the meaningfulness
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+
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+content and more in the meaningfulness
+and authenticity of the actual learning
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+and authenticity of the actual learning
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+
+ align:start position:0%
+and authenticity of the actual learning
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+experience that was Chris Capa professor
+
+ align:start position:0%
+experience that was Chris Capa professor
+ 
+
+ align:start position:0%
+experience that was Chris Capa professor
+of history and Senior associate Dean for
+
+ align:start position:0%
+of history and Senior associate Dean for
+ 
+
+ align:start position:0%
+of history and Senior associate Dean for
+open learning at MIT in addition to
+
+ align:start position:0%
+open learning at MIT in addition to
+ 
+
+ align:start position:0%
+open learning at MIT in addition to
+providing strategic direction for MIT
+
+ align:start position:0%
+providing strategic direction for MIT
+ 
+
+ align:start position:0%
+providing strategic direction for MIT
+open courseware he's also contributed
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+ align:start position:0%
+open courseware he's also contributed
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+
+ align:start position:0%
+open courseware he's also contributed
+materials from three of his courses to
+
+ align:start position:0%
+materials from three of his courses to
+ 
+
+ align:start position:0%
+materials from three of his courses to
+the ocw collection on our website you
+
+ align:start position:0%
+the ocw collection on our website you
+ 
+
+ align:start position:0%
+the ocw collection on our website you
+can find syllabi readings assignments
+
+ align:start position:0%
+can find syllabi readings assignments
+ 
+
+ align:start position:0%
+can find syllabi readings assignments
+and other resources from 21h 221 the
+
+ align:start position:0%
+and other resources from 21h 221 the
+ 
+
+ align:start position:0%
+and other resources from 21h 221 the
+places of migration in United States
+
+ align:start position:0%
+places of migration in United States
+ 
+
+ align:start position:0%
+places of migration in United States
+history 21 h223 war in American society
+
+ align:start position:0%
+history 21 h223 war in American society
+ 
+
+ align:start position:0%
+history 21 h223 war in American society
+and 21 h224 law and Society in US
+
+ align:start position:0%
+and 21 h224 law and Society in US
+ 
+
+ align:start position:0%
+and 21 h224 law and Society in US
+history we'll put the links to these
+
+ align:start position:0%
+history we'll put the links to these
+ 
+
+ align:start position:0%
+history we'll put the links to these
+courses in the show notes for you thank
+
+ align:start position:0%
+courses in the show notes for you thank
+ 
+
+ align:start position:0%
+courses in the show notes for you thank
+you so much for listening until next
+
+ align:start position:0%
+you so much for listening until next
+ 
+
+ align:start position:0%
+you so much for listening until next
+time signing off from Cambridge
+
+ align:start position:0%
+time signing off from Cambridge
+ 
+
+ align:start position:0%
+time signing off from Cambridge
+Massachusetts I'm your host Sarah Hansen
+
+ align:start position:0%
+Massachusetts I'm your host Sarah Hansen
+ 
+
+ align:start position:0%
+Massachusetts I'm your host Sarah Hansen
+from MIT open
+
+ align:start position:0%
+from MIT open
+ 
+
+ align:start position:0%
+from MIT open
+courseware MIT chalk radio's producers
+
+ align:start position:0%
+courseware MIT chalk radio's producers
+ 
+
+ align:start position:0%
+courseware MIT chalk radio's producers
+include myself red Pachi and Dave Lansky
+
+ align:start position:0%
+include myself red Pachi and Dave Lansky
+ 
+
+ align:start position:0%
+include myself red Pachi and Dave Lansky
+show notes for this episode were written
+
+ align:start position:0%
+show notes for this episode were written
+ 
+
+ align:start position:0%
+show notes for this episode were written
+by Peter Chipman Chris capa's ocw cor
+
+ align:start position:0%
+by Peter Chipman Chris capa's ocw cor
+ 
+
+ align:start position:0%
+by Peter Chipman Chris capa's ocw cor
+sites were built by Rees Jenkins Jason
+
+ align:start position:0%
+sites were built by Rees Jenkins Jason
+ 
+
+ align:start position:0%
+sites were built by Rees Jenkins Jason
+player made our episode cassette
+
+ align:start position:0%
+player made our episode cassette
+ 
+
+ align:start position:0%
+player made our episode cassette
+animation on YouTube We're funded by MIT
+
+ align:start position:0%
+animation on YouTube We're funded by MIT
+ 
+
+ align:start position:0%
+animation on YouTube We're funded by MIT
+open learning and supporters like you
\ No newline at end of file
diff --git a/Ht_tyuAWmpM.txt b/Ht_tyuAWmpM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e83bc40e0cdd5a4616ebb95880ae3af8c3a5edd1
--- /dev/null
+++ b/Ht_tyuAWmpM.txt
@@ -0,0 +1,218 @@
+Earlier we talked about about finding equivalent
+FSMs with fewer states.
+
+Now we'll develop an approach for finding
+such FSMs by looking for two states that that
+
+can be merged into a single state without
+changing the behavior of the FSM in any externally
+
+distinguishable manner.
+
+Two states are equivalent if they meet the
+following two criteria.
+
+First, the states must have identical outputs.
+
+This makes sense: the outputs are visible
+to the outside, so if their values differed
+
+between the two states, that difference would
+clearly be externally distinguishable!
+
+Second, for each combination of input values,
+the two states transition to equivalent states.
+
+Our strategy for deriving an equivalent machine
+with fewer states will be to start with our
+
+original FSM, find pairs of equivalent states
+and merge those states.
+
+We'll keep repeating the process until we
+can't find any more equivalent states.
+
+Let's try this on our ant FSM.
+
+First we need to find a pair of states that
+have the same outputs.
+
+As it turns out, there's only one such pair:
+WALL1 and CORNER, both of which assert the
+
+turn-right and forward outputs.
+
+Okay, so let's assume that WALL1 and CORNER
+are equivalent and ask if they transition
+
+to equivalent states for each applicable combination
+of input values.
+
+For these two states, all the transitions
+depend only on the value of the R input, so
+
+we just have to check two cases.
+
+If R is 0, both states transition to CORNER.
+
+If R is 1, both states transition to WALL2.
+
+So both equivalence criteria are satisfied
+and we can conclude that the WALL1 and CORNER
+
+states are equivalent and can be merged.
+
+This gives us the four-state FSM shown here,
+where we've called the single merged state
+
+WALL1.
+
+This smaller, equivalent FSM behaves exactly
+as the previous 5-state FSM.
+
+The implementation of the 5-state machine
+requires 3 state bits; the implementation
+
+of the 4-state machine only requires 2 state
+bits.
+
+Reducing the number of state bits by 1 is
+huge since it reduces the size of the required
+
+ROM by half!
+
+Just as we were able to achieve considerable
+hardware savings by minimizing Boolean equations,
+
+we can do the same in sequential logic by
+merging equivalent states.
+
+Roboant customers are looking forward to the
+price cut!
+
+Let's look at what we'd need to do if we wanted
+to implement the FSM using logic gates instead
+
+a ROM for the combinational logic.
+
+First we have to build the truth table, entering
+all the transitions in the state transition
+
+diagram.
+
+We'll start with the LOST state.
+
+So if the FSM is in this state, the F output
+should be 1.
+
+If both antenna inputs are 0, the next state
+is also LOST.
+
+Assigning the LOST state the encoding 00,
+we've captured this information in the first
+
+row of the table.
+
+If either antenna is touching, the FSM should
+transition from LOST to the rotate-counterclockwise
+
+state.
+
+We've given this an encoding of 01.
+
+There are three combinations of L and R values
+that match this transition, so we've added
+
+three rows to the truth table.
+
+This takes care of all the transitions from
+the LOST state.
+
+Now we can tackle the transitions from the
+rotate-counterclockwise state.
+
+If either antenna is touching, the next state
+is again rotate-counterclockwise.
+
+So we've identified the matching values for
+the inputs and added the appropriate three
+
+rows to the transition table.
+
+We can continue in a similar manner to encode
+the transitions one-by-one.
+
+Here's the final table, where we've used don't
+cares to reduce the number of rows for presentation.
+
+Next we want to come up with Boolean equations
+for each of the outputs of the combinational
+
+logic, i.e., the two next-state bits and the
+three motion-control outputs.
+
+Here are the Karnaugh maps for the two next-state
+bits.
+
+Using our K-map skills from Chapter 4, we'll
+find a cover of the prime implicants for S1-prime
+
+and write down the corresponding product terms
+in a minimal sum-of-products equation.
+
+And then do the same for the other next-state
+bit.
+
+We can follow a similar process to derive
+minimal sum-of-products expressions for the
+
+motion-control outputs.
+
+Implementing each sum-of-products in a straight-forward
+fashion with AND and OR gates, we get the
+
+following schematic for the ant brain.
+
+Pretty neat!
+
+Who knew that maze following behavior could
+be implemented with a couple of D registers
+
+and a handful of logic gates?
+
+There are many complex behaviors that can
+be created with surprisingly simple FSMs.
+
+Early on, the computer graphics folks learned
+that group behaviors like swarming, flocking
+
+and schooling can be modeled by equipping
+each participant with a simple FSM.
+
+So next time you see the massive battle scene
+from the Lord of the Rings movie, think of
+
+many FSMs running in parallel!
+
+Physical behaviors that arise from simple
+interactions between component molecules can
+
+sometimes be more easily modeled using cellular
+automata -
+
+arrays of communicating FSMS - than by trying
+to solve the partial differential equations
+
+that model the constraints on the molecules'
+behavior.
+
+And here's an idea: what if we allowed the
+FSM to modify its own transition table?
+
+Hmm.
+
+Maybe that's a plausible model for evolution!
+
+FSMs are everywhere!
+
+You'll see FSMs for the rest of your life…
\ No newline at end of file
diff --git a/Ih4s5IFphCw.txt b/Ih4s5IFphCw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..439413d49b1c888ca521e3f117298b37d273e358
--- /dev/null
+++ b/Ih4s5IFphCw.txt
@@ -0,0 +1,7930 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu hello and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+welcome so today I want to start to talk
+
+ align:start position:0%
+welcome so today I want to start to talk
+ 
+
+ align:start position:0%
+welcome so today I want to start to talk
+about discreet time
+
+ align:start position:0%
+about discreet time
+ 
+
+ align:start position:0%
+about discreet time
+systems but before beginning there I
+
+ align:start position:0%
+systems but before beginning there I
+ 
+
+ align:start position:0%
+systems but before beginning there I
+want to say just a quick word about
+
+ align:start position:0%
+want to say just a quick word about
+ 
+
+ align:start position:0%
+want to say just a quick word about
+homework I tried to stress this last
+
+ align:start position:0%
+homework I tried to stress this last
+ 
+
+ align:start position:0%
+homework I tried to stress this last
+time that the way you get to know this
+
+ align:start position:0%
+time that the way you get to know this
+ 
+
+ align:start position:0%
+time that the way you get to know this
+stuff is by doing the
+
+ align:start position:0%
+stuff is by doing the
+ 
+
+ align:start position:0%
+stuff is by doing the
+homework and we'd like to provide
+
+ align:start position:0%
+homework and we'd like to provide
+ 
+
+ align:start position:0%
+homework and we'd like to provide
+positive feedback in a direction that
+
+ align:start position:0%
+positive feedback in a direction that
+ 
+
+ align:start position:0%
+positive feedback in a direction that
+will help you get the most out of the
+
+ align:start position:0%
+will help you get the most out of the
+ 
+
+ align:start position:0%
+will help you get the most out of the
+homework so to that end we've already
+
+ align:start position:0%
+homework so to that end we've already
+ 
+
+ align:start position:0%
+homework so to that end we've already
+talked about there's two kinds of
+
+ align:start position:0%
+talked about there's two kinds of
+ 
+
+ align:start position:0%
+talked about there's two kinds of
+problems each homework will have tutor
+
+ align:start position:0%
+problems each homework will have tutor
+ 
+
+ align:start position:0%
+problems each homework will have tutor
+problems that are intended to be
+
+ align:start position:0%
+problems that are intended to be
+ 
+
+ align:start position:0%
+problems that are intended to be
+problems like you will see on an exam
+
+ align:start position:0%
+problems like you will see on an exam
+ 
+
+ align:start position:0%
+problems like you will see on an exam
+but they will also have the feature that
+
+ align:start position:0%
+but they will also have the feature that
+ 
+
+ align:start position:0%
+but they will also have the feature that
+they can be automatically graded so that
+
+ align:start position:0%
+they can be automatically graded so that
+ 
+
+ align:start position:0%
+they can be automatically graded so that
+you can get immediate
+
+ align:start position:0%
+you can get immediate
+ 
+
+ align:start position:0%
+you can get immediate
+feedback about whether you're doing it
+
+ align:start position:0%
+feedback about whether you're doing it
+ 
+
+ align:start position:0%
+feedback about whether you're doing it
+right or
+
+ align:start position:0%
+right or
+ 
+
+ align:start position:0%
+right or
+not there also be harder questions
+
+ align:start position:0%
+not there also be harder questions
+ 
+
+ align:start position:0%
+not there also be harder questions
+questions that look more like real world
+
+ align:start position:0%
+questions that look more like real world
+ 
+
+ align:start position:0%
+questions that look more like real world
+questions so you don't think that this
+
+ align:start position:0%
+questions so you don't think that this
+ 
+
+ align:start position:0%
+questions so you don't think that this
+class is only about toy
+
+ align:start position:0%
+class is only about toy
+ 
+
+ align:start position:0%
+class is only about toy
+problems the idea is to give you
+
+ align:start position:0%
+problems the idea is to give you
+ 
+
+ align:start position:0%
+problems the idea is to give you
+problems that you can imagine running
+
+ align:start position:0%
+problems that you can imagine running
+ 
+
+ align:start position:0%
+problems that you can imagine running
+into those are harder to grade
+
+ align:start position:0%
+into those are harder to grade
+ 
+
+ align:start position:0%
+into those are harder to grade
+automatically so we
+
+ align:start position:0%
+automatically so we
+ 
+
+ align:start position:0%
+automatically so we
+won't instead they'll be graded by a
+
+ align:start position:0%
+won't instead they'll be graded by a
+ 
+
+ align:start position:0%
+won't instead they'll be graded by a
+human that those problems often admit
+
+ align:start position:0%
+human that those problems often admit
+ 
+
+ align:start position:0%
+human that those problems often admit
+several different lines of reasoning so
+
+ align:start position:0%
+several different lines of reasoning so
+ 
+
+ align:start position:0%
+several different lines of reasoning so
+there isn't necessarily a unique right
+
+ align:start position:0%
+there isn't necessarily a unique right
+ 
+
+ align:start position:0%
+there isn't necessarily a unique right
+way to think about
+
+ align:start position:0%
+way to think about
+ 
+
+ align:start position:0%
+way to think about
+it so what we would like to do is
+
+ align:start position:0%
+it so what we would like to do is
+ 
+
+ align:start position:0%
+it so what we would like to do is
+encourage you to after you finish the
+
+ align:start position:0%
+encourage you to after you finish the
+ 
+
+ align:start position:0%
+encourage you to after you finish the
+homework read the
+
+ align:start position:0%
+homework read the
+ 
+
+ align:start position:0%
+homework read the
+solutions now we think it's kind of an
+
+ align:start position:0%
+solutions now we think it's kind of an
+ 
+
+ align:start position:0%
+solutions now we think it's kind of an
+impediment to wait for a week till you
+
+ align:start position:0%
+impediment to wait for a week till you
+ 
+
+ align:start position:0%
+impediment to wait for a week till you
+get your graded homework back because
+
+ align:start position:0%
+get your graded homework back because
+ 
+
+ align:start position:0%
+get your graded homework back because
+people in my experience just don't
+
+ align:start position:0%
+people in my experience just don't
+ 
+
+ align:start position:0%
+people in my experience just don't
+bother so what we would like to do is
+
+ align:start position:0%
+bother so what we would like to do is
+ 
+
+ align:start position:0%
+bother so what we would like to do is
+post the solutions immediately after the
+
+ align:start position:0%
+post the solutions immediately after the
+ 
+
+ align:start position:0%
+post the solutions immediately after the
+your Solutions are due your Solutions
+
+ align:start position:0%
+your Solutions are due your Solutions
+ 
+
+ align:start position:0%
+your Solutions are due your Solutions
+are due if you submit electronically at
+
+ align:start position:0%
+are due if you submit electronically at
+ 
+
+ align:start position:0%
+are due if you submit electronically at
+5:00 pm on the due date so homework one
+
+ align:start position:0%
+5:00 pm on the due date so homework one
+ 
+
+ align:start position:0%
+5:00 pm on the due date so homework one
+is due tomorrow 5:00 p.m electronic
+
+ align:start position:0%
+is due tomorrow 5:00 p.m electronic
+ 
+
+ align:start position:0%
+is due tomorrow 5:00 p.m electronic
+submission okay you can also turn in
+
+ align:start position:0%
+submission okay you can also turn in
+ 
+
+ align:start position:0%
+submission okay you can also turn in
+paper but you have to do that in your
+
+ align:start position:0%
+paper but you have to do that in your
+ 
+
+ align:start position:0%
+paper but you have to do that in your
+recitation immediately after it was due
+
+ align:start position:0%
+recitation immediately after it was due
+ 
+
+ align:start position:0%
+recitation immediately after it was due
+at 5:00 pm we'll post the
+
+ align:start position:0%
+at 5:00 pm we'll post the
+ 
+
+ align:start position:0%
+at 5:00 pm we'll post the
+solutions and we'll encourage you in
+
+ align:start position:0%
+solutions and we'll encourage you in
+ 
+
+ align:start position:0%
+solutions and we'll encourage you in
+quotes to read them
+
+ align:start position:0%
+quotes to read them
+ 
+
+ align:start position:0%
+quotes to read them
+because it's good for you right we hope
+
+ align:start position:0%
+because it's good for you right we hope
+ 
+
+ align:start position:0%
+because it's good for you right we hope
+that that will help you find the errors
+
+ align:start position:0%
+that that will help you find the errors
+ 
+
+ align:start position:0%
+that that will help you find the errors
+that you made but also expose you to
+
+ align:start position:0%
+that you made but also expose you to
+ 
+
+ align:start position:0%
+that you made but also expose you to
+other ways that maybe will be simpler
+
+ align:start position:0%
+other ways that maybe will be simpler
+ 
+
+ align:start position:0%
+other ways that maybe will be simpler
+maybe will be harder your feedback on
+
+ align:start position:0%
+maybe will be harder your feedback on
+ 
+
+ align:start position:0%
+maybe will be harder your feedback on
+you're coming up with a simpler way it
+
+ align:start position:0%
+you're coming up with a simpler way it
+ 
+
+ align:start position:0%
+you're coming up with a simpler way it
+would be greatly appreciated so please
+
+ align:start position:0%
+would be greatly appreciated so please
+ 
+
+ align:start position:0%
+would be greatly appreciated so please
+send me email anytime you think you have
+
+ align:start position:0%
+send me email anytime you think you have
+ 
+
+ align:start position:0%
+send me email anytime you think you have
+a better way of doing things which is
+
+ align:start position:0%
+a better way of doing things which is
+ 
+
+ align:start position:0%
+a better way of doing things which is
+entirely
+
+ align:start position:0%
+entirely
+ 
+
+ align:start position:0%
+entirely
+possible but as further encouragement if
+
+ align:start position:0%
+possible but as further encouragement if
+ 
+
+ align:start position:0%
+possible but as further encouragement if
+you mark up all of your errors and
+
+ align:start position:0%
+you mark up all of your errors and
+ 
+
+ align:start position:0%
+you mark up all of your errors and
+resubmit we'll give you back half the
+
+ align:start position:0%
+resubmit we'll give you back half the
+ 
+
+ align:start position:0%
+resubmit we'll give you back half the
+points you
+
+ align:start position:0%
+points you
+ 
+
+ align:start position:0%
+points you
+lost okay so you get to submit every
+
+ align:start position:0%
+lost okay so you get to submit every
+ 
+
+ align:start position:0%
+lost okay so you get to submit every
+homework twice once for the due date
+
+ align:start position:0%
+homework twice once for the due date
+ 
+
+ align:start position:0%
+homework twice once for the due date
+5:00 p.m. on
+
+ align:start position:0%
+5:00 p.m. on
+ 
+
+ align:start position:0%
+5:00 p.m. on
+Wednesday immediately after that you'll
+
+ align:start position:0%
+Wednesday immediately after that you'll
+ 
+
+ align:start position:0%
+Wednesday immediately after that you'll
+be able to see the published Solutions
+
+ align:start position:0%
+be able to see the published Solutions
+ 
+
+ align:start position:0%
+be able to see the published Solutions
+you can Circle all the errors and say
+
+ align:start position:0%
+you can Circle all the errors and say
+ 
+
+ align:start position:0%
+you can Circle all the errors and say
+algebra or conceptual or I'm an idiot or
+
+ align:start position:0%
+algebra or conceptual or I'm an idiot or
+ 
+
+ align:start position:0%
+algebra or conceptual or I'm an idiot or
+whatever is the right way of thinking
+
+ align:start position:0%
+whatever is the right way of thinking
+ 
+
+ align:start position:0%
+whatever is the right way of thinking
+about what you
+
+ align:start position:0%
+about what you
+ 
+
+ align:start position:0%
+about what you
+did and if you get all of the errors
+
+ align:start position:0%
+did and if you get all of the errors
+ 
+
+ align:start position:0%
+did and if you get all of the errors
+you'll get back half of the points you
+
+ align:start position:0%
+you'll get back half of the points you
+ 
+
+ align:start position:0%
+you'll get back half of the points you
+lost okay if you say I'm right you're
+
+ align:start position:0%
+lost okay if you say I'm right you're
+ 
+
+ align:start position:0%
+lost okay if you say I'm right you're
+wrong uh maybe you won't get all your
+
+ align:start position:0%
+wrong uh maybe you won't get all your
+ 
+
+ align:start position:0%
+wrong uh maybe you won't get all your
+points back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes uh the the resubmission is the same
+
+ align:start position:0%
+yes uh the the resubmission is the same
+ 
+
+ align:start position:0%
+yes uh the the resubmission is the same
+rules if you want to submit by paper you
+
+ align:start position:0%
+rules if you want to submit by paper you
+ 
+
+ align:start position:0%
+rules if you want to submit by paper you
+can turn them in on Friday's recitation
+
+ align:start position:0%
+can turn them in on Friday's recitation
+ 
+
+ align:start position:0%
+can turn them in on Friday's recitation
+you have until Friday at P 5: PM
+
+ align:start position:0%
+you have until Friday at P 5: PM
+ 
+
+ align:start position:0%
+you have until Friday at P 5: PM
+otherwise please notice that you're if
+
+ align:start position:0%
+otherwise please notice that you're if
+ 
+
+ align:start position:0%
+otherwise please notice that you're if
+you're using paper we will not have
+
+ align:start position:0%
+you're using paper we will not have
+ 
+
+ align:start position:0%
+you're using paper we will not have
+returned your
+
+ align:start position:0%
+returned your
+ 
+
+ align:start position:0%
+returned your
+Solutions in time for you to write on
+
+ align:start position:0%
+Solutions in time for you to write on
+ 
+
+ align:start position:0%
+Solutions in time for you to write on
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+so make a
+
+ align:start position:0%
+so make a
+ 
+
+ align:start position:0%
+so make a
+copy so if you want to do the paper
+
+ align:start position:0%
+copy so if you want to do the paper
+ 
+
+ align:start position:0%
+copy so if you want to do the paper
+route make a photo copy before you turn
+
+ align:start position:0%
+route make a photo copy before you turn
+ 
+
+ align:start position:0%
+route make a photo copy before you turn
+it in the first time so that you have
+
+ align:start position:0%
+it in the first time so that you have
+ 
+
+ align:start position:0%
+it in the first time so that you have
+something to write on for the second
+
+ align:start position:0%
+something to write on for the second
+ 
+
+ align:start position:0%
+something to write on for the second
+time if you submit electronically
+
+ align:start position:0%
+time if you submit electronically
+ 
+
+ align:start position:0%
+time if you submit electronically
+there's a feedback button on the on the
+
+ align:start position:0%
+there's a feedback button on the on the
+ 
+
+ align:start position:0%
+there's a feedback button on the on the
+tutor so you can see the thing that you
+
+ align:start position:0%
+tutor so you can see the thing that you
+ 
+
+ align:start position:0%
+tutor so you can see the thing that you
+just submitted so that's not a problem
+
+ align:start position:0%
+just submitted so that's not a problem
+ 
+
+ align:start position:0%
+just submitted so that's not a problem
+if you're doing the electronic thing but
+
+ align:start position:0%
+if you're doing the electronic thing but
+ 
+
+ align:start position:0%
+if you're doing the electronic thing but
+if you're doing paper please uh make a
+
+ align:start position:0%
+if you're doing paper please uh make a
+ 
+
+ align:start position:0%
+if you're doing paper please uh make a
+photo copy before you submit otherwise
+
+ align:start position:0%
+photo copy before you submit otherwise
+ 
+
+ align:start position:0%
+photo copy before you submit otherwise
+it will be hard to mark up your
+
+ align:start position:0%
+it will be hard to mark up your
+ 
+
+ align:start position:0%
+it will be hard to mark up your
+Solutions yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes no but you should probably tell us
+
+ align:start position:0%
+yes no but you should probably tell us
+ 
+
+ align:start position:0%
+yes no but you should probably tell us
+what you'd like us to do we would
+
+ align:start position:0%
+what you'd like us to do we would
+ 
+
+ align:start position:0%
+what you'd like us to do we would
+normally try to make our best guess so
+
+ align:start position:0%
+normally try to make our best guess so
+ 
+
+ align:start position:0%
+normally try to make our best guess so
+if you turn in everything in the paper
+
+ align:start position:0%
+if you turn in everything in the paper
+ 
+
+ align:start position:0%
+if you turn in everything in the paper
+copy we will look at your previous
+
+ align:start position:0%
+copy we will look at your previous
+ 
+
+ align:start position:0%
+copy we will look at your previous
+submissions but it would be best if you
+
+ align:start position:0%
+submissions but it would be best if you
+ 
+
+ align:start position:0%
+submissions but it would be best if you
+said some remark like this overrides the
+
+ align:start position:0%
+said some remark like this overrides the
+ 
+
+ align:start position:0%
+said some remark like this overrides the
+electronic submission or please ignore
+
+ align:start position:0%
+electronic submission or please ignore
+ 
+
+ align:start position:0%
+electronic submission or please ignore
+problems one to
+
+ align:start position:0%
+problems one to
+ 
+
+ align:start position:0%
+problems one to
+four just make sure we know we're going
+
+ align:start position:0%
+four just make sure we know we're going
+ 
+
+ align:start position:0%
+four just make sure we know we're going
+to try to do what you want us to
+
+ align:start position:0%
+to try to do what you want us to
+ 
+
+ align:start position:0%
+to try to do what you want us to
+do other issues about logistics yes so
+
+ align:start position:0%
+do other issues about logistics yes so
+ 
+
+ align:start position:0%
+do other issues about logistics yes so
+just to make sure
+
+ align:start position:0%
+just to make sure
+ 
+
+ align:start position:0%
+just to make sure
+it's we don't have to submit homework
+
+ align:start position:0%
+it's we don't have to submit homework
+ 
+
+ align:start position:0%
+it's we don't have to submit homework
+both electronically and in paper no
+
+ align:start position:0%
+both electronically and in paper no
+ 
+
+ align:start position:0%
+both electronically and in paper no
+absolutely not if you do the electronic
+
+ align:start position:0%
+absolutely not if you do the electronic
+ 
+
+ align:start position:0%
+absolutely not if you do the electronic
+route which is the preferred we like
+
+ align:start position:0%
+route which is the preferred we like
+ 
+
+ align:start position:0%
+route which is the preferred we like
+electronic because it won't get
+
+ align:start position:0%
+electronic because it won't get
+ 
+
+ align:start position:0%
+electronic because it won't get
+lost the graders will absolutely have
+
+ align:start position:0%
+lost the graders will absolutely have
+ 
+
+ align:start position:0%
+lost the graders will absolutely have
+access to it because they're all in one
+
+ align:start position:0%
+access to it because they're all in one
+ 
+
+ align:start position:0%
+access to it because they're all in one
+place we like the electronic route but
+
+ align:start position:0%
+place we like the electronic route but
+ 
+
+ align:start position:0%
+place we like the electronic route but
+if you prefer paper just make sure you
+
+ align:start position:0%
+if you prefer paper just make sure you
+ 
+
+ align:start position:0%
+if you prefer paper just make sure you
+give us paper and one or the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suffices yes did we ever subm the
+
+ align:start position:0%
+suffices yes did we ever subm the
+ 
+
+ align:start position:0%
+suffices yes did we ever subm the
+questions on paper you you don't need
+
+ align:start position:0%
+questions on paper you you don't need
+ 
+
+ align:start position:0%
+questions on paper you you don't need
+to if you submit the tutor problems
+
+ align:start position:0%
+to if you submit the tutor problems
+ 
+
+ align:start position:0%
+to if you submit the tutor problems
+online and it says you're 100% correct
+
+ align:start position:0%
+online and it says you're 100% correct
+ 
+
+ align:start position:0%
+online and it says you're 100% correct
+you're done we don't ever need to see
+
+ align:start position:0%
+you're done we don't ever need to see
+ 
+
+ align:start position:0%
+you're done we don't ever need to see
+anything else you've got full
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+credit other issues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes people are having technical problems
+
+ align:start position:0%
+yes people are having technical problems
+ 
+
+ align:start position:0%
+yes people are having technical problems
+with the tutor please tell us don't just
+
+ align:start position:0%
+with the tutor please tell us don't just
+ 
+
+ align:start position:0%
+with the tutor please tell us don't just
+feel like you have to kick out and do
+
+ align:start position:0%
+feel like you have to kick out and do
+ 
+
+ align:start position:0%
+feel like you have to kick out and do
+the paper version we're trying to we're
+
+ align:start position:0%
+the paper version we're trying to we're
+ 
+
+ align:start position:0%
+the paper version we're trying to we're
+trying to make sure that everything's in
+
+ align:start position:0%
+trying to make sure that everything's in
+ 
+
+ align:start position:0%
+trying to make sure that everything's in
+place this weekend we will try to be
+
+ align:start position:0%
+place this weekend we will try to be
+ 
+
+ align:start position:0%
+place this weekend we will try to be
+very responsive as I told you this is a
+
+ align:start position:0%
+very responsive as I told you this is a
+ 
+
+ align:start position:0%
+very responsive as I told you this is a
+brand new
+
+ align:start position:0%
+brand new
+ 
+
+ align:start position:0%
+brand new
+tutor we're very optimistic about it but
+
+ align:start position:0%
+tutor we're very optimistic about it but
+ 
+
+ align:start position:0%
+tutor we're very optimistic about it but
+we're also realistic software has bugs I
+
+ align:start position:0%
+we're also realistic software has bugs I
+ 
+
+ align:start position:0%
+we're also realistic software has bugs I
+don't tell any of my software people my
+
+ align:start position:0%
+don't tell any of my software people my
+ 
+
+ align:start position:0%
+don't tell any of my software people my
+software friends that uh3 no well well
+
+ align:start position:0%
+software friends that uh3 no well well
+ 
+
+ align:start position:0%
+software friends that uh3 no well well
+maybe I shouldn't say that software has
+
+ align:start position:0%
+maybe I shouldn't say that software has
+ 
+
+ align:start position:0%
+maybe I shouldn't say that software has
+bugs so we're trying to get rid of all
+
+ align:start position:0%
+bugs so we're trying to get rid of all
+ 
+
+ align:start position:0%
+bugs so we're trying to get rid of all
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ours
+
+ align:start position:0%
+ours
+ 
+
+ align:start position:0%
+ours
+yeah I'm
+
+ align:start position:0%
+yeah I'm
+ 
+
+ align:start position:0%
+yeah I'm
+sorry and I'm still you have to shout
+
+ align:start position:0%
+sorry and I'm still you have to shout
+ 
+
+ align:start position:0%
+sorry and I'm still you have to shout
+because my hearing is done
+
+ align:start position:0%
+because my hearing is done
+ 
+
+ align:start position:0%
+because my hearing is done
+out if you run out of submits that's bad
+
+ align:start position:0%
+out if you run out of submits that's bad
+ 
+
+ align:start position:0%
+out if you run out of submits that's bad
+but during this sort of ramp up phase
+
+ align:start position:0%
+but during this sort of ramp up phase
+ 
+
+ align:start position:0%
+but during this sort of ramp up phase
+just send us an email because the goal
+
+ align:start position:0%
+just send us an email because the goal
+ 
+
+ align:start position:0%
+just send us an email because the goal
+is not to have you um run out of submits
+
+ align:start position:0%
+is not to have you um run out of submits
+ 
+
+ align:start position:0%
+is not to have you um run out of submits
+yet
+
+ align:start position:0%
+yet
+ 
+
+ align:start position:0%
+yet
+yes so if you run out if you run out of
+
+ align:start position:0%
+yes so if you run out if you run out of
+ 
+
+ align:start position:0%
+yes so if you run out if you run out of
+submit and your last submission was an
+
+ align:start position:0%
+submit and your last submission was an
+ 
+
+ align:start position:0%
+submit and your last submission was an
+incorrect answer but you turn something
+
+ align:start position:0%
+incorrect answer but you turn something
+ 
+
+ align:start position:0%
+incorrect answer but you turn something
+paper that
+
+ align:start position:0%
+paper that
+ 
+
+ align:start position:0%
+paper that
+answer if you continue to hit submit we
+
+ align:start position:0%
+answer if you continue to hit submit we
+ 
+
+ align:start position:0%
+answer if you continue to hit submit we
+will continue to be aware of it okay
+
+ align:start position:0%
+will continue to be aware of it okay
+ 
+
+ align:start position:0%
+will continue to be aware of it okay
+it's all in the great we know everything
+
+ align:start position:0%
+it's all in the great we know everything
+ 
+
+ align:start position:0%
+it's all in the great we know everything
+you've
+
+ align:start position:0%
+you've
+ 
+
+ align:start position:0%
+you've
+done so just go ahead and hit submit
+
+ align:start position:0%
+done so just go ahead and hit submit
+ 
+
+ align:start position:0%
+done so just go ahead and hit submit
+some more
+
+ align:start position:0%
+some more
+ 
+
+ align:start position:0%
+some more
+times but you can always turn in paper
+
+ align:start position:0%
+times but you can always turn in paper
+ 
+
+ align:start position:0%
+times but you can always turn in paper
+to overwrite it or you can always send
+
+ align:start position:0%
+to overwrite it or you can always send
+ 
+
+ align:start position:0%
+to overwrite it or you can always send
+me an email and say I ran R out of
+
+ align:start position:0%
+me an email and say I ran R out of
+ 
+
+ align:start position:0%
+me an email and say I ran R out of
+submits the answer is
+
+ align:start position:0%
+submits the answer is
+ 
+
+ align:start position:0%
+submits the answer is
+blah okay we're going to try to be very
+
+ align:start position:0%
+blah okay we're going to try to be very
+ 
+
+ align:start position:0%
+blah okay we're going to try to be very
+Cooperative this is
+
+ align:start position:0%
+Cooperative this is
+ 
+
+ align:start position:0%
+Cooperative this is
+new this is supposed to be
+
+ align:start position:0%
+new this is supposed to be
+ 
+
+ align:start position:0%
+new this is supposed to be
+helpful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes that's not supposed to be on your
+
+ align:start position:0%
+yes that's not supposed to be on your
+ 
+
+ align:start position:0%
+yes that's not supposed to be on your
+website that's supposed to be on my
+
+ align:start position:0%
+website that's supposed to be on my
+ 
+
+ align:start position:0%
+website that's supposed to be on my
+website I'll have to look into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if it works use it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay other other obvious errors that
+
+ align:start position:0%
+okay other other obvious errors that
+ 
+
+ align:start position:0%
+okay other other obvious errors that
+we've
+
+ align:start position:0%
+we've
+ 
+
+ align:start position:0%
+we've
+made okay let's go on and talk
+
+ align:start position:0%
+made okay let's go on and talk
+ 
+
+ align:start position:0%
+made okay let's go on and talk
+about3 what I want to do today well so
+
+ align:start position:0%
+about3 what I want to do today well so
+ 
+
+ align:start position:0%
+about3 what I want to do today well so
+last time last time I introduced what I
+
+ align:start position:0%
+last time last time I introduced what I
+ 
+
+ align:start position:0%
+last time last time I introduced what I
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+the 63
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+abstraction which is the idea that we
+
+ align:start position:0%
+abstraction which is the idea that we
+ 
+
+ align:start position:0%
+abstraction which is the idea that we
+represent a system Whatever It
+
+ align:start position:0%
+represent a system Whatever It
+ 
+
+ align:start position:0%
+represent a system Whatever It
+Is by the way it transforms an input
+
+ align:start position:0%
+Is by the way it transforms an input
+ 
+
+ align:start position:0%
+Is by the way it transforms an input
+signal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to an output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signal the goal for today is to start to
+
+ align:start position:0%
+signal the goal for today is to start to
+ 
+
+ align:start position:0%
+signal the goal for today is to start to
+develop Machinery that takes advantage
+
+ align:start position:0%
+develop Machinery that takes advantage
+ 
+
+ align:start position:0%
+develop Machinery that takes advantage
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+representation we'll start by thinking
+
+ align:start position:0%
+representation we'll start by thinking
+ 
+
+ align:start position:0%
+representation we'll start by thinking
+about DT DT is conceptually easier than
+
+ align:start position:0%
+about DT DT is conceptually easier than
+ 
+
+ align:start position:0%
+about DT DT is conceptually easier than
+CT that's why we start there algebra is
+
+ align:start position:0%
+CT that's why we start there algebra is
+ 
+
+ align:start position:0%
+CT that's why we start there algebra is
+slightly easier than calculus that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea what we learn in DT will transfer
+
+ align:start position:0%
+idea what we learn in DT will transfer
+ 
+
+ align:start position:0%
+idea what we learn in DT will transfer
+almost verbatim into CT
+
+ align:start position:0%
+almost verbatim into CT
+ 
+
+ align:start position:0%
+almost verbatim into CT
+CTS like DT but a little harder so
+
+ align:start position:0%
+CTS like DT but a little harder so
+ 
+
+ align:start position:0%
+CTS like DT but a little harder so
+there's some extra stuff but the things
+
+ align:start position:0%
+there's some extra stuff but the things
+ 
+
+ align:start position:0%
+there's some extra stuff but the things
+we learned in DT will still be
+
+ align:start position:0%
+we learned in DT will still be
+ 
+
+ align:start position:0%
+we learned in DT will still be
+applicable in
+
+ align:start position:0%
+applicable in
+ 
+
+ align:start position:0%
+applicable in
+CT discrete time continuous
+
+ align:start position:0%
+CT discrete time continuous
+ 
+
+ align:start position:0%
+CT discrete time continuous
+time um furthermore DT is just
+
+ align:start position:0%
+time um furthermore DT is just
+ 
+
+ align:start position:0%
+time um furthermore DT is just
+important so increasingly applications
+
+ align:start position:0%
+important so increasingly applications
+ 
+
+ align:start position:0%
+important so increasingly applications
+in of this field are in discreete time
+
+ align:start position:0%
+in of this field are in discreete time
+ 
+
+ align:start position:0%
+in of this field are in discreete time
+that wasn't necessarily 220 years ago
+
+ align:start position:0%
+that wasn't necessarily 220 years ago
+ 
+
+ align:start position:0%
+that wasn't necessarily 220 years ago
+it's still the case that there's lots of
+
+ align:start position:0%
+it's still the case that there's lots of
+ 
+
+ align:start position:0%
+it's still the case that there's lots of
+applications that are intrinsically
+
+ align:start position:0%
+applications that are intrinsically
+ 
+
+ align:start position:0%
+applications that are intrinsically
+married to the physics that underly it
+
+ align:start position:0%
+married to the physics that underly it
+ 
+
+ align:start position:0%
+married to the physics that underly it
+that makes it intrinsically CT but a lot
+
+ align:start position:0%
+that makes it intrinsically CT but a lot
+ 
+
+ align:start position:0%
+that makes it intrinsically CT but a lot
+of stuff is done in DT so for a lot of
+
+ align:start position:0%
+of stuff is done in DT so for a lot of
+ 
+
+ align:start position:0%
+of stuff is done in DT so for a lot of
+reasons we're going to start with DT
+
+ align:start position:0%
+reasons we're going to start with DT
+ 
+
+ align:start position:0%
+reasons we're going to start with DT
+first and we're going to look today at
+
+ align:start position:0%
+first and we're going to look today at
+ 
+
+ align:start position:0%
+first and we're going to look today at
+several different representations of
+
+ align:start position:0%
+several different representations of
+ 
+
+ align:start position:0%
+several different representations of
+DT in particular we're going to look at
+
+ align:start position:0%
+DT in particular we're going to look at
+ 
+
+ align:start position:0%
+DT in particular we're going to look at
+difference equations and block
+
+ align:start position:0%
+difference equations and block
+ 
+
+ align:start position:0%
+difference equations and block
+diagrams and uh we're always interested
+
+ align:start position:0%
+diagrams and uh we're always interested
+ 
+
+ align:start position:0%
+diagrams and uh we're always interested
+in verbal descriptions because that's
+
+ align:start position:0%
+in verbal descriptions because that's
+ 
+
+ align:start position:0%
+in verbal descriptions because that's
+the way the real world is described to
+
+ align:start position:0%
+the way the real world is described to
+ 
+
+ align:start position:0%
+the way the real world is described to
+you so what we want to do is understand
+
+ align:start position:0%
+you so what we want to do is understand
+ 
+
+ align:start position:0%
+you so what we want to do is understand
+these understand their strengths and
+
+ align:start position:0%
+these understand their strengths and
+ 
+
+ align:start position:0%
+these understand their strengths and
+weaknesses so that we can capitalize on
+
+ align:start position:0%
+weaknesses so that we can capitalize on
+ 
+
+ align:start position:0%
+weaknesses so that we can capitalize on
+their strengths and go around their
+
+ align:start position:0%
+their strengths and go around their
+ 
+
+ align:start position:0%
+their strengths and go around their
+weaknesses that's the
+
+ align:start position:0%
+weaknesses that's the
+ 
+
+ align:start position:0%
+weaknesses that's the
+idea so the easiest possible
+
+ align:start position:0%
+idea so the easiest possible
+ 
+
+ align:start position:0%
+idea so the easiest possible
+representation is a difference equation
+
+ align:start position:0%
+representation is a difference equation
+ 
+
+ align:start position:0%
+representation is a difference equation
+difference equations are good because
+
+ align:start position:0%
+difference equations are good because
+ 
+
+ align:start position:0%
+difference equations are good because
+they're absolutely
+
+ align:start position:0%
+they're absolutely
+ 
+
+ align:start position:0%
+they're absolutely
+precise and they are the absolutely most
+
+ align:start position:0%
+precise and they are the absolutely most
+ 
+
+ align:start position:0%
+precise and they are the absolutely most
+concise representation we will
+
+ align:start position:0%
+concise representation we will
+ 
+
+ align:start position:0%
+concise representation we will
+have precise and concise those are good
+
+ align:start position:0%
+have precise and concise those are good
+ 
+
+ align:start position:0%
+have precise and concise those are good
+features so here's an example what if my
+
+ align:start position:0%
+features so here's an example what if my
+ 
+
+ align:start position:0%
+features so here's an example what if my
+output y
+
+ align:start position:0%
+output y
+ 
+
+ align:start position:0%
+output y
+where my input x - x n minus
+
+ align:start position:0%
+where my input x - x n minus
+ 
+
+ align:start position:0%
+where my input x - x n minus
+one let's say that the input is a unit
+
+ align:start position:0%
+one let's say that the input is a unit
+ 
+
+ align:start position:0%
+one let's say that the input is a unit
+sample we will often ask for the unit
+
+ align:start position:0%
+sample we will often ask for the unit
+ 
+
+ align:start position:0%
+sample we will often ask for the unit
+sample response the unit sample signal
+
+ align:start position:0%
+sample response the unit sample signal
+ 
+
+ align:start position:0%
+sample response the unit sample signal
+is the most simple nontrivial signal
+
+ align:start position:0%
+is the most simple nontrivial signal
+ 
+
+ align:start position:0%
+is the most simple nontrivial signal
+that we can have it is zero almost
+
+ align:start position:0%
+that we can have it is zero almost
+ 
+
+ align:start position:0%
+that we can have it is zero almost
+everywhere and the only place it's not
+
+ align:start position:0%
+everywhere and the only place it's not
+ 
+
+ align:start position:0%
+everywhere and the only place it's not
+zero is at zero and when it's not zero
+
+ align:start position:0%
+zero is at zero and when it's not zero
+ 
+
+ align:start position:0%
+zero is at zero and when it's not zero
+it's one so that's sort of the easiest
+
+ align:start position:0%
+it's one so that's sort of the easiest
+ 
+
+ align:start position:0%
+it's one so that's sort of the easiest
+thing we can imagine so what we're going
+
+ align:start position:0%
+thing we can imagine so what we're going
+ 
+
+ align:start position:0%
+thing we can imagine so what we're going
+to want to do then is think about what
+
+ align:start position:0%
+to want to do then is think about what
+ 
+
+ align:start position:0%
+to want to do then is think about what
+happens if we put this signal into that
+
+ align:start position:0%
+happens if we put this signal into that
+ 
+
+ align:start position:0%
+happens if we put this signal into that
+system okay that's completely trivial
+
+ align:start position:0%
+system okay that's completely trivial
+ 
+
+ align:start position:0%
+system okay that's completely trivial
+you've all done this a gazillion times
+
+ align:start position:0%
+you've all done this a gazillion times
+ 
+
+ align:start position:0%
+you've all done this a gazillion times
+before and now is your chance to prove
+
+ align:start position:0%
+before and now is your chance to prove
+ 
+
+ align:start position:0%
+before and now is your chance to prove
+it how many of those statements are true
+
+ align:start position:0%
+it how many of those statements are true
+ 
+
+ align:start position:0%
+it how many of those statements are true
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+output of this system when that's the
+
+ align:start position:0%
+output of this system when that's the
+ 
+
+ align:start position:0%
+output of this system when that's the
+input talk to your neighbor you've got
+
+ align:start position:0%
+input talk to your neighbor you've got
+ 
+
+ align:start position:0%
+input talk to your neighbor you've got
+15 seconds this is too
+
+ align:start position:0%
+15 seconds this is too
+ 
+
+ align:start position:0%
+15 seconds this is too
+simple figure out how many of those
+
+ align:start position:0%
+simple figure out how many of those
+ 
+
+ align:start position:0%
+simple figure out how many of those
+statements are true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're allowed to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you're either all bored out of your
+
+ align:start position:0%
+okay you're either all bored out of your
+ 
+
+ align:start position:0%
+okay you're either all bored out of your
+minds or paralyzed with fear I can't
+
+ align:start position:0%
+minds or paralyzed with fear I can't
+ 
+
+ align:start position:0%
+minds or paralyzed with fear I can't
+tell so everybody raise your hand how
+
+ align:start position:0%
+tell so everybody raise your hand how
+ 
+
+ align:start position:0%
+tell so everybody raise your hand how
+many the statements are
+
+ align:start position:0%
+many the statements are
+ 
+
+ align:start position:0%
+many the statements are
+true more hands more hands come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on okay less than half P half
+
+ align:start position:0%
+on okay less than half P half
+ 
+
+ align:start position:0%
+on okay less than half P half
+correct so um I'll just assume that you
+
+ align:start position:0%
+correct so um I'll just assume that you
+ 
+
+ align:start position:0%
+correct so um I'll just assume that you
+ran out of time and I'll go
+
+ align:start position:0%
+ran out of time and I'll go
+ 
+
+ align:start position:0%
+ran out of time and I'll go
+on so this is Trivial right what do I do
+
+ align:start position:0%
+on so this is Trivial right what do I do
+ 
+
+ align:start position:0%
+on so this is Trivial right what do I do
+how do I figure this out yeah step by
+
+ align:start position:0%
+how do I figure this out yeah step by
+ 
+
+ align:start position:0%
+how do I figure this out yeah step by
+step of course yes so if I think about
+
+ align:start position:0%
+step of course yes so if I think about
+ 
+
+ align:start position:0%
+step of course yes so if I think about
+applying this equation to that
+
+ align:start position:0%
+applying this equation to that
+ 
+
+ align:start position:0%
+applying this equation to that
+input then I can think about just
+
+ align:start position:0%
+input then I can think about just
+ 
+
+ align:start position:0%
+input then I can think about just
+substituting n = minus1 n = 0 n = 1 Nal
+
+ align:start position:0%
+substituting n = minus1 n = 0 n = 1 Nal
+ 
+
+ align:start position:0%
+substituting n = minus1 n = 0 n = 1 Nal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Etc and you can sort of see that I'm
+
+ align:start position:0%
+Etc and you can sort of see that I'm
+ 
+
+ align:start position:0%
+Etc and you can sort of see that I'm
+only looking at the input at two
+
+ align:start position:0%
+only looking at the input at two
+ 
+
+ align:start position:0%
+only looking at the input at two
+instance of time so there's a a finite
+
+ align:start position:0%
+instance of time so there's a a finite
+ 
+
+ align:start position:0%
+instance of time so there's a a finite
+range over which the input there's a
+
+ align:start position:0%
+range over which the input there's a
+ 
+
+ align:start position:0%
+range over which the input there's a
+finite range of inputs that can
+
+ align:start position:0%
+finite range of inputs that can
+ 
+
+ align:start position:0%
+finite range of inputs that can
+contribute to the output and in
+
+ align:start position:0%
+contribute to the output and in
+ 
+
+ align:start position:0%
+contribute to the output and in
+particular if I were to say if I were to
+
+ align:start position:0%
+particular if I were to say if I were to
+ 
+
+ align:start position:0%
+particular if I were to say if I were to
+substitute n equals minus1 I would see
+
+ align:start position:0%
+substitute n equals minus1 I would see
+ 
+
+ align:start position:0%
+substitute n equals minus1 I would see
+that the output at time y minus one
+
+ align:start position:0%
+that the output at time y minus one
+ 
+
+ align:start position:0%
+that the output at time y minus one
+depends on inputs before the Delta
+
+ align:start position:0%
+depends on inputs before the Delta
+ 
+
+ align:start position:0%
+depends on inputs before the Delta
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+started so therefore the answer is
+
+ align:start position:0%
+started so therefore the answer is
+ 
+
+ align:start position:0%
+started so therefore the answer is
+zero if I look at the output at time one
+
+ align:start position:0%
+zero if I look at the output at time one
+ 
+
+ align:start position:0%
+zero if I look at the output at time one
+the time one the time zero sorry the
+
+ align:start position:0%
+the time one the time zero sorry the
+ 
+
+ align:start position:0%
+the time one the time zero sorry the
+time zero input is one the time minus
+
+ align:start position:0%
+time zero input is one the time minus
+ 
+
+ align:start position:0%
+time zero input is one the time minus
+one input is zero so my total answer is
+
+ align:start position:0%
+one input is zero so my total answer is
+ 
+
+ align:start position:0%
+one input is zero so my total answer is
+one Etc right this is very
+
+ align:start position:0%
+one Etc right this is very
+ 
+
+ align:start position:0%
+one Etc right this is very
+straightforward it's just plug and
+
+ align:start position:0%
+straightforward it's just plug and
+ 
+
+ align:start position:0%
+straightforward it's just plug and
+chug and what you see is a
+
+ align:start position:0%
+chug and what you see is a
+ 
+
+ align:start position:0%
+chug and what you see is a
+waveform from which it's pretty easy to
+
+ align:start position:0%
+waveform from which it's pretty easy to
+ 
+
+ align:start position:0%
+waveform from which it's pretty easy to
+infer that Y2 was bigger than y1 right
+
+ align:start position:0%
+infer that Y2 was bigger than y1 right
+ 
+
+ align:start position:0%
+infer that Y2 was bigger than y1 right
+so Y2 was bigger than y1 bigger in a
+
+ align:start position:0%
+so Y2 was bigger than y1 bigger in a
+ 
+
+ align:start position:0%
+so Y2 was bigger than y1 bigger in a
+math
+
+ align:start position:0%
+math
+ 
+
+ align:start position:0%
+math
+sense and Y3 is bigger than y 2 not
+
+ align:start position:0%
+sense and Y3 is bigger than y 2 not
+ 
+
+ align:start position:0%
+sense and Y3 is bigger than y 2 not
+right Y3 and Y2 are
+
+ align:start position:0%
+right Y3 and Y2 are
+ 
+
+ align:start position:0%
+right Y3 and Y2 are
+identical so that's not
+
+ align:start position:0%
+identical so that's not
+ 
+
+ align:start position:0%
+identical so that's not
+true Y 2 and in fact everything above
+
+ align:start position:0%
+true Y 2 and in fact everything above
+ 
+
+ align:start position:0%
+true Y 2 and in fact everything above
+that is zero that's
+
+ align:start position:0%
+that is zero that's
+ 
+
+ align:start position:0%
+that is zero that's
+true and if you do a little bit of
+
+ align:start position:0%
+true and if you do a little bit of
+ 
+
+ align:start position:0%
+true and if you do a little bit of
+manipulation you can show that this must
+
+ align:start position:0%
+manipulation you can show that this must
+ 
+
+ align:start position:0%
+manipulation you can show that this must
+have also been TR everyone sort of see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I'm assuming you've seen all this
+
+ align:start position:0%
+that I'm assuming you've seen all this
+ 
+
+ align:start position:0%
+that I'm assuming you've seen all this
+sort of stuff before so I'm going to go
+
+ align:start position:0%
+sort of stuff before so I'm going to go
+ 
+
+ align:start position:0%
+sort of stuff before so I'm going to go
+through it kind of quickly but the
+
+ align:start position:0%
+through it kind of quickly but the
+ 
+
+ align:start position:0%
+through it kind of quickly but the
+answer was four four of those statement
+
+ align:start position:0%
+answer was four four of those statement
+ 
+
+ align:start position:0%
+answer was four four of those statement
+ments were true it was just a refresher
+
+ align:start position:0%
+ments were true it was just a refresher
+ 
+
+ align:start position:0%
+ments were true it was just a refresher
+on how to think about difference
+
+ align:start position:0%
+on how to think about difference
+ 
+
+ align:start position:0%
+on how to think about difference
+equations by comparison I want to
+
+ align:start position:0%
+equations by comparison I want to
+ 
+
+ align:start position:0%
+equations by comparison I want to
+contrast a difference equation on a
+
+ align:start position:0%
+contrast a difference equation on a
+ 
+
+ align:start position:0%
+contrast a difference equation on a
+block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram this is the same system but
+
+ align:start position:0%
+diagram this is the same system but
+ 
+
+ align:start position:0%
+diagram this is the same system but
+represented
+
+ align:start position:0%
+represented
+ 
+
+ align:start position:0%
+represented
+graphically why would you want to do
+
+ align:start position:0%
+graphically why would you want to do
+ 
+
+ align:start position:0%
+graphically why would you want to do
+that okay well there's advantages and
+
+ align:start position:0%
+that okay well there's advantages and
+ 
+
+ align:start position:0%
+that okay well there's advantages and
+disadvantages this is a direct way of
+
+ align:start position:0%
+disadvantages this is a direct way of
+ 
+
+ align:start position:0%
+disadvantages this is a direct way of
+expressing the system if you wanted to
+
+ align:start position:0%
+expressing the system if you wanted to
+ 
+
+ align:start position:0%
+expressing the system if you wanted to
+implement it in Hardware so you can
+
+ align:start position:0%
+implement it in Hardware so you can
+ 
+
+ align:start position:0%
+implement it in Hardware so you can
+imagine building a delay box building an
+
+ align:start position:0%
+imagine building a delay box building an
+ 
+
+ align:start position:0%
+imagine building a delay box building an
+Adder building an
+
+ align:start position:0%
+Adder building an
+ 
+
+ align:start position:0%
+Adder building an
+inverter and constructing a piece of
+
+ align:start position:0%
+inverter and constructing a piece of
+ 
+
+ align:start position:0%
+inverter and constructing a piece of
+Hardware that does the computation so
+
+ align:start position:0%
+Hardware that does the computation so
+ 
+
+ align:start position:0%
+Hardware that does the computation so
+this is more like a hardware realization
+
+ align:start position:0%
+this is more like a hardware realization
+ 
+
+ align:start position:0%
+this is more like a hardware realization
+it's not as
+
+ align:start position:0%
+it's not as
+ 
+
+ align:start position:0%
+it's not as
+compact as the difference
+
+ align:start position:0%
+compact as the difference
+ 
+
+ align:start position:0%
+compact as the difference
+equation it has another idiosyncrasy
+
+ align:start position:0%
+equation it has another idiosyncrasy
+ 
+
+ align:start position:0%
+equation it has another idiosyncrasy
+that we have to have the notion of
+
+ align:start position:0%
+that we have to have the notion of
+ 
+
+ align:start position:0%
+that we have to have the notion of
+rest when we say the system starts at
+
+ align:start position:0%
+rest when we say the system starts at
+ 
+
+ align:start position:0%
+rest when we say the system starts at
+rest which we will say all the time and
+
+ align:start position:0%
+rest which we will say all the time and
+ 
+
+ align:start position:0%
+rest which we will say all the time and
+in fact you can always assume that
+
+ align:start position:0%
+in fact you can always assume that
+ 
+
+ align:start position:0%
+in fact you can always assume that
+unless we tell you something to the
+
+ align:start position:0%
+unless we tell you something to the
+ 
+
+ align:start position:0%
+unless we tell you something to the
+contrary when we say a system is at rest
+
+ align:start position:0%
+contrary when we say a system is at rest
+ 
+
+ align:start position:0%
+contrary when we say a system is at rest
+what we mean is that all the delays in
+
+ align:start position:0%
+what we mean is that all the delays in
+ 
+
+ align:start position:0%
+what we mean is that all the delays in
+the system start out being
+
+ align:start position:0%
+the system start out being
+ 
+
+ align:start position:0%
+the system start out being
+zero so at rest means that this signal
+
+ align:start position:0%
+zero so at rest means that this signal
+ 
+
+ align:start position:0%
+zero so at rest means that this signal
+starts out at zero because that's the
+
+ align:start position:0%
+starts out at zero because that's the
+ 
+
+ align:start position:0%
+starts out at zero because that's the
+only there's only one delay in the
+
+ align:start position:0%
+only there's only one delay in the
+ 
+
+ align:start position:0%
+only there's only one delay in the
+system its output is initially zero so
+
+ align:start position:0%
+system its output is initially zero so
+ 
+
+ align:start position:0%
+system its output is initially zero so
+now we think about the input chugging
+
+ align:start position:0%
+now we think about the input chugging
+ 
+
+ align:start position:0%
+now we think about the input chugging
+along so the input starts out being one
+
+ align:start position:0%
+along so the input starts out being one
+ 
+
+ align:start position:0%
+along so the input starts out being one
+that means the inverted input is minus
+
+ align:start position:0%
+that means the inverted input is minus
+ 
+
+ align:start position:0%
+that means the inverted input is minus
+one that doesn't profit propagate
+
+ align:start position:0%
+one that doesn't profit propagate
+ 
+
+ align:start position:0%
+one that doesn't profit propagate
+through the delay because we're still at
+
+ align:start position:0%
+through the delay because we're still at
+ 
+
+ align:start position:0%
+through the delay because we're still at
+the instant when the input just became
+
+ align:start position:0%
+the instant when the input just became
+ 
+
+ align:start position:0%
+the instant when the input just became
+one for the first
+
+ align:start position:0%
+one for the first
+ 
+
+ align:start position:0%
+one for the first
+time so this one goes through and adds
+
+ align:start position:0%
+time so this one goes through and adds
+ 
+
+ align:start position:0%
+time so this one goes through and adds
+to this zero to give us one and our
+
+ align:start position:0%
+to this zero to give us one and our
+ 
+
+ align:start position:0%
+to this zero to give us one and our
+answer is
+
+ align:start position:0%
+answer is
+ 
+
+ align:start position:0%
+answer is
+one now the clock goes
+
+ align:start position:0%
+one now the clock goes
+ 
+
+ align:start position:0%
+one now the clock goes
+kachunk and at that instant the input
+
+ align:start position:0%
+kachunk and at that instant the input
+ 
+
+ align:start position:0%
+kachunk and at that instant the input
+changes from one to zero because that's
+
+ align:start position:0%
+changes from one to zero because that's
+ 
+
+ align:start position:0%
+changes from one to zero because that's
+what happens
+
+ align:start position:0%
+what happens
+ 
+
+ align:start position:0%
+what happens
+here and at precisely the same instant
+
+ align:start position:0%
+here and at precisely the same instant
+ 
+
+ align:start position:0%
+here and at precisely the same instant
+the delay signal went from zero which it
+
+ align:start position:0%
+the delay signal went from zero which it
+ 
+
+ align:start position:0%
+the delay signal went from zero which it
+was because it started at rest to minus
+
+ align:start position:0%
+was because it started at rest to minus
+ 
+
+ align:start position:0%
+was because it started at rest to minus
+one which was its input just before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kachunk
+
+ align:start position:0%
+kachunk
+ 
+
+ align:start position:0%
+kachunk
+then after the signal settle down this
+
+ align:start position:0%
+then after the signal settle down this
+ 
+
+ align:start position:0%
+then after the signal settle down this
+becomes zero and this becomes minus one
+
+ align:start position:0%
+becomes zero and this becomes minus one
+ 
+
+ align:start position:0%
+becomes zero and this becomes minus one
+and that's our
+
+ align:start position:0%
+and that's our
+ 
+
+ align:start position:0%
+and that's our
+output then U again
+
+ align:start position:0%
+output then U again
+ 
+
+ align:start position:0%
+output then U again
+kachunk the input doesn't change because
+
+ align:start position:0%
+kachunk the input doesn't change because
+ 
+
+ align:start position:0%
+kachunk the input doesn't change because
+it was Zero it's still zero but the
+
+ align:start position:0%
+it was Zero it's still zero but the
+ 
+
+ align:start position:0%
+it was Zero it's still zero but the
+delay now goes from minus one the output
+
+ align:start position:0%
+delay now goes from minus one the output
+ 
+
+ align:start position:0%
+delay now goes from minus one the output
+of the delay goes from minus one to
+
+ align:start position:0%
+of the delay goes from minus one to
+ 
+
+ align:start position:0%
+of the delay goes from minus one to
+zero and after things settle down we get
+
+ align:start position:0%
+zero and after things settle down we get
+ 
+
+ align:start position:0%
+zero and after things settle down we get
+uh zero at the
+
+ align:start position:0%
+uh zero at the
+ 
+
+ align:start position:0%
+uh zero at the
+output and that is a state that
+
+ align:start position:0%
+output and that is a state that
+ 
+
+ align:start position:0%
+output and that is a state that
+persists okay so we have these two
+
+ align:start position:0%
+persists okay so we have these two
+ 
+
+ align:start position:0%
+persists okay so we have these two
+different representations we have
+
+ align:start position:0%
+different representations we have
+ 
+
+ align:start position:0%
+different representations we have
+different equations of block diagrams so
+
+ align:start position:0%
+different equations of block diagrams so
+ 
+
+ align:start position:0%
+different equations of block diagrams so
+here's a question how are they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different in particular I've told you
+
+ align:start position:0%
+different in particular I've told you
+ 
+
+ align:start position:0%
+different in particular I've told you
+that difference equations are concise
+
+ align:start position:0%
+that difference equations are concise
+ 
+
+ align:start position:0%
+that difference equations are concise
+and precise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are there advantages to a block
+
+ align:start position:0%
+are there advantages to a block
+ 
+
+ align:start position:0%
+are there advantages to a block
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+
+ align:start position:0%
+diagram talk to your neighbor come up
+ 
+
+ align:start position:0%
+diagram talk to your neighbor come up
+with a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypothesis what's good about a block
+
+ align:start position:0%
+hypothesis what's good about a block
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+
+ align:start position:0%
+hypothesis what's good about a block
+diagram anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so can anybody think of something good
+
+ align:start position:0%
+so can anybody think of something good
+ 
+
+ align:start position:0%
+so can anybody think of something good
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram yeah you change a system you can
+
+ align:start position:0%
+diagram yeah you change a system you can
+ 
+
+ align:start position:0%
+diagram yeah you change a system you can
+systems andas to
+
+ align:start position:0%
+systems andas to
+ 
+
+ align:start position:0%
+systems andas to
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+
+ align:start position:0%
+so it's easy to see so that could be
+ 
+
+ align:start position:0%
+so it's easy to see so that could be
+something to do with a graphic
+
+ align:start position:0%
+something to do with a graphic
+ 
+
+ align:start position:0%
+something to do with a graphic
+representation it but it could be deeper
+
+ align:start position:0%
+representation it but it could be deeper
+ 
+
+ align:start position:0%
+representation it but it could be deeper
+too can somebody say a deeper reason why
+
+ align:start position:0%
+too can somebody say a deeper reason why
+ 
+
+ align:start position:0%
+too can somebody say a deeper reason why
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+
+ align:start position:0%
+it might be easier to see so that might
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+be a very good that might be a deep
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+
+ align:start position:0%
+be a very good that might be a deep
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+
+ align:start position:0%
+comment too why might it be easier to
+ 
+
+ align:start position:0%
+comment too why might it be easier to
+use the block diagram than it is to use
+
+ align:start position:0%
+use the block diagram than it is to use
+ 
+
+ align:start position:0%
+use the block diagram than it is to use
+the difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+yeah steps how so so there's um like
+
+ align:start position:0%
+yeah steps how so so there's um like
+ 
+
+ align:start position:0%
+yeah steps how so so there's um like
+there's a delay and then there's the
+
+ align:start position:0%
+there's a delay and then there's the
+ 
+
+ align:start position:0%
+there's a delay and then there's the
+feed so it's like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allence so that's kind of right I'm
+
+ align:start position:0%
+allence so that's kind of right I'm
+ 
+
+ align:start position:0%
+allence so that's kind of right I'm
+wondering if you can say so this is kind
+
+ align:start position:0%
+wondering if you can say so this is kind
+ 
+
+ align:start position:0%
+wondering if you can say so this is kind
+of I mean you just do this right you do
+
+ align:start position:0%
+of I mean you just do this right you do
+ 
+
+ align:start position:0%
+of I mean you just do this right you do
+this and then you do that what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difference there's something very
+
+ align:start position:0%
+difference there's something very
+ 
+
+ align:start position:0%
+difference there's something very
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+
+ align:start position:0%
+different about those two
+ 
+
+ align:start position:0%
+different about those two
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+information in the bottom than there is
+ 
+
+ align:start position:0%
+information in the bottom than there is
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+top can somebody tell me the information
+
+ align:start position:0%
+top can somebody tell me the information
+ 
+
+ align:start position:0%
+top can somebody tell me the information
+that's available in the bottom that's
+
+ align:start position:0%
+that's available in the bottom that's
+ 
+
+ align:start position:0%
+that's available in the bottom that's
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+
+ align:start position:0%
+not available in the top yes it do when
+ 
+
+ align:start position:0%
+not available in the top yes it do when
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+
+ align:start position:0%
+you're actually assembling circuits it
+ 
+
+ align:start position:0%
+you're actually assembling circuits it
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+
+ align:start position:0%
+becomes a lot easier to use just the
+ 
+
+ align:start position:0%
+becomes a lot easier to use just the
+graphical representation you know
+
+ align:start position:0%
+graphical representation you know
+ 
+
+ align:start position:0%
+graphical representation you know
+circuit graphical but can but is there
+
+ align:start position:0%
+circuit graphical but can but is there
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+
+ align:start position:0%
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+additional information here that wasn't
+
+ align:start position:0%
+additional information here that wasn't
+ 
+
+ align:start position:0%
+additional information here that wasn't
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+
+ align:start position:0%
+available
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+
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+available
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+ align:start position:0%
+there
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+
+ align:start position:0%
+there
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+
+ align:start position:0%
+yes number of signal path signal paths
+ 
+
+ align:start position:0%
+yes number of signal path signal paths
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes well that sort of goes with
+
+ align:start position:0%
+yes well that sort of goes with
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+
+ align:start position:0%
+yes well that sort of goes with
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes it is easier but there's a very
+
+ align:start position:0%
+yes it is easier but there's a very
+ 
+
+ align:start position:0%
+yes it is easier but there's a very
+precise reason why it's easier there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arrows the arrows tell you what to do
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+arrows the arrows tell you what to do
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+
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+
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+next right so the thing that's different
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+
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+
+ align:start position:0%
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+
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+
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+
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+
+ align:start position:0%
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+ align:start position:0%
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+
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+ align:start position:0%
+declarative it tells you a statement of
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+
+ align:start position:0%
+declarative it tells you a statement of
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+
+ align:start position:0%
+fact not necessarily what you can do
+ 
+
+ align:start position:0%
+fact not necessarily what you can do
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+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+it the block diagram is
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+it the block diagram is
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+
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+
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+
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+
+ align:start position:0%
+and those are very different so the
+ 
+
+ align:start position:0%
+and those are very different so the
+difference equation is concise precise
+
+ align:start position:0%
+difference equation is concise precise
+ 
+
+ align:start position:0%
+difference equation is concise precise
+and declarative the block diagram is
+
+ align:start position:0%
+and declarative the block diagram is
+ 
+
+ align:start position:0%
+and declarative the block diagram is
+imperative do this do this do this it
+
+ align:start position:0%
+imperative do this do this do this it
+ 
+
+ align:start position:0%
+imperative do this do this do this it
+shows you the signal flow path there's
+
+ align:start position:0%
+shows you the signal flow path there's
+ 
+
+ align:start position:0%
+shows you the signal flow path there's
+no question about who causes what right
+
+ align:start position:0%
+no question about who causes what right
+ 
+
+ align:start position:0%
+no question about who causes what right
+in this we could be Computing X from y
+
+ align:start position:0%
+in this we could be Computing X from y
+ 
+
+ align:start position:0%
+in this we could be Computing X from y
+or Y from X there's no indication other
+
+ align:start position:0%
+or Y from X there's no indication other
+ 
+
+ align:start position:0%
+or Y from X there's no indication other
+than some convention someplace that the
+
+ align:start position:0%
+than some convention someplace that the
+ 
+
+ align:start position:0%
+than some convention someplace that the
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+
+ align:start position:0%
+x is the imput but do that make
+ 
+
+ align:start position:0%
+x is the imput but do that make
+sense okay so uh there's a very big
+
+ align:start position:0%
+sense okay so uh there's a very big
+ 
+
+ align:start position:0%
+sense okay so uh there's a very big
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+
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+
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+
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+what is one step another step is lumping
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+
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+
+ align:start position:0%
+things in the same sense that we lump
+ 
+
+ align:start position:0%
+things in the same sense that we lump
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+
+ align:start position:0%
+the coordinates of a three- space Point
+ 
+
+ align:start position:0%
+the coordinates of a three- space Point
+into a single thing called a point or in
+
+ align:start position:0%
+into a single thing called a point or in
+ 
+
+ align:start position:0%
+into a single thing called a point or in
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+the same way we make a vector in linear
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+
+ align:start position:0%
+the same way we make a vector in linear
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+ align:start position:0%
+algebra the idea is going to be that
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+we're going to want to think about whole
+ 
+
+ align:start position:0%
+we're going to want to think about whole
+signals at a time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by and the notation that we will use
+
+ align:start position:0%
+so by and the notation that we will use
+ 
+
+ align:start position:0%
+so by and the notation that we will use
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+
+ align:start position:0%
+we will think about uh how this will be
+ 
+
+ align:start position:0%
+we will think about uh how this will be
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+ align:start position:0%
+the X
+ 
+
+ align:start position:0%
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+
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+
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+
+ align:start position:0%
+signals rather than operations on
+samples okay so I'm trying to to develop
+
+ align:start position:0%
+samples okay so I'm trying to to develop
+ 
+
+ align:start position:0%
+samples okay so I'm trying to to develop
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+
+ align:start position:0%
+a level of abstraction that help helps
+ 
+
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+a level of abstraction that help helps
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+
+ align:start position:0%
+us predict the way systems will behave
+ 
+
+ align:start position:0%
+us predict the way systems will behave
+so the next level of abstraction I want
+
+ align:start position:0%
+so the next level of abstraction I want
+ 
+
+ align:start position:0%
+so the next level of abstraction I want
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+
+ align:start position:0%
+to think about is thinking about whole
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+signals at
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+
+ align:start position:0%
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+ align:start position:0%
+once so if we take this signal idea we
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+
+ align:start position:0%
+once so if we take this signal idea we
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+would say there's an X signal it gets
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+inverted
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+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+delay box to give us a delayed inverted
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+
+ align:start position:0%
+delay box to give us a delayed inverted
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+ align:start position:0%
+signal the delayed inverted signal gets
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+
+ align:start position:0%
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+ align:start position:0%
+added to the original signal and that
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+
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+
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+
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+ align:start position:0%
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+
+ align:start position:0%
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+explicit about that we'll develop a
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+
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+
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+r the right shift
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+
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+
+ align:start position:0%
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+ align:start position:0%
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+
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+whole input signal not the N sample the
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+
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+
+ align:start position:0%
+whole thing
+ 
+
+ align:start position:0%
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+
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+if x is a signal we can operate it on it
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+
+ align:start position:0%
+if x is a signal we can operate it on it
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+
+ align:start position:0%
+by the r operator we can apply r the
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+
+ align:start position:0%
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+ align:start position:0%
+right shift operator to the signal X and
+ 
+
+ align:start position:0%
+right shift operator to the signal X and
+generate a whole new signal which I'll
+
+ align:start position:0%
+generate a whole new signal which I'll
+ 
+
+ align:start position:0%
+generate a whole new signal which I'll
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+Y which will be a shifted version of the
+
+ align:start position:0%
+Y which will be a shifted version of the
+ 
+
+ align:start position:0%
+Y which will be a shifted version of the
+X signal okay you all got
+
+ align:start position:0%
+X signal okay you all got
+ 
+
+ align:start position:0%
+X signal okay you all got
+that and that leads us then to a concise
+
+ align:start position:0%
+that and that leads us then to a concise
+ 
+
+ align:start position:0%
+that and that leads us then to a concise
+representation similar to the difference
+
+ align:start position:0%
+representation similar to the difference
+ 
+
+ align:start position:0%
+representation similar to the difference
+equation but that has the features of
+
+ align:start position:0%
+equation but that has the features of
+ 
+
+ align:start position:0%
+equation but that has the features of
+the block diagram because it's
+
+ align:start position:0%
+the block diagram because it's
+ 
+
+ align:start position:0%
+the block diagram because it's
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+
+ align:start position:0%
+imperative R operating on X tells me
+ 
+
+ align:start position:0%
+imperative R operating on X tells me
+start with X and apply R to it there's a
+
+ align:start position:0%
+start with X and apply R to it there's a
+ 
+
+ align:start position:0%
+start with X and apply R to it there's a
+direction R applied to X is imperative
+
+ align:start position:0%
+direction R applied to X is imperative
+ 
+
+ align:start position:0%
+direction R applied to X is imperative
+it tells me what to do so this is a way
+
+ align:start position:0%
+it tells me what to do so this is a way
+ 
+
+ align:start position:0%
+it tells me what to do so this is a way
+that I can uh make a notation that is as
+
+ align:start position:0%
+that I can uh make a notation that is as
+ 
+
+ align:start position:0%
+that I can uh make a notation that is as
+concise as difference equations but has
+
+ align:start position:0%
+concise as difference equations but has
+ 
+
+ align:start position:0%
+concise as difference equations but has
+the same imperative feature as a block
+
+ align:start position:0%
+the same imperative feature as a block
+ 
+
+ align:start position:0%
+the same imperative feature as a block
+diagram so it's an improved not in that
+
+ align:start position:0%
+diagram so it's an improved not in that
+ 
+
+ align:start position:0%
+diagram so it's an improved not in that
+sense okay make sure that you know what
+
+ align:start position:0%
+sense okay make sure that you know what
+ 
+
+ align:start position:0%
+sense okay make sure that you know what
+it means if I said that Y is rx how many
+
+ align:start position:0%
+it means if I said that Y is rx how many
+ 
+
+ align:start position:0%
+it means if I said that Y is rx how many
+of the following is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true now you have to redeem yourself
+
+ align:start position:0%
+true now you have to redeem yourself
+ 
+
+ align:start position:0%
+true now you have to redeem yourself
+right you less than 50% right so now I
+
+ align:start position:0%
+right you less than 50% right so now I
+ 
+
+ align:start position:0%
+right you less than 50% right so now I
+want 90%
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right oh excuse me not how many which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay everybody raise your hands come
+
+ align:start position:0%
+okay everybody raise your hands come
+ 
+
+ align:start position:0%
+okay everybody raise your hands come
+on this is redemption time ah wonderful
+
+ align:start position:0%
+on this is redemption time ah wonderful
+ 
+
+ align:start position:0%
+on this is redemption time ah wonderful
+you're redeemed so you're about 100%
+
+ align:start position:0%
+you're redeemed so you're about 100%
+ 
+
+ align:start position:0%
+you're redeemed so you're about 100%
+correct um so it to think about that one
+
+ align:start position:0%
+correct um so it to think about that one
+ 
+
+ align:start position:0%
+correct um so it to think about that one
+easy way to think about it is by example
+
+ align:start position:0%
+easy way to think about it is by example
+ 
+
+ align:start position:0%
+easy way to think about it is by example
+examples can't prove that something's
+
+ align:start position:0%
+examples can't prove that something's
+ 
+
+ align:start position:0%
+examples can't prove that something's
+true but they can quickly prove that
+
+ align:start position:0%
+true but they can quickly prove that
+ 
+
+ align:start position:0%
+true but they can quickly prove that
+something's
+
+ align:start position:0%
+something's
+ 
+
+ align:start position:0%
+something's
+false so if you think about the simplest
+
+ align:start position:0%
+false so if you think about the simplest
+ 
+
+ align:start position:0%
+false so if you think about the simplest
+possible signal say you had a unit
+
+ align:start position:0%
+possible signal say you had a unit
+ 
+
+ align:start position:0%
+possible signal say you had a unit
+sample if you applied R to that it would
+
+ align:start position:0%
+sample if you applied R to that it would
+ 
+
+ align:start position:0%
+sample if you applied R to that it would
+shift it to the
+
+ align:start position:0%
+shift it to the
+ 
+
+ align:start position:0%
+shift it to the
+right if it shifts it to the right it's
+
+ align:start position:0%
+right if it shifts it to the right it's
+ 
+
+ align:start position:0%
+right if it shifts it to the right it's
+pretty clear that Y at time one is the
+
+ align:start position:0%
+pretty clear that Y at time one is the
+ 
+
+ align:start position:0%
+pretty clear that Y at time one is the
+same as X at time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and that's a feature
+
+ align:start position:0%
+zero and that's a feature
+ 
+
+ align:start position:0%
+zero and that's a feature
+of this equation and none of the
+
+ align:start position:0%
+of this equation and none of the
+ 
+
+ align:start position:0%
+of this equation and none of the
+others so that proves the others are
+
+ align:start position:0%
+others so that proves the others are
+ 
+
+ align:start position:0%
+others so that proves the others are
+wrong and if you think about a little
+
+ align:start position:0%
+wrong and if you think about a little
+ 
+
+ align:start position:0%
+wrong and if you think about a little
+bit you can generalize that argument to
+
+ align:start position:0%
+bit you can generalize that argument to
+ 
+
+ align:start position:0%
+bit you can generalize that argument to
+prove that the the second one is
+
+ align:start position:0%
+prove that the the second one is
+ 
+
+ align:start position:0%
+prove that the the second one is
+actually true uh for all the cases
+
+ align:start position:0%
+actually true uh for all the cases
+ 
+
+ align:start position:0%
+actually true uh for all the cases
+okay so the idea then is that we want to
+
+ align:start position:0%
+okay so the idea then is that we want to
+ 
+
+ align:start position:0%
+okay so the idea then is that we want to
+think about this hybrid notation this
+
+ align:start position:0%
+think about this hybrid notation this
+ 
+
+ align:start position:0%
+think about this hybrid notation this
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+notation and we want to think about how
+
+ align:start position:0%
+notation and we want to think about how
+ 
+
+ align:start position:0%
+notation and we want to think about how
+to represent simple systems that way so
+
+ align:start position:0%
+to represent simple systems that way so
+ 
+
+ align:start position:0%
+to represent simple systems that way so
+here's an example say I have this system
+
+ align:start position:0%
+here's an example say I have this system
+ 
+
+ align:start position:0%
+here's an example say I have this system
+I can think about that as the Cascade of
+
+ align:start position:0%
+I can think about that as the Cascade of
+ 
+
+ align:start position:0%
+I can think about that as the Cascade of
+a system that starts with
+
+ align:start position:0%
+a system that starts with
+ 
+
+ align:start position:0%
+a system that starts with
+X X is a signal and this whole thing
+
+ align:start position:0%
+X X is a signal and this whole thing
+ 
+
+ align:start position:0%
+X X is a signal and this whole thing
+gets turned into an
+
+ align:start position:0%
+gets turned into an
+ 
+
+ align:start position:0%
+gets turned into an
+operator that operator is can be written
+
+ align:start position:0%
+operator that operator is can be written
+ 
+
+ align:start position:0%
+operator that operator is can be written
+mathematically as one this path added to
+
+ align:start position:0%
+mathematically as one this path added to
+ 
+
+ align:start position:0%
+mathematically as one this path added to
+minus1 times a delay minus one time a
+
+ align:start position:0%
+minus1 times a delay minus one time a
+ 
+
+ align:start position:0%
+minus1 times a delay minus one time a
+delay so one - R operating on X gives me
+
+ align:start position:0%
+delay so one - R operating on X gives me
+ 
+
+ align:start position:0%
+delay so one - R operating on X gives me
+y1 then a similar system operates on y1
+
+ align:start position:0%
+y1 then a similar system operates on y1
+ 
+
+ align:start position:0%
+y1 then a similar system operates on y1
+to give me
+
+ align:start position:0%
+to give me
+ 
+
+ align:start position:0%
+to give me
+Y2 and if the rules of math apply I
+
+ align:start position:0%
+Y2 and if the rules of math apply I
+ 
+
+ align:start position:0%
+Y2 and if the rules of math apply I
+ought to be able to
+
+ align:start position:0%
+ought to be able to
+ 
+
+ align:start position:0%
+ought to be able to
+substitute 1 - RX for
+
+ align:start position:0%
+substitute 1 - RX for
+ 
+
+ align:start position:0%
+substitute 1 - RX for
+y1 and get that expression
+
+ align:start position:0%
+y1 and get that expression
+ 
+
+ align:start position:0%
+y1 and get that expression
+right and if the world were nice and it
+
+ align:start position:0%
+right and if the world were nice and it
+ 
+
+ align:start position:0%
+right and if the world were nice and it
+is if the world were nice then this
+
+ align:start position:0%
+is if the world were nice then this
+ 
+
+ align:start position:0%
+is if the world were nice then this
+expression since it looks like a polom
+
+ align:start position:0%
+expression since it looks like a polom
+ 
+
+ align:start position:0%
+expression since it looks like a polom
+in r
+
+ align:start position:0%
+in r
+ 
+
+ align:start position:0%
+in r
+behave like a polom in
+
+ align:start position:0%
+behave like a polom in
+ 
+
+ align:start position:0%
+behave like a polom in
+R and it's pretty easy to convince
+
+ align:start position:0%
+R and it's pretty easy to convince
+ 
+
+ align:start position:0%
+R and it's pretty easy to convince
+yourself that that's in fact
+
+ align:start position:0%
+yourself that that's in fact
+ 
+
+ align:start position:0%
+yourself that that's in fact
+true so think about the Primitive
+
+ align:start position:0%
+true so think about the Primitive
+ 
+
+ align:start position:0%
+true so think about the Primitive
+definition sample by sample difference
+
+ align:start position:0%
+definition sample by sample difference
+ 
+
+ align:start position:0%
+definition sample by sample difference
+equation what should this
+
+ align:start position:0%
+equation what should this
+ 
+
+ align:start position:0%
+equation what should this
+do well there's a difference
+
+ align:start position:0%
+do well there's a difference
+ 
+
+ align:start position:0%
+do well there's a difference
+representation for this which is here
+
+ align:start position:0%
+representation for this which is here
+ 
+
+ align:start position:0%
+representation for this which is here
+there's a difference representation for
+
+ align:start position:0%
+there's a difference representation for
+ 
+
+ align:start position:0%
+there's a difference representation for
+this which I can substitute
+
+ align:start position:0%
+this which I can substitute
+ 
+
+ align:start position:0%
+this which I can substitute
+twice so I can generate an equivalent
+
+ align:start position:0%
+twice so I can generate an equivalent
+ 
+
+ align:start position:0%
+twice so I can generate an equivalent
+difference equation for the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing and then I can think about
+
+ align:start position:0%
+thing and then I can think about
+ 
+
+ align:start position:0%
+thing and then I can think about
+termwise translating all those into R
+
+ align:start position:0%
+termwise translating all those into R
+ 
+
+ align:start position:0%
+termwise translating all those into R
+expressions and I see that I have proved
+
+ align:start position:0%
+expressions and I see that I have proved
+ 
+
+ align:start position:0%
+expressions and I see that I have proved
+the idea that this particular system at
+
+ align:start position:0%
+the idea that this particular system at
+ 
+
+ align:start position:0%
+the idea that this particular system at
+least behaves as though the operator
+
+ align:start position:0%
+least behaves as though the operator
+ 
+
+ align:start position:0%
+least behaves as though the operator
+Expressions follow the rules of
+
+ align:start position:0%
+Expressions follow the rules of
+ 
+
+ align:start position:0%
+Expressions follow the rules of
+pols it's important so that important
+
+ align:start position:0%
+pols it's important so that important
+ 
+
+ align:start position:0%
+pols it's important so that important
+right because you know how to deal with
+
+ align:start position:0%
+right because you know how to deal with
+ 
+
+ align:start position:0%
+right because you know how to deal with
+pols if there's an isomorphism between
+
+ align:start position:0%
+pols if there's an isomorphism between
+ 
+
+ align:start position:0%
+pols if there's an isomorphism between
+these kinds of discrete time signals and
+
+ align:start position:0%
+these kinds of discrete time signals and
+ 
+
+ align:start position:0%
+these kinds of discrete time signals and
+pols the fact that you know how to deal
+
+ align:start position:0%
+pols the fact that you know how to deal
+ 
+
+ align:start position:0%
+pols the fact that you know how to deal
+with polinomial translates in to you
+
+ align:start position:0%
+with polinomial translates in to you
+ 
+
+ align:start position:0%
+with polinomial translates in to you
+already know how to do systems right so
+
+ align:start position:0%
+already know how to do systems right so
+ 
+
+ align:start position:0%
+already know how to do systems right so
+it's a very powerful kind of thing to
+
+ align:start position:0%
+it's a very powerful kind of thing to
+ 
+
+ align:start position:0%
+it's a very powerful kind of thing to
+draw an isomorphism between two systems
+
+ align:start position:0%
+draw an isomorphism between two systems
+ 
+
+ align:start position:0%
+draw an isomorphism between two systems
+especially when you already know how to
+
+ align:start position:0%
+especially when you already know how to
+ 
+
+ align:start position:0%
+especially when you already know how to
+do one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so let's think about equivalence a
+
+ align:start position:0%
+them so let's think about equivalence a
+ 
+
+ align:start position:0%
+them so let's think about equivalence a
+little more here's a another example so
+
+ align:start position:0%
+little more here's a another example so
+ 
+
+ align:start position:0%
+little more here's a another example so
+here's that same
+
+ align:start position:0%
+here's that same
+ 
+
+ align:start position:0%
+here's that same
+system that's composed of two cascaded
+
+ align:start position:0%
+system that's composed of two cascaded
+ 
+
+ align:start position:0%
+system that's composed of two cascaded
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+engines and the hypothesis is that this
+
+ align:start position:0%
+engines and the hypothesis is that this
+ 
+
+ align:start position:0%
+engines and the hypothesis is that this
+is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same two things I want you to see first
+
+ align:start position:0%
+same two things I want you to see first
+ 
+
+ align:start position:0%
+same two things I want you to see first
+it should be pretty clear that you can
+
+ align:start position:0%
+it should be pretty clear that you can
+ 
+
+ align:start position:0%
+it should be pretty clear that you can
+see how you would derive that thinking
+
+ align:start position:0%
+see how you would derive that thinking
+ 
+
+ align:start position:0%
+see how you would derive that thinking
+about the system as operators
+
+ align:start position:0%
+about the system as operators
+ 
+
+ align:start position:0%
+about the system as operators
+are you should also be able to derive
+
+ align:start position:0%
+are you should also be able to derive
+ 
+
+ align:start position:0%
+are you should also be able to derive
+the equivalence by thinking about the
+
+ align:start position:0%
+the equivalence by thinking about the
+ 
+
+ align:start position:0%
+the equivalence by thinking about the
+individual blocks as difference
+
+ align:start position:0%
+individual blocks as difference
+ 
+
+ align:start position:0%
+individual blocks as difference
+equations but more importantly I'm
+
+ align:start position:0%
+equations but more importantly I'm
+ 
+
+ align:start position:0%
+equations but more importantly I'm
+hoping that you can see a
+
+ align:start position:0%
+hoping that you can see a
+ 
+
+ align:start position:0%
+hoping that you can see a
+caveat assuming both are initially at
+
+ align:start position:0%
+caveat assuming both are initially at
+ 
+
+ align:start position:0%
+caveat assuming both are initially at
+rest that will come up over and over and
+
+ align:start position:0%
+rest that will come up over and over and
+ 
+
+ align:start position:0%
+rest that will come up over and over and
+over and over again for exactly this
+
+ align:start position:0%
+over and over again for exactly this
+ 
+
+ align:start position:0%
+over and over again for exactly this
+reason the equivalence is only true if
+
+ align:start position:0%
+reason the equivalence is only true if
+ 
+
+ align:start position:0%
+reason the equivalence is only true if
+they started
+
+ align:start position:0%
+they started
+ 
+
+ align:start position:0%
+they started
+rest that's not quite the right way to
+
+ align:start position:0%
+rest that's not quite the right way to
+ 
+
+ align:start position:0%
+rest that's not quite the right way to
+say it the equivalence is always true if
+
+ align:start position:0%
+say it the equivalence is always true if
+ 
+
+ align:start position:0%
+say it the equivalence is always true if
+they start at rest that is precisely
+
+ align:start position:0%
+they start at rest that is precisely
+ 
+
+ align:start position:0%
+they start at rest that is precisely
+right if they start at rest it will
+
+ align:start position:0%
+right if they start at rest it will
+ 
+
+ align:start position:0%
+right if they start at rest it will
+always be equivalent can you think of
+
+ align:start position:0%
+always be equivalent can you think of
+ 
+
+ align:start position:0%
+always be equivalent can you think of
+why they have to be at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rest why do they have to be at rest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+smile it's not torture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so if they weren't at rest the
+
+ align:start position:0%
+yes so if they weren't at rest the
+ 
+
+ align:start position:0%
+yes so if they weren't at rest the
+outputs of the delays wouldn't
+
+ align:start position:0%
+outputs of the delays wouldn't
+ 
+
+ align:start position:0%
+outputs of the delays wouldn't
+necessarily be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero there is no simple correspondence
+
+ align:start position:0%
+zero there is no simple correspondence
+ 
+
+ align:start position:0%
+zero there is no simple correspondence
+between these two delays and those two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delays if I told you what are these two
+
+ align:start position:0%
+delays if I told you what are these two
+ 
+
+ align:start position:0%
+delays if I told you what are these two
+delays it may or may not be possible to
+
+ align:start position:0%
+delays it may or may not be possible to
+ 
+
+ align:start position:0%
+delays it may or may not be possible to
+make an equivalent system where there
+
+ align:start position:0%
+make an equivalent system where there
+ 
+
+ align:start position:0%
+make an equivalent system where there
+are two different numbers here right say
+
+ align:start position:0%
+are two different numbers here right say
+ 
+
+ align:start position:0%
+are two different numbers here right say
+this out say this delay starts at one
+
+ align:start position:0%
+this out say this delay starts at one
+ 
+
+ align:start position:0%
+this out say this delay starts at one
+and this delay starts at
+
+ align:start position:0%
+and this delay starts at
+ 
+
+ align:start position:0%
+and this delay starts at
+seven there may or may not be a set of
+
+ align:start position:0%
+seven there may or may not be a set of
+ 
+
+ align:start position:0%
+seven there may or may not be a set of
+numbers for the bottom delays that will
+
+ align:start position:0%
+numbers for the bottom delays that will
+ 
+
+ align:start position:0%
+numbers for the bottom delays that will
+have the same
+
+ align:start position:0%
+have the same
+ 
+
+ align:start position:0%
+have the same
+behavior as those numbers did in the top
+
+ align:start position:0%
+behavior as those numbers did in the top
+ 
+
+ align:start position:0%
+behavior as those numbers did in the top
+system okay but what is guaranteed is if
+
+ align:start position:0%
+system okay but what is guaranteed is if
+ 
+
+ align:start position:0%
+system okay but what is guaranteed is if
+they ALS start at zero everything's
+
+ align:start position:0%
+they ALS start at zero everything's
+ 
+
+ align:start position:0%
+they ALS start at zero everything's
+fine that's the reason we put in the
+
+ align:start position:0%
+fine that's the reason we put in the
+ 
+
+ align:start position:0%
+fine that's the reason we put in the
+caveat initially that both systems start
+
+ align:start position:0%
+caveat initially that both systems start
+ 
+
+ align:start position:0%
+caveat initially that both systems start
+at rest the equivalence that we that we
+
+ align:start position:0%
+at rest the equivalence that we that we
+ 
+
+ align:start position:0%
+at rest the equivalence that we that we
+talk about is equivalence starting from
+
+ align:start position:0%
+talk about is equivalence starting from
+ 
+
+ align:start position:0%
+talk about is equivalence starting from
+rest okay so
+
+ align:start position:0%
+rest okay so
+ 
+
+ align:start position:0%
+rest okay so
+uh think about these
+
+ align:start position:0%
+uh think about these
+ 
+
+ align:start position:0%
+uh think about these
+systems they are
+
+ align:start position:0%
+systems they are
+ 
+
+ align:start position:0%
+systems they are
+equivalent you can try to convince
+
+ align:start position:0%
+equivalent you can try to convince
+ 
+
+ align:start position:0%
+equivalent you can try to convince
+yourself they're equivalent by thinking
+
+ align:start position:0%
+yourself they're equivalent by thinking
+ 
+
+ align:start position:0%
+yourself they're equivalent by thinking
+about uh
+
+ align:start position:0%
+about uh
+ 
+
+ align:start position:0%
+about uh
+operations on block
+
+ align:start position:0%
+operations on block
+ 
+
+ align:start position:0%
+operations on block
+diagrams but what I'd like you to think
+
+ align:start position:0%
+diagrams but what I'd like you to think
+ 
+
+ align:start position:0%
+diagrams but what I'd like you to think
+about is they are a statement of what
+
+ align:start position:0%
+about is they are a statement of what
+ 
+
+ align:start position:0%
+about is they are a statement of what
+property of
+
+ align:start position:0%
+property of
+ 
+
+ align:start position:0%
+property of
+pols the equivalence of those two
+
+ align:start position:0%
+pols the equivalence of those two
+ 
+
+ align:start position:0%
+pols the equivalence of those two
+systems is a statement about what
+
+ align:start position:0%
+systems is a statement about what
+ 
+
+ align:start position:0%
+systems is a statement about what
+property of
+
+ align:start position:0%
+property of
+ 
+
+ align:start position:0%
+property of
+pols is it the commutative property the
+
+ align:start position:0%
+pols is it the commutative property the
+ 
+
+ align:start position:0%
+pols is it the commutative property the
+associative property the distributive
+
+ align:start position:0%
+associative property the distributive
+ 
+
+ align:start position:0%
+associative property the distributive
+property the transitive property or none
+
+ align:start position:0%
+property the transitive property or none
+ 
+
+ align:start position:0%
+property the transitive property or none
+of the above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you're far too
+
+ align:start position:0%
+okay you're far too
+ 
+
+ align:start position:0%
+okay you're far too
+quiet take a break turn to your neighbor
+
+ align:start position:0%
+quiet take a break turn to your neighbor
+ 
+
+ align:start position:0%
+quiet take a break turn to your neighbor
+tell your neighbor what living group
+
+ align:start position:0%
+tell your neighbor what living group
+ 
+
+ align:start position:0%
+tell your neighbor what living group
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+in become accustomed to talking to your
+
+ align:start position:0%
+in become accustomed to talking to your
+ 
+
+ align:start position:0%
+in become accustomed to talking to your
+neighbor and then figure this out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AAL b means b equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a or five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what property is being dis is being
+
+ align:start position:0%
+okay what property is being dis is being
+ 
+
+ align:start position:0%
+okay what property is being dis is being
+described here everybody raise your hand
+
+ align:start position:0%
+described here everybody raise your hand
+ 
+
+ align:start position:0%
+described here everybody raise your hand
+with some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number excellent excellent more than 90%
+
+ align:start position:0%
+number excellent excellent more than 90%
+ 
+
+ align:start position:0%
+number excellent excellent more than 90%
+correct so the idea is that we write
+
+ align:start position:0%
+correct so the idea is that we write
+ 
+
+ align:start position:0%
+correct so the idea is that we write
+this as an R
+
+ align:start position:0%
+this as an R
+ 
+
+ align:start position:0%
+this as an R
+expression so this system says start
+
+ align:start position:0%
+expression so this system says start
+ 
+
+ align:start position:0%
+expression so this system says start
+with X apply this operator to X it's a
+
+ align:start position:0%
+with X apply this operator to X it's a
+ 
+
+ align:start position:0%
+with X apply this operator to X it's a
+little confusing that one goes left and
+
+ align:start position:0%
+little confusing that one goes left and
+ 
+
+ align:start position:0%
+little confusing that one goes left and
+one goes right right so start with X
+
+ align:start position:0%
+one goes right right so start with X
+ 
+
+ align:start position:0%
+one goes right right so start with X
+apply this to X that's the one minus r
+
+ align:start position:0%
+apply this to X that's the one minus r
+ 
+
+ align:start position:0%
+apply this to X that's the one minus r
+operator then take whatever comes out
+
+ align:start position:0%
+operator then take whatever comes out
+ 
+
+ align:start position:0%
+operator then take whatever comes out
+and apply R
+
+ align:start position:0%
+and apply R
+ 
+
+ align:start position:0%
+and apply R
+again similarly down here start with
+
+ align:start position:0%
+again similarly down here start with
+ 
+
+ align:start position:0%
+again similarly down here start with
+X you've got the sum of two things an r
+
+ align:start position:0%
+X you've got the sum of two things an r
+ 
+
+ align:start position:0%
+X you've got the sum of two things an r
+in the top and an r^ 2 minus one in the
+
+ align:start position:0%
+in the top and an r^ 2 minus one in the
+ 
+
+ align:start position:0%
+in the top and an r^ 2 minus one in the
+bottom and the equivalence of those is
+
+ align:start position:0%
+bottom and the equivalence of those is
+ 
+
+ align:start position:0%
+bottom and the equivalence of those is
+the distributive principle right R
+
+ align:start position:0%
+the distributive principle right R
+ 
+
+ align:start position:0%
+the distributive principle right R
+distributes um so it mult multiplication
+
+ align:start position:0%
+distributes um so it mult multiplication
+ 
+
+ align:start position:0%
+distributes um so it mult multiplication
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+addition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay in the interest of time let me
+
+ align:start position:0%
+okay okay in the interest of time let me
+ 
+
+ align:start position:0%
+okay okay in the interest of time let me
+skip that that's an exercise that you
+
+ align:start position:0%
+skip that that's an exercise that you
+ 
+
+ align:start position:0%
+skip that that's an exercise that you
+can uh work on on your own it's very
+
+ align:start position:0%
+can uh work on on your own it's very
+ 
+
+ align:start position:0%
+can uh work on on your own it's very
+straightforward what I want to do is
+
+ align:start position:0%
+straightforward what I want to do is
+ 
+
+ align:start position:0%
+straightforward what I want to do is
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+another more a slightly deeper
+
+ align:start position:0%
+another more a slightly deeper
+ 
+
+ align:start position:0%
+another more a slightly deeper
+issue and that's the difference between
+
+ align:start position:0%
+issue and that's the difference between
+ 
+
+ align:start position:0%
+issue and that's the difference between
+recipes and constraints for whole block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagrams so we can think about this as a
+
+ align:start position:0%
+diagrams so we can think about this as a
+ 
+
+ align:start position:0%
+diagrams so we can think about this as a
+recipe in the sense that we can take the
+
+ align:start position:0%
+recipe in the sense that we can take the
+ 
+
+ align:start position:0%
+recipe in the sense that we can take the
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+operators and think about signals as the
+
+ align:start position:0%
+operators and think about signals as the
+ 
+
+ align:start position:0%
+operators and think about signals as the
+composition of other
+
+ align:start position:0%
+composition of other
+ 
+
+ align:start position:0%
+composition of other
+signals so this says take add this
+
+ align:start position:0%
+signals so this says take add this
+ 
+
+ align:start position:0%
+signals so this says take add this
+signal to that signal this signal is
+
+ align:start position:0%
+signal to that signal this signal is
+ 
+
+ align:start position:0%
+signal to that signal this signal is
+just the delay of that signal this
+
+ align:start position:0%
+just the delay of that signal this
+ 
+
+ align:start position:0%
+just the delay of that signal this
+signal is just the minus one of that
+
+ align:start position:0%
+signal is just the minus one of that
+ 
+
+ align:start position:0%
+signal is just the minus one of that
+signal so you can think about there's a
+
+ align:start position:0%
+signal so you can think about there's a
+ 
+
+ align:start position:0%
+signal so you can think about there's a
+recipe start with X invert it delay it
+
+ align:start position:0%
+recipe start with X invert it delay it
+ 
+
+ align:start position:0%
+recipe start with X invert it delay it
+add it to the
+
+ align:start position:0%
+add it to the
+ 
+
+ align:start position:0%
+add it to the
+original that's the
+
+ align:start position:0%
+original that's the
+ 
+
+ align:start position:0%
+original that's the
+output let's contrast that to this this
+
+ align:start position:0%
+output let's contrast that to this this
+ 
+
+ align:start position:0%
+output let's contrast that to this this
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harder so let's think about the r
+
+ align:start position:0%
+harder so let's think about the r
+ 
+
+ align:start position:0%
+harder so let's think about the r
+operators what we can say here is that
+
+ align:start position:0%
+operators what we can say here is that
+ 
+
+ align:start position:0%
+operators what we can say here is that
+this output is composed of the sum of
+
+ align:start position:0%
+this output is composed of the sum of
+ 
+
+ align:start position:0%
+this output is composed of the sum of
+two things the input and a delayed
+
+ align:start position:0%
+two things the input and a delayed
+ 
+
+ align:start position:0%
+two things the input and a delayed
+version of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output that's a recipe for finding the
+
+ align:start position:0%
+output that's a recipe for finding the
+ 
+
+ align:start position:0%
+output that's a recipe for finding the
+input from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output that's not what we want to
+
+ align:start position:0%
+output that's not what we want to
+ 
+
+ align:start position:0%
+output that's not what we want to
+do so there's a recipe here that says
+
+ align:start position:0%
+do so there's a recipe here that says
+ 
+
+ align:start position:0%
+do so there's a recipe here that says
+start with the
+
+ align:start position:0%
+start with the
+ 
+
+ align:start position:0%
+start with the
+output shift it to the right subtract
+
+ align:start position:0%
+output shift it to the right subtract
+ 
+
+ align:start position:0%
+output shift it to the right subtract
+that from the original and that'll tell
+
+ align:start position:0%
+that from the original and that'll tell
+ 
+
+ align:start position:0%
+that from the original and that'll tell
+you the input but I don't know the
+
+ align:start position:0%
+you the input but I don't know the
+ 
+
+ align:start position:0%
+you the input but I don't know the
+output I know the
+
+ align:start position:0%
+output I know the
+ 
+
+ align:start position:0%
+output I know the
+input what that says is if you knew the
+
+ align:start position:0%
+input what that says is if you knew the
+ 
+
+ align:start position:0%
+input what that says is if you knew the
+output it would have this property it's
+
+ align:start position:0%
+output it would have this property it's
+ 
+
+ align:start position:0%
+output it would have this property it's
+declarative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever the output is it has to have
+
+ align:start position:0%
+whatever the output is it has to have
+ 
+
+ align:start position:0%
+whatever the output is it has to have
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+property but it didn't tell me how to
+
+ align:start position:0%
+property but it didn't tell me how to
+ 
+
+ align:start position:0%
+property but it didn't tell me how to
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+it okay the r operator is
+
+ align:start position:0%
+it okay the r operator is
+ 
+
+ align:start position:0%
+it okay the r operator is
+imperative start with the input apply R
+
+ align:start position:0%
+imperative start with the input apply R
+ 
+
+ align:start position:0%
+imperative start with the input apply R
+to it you get the
+
+ align:start position:0%
+to it you get the
+ 
+
+ align:start position:0%
+to it you get the
+output but you can compose
+
+ align:start position:0%
+output but you can compose
+ 
+
+ align:start position:0%
+output but you can compose
+systems using an imperative operator
+
+ align:start position:0%
+systems using an imperative operator
+ 
+
+ align:start position:0%
+systems using an imperative operator
+that is not where the overall system is
+
+ align:start position:0%
+that is not where the overall system is
+ 
+
+ align:start position:0%
+that is not where the overall system is
+not imperative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what are you going to do with
+
+ align:start position:0%
+so what are you going to do with
+ 
+
+ align:start position:0%
+so what are you going to do with
+something like that well it's a
+
+ align:start position:0%
+something like that well it's a
+ 
+
+ align:start position:0%
+something like that well it's a
+constraint so the question is how do you
+
+ align:start position:0%
+constraint so the question is how do you
+ 
+
+ align:start position:0%
+constraint so the question is how do you
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+that the thing to do in this case is the
+
+ align:start position:0%
+that the thing to do in this case is the
+ 
+
+ align:start position:0%
+that the thing to do in this case is the
+thing you should always do in this
+
+ align:start position:0%
+thing you should always do in this
+ 
+
+ align:start position:0%
+thing you should always do in this
+course fall back to a simpler
+
+ align:start position:0%
+course fall back to a simpler
+ 
+
+ align:start position:0%
+course fall back to a simpler
+method the idea is we're going to start
+
+ align:start position:0%
+method the idea is we're going to start
+ 
+
+ align:start position:0%
+method the idea is we're going to start
+by teaching simple methods and then more
+
+ align:start position:0%
+by teaching simple methods and then more
+ 
+
+ align:start position:0%
+by teaching simple methods and then more
+abstract methods and then more abstract
+
+ align:start position:0%
+abstract methods and then more abstract
+ 
+
+ align:start position:0%
+abstract methods and then more abstract
+methods the reason being that as the
+
+ align:start position:0%
+methods the reason being that as the
+ 
+
+ align:start position:0%
+methods the reason being that as the
+methods become more abstract they become
+
+ align:start position:0%
+methods become more abstract they become
+ 
+
+ align:start position:0%
+methods become more abstract they become
+more powerful you can do things
+
+ align:start position:0%
+more powerful you can do things
+ 
+
+ align:start position:0%
+more powerful you can do things
+quicker but they fail revert to the
+
+ align:start position:0%
+quicker but they fail revert to the
+ 
+
+ align:start position:0%
+quicker but they fail revert to the
+easier method so here the easier method
+
+ align:start position:0%
+easier method so here the easier method
+ 
+
+ align:start position:0%
+easier method so here the easier method
+is sample by
+
+ align:start position:0%
+is sample by
+ 
+
+ align:start position:0%
+is sample by
+sample so let's just think about how
+
+ align:start position:0%
+sample so let's just think about how
+ 
+
+ align:start position:0%
+sample so let's just think about how
+signals would propagate through this
+
+ align:start position:0%
+signals would propagate through this
+ 
+
+ align:start position:0%
+signals would propagate through this
+system so think about this as a sample
+
+ align:start position:0%
+system so think about this as a sample
+ 
+
+ align:start position:0%
+system so think about this as a sample
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+sample uh block diagram
+
+ align:start position:0%
+sample uh block diagram
+ 
+
+ align:start position:0%
+sample uh block diagram
+system say that it starts at rest so the
+
+ align:start position:0%
+system say that it starts at rest so the
+ 
+
+ align:start position:0%
+system say that it starts at rest so the
+initial output so the output at before
+
+ align:start position:0%
+initial output so the output at before
+ 
+
+ align:start position:0%
+initial output so the output at before
+any inputs come in have to be zero
+
+ align:start position:0%
+any inputs come in have to be zero
+ 
+
+ align:start position:0%
+any inputs come in have to be zero
+because the initial condition was that
+
+ align:start position:0%
+because the initial condition was that
+ 
+
+ align:start position:0%
+because the initial condition was that
+delays were all zero
+
+ align:start position:0%
+delays were all zero
+ 
+
+ align:start position:0%
+delays were all zero
+now the input comes in at time
+
+ align:start position:0%
+now the input comes in at time
+ 
+
+ align:start position:0%
+now the input comes in at time
+one so X of0 is one so the output
+
+ align:start position:0%
+one so X of0 is one so the output
+ 
+
+ align:start position:0%
+one so X of0 is one so the output
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+one and now because of the way that
+
+ align:start position:0%
+one and now because of the way that
+ 
+
+ align:start position:0%
+one and now because of the way that
+feedback path
+
+ align:start position:0%
+feedback path
+ 
+
+ align:start position:0%
+feedback path
+works the output there's a second signal
+
+ align:start position:0%
+works the output there's a second signal
+ 
+
+ align:start position:0%
+works the output there's a second signal
+is also the second sample is also
+
+ align:start position:0%
+is also the second sample is also
+ 
+
+ align:start position:0%
+is also the second sample is also
+one did everybody see
+
+ align:start position:0%
+one did everybody see
+ 
+
+ align:start position:0%
+one did everybody see
+that and in fact it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stuck so the idea in the s this system
+
+ align:start position:0%
+stuck so the idea in the s this system
+ 
+
+ align:start position:0%
+stuck so the idea in the s this system
+if you think about it from a sample by
+
+ align:start position:0%
+if you think about it from a sample by
+ 
+
+ align:start position:0%
+if you think about it from a sample by
+sample point of view the signal at the
+
+ align:start position:0%
+sample point of view the signal at the
+ 
+
+ align:start position:0%
+sample point of view the signal at the
+output persists long in fact infinitely
+
+ align:start position:0%
+output persists long in fact infinitely
+ 
+
+ align:start position:0%
+output persists long in fact infinitely
+long after the signal at the input goes
+
+ align:start position:0%
+long after the signal at the input goes
+ 
+
+ align:start position:0%
+long after the signal at the input goes
+away that's very different from what we
+
+ align:start position:0%
+away that's very different from what we
+ 
+
+ align:start position:0%
+away that's very different from what we
+saw in the simpler systems that were
+
+ align:start position:0%
+saw in the simpler systems that were
+ 
+
+ align:start position:0%
+saw in the simpler systems that were
+imperative if in the previous systems
+
+ align:start position:0%
+imperative if in the previous systems
+ 
+
+ align:start position:0%
+imperative if in the previous systems
+you had a finite length signal at the
+
+ align:start position:0%
+you had a finite length signal at the
+ 
+
+ align:start position:0%
+you had a finite length signal at the
+input any number of operations that you
+
+ align:start position:0%
+input any number of operations that you
+ 
+
+ align:start position:0%
+input any number of operations that you
+did to it and then combine those would
+
+ align:start position:0%
+did to it and then combine those would
+ 
+
+ align:start position:0%
+did to it and then combine those would
+give you a finite length output maybe
+
+ align:start position:0%
+give you a finite length output maybe
+ 
+
+ align:start position:0%
+give you a finite length output maybe
+bigger than the last one because of
+
+ align:start position:0%
+bigger than the last one because of
+ 
+
+ align:start position:0%
+bigger than the last one because of
+extra delays in the system but it's if
+
+ align:start position:0%
+extra delays in the system but it's if
+ 
+
+ align:start position:0%
+extra delays in the system but it's if
+it started finite it's
+
+ align:start position:0%
+it started finite it's
+ 
+
+ align:start position:0%
+it started finite it's
+finite this is different here I'm having
+
+ align:start position:0%
+finite this is different here I'm having
+ 
+
+ align:start position:0%
+finite this is different here I'm having
+a a persisting response persists to
+
+ align:start position:0%
+a a persisting response persists to
+ 
+
+ align:start position:0%
+a a persisting response persists to
+Infinity from a transient input and
+
+ align:start position:0%
+Infinity from a transient input and
+ 
+
+ align:start position:0%
+Infinity from a transient input and
+that's because the uh it's because of
+
+ align:start position:0%
+that's because the uh it's because of
+ 
+
+ align:start position:0%
+that's because the uh it's because of
+feedback it's because there's a path
+
+ align:start position:0%
+feedback it's because there's a path
+ 
+
+ align:start position:0%
+feedback it's because there's a path
+that goes that wraps back on
+
+ align:start position:0%
+that goes that wraps back on
+ 
+
+ align:start position:0%
+that goes that wraps back on
+itself so how can we think how do we
+
+ align:start position:0%
+itself so how can we think how do we
+ 
+
+ align:start position:0%
+itself so how can we think how do we
+think about that in terms of our
+
+ align:start position:0%
+think about that in terms of our
+ 
+
+ align:start position:0%
+think about that in terms of our
+operators well having figured out what
+
+ align:start position:0%
+operators well having figured out what
+ 
+
+ align:start position:0%
+operators well having figured out what
+the response looks like there's a
+
+ align:start position:0%
+the response looks like there's a
+ 
+
+ align:start position:0%
+the response looks like there's a
+perfectly valid R expression for this
+
+ align:start position:0%
+perfectly valid R expression for this
+ 
+
+ align:start position:0%
+perfectly valid R expression for this
+signal this is just the unit
+
+ align:start position:0%
+signal this is just the unit
+ 
+
+ align:start position:0%
+signal this is just the unit
+sample plus r * the unit sample plus r 2
+
+ align:start position:0%
+sample plus r * the unit sample plus r 2
+ 
+
+ align:start position:0%
+sample plus r * the unit sample plus r 2
+time the unit sample plus r Cub time the
+
+ align:start position:0%
+time the unit sample plus r Cub time the
+ 
+
+ align:start position:0%
+time the unit sample plus r Cub time the
+unit sample at infin item that's that
+
+ align:start position:0%
+unit sample at infin item that's that
+ 
+
+ align:start position:0%
+unit sample at infin item that's that
+system okay so I've done something very
+
+ align:start position:0%
+system okay so I've done something very
+ 
+
+ align:start position:0%
+system okay so I've done something very
+powerful and not all that obvious I've
+
+ align:start position:0%
+powerful and not all that obvious I've
+ 
+
+ align:start position:0%
+powerful and not all that obvious I've
+taken a system that was not imperative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I've turned it into a system that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imperative this system gives me a recipe
+
+ align:start position:0%
+imperative this system gives me a recipe
+ 
+
+ align:start position:0%
+imperative this system gives me a recipe
+for how to do things start with X delay
+
+ align:start position:0%
+for how to do things start with X delay
+ 
+
+ align:start position:0%
+for how to do things start with X delay
+it by one and add it delay it by another
+
+ align:start position:0%
+it by one and add it delay it by another
+ 
+
+ align:start position:0%
+it by one and add it delay it by another
+one and add it delay it by another one
+
+ align:start position:0%
+one and add it delay it by another one
+ 
+
+ align:start position:0%
+one and add it delay it by another one
+and add it delay it by another one and
+
+ align:start position:0%
+and add it delay it by another one and
+ 
+
+ align:start position:0%
+and add it delay it by another one and
+add it I've converted an A U declarative
+
+ align:start position:0%
+add it I've converted an A U declarative
+ 
+
+ align:start position:0%
+add it I've converted an A U declarative
+statement about how the system should
+
+ align:start position:0%
+statement about how the system should
+ 
+
+ align:start position:0%
+statement about how the system should
+work into an imperative statement about
+
+ align:start position:0%
+work into an imperative statement about
+ 
+
+ align:start position:0%
+work into an imperative statement about
+how the system should work so and I've
+
+ align:start position:0%
+how the system should work so and I've
+ 
+
+ align:start position:0%
+how the system should work so and I've
+got an equivalent system representation
+
+ align:start position:0%
+got an equivalent system representation
+ 
+
+ align:start position:0%
+got an equivalent system representation
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+and you should be saying to yourself do
+
+ align:start position:0%
+and you should be saying to yourself do
+ 
+
+ align:start position:0%
+and you should be saying to yourself do
+I really buy
+
+ align:start position:0%
+I really buy
+ 
+
+ align:start position:0%
+I really buy
+that so is it really going to be the
+
+ align:start position:0%
+that so is it really going to be the
+ 
+
+ align:start position:0%
+that so is it really going to be the
+case that A system that was previously
+
+ align:start position:0%
+case that A system that was previously
+ 
+
+ align:start position:0%
+case that A system that was previously
+described this
+
+ align:start position:0%
+described this
+ 
+
+ align:start position:0%
+described this
+way tell me the
+
+ align:start position:0%
+way tell me the
+ 
+
+ align:start position:0%
+way tell me the
+output operate on it by one minus r and
+
+ align:start position:0%
+output operate on it by one minus r and
+ 
+
+ align:start position:0%
+output operate on it by one minus r and
+that'll be the input should that be the
+
+ align:start position:0%
+that'll be the input should that be the
+ 
+
+ align:start position:0%
+that'll be the input should that be the
+same as this
+
+ align:start position:0%
+same as this
+ 
+
+ align:start position:0%
+same as this
+system if you think about that
+
+ align:start position:0%
+system if you think about that
+ 
+
+ align:start position:0%
+system if you think about that
+mathematically here's a proof it is okay
+
+ align:start position:0%
+mathematically here's a proof it is okay
+ 
+
+ align:start position:0%
+mathematically here's a proof it is okay
+to think about it that way start with
+
+ align:start position:0%
+to think about it that way start with
+ 
+
+ align:start position:0%
+to think about it that way start with
+the idea that X2 =
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X1 this is a statement of the right hand
+
+ align:start position:0%
+X1 this is a statement of the right hand
+ 
+
+ align:start position:0%
+X1 this is a statement of the right hand
+side substitute X1 for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X2 substitute this equivalent expression
+
+ align:start position:0%
+X2 substitute this equivalent expression
+ 
+
+ align:start position:0%
+X2 substitute this equivalent expression
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+X1 and multiply it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out when you do that you find Y2 equals
+
+ align:start position:0%
+out when you do that you find Y2 equals
+ 
+
+ align:start position:0%
+out when you do that you find Y2 equals
+y1 it's
+
+ align:start position:0%
+y1 it's
+ 
+
+ align:start position:0%
+y1 it's
+true and what we've done is showed a
+
+ align:start position:0%
+true and what we've done is showed a
+ 
+
+ align:start position:0%
+true and what we've done is showed a
+very important thing this and this are
+
+ align:start position:0%
+very important thing this and this are
+ 
+
+ align:start position:0%
+very important thing this and this are
+reciprocals when you multiply two pols
+
+ align:start position:0%
+reciprocals when you multiply two pols
+ 
+
+ align:start position:0%
+reciprocals when you multiply two pols
+together and the answer is
+
+ align:start position:0%
+together and the answer is
+ 
+
+ align:start position:0%
+together and the answer is
+one they're
+
+ align:start position:0%
+one they're
+ 
+
+ align:start position:0%
+one they're
+reciprocals we so that implies that we
+
+ align:start position:0%
+reciprocals we so that implies that we
+ 
+
+ align:start position:0%
+reciprocals we so that implies that we
+can treat that first expression we can
+
+ align:start position:0%
+can treat that first expression we can
+ 
+
+ align:start position:0%
+can treat that first expression we can
+think about this uh let's see back up so
+
+ align:start position:0%
+think about this uh let's see back up so
+ 
+
+ align:start position:0%
+think about this uh let's see back up so
+here we had an expression that said
+
+ align:start position:0%
+here we had an expression that said
+ 
+
+ align:start position:0%
+here we had an expression that said
+start with the output operate on it with
+
+ align:start position:0%
+start with the output operate on it with
+ 
+
+ align:start position:0%
+start with the output operate on it with
+this get the input we can think about
+
+ align:start position:0%
+this get the input we can think about
+ 
+
+ align:start position:0%
+this get the input we can think about
+that instead as operate on the output
+
+ align:start position:0%
+that instead as operate on the output
+ 
+
+ align:start position:0%
+that instead as operate on the output
+operate on the
+
+ align:start position:0%
+operate on the
+ 
+
+ align:start position:0%
+operate on the
+input by the reciprocal
+
+ align:start position:0%
+input by the reciprocal
+ 
+
+ align:start position:0%
+input by the reciprocal
+operator now I've designed I've defined
+
+ align:start position:0%
+operator now I've designed I've defined
+ 
+
+ align:start position:0%
+operator now I've designed I've defined
+what does reciprocal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean reciprocal means that thing in the
+
+ align:start position:0%
+mean reciprocal means that thing in the
+ 
+
+ align:start position:0%
+mean reciprocal means that thing in the
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+slide so
+
+ align:start position:0%
+slide so
+ 
+
+ align:start position:0%
+slide so
+now in fact I know from the last Slide
+
+ align:start position:0%
+now in fact I know from the last Slide
+ 
+
+ align:start position:0%
+now in fact I know from the last Slide
+the reciprocal of 1 minus r is 1 plus r
+
+ align:start position:0%
+the reciprocal of 1 minus r is 1 plus r
+ 
+
+ align:start position:0%
+the reciprocal of 1 minus r is 1 plus r
+plus r s plus RB blah blah blah and that
+
+ align:start position:0%
+plus r s plus RB blah blah blah and that
+ 
+
+ align:start position:0%
+plus r s plus RB blah blah blah and that
+follows the normal rules of pooms this
+
+ align:start position:0%
+follows the normal rules of pooms this
+ 
+
+ align:start position:0%
+follows the normal rules of pooms this
+is not a surprise you could have done
+
+ align:start position:0%
+is not a surprise you could have done
+ 
+
+ align:start position:0%
+is not a surprise you could have done
+that you could have derived that same
+
+ align:start position:0%
+that you could have derived that same
+ 
+
+ align:start position:0%
+that you could have derived that same
+expression by thinking about synthetic
+
+ align:start position:0%
+expression by thinking about synthetic
+ 
+
+ align:start position:0%
+expression by thinking about synthetic
+division you could have thought about it
+
+ align:start position:0%
+division you could have thought about it
+ 
+
+ align:start position:0%
+division you could have thought about it
+as a tailor series anything you know
+
+ align:start position:0%
+as a tailor series anything you know
+ 
+
+ align:start position:0%
+as a tailor series anything you know
+about pols should have
+
+ align:start position:0%
+about pols should have
+ 
+
+ align:start position:0%
+about pols should have
+worked so this idea of representing a
+
+ align:start position:0%
+worked so this idea of representing a
+ 
+
+ align:start position:0%
+worked so this idea of representing a
+signal by a system by an operator R is
+
+ align:start position:0%
+signal by a system by an operator R is
+ 
+
+ align:start position:0%
+signal by a system by an operator R is
+extraordinarily
+
+ align:start position:0%
+extraordinarily
+ 
+
+ align:start position:0%
+extraordinarily
+powerful we've been able to take
+
+ align:start position:0%
+powerful we've been able to take
+ 
+
+ align:start position:0%
+powerful we've been able to take
+advantage of non-trivial properties of
+
+ align:start position:0%
+advantage of non-trivial properties of
+ 
+
+ align:start position:0%
+advantage of non-trivial properties of
+pols by having done that and we'll
+
+ align:start position:0%
+pols by having done that and we'll
+ 
+
+ align:start position:0%
+pols by having done that and we'll
+continue that way so the overriding
+
+ align:start position:0%
+continue that way so the overriding
+ 
+
+ align:start position:0%
+continue that way so the overriding
+feature of this system that was not
+
+ align:start position:0%
+feature of this system that was not
+ 
+
+ align:start position:0%
+feature of this system that was not
+uh that could not so this system was not
+
+ align:start position:0%
+uh that could not so this system was not
+ 
+
+ align:start position:0%
+uh that could not so this system was not
+a recipe it was a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraint the feature that made it that
+
+ align:start position:0%
+constraint the feature that made it that
+ 
+
+ align:start position:0%
+constraint the feature that made it that
+way is something we'll call
+
+ align:start position:0%
+way is something we'll call
+ 
+
+ align:start position:0%
+way is something we'll call
+feedback and we'll be able to visualize
+
+ align:start position:0%
+feedback and we'll be able to visualize
+ 
+
+ align:start position:0%
+feedback and we'll be able to visualize
+feedback very simply by looking at the
+
+ align:start position:0%
+feedback very simply by looking at the
+ 
+
+ align:start position:0%
+feedback very simply by looking at the
+block diagram feedback means that
+
+ align:start position:0%
+block diagram feedback means that
+ 
+
+ align:start position:0%
+block diagram feedback means that
+there's a cycle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somewhere so if there's no Cycles then
+
+ align:start position:0%
+somewhere so if there's no Cycles then
+ 
+
+ align:start position:0%
+somewhere so if there's no Cycles then
+it has to be so we call this the network
+
+ align:start position:0%
+it has to be so we call this the network
+ 
+
+ align:start position:0%
+it has to be so we call this the network
+that results when there's no Cycles we
+
+ align:start position:0%
+that results when there's no Cycles we
+ 
+
+ align:start position:0%
+that results when there's no Cycles we
+say it's a cyclic what a clever word
+
+ align:start position:0%
+say it's a cyclic what a clever word
+ 
+
+ align:start position:0%
+say it's a cyclic what a clever word
+right so no cycles and when it's a
+
+ align:start position:0%
+right so no cycles and when it's a
+ 
+
+ align:start position:0%
+right so no cycles and when it's a
+cyclic it will have the property that
+
+ align:start position:0%
+cyclic it will have the property that
+ 
+
+ align:start position:0%
+cyclic it will have the property that
+transient inputs give rise to transient
+
+ align:start position:0%
+transient inputs give rise to transient
+ 
+
+ align:start position:0%
+transient inputs give rise to transient
+outputs if it has a cycle in it then it
+
+ align:start position:0%
+outputs if it has a cycle in it then it
+ 
+
+ align:start position:0%
+outputs if it has a cycle in it then it
+has feedback and feedback has the
+
+ align:start position:0%
+has feedback and feedback has the
+ 
+
+ align:start position:0%
+has feedback and feedback has the
+potential doesn't always do it but has
+
+ align:start position:0%
+potential doesn't always do it but has
+ 
+
+ align:start position:0%
+potential doesn't always do it but has
+the potential to generate a persisting
+
+ align:start position:0%
+the potential to generate a persisting
+ 
+
+ align:start position:0%
+the potential to generate a persisting
+output to a transient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input so uh if we think about a slightly
+
+ align:start position:0%
+input so uh if we think about a slightly
+ 
+
+ align:start position:0%
+input so uh if we think about a slightly
+more complicated
+
+ align:start position:0%
+more complicated
+ 
+
+ align:start position:0%
+more complicated
+example where I've put a number P not in
+
+ align:start position:0%
+example where I've put a number P not in
+ 
+
+ align:start position:0%
+example where I've put a number P not in
+the feedback loop that was not in the
+
+ align:start position:0%
+the feedback loop that was not in the
+ 
+
+ align:start position:0%
+the feedback loop that was not in the
+previous example we can see that the way
+
+ align:start position:0%
+previous example we can see that the way
+ 
+
+ align:start position:0%
+previous example we can see that the way
+the way you can conceive of this since
+
+ align:start position:0%
+the way you can conceive of this since
+ 
+
+ align:start position:0%
+the way you can conceive of this since
+there's a single time when we're
+
+ align:start position:0%
+there's a single time when we're
+ 
+
+ align:start position:0%
+there's a single time when we're
+thinking about the unit sample response
+
+ align:start position:0%
+thinking about the unit sample response
+ 
+
+ align:start position:0%
+thinking about the unit sample response
+there's a single input that's not
+
+ align:start position:0%
+there's a single input that's not
+ 
+
+ align:start position:0%
+there's a single input that's not
+zero and what you can do is think about
+
+ align:start position:0%
+zero and what you can do is think about
+ 
+
+ align:start position:0%
+zero and what you can do is think about
+the feedback the block diagram you can
+
+ align:start position:0%
+the feedback the block diagram you can
+ 
+
+ align:start position:0%
+the feedback the block diagram you can
+think about it's separating
+
+ align:start position:0%
+think about it's separating
+ 
+
+ align:start position:0%
+think about it's separating
+times because there's a one unit of
+
+ align:start position:0%
+times because there's a one unit of
+ 
+
+ align:start position:0%
+times because there's a one unit of
+delay in every
+
+ align:start position:0%
+delay in every
+ 
+
+ align:start position:0%
+delay in every
+cycle so you can think about that as the
+
+ align:start position:0%
+cycle so you can think about that as the
+ 
+
+ align:start position:0%
+cycle so you can think about that as the
+only way you can get from the input at
+
+ align:start position:0%
+only way you can get from the input at
+ 
+
+ align:start position:0%
+only way you can get from the input at
+Time Zero to the output at Time Zero is
+
+ align:start position:0%
+Time Zero to the output at Time Zero is
+ 
+
+ align:start position:0%
+Time Zero to the output at Time Zero is
+through the straightforward path the one
+
+ align:start position:0%
+through the straightforward path the one
+ 
+
+ align:start position:0%
+through the straightforward path the one
+highlighted by Red the only way you can
+
+ align:start position:0%
+highlighted by Red the only way you can
+ 
+
+ align:start position:0%
+highlighted by Red the only way you can
+get from the input at Time Zero to the
+
+ align:start position:0%
+get from the input at Time Zero to the
+ 
+
+ align:start position:0%
+get from the input at Time Zero to the
+output at time one is to make the circle
+
+ align:start position:0%
+output at time one is to make the circle
+ 
+
+ align:start position:0%
+output at time one is to make the circle
+at least at least once uh to make the
+
+ align:start position:0%
+at least at least once uh to make the
+ 
+
+ align:start position:0%
+at least at least once uh to make the
+circle exactly
+
+ align:start position:0%
+circle exactly
+ 
+
+ align:start position:0%
+circle exactly
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+there if you make the circle exactly
+
+ align:start position:0%
+there if you make the circle exactly
+ 
+
+ align:start position:0%
+there if you make the circle exactly
+once then uh instead of being height one
+
+ align:start position:0%
+once then uh instead of being height one
+ 
+
+ align:start position:0%
+once then uh instead of being height one
+it's height P KN because you had to have
+
+ align:start position:0%
+it's height P KN because you had to have
+ 
+
+ align:start position:0%
+it's height P KN because you had to have
+gone through the P KN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once if you go around a third time it's
+
+ align:start position:0%
+once if you go around a third time it's
+ 
+
+ align:start position:0%
+once if you go around a third time it's
+p^ squar p to the 4th Etc so there's a
+
+ align:start position:0%
+p^ squar p to the 4th Etc so there's a
+ 
+
+ align:start position:0%
+p^ squar p to the 4th Etc so there's a
+way of thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why there why is there this persistent
+
+ align:start position:0%
+why there why is there this persistent
+ 
+
+ align:start position:0%
+why there why is there this persistent
+response by looking at the Block
+
+ align:start position:0%
+response by looking at the Block
+ 
+
+ align:start position:0%
+response by looking at the Block
+diagrams what I'm trying to emphasize is
+
+ align:start position:0%
+diagrams what I'm trying to emphasize is
+ 
+
+ align:start position:0%
+diagrams what I'm trying to emphasize is
+that it's useful to be able to think
+
+ align:start position:0%
+that it's useful to be able to think
+ 
+
+ align:start position:0%
+that it's useful to be able to think
+about differential difference equations
+
+ align:start position:0%
+about differential difference equations
+ 
+
+ align:start position:0%
+about differential difference equations
+block diagrams are operators they're all
+
+ align:start position:0%
+block diagrams are operators they're all
+ 
+
+ align:start position:0%
+block diagrams are operators they're all
+useful what you want to know is the
+
+ align:start position:0%
+useful what you want to know is the
+ 
+
+ align:start position:0%
+useful what you want to know is the
+strengths and limitations of each so
+
+ align:start position:0%
+strengths and limitations of each so
+ 
+
+ align:start position:0%
+strengths and limitations of each so
+here what I've showed is a very good way
+
+ align:start position:0%
+here what I've showed is a very good way
+ 
+
+ align:start position:0%
+here what I've showed is a very good way
+to think
+
+ align:start position:0%
+to think
+ 
+
+ align:start position:0%
+to think
+about feedback
+
+ align:start position:0%
+about feedback
+ 
+
+ align:start position:0%
+about feedback
+in terms of block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagrams
+
+ align:start position:0%
+diagrams
+ 
+
+ align:start position:0%
+diagrams
+uh how many of these networks are
+
+ align:start position:0%
+uh how many of these networks are
+ 
+
+ align:start position:0%
+uh how many of these networks are
+cyclic how many of these networks are a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cyclic is this cyclic this
+
+ align:start position:0%
+cyclic is this cyclic this
+ 
+
+ align:start position:0%
+cyclic is this cyclic this
+network no so the none of the paths wrap
+
+ align:start position:0%
+network no so the none of the paths wrap
+ 
+
+ align:start position:0%
+network no so the none of the paths wrap
+that back on itself here's a path here's
+
+ align:start position:0%
+that back on itself here's a path here's
+ 
+
+ align:start position:0%
+that back on itself here's a path here's
+a path here's a path none of those wrap
+
+ align:start position:0%
+a path here's a path none of those wrap
+ 
+
+ align:start position:0%
+a path here's a path none of those wrap
+on itself is this network cyclic sure
+
+ align:start position:0%
+on itself is this network cyclic sure
+ 
+
+ align:start position:0%
+on itself is this network cyclic sure
+the this is cyclic over here this one
+
+ align:start position:0%
+the this is cyclic over here this one
+ 
+
+ align:start position:0%
+the this is cyclic over here this one
+yeah the input this is cyclic this one
+
+ align:start position:0%
+yeah the input this is cyclic this one
+ 
+
+ align:start position:0%
+yeah the input this is cyclic this one
+doubly cylic okay so that's the
+
+ align:start position:0%
+doubly cylic okay so that's the
+ 
+
+ align:start position:0%
+doubly cylic okay so that's the
+idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and this gives rise to a notion that
+
+ align:start position:0%
+um and this gives rise to a notion that
+ 
+
+ align:start position:0%
+um and this gives rise to a notion that
+we will call a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pole a pole is the base of the geometric
+
+ align:start position:0%
+pole a pole is the base of the geometric
+ 
+
+ align:start position:0%
+pole a pole is the base of the geometric
+sequence that results in these simple
+
+ align:start position:0%
+sequence that results in these simple
+ 
+
+ align:start position:0%
+sequence that results in these simple
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+whenever you have
+
+ align:start position:0%
+whenever you have
+ 
+
+ align:start position:0%
+whenever you have
+feedback and we'll be saying a whole lot
+
+ align:start position:0%
+feedback and we'll be saying a whole lot
+ 
+
+ align:start position:0%
+feedback and we'll be saying a whole lot
+more about those uh in upcoming
+
+ align:start position:0%
+more about those uh in upcoming
+ 
+
+ align:start position:0%
+more about those uh in upcoming
+times um in the interest of time I I
+
+ align:start position:0%
+times um in the interest of time I I
+ 
+
+ align:start position:0%
+times um in the interest of time I I
+have to stop now but so the idea from
+
+ align:start position:0%
+have to stop now but so the idea from
+ 
+
+ align:start position:0%
+have to stop now but so the idea from
+today is supposed to have
+
+ align:start position:0%
+today is supposed to have
+ 
+
+ align:start position:0%
+today is supposed to have
+been lots of representations for DT
+
+ align:start position:0%
+been lots of representations for DT
+ 
+
+ align:start position:0%
+been lots of representations for DT
+signals that DT signals and
+
+ align:start position:0%
+signals that DT signals and
+ 
+
+ align:start position:0%
+signals that DT signals and
+systems strengths and weaknesses of each
+
+ align:start position:0%
+systems strengths and weaknesses of each
+ 
+
+ align:start position:0%
+systems strengths and weaknesses of each
+difference equations concise
+
+ align:start position:0%
+difference equations concise
+ 
+
+ align:start position:0%
+difference equations concise
+precise block diagrams visualizing
+
+ align:start position:0%
+precise block diagrams visualizing
+ 
+
+ align:start position:0%
+precise block diagrams visualizing
+signal flow
+
+ align:start position:0%
+signal flow
+ 
+
+ align:start position:0%
+signal flow
+paths operators thinking about things as
+
+ align:start position:0%
+paths operators thinking about things as
+ 
+
+ align:start position:0%
+paths operators thinking about things as
+polinomial and what we'll do in the next
+
+ align:start position:0%
+polinomial and what we'll do in the next
+ 
+
+ align:start position:0%
+polinomial and what we'll do in the next
+few sessions is try to build on that
+
+ align:start position:0%
+few sessions is try to build on that
+ 
+
+ align:start position:0%
+few sessions is try to build on that
+polinomial representation to gain
+
+ align:start position:0%
+polinomial representation to gain
+ 
+
+ align:start position:0%
+polinomial representation to gain
+further insights into the way that
+
+ align:start position:0%
+further insights into the way that
+ 
+
+ align:start position:0%
+further insights into the way that
+systems will
+
+ align:start position:0%
+systems will
+ 
+
+ align:start position:0%
+systems will
+work thank you
\ No newline at end of file
diff --git a/IkpQJSDK940.txt b/IkpQJSDK940.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a3b956421a75437fc1326d1492ecf59d41b1e9a1
--- /dev/null
+++ b/IkpQJSDK940.txt
@@ -0,0 +1,5955 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu hi today we're going to to
+
+ align:start position:0%
+ocw.mit.edu hi today we're going to to
+ 
+
+ align:start position:0%
+ocw.mit.edu hi today we're going to to
+begin our study of higher order
+
+ align:start position:0%
+begin our study of higher order
+ 
+
+ align:start position:0%
+begin our study of higher order
+differential equations in particular
+
+ align:start position:0%
+differential equations in particular
+ 
+
+ align:start position:0%
+differential equations in particular
+we're going to talk about a special
+
+ align:start position:0%
+we're going to talk about a special
+ 
+
+ align:start position:0%
+we're going to talk about a special
+equation called the linear differential
+
+ align:start position:0%
+equation called the linear differential
+ 
+
+ align:start position:0%
+equation called the linear differential
+equation which came up by the way you'll
+
+ align:start position:0%
+equation which came up by the way you'll
+ 
+
+ align:start position:0%
+equation which came up by the way you'll
+notice in first order equations as a
+
+ align:start position:0%
+notice in first order equations as a
+ 
+
+ align:start position:0%
+notice in first order equations as a
+special type but we're going to
+
+ align:start position:0%
+special type but we're going to
+ 
+
+ align:start position:0%
+special type but we're going to
+generalize that and the only Liberty I'm
+
+ align:start position:0%
+generalize that and the only Liberty I'm
+ 
+
+ align:start position:0%
+generalize that and the only Liberty I'm
+going to take during the lecture is to
+
+ align:start position:0%
+going to take during the lecture is to
+ 
+
+ align:start position:0%
+going to take during the lecture is to
+restrict our study to the case of
+
+ align:start position:0%
+restrict our study to the case of
+ 
+
+ align:start position:0%
+restrict our study to the case of
+differential equations of order two so
+
+ align:start position:0%
+differential equations of order two so
+ 
+
+ align:start position:0%
+differential equations of order two so
+that we won't have unwieldy Expressions
+
+ align:start position:0%
+that we won't have unwieldy Expressions
+ 
+
+ align:start position:0%
+that we won't have unwieldy Expressions
+all over the board the idea is that what
+
+ align:start position:0%
+all over the board the idea is that what
+ 
+
+ align:start position:0%
+all over the board the idea is that what
+happen s in the case of Nal 2 happens
+
+ align:start position:0%
+happen s in the case of Nal 2 happens
+ 
+
+ align:start position:0%
+happen s in the case of Nal 2 happens
+for all orders n except for a little
+
+ align:start position:0%
+for all orders n except for a little
+ 
+
+ align:start position:0%
+for all orders n except for a little
+modification in the algebra but we'll
+
+ align:start position:0%
+modification in the algebra but we'll
+ 
+
+ align:start position:0%
+modification in the algebra but we'll
+talk about that more in the exercises at
+
+ align:start position:0%
+talk about that more in the exercises at
+ 
+
+ align:start position:0%
+talk about that more in the exercises at
+any rate for the time being we simply
+
+ align:start position:0%
+any rate for the time being we simply
+ 
+
+ align:start position:0%
+any rate for the time being we simply
+call today's lecture linear differential
+
+ align:start position:0%
+call today's lecture linear differential
+ 
+
+ align:start position:0%
+call today's lecture linear differential
+equations and now I must Define for you
+
+ align:start position:0%
+equations and now I must Define for you
+ 
+
+ align:start position:0%
+equations and now I must Define for you
+what I mean by a linear differential
+
+ align:start position:0%
+what I mean by a linear differential
+ 
+
+ align:start position:0%
+what I mean by a linear differential
+equation and I'll motivate this more as
+
+ align:start position:0%
+equation and I'll motivate this more as
+ 
+
+ align:start position:0%
+equation and I'll motivate this more as
+we go along for the time being a linear
+
+ align:start position:0%
+we go along for the time being a linear
+ 
+
+ align:start position:0%
+we go along for the time being a linear
+differential equation is simply one
+
+ align:start position:0%
+differential equation is simply one
+ 
+
+ align:start position:0%
+differential equation is simply one
+which has this very special form what
+
+ align:start position:0%
+which has this very special form what
+ 
+
+ align:start position:0%
+which has this very special form what
+you have is a a y Prime term appearing
+
+ align:start position:0%
+you have is a a y Prime term appearing
+ 
+
+ align:start position:0%
+you have is a a y Prime term appearing
+then some function of X alone
+
+ align:start position:0%
+then some function of X alone
+ 
+
+ align:start position:0%
+then some function of X alone
+multiplying y prime plus some function
+
+ align:start position:0%
+multiplying y prime plus some function
+ 
+
+ align:start position:0%
+multiplying y prime plus some function
+of X alone multiplying Y and on the
+
+ align:start position:0%
+of X alone multiplying Y and on the
+ 
+
+ align:start position:0%
+of X alone multiplying Y and on the
+right some function of X alone and an
+
+ align:start position:0%
+right some function of X alone and an
+ 
+
+ align:start position:0%
+right some function of X alone and an
+analogous result would hold for higher
+
+ align:start position:0%
+analogous result would hold for higher
+ 
+
+ align:start position:0%
+analogous result would hold for higher
+order in other words you have the
+
+ align:start position:0%
+order in other words you have the
+ 
+
+ align:start position:0%
+order in other words you have the
+various derivatives of Y appearing y by
+
+ align:start position:0%
+various derivatives of Y appearing y by
+ 
+
+ align:start position:0%
+various derivatives of Y appearing y by
+itself the coefficients are always
+
+ align:start position:0%
+itself the coefficients are always
+ 
+
+ align:start position:0%
+itself the coefficients are always
+functions of X alone and no power is or
+
+ align:start position:0%
+functions of X alone and no power is or
+ 
+
+ align:start position:0%
+functions of X alone and no power is or
+no derivative or Y is raised to any
+
+ align:start position:0%
+no derivative or Y is raised to any
+ 
+
+ align:start position:0%
+no derivative or Y is raised to any
+power in particular notice here it's a
+
+ align:start position:0%
+power in particular notice here it's a
+ 
+
+ align:start position:0%
+power in particular notice here it's a
+very small point but notice here that I
+
+ align:start position:0%
+very small point but notice here that I
+ 
+
+ align:start position:0%
+very small point but notice here that I
+assume that the leading coefficient here
+
+ align:start position:0%
+assume that the leading coefficient here
+ 
+
+ align:start position:0%
+assume that the leading coefficient here
+is one for example somebody might have
+
+ align:start position:0%
+is one for example somebody might have
+ 
+
+ align:start position:0%
+is one for example somebody might have
+said couldn't you have had some function
+
+ align:start position:0%
+said couldn't you have had some function
+ 
+
+ align:start position:0%
+said couldn't you have had some function
+of x * y Prime the answer is yes I could
+
+ align:start position:0%
+of x * y Prime the answer is yes I could
+ 
+
+ align:start position:0%
+of x * y Prime the answer is yes I could
+have but I'm assuming that if I had a
+
+ align:start position:0%
+have but I'm assuming that if I had a
+ 
+
+ align:start position:0%
+have but I'm assuming that if I had a
+function say R ofx multiplying y Prime I
+
+ align:start position:0%
+function say R ofx multiplying y Prime I
+ 
+
+ align:start position:0%
+function say R ofx multiplying y Prime I
+could have multiplied both divided both
+
+ align:start position:0%
+could have multiplied both divided both
+ 
+
+ align:start position:0%
+could have multiplied both divided both
+sides of this equation through by that
+
+ align:start position:0%
+sides of this equation through by that
+ 
+
+ align:start position:0%
+sides of this equation through by that
+coefficient and wound up with an
+
+ align:start position:0%
+coefficient and wound up with an
+ 
+
+ align:start position:0%
+coefficient and wound up with an
+equation of this particular type another
+
+ align:start position:0%
+equation of this particular type another
+ 
+
+ align:start position:0%
+equation of this particular type another
+without loss of generality and this is
+
+ align:start position:0%
+without loss of generality and this is
+ 
+
+ align:start position:0%
+without loss of generality and this is
+very important though many of my
+
+ align:start position:0%
+very important though many of my
+ 
+
+ align:start position:0%
+very important though many of my
+theorems are going to be messed up a
+
+ align:start position:0%
+theorems are going to be messed up a
+ 
+
+ align:start position:0%
+theorems are going to be messed up a
+little bit if the coefficient of Y
+
+ align:start position:0%
+little bit if the coefficient of Y
+ 
+
+ align:start position:0%
+little bit if the coefficient of Y
+double Prime isn't one in other words
+
+ align:start position:0%
+double Prime isn't one in other words
+ 
+
+ align:start position:0%
+double Prime isn't one in other words
+the algebra will become a little bit
+
+ align:start position:0%
+the algebra will become a little bit
+ 
+
+ align:start position:0%
+the algebra will become a little bit
+tougher I'll speak about that later in
+
+ align:start position:0%
+tougher I'll speak about that later in
+ 
+
+ align:start position:0%
+tougher I'll speak about that later in
+the lecture if I remember to but the
+
+ align:start position:0%
+the lecture if I remember to but the
+ 
+
+ align:start position:0%
+the lecture if I remember to but the
+idea is for the time being this is all
+
+ align:start position:0%
+idea is for the time being this is all
+ 
+
+ align:start position:0%
+idea is for the time being this is all
+we mean by a linear differential
+
+ align:start position:0%
+we mean by a linear differential
+ 
+
+ align:start position:0%
+we mean by a linear differential
+equation and perhaps the best way to
+
+ align:start position:0%
+equation and perhaps the best way to
+ 
+
+ align:start position:0%
+equation and perhaps the best way to
+emphasize what we really mean by linear
+
+ align:start position:0%
+emphasize what we really mean by linear
+ 
+
+ align:start position:0%
+emphasize what we really mean by linear
+differential equation is to show what we
+
+ align:start position:0%
+differential equation is to show what we
+ 
+
+ align:start position:0%
+differential equation is to show what we
+mean by a nonlinear differential
+
+ align:start position:0%
+mean by a nonlinear differential
+ 
+
+ align:start position:0%
+mean by a nonlinear differential
+equation a differential equ equation
+
+ align:start position:0%
+equation a differential equ equation
+ 
+
+ align:start position:0%
+equation a differential equ equation
+which is not linear for example y Prime
+
+ align:start position:0%
+which is not linear for example y Prime
+ 
+
+ align:start position:0%
+which is not linear for example y Prime
++ y Prime 2 + y = sinx would not be a
+
+ align:start position:0%
++ y Prime 2 + y = sinx would not be a
+ 
+
+ align:start position:0%
++ y Prime 2 + y = sinx would not be a
+linear equation because the Y Prime term
+
+ align:start position:0%
+linear equation because the Y Prime term
+ 
+
+ align:start position:0%
+linear equation because the Y Prime term
+is being raised to a power other than
+
+ align:start position:0%
+is being raised to a power other than
+ 
+
+ align:start position:0%
+is being raised to a power other than
+the first Power see it's squid y Prime +
+
+ align:start position:0%
+the first Power see it's squid y Prime +
+ 
+
+ align:start position:0%
+the first Power see it's squid y Prime +
+y * y Prime = e x is not a linear
+
+ align:start position:0%
+y * y Prime = e x is not a linear
+ 
+
+ align:start position:0%
+y * y Prime = e x is not a linear
+equation because the multiplier of Y
+
+ align:start position:0%
+equation because the multiplier of Y
+ 
+
+ align:start position:0%
+equation because the multiplier of Y
+Prime is y as opposed to just a function
+
+ align:start position:0%
+Prime is y as opposed to just a function
+ 
+
+ align:start position:0%
+Prime is y as opposed to just a function
+of X which is what the definition calls
+
+ align:start position:0%
+of X which is what the definition calls
+ 
+
+ align:start position:0%
+of X which is what the definition calls
+for y Prime + XY Prime + y^2 = x Cub is
+
+ align:start position:0%
+for y Prime + XY Prime + y^2 = x Cub is
+ 
+
+ align:start position:0%
+for y Prime + XY Prime + y^2 = x Cub is
+not linear and the reason that it's not
+
+ align:start position:0%
+not linear and the reason that it's not
+ 
+
+ align:start position:0%
+not linear and the reason that it's not
+linear is because y appears to a power
+
+ align:start position:0%
+linear is because y appears to a power
+ 
+
+ align:start position:0%
+linear is because y appears to a power
+higher than the first maybe I should
+
+ align:start position:0%
+higher than the first maybe I should
+ 
+
+ align:start position:0%
+higher than the first maybe I should
+Circle the things that prevent these
+
+ align:start position:0%
+Circle the things that prevent these
+ 
+
+ align:start position:0%
+Circle the things that prevent these
+things from being linear so that you can
+
+ align:start position:0%
+things from being linear so that you can
+ 
+
+ align:start position:0%
+things from being linear so that you can
+see what's happening here y Prime + e x
+
+ align:start position:0%
+see what's happening here y Prime + e x
+ 
+
+ align:start position:0%
+see what's happening here y Prime + e x
+y Prime + x Cub y = tan Y is not linear
+
+ align:start position:0%
+y Prime + x Cub y = tan Y is not linear
+ 
+
+ align:start position:0%
+y Prime + x Cub y = tan Y is not linear
+because even though the left hand side
+
+ align:start position:0%
+because even though the left hand side
+ 
+
+ align:start position:0%
+because even though the left hand side
+is fine notice that the function on the
+
+ align:start position:0%
+is fine notice that the function on the
+ 
+
+ align:start position:0%
+is fine notice that the function on the
+right hand side is a function of Y
+
+ align:start position:0%
+right hand side is a function of Y
+ 
+
+ align:start position:0%
+right hand side is a function of Y
+depends on y rather than just X
+
+ align:start position:0%
+depends on y rather than just X
+ 
+
+ align:start position:0%
+depends on y rather than just X
+alone and to finish this off an example
+
+ align:start position:0%
+alone and to finish this off an example
+ 
+
+ align:start position:0%
+alone and to finish this off an example
+of a linear equation would be what well
+
+ align:start position:0%
+of a linear equation would be what well
+ 
+
+ align:start position:0%
+of a linear equation would be what well
+almost this one y prime plus e x y Prime
+
+ align:start position:0%
+almost this one y prime plus e x y Prime
+ 
+
+ align:start position:0%
+almost this one y prime plus e x y Prime
++ x Cub y equal tangent X you see a y
+
+ align:start position:0%
++ x Cub y equal tangent X you see a y
+ 
+
+ align:start position:0%
++ x Cub y equal tangent X you see a y
+Prime term y Prime to the first power
+
+ align:start position:0%
+Prime term y Prime to the first power
+ 
+
+ align:start position:0%
+Prime term y Prime to the first power
+being multiplied by a function of X
+
+ align:start position:0%
+being multiplied by a function of X
+ 
+
+ align:start position:0%
+being multiplied by a function of X
+alone y to the first power being
+
+ align:start position:0%
+alone y to the first power being
+ 
+
+ align:start position:0%
+alone y to the first power being
+multiplied by by a function of X alone
+
+ align:start position:0%
+multiplied by by a function of X alone
+ 
+
+ align:start position:0%
+multiplied by by a function of X alone
+and the right hand side being a function
+
+ align:start position:0%
+and the right hand side being a function
+ 
+
+ align:start position:0%
+and the right hand side being a function
+of X explicitly by itself and notice by
+
+ align:start position:0%
+of X explicitly by itself and notice by
+ 
+
+ align:start position:0%
+of X explicitly by itself and notice by
+the way don't get caught in a
+
+ align:start position:0%
+the way don't get caught in a
+ 
+
+ align:start position:0%
+the way don't get caught in a
+psychological hangup here when I say
+
+ align:start position:0%
+psychological hangup here when I say
+ 
+
+ align:start position:0%
+psychological hangup here when I say
+linear it's I'm modifying the equation
+
+ align:start position:0%
+linear it's I'm modifying the equation
+ 
+
+ align:start position:0%
+linear it's I'm modifying the equation
+not what the coefficients look like in
+
+ align:start position:0%
+not what the coefficients look like in
+ 
+
+ align:start position:0%
+not what the coefficients look like in
+other words certainly we don't think of
+
+ align:start position:0%
+other words certainly we don't think of
+ 
+
+ align:start position:0%
+other words certainly we don't think of
+e to the X as a linear function we don't
+
+ align:start position:0%
+e to the X as a linear function we don't
+ 
+
+ align:start position:0%
+e to the X as a linear function we don't
+think of X cubed as being linear we
+
+ align:start position:0%
+think of X cubed as being linear we
+ 
+
+ align:start position:0%
+think of X cubed as being linear we
+don't think of tangent X as being linear
+
+ align:start position:0%
+don't think of tangent X as being linear
+ 
+
+ align:start position:0%
+don't think of tangent X as being linear
+the coefficients do not have to be
+
+ align:start position:0%
+the coefficients do not have to be
+ 
+
+ align:start position:0%
+the coefficients do not have to be
+linear functions of x they have to be
+
+ align:start position:0%
+linear functions of x they have to be
+ 
+
+ align:start position:0%
+linear functions of x they have to be
+functions of X alone it's the equation
+
+ align:start position:0%
+functions of X alone it's the equation
+ 
+
+ align:start position:0%
+functions of X alone it's the equation
+that's called linear and maybe the best
+
+ align:start position:0%
+that's called linear and maybe the best
+ 
+
+ align:start position:0%
+that's called linear and maybe the best
+way to explain that is in the following
+
+ align:start position:0%
+way to explain that is in the following
+ 
+
+ align:start position:0%
+way to explain that is in the following
+way let's look at y prime plus P of X Y
+
+ align:start position:0%
+way let's look at y prime plus P of X Y
+ 
+
+ align:start position:0%
+way let's look at y prime plus P of X Y
+prime plus q ofx y my claim is I can
+
+ align:start position:0%
+prime plus q ofx y my claim is I can
+ 
+
+ align:start position:0%
+prime plus q ofx y my claim is I can
+think of this as a function machine
+
+ align:start position:0%
+think of this as a function machine
+ 
+
+ align:start position:0%
+think of this as a function machine
+where the input is y and the Machine is
+
+ align:start position:0%
+where the input is y and the Machine is
+ 
+
+ align:start position:0%
+where the input is y and the Machine is
+told look at whatever y comes in
+
+ align:start position:0%
+told look at whatever y comes in
+ 
+
+ align:start position:0%
+told look at whatever y comes in
+differentiate it twice add on P of x *
+
+ align:start position:0%
+differentiate it twice add on P of x *
+ 
+
+ align:start position:0%
+differentiate it twice add on P of x *
+the first derivative plus Q ofx * the
+
+ align:start position:0%
+the first derivative plus Q ofx * the
+ 
+
+ align:start position:0%
+the first derivative plus Q ofx * the
+function and that will be the output in
+
+ align:start position:0%
+function and that will be the output in
+ 
+
+ align:start position:0%
+function and that will be the output in
+other words I could think of a machine
+
+ align:start position:0%
+other words I could think of a machine
+ 
+
+ align:start position:0%
+other words I could think of a machine
+where the input of the machine is y and
+
+ align:start position:0%
+where the input of the machine is y and
+ 
+
+ align:start position:0%
+where the input of the machine is y and
+let me call the machine the L machine to
+
+ align:start position:0%
+let me call the machine the L machine to
+ 
+
+ align:start position:0%
+let me call the machine the L machine to
+emphasize the word linear see what L
+
+ align:start position:0%
+emphasize the word linear see what L
+ 
+
+ align:start position:0%
+emphasize the word linear see what L
+does is this the domain of L are
+
+ align:start position:0%
+does is this the domain of L are
+ 
+
+ align:start position:0%
+does is this the domain of L are
+functions which are twice differentiable
+
+ align:start position:0%
+functions which are twice differentiable
+ 
+
+ align:start position:0%
+functions which are twice differentiable
+after all to for this to make sense I
+
+ align:start position:0%
+after all to for this to make sense I
+ 
+
+ align:start position:0%
+after all to for this to make sense I
+have to be able to differentiate Y at
+
+ align:start position:0%
+have to be able to differentiate Y at
+ 
+
+ align:start position:0%
+have to be able to differentiate Y at
+least twice so the input of the L
+
+ align:start position:0%
+least twice so the input of the L
+ 
+
+ align:start position:0%
+least twice so the input of the L
+machine is a twice differentiable
+
+ align:start position:0%
+machine is a twice differentiable
+ 
+
+ align:start position:0%
+machine is a twice differentiable
+function of X and the output is some
+
+ align:start position:0%
+function of X and the output is some
+ 
+
+ align:start position:0%
+function of X and the output is some
+function of X you see y Prime y Prime
+
+ align:start position:0%
+function of X you see y Prime y Prime
+ 
+
+ align:start position:0%
+function of X you see y Prime y Prime
+are functions of x p and Q are functions
+
+ align:start position:0%
+are functions of x p and Q are functions
+ 
+
+ align:start position:0%
+are functions of x p and Q are functions
+of X Y is a function of X all these
+
+ align:start position:0%
+of X Y is a function of X all these
+ 
+
+ align:start position:0%
+of X Y is a function of X all these
+things combine them to give you a
+
+ align:start position:0%
+things combine them to give you a
+ 
+
+ align:start position:0%
+things combine them to give you a
+function of X let me show you how this
+
+ align:start position:0%
+function of X let me show you how this
+ 
+
+ align:start position:0%
+function of X let me show you how this
+machine works for example if the L
+
+ align:start position:0%
+machine works for example if the L
+ 
+
+ align:start position:0%
+machine works for example if the L
+machine is y prime plus e the X Y Prime
+
+ align:start position:0%
+machine is y prime plus e the X Y Prime
+ 
+
+ align:start position:0%
+machine is y prime plus e the X Y Prime
++ x Cub y see other was L of y equals
+
+ align:start position:0%
++ x Cub y see other was L of y equals
+ 
+
+ align:start position:0%
++ x Cub y see other was L of y equals
+this if I feed in sinx to the L machine
+
+ align:start position:0%
+this if I feed in sinx to the L machine
+ 
+
+ align:start position:0%
+this if I feed in sinx to the L machine
+what does the L machine do it takes sinx
+
+ align:start position:0%
+what does the L machine do it takes sinx
+ 
+
+ align:start position:0%
+what does the L machine do it takes sinx
+it differentiates it twice adds on e x *
+
+ align:start position:0%
+it differentiates it twice adds on e x *
+ 
+
+ align:start position:0%
+it differentiates it twice adds on e x *
+the first derivative and X Cub time the
+
+ align:start position:0%
+the first derivative and X Cub time the
+ 
+
+ align:start position:0%
+the first derivative and X Cub time the
+function itself which is sinx going
+
+ align:start position:0%
+function itself which is sinx going
+ 
+
+ align:start position:0%
+function itself which is sinx going
+through this operation which is Trivial
+
+ align:start position:0%
+through this operation which is Trivial
+ 
+
+ align:start position:0%
+through this operation which is Trivial
+L of sinx would be X Cub - 1 sinx plus e
+
+ align:start position:0%
+L of sinx would be X Cub - 1 sinx plus e
+ 
+
+ align:start position:0%
+L of sinx would be X Cub - 1 sinx plus e
+x cine X by the way to help you
+
+ align:start position:0%
+x cine X by the way to help you
+ 
+
+ align:start position:0%
+x cine X by the way to help you
+understand what we mean by a solution
+
+ align:start position:0%
+understand what we mean by a solution
+ 
+
+ align:start position:0%
+understand what we mean by a solution
+notice that what we're saying is that if
+
+ align:start position:0%
+notice that what we're saying is that if
+ 
+
+ align:start position:0%
+notice that what we're saying is that if
+we were to refer back to this particular
+
+ align:start position:0%
+we were to refer back to this particular
+ 
+
+ align:start position:0%
+we were to refer back to this particular
+equation Y = sinx would not be a
+
+ align:start position:0%
+equation Y = sinx would not be a
+ 
+
+ align:start position:0%
+equation Y = sinx would not be a
+solution of this equation because when I
+
+ align:start position:0%
+solution of this equation because when I
+ 
+
+ align:start position:0%
+solution of this equation because when I
+feed sinx into the L machine I do not
+
+ align:start position:0%
+feed sinx into the L machine I do not
+ 
+
+ align:start position:0%
+feed sinx into the L machine I do not
+get tangent X which is what a solution
+
+ align:start position:0%
+get tangent X which is what a solution
+ 
+
+ align:start position:0%
+get tangent X which is what a solution
+would mean in other words in terms of
+
+ align:start position:0%
+would mean in other words in terms of
+ 
+
+ align:start position:0%
+would mean in other words in terms of
+our new notation this says L of y equals
+
+ align:start position:0%
+our new notation this says L of y equals
+ 
+
+ align:start position:0%
+our new notation this says L of y equals
+Tan x so anything which is a solution
+
+ align:start position:0%
+Tan x so anything which is a solution
+ 
+
+ align:start position:0%
+Tan x so anything which is a solution
+means if I shove in y to the machine the
+
+ align:start position:0%
+means if I shove in y to the machine the
+ 
+
+ align:start position:0%
+means if I shove in y to the machine the
+output would have to be Tan x to look at
+
+ align:start position:0%
+output would have to be Tan x to look at
+ 
+
+ align:start position:0%
+output would have to be Tan x to look at
+this from a different perspective if the
+
+ align:start position:0%
+this from a different perspective if the
+ 
+
+ align:start position:0%
+this from a different perspective if the
+right hand side of my equation had been
+
+ align:start position:0%
+right hand side of my equation had been
+ 
+
+ align:start position:0%
+right hand side of my equation had been
+this in other words if Tan x had been
+
+ align:start position:0%
+this in other words if Tan x had been
+ 
+
+ align:start position:0%
+this in other words if Tan x had been
+replaced by X Cub - 1 sinx plus e x cinx
+
+ align:start position:0%
+replaced by X Cub - 1 sinx plus e x cinx
+ 
+
+ align:start position:0%
+replaced by X Cub - 1 sinx plus e x cinx
+then y = sinx would have been a solution
+
+ align:start position:0%
+then y = sinx would have been a solution
+ 
+
+ align:start position:0%
+then y = sinx would have been a solution
+of this particular equation but enough
+
+ align:start position:0%
+of this particular equation but enough
+ 
+
+ align:start position:0%
+of this particular equation but enough
+about that and we'll emphasize that more
+
+ align:start position:0%
+about that and we'll emphasize that more
+ 
+
+ align:start position:0%
+about that and we'll emphasize that more
+in the exercises the key Point as to why
+
+ align:start position:0%
+in the exercises the key Point as to why
+ 
+
+ align:start position:0%
+in the exercises the key Point as to why
+the word linear is used is that linear
+
+ align:start position:0%
+the word linear is used is that linear
+ 
+
+ align:start position:0%
+the word linear is used is that linear
+modifies our L machine not the
+
+ align:start position:0%
+modifies our L machine not the
+ 
+
+ align:start position:0%
+modifies our L machine not the
+coefficients of the differential
+
+ align:start position:0%
+coefficients of the differential
+ 
+
+ align:start position:0%
+coefficients of the differential
+equation see what did linear mean when
+
+ align:start position:0%
+equation see what did linear mean when
+ 
+
+ align:start position:0%
+equation see what did linear mean when
+we were dealing with ordinary linear
+
+ align:start position:0%
+we were dealing with ordinary linear
+ 
+
+ align:start position:0%
+we were dealing with ordinary linear
+change of variables back in Block four
+
+ align:start position:0%
+change of variables back in Block four
+ 
+
+ align:start position:0%
+change of variables back in Block four
+of the course when we talked about U =
+
+ align:start position:0%
+of the course when we talked about U =
+ 
+
+ align:start position:0%
+of the course when we talked about U =
+ax + b y and talked about linear
+
+ align:start position:0%
+ax + b y and talked about linear
+ 
+
+ align:start position:0%
+ax + b y and talked about linear
+approximations linear meant if the
+
+ align:start position:0%
+approximations linear meant if the
+ 
+
+ align:start position:0%
+approximations linear meant if the
+mapping was linear L of a constant times
+
+ align:start position:0%
+mapping was linear L of a constant times
+ 
+
+ align:start position:0%
+mapping was linear L of a constant times
+the input would be the constant time L
+
+ align:start position:0%
+the input would be the constant time L
+ 
+
+ align:start position:0%
+the input would be the constant time L
+of the input in other words you could
+
+ align:start position:0%
+of the input in other words you could
+ 
+
+ align:start position:0%
+of the input in other words you could
+Factor the constant out notice by the
+
+ align:start position:0%
+Factor the constant out notice by the
+ 
+
+ align:start position:0%
+Factor the constant out notice by the
+way if I Fe if I feed CU into my L
+
+ align:start position:0%
+way if I Fe if I feed CU into my L
+ 
+
+ align:start position:0%
+way if I Fe if I feed CU into my L
+machine what will the output be see be
+
+ align:start position:0%
+machine what will the output be see be
+ 
+
+ align:start position:0%
+machine what will the output be see be
+very careful here don't be blinded by
+
+ align:start position:0%
+very careful here don't be blinded by
+ 
+
+ align:start position:0%
+very careful here don't be blinded by
+the y y stands for the for the
+
+ align:start position:0%
+the y y stands for the for the
+ 
+
+ align:start position:0%
+the y y stands for the for the
+placeholder the input in other words L
+
+ align:start position:0%
+placeholder the input in other words L
+ 
+
+ align:start position:0%
+placeholder the input in other words L
+of anything is the second derivative of
+
+ align:start position:0%
+of anything is the second derivative of
+ 
+
+ align:start position:0%
+of anything is the second derivative of
+that anything plus P * the first
+
+ align:start position:0%
+that anything plus P * the first
+ 
+
+ align:start position:0%
+that anything plus P * the first
+derivative plus Q times that input the
+
+ align:start position:0%
+derivative plus Q times that input the
+ 
+
+ align:start position:0%
+derivative plus Q times that input the
+anything that I put in here so notice
+
+ align:start position:0%
+anything that I put in here so notice
+ 
+
+ align:start position:0%
+anything that I put in here so notice
+that L of Cu would be the quantity CU
+
+ align:start position:0%
+that L of Cu would be the quantity CU
+ 
+
+ align:start position:0%
+that L of Cu would be the quantity CU
+prime plus P of x * CU prime plus Q ofx
+
+ align:start position:0%
+prime plus P of x * CU prime plus Q ofx
+ 
+
+ align:start position:0%
+prime plus P of x * CU prime plus Q ofx
+* CU in other words L of Cu is equal to
+
+ align:start position:0%
+* CU in other words L of Cu is equal to
+ 
+
+ align:start position:0%
+* CU in other words L of Cu is equal to
+this expression here notice that
+
+ align:start position:0%
+this expression here notice that
+ 
+
+ align:start position:0%
+this expression here notice that
+different differentiating a constant
+
+ align:start position:0%
+different differentiating a constant
+ 
+
+ align:start position:0%
+different differentiating a constant
+times a function of X means that we skip
+
+ align:start position:0%
+times a function of X means that we skip
+ 
+
+ align:start position:0%
+times a function of X means that we skip
+over the constant and just differentiate
+
+ align:start position:0%
+over the constant and just differentiate
+ 
+
+ align:start position:0%
+over the constant and just differentiate
+the function of X in other words
+
+ align:start position:0%
+the function of X in other words
+ 
+
+ align:start position:0%
+the function of X in other words
+differentiating this twice would just be
+
+ align:start position:0%
+differentiating this twice would just be
+ 
+
+ align:start position:0%
+differentiating this twice would just be
+the constant time uble Prime I can take
+
+ align:start position:0%
+the constant time uble Prime I can take
+ 
+
+ align:start position:0%
+the constant time uble Prime I can take
+the constant out here I can take the
+
+ align:start position:0%
+the constant out here I can take the
+ 
+
+ align:start position:0%
+the constant out here I can take the
+constant out here in other words C
+
+ align:start position:0%
+constant out here in other words C
+ 
+
+ align:start position:0%
+constant out here in other words C
+factors out that's where linearity comes
+
+ align:start position:0%
+factors out that's where linearity comes
+ 
+
+ align:start position:0%
+factors out that's where linearity comes
+in this is linear in c i factored the C
+
+ align:start position:0%
+in this is linear in c i factored the C
+ 
+
+ align:start position:0%
+in this is linear in c i factored the C
+out what's left is What U prime plus p u
+
+ align:start position:0%
+out what's left is What U prime plus p u
+ 
+
+ align:start position:0%
+out what's left is What U prime plus p u
+Prime + q u that's what we're calling L
+
+ align:start position:0%
+Prime + q u that's what we're calling L
+ 
+
+ align:start position:0%
+Prime + q u that's what we're calling L
+of U so L of C * U is C * L of U which
+
+ align:start position:0%
+of U so L of C * U is C * L of U which
+ 
+
+ align:start position:0%
+of U so L of C * U is C * L of U which
+is a linear property and by the way
+
+ align:start position:0%
+is a linear property and by the way
+ 
+
+ align:start position:0%
+is a linear property and by the way
+again let me emphasize why linearity
+
+ align:start position:0%
+again let me emphasize why linearity
+ 
+
+ align:start position:0%
+again let me emphasize why linearity
+definition was given the way it was for
+
+ align:start position:0%
+definition was given the way it was for
+ 
+
+ align:start position:0%
+definition was given the way it was for
+example I just say here that it's not
+
+ align:start position:0%
+example I just say here that it's not
+ 
+
+ align:start position:0%
+example I just say here that it's not
+true if nonlinear but for example
+
+ align:start position:0%
+true if nonlinear but for example
+ 
+
+ align:start position:0%
+true if nonlinear but for example
+suppose I had an equation that had y
+
+ align:start position:0%
+suppose I had an equation that had y
+ 
+
+ align:start position:0%
+suppose I had an equation that had y
+Prime multiplied by a function of Y
+
+ align:start position:0%
+Prime multiplied by a function of Y
+ 
+
+ align:start position:0%
+Prime multiplied by a function of Y
+rather than a function of X in other
+
+ align:start position:0%
+rather than a function of X in other
+ 
+
+ align:start position:0%
+rather than a function of X in other
+words let's look at L of y equals y * y
+
+ align:start position:0%
+words let's look at L of y equals y * y
+ 
+
+ align:start position:0%
+words let's look at L of y equals y * y
+Prime if I now replace y by C * U this
+
+ align:start position:0%
+Prime if I now replace y by C * U this
+ 
+
+ align:start position:0%
+Prime if I now replace y by C * U this
+becomes what Y is replaced by C * u y
+
+ align:start position:0%
+becomes what Y is replaced by C * u y
+ 
+
+ align:start position:0%
+becomes what Y is replaced by C * u y
+Prime is replaced by the derivative of
+
+ align:start position:0%
+Prime is replaced by the derivative of
+ 
+
+ align:start position:0%
+Prime is replaced by the derivative of
+Cu well what is the derivative of Cu U
+
+ align:start position:0%
+Cu well what is the derivative of Cu U
+ 
+
+ align:start position:0%
+Cu well what is the derivative of Cu U
+if C is a constant it's C * U Prime in
+
+ align:start position:0%
+if C is a constant it's C * U Prime in
+ 
+
+ align:start position:0%
+if C is a constant it's C * U Prime in
+other words the right hand side here is
+
+ align:start position:0%
+other words the right hand side here is
+ 
+
+ align:start position:0%
+other words the right hand side here is
+just c^ 2 U * U Prime U * U Prime is L
+
+ align:start position:0%
+just c^ 2 U * U Prime U * U Prime is L
+ 
+
+ align:start position:0%
+just c^ 2 U * U Prime U * U Prime is L
+of U in other words in this example L of
+
+ align:start position:0%
+of U in other words in this example L of
+ 
+
+ align:start position:0%
+of U in other words in this example L of
+cuu would not be c l of U it would be C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squid L of U which is not the linear
+
+ align:start position:0%
+squid L of U which is not the linear
+ 
+
+ align:start position:0%
+squid L of U which is not the linear
+property that we're talking about
+
+ align:start position:0%
+property that we're talking about
+ 
+
+ align:start position:0%
+property that we're talking about
+finally the other property of linearity
+
+ align:start position:0%
+finally the other property of linearity
+ 
+
+ align:start position:0%
+finally the other property of linearity
+is that if U if I replace my input by
+
+ align:start position:0%
+is that if U if I replace my input by
+ 
+
+ align:start position:0%
+is that if U if I replace my input by
+the sum of two differentiable functions
+
+ align:start position:0%
+the sum of two differentiable functions
+ 
+
+ align:start position:0%
+the sum of two differentiable functions
+U1 and U2 that L of U1 + U2 turns out to
+
+ align:start position:0%
+U1 and U2 that L of U1 + U2 turns out to
+ 
+
+ align:start position:0%
+U1 and U2 that L of U1 + U2 turns out to
+be L of U1 plus L of U2 and the proof
+
+ align:start position:0%
+be L of U1 plus L of U2 and the proof
+ 
+
+ align:start position:0%
+be L of U1 plus L of U2 and the proof
+again is just by looking at the
+
+ align:start position:0%
+again is just by looking at the
+ 
+
+ align:start position:0%
+again is just by looking at the
+definition if I feed U1 plus U2 into my
+
+ align:start position:0%
+definition if I feed U1 plus U2 into my
+ 
+
+ align:start position:0%
+definition if I feed U1 plus U2 into my
+L machine I have what U1 plus U2 prime
+
+ align:start position:0%
+L machine I have what U1 plus U2 prime
+ 
+
+ align:start position:0%
+L machine I have what U1 plus U2 prime
+plus P of x * U 1 + U2 prime plus Q of x
+
+ align:start position:0%
+plus P of x * U 1 + U2 prime plus Q of x
+ 
+
+ align:start position:0%
+plus P of x * U 1 + U2 prime plus Q of x
+* U1 + U2 the derivative of the sum is a
+
+ align:start position:0%
+* U1 + U2 the derivative of the sum is a
+ 
+
+ align:start position:0%
+* U1 + U2 the derivative of the sum is a
+sum of the derivatives so I can split
+
+ align:start position:0%
+sum of the derivatives so I can split
+ 
+
+ align:start position:0%
+sum of the derivatives so I can split
+this up into U1 prime plus U2 Prime
+
+ align:start position:0%
+this up into U1 prime plus U2 Prime
+ 
+
+ align:start position:0%
+this up into U1 prime plus U2 Prime
+similarly this is p U1 Prime P U2 Prime
+
+ align:start position:0%
+similarly this is p U1 Prime P U2 Prime
+ 
+
+ align:start position:0%
+similarly this is p U1 Prime P U2 Prime
+this is q1 qu2 I break down the U1 terms
+
+ align:start position:0%
+this is q1 qu2 I break down the U1 terms
+ 
+
+ align:start position:0%
+this is q1 qu2 I break down the U1 terms
+together the U2 terms together this by
+
+ align:start position:0%
+together the U2 terms together this by
+ 
+
+ align:start position:0%
+together the U2 terms together this by
+definition is L of
+
+ align:start position:0%
+definition is L of
+ 
+
+ align:start position:0%
+definition is L of
+U1 this by definition of l is L of U2 in
+
+ align:start position:0%
+U1 this by definition of l is L of U2 in
+ 
+
+ align:start position:0%
+U1 this by definition of l is L of U2 in
+other words l L of U1 + U2 is L of U1
+
+ align:start position:0%
+other words l L of U1 + U2 is L of U1
+ 
+
+ align:start position:0%
+other words l L of U1 + U2 is L of U1
+plus L of U2 by the way conditions 1 and
+
+ align:start position:0%
+plus L of U2 by the way conditions 1 and
+ 
+
+ align:start position:0%
+plus L of U2 by the way conditions 1 and
+two can be stated equivalently by the
+
+ align:start position:0%
+two can be stated equivalently by the
+ 
+
+ align:start position:0%
+two can be stated equivalently by the
+one statement L of C1 U1 plus C2 U2 is
+
+ align:start position:0%
+one statement L of C1 U1 plus C2 U2 is
+ 
+
+ align:start position:0%
+one statement L of C1 U1 plus C2 U2 is
+C1 L of U1 plus C2 L of U2 the proof
+
+ align:start position:0%
+C1 L of U1 plus C2 L of U2 the proof
+ 
+
+ align:start position:0%
+C1 L of U1 plus C2 L of U2 the proof
+will be left as an exercise it's a
+
+ align:start position:0%
+will be left as an exercise it's a
+ 
+
+ align:start position:0%
+will be left as an exercise it's a
+fairly trivial observation and I think
+
+ align:start position:0%
+fairly trivial observation and I think
+ 
+
+ align:start position:0%
+fairly trivial observation and I think
+as I you may remember that we did
+
+ align:start position:0%
+as I you may remember that we did
+ 
+
+ align:start position:0%
+as I you may remember that we did
+something at least similar to this in
+
+ align:start position:0%
+something at least similar to this in
+ 
+
+ align:start position:0%
+something at least similar to this in
+Block four when we talked about linear
+
+ align:start position:0%
+Block four when we talked about linear
+ 
+
+ align:start position:0%
+Block four when we talked about linear
+mappings when we were mapping the XY
+
+ align:start position:0%
+mappings when we were mapping the XY
+ 
+
+ align:start position:0%
+mappings when we were mapping the XY
+plane into the UV plane okay but at any
+
+ align:start position:0%
+plane into the UV plane okay but at any
+ 
+
+ align:start position:0%
+plane into the UV plane okay but at any
+rate let's see what all this means why
+
+ align:start position:0%
+rate let's see what all this means why
+ 
+
+ align:start position:0%
+rate let's see what all this means why
+why are these properties so important
+
+ align:start position:0%
+why are these properties so important
+ 
+
+ align:start position:0%
+why are these properties so important
+and so let's call our next sub subtopic
+
+ align:start position:0%
+and so let's call our next sub subtopic
+ 
+
+ align:start position:0%
+and so let's call our next sub subtopic
+properties of linear equations and the
+
+ align:start position:0%
+properties of linear equations and the
+ 
+
+ align:start position:0%
+properties of linear equations and the
+first thing that I'd like to point out
+
+ align:start position:0%
+first thing that I'd like to point out
+ 
+
+ align:start position:0%
+first thing that I'd like to point out
+is that if the right hand side of our
+
+ align:start position:0%
+is that if the right hand side of our
+ 
+
+ align:start position:0%
+is that if the right hand side of our
+linear differential equation is zero the
+
+ align:start position:0%
+linear differential equation is zero the
+ 
+
+ align:start position:0%
+linear differential equation is zero the
+interesting fact is that any linear
+
+ align:start position:0%
+interesting fact is that any linear
+ 
+
+ align:start position:0%
+interesting fact is that any linear
+combination of solutions of that
+
+ align:start position:0%
+combination of solutions of that
+ 
+
+ align:start position:0%
+combination of solutions of that
+equation is again a solution and in
+
+ align:start position:0%
+equation is again a solution and in
+ 
+
+ align:start position:0%
+equation is again a solution and in
+other words if I find some function U1
+
+ align:start position:0%
+other words if I find some function U1
+ 
+
+ align:start position:0%
+other words if I find some function U1
+of X that satisfies the equation L of y
+
+ align:start position:0%
+of X that satisfies the equation L of y
+ 
+
+ align:start position:0%
+of X that satisfies the equation L of y
+equals 0 in other words L of U1 is 0 and
+
+ align:start position:0%
+equals 0 in other words L of U1 is 0 and
+ 
+
+ align:start position:0%
+equals 0 in other words L of U1 is 0 and
+I also know that L of U2 is zero then
+
+ align:start position:0%
+I also know that L of U2 is zero then
+ 
+
+ align:start position:0%
+I also know that L of U2 is zero then
+the amazing thing is that L of C1 U1
+
+ align:start position:0%
+the amazing thing is that L of C1 U1
+ 
+
+ align:start position:0%
+the amazing thing is that L of C1 U1
+plus C2 U2 is also zero in other words
+
+ align:start position:0%
+plus C2 U2 is also zero in other words
+ 
+
+ align:start position:0%
+plus C2 U2 is also zero in other words
+any linear combination of U1 and U2
+
+ align:start position:0%
+any linear combination of U1 and U2
+ 
+
+ align:start position:0%
+any linear combination of U1 and U2
+where U1 and U2 are solutions of L of y
+
+ align:start position:0%
+where U1 and U2 are solutions of L of y
+ 
+
+ align:start position:0%
+where U1 and U2 are solutions of L of y
+equals 0 will also be a solution of L of
+
+ align:start position:0%
+equals 0 will also be a solution of L of
+ 
+
+ align:start position:0%
+equals 0 will also be a solution of L of
+y equal 0 and the proof again is trivial
+
+ align:start position:0%
+y equal 0 and the proof again is trivial
+ 
+
+ align:start position:0%
+y equal 0 and the proof again is trivial
+namely by Def by the properties of
+
+ align:start position:0%
+namely by Def by the properties of
+ 
+
+ align:start position:0%
+namely by Def by the properties of
+linearity L of C1 U1 plus C2 U2 is what
+
+ align:start position:0%
+linearity L of C1 U1 plus C2 U2 is what
+ 
+
+ align:start position:0%
+linearity L of C1 U1 plus C2 U2 is what
+it's C1 L of U1 plus C2 L of U2 L of U1
+
+ align:start position:0%
+it's C1 L of U1 plus C2 L of U2 L of U1
+ 
+
+ align:start position:0%
+it's C1 L of U1 plus C2 L of U2 L of U1
+is zero L of U2 is zero that was given
+
+ align:start position:0%
+is zero L of U2 is zero that was given
+ 
+
+ align:start position:0%
+is zero L of U2 is zero that was given
+you see consequently this is zero see a
+
+ align:start position:0%
+you see consequently this is zero see a
+ 
+
+ align:start position:0%
+you see consequently this is zero see a
+constant time0 plus a constant time 0 is
+
+ align:start position:0%
+constant time0 plus a constant time 0 is
+ 
+
+ align:start position:0%
+constant time0 plus a constant time 0 is
+zero and that's exactly what we wanted
+
+ align:start position:0%
+zero and that's exactly what we wanted
+ 
+
+ align:start position:0%
+zero and that's exactly what we wanted
+to show over here a second important
+
+ align:start position:0%
+to show over here a second important
+ 
+
+ align:start position:0%
+to show over here a second important
+factor is that if I have a solution of L
+
+ align:start position:0%
+factor is that if I have a solution of L
+ 
+
+ align:start position:0%
+factor is that if I have a solution of L
+yal 0 say l of U is z and I also have a
+
+ align:start position:0%
+yal 0 say l of U is z and I also have a
+ 
+
+ align:start position:0%
+yal 0 say l of U is z and I also have a
+solution V of the equation L of yal f
+
+ align:start position:0%
+solution V of the equation L of yal f
+ 
+
+ align:start position:0%
+solution V of the equation L of yal f
+ofx in other words if L of U is zero and
+
+ align:start position:0%
+ofx in other words if L of U is zero and
+ 
+
+ align:start position:0%
+ofx in other words if L of U is zero and
+L of V is f ofx the amazing thing is
+
+ align:start position:0%
+L of V is f ofx the amazing thing is
+ 
+
+ align:start position:0%
+L of V is f ofx the amazing thing is
+that if I add these two solutions
+
+ align:start position:0%
+that if I add these two solutions
+ 
+
+ align:start position:0%
+that if I add these two solutions
+together the resulting function will be
+
+ align:start position:0%
+together the resulting function will be
+ 
+
+ align:start position:0%
+together the resulting function will be
+a solution of the equation L of yal f
+
+ align:start position:0%
+a solution of the equation L of yal f
+ 
+
+ align:start position:0%
+a solution of the equation L of yal f
+ofx in other words if L of U is z and L
+
+ align:start position:0%
+ofx in other words if L of U is z and L
+ 
+
+ align:start position:0%
+ofx in other words if L of U is z and L
+of V is f ofx then L of U + V is also
+
+ align:start position:0%
+of V is f ofx then L of U + V is also
+ 
+
+ align:start position:0%
+of V is f ofx then L of U + V is also
+equal to F ofx what this means is that
+
+ align:start position:0%
+equal to F ofx what this means is that
+ 
+
+ align:start position:0%
+equal to F ofx what this means is that
+whenever I add on to a solution of this
+
+ align:start position:0%
+whenever I add on to a solution of this
+ 
+
+ align:start position:0%
+whenever I add on to a solution of this
+equation any solution of this equation I
+
+ align:start position:0%
+equation any solution of this equation I
+ 
+
+ align:start position:0%
+equation any solution of this equation I
+again get back a solution of this
+
+ align:start position:0%
+again get back a solution of this
+ 
+
+ align:start position:0%
+again get back a solution of this
+equation the proof Again by definition
+
+ align:start position:0%
+equation the proof Again by definition
+ 
+
+ align:start position:0%
+equation the proof Again by definition
+of linearity is Trivial namely by
+
+ align:start position:0%
+of linearity is Trivial namely by
+ 
+
+ align:start position:0%
+of linearity is Trivial namely by
+linearity L of U + V is L of U plus L of
+
+ align:start position:0%
+linearity L of U + V is L of U plus L of
+ 
+
+ align:start position:0%
+linearity L of U + V is L of U plus L of
+V but we're given that L of U is z we're
+
+ align:start position:0%
+V but we're given that L of U is z we're
+ 
+
+ align:start position:0%
+V but we're given that L of U is z we're
+given that L of V is f ofx and
+
+ align:start position:0%
+given that L of V is f ofx and
+ 
+
+ align:start position:0%
+given that L of V is f ofx and
+consequently 0 plus f of x X is f ofx so
+
+ align:start position:0%
+consequently 0 plus f of x X is f ofx so
+ 
+
+ align:start position:0%
+consequently 0 plus f of x X is f ofx so
+L of U plus v is f ofx as asserted by
+
+ align:start position:0%
+L of U plus v is f ofx as asserted by
+ 
+
+ align:start position:0%
+L of U plus v is f ofx as asserted by
+the way let me point out here do not
+
+ align:start position:0%
+the way let me point out here do not
+ 
+
+ align:start position:0%
+the way let me point out here do not
+Overlook the power of
+
+ align:start position:0%
+Overlook the power of
+ 
+
+ align:start position:0%
+Overlook the power of
+linearity there is a very big danger
+
+ align:start position:0%
+linearity there is a very big danger
+ 
+
+ align:start position:0%
+linearity there is a very big danger
+that what you might say here is wasn't
+
+ align:start position:0%
+that what you might say here is wasn't
+ 
+
+ align:start position:0%
+that what you might say here is wasn't
+this result true just by adding equals
+
+ align:start position:0%
+this result true just by adding equals
+ 
+
+ align:start position:0%
+this result true just by adding equals
+to equals in other words couldn't I just
+
+ align:start position:0%
+to equals in other words couldn't I just
+ 
+
+ align:start position:0%
+to equals in other words couldn't I just
+add these two results and the answer is
+
+ align:start position:0%
+add these two results and the answer is
+ 
+
+ align:start position:0%
+add these two results and the answer is
+yes you can but when you add equals to
+
+ align:start position:0%
+yes you can but when you add equals to
+ 
+
+ align:start position:0%
+yes you can but when you add equals to
+equals here notice that what you get is
+
+ align:start position:0%
+equals here notice that what you get is
+ 
+
+ align:start position:0%
+equals here notice that what you get is
+what L of U plus L of V is equal to 0 +
+
+ align:start position:0%
+what L of U plus L of V is equal to 0 +
+ 
+
+ align:start position:0%
+what L of U plus L of V is equal to 0 +
+f ofx in other words what you can prove
+
+ align:start position:0%
+f ofx in other words what you can prove
+ 
+
+ align:start position:0%
+f ofx in other words what you can prove
+by equals added to equals is that L of U
+
+ align:start position:0%
+by equals added to equals is that L of U
+ 
+
+ align:start position:0%
+by equals added to equals is that L of U
+plus L of V is f ofx it was linearity
+
+ align:start position:0%
+plus L of V is f ofx it was linearity
+ 
+
+ align:start position:0%
+plus L of V is f ofx it was linearity
+that allowed us to say that L of U plus
+
+ align:start position:0%
+that allowed us to say that L of U plus
+ 
+
+ align:start position:0%
+that allowed us to say that L of U plus
+L of V was the same as L of U plus v and
+
+ align:start position:0%
+L of V was the same as L of U plus v and
+ 
+
+ align:start position:0%
+L of V was the same as L of U plus v and
+to show you that in terms of a simple
+
+ align:start position:0%
+to show you that in terms of a simple
+ 
+
+ align:start position:0%
+to show you that in terms of a simple
+analogy let's suppose I take the
+
+ align:start position:0%
+analogy let's suppose I take the
+ 
+
+ align:start position:0%
+analogy let's suppose I take the
+function f to be defined by F ofx is X -
+
+ align:start position:0%
+function f to be defined by F ofx is X -
+ 
+
+ align:start position:0%
+function f to be defined by F ofx is X -
+2 * x - 3 well trivially when X is 2 or
+
+ align:start position:0%
+2 * x - 3 well trivially when X is 2 or
+ 
+
+ align:start position:0%
+2 * x - 3 well trivially when X is 2 or
+X is three f ofx is zero right other
+
+ align:start position:0%
+X is three f ofx is zero right other
+ 
+
+ align:start position:0%
+X is three f ofx is zero right other
+words F of two is z f of 3 is zero Now
+
+ align:start position:0%
+words F of two is z f of 3 is zero Now
+ 
+
+ align:start position:0%
+words F of two is z f of 3 is zero Now
+by equals added to equals you can
+
+ align:start position:0%
+by equals added to equals you can
+ 
+
+ align:start position:0%
+by equals added to equals you can
+certainly say that F of 2 plus f of3 is
+
+ align:start position:0%
+certainly say that F of 2 plus f of3 is
+ 
+
+ align:start position:0%
+certainly say that F of 2 plus f of3 is
+zero but you can't say that F of the
+
+ align:start position:0%
+zero but you can't say that F of the
+ 
+
+ align:start position:0%
+zero but you can't say that F of the
+quantity 2 + 3 is zero in fact 2 + 3 is
+
+ align:start position:0%
+quantity 2 + 3 is zero in fact 2 + 3 is
+ 
+
+ align:start position:0%
+quantity 2 + 3 is zero in fact 2 + 3 is
+five if I put five in here I get what F
+
+ align:start position:0%
+five if I put five in here I get what F
+ 
+
+ align:start position:0%
+five if I put five in here I get what F
+of 5 is 5 - 2 * 5 - 3 that's 3 * 2 or 6
+
+ align:start position:0%
+of 5 is 5 - 2 * 5 - 3 that's 3 * 2 or 6
+ 
+
+ align:start position:0%
+of 5 is 5 - 2 * 5 - 3 that's 3 * 2 or 6
+in other words F of 2 + f of 3 is z but
+
+ align:start position:0%
+in other words F of 2 + f of 3 is z but
+ 
+
+ align:start position:0%
+in other words F of 2 + f of 3 is z but
+F of 2 + 3 is not zero it's 6 you see
+
+ align:start position:0%
+F of 2 + 3 is not zero it's 6 you see
+ 
+
+ align:start position:0%
+F of 2 + 3 is not zero it's 6 you see
+equals added to equals gives you this
+
+ align:start position:0%
+equals added to equals gives you this
+ 
+
+ align:start position:0%
+equals added to equals gives you this
+result but it's linearity that you need
+
+ align:start position:0%
+result but it's linearity that you need
+ 
+
+ align:start position:0%
+result but it's linearity that you need
+to be able to get from here to here this
+
+ align:start position:0%
+to be able to get from here to here this
+ 
+
+ align:start position:0%
+to be able to get from here to here this
+was not a linear function you see well
+
+ align:start position:0%
+was not a linear function you see well
+ 
+
+ align:start position:0%
+was not a linear function you see well
+let me give you an example of how to use
+
+ align:start position:0%
+let me give you an example of how to use
+ 
+
+ align:start position:0%
+let me give you an example of how to use
+all this stuff let's find all solutions
+
+ align:start position:0%
+all this stuff let's find all solutions
+ 
+
+ align:start position:0%
+all this stuff let's find all solutions
+of the differential equation Y Prime - 4
+
+ align:start position:0%
+of the differential equation Y Prime - 4
+ 
+
+ align:start position:0%
+of the differential equation Y Prime - 4
+y Prime + 3 y = Z special case where the
+
+ align:start position:0%
+y Prime + 3 y = Z special case where the
+ 
+
+ align:start position:0%
+y Prime + 3 y = Z special case where the
+right hand side is zero my coefficients
+
+ align:start position:0%
+right hand side is zero my coefficients
+ 
+
+ align:start position:0%
+right hand side is zero my coefficients
+of Y and Y Prime notice are still
+
+ align:start position:0%
+of Y and Y Prime notice are still
+ 
+
+ align:start position:0%
+of Y and Y Prime notice are still
+functions of X they happen to be
+
+ align:start position:0%
+functions of X they happen to be
+ 
+
+ align:start position:0%
+functions of X they happen to be
+constant but the requirement that P of x
+
+ align:start position:0%
+constant but the requirement that P of x
+ 
+
+ align:start position:0%
+constant but the requirement that P of x
+and q of X be constants is certainly not
+
+ align:start position:0%
+and q of X be constants is certainly not
+ 
+
+ align:start position:0%
+and q of X be constants is certainly not
+outlawed in other words one special case
+
+ align:start position:0%
+outlawed in other words one special case
+ 
+
+ align:start position:0%
+outlawed in other words one special case
+of a function of X is the function of X
+
+ align:start position:0%
+of a function of X is the function of X
+ 
+
+ align:start position:0%
+of a function of X is the function of X
+which is identically a constant so this
+
+ align:start position:0%
+which is identically a constant so this
+ 
+
+ align:start position:0%
+which is identically a constant so this
+qualifies as a linear equation let me
+
+ align:start position:0%
+qualifies as a linear equation let me
+ 
+
+ align:start position:0%
+qualifies as a linear equation let me
+show you then how I try to find all
+
+ align:start position:0%
+show you then how I try to find all
+ 
+
+ align:start position:0%
+show you then how I try to find all
+solutions of this equation as we've
+
+ align:start position:0%
+solutions of this equation as we've
+ 
+
+ align:start position:0%
+solutions of this equation as we've
+mentioned before both in part one of our
+
+ align:start position:0%
+mentioned before both in part one of our
+ 
+
+ align:start position:0%
+mentioned before both in part one of our
+course and as a motivation for defining
+
+ align:start position:0%
+course and as a motivation for defining
+ 
+
+ align:start position:0%
+course and as a motivation for defining
+e to the iix a trial solution of this
+
+ align:start position:0%
+e to the iix a trial solution of this
+ 
+
+ align:start position:0%
+e to the iix a trial solution of this
+equation involves using e to the RX
+
+ align:start position:0%
+equation involves using e to the RX
+ 
+
+ align:start position:0%
+equation involves using e to the RX
+because when you differentiate e to the
+
+ align:start position:0%
+because when you differentiate e to the
+ 
+
+ align:start position:0%
+because when you differentiate e to the
+RX you get e to the RX back again if I
+
+ align:start position:0%
+RX you get e to the RX back again if I
+ 
+
+ align:start position:0%
+RX you get e to the RX back again if I
+differentiate e to the RX I get r e to
+
+ align:start position:0%
+differentiate e to the RX I get r e to
+ 
+
+ align:start position:0%
+differentiate e to the RX I get r e to
+the RX differentiate again I get R 2 e
+
+ align:start position:0%
+the RX differentiate again I get R 2 e
+ 
+
+ align:start position:0%
+the RX differentiate again I get R 2 e
+to the RX I plug that into here factor
+
+ align:start position:0%
+to the RX I plug that into here factor
+ 
+
+ align:start position:0%
+to the RX I plug that into here factor
+out the e to the RX and I wind up with e
+
+ align:start position:0%
+out the e to the RX and I wind up with e
+ 
+
+ align:start position:0%
+out the e to the RX and I wind up with e
+to the RX * r^ 2 - 4 r + 3 must equal Z
+
+ align:start position:0%
+to the RX * r^ 2 - 4 r + 3 must equal Z
+ 
+
+ align:start position:0%
+to the RX * r^ 2 - 4 r + 3 must equal Z
+since e to the RX is not zero it must be
+
+ align:start position:0%
+since e to the RX is not zero it must be
+ 
+
+ align:start position:0%
+since e to the RX is not zero it must be
+that r^ 2 - 4 r + 3 is zero and that
+
+ align:start position:0%
+that r^ 2 - 4 r + 3 is zero and that
+ 
+
+ align:start position:0%
+that r^ 2 - 4 r + 3 is zero and that
+says that either R is 1 or R is three
+
+ align:start position:0%
+says that either R is 1 or R is three
+ 
+
+ align:start position:0%
+says that either R is 1 or R is three
+remembering what R is it means that my
+
+ align:start position:0%
+remembering what R is it means that my
+ 
+
+ align:start position:0%
+remembering what R is it means that my
+trial Solutions should be correct when R
+
+ align:start position:0%
+trial Solutions should be correct when R
+ 
+
+ align:start position:0%
+trial Solutions should be correct when R
+is one or R is three leaving the details
+
+ align:start position:0%
+is one or R is three leaving the details
+ 
+
+ align:start position:0%
+is one or R is three leaving the details
+for you to verify it does turn out that
+
+ align:start position:0%
+for you to verify it does turn out that
+ 
+
+ align:start position:0%
+for you to verify it does turn out that
+L of e to the x is z see R is 1 L of e
+
+ align:start position:0%
+L of e to the x is z see R is 1 L of e
+ 
+
+ align:start position:0%
+L of e to the x is z see R is 1 L of e
+to 3x R is3 is zero in other words if I
+
+ align:start position:0%
+to 3x R is3 is zero in other words if I
+ 
+
+ align:start position:0%
+to 3x R is3 is zero in other words if I
+were to replace y by E to X or by E to
+
+ align:start position:0%
+were to replace y by E to X or by E to
+ 
+
+ align:start position:0%
+were to replace y by E to X or by E to
+3x this equation is satisfied and in
+
+ align:start position:0%
+3x this equation is satisfied and in
+ 
+
+ align:start position:0%
+3x this equation is satisfied and in
+terms of our definition of l this is the
+
+ align:start position:0%
+terms of our definition of l this is the
+ 
+
+ align:start position:0%
+terms of our definition of l this is the
+abbreviation for writing this well by
+
+ align:start position:0%
+abbreviation for writing this well by
+ 
+
+ align:start position:0%
+abbreviation for writing this well by
+our first property the fact that this
+
+ align:start position:0%
+our first property the fact that this
+ 
+
+ align:start position:0%
+our first property the fact that this
+satisfies L of yals 0 and this satisfies
+
+ align:start position:0%
+satisfies L of yals 0 and this satisfies
+ 
+
+ align:start position:0%
+satisfies L of yals 0 and this satisfies
+L of y equals 0 we had what any linear
+
+ align:start position:0%
+L of y equals 0 we had what any linear
+ 
+
+ align:start position:0%
+L of y equals 0 we had what any linear
+combination of these two must satisfy L
+
+ align:start position:0%
+combination of these two must satisfy L
+ 
+
+ align:start position:0%
+combination of these two must satisfy L
+of y equal 0 in other words I now know
+
+ align:start position:0%
+of y equal 0 in other words I now know
+ 
+
+ align:start position:0%
+of y equal 0 in other words I now know
+in one Fell Swoop that every function of
+
+ align:start position:0%
+in one Fell Swoop that every function of
+ 
+
+ align:start position:0%
+in one Fell Swoop that every function of
+the form C1 e to X Plus C2 e to 3x must
+
+ align:start position:0%
+the form C1 e to X Plus C2 e to 3x must
+ 
+
+ align:start position:0%
+the form C1 e to X Plus C2 e to 3x must
+also be a solution of this equation okay
+
+ align:start position:0%
+also be a solution of this equation okay
+ 
+
+ align:start position:0%
+also be a solution of this equation okay
+by the way that's another motivation and
+
+ align:start position:0%
+by the way that's another motivation and
+ 
+
+ align:start position:0%
+by the way that's another motivation and
+why we'll be doing this in block a for
+
+ align:start position:0%
+why we'll be doing this in block a for
+ 
+
+ align:start position:0%
+why we'll be doing this in block a for
+going further into the study of vector
+
+ align:start position:0%
+going further into the study of vector
+ 
+
+ align:start position:0%
+going further into the study of vector
+spaces notice in a sense what you're
+
+ align:start position:0%
+spaces notice in a sense what you're
+ 
+
+ align:start position:0%
+spaces notice in a sense what you're
+saying is you have found a whole family
+
+ align:start position:0%
+saying is you have found a whole family
+ 
+
+ align:start position:0%
+saying is you have found a whole family
+of solutions which are linear
+
+ align:start position:0%
+of solutions which are linear
+ 
+
+ align:start position:0%
+of solutions which are linear
+combinations of e to the X and E to 3x
+
+ align:start position:0%
+combinations of e to the X and E to 3x
+ 
+
+ align:start position:0%
+combinations of e to the X and E to 3x
+that somehow or other e to 3x and e to
+
+ align:start position:0%
+that somehow or other e to 3x and e to
+ 
+
+ align:start position:0%
+that somehow or other e to 3x and e to
+the X behave like I and J did in the
+
+ align:start position:0%
+the X behave like I and J did in the
+ 
+
+ align:start position:0%
+the X behave like I and J did in the
+plane namely every solution of this type
+
+ align:start position:0%
+plane namely every solution of this type
+ 
+
+ align:start position:0%
+plane namely every solution of this type
+can be written as what a constant time e
+
+ align:start position:0%
+can be written as what a constant time e
+ 
+
+ align:start position:0%
+can be written as what a constant time e
+to X plus a constant time e to 3x this
+
+ align:start position:0%
+to X plus a constant time e to 3x this
+ 
+
+ align:start position:0%
+to X plus a constant time e to 3x this
+is like a two-dimensional Vector space
+
+ align:start position:0%
+is like a two-dimensional Vector space
+ 
+
+ align:start position:0%
+is like a two-dimensional Vector space
+but I'm not going to pursue that any
+
+ align:start position:0%
+but I'm not going to pursue that any
+ 
+
+ align:start position:0%
+but I'm not going to pursue that any
+further right now I just want to give
+
+ align:start position:0%
+further right now I just want to give
+ 
+
+ align:start position:0%
+further right now I just want to give
+you a preview of Coming Attractions but
+
+ align:start position:0%
+you a preview of Coming Attractions but
+ 
+
+ align:start position:0%
+you a preview of Coming Attractions but
+at any rate to summarize what we've done
+
+ align:start position:0%
+at any rate to summarize what we've done
+ 
+
+ align:start position:0%
+at any rate to summarize what we've done
+so far is that we have now found that
+
+ align:start position:0%
+so far is that we have now found that
+ 
+
+ align:start position:0%
+so far is that we have now found that
+one family of solutions of that equation
+
+ align:start position:0%
+one family of solutions of that equation
+ 
+
+ align:start position:0%
+one family of solutions of that equation
+is y = C1 e to X plus c 2 e to 3x I
+
+ align:start position:0%
+is y = C1 e to X plus c 2 e to 3x I
+ 
+
+ align:start position:0%
+is y = C1 e to X plus c 2 e to 3x I
+emphasize one family because so far
+
+ align:start position:0%
+emphasize one family because so far
+ 
+
+ align:start position:0%
+emphasize one family because so far
+these are the solutions I found by
+
+ align:start position:0%
+these are the solutions I found by
+ 
+
+ align:start position:0%
+these are the solutions I found by
+assuming that the solution had to have
+
+ align:start position:0%
+assuming that the solution had to have
+ 
+
+ align:start position:0%
+assuming that the solution had to have
+the form Y is e to the RX I don't know
+
+ align:start position:0%
+the form Y is e to the RX I don't know
+ 
+
+ align:start position:0%
+the form Y is e to the RX I don't know
+as yet whether there are other types of
+
+ align:start position:0%
+as yet whether there are other types of
+ 
+
+ align:start position:0%
+as yet whether there are other types of
+solutions I'll worry about that in a
+
+ align:start position:0%
+solutions I'll worry about that in a
+ 
+
+ align:start position:0%
+solutions I'll worry about that in a
+little while at any rate the next most
+
+ align:start position:0%
+little while at any rate the next most
+ 
+
+ align:start position:0%
+little while at any rate the next most
+natural question to ask here is this
+
+ align:start position:0%
+natural question to ask here is this
+ 
+
+ align:start position:0%
+natural question to ask here is this
+look at I have two arbitrary constants
+
+ align:start position:0%
+look at I have two arbitrary constants
+ 
+
+ align:start position:0%
+look at I have two arbitrary constants
+and because I have two arbitrary
+
+ align:start position:0%
+and because I have two arbitrary
+ 
+
+ align:start position:0%
+and because I have two arbitrary
+constants it seems to me that just like
+
+ align:start position:0%
+constants it seems to me that just like
+ 
+
+ align:start position:0%
+constants it seems to me that just like
+in the first order case not only should
+
+ align:start position:0%
+in the first order case not only should
+ 
+
+ align:start position:0%
+in the first order case not only should
+I be able to find a solution that passes
+
+ align:start position:0%
+I be able to find a solution that passes
+ 
+
+ align:start position:0%
+I be able to find a solution that passes
+through a particular point but I have
+
+ align:start position:0%
+through a particular point but I have
+ 
+
+ align:start position:0%
+through a particular point but I have
+another degree of freedom to play around
+
+ align:start position:0%
+another degree of freedom to play around
+ 
+
+ align:start position:0%
+another degree of freedom to play around
+with maybe I can require not only that
+
+ align:start position:0%
+with maybe I can require not only that
+ 
+
+ align:start position:0%
+with maybe I can require not only that
+the curve passes through a given point
+
+ align:start position:0%
+the curve passes through a given point
+ 
+
+ align:start position:0%
+the curve passes through a given point
+but that it have a particular slope when
+
+ align:start position:0%
+but that it have a particular slope when
+ 
+
+ align:start position:0%
+but that it have a particular slope when
+it passes through that point in other
+
+ align:start position:0%
+it passes through that point in other
+ 
+
+ align:start position:0%
+it passes through that point in other
+words with one constant I could make it
+
+ align:start position:0%
+words with one constant I could make it
+ 
+
+ align:start position:0%
+words with one constant I could make it
+pass through a point with two maybe I
+
+ align:start position:0%
+pass through a point with two maybe I
+ 
+
+ align:start position:0%
+pass through a point with two maybe I
+could make it pass through a point
+
+ align:start position:0%
+could make it pass through a point
+ 
+
+ align:start position:0%
+could make it pass through a point
+having a given slope so the question now
+
+ align:start position:0%
+having a given slope so the question now
+ 
+
+ align:start position:0%
+having a given slope so the question now
+is can I
+
+ align:start position:0%
+is can I
+ 
+
+ align:start position:0%
+is can I
+determine C1 and C2 such that for a
+
+ align:start position:0%
+determine C1 and C2 such that for a
+ 
+
+ align:start position:0%
+determine C1 and C2 such that for a
+given point x0 y0 I can find a curve a
+
+ align:start position:0%
+given point x0 y0 I can find a curve a
+ 
+
+ align:start position:0%
+given point x0 y0 I can find a curve a
+member of this family which passes
+
+ align:start position:0%
+member of this family which passes
+ 
+
+ align:start position:0%
+member of this family which passes
+through the point x0 y0 and has slope
+
+ align:start position:0%
+through the point x0 y0 and has slope
+ 
+
+ align:start position:0%
+through the point x0 y0 and has slope
+equal to z0 why I use z0 instead of M
+
+ align:start position:0%
+equal to z0 why I use z0 instead of M
+ 
+
+ align:start position:0%
+equal to z0 why I use z0 instead of M
+here will become clear I hope in a few
+
+ align:start position:0%
+here will become clear I hope in a few
+ 
+
+ align:start position:0%
+here will become clear I hope in a few
+moments but the point is to see if I can
+
+ align:start position:0%
+moments but the point is to see if I can
+ 
+
+ align:start position:0%
+moments but the point is to see if I can
+satisfy this system of equations let's
+
+ align:start position:0%
+satisfy this system of equations let's
+ 
+
+ align:start position:0%
+satisfy this system of equations let's
+see what happens if I replace X and Y by
+
+ align:start position:0%
+see what happens if I replace X and Y by
+ 
+
+ align:start position:0%
+see what happens if I replace X and Y by
+x0 and y0 one of my equations that must
+
+ align:start position:0%
+x0 and y0 one of my equations that must
+ 
+
+ align:start position:0%
+x0 and y0 one of my equations that must
+be satisfied by C1 and C2 is this
+
+ align:start position:0%
+be satisfied by C1 and C2 is this
+ 
+
+ align:start position:0%
+be satisfied by C1 and C2 is this
+the derivative of this which is a slope
+
+ align:start position:0%
+the derivative of this which is a slope
+ 
+
+ align:start position:0%
+the derivative of this which is a slope
+is C1 e to X+ 3 C2 e 3x so if the slope
+
+ align:start position:0%
+is C1 e to X+ 3 C2 e 3x so if the slope
+ 
+
+ align:start position:0%
+is C1 e to X+ 3 C2 e 3x so if the slope
+is going to be z0 when X is equal to x0
+
+ align:start position:0%
+is going to be z0 when X is equal to x0
+ 
+
+ align:start position:0%
+is going to be z0 when X is equal to x0
+this equation must also be obeyed
+
+ align:start position:0%
+this equation must also be obeyed
+ 
+
+ align:start position:0%
+this equation must also be obeyed
+consequently I must now solve see if I
+
+ align:start position:0%
+consequently I must now solve see if I
+ 
+
+ align:start position:0%
+consequently I must now solve see if I
+can solve these two equations for C1 and
+
+ align:start position:0%
+can solve these two equations for C1 and
+ 
+
+ align:start position:0%
+can solve these two equations for C1 and
+C2 by the way this is very important to
+
+ align:start position:0%
+C2 by the way this is very important to
+ 
+
+ align:start position:0%
+C2 by the way this is very important to
+notice notice that this is two equations
+
+ align:start position:0%
+notice notice that this is two equations
+ 
+
+ align:start position:0%
+notice notice that this is two equations
+and two unknowns and that my unknowns
+
+ align:start position:0%
+and two unknowns and that my unknowns
+ 
+
+ align:start position:0%
+and two unknowns and that my unknowns
+are C1 and C2 that once I specify x0 y0
+
+ align:start position:0%
+are C1 and C2 that once I specify x0 y0
+ 
+
+ align:start position:0%
+are C1 and C2 that once I specify x0 y0
+and z0 everything else is a known number
+
+ align:start position:0%
+and z0 everything else is a known number
+ 
+
+ align:start position:0%
+and z0 everything else is a known number
+in this problem to see whether this has
+
+ align:start position:0%
+in this problem to see whether this has
+ 
+
+ align:start position:0%
+in this problem to see whether this has
+a unique solution the determinant of
+
+ align:start position:0%
+a unique solution the determinant of
+ 
+
+ align:start position:0%
+a unique solution the determinant of
+coefficients must be unequal to zero but
+
+ align:start position:0%
+coefficients must be unequal to zero but
+ 
+
+ align:start position:0%
+coefficients must be unequal to zero but
+look at what the determinant of
+
+ align:start position:0%
+look at what the determinant of
+ 
+
+ align:start position:0%
+look at what the determinant of
+coefficients is it's ex0 e 3x0 e x0 3 e
+
+ align:start position:0%
+coefficients is it's ex0 e 3x0 e x0 3 e
+ 
+
+ align:start position:0%
+coefficients is it's ex0 e 3x0 e x0 3 e
+3x0 that determinant is what 3 e to 4X 0
+
+ align:start position:0%
+3x0 that determinant is what 3 e to 4X 0
+ 
+
+ align:start position:0%
+3x0 that determinant is what 3 e to 4X 0
+minus E to 4X 0 that's twice e to 4X Z
+
+ align:start position:0%
+minus E to 4X 0 that's twice e to 4X Z
+ 
+
+ align:start position:0%
+minus E to 4X 0 that's twice e to 4X Z
+and since the exponential can never be
+
+ align:start position:0%
+and since the exponential can never be
+ 
+
+ align:start position:0%
+and since the exponential can never be
+negative this can never be zero this
+
+ align:start position:0%
+negative this can never be zero this
+ 
+
+ align:start position:0%
+negative this can never be zero this
+determinant cannot be zero in other
+
+ align:start position:0%
+determinant cannot be zero in other
+ 
+
+ align:start position:0%
+determinant cannot be zero in other
+words there is a unique member of the
+
+ align:start position:0%
+words there is a unique member of the
+ 
+
+ align:start position:0%
+words there is a unique member of the
+family y = C1 E X Plus C2 e 3x that
+
+ align:start position:0%
+family y = C1 E X Plus C2 e 3x that
+ 
+
+ align:start position:0%
+family y = C1 E X Plus C2 e 3x that
+passes through the point x0 y0 with a
+
+ align:start position:0%
+passes through the point x0 y0 with a
+ 
+
+ align:start position:0%
+passes through the point x0 y0 with a
+given slope z0 that's what we prove over
+
+ align:start position:0%
+given slope z0 that's what we prove over
+ 
+
+ align:start position:0%
+given slope z0 that's what we prove over
+here the only question that comes up is
+
+ align:start position:0%
+here the only question that comes up is
+ 
+
+ align:start position:0%
+here the only question that comes up is
+is that we have now shown what that at
+
+ align:start position:0%
+is that we have now shown what that at
+ 
+
+ align:start position:0%
+is that we have now shown what that at
+every point in space there is one
+
+ align:start position:0%
+every point in space there is one
+ 
+
+ align:start position:0%
+every point in space there is one
+solution from this family that passes
+
+ align:start position:0%
+solution from this family that passes
+ 
+
+ align:start position:0%
+solution from this family that passes
+through the given point with any given
+
+ align:start position:0%
+through the given point with any given
+ 
+
+ align:start position:0%
+through the given point with any given
+slope that you want it to have the
+
+ align:start position:0%
+slope that you want it to have the
+ 
+
+ align:start position:0%
+slope that you want it to have the
+question is that before we can call this
+
+ align:start position:0%
+question is that before we can call this
+ 
+
+ align:start position:0%
+question is that before we can call this
+the general solution we have to be sure
+
+ align:start position:0%
+the general solution we have to be sure
+ 
+
+ align:start position:0%
+the general solution we have to be sure
+that there are no other solutions to the
+
+ align:start position:0%
+that there are no other solutions to the
+ 
+
+ align:start position:0%
+that there are no other solutions to the
+equation Y Prime minus 4 y Prime + 3 yal
+
+ align:start position:0%
+equation Y Prime minus 4 y Prime + 3 yal
+ 
+
+ align:start position:0%
+equation Y Prime minus 4 y Prime + 3 yal
+0 in other words the question is are are
+
+ align:start position:0%
+0 in other words the question is are are
+ 
+
+ align:start position:0%
+0 in other words the question is are are
+there other types of solutions solutions
+
+ align:start position:0%
+there other types of solutions solutions
+ 
+
+ align:start position:0%
+there other types of solutions solutions
+that aren't of the form e to the x or E
+
+ align:start position:0%
+that aren't of the form e to the x or E
+ 
+
+ align:start position:0%
+that aren't of the form e to the x or E
+to 3x or linear combinations thereof and
+
+ align:start position:0%
+to 3x or linear combinations thereof and
+ 
+
+ align:start position:0%
+to 3x or linear combinations thereof and
+the crucial theorem is this suppose we
+
+ align:start position:0%
+the crucial theorem is this suppose we
+ 
+
+ align:start position:0%
+the crucial theorem is this suppose we
+can write our second order equation in
+
+ align:start position:0%
+can write our second order equation in
+ 
+
+ align:start position:0%
+can write our second order equation in
+the form y Prime is some function of X Y
+
+ align:start position:0%
+the form y Prime is some function of X Y
+ 
+
+ align:start position:0%
+the form y Prime is some function of X Y
+and Y Prime and notice how analogous
+
+ align:start position:0%
+and Y Prime and notice how analogous
+ 
+
+ align:start position:0%
+and Y Prime and notice how analogous
+this is to the key theorem of our last
+
+ align:start position:0%
+this is to the key theorem of our last
+ 
+
+ align:start position:0%
+this is to the key theorem of our last
+lecture suppose when we treat x f as a
+
+ align:start position:0%
+lecture suppose when we treat x f as a
+ 
+
+ align:start position:0%
+lecture suppose when we treat x f as a
+function of the three independent
+
+ align:start position:0%
+function of the three independent
+ 
+
+ align:start position:0%
+function of the three independent
+variables X Y and Z it turns out that f
+
+ align:start position:0%
+variables X Y and Z it turns out that f
+ 
+
+ align:start position:0%
+variables X Y and Z it turns out that f
+f suby f subz are all continuous in some
+
+ align:start position:0%
+f suby f subz are all continuous in some
+ 
+
+ align:start position:0%
+f suby f subz are all continuous in some
+region R then the amazing result is that
+
+ align:start position:0%
+region R then the amazing result is that
+ 
+
+ align:start position:0%
+region R then the amazing result is that
+for each triplet x0 y0 z0 in R see R is
+
+ align:start position:0%
+for each triplet x0 y0 z0 in R see R is
+ 
+
+ align:start position:0%
+for each triplet x0 y0 z0 in R see R is
+three-dimensional here because f is
+
+ align:start position:0%
+three-dimensional here because f is
+ 
+
+ align:start position:0%
+three-dimensional here because f is
+defined on three space there is a unique
+
+ align:start position:0%
+defined on three space there is a unique
+ 
+
+ align:start position:0%
+defined on three space there is a unique
+solution curve which passes through the
+
+ align:start position:0%
+solution curve which passes through the
+ 
+
+ align:start position:0%
+solution curve which passes through the
+point x0 y0 with slope equal to z0 again
+
+ align:start position:0%
+point x0 y0 with slope equal to z0 again
+ 
+
+ align:start position:0%
+point x0 y0 with slope equal to z0 again
+notice here the coding system we are not
+
+ align:start position:0%
+notice here the coding system we are not
+ 
+
+ align:start position:0%
+notice here the coding system we are not
+talking about a solution passing through
+
+ align:start position:0%
+talking about a solution passing through
+ 
+
+ align:start position:0%
+talking about a solution passing through
+x0 y0 z0 the solution curve is in the
+
+ align:start position:0%
+x0 y0 z0 the solution curve is in the
+ 
+
+ align:start position:0%
+x0 y0 z0 the solution curve is in the
+plane see dydx is a slope of a curve in
+
+ align:start position:0%
+plane see dydx is a slope of a curve in
+ 
+
+ align:start position:0%
+plane see dydx is a slope of a curve in
+the plane we have one independent
+
+ align:start position:0%
+the plane we have one independent
+ 
+
+ align:start position:0%
+the plane we have one independent
+variable what we're saying is what that
+
+ align:start position:0%
+variable what we're saying is what that
+ 
+
+ align:start position:0%
+variable what we're saying is what that
+there is a unique solution that passes
+
+ align:start position:0%
+there is a unique solution that passes
+ 
+
+ align:start position:0%
+there is a unique solution that passes
+through the point x0 y0 with slope equal
+
+ align:start position:0%
+through the point x0 y0 with slope equal
+ 
+
+ align:start position:0%
+through the point x0 y0 with slope equal
+to z0 under those conditions the
+
+ align:start position:0%
+to z0 under those conditions the
+ 
+
+ align:start position:0%
+to z0 under those conditions the
+solution will be unique well let's
+
+ align:start position:0%
+solution will be unique well let's
+ 
+
+ align:start position:0%
+solution will be unique well let's
+accept the truth of this theorem and
+
+ align:start position:0%
+accept the truth of this theorem and
+ 
+
+ align:start position:0%
+accept the truth of this theorem and
+apply it to a linear differential
+
+ align:start position:0%
+apply it to a linear differential
+ 
+
+ align:start position:0%
+apply it to a linear differential
+equation given the most General linear
+
+ align:start position:0%
+equation given the most General linear
+ 
+
+ align:start position:0%
+equation given the most General linear
+differential equation to put it into the
+
+ align:start position:0%
+differential equation to put it into the
+ 
+
+ align:start position:0%
+differential equation to put it into the
+form of the crucial theorem I transpose
+
+ align:start position:0%
+form of the crucial theorem I transpose
+ 
+
+ align:start position:0%
+form of the crucial theorem I transpose
+everything but y Prime onto the right
+
+ align:start position:0%
+everything but y Prime onto the right
+ 
+
+ align:start position:0%
+everything but y Prime onto the right
+hand side of the equation I get y Prime
+
+ align:start position:0%
+hand side of the equation I get y Prime
+ 
+
+ align:start position:0%
+hand side of the equation I get y Prime
+f ofx - P of x y primeus q ofx y
+
+ align:start position:0%
+f ofx - P of x y primeus q ofx y
+ 
+
+ align:start position:0%
+f ofx - P of x y primeus q ofx y
+therefore my capital F of XYZ is obtain
+
+ align:start position:0%
+therefore my capital F of XYZ is obtain
+ 
+
+ align:start position:0%
+therefore my capital F of XYZ is obtain
+simply by replacing y Prime by Z in here
+
+ align:start position:0%
+simply by replacing y Prime by Z in here
+ 
+
+ align:start position:0%
+simply by replacing y Prime by Z in here
+see I simply replace y Prime by Z like I
+
+ align:start position:0%
+see I simply replace y Prime by Z like I
+ 
+
+ align:start position:0%
+see I simply replace y Prime by Z like I
+did over here I wind up with what y
+
+ align:start position:0%
+did over here I wind up with what y
+ 
+
+ align:start position:0%
+did over here I wind up with what y
+capital F of XYZ is little F ofx minus
+
+ align:start position:0%
+capital F of XYZ is little F ofx minus
+ 
+
+ align:start position:0%
+capital F of XYZ is little F ofx minus
+pz minus qy well look at this is this is
+
+ align:start position:0%
+pz minus qy well look at this is this is
+ 
+
+ align:start position:0%
+pz minus qy well look at this is this is
+certainly a continuous function as soon
+
+ align:start position:0%
+certainly a continuous function as soon
+ 
+
+ align:start position:0%
+certainly a continuous function as soon
+as FP and Q are continuous the partial
+
+ align:start position:0%
+as FP and Q are continuous the partial
+ 
+
+ align:start position:0%
+as FP and Q are continuous the partial
+of capital F with respect to Y remember
+
+ align:start position:0%
+of capital F with respect to Y remember
+ 
+
+ align:start position:0%
+of capital F with respect to Y remember
+I'm treating X Y and Z as independent
+
+ align:start position:0%
+I'm treating X Y and Z as independent
+ 
+
+ align:start position:0%
+I'm treating X Y and Z as independent
+variables if I differentiate with
+
+ align:start position:0%
+variables if I differentiate with
+ 
+
+ align:start position:0%
+variables if I differentiate with
+respect to Y notice that this drops out
+
+ align:start position:0%
+respect to Y notice that this drops out
+ 
+
+ align:start position:0%
+respect to Y notice that this drops out
+the partial of capital F with respect to
+
+ align:start position:0%
+the partial of capital F with respect to
+ 
+
+ align:start position:0%
+the partial of capital F with respect to
+Y is just minus Q ofx the partial of
+
+ align:start position:0%
+Y is just minus Q ofx the partial of
+ 
+
+ align:start position:0%
+Y is just minus Q ofx the partial of
+capital F with respect to Z is just
+
+ align:start position:0%
+capital F with respect to Z is just
+ 
+
+ align:start position:0%
+capital F with respect to Z is just
+minus P of X consequently if little f p
+
+ align:start position:0%
+minus P of X consequently if little f p
+ 
+
+ align:start position:0%
+minus P of X consequently if little f p
+and Q are all continuous functions of X
+
+ align:start position:0%
+and Q are all continuous functions of X
+ 
+
+ align:start position:0%
+and Q are all continuous functions of X
+automatically capital F capital F suby
+
+ align:start position:0%
+automatically capital F capital F suby
+ 
+
+ align:start position:0%
+automatically capital F capital F suby
+capital F subz will also be Contin
+
+ align:start position:0%
+capital F subz will also be Contin
+ 
+
+ align:start position:0%
+capital F subz will also be Contin
+functions consequently according to that
+
+ align:start position:0%
+functions consequently according to that
+ 
+
+ align:start position:0%
+functions consequently according to that
+crucial theorem any solution that I find
+
+ align:start position:0%
+crucial theorem any solution that I find
+ 
+
+ align:start position:0%
+crucial theorem any solution that I find
+will be a unique solution and even more
+
+ align:start position:0%
+will be a unique solution and even more
+ 
+
+ align:start position:0%
+will be a unique solution and even more
+to the point even if I can't find the
+
+ align:start position:0%
+to the point even if I can't find the
+ 
+
+ align:start position:0%
+to the point even if I can't find the
+solution the theorem tells me that there
+
+ align:start position:0%
+solution the theorem tells me that there
+ 
+
+ align:start position:0%
+solution the theorem tells me that there
+is a unique solution well I think that
+
+ align:start position:0%
+is a unique solution well I think that
+ 
+
+ align:start position:0%
+is a unique solution well I think that
+the P's and the q's sort of get you a
+
+ align:start position:0%
+the P's and the q's sort of get you a
+ 
+
+ align:start position:0%
+the P's and the q's sort of get you a
+little bit messed up let's do a specific
+
+ align:start position:0%
+little bit messed up let's do a specific
+ 
+
+ align:start position:0%
+little bit messed up let's do a specific
+uh illustration of this again let's find
+
+ align:start position:0%
+uh illustration of this again let's find
+ 
+
+ align:start position:0%
+uh illustration of this again let's find
+now all solutions of the equation Y
+
+ align:start position:0%
+now all solutions of the equation Y
+ 
+
+ align:start position:0%
+now all solutions of the equation Y
+Prime - 4 y Prime + 3 y equal e 2x the
+
+ align:start position:0%
+Prime - 4 y Prime + 3 y equal e 2x the
+ 
+
+ align:start position:0%
+Prime - 4 y Prime + 3 y equal e 2x the
+same equation as before only the right
+
+ align:start position:0%
+same equation as before only the right
+ 
+
+ align:start position:0%
+same equation as before only the right
+hand side is e 2x rather than zero the
+
+ align:start position:0%
+hand side is e 2x rather than zero the
+ 
+
+ align:start position:0%
+hand side is e 2x rather than zero the
+key result is going to be this I already
+
+ align:start position:0%
+key result is going to be this I already
+ 
+
+ align:start position:0%
+key result is going to be this I already
+know how to solve this equation when the
+
+ align:start position:0%
+know how to solve this equation when the
+ 
+
+ align:start position:0%
+know how to solve this equation when the
+right hand side is zero remember one of
+
+ align:start position:0%
+right hand side is zero remember one of
+ 
+
+ align:start position:0%
+right hand side is zero remember one of
+my properties of linearity was that if I
+
+ align:start position:0%
+my properties of linearity was that if I
+ 
+
+ align:start position:0%
+my properties of linearity was that if I
+could find any solution of this equation
+
+ align:start position:0%
+could find any solution of this equation
+ 
+
+ align:start position:0%
+could find any solution of this equation
+then by adding onto it any solution of
+
+ align:start position:0%
+then by adding onto it any solution of
+ 
+
+ align:start position:0%
+then by adding onto it any solution of
+the equation where the right hand side
+
+ align:start position:0%
+the equation where the right hand side
+ 
+
+ align:start position:0%
+the equation where the right hand side
+is zero by the way when the right hand
+
+ align:start position:0%
+is zero by the way when the right hand
+ 
+
+ align:start position:0%
+is zero by the way when the right hand
+side is zero the equation is called uh
+
+ align:start position:0%
+side is zero the equation is called uh
+ 
+
+ align:start position:0%
+side is zero the equation is called uh
+homogeneous and I don't think that's too
+
+ align:start position:0%
+homogeneous and I don't think that's too
+ 
+
+ align:start position:0%
+homogeneous and I don't think that's too
+important other than to know the
+
+ align:start position:0%
+important other than to know the
+ 
+
+ align:start position:0%
+important other than to know the
+language when it's mentioned but this is
+
+ align:start position:0%
+language when it's mentioned but this is
+ 
+
+ align:start position:0%
+language when it's mentioned but this is
+called homogeneous if the right hand
+
+ align:start position:0%
+called homogeneous if the right hand
+ 
+
+ align:start position:0%
+called homogeneous if the right hand
+side is zero but what our key theorem
+
+ align:start position:0%
+side is zero but what our key theorem
+ 
+
+ align:start position:0%
+side is zero but what our key theorem
+says is look at we have solved this
+
+ align:start position:0%
+says is look at we have solved this
+ 
+
+ align:start position:0%
+says is look at we have solved this
+problem we have found the general
+
+ align:start position:0%
+problem we have found the general
+ 
+
+ align:start position:0%
+problem we have found the general
+solution when the right hand side is
+
+ align:start position:0%
+solution when the right hand side is
+ 
+
+ align:start position:0%
+solution when the right hand side is
+zero consequently if I could find just
+
+ align:start position:0%
+zero consequently if I could find just
+ 
+
+ align:start position:0%
+zero consequently if I could find just
+one solution of this equation by hook or
+
+ align:start position:0%
+one solution of this equation by hook or
+ 
+
+ align:start position:0%
+one solution of this equation by hook or
+by crook just steal one sneak one in if
+
+ align:start position:0%
+by crook just steal one sneak one in if
+ 
+
+ align:start position:0%
+by crook just steal one sneak one in if
+I can find one solution of that equation
+
+ align:start position:0%
+I can find one solution of that equation
+ 
+
+ align:start position:0%
+I can find one solution of that equation
+if I add that onto the General solution
+
+ align:start position:0%
+if I add that onto the General solution
+ 
+
+ align:start position:0%
+if I add that onto the General solution
+of the homogeneous equation that will be
+
+ align:start position:0%
+of the homogeneous equation that will be
+ 
+
+ align:start position:0%
+of the homogeneous equation that will be
+the general solution of this equation
+
+ align:start position:0%
+the general solution of this equation
+ 
+
+ align:start position:0%
+the general solution of this equation
+what does that mean let's see how we'll
+
+ align:start position:0%
+what does that mean let's see how we'll
+ 
+
+ align:start position:0%
+what does that mean let's see how we'll
+tackle this what I'm going to do is I
+
+ align:start position:0%
+tackle this what I'm going to do is I
+ 
+
+ align:start position:0%
+tackle this what I'm going to do is I
+look at this equation and here's how I
+
+ align:start position:0%
+look at this equation and here's how I
+ 
+
+ align:start position:0%
+look at this equation and here's how I
+get sneaky I say look at when I
+
+ align:start position:0%
+get sneaky I say look at when I
+ 
+
+ align:start position:0%
+get sneaky I say look at when I
+differentiate and I'm all through what I
+
+ align:start position:0%
+differentiate and I'm all through what I
+ 
+
+ align:start position:0%
+differentiate and I'm all through what I
+want to wind up with is e to 2x well the
+
+ align:start position:0%
+want to wind up with is e to 2x well the
+ 
+
+ align:start position:0%
+want to wind up with is e to 2x well the
+only function whose derivative gives you
+
+ align:start position:0%
+only function whose derivative gives you
+ 
+
+ align:start position:0%
+only function whose derivative gives you
+a factor of e to 2x more or less is some
+
+ align:start position:0%
+a factor of e to 2x more or less is some
+ 
+
+ align:start position:0%
+a factor of e to 2x more or less is some
+constant time e to 2x itself so I say to
+
+ align:start position:0%
+constant time e to 2x itself so I say to
+ 
+
+ align:start position:0%
+constant time e to 2x itself so I say to
+myself let me try for a solution in the
+
+ align:start position:0%
+myself let me try for a solution in the
+ 
+
+ align:start position:0%
+myself let me try for a solution in the
+form y equal some constant * e 2x see my
+
+ align:start position:0%
+form y equal some constant * e 2x see my
+ 
+
+ align:start position:0%
+form y equal some constant * e 2x see my
+tri solution will have this form well YT
+
+ align:start position:0%
+tri solution will have this form well YT
+ 
+
+ align:start position:0%
+tri solution will have this form well YT
+Prime would be this YT Prime would be
+
+ align:start position:0%
+Prime would be this YT Prime would be
+ 
+
+ align:start position:0%
+Prime would be this YT Prime would be
+this if I now substitute back into the
+
+ align:start position:0%
+this if I now substitute back into the
+ 
+
+ align:start position:0%
+this if I now substitute back into the
+original equation YT Prime - 4 YT Prime
+
+ align:start position:0%
+original equation YT Prime - 4 YT Prime
+ 
+
+ align:start position:0%
+original equation YT Prime - 4 YT Prime
++ 3 YT must be identically equal to e to
+
+ align:start position:0%
++ 3 YT must be identically equal to e to
+ 
+
+ align:start position:0%
++ 3 YT must be identically equal to e to
+X that leads to the fact that minus a e
+
+ align:start position:0%
+X that leads to the fact that minus a e
+ 
+
+ align:start position:0%
+X that leads to the fact that minus a e
+2X must be the same as e to 2X and that
+
+ align:start position:0%
+2X must be the same as e to 2X and that
+ 
+
+ align:start position:0%
+2X must be the same as e to 2X and that
+tells me that if there is a solution a
+
+ align:start position:0%
+tells me that if there is a solution a
+ 
+
+ align:start position:0%
+tells me that if there is a solution a
+had better be minus one you see if x is
+
+ align:start position:0%
+had better be minus one you see if x is
+ 
+
+ align:start position:0%
+had better be minus one you see if x is
+Zer here this says - AAL 1 a quick check
+
+ align:start position:0%
+Zer here this says - AAL 1 a quick check
+ 
+
+ align:start position:0%
+Zer here this says - AAL 1 a quick check
+will show that Min - e 2x is a solution
+
+ align:start position:0%
+will show that Min - e 2x is a solution
+ 
+
+ align:start position:0%
+will show that Min - e 2x is a solution
+of the equation so a particular solution
+
+ align:start position:0%
+of the equation so a particular solution
+ 
+
+ align:start position:0%
+of the equation so a particular solution
+of this equation is minus E 2x I found
+
+ align:start position:0%
+of this equation is minus E 2x I found
+ 
+
+ align:start position:0%
+of this equation is minus E 2x I found
+one solution now here's the power of all
+
+ align:start position:0%
+one solution now here's the power of all
+ 
+
+ align:start position:0%
+one solution now here's the power of all
+this Theory with this one solution I now
+
+ align:start position:0%
+this Theory with this one solution I now
+ 
+
+ align:start position:0%
+this Theory with this one solution I now
+go back to the homogeneous equation
+
+ align:start position:0%
+go back to the homogeneous equation
+ 
+
+ align:start position:0%
+go back to the homogeneous equation
+which had as its General solution C1 e
+
+ align:start position:0%
+which had as its General solution C1 e
+ 
+
+ align:start position:0%
+which had as its General solution C1 e
+to X Plus C2 e to 3x I add these two
+
+ align:start position:0%
+to X Plus C2 e to 3x I add these two
+ 
+
+ align:start position:0%
+to X Plus C2 e to 3x I add these two
+together and that is the general
+
+ align:start position:0%
+together and that is the general
+ 
+
+ align:start position:0%
+together and that is the general
+solution that is the general solution of
+
+ align:start position:0%
+solution that is the general solution of
+ 
+
+ align:start position:0%
+solution that is the general solution of
+the equation that I started with by the
+
+ align:start position:0%
+the equation that I started with by the
+ 
+
+ align:start position:0%
+the equation that I started with by the
+way notice this as a check if this were
+
+ align:start position:0%
+way notice this as a check if this were
+ 
+
+ align:start position:0%
+way notice this as a check if this were
+the general solution I should be able to
+
+ align:start position:0%
+the general solution I should be able to
+ 
+
+ align:start position:0%
+the general solution I should be able to
+find unique values for C1 and C2 that
+
+ align:start position:0%
+find unique values for C1 and C2 that
+ 
+
+ align:start position:0%
+find unique values for C1 and C2 that
+allow me to make the curve a solution
+
+ align:start position:0%
+allow me to make the curve a solution
+ 
+
+ align:start position:0%
+allow me to make the curve a solution
+curve pass through x0 y0 with slope
+
+ align:start position:0%
+curve pass through x0 y0 with slope
+ 
+
+ align:start position:0%
+curve pass through x0 y0 with slope
+equal to0 0 notice that that would
+
+ align:start position:0%
+equal to0 0 notice that that would
+ 
+
+ align:start position:0%
+equal to0 0 notice that that would
+result in this system of equations and I
+
+ align:start position:0%
+result in this system of equations and I
+ 
+
+ align:start position:0%
+result in this system of equations and I
+hope that you notice that since x0 y0
+
+ align:start position:0%
+hope that you notice that since x0 y0
+ 
+
+ align:start position:0%
+hope that you notice that since x0 y0
+and z0 are constants to determine
+
+ align:start position:0%
+and z0 are constants to determine
+ 
+
+ align:start position:0%
+and z0 are constants to determine
+whether C1 and C2 are uniquely
+
+ align:start position:0%
+whether C1 and C2 are uniquely
+ 
+
+ align:start position:0%
+whether C1 and C2 are uniquely
+determined or not hinges on the fact
+
+ align:start position:0%
+determined or not hinges on the fact
+ 
+
+ align:start position:0%
+determined or not hinges on the fact
+that the coefficient M Matrix the
+
+ align:start position:0%
+that the coefficient M Matrix the
+ 
+
+ align:start position:0%
+that the coefficient M Matrix the
+determinant of coefficients is still the
+
+ align:start position:0%
+determinant of coefficients is still the
+ 
+
+ align:start position:0%
+determinant of coefficients is still the
+same determinant of coefficients that I
+
+ align:start position:0%
+same determinant of coefficients that I
+ 
+
+ align:start position:0%
+same determinant of coefficients that I
+had in the homogeneous Case by the way
+
+ align:start position:0%
+had in the homogeneous Case by the way
+ 
+
+ align:start position:0%
+had in the homogeneous Case by the way
+let me just stress one more point that I
+
+ align:start position:0%
+let me just stress one more point that I
+ 
+
+ align:start position:0%
+let me just stress one more point that I
+forgot to mention over here
+
+ align:start position:0%
+forgot to mention over here
+ 
+
+ align:start position:0%
+forgot to mention over here
+when I wrote down this equation notice
+
+ align:start position:0%
+when I wrote down this equation notice
+ 
+
+ align:start position:0%
+when I wrote down this equation notice
+that for the fundamental theorem to be
+
+ align:start position:0%
+that for the fundamental theorem to be
+ 
+
+ align:start position:0%
+that for the fundamental theorem to be
+true all that we required was that PQ
+
+ align:start position:0%
+true all that we required was that PQ
+ 
+
+ align:start position:0%
+true all that we required was that PQ
+and little F be continuous notice that P
+
+ align:start position:0%
+and little F be continuous notice that P
+ 
+
+ align:start position:0%
+and little F be continuous notice that P
+in this problem is minus 4 q is 3 and F
+
+ align:start position:0%
+in this problem is minus 4 q is 3 and F
+ 
+
+ align:start position:0%
+in this problem is minus 4 q is 3 and F
+is e to 2x certainly the function f ofx
+
+ align:start position:0%
+is e to 2x certainly the function f ofx
+ 
+
+ align:start position:0%
+is e to 2x certainly the function f ofx
+the function which is identically minus
+
+ align:start position:0%
+the function which is identically minus
+ 
+
+ align:start position:0%
+the function which is identically minus
+4 the function which is identically
+
+ align:start position:0%
+4 the function which is identically
+ 
+
+ align:start position:0%
+4 the function which is identically
+three and the function which is e to 2x
+
+ align:start position:0%
+three and the function which is e to 2x
+ 
+
+ align:start position:0%
+three and the function which is e to 2x
+are all continuous functions so what
+
+ align:start position:0%
+are all continuous functions so what
+ 
+
+ align:start position:0%
+are all continuous functions so what
+that told me was that once I find one
+
+ align:start position:0%
+that told me was that once I find one
+ 
+
+ align:start position:0%
+that told me was that once I find one
+one family of solutions I found them all
+
+ align:start position:0%
+one family of solutions I found them all
+ 
+
+ align:start position:0%
+one family of solutions I found them all
+so in the linear case there is a general
+
+ align:start position:0%
+so in the linear case there is a general
+ 
+
+ align:start position:0%
+so in the linear case there is a general
+solution there are no singular Solutions
+
+ align:start position:0%
+solution there are no singular Solutions
+ 
+
+ align:start position:0%
+solution there are no singular Solutions
+in a problem of this type there can't be
+
+ align:start position:0%
+in a problem of this type there can't be
+ 
+
+ align:start position:0%
+in a problem of this type there can't be
+any mongle solutions because this
+
+ align:start position:0%
+any mongle solutions because this
+ 
+
+ align:start position:0%
+any mongle solutions because this
+particular equation meets the
+
+ align:start position:0%
+particular equation meets the
+ 
+
+ align:start position:0%
+particular equation meets the
+requirements of the crucial theorem at
+
+ align:start position:0%
+requirements of the crucial theorem at
+ 
+
+ align:start position:0%
+requirements of the crucial theorem at
+any rate the exercises will take care of
+
+ align:start position:0%
+any rate the exercises will take care of
+ 
+
+ align:start position:0%
+any rate the exercises will take care of
+this in giving you drill let me simply
+
+ align:start position:0%
+this in giving you drill let me simply
+ 
+
+ align:start position:0%
+this in giving you drill let me simply
+summarize what we've done today in terms
+
+ align:start position:0%
+summarize what we've done today in terms
+ 
+
+ align:start position:0%
+summarize what we've done today in terms
+of linear differential equations the
+
+ align:start position:0%
+of linear differential equations the
+ 
+
+ align:start position:0%
+of linear differential equations the
+summary is this let's suppose that we're
+
+ align:start position:0%
+summary is this let's suppose that we're
+ 
+
+ align:start position:0%
+summary is this let's suppose that we're
+given a general second order is what
+
+ align:start position:0%
+given a general second order is what
+ 
+
+ align:start position:0%
+given a general second order is what
+I've been dealing with but it's true for
+
+ align:start position:0%
+I've been dealing with but it's true for
+ 
+
+ align:start position:0%
+I've been dealing with but it's true for
+higher orders 2 linear equation of the
+
+ align:start position:0%
+higher orders 2 linear equation of the
+ 
+
+ align:start position:0%
+higher orders 2 linear equation of the
+form y Prime + py Prime + qy = f ofx
+
+ align:start position:0%
+form y Prime + py Prime + qy = f ofx
+ 
+
+ align:start position:0%
+form y Prime + py Prime + qy = f ofx
+where p and Q are arbitrary functions of
+
+ align:start position:0%
+where p and Q are arbitrary functions of
+ 
+
+ align:start position:0%
+where p and Q are arbitrary functions of
+X what I'm saying is to find the general
+
+ align:start position:0%
+X what I'm saying is to find the general
+ 
+
+ align:start position:0%
+X what I'm saying is to find the general
+solution of this equation and by The
+
+ align:start position:0%
+solution of this equation and by The
+ 
+
+ align:start position:0%
+solution of this equation and by The
+crucial theorem this General solution
+
+ align:start position:0%
+crucial theorem this General solution
+ 
+
+ align:start position:0%
+crucial theorem this General solution
+will exist if FP and Q are continuous
+
+ align:start position:0%
+will exist if FP and Q are continuous
+ 
+
+ align:start position:0%
+will exist if FP and Q are continuous
+first of all what I do is I find the
+
+ align:start position:0%
+first of all what I do is I find the
+ 
+
+ align:start position:0%
+first of all what I do is I find the
+general solution y subh of the
+
+ align:start position:0%
+general solution y subh of the
+ 
+
+ align:start position:0%
+general solution y subh of the
+homogeneous equation L of y equals 0 in
+
+ align:start position:0%
+homogeneous equation L of y equals 0 in
+ 
+
+ align:start position:0%
+homogeneous equation L of y equals 0 in
+other words I simply replace the right
+
+ align:start position:0%
+other words I simply replace the right
+ 
+
+ align:start position:0%
+other words I simply replace the right
+hand side of this equation by zero and
+
+ align:start position:0%
+hand side of this equation by zero and
+ 
+
+ align:start position:0%
+hand side of this equation by zero and
+find the general solution of this
+
+ align:start position:0%
+find the general solution of this
+ 
+
+ align:start position:0%
+find the general solution of this
+equation in terms of a theory what we're
+
+ align:start position:0%
+equation in terms of a theory what we're
+ 
+
+ align:start position:0%
+equation in terms of a theory what we're
+saying also is and this I'll say this as
+
+ align:start position:0%
+saying also is and this I'll say this as
+ 
+
+ align:start position:0%
+saying also is and this I'll say this as
+an aside if I can find two solutions of
+
+ align:start position:0%
+an aside if I can find two solutions of
+ 
+
+ align:start position:0%
+an aside if I can find two solutions of
+this equation which are not Scala
+
+ align:start position:0%
+this equation which are not Scala
+ 
+
+ align:start position:0%
+this equation which are not Scala
+multiples of one another in other words
+
+ align:start position:0%
+multiples of one another in other words
+ 
+
+ align:start position:0%
+multiples of one another in other words
+if I can find two functions U1 and U2
+
+ align:start position:0%
+if I can find two functions U1 and U2
+ 
+
+ align:start position:0%
+if I can find two functions U1 and U2
+such that L of U1 and L of U2 are zero
+
+ align:start position:0%
+such that L of U1 and L of U2 are zero
+ 
+
+ align:start position:0%
+such that L of U1 and L of U2 are zero
+but that U2 is not a constant time U1
+
+ align:start position:0%
+but that U2 is not a constant time U1
+ 
+
+ align:start position:0%
+but that U2 is not a constant time U1
+then that homogeneous solution in other
+
+ align:start position:0%
+then that homogeneous solution in other
+ 
+
+ align:start position:0%
+then that homogeneous solution in other
+words the solution of this equation will
+
+ align:start position:0%
+words the solution of this equation will
+ 
+
+ align:start position:0%
+words the solution of this equation will
+simply be C1 U1 plus C2 U2 see other
+
+ align:start position:0%
+simply be C1 U1 plus C2 U2 see other
+ 
+
+ align:start position:0%
+simply be C1 U1 plus C2 U2 see other
+words all linear combinations of these
+
+ align:start position:0%
+words all linear combinations of these
+ 
+
+ align:start position:0%
+words all linear combinations of these
+two and the proof of that is quite
+
+ align:start position:0%
+two and the proof of that is quite
+ 
+
+ align:start position:0%
+two and the proof of that is quite
+simple namely what we want is what given
+
+ align:start position:0%
+simple namely what we want is what given
+ 
+
+ align:start position:0%
+simple namely what we want is what given
+the point x0 y0 we want to be sure that
+
+ align:start position:0%
+the point x0 y0 we want to be sure that
+ 
+
+ align:start position:0%
+the point x0 y0 we want to be sure that
+we can determine C1 and C2 such that a
+
+ align:start position:0%
+we can determine C1 and C2 such that a
+ 
+
+ align:start position:0%
+we can determine C1 and C2 such that a
+curve passes through x0 y0 with slope z0
+
+ align:start position:0%
+curve passes through x0 y0 with slope z0
+ 
+
+ align:start position:0%
+curve passes through x0 y0 with slope z0
+that means I must be able to do what I
+
+ align:start position:0%
+that means I must be able to do what I
+ 
+
+ align:start position:0%
+that means I must be able to do what I
+must be able to solve this pair of
+
+ align:start position:0%
+must be able to solve this pair of
+ 
+
+ align:start position:0%
+must be able to solve this pair of
+equations namely if I replace X by x0
+
+ align:start position:0%
+equations namely if I replace X by x0
+ 
+
+ align:start position:0%
+equations namely if I replace X by x0
+and Y by y0 and if I differentiate the
+
+ align:start position:0%
+and Y by y0 and if I differentiate the
+ 
+
+ align:start position:0%
+and Y by y0 and if I differentiate the
+equation and then replace X by x0 and
+
+ align:start position:0%
+equation and then replace X by x0 and
+ 
+
+ align:start position:0%
+equation and then replace X by x0 and
+dydx by z0 because that's the derivative
+
+ align:start position:0%
+dydx by z0 because that's the derivative
+ 
+
+ align:start position:0%
+dydx by z0 because that's the derivative
+the slope I want at this point I again
+
+ align:start position:0%
+the slope I want at this point I again
+ 
+
+ align:start position:0%
+the slope I want at this point I again
+wind up with what two equations with two
+
+ align:start position:0%
+wind up with what two equations with two
+ 
+
+ align:start position:0%
+wind up with what two equations with two
+unknowns remember once I specify x0 y0
+
+ align:start position:0%
+unknowns remember once I specify x0 y0
+ 
+
+ align:start position:0%
+unknowns remember once I specify x0 y0
+and z0
+
+ align:start position:0%
+and z0
+ 
+
+ align:start position:0%
+and z0
+these are given constants C1 and C2 are
+
+ align:start position:0%
+these are given constants C1 and C2 are
+ 
+
+ align:start position:0%
+these are given constants C1 and C2 are
+my only variables to see whether there
+
+ align:start position:0%
+my only variables to see whether there
+ 
+
+ align:start position:0%
+my only variables to see whether there
+is a unique solution here it means that
+
+ align:start position:0%
+is a unique solution here it means that
+ 
+
+ align:start position:0%
+is a unique solution here it means that
+this determinant of coefficients must be
+
+ align:start position:0%
+this determinant of coefficients must be
+ 
+
+ align:start position:0%
+this determinant of coefficients must be
+unequal to zero the determinant of
+
+ align:start position:0%
+unequal to zero the determinant of
+ 
+
+ align:start position:0%
+unequal to zero the determinant of
+coefficients is just U1 U2 Prime minus
+
+ align:start position:0%
+coefficients is just U1 U2 Prime minus
+ 
+
+ align:start position:0%
+coefficients is just U1 U2 Prime minus
+U1 Prime U2 that must be une equal to
+
+ align:start position:0%
+U1 Prime U2 that must be une equal to
+ 
+
+ align:start position:0%
+U1 Prime U2 that must be une equal to
+zero this suggests the quotient rule
+
+ align:start position:0%
+zero this suggests the quotient rule
+ 
+
+ align:start position:0%
+zero this suggests the quotient rule
+again for this expression to be une
+
+ align:start position:0%
+again for this expression to be une
+ 
+
+ align:start position:0%
+again for this expression to be une
+equal to Z is the same as this / U1 2 to
+
+ align:start position:0%
+equal to Z is the same as this / U1 2 to
+ 
+
+ align:start position:0%
+equal to Z is the same as this / U1 2 to
+Beal to Z this expression here is not
+
+ align:start position:0%
+Beal to Z this expression here is not
+ 
+
+ align:start position:0%
+Beal to Z this expression here is not
+nothing more than a derivative of U2 /
+
+ align:start position:0%
+nothing more than a derivative of U2 /
+ 
+
+ align:start position:0%
+nothing more than a derivative of U2 /
+U1 with respect to X and for that to be
+
+ align:start position:0%
+U1 with respect to X and for that to be
+ 
+
+ align:start position:0%
+U1 with respect to X and for that to be
+unequal to zero simply says what that U2
+
+ align:start position:0%
+unequal to zero simply says what that U2
+ 
+
+ align:start position:0%
+unequal to zero simply says what that U2
+over U1 is not a constant and that says
+
+ align:start position:0%
+over U1 is not a constant and that says
+ 
+
+ align:start position:0%
+over U1 is not a constant and that says
+that U2 is not a constant times U1 in
+
+ align:start position:0%
+that U2 is not a constant times U1 in
+ 
+
+ align:start position:0%
+that U2 is not a constant times U1 in
+other words this is just an aside to
+
+ align:start position:0%
+other words this is just an aside to
+ 
+
+ align:start position:0%
+other words this is just an aside to
+show you how you find the general
+
+ align:start position:0%
+show you how you find the general
+ 
+
+ align:start position:0%
+show you how you find the general
+solution of the homogeneous equation but
+
+ align:start position:0%
+solution of the homogeneous equation but
+ 
+
+ align:start position:0%
+solution of the homogeneous equation but
+the point is what first of all you find
+
+ align:start position:0%
+the point is what first of all you find
+ 
+
+ align:start position:0%
+the point is what first of all you find
+the general solution of the homogeneous
+
+ align:start position:0%
+the general solution of the homogeneous
+ 
+
+ align:start position:0%
+the general solution of the homogeneous
+equation meaning you take L of yals f
+
+ align:start position:0%
+equation meaning you take L of yals f
+ 
+
+ align:start position:0%
+equation meaning you take L of yals f
+ofx replace F ofx by zero and find the
+
+ align:start position:0%
+ofx replace F ofx by zero and find the
+ 
+
+ align:start position:0%
+ofx replace F ofx by zero and find the
+general solution of L of y equals z
+
+ align:start position:0%
+general solution of L of y equals z
+ 
+
+ align:start position:0%
+general solution of L of y equals z
+after you've done that you find any old
+
+ align:start position:0%
+after you've done that you find any old
+ 
+
+ align:start position:0%
+after you've done that you find any old
+solution y sub P of the given equation L
+
+ align:start position:0%
+solution y sub P of the given equation L
+ 
+
+ align:start position:0%
+solution y sub P of the given equation L
+of yals f ofx just one solution by hooka
+
+ align:start position:0%
+of yals f ofx just one solution by hooka
+ 
+
+ align:start position:0%
+of yals f ofx just one solution by hooka
+by crook then finally when you have the
+
+ align:start position:0%
+by crook then finally when you have the
+ 
+
+ align:start position:0%
+by crook then finally when you have the
+general solution of the reduced the
+
+ align:start position:0%
+general solution of the reduced the
+ 
+
+ align:start position:0%
+general solution of the reduced the
+homogeneous equation and the particular
+
+ align:start position:0%
+homogeneous equation and the particular
+ 
+
+ align:start position:0%
+homogeneous equation and the particular
+solution of this equation the general
+
+ align:start position:0%
+solution of this equation the general
+ 
+
+ align:start position:0%
+solution of this equation the general
+solution of this equation will just be
+
+ align:start position:0%
+solution of this equation will just be
+ 
+
+ align:start position:0%
+solution of this equation will just be
+the sum of these two all right and
+
+ align:start position:0%
+the sum of these two all right and
+ 
+
+ align:start position:0%
+the sum of these two all right and
+that's what we're going to be talking
+
+ align:start position:0%
+that's what we're going to be talking
+ 
+
+ align:start position:0%
+that's what we're going to be talking
+about in the next few lessons see what
+
+ align:start position:0%
+about in the next few lessons see what
+ 
+
+ align:start position:0%
+about in the next few lessons see what
+we're going to drill on is what this
+
+ align:start position:0%
+we're going to drill on is what this
+ 
+
+ align:start position:0%
+we're going to drill on is what this
+stuff means and I think you can now
+
+ align:start position:0%
+stuff means and I think you can now
+ 
+
+ align:start position:0%
+stuff means and I think you can now
+guess what the next lectures are going
+
+ align:start position:0%
+guess what the next lectures are going
+ 
+
+ align:start position:0%
+guess what the next lectures are going
+to be about after all since to find the
+
+ align:start position:0%
+to be about after all since to find the
+ 
+
+ align:start position:0%
+to be about after all since to find the
+general solution of the linear
+
+ align:start position:0%
+general solution of the linear
+ 
+
+ align:start position:0%
+general solution of the linear
+differential equation I need the general
+
+ align:start position:0%
+differential equation I need the general
+ 
+
+ align:start position:0%
+differential equation I need the general
+solution of the homogeneous equation and
+
+ align:start position:0%
+solution of the homogeneous equation and
+ 
+
+ align:start position:0%
+solution of the homogeneous equation and
+a particular solution of the original
+
+ align:start position:0%
+a particular solution of the original
+ 
+
+ align:start position:0%
+a particular solution of the original
+equation the two separate topics I now
+
+ align:start position:0%
+equation the two separate topics I now
+ 
+
+ align:start position:0%
+equation the two separate topics I now
+have to tackle are one how do I find the
+
+ align:start position:0%
+have to tackle are one how do I find the
+ 
+
+ align:start position:0%
+have to tackle are one how do I find the
+general solution of the reduced equation
+
+ align:start position:0%
+general solution of the reduced equation
+ 
+
+ align:start position:0%
+general solution of the reduced equation
+and two how do I find a particular
+
+ align:start position:0%
+and two how do I find a particular
+ 
+
+ align:start position:0%
+and two how do I find a particular
+solution of the original equation that
+
+ align:start position:0%
+solution of the original equation that
+ 
+
+ align:start position:0%
+solution of the original equation that
+by the way comes Under The Heading of
+
+ align:start position:0%
+by the way comes Under The Heading of
+ 
+
+ align:start position:0%
+by the way comes Under The Heading of
+cookbook again that's drill but this is
+
+ align:start position:0%
+cookbook again that's drill but this is
+ 
+
+ align:start position:0%
+cookbook again that's drill but this is
+the underlying Theory the underlying
+
+ align:start position:0%
+the underlying Theory the underlying
+ 
+
+ align:start position:0%
+the underlying Theory the underlying
+philosophy we will talk more about how
+
+ align:start position:0%
+philosophy we will talk more about how
+ 
+
+ align:start position:0%
+philosophy we will talk more about how
+to handle the techniques in our
+
+ align:start position:0%
+to handle the techniques in our
+ 
+
+ align:start position:0%
+to handle the techniques in our
+subsequent lectures at any rate then
+
+ align:start position:0%
+subsequent lectures at any rate then
+ 
+
+ align:start position:0%
+subsequent lectures at any rate then
+until next time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goodbye funding for the publication of
+
+ align:start position:0%
+goodbye funding for the publication of
+ 
+
+ align:start position:0%
+goodbye funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
+ align:start position:0%
+and Paul rosenbom
+ 
+
+ align:start position:0%
+and Paul rosenbom
+foundation help ocw continue to provide
+
+ align:start position:0%
+foundation help ocw continue to provide
+ 
+
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+foundation help ocw continue to provide
+free and open access to MIT courses by
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+free and open access to MIT courses by
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+free and open access to MIT courses by
+making a donation at ocw.mit.edu/donate
\ No newline at end of file
diff --git a/J2uMjEDsE6s.txt b/J2uMjEDsE6s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..69761caa1615efccaea15a8143727ccf62b4cff1
--- /dev/null
+++ b/J2uMjEDsE6s.txt
@@ -0,0 +1,2120 @@
+PROFESSOR: This class is talking
+about two lectures, both about
+
+protein folding, fixed angled
+chains, things like that.
+
+There's a few
+questions about them.
+
+One is mostly about
+these open problems,
+
+equilateral, equiangular,
+obtuse 3D chains,
+
+fixed angle open problem
+is, are they locked?
+
+So the question is about,
+what about any subset
+
+of those combinations?
+
+So this originally comes
+from an open problem
+
+I think posed in 1999, one of
+the first 3D linkage papers,
+
+and it asked whether equilateral
+universal joints can lock,
+
+and that's still open.
+
+For universal joints,
+these two constraints
+
+don't make a lot of
+sense because who
+
+cares if it's
+initially equiangular.
+
+As soon as you move it, it
+will no longer be equiangular.
+
+And obtuseness I don't
+think matters too much,
+
+although it potentially could.
+
+So for that problem, equilateral
+seems to be the core.
+
+For fixed angle,
+though, we conjecture
+
+that fixed angle equilateral is
+not enough from this example.
+
+It's still not
+proved to be locked.
+
+I don't know if it's hard,
+but it's probably tedious,
+
+so it hasn't been done.
+
+This was the crossed
+legs example.
+
+All the edge lengths
+are the same,
+
+and if you don't allow
+the touching part,
+
+then all the angles
+are also the same.
+
+So this is everything
+except the obtuse property
+
+and it's probably locked, so
+dropping obtuse is no good.
+
+The other things you could drop
+are equilateral or equiangular.
+
+This is if you drop equiangular.
+
+Fixed angle equilateral is
+not terribly constraining
+
+because you can
+simulate a long bar
+
+by having a lot of
+180 degree angles.
+
+This is obtuse and
+it's equilateral
+
+but it's not
+equiangular and it's
+
+locked for a trivial reason.
+
+So this is dropping equiangular.
+
+If I drop equilateral,
+I can also
+
+just make a knitting
+needles example.
+
+I take a really long link, and
+this thing is basically string,
+
+so I don't really care.
+
+This connection can be done
+with a lot of obtuse angles,
+
+and then have a
+really long link.
+
+So dropping any of
+the three constraints
+
+makes it easy to lock, so
+for fixed angle chains,
+
+you need equilateral,
+equiangular, and obtuse.
+
+All these things
+together potentially mean
+
+you're not locked,
+but we don't know.
+
+That's the open problem.
+
+Of course, we don't
+necessarily need
+
+exactly equilateral
+or equiangular.
+
+Hopefully, within some small min
+to max ratio would be enough,
+
+but we don't know.
+
+Next question is, why did we
+model the ribosome as a cone?
+
+That seems rather simple.
+
+Is this realistic?
+
+And partly, when I
+taught the class in 2010,
+
+I didn't use any images I
+couldn't get permission for.
+
+This year I'm more lax.
+
+We'll ask for forgiveness
+instead of permission.
+
+This is a paper
+from Science 2000.
+
+This is what the ribosome
+actually looks like.
+
+There's many different
+figures of it,
+
+but I particularly like this
+one because it highlights
+
+a tunnel in the center
+of the ribosome.
+
+And so the idea is this is a
+machine for converting MRNA
+
+into your proteins,
+and the idea is
+
+the protein comes through here.
+
+There's a little
+bump in the tunnel.
+
+Some people conjecture this
+is where the amino acid gets
+
+attached, and then
+it feeds through here
+
+and starts spitting out.
+
+And as I said, there's
+barely enough room
+
+here for an alpha helix, so
+probably not too much folding
+
+happens inside and the folding
+should just happen over here.
+
+And the observation is if
+you have a reasonable size
+
+protein that's only going
+to be about this big,
+
+then there's this big,
+flat wall at the exit,
+
+so you have a plane
+there and this half space
+
+is more or less a big obstacle.
+
+It's the alpha cone model
+where alpha is 180, I think,
+
+if alpha is the half angle.
+
+So it's not really a cone.
+
+It's a cone that's been opened
+up all the way to a plane,
+
+but that's one of the situations
+that's handled by the theorems
+
+that we talked about.
+
+So that's why the cone model.
+
+We generalize to
+cones just because it
+
+works for general
+cones, but the real one
+
+is a sort of flat cone.
+
+That's where that comes from.
+
+I think actually we proved the
+theorem before we knew this,
+
+but then we looked it
+up and it was true.
+
+And the last question
+is about the lecture 21,
+
+which some of you may not have
+watched because it's optional,
+
+but there's this model
+called the HP model
+
+for protein folding.
+
+It's a model of
+protein energy and it
+
+says you have a chain
+of H and P nodes,
+
+and basically, the H nodes
+are attracted to each other
+
+and the P nodes don't care.
+
+And the model is that the H
+nodes are hydrophobic so they
+
+want to be next to each other
+so they're not next to water,
+
+which is surrounding
+the whole molecule,
+
+and the P nodes don't care,
+or they're hydrophilic.
+
+And it's known that if
+you have an HP string
+
+and you want to find the optimal
+folding into a 2D or a 3D
+
+structure, that's NP-hard,
+which is kind of weird
+
+because somehow
+nature does it, maybe
+
+because it found the easy
+instances by evolution,
+
+or maybe there's
+something we're missing.
+
+This model doesn't
+capture reality.
+
+We don't know.
+
+But it captures part of reality,
+as least as we observe it.
+
+Unfortunately, these
+hardness proofs
+
+are a little too
+complicated to cover here,
+
+but I can at least answer
+what are they reducing from.
+
+There's two proofs.
+
+I guess they were basically the
+same time, I think around 2001.
+
+The first one here
+is in 3D, and these
+
+are by two MIT professors.
+
+There's this big construction
+but the reduction
+
+is from bin packing.
+
+So you have a bunch
+of fixed size bins
+
+and you have a bunch of
+items of varying sizes
+
+and you just want
+to fit them all
+
+in using the fewest
+bins possible.
+
+And the rough idea of the
+construction of this one, this
+
+is how an individual
+number is represented.
+
+The rough idea is you
+have this big cube.
+
+You fill the sides
+with stuff to protect
+
+from the outside boundary.
+
+The insides are just
+used for connections,
+
+and then the front face
+here is this stuff.
+
+You construct
+these bins, and you
+
+construct numbers which
+have to fit inside the bins.
+
+That's the rough idea.
+
+The details are complicated.
+
+The 2D proof by
+several people is
+
+from Hamiltonicity in
+maximum degree-4 graphs.
+
+So you have a graph
+for every vertex that
+
+has at most four incident edges.
+
+You want to find a
+Hamiltonian cycle, I think.
+
+It's much harder to see
+this picture, I would say.
+
+There's no one diagram
+that summarizes it.
+
+This is roughly
+the construction,
+
+which is quite complicated,
+and I'll just leave it at that.
+
+That's what they're
+reduced from.
+
+I think an interesting
+open problem
+
+would be to find a simple or
+cleaner proof of these results.
+
+Now that it's known
+that they're hard,
+
+it's probably easy
+or hardness proofs.
+
+There's also some open
+questions from lecture,
+
+like is it APX hard?
+
+Is it approximable to a 1
+plus epsilon factor or 1 minus
+
+epsilon factor for any
+epsilon or is there
+
+some limit to approximability?
+
+We saw a nice approximation
+4/3 whatever, 3/4 whatever,
+
+but can you do better?
+
+Still open.
+
+So that was the questions,
+and then this is a question
+
+that you usually ask
+in every lecture.
+
+You didn't actually
+ask it on this one,
+
+but I copied and pasted.
+
+So there's some
+interesting progress
+
+from this class two years ago,
+and I think in the open problem
+
+session initially, probably
+also a class project
+
+related to this part.
+
+So this is back in lecture 20.
+
+We had this proof,
+which is kind of fun,
+
+that flattening a
+fixed angle chain,
+
+deciding whether there
+was a flat folded state,
+
+is weakly NP hard,
+weakly meaning
+
+it depended a lot on what
+these numbers look like
+
+and it was a reduction
+from partitions.
+
+You had to split up the
+numbers into two equal parts,
+
+and if you did, then this
+key would fit in the slot
+
+and you're OK.
+
+If you didn't, the key would
+collide with something here.
+
+So this means the
+problem is hard
+
+if your edge lengths
+are vastly different.
+
+They would have to differ
+by a ratio of exponential
+
+in the number of edges for
+this to really be hard.
+
+So a natural question is,
+well, what if all the lengths
+
+are equal, equilateral chains?
+
+Turns out that is still hard,
+and this is a paper just
+
+published last year with
+Sarah Eisenstadt, who
+
+took the class then.
+
+And there's a bunch
+of results here.
+
+All of these are NP hardness
+results, strong NP hardness,
+
+so it doesn't depend
+on the numbers.
+
+We've got flattening results.
+
+There's also min flat
+span and max flat span.
+
+Once you have that
+flattening is hard,
+
+these are pretty
+easy to show hard,
+
+so I won't talk
+about them so much.
+
+But basically, we consider
+different ranges of angles
+
+and what you might allow.
+
+In some cases, we can get
+perfect equilateral chains.
+
+In some cases, they have to
+range between, say, 1 and 2
+
+in length.
+
+A natural question
+is obtuse angles.
+
+We don't quite know that.
+
+The best we have is 60 degrees
+minus epsilon and larger.
+
+This is nice for
+orthogonal chains,
+
+but it's not for
+chains, it's for trees.
+
+So still some open questions
+here, but lots of hardness
+
+results.
+
+I thought I'd show you roughly
+what the hardness proofs look
+
+like because
+they're kind of fun.
+
+They all follow this
+kind of structure.
+
+This is a gadget, and
+it's a fixed angle chain.
+
+Here I'm going to show
+everything with 90 degrees
+
+because it's easier
+to think about.
+
+And it's kind of like--
+I'm thinking plunger,
+
+but it's something like that.
+
+You can decide which
+parts get pushed in
+
+and which parts get popped out,
+and this L shape can basically
+
+shift left and right to
+three different places
+
+if I did it right-- this
+one, this one, and this one.
+
+So that's a useful construction,
+as you might imagine,
+
+and the idea is you take that
+and you add on these guys.
+
+So I've got another kind
+of plungey thing like this,
+
+and this guy can move left
+and right to various extents.
+
+That's not very intuitive.
+
+So then this connects
+to these little guys,
+
+and these can just
+flip up or down
+
+if it's a flat embedding
+of a fixed angle chain.
+
+And so the idea is you have
+three of these pokey elements
+
+and they can attach.
+
+They bump into these
+different things.
+
+And if it's up,
+then this can be up,
+
+but when they're down-- like
+this guy is currently down,
+
+but it could be pushed
+up-- then this guy
+
+must be flipped down like that.
+
+That's the rough idea of how
+these parts fit together.
+
+And so then this is how you end
+up building some kind of three
+
+sat problem.
+
+So you have some variables.
+
+They can either
+be true or false.
+
+And the idea is that the
+true guys are on the top,
+
+the bottom guys
+are on the bottom,
+
+and there's some complicated
+interaction between them
+
+to make sure that they can't
+both be true and false.
+
+Basically, you want
+these things to point
+
+in whenever possible because
+then these guys can go down.
+
+Otherwise, you would collide.
+
+And if this guy's in,
+the corresponding guys
+
+in the bottom must
+be down, and that's
+
+enforced by this long
+thing, which is either
+
+completely down
+or completely up.
+
+So when it's completely
+down, these guys
+
+all have to be
+down, which is going
+
+to be a problem down below
+if things aren't satisfied.
+
+When it's up, all of these
+guys would have to be up.
+
+Some of them could be
+up if you feel like it,
+
+but really, you'd
+probably put them
+
+all down whenever you
+can because then you
+
+can take these guys
+and stick them down.
+
+So this is how
+you set variables,
+
+and then the other
+things I showed
+
+were clauses, essentially.
+
+At least one of those
+pins had to be pushed down
+
+and you don't know which one,
+and that's the hard part.
+
+Rough sketch of how
+this proof looks.
+
+One thing is here,
+for this to work,
+
+these edges can't be spinnable.
+
+When I go here, I must
+immediately go back down.
+
+I can't flip it.
+
+So these are rigid edges.
+
+That's not really
+the original problem,
+
+but you can simulate
+rigid edges,
+
+and this is where
+the angles get small.
+
+You can simulate rigid edges
+with a very sharp zigzag
+
+because if you ever
+flipped one of these,
+
+it would collide with
+the previous edge.
+
+So for sufficiently
+sharp angles,
+
+you can force parts to stay
+straight in this funny way,
+
+which is not great, but
+it's one way to force it.
+
+We can also do it with trees
+or various other techniques,
+
+but that's how the proof looks.
+
+So that is flattening fixed
+angle chains, strongly NP hard.
+
+We go next to one
+more topic for fun.
+
+This is the topic of flips.
+
+I guess I have an
+image for this.
+
+This is a problem
+posed by Paul Erdos,
+
+I think when he was a student.
+
+He was a very famous
+mathematician.
+
+1935, he asked this question.
+
+This is the whole question
+as originally written.
+
+You have a polygon and you take
+the convex hull of the polygon,
+
+and you take these regions
+which are in the convex hull
+
+but outside the polygon.
+
+We call those pockets.
+
+And you imagine
+flipping those outside,
+
+reflecting through
+that supporting line,
+
+that tangent on the outside,
+so then you get this polygon.
+
+Here you get two pockets.
+
+Maybe you flip both of them, and
+then you get a convex polygon.
+
+Now you have no pockets,
+and so you're done.
+
+And the question is as posed.
+
+Prove that after a finite
+number of such steps,
+
+the polygon would become convex.
+
+So you might call this
+a conjecture by Erdos
+
+that it is finite.
+
+He'd never published a proof.
+
+There's one issue with
+the problem as stated.
+
+You can't actually
+flip both pockets
+
+at once if you want
+to avoid collisions.
+
+The relation to
+linkages is we imagine
+
+these flips could actually
+happen by a rotation,
+
+but you could also
+just imagine them
+
+as reflecting instantaneously.
+
+There's this issue.
+
+If you flip two
+pockets at once, you
+
+might have collisions
+afterwards.
+
+The way this problem has been
+interpreted by most people
+
+is don't flip them all at once.
+
+Just flip them one
+at a time, and then
+
+you guarantee, because
+this is a supporting line,
+
+a tangent line, of
+the convex hull,
+
+when you flip one pocket out,
+it will go to the other side
+
+so it can't intersect
+the rest of the polygon.
+
+So you would avoid collision
+if you do one flip at a time.
+
+Now, this was observed, I
+guess, a few years later
+
+by Bela de Sz.
+
+Nagy, and he also
+published the first proof.
+
+Before we get there,
+a weird property
+
+and why you might worry about
+this being finite or infinite
+
+is if you take
+this quadrilateral
+
+and make this very narrow,
+this edge very small
+
+relative to the
+horizontal edge, then
+
+you can require arbitrarily
+many flips to convexify.
+
+Even for n equals 4, you
+could require a million flips.
+
+So definitely there's
+some dependence
+
+on the ratio between the longest
+length and the smallest length,
+
+though in open
+problem, what we still
+
+don't know is whether you
+can bound the number of flips
+
+in terms of n and that ratio.
+
+Is it pseudo-polynomial?
+
+Who knows?
+
+So it turns out
+it's always finite,
+
+and there have been many proofs
+over the years of this result.
+
+It's kind of been
+rediscovered many times.
+
+Nagy solved it originally
+in 1939, and he cited Erdos.
+
+These two guys
+didn't cite anyone,
+
+so they may have come up with
+the problem independently.
+
+This paper, these are
+two Russian proofs.
+
+Then this paper cited--
+they knew about everything.
+
+They cited all of them.
+
+They cited Reshetnyak.
+
+I don't think they necessarily
+knew about Yusupov.
+
+Independently, Kaluza
+posed the problem in 1981
+
+and Wegner solved it, and
+then to finally clean it up,
+
+Grunbaum, who we saw
+from un-un-unfoldable,
+
+knew about everything.
+
+Presumably, this is everything.
+
+Of course, we might
+have missed one.
+
+But he knew all the above,
+came up with his own proof.
+
+And then Godfried
+Touissant, father
+
+of computational geometry,
+one of them, knew about these
+
+and came up with yet
+another, simpler proof.
+
+So the story of
+this is kind of fun.
+
+When I taught this class for
+the very first time, 2003 or so,
+
+I thought, OK, cool.
+
+This is a classic theorem.
+
+Everyone should know it.
+
+So I thought I'd cover the
+latest proof that's presumably
+
+the best, so I covered
+Godfried's proof.
+
+I was a little unhappy with
+it, but I finished writing down
+
+the proof, and then one of
+the students raised their hand
+
+and asked, is that really right?
+
+Can you do that in step two?
+
+And the answer was
+no, you can't do that.
+
+It basically skipped a step.
+
+And so I thought, oh gee.
+
+And so I corresponded
+with O'Rourke and Godfried
+
+that weekend and was like,
+is something missing here?
+
+Maybe we should go back to
+some of the other proofs
+
+because we've got
+lots to choose from.
+
+So we went to the original,
+which is a very short proof.
+
+It's only one page long,
+maybe one and a half pages.
+
+And so this is fun.
+
+This is 1939, the way
+mathematics used to be done.
+
+And it's funny because
+Grunbaum's proof was based
+
+on Nagy's proof and
+Toussaint's proof
+
+was based on Grunbaum's
+proof, so in the end,
+
+these proofs were very similar.
+
+In fact, they differed
+exactly in the one step,
+
+which was kind of omitted here.
+
+So I thought, OK great.
+
+Here we have a fill-in
+on how to do it.
+
+And so the next class, I
+went up and I presented it.
+
+I was really happy.
+
+Isn't this cool,
+1939 mathematics?
+
+It's really awesome,
+and it's one line
+
+that filled in this step.
+
+The same student raises
+his hand and is like,
+
+I don't think that's true.
+
+So now the step was filled
+in but it was wrong.
+
+So it turns out actually
+most of these proofs
+
+are wrong, but not all
+of them, fortunately,
+
+so the theorem is still true.
+
+So that one was wrong, this one
+was wrong, this one was wrong,
+
+this one skipped a
+step that was key,
+
+this one essentially also
+skipped the step that was key.
+
+So in the end, there's two
+correct proofs, Reshetnyak
+
+and Bing and Kazarinoff,
+which was surprising.
+
+So I thought I'd show you one
+of the errors in the Nagy proof.
+
+There's one other
+interesting feature here,
+
+which is, why wasn't this
+discovered until our class?
+
+The student was Blaise Gassand,
+and so then we wrote a paper
+
+about it and we have our
+own proof, of course.
+
+Now, some people
+may have realized
+
+there was an error in
+some of the proofs.
+
+Bing and Kazarinoff, one of
+the correct proofs, a very nice
+
+one, wrote-- here's the
+original Russian sentence.
+
+The English translation
+is, "the proof
+
+of this theorem given
+by Nagy is incorrect,"
+
+which leaves something
+to be desired.
+
+And Grunbaum, who
+can read Russian--
+
+we had to get them
+translated-- mentioned this.
+
+So he noticed that point. "They
+remarked that Nagy's proof is
+
+invalid but there's no
+basis for this claim."
+
+Then it remained undiscovered
+until 2005 or something.
+
+Kind of funny.
+
+Good thing there's so many
+proofs to choose from.
+
+So this is Nagy's
+original proof.
+
+You can see the example
+where flipping two pockets
+
+simultaneously
+causes a crossing.
+
+Don't read the whole
+thing, obviously,
+
+but there's one
+sentence here which is,
+
+if you take a polygon, call
+it p0, and you flip a pocket
+
+and you get p1, and you flip
+a pocket and you get p2,
+
+and you take the convex
+hull of p and you get c0,
+
+and you take the convex hull
+of p1 and you get c1, p2,
+
+you get c2.
+
+And then you interleave
+these polygons
+
+so that the polygon is a convex
+hull, next polygon is a convex
+
+hull, because you're
+always flipping out,
+
+each of these polygons obviously
+contains the foregoing ones.
+
+And so that seemed really
+nice and we thought,
+
+oh, this is so elegant.
+
+They used this to prove that
+the limit of the p's is convex
+
+because the limit
+of the p's then
+
+would be the limit of the c's
+because it was interleaving.
+
+But it's not true
+that these things
+
+contain the previous ones
+because if you have two pockets
+
+and you flip one of
+them, it's this one
+
+pocket versus multiple
+pockets issue.
+
+If you flip one of
+them, that will not
+
+contain the convex
+hull of the original
+
+because you haven't
+flipped them all.
+
+If you flipped all the
+pockets, than you would contain
+
+the convex hull of
+the original, but that
+
+would end up arguing
+that some flip
+
+sequences work, not all of them.
+
+So this is annoying,
+and I think this
+
+is where I run out of slides.
+
+But we have some time, so I can
+give you a sketch of the proof.
+
+This is the Bing and Kazarinoff
+proof or our version of it.
+
+Give you an idea
+of how this works.
+
+It's an easy proof, it's just
+easy also to get it wrong
+
+or to skip one of the steps.
+
+I will just do a proof
+by picture, I think.
+
+So suppose you have a
+polygon on the plane,
+
+and let's say you flip a pocket.
+
+So this would look
+something like that.
+
+A little hard to
+do a reflection.
+
+So this is the
+reflective polygon,
+
+and if we look at each of
+the vertices over here,
+
+these guys don't move,
+these guys moved over here,
+
+reflecting through that line.
+
+Observation one.
+
+If I take some point x
+interior to the polygon,
+
+then these points that move
+get farther away from x.
+
+Why?
+
+Because if you look
+at this line here,
+
+let's say you look at a
+vertex and where it goes.
+
+This line is the Voronoi
+diagram of those two points.
+
+This is the perpendicular
+bisector of this and this.
+
+That's the meaning
+of reflection.
+
+So that means everything
+to the left of the line
+
+here is closer to this
+point than that point.
+
+Everything to the
+right of the line
+
+is closer to this
+point than that point.
+
+Now x, which is
+interior to the polygon,
+
+must be to the left of the
+line because the whole polygon
+
+is to the left of the line.
+
+So distance from x to
+this vertex increases.
+
+I mean, x will remain
+inside because as you flip,
+
+you only get bigger.
+
+So if I take a point x
+and I look at the distance
+
+to some vertex, it can only
+monotonically increase.
+
+It also can't get
+arbitrarily large
+
+because the maximum
+it could possibly be
+
+is half the perimeter
+of the polygon.
+
+The perimeter of the
+polygon is preserved
+
+so it can only stretch so far.
+
+So if you look at this distance,
+it's monotonically increasing
+
+and it's bounded because
+it can never get bigger
+
+than the perimeter
+of the polygon.
+
+Therefore, it has a limit.
+
+That distance has
+a limit because
+
+monotone bounded sequences
+always have a unique limit.
+
+So cool.
+
+Distance from x to some
+vertex has a limit.
+
+Well, I'm going to do this for
+three different points, x, that
+
+lie on some non-degenerate
+triangle, so not all on a line.
+
+That means the three
+distances from these points
+
+to this vertex all
+converge to some limit.
+
+And therefore, that
+point converges
+
+to a limit, namely the
+intersection of those three
+
+circles centered
+at those points.
+
+So this proves that
+the polygon has
+
+a limit because every
+vertex has a limiting point.
+
+Cool.
+
+Now the tricky part is to
+argue that limit is convex,
+
+and this is where
+everyone had an issue.
+
+The first thing we argue is that
+the angles converge to a limit.
+
+This is kind of a
+technicality because we
+
+know the points
+converge to a limit,
+
+so surely the angle does.
+
+The only issue is, well,
+if all the points converge
+
+to the same point, then the
+angle would not have a limit,
+
+but that's easy to
+argue can't happen
+
+because these edge
+links are preserved.
+
+So I will just skip that one.
+
+It follows from some
+of the things we said.
+
+Now we get to the fun part.
+
+This polygon has a limit.
+
+The angles have limits.
+
+So I want to look at
+the limiting angles.
+
+I want to in particular
+look at the vertices that
+
+move because if you flip an
+infinite number of times, that
+
+means some vertex must move
+an infinite number of times,
+
+because every time you
+flip, somebody moves.
+
+These guys are
+considered not moving
+
+even though they're kind
+of involved in the flip.
+
+So if you look at the moved
+guys, what is their angle?
+
+So before, there
+was some angle here,
+
+and afterwards, the interior
+angle is the reverse.
+
+If this was reflex
+before, it's convex now.
+
+If there were a convex
+angle over here like this,
+
+it would become
+reflex over here.
+
+You alternate between
+being less than 180
+
+and greater than 180
+every time you move.
+
+So if you have a vertex that is
+moving infinitely many times,
+
+its angle must alternate
+between less than 180 convex
+
+and greater than 180 reflex
+infinitely many times.
+
+If that happens and you
+have a unique limit angle,
+
+your limit angle must be 180.
+
+That's interesting.
+
+If our vertex moves
+infinitely many times,
+
+then its limit angle
+equals 180, must be flat.
+
+Very close to a
+contradiction at this point.
+
+These guys are going to
+end up looking like this.
+
+Well, let's look
+at the other guys.
+
+So we have some limit polygon.
+
+In the limit polygon, there
+are some flat vertices,
+
+but there must also be
+some non-flat vertices.
+
+You can't just go straight
+and hope to close a cycle.
+
+So there's maybe some
+convex ones like this.
+
+There may be some reflex ones.
+
+At some point,
+these vertices must
+
+stop moving because everyone
+who moves infinitely many times
+
+has a limit angle flat.
+
+So anybody who is--
+we call it "pointed"
+
+here, although it's a little
+different from pointed pseudo
+
+triangulations.
+
+Anyone who's not
+a flat angle must
+
+stop moving after finite time.
+
+So let's go to that time
+when all of these guys
+
+have stopped moving.
+
+So your limit
+polygon is something.
+
+We don't know whether
+it's convex or whatever.
+
+It could have many flat angles.
+
+It's got to have at
+least one of them
+
+if we assume there's
+something infinite here.
+
+This is the limit polygon.
+
+Now, at finite time,
+we know that these guys
+
+have stopped moving, meaning
+we're done with those guys.
+
+I've drawn the limit here, but
+also the finite thing, which
+
+must be on the inside, right?
+
+This must be
+something like this.
+
+Somehow it's going to flip and
+reach the infinitely many times
+
+and reach this in the limit.
+
+Hm.
+
+That looks weird.
+
+So the way to argue
+this in the clean way
+
+is if you look at the
+convex hull of the limit,
+
+let's say, convex hull
+of the limit is this.
+
+And look at the convex
+hull of this finite time
+
+when the squared vertices
+have stopped moving.
+
+Convex hull will
+be-- well, it's got
+
+to be at least this because
+these guys are already there.
+
+The convex hull is defined
+by the square points.
+
+You don't care about
+the flat vertices.
+
+That won't affect
+the convex hull.
+
+So that means the convex
+hull equals the limit convex
+
+hull at this finite time.
+
+Now you're about to
+do another flip, which
+
+means you're going to
+go outside that convex
+
+hull and contradiction.
+
+Is that clear?
+
+Maybe go through that
+part one more time.
+
+After finite time, when all
+of the non-flat vertices
+
+have stopped moving, we have
+reached the final convex hull.
+
+That means you can't do any more
+flips because every flip makes
+
+the convex hull
+bigger, so you actually
+
+had to stop at that time.
+
+That's kind of a fun proof.
+
+The key is really this
+part, that if a vertex flips
+
+infinitely many times, then
+that limit angle must be flat,
+
+and so they really don't
+participate in the convex hull.
+
+This is the Bing and
+Kazarinoff key idea.
+
+AUDIENCE: Two questions.
+
+Does anyone do this for 3D?
+
+PROFESSOR: 3D is a good.
+
+People have tried to
+define flips for 3D,
+
+and I think there's never really
+been a successful definition.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Yeah, and
+exactly how to flip it.
+
+I mean, you can define
+pocket in the same way,
+
+but then the boundary
+won't be a single plane.
+
+It'll be some convex
+cap, and so flipping, you
+
+can't really just reflect.
+
+It's kind of annoying.
+
+AUDIENCE: The
+other question was,
+
+you have a sequence
+of simple operations
+
+that takes you from
+non-convex to convex.
+
+Does anybody use that
+in a proof to say,
+
+these things are preserved
+across the operations?
+
+You said perimeter
+was preserved.
+
+What about shortest paths?
+
+PROFESSOR: So is this
+useful for something?
+
+Shortest paths are
+certainly not preserved.
+
+Edge lengths are preserved.
+
+Of course, we know how to do
+that with the carpenter's rule
+
+theorem, just staying in 2D,
+so it's not that exciting.
+
+But the operations are
+definitely a lot simpler.
+
+I think the easy
+answer to your question
+
+is there are many
+natural, simple moves,
+
+and this is the first one
+that people considered,
+
+but actually, there
+are a lot more,
+
+and I'm going to
+talk about those.
+
+The main application I know
+for this stuff is basically,
+
+people wanted to generate random
+closed walks in 3D typically,
+
+and so they wanted to find
+a small set of operations
+
+they could just perform
+randomly and hope
+
+that that was a rapidly
+mixing Markov chain,
+
+so eventually, you'd have
+a kind of random thing.
+
+I don't think there
+are any rapid mixing
+
+results, at least
+that I'm aware of.
+
+In order to hope to
+get the space randomly,
+
+you would at least have to
+be able to make anything.
+
+So for that, the question is,
+can you convexify anything,
+
+because if you can convexify
+anything, then at least
+
+you can make anything,
+more or less.
+
+So that's where these
+questions come from.
+
+We focus more on
+the universality,
+
+but I think what people care
+about is this random generation
+
+business.
+
+To that end, of course,
+for random generation,
+
+you don't really
+care about crossings.
+
+And so another fun
+extension which
+
+was in, I think, our
+paper for the first time,
+
+although there's a weaker
+version in Grunbaum's paper,
+
+if you start with a
+non-crossing, this proof
+
+still works.
+
+You need to add a little
+more to the argument.
+
+Either you decrease the number
+of crossings, which can only
+
+happen a finite number of times,
+or this kind of stuff works.
+
+You can make crossing polygons,
+too, which is kind of cool.
+
+So that's the end
+of basic flips.
+
+Then we have something called a
+flip turn, which is kind of fun
+
+and in some ways better behaved,
+and gets to your question
+
+of what else is preserved.
+
+So let's say you have
+a pocket like this.
+
+So normally with a
+flip, we would reflect.
+
+With a flip turn, you reflect
+and then also flip this way,
+
+so it's the same as rotating
+180 degrees about the center.
+
+In addition to
+preserving perimeter,
+
+this preserves the
+edge directions.
+
+This matches this, this matches
+this, this matches this.
+
+It does not preserve
+the edge order, however.
+
+Here, we preserve
+the edge order.
+
+Here, we've reversed the
+order of those three edges.
+
+So all this is really
+doing is permuting
+
+the sequence of edges.
+
+The edge directions and the
+edge lengths are all the same.
+
+So this means you could make
+at most n factorial moves here.
+
+Immediately, it's different
+from this situation
+
+where even for n
+equals 4, you could
+
+have arbitrarily many moves.
+
+Here, it's at most n factorial.
+
+That was the original bound.
+
+It turns out every
+polygon convexifies
+
+after order n
+squared flip turns.
+
+It's a fun proof but I don't
+have time to cover it here.
+
+That's flip turns.
+
+Then we go to deflations.
+
+This is the inverse of a flip.
+
+So suppose you take a polygon
+and you do an operation
+
+that, if flipped, would result
+in the original polygon,
+
+exactly the opposite of a flip.
+
+This was conjectured to also
+finish after finite time,
+
+but in fact it doesn't.
+
+If you take any quadrilateral
+satisfying Kawasaki,
+
+so if you add up the
+opposite edge lengths
+
+and they're equal-- so 6
+plus 3 is 9, 4 plus 5 is 9--
+
+then there it is at least
+a flat limit possibly.
+
+That's the Kawasaki thing.
+
+And in fact, it will
+converge to that flat limit
+
+and it will take infinite
+time to get there.
+
+So that's kind of fun.
+
+It gets very hard to
+draw the pictures.
+
+This is really the main example
+of an infinitely deflating
+
+polygon.
+
+We have a paper called
+"Deflating the Pentagon," which
+
+got some fun political
+views at some point.
+
+It's about a
+pentagon, five sides.
+
+And essentially, unless you have
+a flat vertex, in which case
+
+you are quadrilateral, there
+is no infinitely deflating
+
+pentagon, which means you can
+deflate the pentagon always
+
+in finite time.
+
+It is open for
+hexagons and higher
+
+whether there is another
+example different
+
+from the quadrilateral.
+
+Then there's the idea of a pop.
+
+This is an even simpler
+operation than a flip.
+
+You just take two
+edges, like here we're
+
+taking these two edges,
+and, ignoring crossings,
+
+you just flip as if
+that were a pocket lid,
+
+so if this were a pocket.
+
+Then you get this polygon.
+
+Now here, you can be
+forced to get crossings.
+
+No matter how you flip,
+you might get a crossing.
+
+Still, we're wondering--
+who cares about crossings--
+
+are pops enough to make
+anything, or to convexify?
+
+And the answer is no.
+
+There's this set of polygons
+called alternating polygons
+
+where the vertices
+alternate between the x-axis
+
+and the y-axis.
+
+And you can prove that no
+matter what pop you do,
+
+you are still an
+alternating polygon,
+
+and alternating polygons,
+you can also prove,
+
+are never convex,
+so you're stuck.
+
+This was open for many years but
+finally solved a few years ago.
+
+There's also pop turns, which
+is where you take two edges
+
+and you do a 180 degree
+rotation like this.
+
+And there, we can prove
+if you allow crossings,
+
+you can convexify any polygon.
+
+I don't have a figure of that
+because it's just an algorithm.
+
+We haven't actually run
+it on a nice example.
+
+If you avoid crossings, we can
+characterize when it's possible
+
+and when it's impossible.
+
+And those are pretty much
+all the simple operations
+
+that at least have been studied.
+
+There's probably more to
+think about, but that's it,
+
+and that's the end of
+my part of the class.
\ No newline at end of file
diff --git a/K5n0BMKZR_Q.txt b/K5n0BMKZR_Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..497e6260b3d360c75e6f9a64c865f6468ba9a8a4
--- /dev/null
+++ b/K5n0BMKZR_Q.txt
@@ -0,0 +1,431 @@
+PROFESSOR: Welcome to
+another help session
+
+on recombinant DNA.
+
+Today, we're going to
+be discussing about
+
+transformation and protein
+expression.
+
+As you can imagine, there are
+often many times we will need
+
+a large amount of protein.
+
+But it can be difficult to get
+it from the original source.
+
+For example, you need insulin
+to treat diabetes, but it's
+
+not exactly practical to get a
+lot of insulin from humans.
+
+In order to get a lot of the
+desired protein, often other
+
+organisms will be used to
+express this protein.
+
+But it's a multi-step process.
+
+For example, let's say we want
+to express our human insulin
+
+in bacteria.
+
+Well, the human gene has both
+introns and exons, as you
+
+remember from lecture.
+
+Exons are what are actually
+cut together in order to
+
+produce the final mature mRNA,
+which is later used to express
+
+the protein.
+
+Bacteria, on the other hand,
+don't have introns.
+
+They just have exons.
+
+So they are only capable of
+reading a gene that just has
+
+the exons and then producing
+the protein from that.
+
+In order to take a version of
+the gene that's from the
+
+eukaryotic cell and get it
+to be expressed in the
+
+prokaryotic, we first have to
+make something called cDNA.
+
+So let's begin.
+
+We're going to take our
+cell of interest.
+
+And the first step in creating
+the cDNA is we're going to
+
+isolate the mRNA of interest--
+
+this is the mRNA for insulin,
+for example--
+
+from the cell.
+
+And once we have our mRNA, we
+are going to add something
+
+called reverse transcriptase.
+
+This is a protein that's a DNA
+polymerase that's going to use
+
+the single-stranded RNA
+as its template.
+
+So it's going to take the RNA
+and it's going to put together
+
+this double-stranded DNA
+that we're going
+
+to refer to as cDNA.
+
+So this is the DNA for the gene,
+but unlike the original
+
+gene, it only has the exons.
+
+It doesn't have any
+of the introns.
+
+The next step, of course,
+is to get the
+
+cDNA into the bacteria.
+
+We do this using something
+called a vector.
+
+The vector is just a means of
+getting DNA into a cell.
+
+One common type of vector
+is a plasmid.
+
+The plasmid is a circular piece
+of DNA that the bacteria
+
+can then take up and read.
+
+The way we're going to get our
+cDNA into this plasmid is
+
+through the use of restriction
+enzymes.
+
+As you remember from our
+previous help session,
+
+restriction enzymes can cut up
+DNA and create these overhang
+
+of the nucleotides.
+
+So we're going to cut up the
+cDNA, and we're going to cut
+
+up the plasmid, and they're
+going to have overhangs that
+
+are complementary.
+
+This means that when we add
+the cDNA to the plasmids,
+
+they're going to hybridize,
+and then
+
+we can add DNA ligase.
+
+We add DNA ligase, it will
+create a phosphodiester bond
+
+between the cDNA and the
+plasmid vectors.
+
+And finally we'll get the cDNA
+inserted into our plasmid.
+
+The next step, of course, is
+getting the plasmid into the
+
+bacteria in order for the
+protein to be expressed.
+
+There are multiple, different
+ways to do this.
+
+One common way is called
+heat shock.
+
+What happens is that the
+bacteria is heated up and then
+
+cooled rapidly, and this creates
+lots of little holes
+
+in the membrane, which
+allow the plasma to
+
+get into the cell.
+
+Once you have the plasmid in
+the bacteria, your job is
+
+pretty much done.
+
+Now the bacteria will naturally
+express this
+
+protein, so you can grow up
+the bacteria in large
+
+quantities and get a lot of
+the protein of interest.
+
+Referring back briefly to the
+vector, there are several
+
+parts that are important
+for it to have.
+
+We're going to need to have the
+origin of replication, the
+
+promoter, and the selection
+marker.
+
+The origin of replication
+initiation, or ORI, is
+
+necessary if we want the
+bacteria to produce more
+
+copies of this plasmid.
+
+So once the plasmid gets into
+the bacteria, if we don't have
+
+an ORI, as the bacteria grows
+and reproduces, none of the
+
+daughter cells will
+have this plasmid.
+
+We'll have to continually
+transform them.
+
+However if it has the ORI,
+as a bacteria grows and
+
+reproduces, it will also
+replicate this plasmid.
+
+Another very important thing
+to have is the promoter.
+
+The promoter is a section of DNA
+which signals for the RNA
+
+polymerase to bind.
+
+The RNA's polymerase will bind
+to the promoter, and then will
+
+proceed down the DNA on the
+plasmid to read the actual
+
+gene and transcribe it.
+
+So the mRNA, which then
+ultimately can
+
+be made into protein.
+
+Finally, you need a
+selection marker.
+
+Now as we talked about earlier,
+when you heat shock
+
+the bacteria, the plasmid
+will get taken up.
+
+However, not all the
+bacteria might take
+
+up some of the plasmid.
+
+In order to get rid of the
+unwanted bacteria, the
+
+bacteria that doesn't have the
+plasmid, we're going to use
+
+selection marker.
+
+A very common selection marker
+for bacteria is antibiotic
+
+resistance.
+
+For example, if the plasmid
+provides ampicillin
+
+resistance, then this means that
+any bacteria that takes
+
+up the plasmid will be resistant
+to ampicillin.
+
+The bacteria that don't will
+still be vulnerable to it.
+
+So you could plate all of your
+bacteria on a plate containing
+
+ampicillin, and the ones that
+have the plasmid will survive.
+
+The ones that don't have the
+plasmid will perish.
+
+So let's go once more to the
+original example and discuss
+
+about what we're going to
+need for our vector.
+
+So again, we want to express
+human insulin in
+
+the bacterial system.
+
+There are six possibilities
+for what we
+
+can need on our vector.
+
+You can need the bacterial
+ORI, the human ORI, the
+
+bacterial promoter, the human
+promoter, the bacterial
+
+selection marker, the human
+selection marker.
+
+Pause for a minute.
+
+Give you a chance to decide
+what you think the vector
+
+needs, and then we'll
+go over it together.
+
+OK.
+
+Does it need a bacterial ORI?
+
+Yes.
+
+If we want to grow up a large
+amount of insulin, we're going
+
+to put the plasmid
+in the bacteria.
+
+The bacteria needs to create
+more of this plasmid.
+
+Does it need human ORI?
+
+No, we're not actually assorting
+the plasmid into a
+
+human cell.
+
+So the human cell is never
+going to need to
+
+create more of them.
+
+Just the bacterial cell.
+
+What about a bacterial
+promoter?
+
+Yes.
+
+Even though it's a human
+gene, the promoter has
+
+to be for the bacteria.
+
+Because it's going to be the
+bacterial RNA polymerase that
+
+will bind to the promoter,
+and ultimately make the
+
+mRNA from the cDNA.
+
+What about a human promoter?
+
+No, we don't need a human
+promoter because the human RNA
+
+polymerase won't be involved.
+
+Again, this is only going to
+be in the bacterial cells.
+
+It's not going to be in the
+human cell, so it doesn't need
+
+a human promoter.
+
+And finally for the selection
+markers, once again, we only
+
+need the bacterial selection
+marker, not the human
+
+selection marker.
+
+We're not dealing with full
+human cells at this point.
+
+We're just dealing with a
+plasmid, so we only need to
+
+select for bacteria cells that
+have the plasmid of interest.
+
+This has been another help
+section on recombinant DNA.
+
+Thank you for your time.
\ No newline at end of file
diff --git a/MJM1AzpB6Y4.txt b/MJM1AzpB6Y4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6653093405c236ad6583e9f318ead9cf3a6651d8
--- /dev/null
+++ b/MJM1AzpB6Y4.txt
@@ -0,0 +1,587 @@
+align:start position:0%
+ 
+we got here finally in terms of position
+
+ align:start position:0%
+we got here finally in terms of position
+ 
+
+ align:start position:0%
+we got here finally in terms of position
+and in terms of momentum so this was not
+
+ align:start position:0%
+and in terms of momentum so this was not
+ 
+
+ align:start position:0%
+and in terms of momentum so this was not
+an accident that it worked for position
+
+ align:start position:0%
+an accident that it worked for position
+ 
+
+ align:start position:0%
+an accident that it worked for position
+and wave number
+
+ align:start position:0%
+and wave number
+ 
+
+ align:start position:0%
+and wave number
+it works with position and for momentum
+
+ align:start position:0%
+it works with position and for momentum
+ 
+
+ align:start position:0%
+it works with position and for momentum
+and remember this Phi of P now has
+
+ align:start position:0%
+and remember this Phi of P now has
+ 
+
+ align:start position:0%
+and remember this Phi of P now has
+interpretation of the weight that is
+
+ align:start position:0%
+interpretation of the weight that is
+ 
+
+ align:start position:0%
+interpretation of the weight that is
+associated with a plane wave of momentum
+
+ align:start position:0%
+associated with a plane wave of momentum
+ 
+
+ align:start position:0%
+associated with a plane wave of momentum
+P and you're summing over P in here so
+
+ align:start position:0%
+P and you're summing over P in here so
+ 
+
+ align:start position:0%
+P and you're summing over P in here so
+we'll do the natural thing that we did
+
+ align:start position:0%
+we'll do the natural thing that we did
+ 
+
+ align:start position:0%
+we'll do the natural thing that we did
+with X will interpret Phi of P squared
+
+ align:start position:0%
+with X will interpret Phi of P squared
+ 
+
+ align:start position:0%
+with X will interpret Phi of P squared
+Phi of P squared DP as the probability
+
+ align:start position:0%
+Phi of P squared DP as the probability
+ 
+
+ align:start position:0%
+Phi of P squared DP as the probability
+is the probability to find the particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with momentum in the range P P plus DP
+
+ align:start position:0%
+with momentum in the range P P plus DP
+ 
+
+ align:start position:0%
+with momentum in the range P P plus DP
+just the same way as we would say that
+
+ align:start position:0%
+just the same way as we would say that
+ 
+
+ align:start position:0%
+just the same way as we would say that
+size squared of X DX is the probability
+
+ align:start position:0%
+size squared of X DX is the probability
+ 
+
+ align:start position:0%
+size squared of X DX is the probability
+to find the particle between X and X
+
+ align:start position:0%
+to find the particle between X and X
+ 
+
+ align:start position:0%
+to find the particle between X and X
+plus DX so this is allowed now by the
+
+ align:start position:0%
+plus DX so this is allowed now by the
+ 
+
+ align:start position:0%
+plus DX so this is allowed now by the
+conservation of probability and this
+
+ align:start position:0%
+conservation of probability and this
+ 
+
+ align:start position:0%
+conservation of probability and this
+therefore makes sense it's a postulate
+
+ align:start position:0%
+therefore makes sense it's a postulate
+ 
+
+ align:start position:0%
+therefore makes sense it's a postulate
+though it's not something I can derive I
+
+ align:start position:0%
+though it's not something I can derive I
+ 
+
+ align:start position:0%
+though it's not something I can derive I
+can just argue that is consistent to
+
+ align:start position:0%
+can just argue that is consistent to
+ 
+
+ align:start position:0%
+can just argue that is consistent to
+think in that way and and that's the way
+
+ align:start position:0%
+think in that way and and that's the way
+ 
+
+ align:start position:0%
+think in that way and and that's the way
+we finally promote this Phi of P which
+
+ align:start position:0%
+we finally promote this Phi of P which
+ 
+
+ align:start position:0%
+we finally promote this Phi of P which
+did encode sigh of X
+
+ align:start position:0%
+did encode sigh of X
+ 
+
+ align:start position:0%
+did encode sigh of X
+five P has the same information of fire
+
+ align:start position:0%
+five P has the same information of fire
+ 
+
+ align:start position:0%
+five P has the same information of fire
+of X Phi of P is the weight of the
+
+ align:start position:0%
+of X Phi of P is the weight of the
+ 
+
+ align:start position:0%
+of X Phi of P is the weight of the
+superposition but finally it's given an
+
+ align:start position:0%
+superposition but finally it's given an
+ 
+
+ align:start position:0%
+superposition but finally it's given an
+probabilistic interpretation it
+
+ align:start position:0%
+probabilistic interpretation it
+ 
+
+ align:start position:0%
+probabilistic interpretation it
+represents a probability to find the
+
+ align:start position:0%
+represents a probability to find the
+ 
+
+ align:start position:0%
+represents a probability to find the
+particle with some momentum so this is
+
+ align:start position:0%
+particle with some momentum so this is
+ 
+
+ align:start position:0%
+particle with some momentum so this is
+what this is going to allow us to do
+
+ align:start position:0%
+what this is going to allow us to do
+ 
+
+ align:start position:0%
+what this is going to allow us to do
+expectation values in a minute but I
+
+ align:start position:0%
+expectation values in a minute but I
+ 
+
+ align:start position:0%
+expectation values in a minute but I
+want to close off this discussion by
+
+ align:start position:0%
+want to close off this discussion by
+ 
+
+ align:start position:0%
+want to close off this discussion by
+writing for you the three-dimensional
+
+ align:start position:0%
+writing for you the three-dimensional
+ 
+
+ align:start position:0%
+writing for you the three-dimensional
+versions of these equations 3d version
+
+ align:start position:0%
+versions of these equations 3d version
+ 
+
+ align:start position:0%
+versions of these equations 3d version
+of Fourier transform so this is what we
+
+ align:start position:0%
+of Fourier transform so this is what we
+ 
+
+ align:start position:0%
+of Fourier transform so this is what we
+want to rewrite so what would it be if
+
+ align:start position:0%
+want to rewrite so what would it be if
+ 
+
+ align:start position:0%
+want to rewrite so what would it be if
+size of the vector X since you're going
+
+ align:start position:0%
+size of the vector X since you're going
+ 
+
+ align:start position:0%
+size of the vector X since you're going
+to have three integrals because you're
+
+ align:start position:0%
+to have three integrals because you're
+ 
+
+ align:start position:0%
+to have three integrals because you're
+going to it over three components of
+
+ align:start position:0%
+going to it over three components of
+ 
+
+ align:start position:0%
+going to it over three components of
+movement that this factor appears three
+
+ align:start position:0%
+movement that this factor appears three
+ 
+
+ align:start position:0%
+movement that this factor appears three
+times so actually it's 2 pi H bar to the
+
+ align:start position:0%
+times so actually it's 2 pi H bar to the
+ 
+
+ align:start position:0%
+times so actually it's 2 pi H bar to the
+three-halves integral Phi of vector P e
+
+ align:start position:0%
+three-halves integral Phi of vector P e
+ 
+
+ align:start position:0%
+three-halves integral Phi of vector P e
+to the I vector P dot product vector X H
+
+ align:start position:0%
+to the I vector P dot product vector X H
+ 
+
+ align:start position:0%
+to the I vector P dot product vector X H
+bar V Cube P and Phi of P vector the
+
+ align:start position:0%
+bar V Cube P and Phi of P vector the
+ 
+
+ align:start position:0%
+bar V Cube P and Phi of P vector the
+inverse theorem same factor we keep the
+
+ align:start position:0%
+inverse theorem same factor we keep the
+ 
+
+ align:start position:0%
+inverse theorem same factor we keep the
+nice symmetry between X and P sy of X
+
+ align:start position:0%
+nice symmetry between X and P sy of X
+ 
+
+ align:start position:0%
+nice symmetry between X and P sy of X
+vector negative exponent same dot
+
+ align:start position:0%
+vector negative exponent same dot
+ 
+
+ align:start position:0%
+vector negative exponent same dot
+product but negative exponent D cube X
+
+ align:start position:0%
+product but negative exponent D cube X
+ 
+
+ align:start position:0%
+product but negative exponent D cube X
+so this are the three-dimensional
+
+ align:start position:0%
+so this are the three-dimensional
+ 
+
+ align:start position:0%
+so this are the three-dimensional
+versions of your X versus P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there is a three-dimensional version
+
+ align:start position:0%
+and there is a three-dimensional version
+ 
+
+ align:start position:0%
+and there is a three-dimensional version
+of parsable so oh there's a
+
+ align:start position:0%
+of parsable so oh there's a
+ 
+
+ align:start position:0%
+of parsable so oh there's a
+three-dimensional version of the Delta
+
+ align:start position:0%
+three-dimensional version of the Delta
+ 
+
+ align:start position:0%
+three-dimensional version of the Delta
+function just like we had a delta
+
+ align:start position:0%
+function just like we had a delta
+ 
+
+ align:start position:0%
+function just like we had a delta
+function here adult a function in
+
+ align:start position:0%
+function here adult a function in
+ 
+
+ align:start position:0%
+function here adult a function in
+three-dimensional space would be Delta
+
+ align:start position:0%
+three-dimensional space would be Delta
+ 
+
+ align:start position:0%
+three-dimensional space would be Delta
+cube X minus X prime would be 1 over 2
+
+ align:start position:0%
+cube X minus X prime would be 1 over 2
+ 
+
+ align:start position:0%
+cube X minus X prime would be 1 over 2
+PI cubed integral D cubed K e to the I K
+
+ align:start position:0%
+PI cubed integral D cubed K e to the I K
+ 
+
+ align:start position:0%
+PI cubed integral D cubed K e to the I K
+vector X minus X prime vector it's all
+
+ align:start position:0%
+vector X minus X prime vector it's all
+ 
+
+ align:start position:0%
+vector X minus X prime vector it's all
+quite analogous I I think you should
+
+ align:start position:0%
+quite analogous I I think you should
+ 
+
+ align:start position:0%
+quite analogous I I think you should
+appreciate that you don't have to
+
+ align:start position:0%
+appreciate that you don't have to
+ 
+
+ align:start position:0%
+appreciate that you don't have to
+memorize them or anything like that they
+
+ align:start position:0%
+memorize them or anything like that they
+ 
+
+ align:start position:0%
+memorize them or anything like that they
+would be in any formula sheet but
+
+ align:start position:0%
+would be in any formula sheet but
+ 
+
+ align:start position:0%
+would be in any formula sheet but
+they're very analogous expressions
+
+ align:start position:0%
+they're very analogous expressions
+ 
+
+ align:start position:0%
+they're very analogous expressions
+percival also works in the same way and
+
+ align:start position:0%
+percival also works in the same way and
+ 
+
+ align:start position:0%
+percival also works in the same way and
+you have just as you would imagine that
+
+ align:start position:0%
+you have just as you would imagine that
+ 
+
+ align:start position:0%
+you have just as you would imagine that
+the interval all over 3-dimensional
+
+ align:start position:0%
+the interval all over 3-dimensional
+ 
+
+ align:start position:0%
+the interval all over 3-dimensional
+space of Phi of x squared is equal to
+
+ align:start position:0%
+space of Phi of x squared is equal to
+ 
+
+ align:start position:0%
+space of Phi of x squared is equal to
+the integral over 3-dimensional momentum
+
+ align:start position:0%
+the integral over 3-dimensional momentum
+ 
+
+ align:start position:0%
+the integral over 3-dimensional momentum
+space of Phi of P squared so the three
+
+ align:start position:0%
+space of Phi of P squared so the three
+ 
+
+ align:start position:0%
+space of Phi of P squared so the three
+results the phoria theorem the Delta
+
+ align:start position:0%
+results the phoria theorem the Delta
+ 
+
+ align:start position:0%
+results the phoria theorem the Delta
+function and Parsifal hold equally well
\ No newline at end of file
diff --git a/MMn7q1M7pGI.txt b/MMn7q1M7pGI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7b4f7895a58c7fa868b52771a71046eefeec3725
--- /dev/null
+++ b/MMn7q1M7pGI.txt
@@ -0,0 +1,1243 @@
+align:start position:0%
+ 
+now we're ready to prove the law of
+
+ align:start position:0%
+now we're ready to prove the law of
+ 
+
+ align:start position:0%
+now we're ready to prove the law of
+large numbers and while we're at it to
+
+ align:start position:0%
+large numbers and while we're at it to
+ 
+
+ align:start position:0%
+large numbers and while we're at it to
+get a quantitative version which will be
+
+ align:start position:0%
+get a quantitative version which will be
+ 
+
+ align:start position:0%
+get a quantitative version which will be
+the basis for our theory of sampling and
+
+ align:start position:0%
+the basis for our theory of sampling and
+ 
+
+ align:start position:0%
+the basis for our theory of sampling and
+estimation so let's remember that the
+
+ align:start position:0%
+estimation so let's remember that the
+ 
+
+ align:start position:0%
+estimation so let's remember that the
+law of large numbers says that if you
+
+ align:start position:0%
+law of large numbers says that if you
+ 
+
+ align:start position:0%
+law of large numbers says that if you
+have n independent identically
+
+ align:start position:0%
+have n independent identically
+ 
+
+ align:start position:0%
+have n independent identically
+distributed random variables with mean
+
+ align:start position:0%
+distributed random variables with mean
+ 
+
+ align:start position:0%
+distributed random variables with mean
+mu and we let a n be their average then
+
+ align:start position:0%
+mu and we let a n be their average then
+ 
+
+ align:start position:0%
+mu and we let a n be their average then
+for every positive number Delta the
+
+ align:start position:0%
+for every positive number Delta the
+ 
+
+ align:start position:0%
+for every positive number Delta the
+probability that the average differ
+
+ align:start position:0%
+probability that the average differ
+ 
+
+ align:start position:0%
+probability that the average differ
+from the mean by more than Delta goes to
+
+ align:start position:0%
+from the mean by more than Delta goes to
+ 
+
+ align:start position:0%
+from the mean by more than Delta goes to
+zero as the number of Trials increases
+
+ align:start position:0%
+zero as the number of Trials increases
+ 
+
+ align:start position:0%
+zero as the number of Trials increases
+remember that means that uh if you tell
+
+ align:start position:0%
+remember that means that uh if you tell
+ 
+
+ align:start position:0%
+remember that means that uh if you tell
+me what you think close means um and
+
+ align:start position:0%
+me what you think close means um and
+ 
+
+ align:start position:0%
+me what you think close means um and
+what you think very likely means then I
+
+ align:start position:0%
+what you think very likely means then I
+ 
+
+ align:start position:0%
+what you think very likely means then I
+can guarantee that by doing enough
+
+ align:start position:0%
+can guarantee that by doing enough
+ 
+
+ align:start position:0%
+can guarantee that by doing enough
+trials uh the the likelihood that the
+
+ align:start position:0%
+trials uh the the likelihood that the
+ 
+
+ align:start position:0%
+trials uh the the likelihood that the
+mean will be that close to the average
+
+ align:start position:0%
+mean will be that close to the average
+ 
+
+ align:start position:0%
+mean will be that close to the average
+uh within will be outside the tolerance
+
+ align:start position:0%
+uh within will be outside the tolerance
+ 
+
+ align:start position:0%
+uh within will be outside the tolerance
+is as small as you thought small should
+
+ align:start position:0%
+is as small as you thought small should
+ 
+
+ align:start position:0%
+is as small as you thought small should
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+and we're ready for the proof but in the
+
+ align:start position:0%
+and we're ready for the proof but in the
+ 
+
+ align:start position:0%
+and we're ready for the proof but in the
+proof there's one extra fact that we're
+
+ align:start position:0%
+proof there's one extra fact that we're
+ 
+
+ align:start position:0%
+proof there's one extra fact that we're
+going to use that we didn't explicitly
+
+ align:start position:0%
+going to use that we didn't explicitly
+ 
+
+ align:start position:0%
+going to use that we didn't explicitly
+mention which is that not only are all
+
+ align:start position:0%
+mention which is that not only are all
+ 
+
+ align:start position:0%
+mention which is that not only are all
+of these random variables identically
+
+ align:start position:0%
+of these random variables identically
+ 
+
+ align:start position:0%
+of these random variables identically
+distributed and independent but we're
+
+ align:start position:0%
+distributed and independent but we're
+ 
+
+ align:start position:0%
+distributed and independent but we're
+actually going to assume that they have
+
+ align:start position:0%
+actually going to assume that they have
+ 
+
+ align:start position:0%
+actually going to assume that they have
+a variance now not every random variable
+
+ align:start position:0%
+a variance now not every random variable
+ 
+
+ align:start position:0%
+a variance now not every random variable
+has a finite variance even if it has a
+
+ align:start position:0%
+has a finite variance even if it has a
+ 
+
+ align:start position:0%
+has a finite variance even if it has a
+finite mean in fact there are random
+
+ align:start position:0%
+finite mean in fact there are random
+ 
+
+ align:start position:0%
+finite mean in fact there are random
+variables that don't even have finite
+
+ align:start position:0%
+variables that don't even have finite
+ 
+
+ align:start position:0%
+variables that don't even have finite
+means and we'll look at them uh on the
+
+ align:start position:0%
+means and we'll look at them uh on the
+ 
+
+ align:start position:0%
+means and we'll look at them uh on the
+last day of class but uh so we're going
+
+ align:start position:0%
+last day of class but uh so we're going
+ 
+
+ align:start position:0%
+last day of class but uh so we're going
+to going to explicitly assume that all
+
+ align:start position:0%
+to going to explicitly assume that all
+ 
+
+ align:start position:0%
+to going to explicitly assume that all
+of these random variables have the same
+
+ align:start position:0%
+of these random variables have the same
+ 
+
+ align:start position:0%
+of these random variables have the same
+variance namely the squ the standard
+
+ align:start position:0%
+variance namely the squ the standard
+ 
+
+ align:start position:0%
+variance namely the squ the standard
+deviation Sigma
+
+ align:start position:0%
+deviation Sigma
+ 
+
+ align:start position:0%
+deviation Sigma
+squared and we'll be using that fact in
+
+ align:start position:0%
+squared and we'll be using that fact in
+ 
+
+ align:start position:0%
+squared and we'll be using that fact in
+the proof all right now the first
+
+ align:start position:0%
+the proof all right now the first
+ 
+
+ align:start position:0%
+the proof all right now the first
+question to ask uh is what is the
+
+ align:start position:0%
+question to ask uh is what is the
+ 
+
+ align:start position:0%
+question to ask uh is what is the
+expectation of the average and the
+
+ align:start position:0%
+expectation of the average and the
+ 
+
+ align:start position:0%
+expectation of the average and the
+expectation of the average is simply the
+
+ align:start position:0%
+expectation of the average is simply the
+ 
+
+ align:start position:0%
+expectation of the average is simply the
+expectation let's prove that the
+
+ align:start position:0%
+expectation let's prove that the
+ 
+
+ align:start position:0%
+expectation let's prove that the
+expectation of the average is by
+
+ align:start position:0%
+expectation of the average is by
+ 
+
+ align:start position:0%
+expectation of the average is by
+definition the expectation of the sum of
+
+ align:start position:0%
+definition the expectation of the sum of
+ 
+
+ align:start position:0%
+definition the expectation of the sum of
+the RS Over N um and by additivity
+
+ align:start position:0%
+the RS Over N um and by additivity
+ 
+
+ align:start position:0%
+the RS Over N um and by additivity
+of uh expectation that's the sum of the
+
+ align:start position:0%
+of uh expectation that's the sum of the
+ 
+
+ align:start position:0%
+of uh expectation that's the sum of the
+expectation of each of the RS Over N but
+
+ align:start position:0%
+expectation of each of the RS Over N but
+ 
+
+ align:start position:0%
+expectation of each of the RS Over N but
+each of them has expectation mu so the
+
+ align:start position:0%
+each of them has expectation mu so the
+ 
+
+ align:start position:0%
+each of them has expectation mu so the
+numerator is n mu and the n's cancel and
+
+ align:start position:0%
+numerator is n mu and the n's cancel and
+ 
+
+ align:start position:0%
+numerator is n mu and the n's cancel and
+so and sure enough the average has the
+
+ align:start position:0%
+so and sure enough the average has the
+ 
+
+ align:start position:0%
+so and sure enough the average has the
+same expectation as each of the
+
+ align:start position:0%
+same expectation as each of the
+ 
+
+ align:start position:0%
+same expectation as each of the
+individual variables each of the
+
+ align:start position:0%
+individual variables each of the
+ 
+
+ align:start position:0%
+individual variables each of the
+trials now that lets us apply the chbby
+
+ align:start position:0%
+trials now that lets us apply the chbby
+ 
+
+ align:start position:0%
+trials now that lets us apply the chbby
+Chev bound to the random variable a n
+
+ align:start position:0%
+Chev bound to the random variable a n
+ 
+
+ align:start position:0%
+Chev bound to the random variable a n
+because now we know what its mean is and
+
+ align:start position:0%
+because now we know what its mean is and
+ 
+
+ align:start position:0%
+because now we know what its mean is and
+its mean is independent of n we can ask
+
+ align:start position:0%
+its mean is independent of n we can ask
+ 
+
+ align:start position:0%
+its mean is independent of n we can ask
+we can apply chbby Chev to the
+
+ align:start position:0%
+we can apply chbby Chev to the
+ 
+
+ align:start position:0%
+we can apply chbby Chev to the
+probability that the average of n trials
+
+ align:start position:0%
+probability that the average of n trials
+ 
+
+ align:start position:0%
+probability that the average of n trials
+uh differs from its mean by more than
+
+ align:start position:0%
+uh differs from its mean by more than
+ 
+
+ align:start position:0%
+uh differs from its mean by more than
+Delta and according to Chev that's
+
+ align:start position:0%
+Delta and according to Chev that's
+ 
+
+ align:start position:0%
+Delta and according to Chev that's
+bounded by the variance of the average
+
+ align:start position:0%
+bounded by the variance of the average
+ 
+
+ align:start position:0%
+bounded by the variance of the average
+divided by n squar so I will have proved
+
+ align:start position:0%
+divided by n squar so I will have proved
+ 
+
+ align:start position:0%
+divided by n squar so I will have proved
+the law of large numbers if I can prove
+
+ align:start position:0%
+the law of large numbers if I can prove
+ 
+
+ align:start position:0%
+the law of large numbers if I can prove
+that the limit as n approaches Infinity
+
+ align:start position:0%
+that the limit as n approaches Infinity
+ 
+
+ align:start position:0%
+that the limit as n approaches Infinity
+of the variance goes to zero because
+
+ align:start position:0%
+of the variance goes to zero because
+ 
+
+ align:start position:0%
+of the variance goes to zero because
+that means that the right hand side will
+
+ align:start position:0%
+that means that the right hand side will
+ 
+
+ align:start position:0%
+that means that the right hand side will
+be going to zero over Delta squ namely
+
+ align:start position:0%
+be going to zero over Delta squ namely
+ 
+
+ align:start position:0%
+be going to zero over Delta squ namely
+going to zero which is what the law of
+
+ align:start position:0%
+going to zero which is what the law of
+ 
+
+ align:start position:0%
+going to zero which is what the law of
+large numbers says so we've reduced the
+
+ align:start position:0%
+large numbers says so we've reduced the
+ 
+
+ align:start position:0%
+large numbers says so we've reduced the
+proof of the law of large numbers to
+
+ align:start position:0%
+proof of the law of large numbers to
+ 
+
+ align:start position:0%
+proof of the law of large numbers to
+proving that the variance goes to zero
+
+ align:start position:0%
+proving that the variance goes to zero
+ 
+
+ align:start position:0%
+proving that the variance goes to zero
+as n approaches Infinity where a n is
+
+ align:start position:0%
+as n approaches Infinity where a n is
+ 
+
+ align:start position:0%
+as n approaches Infinity where a n is
+the average of n identically distributed
+
+ align:start position:0%
+the average of n identically distributed
+ 
+
+ align:start position:0%
+the average of n identically distributed
+variables with common mean mu and
+
+ align:start position:0%
+variables with common mean mu and
+ 
+
+ align:start position:0%
+variables with common mean mu and
+standard deviation
+
+ align:start position:0%
+standard deviation
+ 
+
+ align:start position:0%
+standard deviation
+Sigma well let's calculate the variance
+
+ align:start position:0%
+Sigma well let's calculate the variance
+ 
+
+ align:start position:0%
+Sigma well let's calculate the variance
+of a an a n again is the is the average
+
+ align:start position:0%
+of a an a n again is the is the average
+ 
+
+ align:start position:0%
+of a an a n again is the is the average
+of the sum of the RS over n and since
+
+ align:start position:0%
+of the sum of the RS over n and since
+ 
+
+ align:start position:0%
+of the sum of the RS over n and since
+we're assuming Independence of the RS
+
+ align:start position:0%
+we're assuming Independence of the RS
+ 
+
+ align:start position:0%
+we're assuming Independence of the RS
+the variance sum Rule and it just tells
+
+ align:start position:0%
+the variance sum Rule and it just tells
+ 
+
+ align:start position:0%
+the variance sum Rule and it just tells
+us that this is the sum of the variances
+
+ align:start position:0%
+us that this is the sum of the variances
+ 
+
+ align:start position:0%
+us that this is the sum of the variances
+now if we factor out the r 1/ n now this
+
+ align:start position:0%
+now if we factor out the r 1/ n now this
+ 
+
+ align:start position:0%
+now if we factor out the r 1/ n now this
+is a factor of 1 / n times this sum when
+
+ align:start position:0%
+is a factor of 1 / n times this sum when
+ 
+
+ align:start position:0%
+is a factor of 1 / n times this sum when
+we factor a constant out of the variance
+
+ align:start position:0%
+we factor a constant out of the variance
+ 
+
+ align:start position:0%
+we factor a constant out of the variance
+it squares so the denominator here
+
+ align:start position:0%
+it squares so the denominator here
+ 
+
+ align:start position:0%
+it squares so the denominator here
+becomes n sared and that's critical and
+
+ align:start position:0%
+becomes n sared and that's critical and
+ 
+
+ align:start position:0%
+becomes n sared and that's critical and
+the numerator is the sum of the N Vari
+
+ align:start position:0%
+the numerator is the sum of the N Vari
+ 
+
+ align:start position:0%
+the numerator is the sum of the N Vari
+es now each variance is Sigma squ and
+
+ align:start position:0%
+es now each variance is Sigma squ and
+ 
+
+ align:start position:0%
+es now each variance is Sigma squ and
+we've got n of them so we wind up with n
+
+ align:start position:0%
+we've got n of them so we wind up with n
+ 
+
+ align:start position:0%
+we've got n of them so we wind up with n
+Sigma squ over n^ 2 which is of course
+
+ align:start position:0%
+Sigma squ over n^ 2 which is of course
+ 
+
+ align:start position:0%
+Sigma squ over n^ 2 which is of course
+equal to Sigma s over n and sigma square
+
+ align:start position:0%
+equal to Sigma s over n and sigma square
+ 
+
+ align:start position:0%
+equal to Sigma s over n and sigma square
+is a constant and N is going to Infinity
+
+ align:start position:0%
+is a constant and N is going to Infinity
+ 
+
+ align:start position:0%
+is a constant and N is going to Infinity
+so sure enough the right hand side goes
+
+ align:start position:0%
+so sure enough the right hand side goes
+ 
+
+ align:start position:0%
+so sure enough the right hand side goes
+to zero as n increases which is all we
+
+ align:start position:0%
+to zero as n increases which is all we
+ 
+
+ align:start position:0%
+to zero as n increases which is all we
+needed to do to conclude the weak law of
+
+ align:start position:0%
+needed to do to conclude the weak law of
+ 
+
+ align:start position:0%
+needed to do to conclude the weak law of
+large numbers now if we go back and look
+
+ align:start position:0%
+large numbers now if we go back and look
+ 
+
+ align:start position:0%
+large numbers now if we go back and look
+at this proof the only thing that it
+
+ align:start position:0%
+at this proof the only thing that it
+ 
+
+ align:start position:0%
+at this proof the only thing that it
+used about the r RS was that they had
+
+ align:start position:0%
+used about the r RS was that they had
+ 
+
+ align:start position:0%
+used about the r RS was that they had
+the same mean mu and they actually had
+
+ align:start position:0%
+the same mean mu and they actually had
+ 
+
+ align:start position:0%
+the same mean mu and they actually had
+the same variance Sigma St Sigma squar
+
+ align:start position:0%
+the same variance Sigma St Sigma squar
+ 
+
+ align:start position:0%
+the same variance Sigma St Sigma squar
+and they that the Varian is added that
+
+ align:start position:0%
+and they that the Varian is added that
+ 
+
+ align:start position:0%
+and they that the Varian is added that
+was the key step in the proof that the
+
+ align:start position:0%
+was the key step in the proof that the
+ 
+
+ align:start position:0%
+was the key step in the proof that the
+variance of the sum of the RS was equal
+
+ align:start position:0%
+variance of the sum of the RS was equal
+ 
+
+ align:start position:0%
+variance of the sum of the RS was equal
+to the sum of the variances now
+
+ align:start position:0%
+to the sum of the variances now
+ 
+
+ align:start position:0%
+to the sum of the variances now
+additivity of variances only requires
+
+ align:start position:0%
+additivity of variances only requires
+ 
+
+ align:start position:0%
+additivity of variances only requires
+pairwise Independence it didn't even
+
+ align:start position:0%
+pairwise Independence it didn't even
+ 
+
+ align:start position:0%
+pairwise Independence it didn't even
+require the hypothesis that they were
+
+ align:start position:0%
+require the hypothesis that they were
+ 
+
+ align:start position:0%
+require the hypothesis that they were
+mutually independent and it didn't
+
+ align:start position:0%
+mutually independent and it didn't
+ 
+
+ align:start position:0%
+mutually independent and it didn't
+require uh the previous proof that we
+
+ align:start position:0%
+require uh the previous proof that we
+ 
+
+ align:start position:0%
+require uh the previous proof that we
+went through did not ever use the fact
+
+ align:start position:0%
+went through did not ever use the fact
+ 
+
+ align:start position:0%
+went through did not ever use the fact
+that the r had the same distribution
+
+ align:start position:0%
+that the r had the same distribution
+ 
+
+ align:start position:0%
+that the r had the same distribution
+that they need not be identically
+
+ align:start position:0%
+that they need not be identically
+ 
+
+ align:start position:0%
+that they need not be identically
+distributed it was sufficient that they
+
+ align:start position:0%
+distributed it was sufficient that they
+ 
+
+ align:start position:0%
+distributed it was sufficient that they
+have the same mean we can summarize what
+
+ align:start position:0%
+have the same mean we can summarize what
+ 
+
+ align:start position:0%
+have the same mean we can summarize what
+we really proved when we thought we were
+
+ align:start position:0%
+we really proved when we thought we were
+ 
+
+ align:start position:0%
+we really proved when we thought we were
+proving the law of large numbers we
+
+ align:start position:0%
+proving the law of large numbers we
+ 
+
+ align:start position:0%
+proving the law of large numbers we
+actually proved a precise quantitative
+
+ align:start position:0%
+actually proved a precise quantitative
+ 
+
+ align:start position:0%
+actually proved a precise quantitative
+theorem that says that if R1 through RN
+
+ align:start position:0%
+theorem that says that if R1 through RN
+ 
+
+ align:start position:0%
+theorem that says that if R1 through RN
+are pairwise independent random
+
+ align:start position:0%
+are pairwise independent random
+ 
+
+ align:start position:0%
+are pairwise independent random
+variables with the same finite mean mu
+
+ align:start position:0%
+variables with the same finite mean mu
+ 
+
+ align:start position:0%
+variables with the same finite mean mu
+and variant Sigma Sigma squar and we let
+
+ align:start position:0%
+and variant Sigma Sigma squar and we let
+ 
+
+ align:start position:0%
+and variant Sigma Sigma squar and we let
+a n be the average of those R of those n
+
+ align:start position:0%
+a n be the average of those R of those n
+ 
+
+ align:start position:0%
+a n be the average of those R of those n
+variables then the probability that the
+
+ align:start position:0%
+variables then the probability that the
+ 
+
+ align:start position:0%
+variables then the probability that the
+average differs from the mean by more
+
+ align:start position:0%
+average differs from the mean by more
+ 
+
+ align:start position:0%
+average differs from the mean by more
+than Delta is less than or equal to this
+
+ align:start position:0%
+than Delta is less than or equal to this
+ 
+
+ align:start position:0%
+than Delta is less than or equal to this
+definite number that we derived 1 / n *
+
+ align:start position:0%
+definite number that we derived 1 / n *
+ 
+
+ align:start position:0%
+definite number that we derived 1 / n *
+Sigma over Delta squar and this was what
+
+ align:start position:0%
+Sigma over Delta squar and this was what
+ 
+
+ align:start position:0%
+Sigma over Delta squar and this was what
+we previously proved when we thought we
+
+ align:start position:0%
+we previously proved when we thought we
+ 
+
+ align:start position:0%
+we previously proved when we thought we
+were just proving the law of large
+
+ align:start position:0%
+were just proving the law of large
+ 
+
+ align:start position:0%
+were just proving the law of large
+numbers we actually got this much
+
+ align:start position:0%
+numbers we actually got this much
+ 
+
+ align:start position:0%
+numbers we actually got this much
+tighter quantitative theorem now what
+
+ align:start position:0%
+tighter quantitative theorem now what
+ 
+
+ align:start position:0%
+tighter quantitative theorem now what
+this tells us here is that now if you
+
+ align:start position:0%
+this tells us here is that now if you
+ 
+
+ align:start position:0%
+this tells us here is that now if you
+tell me what Delta is and you tell me
+
+ align:start position:0%
+tell me what Delta is and you tell me
+ 
+
+ align:start position:0%
+tell me what Delta is and you tell me
+how small you want this to be well I
+
+ align:start position:0%
+how small you want this to be well I
+ 
+
+ align:start position:0%
+how small you want this to be well I
+know what's I'm given Sigma and I and
+
+ align:start position:0%
+know what's I'm given Sigma and I and
+ 
+
+ align:start position:0%
+know what's I'm given Sigma and I and
+you give me the Delta that you specified
+
+ align:start position:0%
+you give me the Delta that you specified
+ 
+
+ align:start position:0%
+you give me the Delta that you specified
+and since uh if you tell me how small
+
+ align:start position:0%
+and since uh if you tell me how small
+ 
+
+ align:start position:0%
+and since uh if you tell me how small
+you want this to be I will know how big
+
+ align:start position:0%
+you want this to be I will know how big
+ 
+
+ align:start position:0%
+you want this to be I will know how big
+an N to choose so this tells me how big
+
+ align:start position:0%
+an N to choose so this tells me how big
+ 
+
+ align:start position:0%
+an N to choose so this tells me how big
+a sample I need how many tries I have to
+
+ align:start position:0%
+a sample I need how many tries I have to
+ 
+
+ align:start position:0%
+a sample I need how many tries I have to
+make in order to get the probability
+
+ align:start position:0%
+make in order to get the probability
+ 
+
+ align:start position:0%
+make in order to get the probability
+that the mean is within a specified
+
+ align:start position:0%
+that the mean is within a specified
+ 
+
+ align:start position:0%
+that the mean is within a specified
+tolerance Delta as small as you
+
+ align:start position:0%
+tolerance Delta as small as you
+ 
+
+ align:start position:0%
+tolerance Delta as small as you
+specified and that is our independent
+
+ align:start position:0%
+specified and that is our independent
+ 
+
+ align:start position:0%
+specified and that is our independent
+sampling theorem that's why it's called
+
+ align:start position:0%
+sampling theorem that's why it's called
+ 
+
+ align:start position:0%
+sampling theorem that's why it's called
+independent sampling because we now know
+
+ align:start position:0%
+independent sampling because we now know
+ 
+
+ align:start position:0%
+independent sampling because we now know
+how big a sample is needed to estimate
+
+ align:start position:0%
+how big a sample is needed to estimate
+ 
+
+ align:start position:0%
+how big a sample is needed to estimate
+the mean of any random variable with any
+
+ align:start position:0%
+the mean of any random variable with any
+ 
+
+ align:start position:0%
+the mean of any random variable with any
+desired tolerance and any desired
+
+ align:start position:0%
+desired tolerance and any desired
+ 
+
+ align:start position:0%
+desired tolerance and any desired
+probability where of course the variance
+
+ align:start position:0%
+probability where of course the variance
+ 
+
+ align:start position:0%
+probability where of course the variance
+has to be finite the tolerance has to be
+
+ align:start position:0%
+has to be finite the tolerance has to be
+ 
+
+ align:start position:0%
+has to be finite the tolerance has to be
+positive tolerance is Delta and the
+
+ align:start position:0%
+positive tolerance is Delta and the
+ 
+
+ align:start position:0%
+positive tolerance is Delta and the
+probability uh has to be less than one
\ No newline at end of file
diff --git a/O91G3Likq3w.txt b/O91G3Likq3w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..788f7d8f7058baa2d9e89b2a8398bae27b83ab5b
--- /dev/null
+++ b/O91G3Likq3w.txt
@@ -0,0 +1,8347 @@
+align:start position:0%
+ 
+okay why don't we get
+
+ align:start position:0%
+okay why don't we get
+ 
+
+ align:start position:0%
+okay why don't we get
+started so we've been talking about DC
+
+ align:start position:0%
+started so we've been talking about DC
+ 
+
+ align:start position:0%
+started so we've been talking about DC
+to DC
+
+ align:start position:0%
+to DC
+ 
+
+ align:start position:0%
+to DC
+converters and you know sort of
+
+ align:start position:0%
+converters and you know sort of
+ 
+
+ align:start position:0%
+converters and you know sort of
+analyzing them and understanding what
+
+ align:start position:0%
+analyzing them and understanding what
+ 
+
+ align:start position:0%
+analyzing them and understanding what
+they'll do in in steady
+
+ align:start position:0%
+they'll do in in steady
+ 
+
+ align:start position:0%
+they'll do in in steady
+state and I'd like to today bring that
+
+ align:start position:0%
+state and I'd like to today bring that
+ 
+
+ align:start position:0%
+state and I'd like to today bring that
+maybe one step closer to things you have
+
+ align:start position:0%
+maybe one step closer to things you have
+ 
+
+ align:start position:0%
+maybe one step closer to things you have
+to think about to design one okay but
+
+ align:start position:0%
+to think about to design one okay but
+ 
+
+ align:start position:0%
+to think about to design one okay but
+just as a reminder
+
+ align:start position:0%
+just as a reminder
+ 
+
+ align:start position:0%
+just as a reminder
+last class we introduced what's known as
+
+ align:start position:0%
+last class we introduced what's known as
+ 
+
+ align:start position:0%
+last class we introduced what's known as
+the buck boost converter or the up or
+
+ align:start position:0%
+the buck boost converter or the up or
+ 
+
+ align:start position:0%
+the buck boost converter or the up or
+the inverting buck boost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converter and one version of that looks
+
+ align:start position:0%
+converter and one version of that looks
+ 
+
+ align:start position:0%
+converter and one version of that looks
+like this we have an input voltage that
+
+ align:start position:0%
+like this we have an input voltage that
+ 
+
+ align:start position:0%
+like this we have an input voltage that
+I'll call
+
+ align:start position:0%
+I'll call
+ 
+
+ align:start position:0%
+I'll call
+V1
+
+ align:start position:0%
+V1
+ 
+
+ align:start position:0%
+V1
+um for example a
+
+ align:start position:0%
+um for example a
+ 
+
+ align:start position:0%
+um for example a
+switch a
+
+ align:start position:0%
+switch a
+ 
+
+ align:start position:0%
+switch a
+diode here's my output that'll be
+
+ align:start position:0%
+diode here's my output that'll be
+ 
+
+ align:start position:0%
+diode here's my output that'll be
+V2 and then we have a filter capacitor
+
+ align:start position:0%
+V2 and then we have a filter capacitor
+ 
+
+ align:start position:0%
+V2 and then we have a filter capacitor
+in this example I'm going to put the
+
+ align:start position:0%
+in this example I'm going to put the
+ 
+
+ align:start position:0%
+in this example I'm going to put the
+filter capacitor
+
+ align:start position:0%
+filter capacitor
+ 
+
+ align:start position:0%
+filter capacitor
+here okay because this is the sort of
+
+ align:start position:0%
+here okay because this is the sort of
+ 
+
+ align:start position:0%
+here okay because this is the sort of
+the actual switching Loop and then an
+
+ align:start position:0%
+the actual switching Loop and then an
+ 
+
+ align:start position:0%
+the actual switching Loop and then an
+inductor where we have
+
+ align:start position:0%
+inductor where we have
+ 
+
+ align:start position:0%
+inductor where we have
+I and right and what we've said so far
+
+ align:start position:0%
+I and right and what we've said so far
+ 
+
+ align:start position:0%
+I and right and what we've said so far
+is let's think about the case where um L
+
+ align:start position:0%
+is let's think about the case where um L
+ 
+
+ align:start position:0%
+is let's think about the case where um L
+and C are
+
+ align:start position:0%
+and C are
+ 
+
+ align:start position:0%
+and C are
+big right that that they're
+
+ align:start position:0%
+big right that that they're
+ 
+
+ align:start position:0%
+big right that that they're
+approximately infinite and that's not a
+
+ align:start position:0%
+approximately infinite and that's not a
+ 
+
+ align:start position:0%
+approximately infinite and that's not a
+bad place to start for analysis because
+
+ align:start position:0%
+bad place to start for analysis because
+ 
+
+ align:start position:0%
+bad place to start for analysis because
+you can learn a lot of things about that
+
+ align:start position:0%
+you can learn a lot of things about that
+ 
+
+ align:start position:0%
+you can learn a lot of things about that
+and what that means is that I is
+
+ align:start position:0%
+and what that means is that I is
+ 
+
+ align:start position:0%
+and what that means is that I is
+approximately equal to its DC value I
+
+ align:start position:0%
+approximately equal to its DC value I
+ 
+
+ align:start position:0%
+approximately equal to its DC value I
+and VC is approximately equal to its DC
+
+ align:start position:0%
+and VC is approximately equal to its DC
+ 
+
+ align:start position:0%
+and VC is approximately equal to its DC
+value Capital VC okay we said
+
+ align:start position:0%
+value Capital VC okay we said
+ 
+
+ align:start position:0%
+value Capital VC okay we said
+okay um if I had to think
+
+ align:start position:0%
+okay um if I had to think
+ 
+
+ align:start position:0%
+okay um if I had to think
+about uh this
+
+ align:start position:0%
+about uh this
+ 
+
+ align:start position:0%
+about uh this
+converter right I might think about the
+
+ align:start position:0%
+converter right I might think about the
+ 
+
+ align:start position:0%
+converter right I might think about the
+switch voltage V
+
+ align:start position:0%
+switch voltage V
+ 
+
+ align:start position:0%
+switch voltage V
+switch and the switch current I
+
+ align:start position:0%
+switch and the switch current I
+ 
+
+ align:start position:0%
+switch and the switch current I
+switch and the diode voltage
+
+ align:start position:0%
+switch and the diode voltage
+ 
+
+ align:start position:0%
+switch and the diode voltage
+VD and the diode current
+
+ align:start position:0%
+VD and the diode current
+ 
+
+ align:start position:0%
+VD and the diode current
+ID right and what we discovered about
+
+ align:start position:0%
+ID right and what we discovered about
+ 
+
+ align:start position:0%
+ID right and what we discovered about
+this converter last
+
+ align:start position:0%
+this converter last
+ 
+
+ align:start position:0%
+this converter last
+time is that if I thought of here I have
+
+ align:start position:0%
+time is that if I thought of here I have
+ 
+
+ align:start position:0%
+time is that if I thought of here I have
+say an input current that I'm going to
+
+ align:start position:0%
+say an input current that I'm going to
+ 
+
+ align:start position:0%
+say an input current that I'm going to
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+i1 and an output current um that I'm
+
+ align:start position:0%
+i1 and an output current um that I'm
+ 
+
+ align:start position:0%
+i1 and an output current um that I'm
+going to call
+
+ align:start position:0%
+going to call
+ 
+
+ align:start position:0%
+going to call
+I2 okay and if I said okay suppose this
+
+ align:start position:0%
+I2 okay and if I said okay suppose this
+ 
+
+ align:start position:0%
+I2 okay and if I said okay suppose this
+thing filters perfect
+
+ align:start position:0%
+thing filters perfect
+ 
+
+ align:start position:0%
+thing filters perfect
+and i1 is approximately equal to its DC
+
+ align:start position:0%
+and i1 is approximately equal to its DC
+ 
+
+ align:start position:0%
+and i1 is approximately equal to its DC
+value capital i1 and I2 is approximately
+
+ align:start position:0%
+value capital i1 and I2 is approximately
+ 
+
+ align:start position:0%
+value capital i1 and I2 is approximately
+equal to it DC value Capital I2 and in
+
+ align:start position:0%
+equal to it DC value Capital I2 and in
+ 
+
+ align:start position:0%
+equal to it DC value Capital I2 and in
+order to really get that you'd probably
+
+ align:start position:0%
+order to really get that you'd probably
+ 
+
+ align:start position:0%
+order to really get that you'd probably
+need a tiny bit of source impedance here
+
+ align:start position:0%
+need a tiny bit of source impedance here
+ 
+
+ align:start position:0%
+need a tiny bit of source impedance here
+but let's assume that's the case right
+
+ align:start position:0%
+but let's assume that's the case right
+ 
+
+ align:start position:0%
+but let's assume that's the case right
+what we saw for this
+
+ align:start position:0%
+what we saw for this
+ 
+
+ align:start position:0%
+what we saw for this
+converter is that
+
+ align:start position:0%
+converter is that
+ 
+
+ align:start position:0%
+converter is that
+ilil the DC
+
+ align:start position:0%
+ilil the DC
+ 
+
+ align:start position:0%
+ilil the DC
+current in the inductor is equal to the
+
+ align:start position:0%
+current in the inductor is equal to the
+ 
+
+ align:start position:0%
+current in the inductor is equal to the
+magnitude of i1 plus the magnitude of I
+
+ align:start position:0%
+magnitude of i1 plus the magnitude of I
+ 
+
+ align:start position:0%
+magnitude of i1 plus the magnitude of I
+2 and the DC capacitor voltage
+
+ align:start position:0%
+2 and the DC capacitor voltage
+ 
+
+ align:start position:0%
+2 and the DC capacitor voltage
+VC is equal to the magnitude of vc1
+
+ align:start position:0%
+VC is equal to the magnitude of vc1
+ 
+
+ align:start position:0%
+VC is equal to the magnitude of vc1
+V1 plus the magnitude of
+
+ align:start position:0%
+V1 plus the magnitude of
+ 
+
+ align:start position:0%
+V1 plus the magnitude of
+V2 okay and so basically the capacitor
+
+ align:start position:0%
+V2 okay and so basically the capacitor
+ 
+
+ align:start position:0%
+V2 okay and so basically the capacitor
+has to see the sum of the magnitudes of
+
+ align:start position:0%
+has to see the sum of the magnitudes of
+ 
+
+ align:start position:0%
+has to see the sum of the magnitudes of
+the input and output voltage and the
+
+ align:start position:0%
+the input and output voltage and the
+ 
+
+ align:start position:0%
+the input and output voltage and the
+inductor current carries the
+
+ align:start position:0%
+inductor current carries the
+ 
+
+ align:start position:0%
+inductor current carries the
+um sum of the
+
+ align:start position:0%
+um sum of the
+ 
+
+ align:start position:0%
+um sum of the
+uh input and output currents
+
+ align:start position:0%
+uh input and output currents
+ 
+
+ align:start position:0%
+uh input and output currents
+okay and then if I thought well okay
+
+ align:start position:0%
+okay and then if I thought well okay
+ 
+
+ align:start position:0%
+okay and then if I thought well okay
+what is the switch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage okay when the switch is off what
+
+ align:start position:0%
+voltage okay when the switch is off what
+ 
+
+ align:start position:0%
+voltage okay when the switch is off what
+voltage does it block well that blocks
+
+ align:start position:0%
+voltage does it block well that blocks
+ 
+
+ align:start position:0%
+voltage does it block well that blocks
+VC and the same thing when the diode is
+
+ align:start position:0%
+VC and the same thing when the diode is
+ 
+
+ align:start position:0%
+VC and the same thing when the diode is
+off it also blocks VC so V switch Max is
+
+ align:start position:0%
+off it also blocks VC so V switch Max is
+ 
+
+ align:start position:0%
+off it also blocks VC so V switch Max is
+equal to VD
+
+ align:start position:0%
+equal to VD
+ 
+
+ align:start position:0%
+equal to VD
+Max is equal to VC which is equal to the
+
+ align:start position:0%
+Max is equal to VC which is equal to the
+ 
+
+ align:start position:0%
+Max is equal to VC which is equal to the
+magnitude of V1 1 plus the magnitude of
+
+ align:start position:0%
+magnitude of V1 1 plus the magnitude of
+ 
+
+ align:start position:0%
+magnitude of V1 1 plus the magnitude of
+V2 and if I thought of I switch
+
+ align:start position:0%
+V2 and if I thought of I switch
+ 
+
+ align:start position:0%
+V2 and if I thought of I switch
+Max and ID Max well when they're on they
+
+ align:start position:0%
+Max and ID Max well when they're on they
+ 
+
+ align:start position:0%
+Max and ID Max well when they're on they
+carry the inductor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current which is the magnitude of the
+
+ align:start position:0%
+current which is the magnitude of the
+ 
+
+ align:start position:0%
+current which is the magnitude of the
+input current and the output current the
+
+ align:start position:0%
+input current and the output current the
+ 
+
+ align:start position:0%
+input current and the output current the
+DC input and output current okay so at
+
+ align:start position:0%
+DC input and output current okay so at
+ 
+
+ align:start position:0%
+DC input and output current okay so at
+least now I have a sense of what the
+
+ align:start position:0%
+least now I have a sense of what the
+ 
+
+ align:start position:0%
+least now I have a sense of what the
+stresses are on the diodes and and
+
+ align:start position:0%
+stresses are on the diodes and and
+ 
+
+ align:start position:0%
+stresses are on the diodes and and
+transistors and the inductor and
+
+ align:start position:0%
+transistors and the inductor and
+ 
+
+ align:start position:0%
+transistors and the inductor and
+capacitor right why do I care about that
+
+ align:start position:0%
+capacitor right why do I care about that
+ 
+
+ align:start position:0%
+capacitor right why do I care about that
+because ultimately I have to go buy
+
+ align:start position:0%
+because ultimately I have to go buy
+ 
+
+ align:start position:0%
+because ultimately I have to go buy
+switches that can carry and diodes that
+
+ align:start position:0%
+switches that can carry and diodes that
+ 
+
+ align:start position:0%
+switches that can carry and diodes that
+can carry the current without blowing up
+
+ align:start position:0%
+can carry the current without blowing up
+ 
+
+ align:start position:0%
+can carry the current without blowing up
+and can block the voltage without
+
+ align:start position:0%
+and can block the voltage without
+ 
+
+ align:start position:0%
+and can block the voltage without
+blowing up and I've got to go buy
+
+ align:start position:0%
+blowing up and I've got to go buy
+ 
+
+ align:start position:0%
+blowing up and I've got to go buy
+capacitors that can block the voltage
+
+ align:start position:0%
+capacitors that can block the voltage
+ 
+
+ align:start position:0%
+capacitors that can block the voltage
+and inductors that can carry the current
+
+ align:start position:0%
+and inductors that can carry the current
+ 
+
+ align:start position:0%
+and inductors that can carry the current
+right so we have to start going through
+
+ align:start position:0%
+right so we have to start going through
+ 
+
+ align:start position:0%
+right so we have to start going through
+this analysis to say how much voltage
+
+ align:start position:0%
+this analysis to say how much voltage
+ 
+
+ align:start position:0%
+this analysis to say how much voltage
+and current do I need in the circuit
+
+ align:start position:0%
+and current do I need in the circuit
+ 
+
+ align:start position:0%
+and current do I need in the circuit
+okay how does this circuit compare to
+
+ align:start position:0%
+okay how does this circuit compare to
+ 
+
+ align:start position:0%
+okay how does this circuit compare to
+like a buck converter or a boost
+
+ align:start position:0%
+like a buck converter or a boost
+ 
+
+ align:start position:0%
+like a buck converter or a boost
+converter okay well if I took
+
+ align:start position:0%
+converter okay well if I took
+ 
+
+ align:start position:0%
+converter okay well if I took
+my buck
+
+ align:start position:0%
+my buck
+ 
+
+ align:start position:0%
+my buck
+converter okay so here's my buck
+
+ align:start position:0%
+converter okay so here's my buck
+ 
+
+ align:start position:0%
+converter okay so here's my buck
+converter in this
+
+ align:start position:0%
+converter in this
+ 
+
+ align:start position:0%
+converter in this
+case I'm going to put the I'm going to
+
+ align:start position:0%
+case I'm going to put the I'm going to
+ 
+
+ align:start position:0%
+case I'm going to put the I'm going to
+think about the capacitor at the input
+
+ align:start position:0%
+think about the capacitor at the input
+ 
+
+ align:start position:0%
+think about the capacitor at the input
+because that's where the switching
+
+ align:start position:0%
+because that's where the switching
+ 
+
+ align:start position:0%
+because that's where the switching
+current goes okay and here's my switch
+
+ align:start position:0%
+current goes okay and here's my switch
+ 
+
+ align:start position:0%
+current goes okay and here's my switch
+here's my
+
+ align:start position:0%
+here's my
+ 
+
+ align:start position:0%
+here's my
+diode and here's my inductor I won't
+
+ align:start position:0%
+diode and here's my inductor I won't
+ 
+
+ align:start position:0%
+diode and here's my inductor I won't
+worry about I don't actually need an
+
+ align:start position:0%
+worry about I don't actually need an
+ 
+
+ align:start position:0%
+worry about I don't actually need an
+capacitor at the output although I would
+
+ align:start position:0%
+capacitor at the output although I would
+ 
+
+ align:start position:0%
+capacitor at the output although I would
+typically put one so here's V2 so I
+
+ align:start position:0%
+typically put one so here's V2 so I
+ 
+
+ align:start position:0%
+typically put one so here's V2 so I
+could again think of V
+
+ align:start position:0%
+could again think of V
+ 
+
+ align:start position:0%
+could again think of V
+switch and I
+
+ align:start position:0%
+switch and I
+ 
+
+ align:start position:0%
+switch and I
+switch and
+
+ align:start position:0%
+switch and
+ 
+
+ align:start position:0%
+switch and
+VD and
+
+ align:start position:0%
+VD and
+ 
+
+ align:start position:0%
+VD and
+ID all
+
+ align:start position:0%
+ID all
+ 
+
+ align:start position:0%
+ID all
+right this would
+
+ align:start position:0%
+right this would
+ 
+
+ align:start position:0%
+right this would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+VC and this would be
+
+ align:start position:0%
+VC and this would be
+ 
+
+ align:start position:0%
+VC and this would be
+I and again I'm going to think of LC lnc
+
+ align:start position:0%
+I and again I'm going to think of LC lnc
+ 
+
+ align:start position:0%
+I and again I'm going to think of LC lnc
+big right really really big so that
+
+ align:start position:0%
+big right really really big so that
+ 
+
+ align:start position:0%
+big right really really big so that
+basically the inductor current and the
+
+ align:start position:0%
+basically the inductor current and the
+ 
+
+ align:start position:0%
+basically the inductor current and the
+capacitor voltage here here are
+
+ align:start position:0%
+capacitor voltage here here are
+ 
+
+ align:start position:0%
+capacitor voltage here here are
+basically constant
+
+ align:start position:0%
+basically constant
+ 
+
+ align:start position:0%
+basically constant
+okay in that case what I get is V
+
+ align:start position:0%
+okay in that case what I get is V
+ 
+
+ align:start position:0%
+okay in that case what I get is V
+switch when it's off and VD when it's
+
+ align:start position:0%
+switch when it's off and VD when it's
+ 
+
+ align:start position:0%
+switch when it's off and VD when it's
+off are both equal to this capacitor
+
+ align:start position:0%
+off are both equal to this capacitor
+ 
+
+ align:start position:0%
+off are both equal to this capacitor
+voltage which is equal to
+
+ align:start position:0%
+voltage which is equal to
+ 
+
+ align:start position:0%
+voltage which is equal to
+V1 right and I
+
+ align:start position:0%
+V1 right and I
+ 
+
+ align:start position:0%
+V1 right and I
+switch equals ID when when the switch
+
+ align:start position:0%
+switch equals ID when when the switch
+ 
+
+ align:start position:0%
+switch equals ID when when the switch
+and diode are on they carry the inductor
+
+ align:start position:0%
+and diode are on they carry the inductor
+ 
+
+ align:start position:0%
+and diode are on they carry the inductor
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+which is also equal to I2 if the
+
+ align:start position:0%
+which is also equal to I2 if the
+ 
+
+ align:start position:0%
+which is also equal to I2 if the
+inductor current is really big and I
+
+ align:start position:0%
+inductor current is really big and I
+ 
+
+ align:start position:0%
+inductor current is really big and I
+just have a DC current right and this is
+
+ align:start position:0%
+just have a DC current right and this is
+ 
+
+ align:start position:0%
+just have a DC current right and this is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+i1 this is
+
+ align:start position:0%
+i1 this is
+ 
+
+ align:start position:0%
+i1 this is
+I2 so that's for a buck
+
+ align:start position:0%
+I2 so that's for a buck
+ 
+
+ align:start position:0%
+I2 so that's for a buck
+converter what about a boost converter
+
+ align:start position:0%
+converter what about a boost converter
+ 
+
+ align:start position:0%
+converter what about a boost converter
+well a boost converter looked like this
+
+ align:start position:0%
+well a boost converter looked like this
+ 
+
+ align:start position:0%
+well a boost converter looked like this
+here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V1 here's I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in this case I'm going to put the
+
+ align:start position:0%
+and in this case I'm going to put the
+ 
+
+ align:start position:0%
+and in this case I'm going to put the
+capacitor here because the pulse current
+
+ align:start position:0%
+capacitor here because the pulse current
+ 
+
+ align:start position:0%
+capacitor here because the pulse current
+comes through the
+
+ align:start position:0%
+comes through the
+ 
+
+ align:start position:0%
+comes through the
+diode
+
+ align:start position:0%
+diode
+ 
+
+ align:start position:0%
+diode
+okay and here's
+
+ align:start position:0%
+okay and here's
+ 
+
+ align:start position:0%
+okay and here's
+V2 okay so again I have sort of V
+
+ align:start position:0%
+V2 okay so again I have sort of V
+ 
+
+ align:start position:0%
+V2 okay so again I have sort of V
+switch I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switch DD and
+
+ align:start position:0%
+switch DD and
+ 
+
+ align:start position:0%
+switch DD and
+ID okay now in this
+
+ align:start position:0%
+ID okay now in this
+ 
+
+ align:start position:0%
+ID okay now in this
+case I is again constant if L and C are
+
+ align:start position:0%
+case I is again constant if L and C are
+ 
+
+ align:start position:0%
+case I is again constant if L and C are
+big okay so that the switch current and
+
+ align:start position:0%
+big okay so that the switch current and
+ 
+
+ align:start position:0%
+big okay so that the switch current and
+the diode current when they're
+
+ align:start position:0%
+the diode current when they're
+ 
+
+ align:start position:0%
+the diode current when they're
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um is equal to i l which is also equal
+
+ align:start position:0%
+um is equal to i l which is also equal
+ 
+
+ align:start position:0%
+um is equal to i l which is also equal
+to i1 right because whatever the current
+
+ align:start position:0%
+to i1 right because whatever the current
+ 
+
+ align:start position:0%
+to i1 right because whatever the current
+is coming out of i1 is now the current
+
+ align:start position:0%
+is coming out of i1 is now the current
+ 
+
+ align:start position:0%
+is coming out of i1 is now the current
+that's being switched through the diode
+
+ align:start position:0%
+that's being switched through the diode
+ 
+
+ align:start position:0%
+that's being switched through the diode
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+transistor um V switch is equal to VD is
+
+ align:start position:0%
+transistor um V switch is equal to VD is
+ 
+
+ align:start position:0%
+transistor um V switch is equal to VD is
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VC which is equal to V two in this
+
+ align:start position:0%
+VC which is equal to V two in this
+ 
+
+ align:start position:0%
+VC which is equal to V two in this
+case okay so why am I going through
+
+ align:start position:0%
+case okay so why am I going through
+ 
+
+ align:start position:0%
+case okay so why am I going through
+this well for either the bucker boost
+
+ align:start position:0%
+this well for either the bucker boost
+ 
+
+ align:start position:0%
+this well for either the bucker boost
+converter keep in mind in the Boost
+
+ align:start position:0%
+converter keep in mind in the Boost
+ 
+
+ align:start position:0%
+converter keep in mind in the Boost
+converter V2 is the big voltage between
+
+ align:start position:0%
+converter V2 is the big voltage between
+ 
+
+ align:start position:0%
+converter V2 is the big voltage between
+the input and output voltage and I and
+
+ align:start position:0%
+the input and output voltage and I and
+ 
+
+ align:start position:0%
+the input and output voltage and I and
+i1 is the bigger of the currents between
+
+ align:start position:0%
+i1 is the bigger of the currents between
+ 
+
+ align:start position:0%
+i1 is the bigger of the currents between
+the input and output
+
+ align:start position:0%
+the input and output
+ 
+
+ align:start position:0%
+the input and output
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+likewise the switch voltage is V1 that's
+
+ align:start position:0%
+likewise the switch voltage is V1 that's
+ 
+
+ align:start position:0%
+likewise the switch voltage is V1 that's
+the bigger of the input and output
+
+ align:start position:0%
+the bigger of the input and output
+ 
+
+ align:start position:0%
+the bigger of the input and output
+voltage right
+
+ align:start position:0%
+voltage right
+ 
+
+ align:start position:0%
+voltage right
+and the current is I2 which is the
+
+ align:start position:0%
+and the current is I2 which is the
+ 
+
+ align:start position:0%
+and the current is I2 which is the
+bigger of the input and output current
+
+ align:start position:0%
+bigger of the input and output current
+ 
+
+ align:start position:0%
+bigger of the input and output current
+so for either of these converters I
+
+ align:start position:0%
+so for either of these converters I
+ 
+
+ align:start position:0%
+so for either of these converters I
+might write the the V switch is equal to
+
+ align:start position:0%
+might write the the V switch is equal to
+ 
+
+ align:start position:0%
+might write the the V switch is equal to
+V diode which is equal to the
+
+ align:start position:0%
+V diode which is equal to the
+ 
+
+ align:start position:0%
+V diode which is equal to the
+maximum of magnitude of V1 and
+
+ align:start position:0%
+maximum of magnitude of V1 and
+ 
+
+ align:start position:0%
+maximum of magnitude of V1 and
+V2 and I and this is also equal to the
+
+ align:start position:0%
+V2 and I and this is also equal to the
+ 
+
+ align:start position:0%
+V2 and I and this is also equal to the
+capacitor
+
+ align:start position:0%
+capacitor
+ 
+
+ align:start position:0%
+capacitor
+voltage and the inductor current is
+
+ align:start position:0%
+voltage and the inductor current is
+ 
+
+ align:start position:0%
+voltage and the inductor current is
+equal to the switch current
+
+ align:start position:0%
+equal to the switch current
+ 
+
+ align:start position:0%
+equal to the switch current
+is equal to the diode current is equal
+
+ align:start position:0%
+is equal to the diode current is equal
+ 
+
+ align:start position:0%
+is equal to the diode current is equal
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+maximum of i1 and
+
+ align:start position:0%
+maximum of i1 and
+ 
+
+ align:start position:0%
+maximum of i1 and
+I2 okay so how do these two
+
+ align:start position:0%
+I2 okay so how do these two
+ 
+
+ align:start position:0%
+I2 okay so how do these two
+compare right the buck and the Boost
+
+ align:start position:0%
+compare right the buck and the Boost
+ 
+
+ align:start position:0%
+compare right the buck and the Boost
+converter can only do a very specific
+
+ align:start position:0%
+converter can only do a very specific
+ 
+
+ align:start position:0%
+converter can only do a very specific
+function right one can step down the
+
+ align:start position:0%
+function right one can step down the
+ 
+
+ align:start position:0%
+function right one can step down the
+other can step up they can't go both do
+
+ align:start position:0%
+other can step up they can't go both do
+ 
+
+ align:start position:0%
+other can step up they can't go both do
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+right but the stresses on them in either
+
+ align:start position:0%
+right but the stresses on them in either
+ 
+
+ align:start position:0%
+right but the stresses on them in either
+case basically the switch in the dial
+
+ align:start position:0%
+case basically the switch in the dial
+ 
+
+ align:start position:0%
+case basically the switch in the dial
+and the capacitor see the maximum of the
+
+ align:start position:0%
+and the capacitor see the maximum of the
+ 
+
+ align:start position:0%
+and the capacitor see the maximum of the
+input out output voltages and the indu
+
+ align:start position:0%
+input out output voltages and the indu
+ 
+
+ align:start position:0%
+input out output voltages and the indu
+switch current in the died currency the
+
+ align:start position:0%
+switch current in the died currency the
+ 
+
+ align:start position:0%
+switch current in the died currency the
+maximum of the input and output
+
+ align:start position:0%
+maximum of the input and output
+ 
+
+ align:start position:0%
+maximum of the input and output
+currents if I use a buck boost
+
+ align:start position:0%
+currents if I use a buck boost
+ 
+
+ align:start position:0%
+currents if I use a buck boost
+converter I can go up or down at least
+
+ align:start position:0%
+converter I can go up or down at least
+ 
+
+ align:start position:0%
+converter I can go up or down at least
+in magnitude but now I see higher
+
+ align:start position:0%
+in magnitude but now I see higher
+ 
+
+ align:start position:0%
+in magnitude but now I see higher
+stresses instead of seeing the maximum
+
+ align:start position:0%
+stresses instead of seeing the maximum
+ 
+
+ align:start position:0%
+stresses instead of seeing the maximum
+of the input output voltage I see the
+
+ align:start position:0%
+of the input output voltage I see the
+ 
+
+ align:start position:0%
+of the input output voltage I see the
+sum of the input and output voltage
+
+ align:start position:0%
+sum of the input and output voltage
+ 
+
+ align:start position:0%
+sum of the input and output voltage
+magnitudes and the sum of the input
+
+ align:start position:0%
+magnitudes and the sum of the input
+ 
+
+ align:start position:0%
+magnitudes and the sum of the input
+output current magnitudes right that
+
+ align:start position:0%
+output current magnitudes right that
+ 
+
+ align:start position:0%
+output current magnitudes right that
+means for a given conversion ratio the
+
+ align:start position:0%
+means for a given conversion ratio the
+ 
+
+ align:start position:0%
+means for a given conversion ratio the
+buck boost converter is going to have a
+
+ align:start position:0%
+buck boost converter is going to have a
+ 
+
+ align:start position:0%
+buck boost converter is going to have a
+higher stress on the switches and the
+
+ align:start position:0%
+higher stress on the switches and the
+ 
+
+ align:start position:0%
+higher stress on the switches and the
+dodes and the inductors and
+
+ align:start position:0%
+dodes and the inductors and
+ 
+
+ align:start position:0%
+dodes and the inductors and
+capacitors than a buck converter or a
+
+ align:start position:0%
+capacitors than a buck converter or a
+ 
+
+ align:start position:0%
+capacitors than a buck converter or a
+boost converter okay why is
+
+ align:start position:0%
+boost converter okay why is
+ 
+
+ align:start position:0%
+boost converter okay why is
+that in a buck boost converter remember
+
+ align:start position:0%
+that in a buck boost converter remember
+ 
+
+ align:start position:0%
+that in a buck boost converter remember
+we said how it ran was basically I take
+
+ align:start position:0%
+we said how it ran was basically I take
+ 
+
+ align:start position:0%
+we said how it ran was basically I take
+energy from the input I put it into the
+
+ align:start position:0%
+energy from the input I put it into the
+ 
+
+ align:start position:0%
+energy from the input I put it into the
+inductor in the first part of the cycle
+
+ align:start position:0%
+inductor in the first part of the cycle
+ 
+
+ align:start position:0%
+inductor in the first part of the cycle
+and then the second part of the cycle I
+
+ align:start position:0%
+and then the second part of the cycle I
+ 
+
+ align:start position:0%
+and then the second part of the cycle I
+take that energy out of the inductor and
+
+ align:start position:0%
+take that energy out of the inductor and
+ 
+
+ align:start position:0%
+take that energy out of the inductor and
+put it in the output so all of the
+
+ align:start position:0%
+put it in the output so all of the
+ 
+
+ align:start position:0%
+put it in the output so all of the
+energy flowing through the circuit from
+
+ align:start position:0%
+energy flowing through the circuit from
+ 
+
+ align:start position:0%
+energy flowing through the circuit from
+the input to the output ultimately got
+
+ align:start position:0%
+the input to the output ultimately got
+ 
+
+ align:start position:0%
+the input to the output ultimately got
+stored in that
+
+ align:start position:0%
+stored in that
+ 
+
+ align:start position:0%
+stored in that
+inductor
+
+ align:start position:0%
+inductor
+ 
+
+ align:start position:0%
+inductor
+okay with a buck converter or a boost
+
+ align:start position:0%
+okay with a buck converter or a boost
+ 
+
+ align:start position:0%
+okay with a buck converter or a boost
+converter that's not quite true in the
+
+ align:start position:0%
+converter that's not quite true in the
+ 
+
+ align:start position:0%
+converter that's not quite true in the
+first part of the cycle we turn the
+
+ align:start position:0%
+first part of the cycle we turn the
+ 
+
+ align:start position:0%
+first part of the cycle we turn the
+switch on and we store up some energy in
+
+ align:start position:0%
+switch on and we store up some energy in
+ 
+
+ align:start position:0%
+switch on and we store up some energy in
+the inductor but we also have direct
+
+ align:start position:0%
+the inductor but we also have direct
+ 
+
+ align:start position:0%
+the inductor but we also have direct
+current path from the input to the
+
+ align:start position:0%
+current path from the input to the
+ 
+
+ align:start position:0%
+current path from the input to the
+output through the
+
+ align:start position:0%
+output through the
+ 
+
+ align:start position:0%
+output through the
+inductor and in the second part of the
+
+ align:start position:0%
+inductor and in the second part of the
+ 
+
+ align:start position:0%
+inductor and in the second part of the
+cycle we take the energy out of the
+
+ align:start position:0%
+cycle we take the energy out of the
+ 
+
+ align:start position:0%
+cycle we take the energy out of the
+inductor and put it in the output so in
+
+ align:start position:0%
+inductor and put it in the output so in
+ 
+
+ align:start position:0%
+inductor and put it in the output so in
+a buck converter only part of the energy
+
+ align:start position:0%
+a buck converter only part of the energy
+ 
+
+ align:start position:0%
+a buck converter only part of the energy
+ends up stored in this in the inductor
+
+ align:start position:0%
+ends up stored in this in the inductor
+ 
+
+ align:start position:0%
+ends up stored in this in the inductor
+and part of it sort of flows straight
+
+ align:start position:0%
+and part of it sort of flows straight
+ 
+
+ align:start position:0%
+and part of it sort of flows straight
+through from the input to the output and
+
+ align:start position:0%
+through from the input to the output and
+ 
+
+ align:start position:0%
+through from the input to the output and
+the same thing can be said for the Boost
+
+ align:start position:0%
+the same thing can be said for the Boost
+ 
+
+ align:start position:0%
+the same thing can be said for the Boost
+converter the consequence of this is is
+
+ align:start position:0%
+converter the consequence of this is is
+ 
+
+ align:start position:0%
+converter the consequence of this is is
+that to do a given conversion function
+
+ align:start position:0%
+that to do a given conversion function
+ 
+
+ align:start position:0%
+that to do a given conversion function
+the buck boost converter imposes much
+
+ align:start position:0%
+the buck boost converter imposes much
+ 
+
+ align:start position:0%
+the buck boost converter imposes much
+greater stresses on its components than
+
+ align:start position:0%
+greater stresses on its components than
+ 
+
+ align:start position:0%
+greater stresses on its components than
+the buck converter or the Boost
+
+ align:start position:0%
+the buck converter or the Boost
+ 
+
+ align:start position:0%
+the buck converter or the Boost
+converter all right so we can get away
+
+ align:start position:0%
+converter all right so we can get away
+ 
+
+ align:start position:0%
+converter all right so we can get away
+with a lot of things
+
+ align:start position:0%
+with a lot of things
+ 
+
+ align:start position:0%
+with a lot of things
+in terms of reducing the stresses on the
+
+ align:start position:0%
+in terms of reducing the stresses on the
+ 
+
+ align:start position:0%
+in terms of reducing the stresses on the
+component by being in this sort of
+
+ align:start position:0%
+component by being in this sort of
+ 
+
+ align:start position:0%
+component by being in this sort of
+direct conversion approach where I'm
+
+ align:start position:0%
+direct conversion approach where I'm
+ 
+
+ align:start position:0%
+direct conversion approach where I'm
+sort of not storing all the inter energy
+
+ align:start position:0%
+sort of not storing all the inter energy
+ 
+
+ align:start position:0%
+sort of not storing all the inter energy
+in intermediate form than I can with a
+
+ align:start position:0%
+in intermediate form than I can with a
+ 
+
+ align:start position:0%
+in intermediate form than I can with a
+buck boost
+
+ align:start position:0%
+buck boost
+ 
+
+ align:start position:0%
+buck boost
+converter questions about that or about
+
+ align:start position:0%
+converter questions about that or about
+ 
+
+ align:start position:0%
+converter questions about that or about
+any of the prior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material so one of the things we're
+
+ align:start position:0%
+material so one of the things we're
+ 
+
+ align:start position:0%
+material so one of the things we're
+going to want to think about as we kind
+
+ align:start position:0%
+going to want to think about as we kind
+ 
+
+ align:start position:0%
+going to want to think about as we kind
+of move from Theory to thinking about
+
+ align:start position:0%
+of move from Theory to thinking about
+ 
+
+ align:start position:0%
+of move from Theory to thinking about
+design is boy how how you know if I'm
+
+ align:start position:0%
+design is boy how how you know if I'm
+ 
+
+ align:start position:0%
+design is boy how how you know if I'm
+going to do things one way or another
+
+ align:start position:0%
+going to do things one way or another
+ 
+
+ align:start position:0%
+going to do things one way or another
+how can I get away with you know smaller
+
+ align:start position:0%
+how can I get away with you know smaller
+ 
+
+ align:start position:0%
+how can I get away with you know smaller
+voltage and current switches and and
+
+ align:start position:0%
+voltage and current switches and and
+ 
+
+ align:start position:0%
+voltage and current switches and and
+less energy storage in my passive
+
+ align:start position:0%
+less energy storage in my passive
+ 
+
+ align:start position:0%
+less energy storage in my passive
+components and some ways of doing things
+
+ align:start position:0%
+components and some ways of doing things
+ 
+
+ align:start position:0%
+components and some ways of doing things
+are going to be much better than others
+
+ align:start position:0%
+are going to be much better than others
+ 
+
+ align:start position:0%
+are going to be much better than others
+okay and that's part of the art of
+
+ align:start position:0%
+okay and that's part of the art of
+ 
+
+ align:start position:0%
+okay and that's part of the art of
+design is figuring out well gez what do
+
+ align:start position:0%
+design is figuring out well gez what do
+ 
+
+ align:start position:0%
+design is figuring out well gez what do
+I need to do and how is that going to
+
+ align:start position:0%
+I need to do and how is that going to
+ 
+
+ align:start position:0%
+I need to do and how is that going to
+translate into the size and loss and
+
+ align:start position:0%
+translate into the size and loss and
+ 
+
+ align:start position:0%
+translate into the size and loss and
+weight of the thing I'm designing okay
+
+ align:start position:0%
+weight of the thing I'm designing okay
+ 
+
+ align:start position:0%
+weight of the thing I'm designing okay
+and I want to take some initial steps
+
+ align:start position:0%
+and I want to take some initial steps
+ 
+
+ align:start position:0%
+and I want to take some initial steps
+today towards thinking about how we
+
+ align:start position:0%
+today towards thinking about how we
+ 
+
+ align:start position:0%
+today towards thinking about how we
+might do that
+
+ align:start position:0%
+might do that
+ 
+
+ align:start position:0%
+might do that
+okay and one of the things we're going
+
+ align:start position:0%
+okay and one of the things we're going
+ 
+
+ align:start position:0%
+okay and one of the things we're going
+to have to do in order to do that is
+
+ align:start position:0%
+to have to do in order to do that is
+ 
+
+ align:start position:0%
+to have to do in order to do that is
+we're going to have to throw out this
+
+ align:start position:0%
+we're going to have to throw out this
+ 
+
+ align:start position:0%
+we're going to have to throw out this
+assumption right it's you know for
+
+ align:start position:0%
+assumption right it's you know for
+ 
+
+ align:start position:0%
+assumption right it's you know for
+purposes of figuring out my conversion
+
+ align:start position:0%
+purposes of figuring out my conversion
+ 
+
+ align:start position:0%
+purposes of figuring out my conversion
+ratio and those kind of things you know
+
+ align:start position:0%
+ratio and those kind of things you know
+ 
+
+ align:start position:0%
+ratio and those kind of things you know
+I can imagine that my inductors and
+
+ align:start position:0%
+I can imagine that my inductors and
+ 
+
+ align:start position:0%
+I can imagine that my inductors and
+capacitors are really big that's a
+
+ align:start position:0%
+capacitors are really big that's a
+ 
+
+ align:start position:0%
+capacitors are really big that's a
+perfectly valid thing to do and we do it
+
+ align:start position:0%
+perfectly valid thing to do and we do it
+ 
+
+ align:start position:0%
+perfectly valid thing to do and we do it
+all the time but if I'm going to go
+
+ align:start position:0%
+all the time but if I'm going to go
+ 
+
+ align:start position:0%
+all the time but if I'm going to go
+build this thing you know
+
+ align:start position:0%
+build this thing you know
+ 
+
+ align:start position:0%
+build this thing you know
+first of all I can't go out and buy a
+
+ align:start position:0%
+first of all I can't go out and buy a
+ 
+
+ align:start position:0%
+first of all I can't go out and buy a
+one Henry inductor very easily and the
+
+ align:start position:0%
+one Henry inductor very easily and the
+ 
+
+ align:start position:0%
+one Henry inductor very easily and the
+bigger the inductance I buy what we're
+
+ align:start position:0%
+bigger the inductance I buy what we're
+ 
+
+ align:start position:0%
+bigger the inductance I buy what we're
+going to see is the more energy it has
+
+ align:start position:0%
+going to see is the more energy it has
+ 
+
+ align:start position:0%
+going to see is the more energy it has
+to store and the bigger it is and the
+
+ align:start position:0%
+to store and the bigger it is and the
+ 
+
+ align:start position:0%
+to store and the bigger it is and the
+losser is and everything else right so I
+
+ align:start position:0%
+losser is and everything else right so I
+ 
+
+ align:start position:0%
+losser is and everything else right so I
+need to start figuring out well how big
+
+ align:start position:0%
+need to start figuring out well how big
+ 
+
+ align:start position:0%
+need to start figuring out well how big
+does lnc have to be in order to achieve
+
+ align:start position:0%
+does lnc have to be in order to achieve
+ 
+
+ align:start position:0%
+does lnc have to be in order to achieve
+my goals okay and that's what I'd like
+
+ align:start position:0%
+my goals okay and that's what I'd like
+ 
+
+ align:start position:0%
+my goals okay and that's what I'd like
+to talk about today and the first thing
+
+ align:start position:0%
+to talk about today and the first thing
+ 
+
+ align:start position:0%
+to talk about today and the first thing
+we got to do is figure out what is the
+
+ align:start position:0%
+we got to do is figure out what is the
+ 
+
+ align:start position:0%
+we got to do is figure out what is the
+what is the impact of a finite
+
+ align:start position:0%
+what is the impact of a finite
+ 
+
+ align:start position:0%
+what is the impact of a finite
+component values on the converter
+
+ align:start position:0%
+component values on the converter
+ 
+
+ align:start position:0%
+component values on the converter
+okay and what we're going to see is
+
+ align:start position:0%
+okay and what we're going to see is
+ 
+
+ align:start position:0%
+okay and what we're going to see is
+there's a few things that might you know
+
+ align:start position:0%
+there's a few things that might you know
+ 
+
+ align:start position:0%
+there's a few things that might you know
+I one one of the things I have to do is
+
+ align:start position:0%
+I one one of the things I have to do is
+ 
+
+ align:start position:0%
+I one one of the things I have to do is
+figure out in any of these converters
+
+ align:start position:0%
+figure out in any of these converters
+ 
+
+ align:start position:0%
+figure out in any of these converters
+what value of L do I pick what value of
+
+ align:start position:0%
+what value of L do I pick what value of
+ 
+
+ align:start position:0%
+what value of L do I pick what value of
+C do I pick how I figure those out
+
+ align:start position:0%
+C do I pick how I figure those out
+ 
+
+ align:start position:0%
+C do I pick how I figure those out
+depends upon a few things okay um things
+
+ align:start position:0%
+depends upon a few things okay um things
+ 
+
+ align:start position:0%
+depends upon a few things okay um things
+that might determine that first of all
+
+ align:start position:0%
+that might determine that first of all
+ 
+
+ align:start position:0%
+that might determine that first of all
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Ripple right how much voltage and
+
+ align:start position:0%
+Ripple right how much voltage and
+ 
+
+ align:start position:0%
+Ripple right how much voltage and
+current Ripple are permissible in the
+
+ align:start position:0%
+current Ripple are permissible in the
+ 
+
+ align:start position:0%
+current Ripple are permissible in the
+circuit and we're going to focus on
+
+ align:start position:0%
+circuit and we're going to focus on
+ 
+
+ align:start position:0%
+circuit and we're going to focus on
+Ripple today there's also the question
+
+ align:start position:0%
+Ripple today there's also the question
+ 
+
+ align:start position:0%
+Ripple today there's also the question
+of um transient Dynamics we'll look at
+
+ align:start position:0%
+of um transient Dynamics we'll look at
+ 
+
+ align:start position:0%
+of um transient Dynamics we'll look at
+that a little bit later in the term and
+
+ align:start position:0%
+that a little bit later in the term and
+ 
+
+ align:start position:0%
+that a little bit later in the term and
+that can also impact the decisions you
+
+ align:start position:0%
+that can also impact the decisions you
+ 
+
+ align:start position:0%
+that can also impact the decisions you
+make but it's sort of you know Ripple
+
+ align:start position:0%
+make but it's sort of you know Ripple
+ 
+
+ align:start position:0%
+make but it's sort of you know Ripple
+first transient Dynamic second and the
+
+ align:start position:0%
+first transient Dynamic second and the
+ 
+
+ align:start position:0%
+first transient Dynamic second and the
+other thing that's going to is going to
+
+ align:start position:0%
+other thing that's going to is going to
+ 
+
+ align:start position:0%
+other thing that's going to is going to
+come into the play is sort of how big
+
+ align:start position:0%
+come into the play is sort of how big
+ 
+
+ align:start position:0%
+come into the play is sort of how big
+and lossy and expensive are the
+
+ align:start position:0%
+and lossy and expensive are the
+ 
+
+ align:start position:0%
+and lossy and expensive are the
+components okay and we'll touch on that
+
+ align:start position:0%
+components okay and we'll touch on that
+ 
+
+ align:start position:0%
+components okay and we'll touch on that
+today a little bit we'll at least get a
+
+ align:start position:0%
+today a little bit we'll at least get a
+ 
+
+ align:start position:0%
+today a little bit we'll at least get a
+sort of a rough measure of how that goes
+
+ align:start position:0%
+sort of a rough measure of how that goes
+ 
+
+ align:start position:0%
+sort of a rough measure of how that goes
+okay so let's start to think about
+
+ align:start position:0%
+okay so let's start to think about
+ 
+
+ align:start position:0%
+okay so let's start to think about
+um how we might uh
+
+ align:start position:0%
+um how we might uh
+ 
+
+ align:start position:0%
+um how we might uh
+start calc sizing components in order
+
+ align:start position:0%
+start calc sizing components in order
+ 
+
+ align:start position:0%
+start calc sizing components in order
+that we need to figure out a way to
+
+ align:start position:0%
+that we need to figure out a way to
+ 
+
+ align:start position:0%
+that we need to figure out a way to
+calculate Ripple in the components okay
+
+ align:start position:0%
+calculate Ripple in the components okay
+ 
+
+ align:start position:0%
+calculate Ripple in the components okay
+so here's the game we're going to play
+
+ align:start position:0%
+so here's the game we're going to play
+ 
+
+ align:start position:0%
+so here's the game we're going to play
+let's think about the Boost converter
+
+ align:start position:0%
+let's think about the Boost converter
+ 
+
+ align:start position:0%
+let's think about the Boost converter
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+okay so here's my Boost converter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to worry about what
+
+ align:start position:0%
+and I'm going to worry about what
+ 
+
+ align:start position:0%
+and I'm going to worry about what
+the Ripple for example on the capacitor
+
+ align:start position:0%
+the Ripple for example on the capacitor
+ 
+
+ align:start position:0%
+the Ripple for example on the capacitor
+voltage is and I'm also going to about
+
+ align:start position:0%
+voltage is and I'm also going to about
+ 
+
+ align:start position:0%
+voltage is and I'm also going to about
+worry about what the Ripple in the
+
+ align:start position:0%
+worry about what the Ripple in the
+ 
+
+ align:start position:0%
+worry about what the Ripple in the
+inductor current is
+
+ align:start position:0%
+inductor current is
+ 
+
+ align:start position:0%
+inductor current is
+okay I you know if I make an lnc really
+
+ align:start position:0%
+okay I you know if I make an lnc really
+ 
+
+ align:start position:0%
+okay I you know if I make an lnc really
+big then the Ripple goes to zero but I
+
+ align:start position:0%
+big then the Ripple goes to zero but I
+ 
+
+ align:start position:0%
+big then the Ripple goes to zero but I
+can't afford to make them too big
+
+ align:start position:0%
+can't afford to make them too big
+ 
+
+ align:start position:0%
+can't afford to make them too big
+because the components will be too big
+
+ align:start position:0%
+because the components will be too big
+ 
+
+ align:start position:0%
+because the components will be too big
+and too lossy okay so what does this
+
+ align:start position:0%
+and too lossy okay so what does this
+ 
+
+ align:start position:0%
+and too lossy okay so what does this
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+like um Let me let me plot for a
+
+ align:start position:0%
+like um Let me let me plot for a
+ 
+
+ align:start position:0%
+like um Let me let me plot for a
+second what id would look
+
+ align:start position:0%
+second what id would look
+ 
+
+ align:start position:0%
+second what id would look
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+and what what do I mean by ID let's look
+
+ align:start position:0%
+and what what do I mean by ID let's look
+ 
+
+ align:start position:0%
+and what what do I mean by ID let's look
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+okay why because that's going to be a
+
+ align:start position:0%
+okay why because that's going to be a
+ 
+
+ align:start position:0%
+okay why because that's going to be a
+key to figuring
+
+ align:start position:0%
+key to figuring
+ 
+
+ align:start position:0%
+key to figuring
+out how much Ripple I end up on the
+
+ align:start position:0%
+out how much Ripple I end up on the
+ 
+
+ align:start position:0%
+out how much Ripple I end up on the
+capacitor voltage so what happens in
+
+ align:start position:0%
+capacitor voltage so what happens in
+ 
+
+ align:start position:0%
+capacitor voltage so what happens in
+this converter in the first part of the
+
+ align:start position:0%
+this converter in the first part of the
+ 
+
+ align:start position:0%
+this converter in the first part of the
+cycle Q of T is high and the switch is
+
+ align:start position:0%
+cycle Q of T is high and the switch is
+ 
+
+ align:start position:0%
+cycle Q of T is high and the switch is
+on and ID is
+
+ align:start position:0%
+on and ID is
+ 
+
+ align:start position:0%
+on and ID is
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+okay and in the second part of the cycle
+
+ align:start position:0%
+okay and in the second part of the cycle
+ 
+
+ align:start position:0%
+okay and in the second part of the cycle
+so that goes on for sometime DT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and in the second part of the cycle
+
+ align:start position:0%
+okay and in the second part of the cycle
+ 
+
+ align:start position:0%
+okay and in the second part of the cycle
+the output goes to
+
+ align:start position:0%
+the output goes to
+ 
+
+ align:start position:0%
+the output goes to
+V2 right so uh I'm
+
+ align:start position:0%
+V2 right so uh I'm
+ 
+
+ align:start position:0%
+V2 right so uh I'm
+sorry in the first part of the cycle ID
+
+ align:start position:0%
+sorry in the first part of the cycle ID
+ 
+
+ align:start position:0%
+sorry in the first part of the cycle ID
+is zero because I is going through
+
+ align:start position:0%
+is zero because I is going through
+ 
+
+ align:start position:0%
+is zero because I is going through
+um is going through the switch in the
+
+ align:start position:0%
+um is going through the switch in the
+ 
+
+ align:start position:0%
+um is going through the switch in the
+second part of the cycle ID is equal to
+
+ align:start position:0%
+second part of the cycle ID is equal to
+ 
+
+ align:start position:0%
+second part of the cycle ID is equal to
+I right so this I'm just going to call I
+
+ align:start position:0%
+I right so this I'm just going to call I
+ 
+
+ align:start position:0%
+I right so this I'm just going to call I
+capital I okay now now I'm kind of
+
+ align:start position:0%
+capital I okay now now I'm kind of
+ 
+
+ align:start position:0%
+capital I okay now now I'm kind of
+assuming the L is really really big here
+
+ align:start position:0%
+assuming the L is really really big here
+ 
+
+ align:start position:0%
+assuming the L is really really big here
+I'm going to ignore the Ripple current
+
+ align:start position:0%
+I'm going to ignore the Ripple current
+ 
+
+ align:start position:0%
+I'm going to ignore the Ripple current
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+inductor in order to calculate the
+
+ align:start position:0%
+inductor in order to calculate the
+ 
+
+ align:start position:0%
+inductor in order to calculate the
+Ripple voltage on the
+
+ align:start position:0%
+Ripple voltage on the
+ 
+
+ align:start position:0%
+Ripple voltage on the
+capacitor all right and it turns out you
+
+ align:start position:0%
+capacitor all right and it turns out you
+ 
+
+ align:start position:0%
+capacitor all right and it turns out you
+can do that freely and you'll still get
+
+ align:start position:0%
+can do that freely and you'll still get
+ 
+
+ align:start position:0%
+can do that freely and you'll still get
+the right answer okay and I'll show you
+
+ align:start position:0%
+the right answer okay and I'll show you
+ 
+
+ align:start position:0%
+the right answer okay and I'll show you
+that in a moment
+
+ align:start position:0%
+that in a moment
+ 
+
+ align:start position:0%
+that in a moment
+okay but this is what id looks
+
+ align:start position:0%
+okay but this is what id looks
+ 
+
+ align:start position:0%
+okay but this is what id looks
+like okay so here's T and this is
+
+ align:start position:0%
+like okay so here's T and this is
+ 
+
+ align:start position:0%
+like okay so here's T and this is
+ID okay
+
+ align:start position:0%
+ID okay
+ 
+
+ align:start position:0%
+ID okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well what's ID's average
+
+ align:start position:0%
+well what's ID's average
+ 
+
+ align:start position:0%
+well what's ID's average
+value right if I were to calculate the
+
+ align:start position:0%
+value right if I were to calculate the
+ 
+
+ align:start position:0%
+value right if I were to calculate the
+average value of the diode current
+
+ align:start position:0%
+average value of the diode current
+ 
+
+ align:start position:0%
+average value of the diode current
+ID that would simply be the average of
+
+ align:start position:0%
+ID that would simply be the average of
+ 
+
+ align:start position:0%
+ID that would simply be the average of
+this pulse waveform which is basically
+
+ align:start position:0%
+this pulse waveform which is basically
+ 
+
+ align:start position:0%
+this pulse waveform which is basically
+um 1 minus D *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+okay so maybe what I would do is say
+
+ align:start position:0%
+okay so maybe what I would do is say
+ 
+
+ align:start position:0%
+okay so maybe what I would do is say
+okay let me come up with a model for
+
+ align:start position:0%
+okay let me come up with a model for
+ 
+
+ align:start position:0%
+okay let me come up with a model for
+this converter that I don't really care
+
+ align:start position:0%
+this converter that I don't really care
+ 
+
+ align:start position:0%
+this converter that I don't really care
+about what's going on over here right in
+
+ align:start position:0%
+about what's going on over here right in
+ 
+
+ align:start position:0%
+about what's going on over here right in
+terms of figuring out the capacitor
+
+ align:start position:0%
+terms of figuring out the capacitor
+ 
+
+ align:start position:0%
+terms of figuring out the capacitor
+voltage Ripple all I care is about what
+
+ align:start position:0%
+voltage Ripple all I care is about what
+ 
+
+ align:start position:0%
+voltage Ripple all I care is about what
+current's coming through the diode and
+
+ align:start position:0%
+current's coming through the diode and
+ 
+
+ align:start position:0%
+current's coming through the diode and
+driving this output circuit okay so I
+
+ align:start position:0%
+driving this output circuit okay so I
+ 
+
+ align:start position:0%
+driving this output circuit okay so I
+might model this this
+
+ align:start position:0%
+might model this this
+ 
+
+ align:start position:0%
+might model this this
+way model this as some Ripple current
+
+ align:start position:0%
+way model this as some Ripple current
+ 
+
+ align:start position:0%
+way model this as some Ripple current
+ID okay that is then going
+
+ align:start position:0%
+ID okay that is then going
+ 
+
+ align:start position:0%
+ID okay that is then going
+into my capacitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VC and my load
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistor okay any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that now if I design this
+
+ align:start position:0%
+that now if I design this
+ 
+
+ align:start position:0%
+that now if I design this
+circuit I'm interested in the Ripple on
+
+ align:start position:0%
+circuit I'm interested in the Ripple on
+ 
+
+ align:start position:0%
+circuit I'm interested in the Ripple on
+the capacitor and what I'm likely to do
+
+ align:start position:0%
+the capacitor and what I'm likely to do
+ 
+
+ align:start position:0%
+the capacitor and what I'm likely to do
+is put the switching frequency you know
+
+ align:start position:0%
+is put the switching frequency you know
+ 
+
+ align:start position:0%
+is put the switching frequency you know
+T is equal to one over this is equal to
+
+ align:start position:0%
+T is equal to one over this is equal to
+ 
+
+ align:start position:0%
+T is equal to one over this is equal to
+one over the switching frequency right
+
+ align:start position:0%
+one over the switching frequency right
+ 
+
+ align:start position:0%
+one over the switching frequency right
+what I'm likely to do is to make this RC
+
+ align:start position:0%
+what I'm likely to do is to make this RC
+ 
+
+ align:start position:0%
+what I'm likely to do is to make this RC
+such that it filters that Ripple current
+
+ align:start position:0%
+such that it filters that Ripple current
+ 
+
+ align:start position:0%
+such that it filters that Ripple current
+right I've got this pulsating current in
+
+ align:start position:0%
+right I've got this pulsating current in
+ 
+
+ align:start position:0%
+right I've got this pulsating current in
+and what I really want is VC to be
+
+ align:start position:0%
+and what I really want is VC to be
+ 
+
+ align:start position:0%
+and what I really want is VC to be
+almost constant and hence the V2 is
+
+ align:start position:0%
+almost constant and hence the V2 is
+ 
+
+ align:start position:0%
+almost constant and hence the V2 is
+almost constant right so that means that
+
+ align:start position:0%
+almost constant right so that means that
+ 
+
+ align:start position:0%
+almost constant right so that means that
+the the sort of the AC component of this
+
+ align:start position:0%
+the the sort of the AC component of this
+ 
+
+ align:start position:0%
+the the sort of the AC component of this
+pulsating waveform we really want to go
+
+ align:start position:0%
+pulsating waveform we really want to go
+ 
+
+ align:start position:0%
+pulsating waveform we really want to go
+through the capacitor almost
+
+ align:start position:0%
+through the capacitor almost
+ 
+
+ align:start position:0%
+through the capacitor almost
+exclusively and you know the DC
+
+ align:start position:0%
+exclusively and you know the DC
+ 
+
+ align:start position:0%
+exclusively and you know the DC
+component of this current 1 minus D is
+
+ align:start position:0%
+component of this current 1 minus D is
+ 
+
+ align:start position:0%
+component of this current 1 minus D is
+what goes to to the output right well
+
+ align:start position:0%
+what goes to to the output right well
+ 
+
+ align:start position:0%
+what goes to to the output right well
+what do I need to make that happen what
+
+ align:start position:0%
+what do I need to make that happen what
+ 
+
+ align:start position:0%
+what do I need to make that happen what
+I need is uh 2 pi F
+
+ align:start position:0%
+I need is uh 2 pi F
+ 
+
+ align:start position:0%
+I need is uh 2 pi F
+switch ought to be much greater than
+
+ align:start position:0%
+switch ought to be much greater than
+ 
+
+ align:start position:0%
+switch ought to be much greater than
+one/
+
+ align:start position:0%
+one/
+ 
+
+ align:start position:0%
+one/
+RC right so that this RC network filters
+
+ align:start position:0%
+RC right so that this RC network filters
+ 
+
+ align:start position:0%
+RC right so that this RC network filters
+the pulsating component of this current
+
+ align:start position:0%
+the pulsating component of this current
+ 
+
+ align:start position:0%
+the pulsating component of this current
+and so that gets the DC current going
+
+ align:start position:0%
+and so that gets the DC current going
+ 
+
+ align:start position:0%
+and so that gets the DC current going
+this way and the Ripple current going
+
+ align:start position:0%
+this way and the Ripple current going
+ 
+
+ align:start position:0%
+this way and the Ripple current going
+this way okay any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that how did you get that
+
+ align:start position:0%
+that how did you get that
+ 
+
+ align:start position:0%
+that how did you get that
+RC uh okay so the the time constant of
+
+ align:start position:0%
+RC uh okay so the the time constant of
+ 
+
+ align:start position:0%
+RC uh okay so the the time constant of
+this is RC that means it's pole is it
+
+ align:start position:0%
+this is RC that means it's pole is it
+ 
+
+ align:start position:0%
+this is RC that means it's pole is it
+Min is it s is equal to minus one/
+
+ align:start position:0%
+Min is it s is equal to minus one/
+ 
+
+ align:start position:0%
+Min is it s is equal to minus one/
+RC and so I'm
+
+ align:start position:0%
+RC and so I'm
+ 
+
+ align:start position:0%
+RC and so I'm
+putting the switching frequency the
+
+ align:start position:0%
+putting the switching frequency the
+ 
+
+ align:start position:0%
+putting the switching frequency the
+Ripple frequency far beyond that so that
+
+ align:start position:0%
+Ripple frequency far beyond that so that
+ 
+
+ align:start position:0%
+Ripple frequency far beyond that so that
+this becomes essentially a low pass
+
+ align:start position:0%
+this becomes essentially a low pass
+ 
+
+ align:start position:0%
+this becomes essentially a low pass
+filter so I'm putting it well beyond the
+
+ align:start position:0%
+filter so I'm putting it well beyond the
+ 
+
+ align:start position:0%
+filter so I'm putting it well beyond the
+cut
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off okay okay so suppose I do
+
+ align:start position:0%
+off okay okay so suppose I do
+ 
+
+ align:start position:0%
+off okay okay so suppose I do
+that okay um maybe what I should be
+
+ align:start position:0%
+that okay um maybe what I should be
+ 
+
+ align:start position:0%
+that okay um maybe what I should be
+thinking about is if I can make the
+
+ align:start position:0%
+thinking about is if I can make the
+ 
+
+ align:start position:0%
+thinking about is if I can make the
+approximation that all the Ripple
+
+ align:start position:0%
+approximation that all the Ripple
+ 
+
+ align:start position:0%
+approximation that all the Ripple
+current is going to the capacitor and
+
+ align:start position:0%
+current is going to the capacitor and
+ 
+
+ align:start position:0%
+current is going to the capacitor and
+all the DC currents going to the
+
+ align:start position:0%
+all the DC currents going to the
+ 
+
+ align:start position:0%
+all the DC currents going to the
+resistor and I only want to focus on the
+
+ align:start position:0%
+resistor and I only want to focus on the
+ 
+
+ align:start position:0%
+resistor and I only want to focus on the
+Ripple why don't I think about with the
+
+ align:start position:0%
+Ripple why don't I think about with the
+ 
+
+ align:start position:0%
+Ripple why don't I think about with the
+Ripple current let me make an AC model
+
+ align:start position:0%
+Ripple current let me make an AC model
+ 
+
+ align:start position:0%
+Ripple current let me make an AC model
+for this thing and just subtract off the
+
+ align:start position:0%
+for this thing and just subtract off the
+ 
+
+ align:start position:0%
+for this thing and just subtract off the
+DC component okay I know none of the
+
+ align:start position:0%
+DC component okay I know none of the
+ 
+
+ align:start position:0%
+DC component okay I know none of the
+Ripple I know none of the DC currents
+
+ align:start position:0%
+Ripple I know none of the DC currents
+ 
+
+ align:start position:0%
+Ripple I know none of the DC currents
+going into the capacitor right we we
+
+ align:start position:0%
+going into the capacitor right we we
+ 
+
+ align:start position:0%
+going into the capacitor right we we
+sort of know that from the fact of
+
+ align:start position:0%
+sort of know that from the fact of
+ 
+
+ align:start position:0%
+sort of know that from the fact of
+periodic steady state okay so maybe what
+
+ align:start position:0%
+periodic steady state okay so maybe what
+ 
+
+ align:start position:0%
+periodic steady state okay so maybe what
+I could do is make a new
+
+ align:start position:0%
+I could do is make a new
+ 
+
+ align:start position:0%
+I could do is make a new
+model that I'm going to call ID
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tilda which is exactly which is exactly
+
+ align:start position:0%
+Tilda which is exactly which is exactly
+ 
+
+ align:start position:0%
+Tilda which is exactly which is exactly
+just the AC component of this waveform
+
+ align:start position:0%
+just the AC component of this waveform
+ 
+
+ align:start position:0%
+just the AC component of this waveform
+ID okay so I'm going to subtract off the
+
+ align:start position:0%
+ID okay so I'm going to subtract off the
+ 
+
+ align:start position:0%
+ID okay so I'm going to subtract off the
+DC value and just keep the AC value
+
+ align:start position:0%
+DC value and just keep the AC value
+ 
+
+ align:start position:0%
+DC value and just keep the AC value
+what's that going to be well in the
+
+ align:start position:0%
+what's that going to be well in the
+ 
+
+ align:start position:0%
+what's that going to be well in the
+first part of the cycle it's going to be
+
+ align:start position:0%
+first part of the cycle it's going to be
+ 
+
+ align:start position:0%
+first part of the cycle it's going to be
+zero - 1 - D iil so this will be
+
+ align:start position:0%
+zero - 1 - D iil so this will be
+ 
+
+ align:start position:0%
+zero - 1 - D iil so this will be
+minus 1 - D
+
+ align:start position:0%
+minus 1 - D
+ 
+
+ align:start position:0%
+minus 1 - D
+iil okay in the first part of the cycle
+
+ align:start position:0%
+iil okay in the first part of the cycle
+ 
+
+ align:start position:0%
+iil okay in the first part of the cycle
+in the second part of the
+
+ align:start position:0%
+in the second part of the
+ 
+
+ align:start position:0%
+in the second part of the
+cycle it would be ID minus one minus D
+
+ align:start position:0%
+cycle it would be ID minus one minus D
+ 
+
+ align:start position:0%
+cycle it would be ID minus one minus D
+which would make it
+
+ align:start position:0%
+which would make it
+ 
+
+ align:start position:0%
+which would make it
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+okay like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this right and this is DT this is T okay
+
+ align:start position:0%
+this right and this is DT this is T okay
+ 
+
+ align:start position:0%
+this right and this is DT this is T okay
+so this is the AC component of the
+
+ align:start position:0%
+so this is the AC component of the
+ 
+
+ align:start position:0%
+so this is the AC component of the
+Ripple current coming through the diode
+
+ align:start position:0%
+Ripple current coming through the diode
+ 
+
+ align:start position:0%
+Ripple current coming through the diode
+so here we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have ID
+
+ align:start position:0%
+have ID
+ 
+
+ align:start position:0%
+have ID
+Tilda okay and where that's really going
+
+ align:start position:0%
+Tilda okay and where that's really going
+ 
+
+ align:start position:0%
+Tilda okay and where that's really going
+is is all going into the
+
+ align:start position:0%
+is is all going into the
+ 
+
+ align:start position:0%
+is is all going into the
+capacitor right that's my approximation
+
+ align:start position:0%
+capacitor right that's my approximation
+ 
+
+ align:start position:0%
+capacitor right that's my approximation
+all the Ripple current goes into the
+
+ align:start position:0%
+all the Ripple current goes into the
+ 
+
+ align:start position:0%
+all the Ripple current goes into the
+capacitor okay um if I make this
+
+ align:start position:0%
+capacitor okay um if I make this
+ 
+
+ align:start position:0%
+capacitor okay um if I make this
+approximation then I ought to be able to
+
+ align:start position:0%
+approximation then I ought to be able to
+ 
+
+ align:start position:0%
+approximation then I ought to be able to
+calculate the the Ripple voltage on the
+
+ align:start position:0%
+calculate the the Ripple voltage on the
+ 
+
+ align:start position:0%
+calculate the the Ripple voltage on the
+capacitor VC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tilda does that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense so what should
+
+ align:start position:0%
+sense so what should
+ 
+
+ align:start position:0%
+sense so what should
+happen well if I have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um in the first part of the cycle right
+
+ align:start position:0%
+um in the first part of the cycle right
+ 
+
+ align:start position:0%
+um in the first part of the cycle right
+here's VC tlda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in the first part of the
+
+ align:start position:0%
+okay in the first part of the
+ 
+
+ align:start position:0%
+okay in the first part of the
+cycle I've got a negative constant
+
+ align:start position:0%
+cycle I've got a negative constant
+ 
+
+ align:start position:0%
+cycle I've got a negative constant
+current through the
+
+ align:start position:0%
+current through the
+ 
+
+ align:start position:0%
+current through the
+capacitor right so basically the
+
+ align:start position:0%
+capacitor right so basically the
+ 
+
+ align:start position:0%
+capacitor right so basically the
+capacitor voltage ought to be falling in
+
+ align:start position:0%
+capacitor voltage ought to be falling in
+ 
+
+ align:start position:0%
+capacitor voltage ought to be falling in
+the first part of the cycle
+
+ align:start position:0%
+the first part of the cycle
+ 
+
+ align:start position:0%
+the first part of the cycle
+linearly
+
+ align:start position:0%
+linearly
+ 
+
+ align:start position:0%
+linearly
+okay for
+
+ align:start position:0%
+okay for
+ 
+
+ align:start position:0%
+okay for
+DT and then should be rising in the
+
+ align:start position:0%
+DT and then should be rising in the
+ 
+
+ align:start position:0%
+DT and then should be rising in the
+second part of the cycle for
+
+ align:start position:0%
+second part of the cycle for
+ 
+
+ align:start position:0%
+second part of the cycle for
+DT okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is what the Ripple current this is
+
+ align:start position:0%
+this is what the Ripple current this is
+ 
+
+ align:start position:0%
+this is what the Ripple current this is
+what the Ripple voltage VC Tilda is
+
+ align:start position:0%
+what the Ripple voltage VC Tilda is
+ 
+
+ align:start position:0%
+what the Ripple voltage VC Tilda is
+going to look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like all right under my
+
+ align:start position:0%
+like all right under my
+ 
+
+ align:start position:0%
+like all right under my
+approximation all right well what does
+
+ align:start position:0%
+approximation all right well what does
+ 
+
+ align:start position:0%
+approximation all right well what does
+that mean well it turns out that if I
+
+ align:start position:0%
+that mean well it turns out that if I
+ 
+
+ align:start position:0%
+that mean well it turns out that if I
+have a triangle wave its midpoint is
+
+ align:start position:0%
+have a triangle wave its midpoint is
+ 
+
+ align:start position:0%
+have a triangle wave its midpoint is
+halfway between the two extremes so this
+
+ align:start position:0%
+halfway between the two extremes so this
+ 
+
+ align:start position:0%
+halfway between the two extremes so this
+I might
+
+ align:start position:0%
+I might
+ 
+
+ align:start position:0%
+I might
+call Delta VC P to Peak and it turns out
+
+ align:start position:0%
+call Delta VC P to Peak and it turns out
+ 
+
+ align:start position:0%
+call Delta VC P to Peak and it turns out
+what that means is this will be Delta VC
+
+ align:start position:0%
+what that means is this will be Delta VC
+ 
+
+ align:start position:0%
+what that means is this will be Delta VC
+Peak to Peak over two and this will be
+
+ align:start position:0%
+Peak to Peak over two and this will be
+ 
+
+ align:start position:0%
+Peak to Peak over two and this will be
+Delta VC Peak to Peak over two okay well
+
+ align:start position:0%
+Delta VC Peak to Peak over two okay well
+ 
+
+ align:start position:0%
+Delta VC Peak to Peak over two okay well
+what is this value and I should have
+
+ align:start position:0%
+what is this value and I should have
+ 
+
+ align:start position:0%
+what is this value and I should have
+said this is DT and this is
+
+ align:start position:0%
+said this is DT and this is
+ 
+
+ align:start position:0%
+said this is DT and this is
+T all
+
+ align:start position:0%
+T all
+ 
+
+ align:start position:0%
+T all
+right IC is equal to C DVC
+
+ align:start position:0%
+right IC is equal to C DVC
+ 
+
+ align:start position:0%
+right IC is equal to C DVC
+DT right Delta VC Peak to Peak ought to
+
+ align:start position:0%
+DT right Delta VC Peak to Peak ought to
+ 
+
+ align:start position:0%
+DT right Delta VC Peak to Peak ought to
+be equal to 1 / C the
+
+ align:start position:0%
+be equal to 1 / C the
+ 
+
+ align:start position:0%
+be equal to 1 / C the
+integral uh I could do it um from here
+
+ align:start position:0%
+integral uh I could do it um from here
+ 
+
+ align:start position:0%
+integral uh I could do it um from here
+to Here For
+
+ align:start position:0%
+to Here For
+ 
+
+ align:start position:0%
+to Here For
+example of uh between DT and T of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+icdt which works out to be what that's 1
+
+ align:start position:0%
+icdt which works out to be what that's 1
+ 
+
+ align:start position:0%
+icdt which works out to be what that's 1
+/ C the current is constant at Dil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that happens for um a Time 1 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT right so this is Delta VC Peak to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Peak does everybody buy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so what can I say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the capacitor Ripple voltage under
+
+ align:start position:0%
+then the capacitor Ripple voltage under
+ 
+
+ align:start position:0%
+then the capacitor Ripple voltage under
+these approximations
+
+ align:start position:0%
+these approximations
+ 
+
+ align:start position:0%
+these approximations
+is inversely proportional to the
+
+ align:start position:0%
+is inversely proportional to the
+ 
+
+ align:start position:0%
+is inversely proportional to the
+capacitor value right so if I were to
+
+ align:start position:0%
+capacitor value right so if I were to
+ 
+
+ align:start position:0%
+capacitor value right so if I were to
+come up to you and say you know what I'm
+
+ align:start position:0%
+come up to you and say you know what I'm
+ 
+
+ align:start position:0%
+come up to you and say you know what I'm
+only going to allow you know 100 molts
+
+ align:start position:0%
+only going to allow you know 100 molts
+ 
+
+ align:start position:0%
+only going to allow you know 100 molts
+of Ripple in my
+
+ align:start position:0%
+of Ripple in my
+ 
+
+ align:start position:0%
+of Ripple in my
+output or some value other value of
+
+ align:start position:0%
+output or some value other value of
+ 
+
+ align:start position:0%
+output or some value other value of
+delta VC Peak to Peak this equation
+
+ align:start position:0%
+delta VC Peak to Peak this equation
+ 
+
+ align:start position:0%
+delta VC Peak to Peak this equation
+tells me what that should be right this
+
+ align:start position:0%
+tells me what that should be right this
+ 
+
+ align:start position:0%
+tells me what that should be right this
+just says basically C has to be greater
+
+ align:start position:0%
+just says basically C has to be greater
+ 
+
+ align:start position:0%
+just says basically C has to be greater
+than or equal to um D * 1 minus
+
+ align:start position:0%
+than or equal to um D * 1 minus
+ 
+
+ align:start position:0%
+than or equal to um D * 1 minus
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+i t over Delta v c Peak to Peak
+
+ align:start position:0%
+i t over Delta v c Peak to Peak
+ 
+
+ align:start position:0%
+i t over Delta v c Peak to Peak
+right so if I if you tell me okay what's
+
+ align:start position:0%
+right so if I if you tell me okay what's
+ 
+
+ align:start position:0%
+right so if I if you tell me okay what's
+my load current and my switching period
+
+ align:start position:0%
+my load current and my switching period
+ 
+
+ align:start position:0%
+my load current and my switching period
+my duty ratio this tells me how big does
+
+ align:start position:0%
+my duty ratio this tells me how big does
+ 
+
+ align:start position:0%
+my duty ratio this tells me how big does
+the capacitor have to be in order to
+
+ align:start position:0%
+the capacitor have to be in order to
+ 
+
+ align:start position:0%
+the capacitor have to be in order to
+reduce the output Ripple down to an
+
+ align:start position:0%
+reduce the output Ripple down to an
+ 
+
+ align:start position:0%
+reduce the output Ripple down to an
+acceptable value that I
+
+ align:start position:0%
+acceptable value that I
+ 
+
+ align:start position:0%
+acceptable value that I
+set okay any questions on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now it turns out that I could do the
+
+ align:start position:0%
+now it turns out that I could do the
+ 
+
+ align:start position:0%
+now it turns out that I could do the
+same kind of
+
+ align:start position:0%
+same kind of
+ 
+
+ align:start position:0%
+same kind of
+calculation for the inductor current
+
+ align:start position:0%
+calculation for the inductor current
+ 
+
+ align:start position:0%
+calculation for the inductor current
+Ripple all right and I should say by the
+
+ align:start position:0%
+Ripple all right and I should say by the
+ 
+
+ align:start position:0%
+Ripple all right and I should say by the
+way that in a typical converter I
+
+ align:start position:0%
+way that in a typical converter I
+ 
+
+ align:start position:0%
+way that in a typical converter I
+usually am not allowing very much
+
+ align:start position:0%
+usually am not allowing very much
+ 
+
+ align:start position:0%
+usually am not allowing very much
+capacitor voltage Ripple right if I want
+
+ align:start position:0%
+capacitor voltage Ripple right if I want
+ 
+
+ align:start position:0%
+capacitor voltage Ripple right if I want
+a DCd converter you know this has to be
+
+ align:start position:0%
+a DCd converter you know this has to be
+ 
+
+ align:start position:0%
+a DCd converter you know this has to be
+small and we'll come into what we mean
+
+ align:start position:0%
+small and we'll come into what we mean
+ 
+
+ align:start position:0%
+small and we'll come into what we mean
+by how small is small okay inductor
+
+ align:start position:0%
+by how small is small okay inductor
+ 
+
+ align:start position:0%
+by how small is small okay inductor
+current Ripple maybe we can allow a bit
+
+ align:start position:0%
+current Ripple maybe we can allow a bit
+ 
+
+ align:start position:0%
+current Ripple maybe we can allow a bit
+more but we can do the same trick to
+
+ align:start position:0%
+more but we can do the same trick to
+ 
+
+ align:start position:0%
+more but we can do the same trick to
+calculate it right so if I were to come
+
+ align:start position:0%
+calculate it right so if I were to come
+ 
+
+ align:start position:0%
+calculate it right so if I were to come
+up here and say okay let me go through
+
+ align:start position:0%
+up here and say okay let me go through
+ 
+
+ align:start position:0%
+up here and say okay let me go through
+the same really quick
+
+ align:start position:0%
+the same really quick
+ 
+
+ align:start position:0%
+the same really quick
+procedure okay so here we go here's my
+
+ align:start position:0%
+procedure okay so here we go here's my
+ 
+
+ align:start position:0%
+procedure okay so here we go here's my
+uh converter and what I'm really going
+
+ align:start position:0%
+uh converter and what I'm really going
+ 
+
+ align:start position:0%
+uh converter and what I'm really going
+to think about now is uh what is this
+
+ align:start position:0%
+to think about now is uh what is this
+ 
+
+ align:start position:0%
+to think about now is uh what is this
+voltage suppose I Define this voltage um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VX here
+
+ align:start position:0%
+VX here
+ 
+
+ align:start position:0%
+VX here
+okay I could come up with a model that
+
+ align:start position:0%
+okay I could come up with a model that
+ 
+
+ align:start position:0%
+okay I could come up with a model that
+looks like this I have uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V1 and then an
+
+ align:start position:0%
+V1 and then an
+ 
+
+ align:start position:0%
+V1 and then an
+inductor and then a voltage that I'll
+
+ align:start position:0%
+inductor and then a voltage that I'll
+ 
+
+ align:start position:0%
+inductor and then a voltage that I'll
+call a pulsating voltage that I'm going
+
+ align:start position:0%
+call a pulsating voltage that I'm going
+ 
+
+ align:start position:0%
+call a pulsating voltage that I'm going
+to call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VX and what does VX look like VX looks
+
+ align:start position:0%
+VX and what does VX look like VX looks
+ 
+
+ align:start position:0%
+VX and what does VX look like VX looks
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this in the first part of the cycle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the first part of the cycle when the
+
+ align:start position:0%
+in the first part of the cycle when the
+ 
+
+ align:start position:0%
+in the first part of the cycle when the
+switch is on VX is
+
+ align:start position:0%
+switch is on VX is
+ 
+
+ align:start position:0%
+switch is on VX is
+zero until sometime
+
+ align:start position:0%
+zero until sometime
+ 
+
+ align:start position:0%
+zero until sometime
+DT in the second part of the cycle um
+
+ align:start position:0%
+DT in the second part of the cycle um
+ 
+
+ align:start position:0%
+DT in the second part of the cycle um
+the switch is off and the diode is on
+
+ align:start position:0%
+the switch is off and the diode is on
+ 
+
+ align:start position:0%
+the switch is off and the diode is on
+and it's equal to VC which is the same
+
+ align:start position:0%
+and it's equal to VC which is the same
+ 
+
+ align:start position:0%
+and it's equal to VC which is the same
+as V2 right so here I go here's V
+
+ align:start position:0%
+as V2 right so here I go here's V
+ 
+
+ align:start position:0%
+as V2 right so here I go here's V
+Capital VC okay so the switch voltage
+
+ align:start position:0%
+Capital VC okay so the switch voltage
+ 
+
+ align:start position:0%
+Capital VC okay so the switch voltage
+I'm sorry the switch voltage comes up
+
+ align:start position:0%
+I'm sorry the switch voltage comes up
+ 
+
+ align:start position:0%
+I'm sorry the switch voltage comes up
+here okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I could then say okay this is VX of
+
+ align:start position:0%
+and I could then say okay this is VX of
+ 
+
+ align:start position:0%
+and I could then say okay this is VX of
+T in my ripple model and the average
+
+ align:start position:0%
+T in my ripple model and the average
+ 
+
+ align:start position:0%
+T in my ripple model and the average
+voltage here which is the same thing as
+
+ align:start position:0%
+voltage here which is the same thing as
+ 
+
+ align:start position:0%
+voltage here which is the same thing as
+the average value of V1 is 1 minus D
+
+ align:start position:0%
+the average value of V1 is 1 minus D
+ 
+
+ align:start position:0%
+the average value of V1 is 1 minus D
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+VC right is the average voltage of this
+
+ align:start position:0%
+VC right is the average voltage of this
+ 
+
+ align:start position:0%
+VC right is the average voltage of this
+pulsating
+
+ align:start position:0%
+pulsating
+ 
+
+ align:start position:0%
+pulsating
+waveform okay I could then say all right
+
+ align:start position:0%
+waveform okay I could then say all right
+ 
+
+ align:start position:0%
+waveform okay I could then say all right
+this is what the circuit model looks
+
+ align:start position:0%
+this is what the circuit model looks
+ 
+
+ align:start position:0%
+this is what the circuit model looks
+like let me just consider its AC values
+
+ align:start position:0%
+like let me just consider its AC values
+ 
+
+ align:start position:0%
+like let me just consider its AC values
+right let me consider the Ripple current
+
+ align:start position:0%
+right let me consider the Ripple current
+ 
+
+ align:start position:0%
+right let me consider the Ripple current
+only in this thing so okay what happens
+
+ align:start position:0%
+only in this thing so okay what happens
+ 
+
+ align:start position:0%
+only in this thing so okay what happens
+what's the Ripple in capital V1 it's
+
+ align:start position:0%
+what's the Ripple in capital V1 it's
+ 
+
+ align:start position:0%
+what's the Ripple in capital V1 it's
+nothing right then I have my inductor
+
+ align:start position:0%
+nothing right then I have my inductor
+ 
+
+ align:start position:0%
+nothing right then I have my inductor
+and this is L with a current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I right here's I this will be I Tilda
+
+ align:start position:0%
+I right here's I this will be I Tilda
+ 
+
+ align:start position:0%
+I right here's I this will be I Tilda
+the AC component only this thing I may
+
+ align:start position:0%
+the AC component only this thing I may
+ 
+
+ align:start position:0%
+the AC component only this thing I may
+have a ripple voltage looks like
+
+ align:start position:0%
+have a ripple voltage looks like
+ 
+
+ align:start position:0%
+have a ripple voltage looks like
+this in the first part of the cycle this
+
+ align:start position:0%
+this in the first part of the cycle this
+ 
+
+ align:start position:0%
+this in the first part of the cycle this
+is minus one minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+VC and the second part of the cycle it's
+
+ align:start position:0%
+VC and the second part of the cycle it's
+ 
+
+ align:start position:0%
+VC and the second part of the cycle it's
+VC minus one minus DVC which is
+
+ align:start position:0%
+VC minus one minus DVC which is
+ 
+
+ align:start position:0%
+VC minus one minus DVC which is
+DVC okay so this is what um VX Tilda
+
+ align:start position:0%
+DVC okay so this is what um VX Tilda
+ 
+
+ align:start position:0%
+DVC okay so this is what um VX Tilda
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+like okay and here's vx to in my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circuit all right and of course V
+
+ align:start position:0%
+circuit all right and of course V
+ 
+
+ align:start position:0%
+circuit all right and of course V
+subel is just minus VX
+
+ align:start position:0%
+subel is just minus VX
+ 
+
+ align:start position:0%
+subel is just minus VX
+TOA right so then I can I can figure out
+
+ align:start position:0%
+TOA right so then I can I can figure out
+ 
+
+ align:start position:0%
+TOA right so then I can I can figure out
+that okay
+
+ align:start position:0%
+that okay
+ 
+
+ align:start position:0%
+that okay
+um basically the negative of this
+
+ align:start position:0%
+um basically the negative of this
+ 
+
+ align:start position:0%
+um basically the negative of this
+voltage is the voltage on the
+
+ align:start position:0%
+voltage is the voltage on the
+ 
+
+ align:start position:0%
+voltage is the voltage on the
+inductor right so V subel is equal to
+
+ align:start position:0%
+inductor right so V subel is equal to
+ 
+
+ align:start position:0%
+inductor right so V subel is equal to
+ldt so Delta iil Peak to Peak is simply
+
+ align:start position:0%
+ldt so Delta iil Peak to Peak is simply
+ 
+
+ align:start position:0%
+ldt so Delta iil Peak to Peak is simply
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+um 1 over L the integral from 0 to DT of
+
+ align:start position:0%
+um 1 over L the integral from 0 to DT of
+ 
+
+ align:start position:0%
+um 1 over L the integral from 0 to DT of
+vbl DT okay and so what am I expecting
+
+ align:start position:0%
+vbl DT okay and so what am I expecting
+ 
+
+ align:start position:0%
+vbl DT okay and so what am I expecting
+I'm putting VX is negative constant
+
+ align:start position:0%
+I'm putting VX is negative constant
+ 
+
+ align:start position:0%
+I'm putting VX is negative constant
+voltage
+
+ align:start position:0%
+voltage
+ 
+
+ align:start position:0%
+voltage
+so that means VL is a positive constant
+
+ align:start position:0%
+so that means VL is a positive constant
+ 
+
+ align:start position:0%
+so that means VL is a positive constant
+voltage in the first part of the cycle
+
+ align:start position:0%
+voltage in the first part of the cycle
+ 
+
+ align:start position:0%
+voltage in the first part of the cycle
+and I should get a inductor Ripple
+
+ align:start position:0%
+and I should get a inductor Ripple
+ 
+
+ align:start position:0%
+and I should get a inductor Ripple
+current here that does
+
+ align:start position:0%
+current here that does
+ 
+
+ align:start position:0%
+current here that does
+this and then in the Nega second part of
+
+ align:start position:0%
+this and then in the Nega second part of
+ 
+
+ align:start position:0%
+this and then in the Nega second part of
+the cycle it does this so again the
+
+ align:start position:0%
+the cycle it does this so again the
+ 
+
+ align:start position:0%
+the cycle it does this so again the
+voltage the voltage Ripple I'm sorry the
+
+ align:start position:0%
+voltage the voltage Ripple I'm sorry the
+ 
+
+ align:start position:0%
+voltage the voltage Ripple I'm sorry the
+inductor current Ripple i l Tilda is
+
+ align:start position:0%
+inductor current Ripple i l Tilda is
+ 
+
+ align:start position:0%
+inductor current Ripple i l Tilda is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+triangular and this
+
+ align:start position:0%
+triangular and this
+ 
+
+ align:start position:0%
+triangular and this
+amount
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is going to be Delta i l Peak to
+
+ align:start position:0%
+here is going to be Delta i l Peak to
+ 
+
+ align:start position:0%
+here is going to be Delta i l Peak to
+Peak which I can calculate that as 1
+
+ align:start position:0%
+Peak which I can calculate that as 1
+ 
+
+ align:start position:0%
+Peak which I can calculate that as 1
+over L this is going to be 1 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DVC which goes on for a time period
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT okay and what I get in the end is
+
+ align:start position:0%
+DT okay and what I get in the end is
+ 
+
+ align:start position:0%
+DT okay and what I get in the end is
+that uh L ought to be greater than or
+
+ align:start position:0%
+that uh L ought to be greater than or
+ 
+
+ align:start position:0%
+that uh L ought to be greater than or
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to 1us D
+
+ align:start position:0%
+to 1us D
+ 
+
+ align:start position:0%
+to 1us D
+time D time
+
+ align:start position:0%
+time D time
+ 
+
+ align:start position:0%
+time D time
+VC T over Delta I Peak to
+
+ align:start position:0%
+VC T over Delta I Peak to
+ 
+
+ align:start position:0%
+VC T over Delta I Peak to
+Peak right so if I have a limitation on
+
+ align:start position:0%
+Peak right so if I have a limitation on
+ 
+
+ align:start position:0%
+Peak right so if I have a limitation on
+the allowable Ripple current in the
+
+ align:start position:0%
+the allowable Ripple current in the
+ 
+
+ align:start position:0%
+the allowable Ripple current in the
+inductor I can calculate for a given
+
+ align:start position:0%
+inductor I can calculate for a given
+ 
+
+ align:start position:0%
+inductor I can calculate for a given
+operating condition how big that
+
+ align:start position:0%
+operating condition how big that
+ 
+
+ align:start position:0%
+operating condition how big that
+inductor needs to
+
+ align:start position:0%
+inductor needs to
+ 
+
+ align:start position:0%
+inductor needs to
+be and the only assumption I made was
+
+ align:start position:0%
+be and the only assumption I made was
+ 
+
+ align:start position:0%
+be and the only assumption I made was
+that I ignored the Ripple in
+
+ align:start position:0%
+that I ignored the Ripple in
+ 
+
+ align:start position:0%
+that I ignored the Ripple in
+V2 when I calculated this okay are there
+
+ align:start position:0%
+V2 when I calculated this okay are there
+ 
+
+ align:start position:0%
+V2 when I calculated this okay are there
+any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that now interesting I made some
+
+ align:start position:0%
+that now interesting I made some
+ 
+
+ align:start position:0%
+that now interesting I made some
+approximations right when I when I
+
+ align:start position:0%
+approximations right when I when I
+ 
+
+ align:start position:0%
+approximations right when I when I
+calculated the capacitor voltage Ripple
+
+ align:start position:0%
+calculated the capacitor voltage Ripple
+ 
+
+ align:start position:0%
+calculated the capacitor voltage Ripple
+I ignored the inductor current Ripple
+
+ align:start position:0%
+I ignored the inductor current Ripple
+ 
+
+ align:start position:0%
+I ignored the inductor current Ripple
+and when I calculated the inductor
+
+ align:start position:0%
+and when I calculated the inductor
+ 
+
+ align:start position:0%
+and when I calculated the inductor
+current Ripple I ignored the capacitor
+
+ align:start position:0%
+current Ripple I ignored the capacitor
+ 
+
+ align:start position:0%
+current Ripple I ignored the capacitor
+voltage Ripple doesn't matter that I did
+
+ align:start position:0%
+voltage Ripple doesn't matter that I did
+ 
+
+ align:start position:0%
+voltage Ripple doesn't matter that I did
+that the answer is no why
+
+ align:start position:0%
+that the answer is no why
+ 
+
+ align:start position:0%
+that the answer is no why
+because I pretended that that I was
+
+ align:start position:0%
+because I pretended that that I was
+ 
+
+ align:start position:0%
+because I pretended that that I was
+constant at a constant current when I
+
+ align:start position:0%
+constant at a constant current when I
+ 
+
+ align:start position:0%
+constant at a constant current when I
+calculated this waveform right well what
+
+ align:start position:0%
+calculated this waveform right well what
+ 
+
+ align:start position:0%
+calculated this waveform right well what
+does I look like
+
+ align:start position:0%
+does I look like
+ 
+
+ align:start position:0%
+does I look like
+iil has some Ripple in it and sort of
+
+ align:start position:0%
+iil has some Ripple in it and sort of
+ 
+
+ align:start position:0%
+iil has some Ripple in it and sort of
+this triangular Ripple falling the only
+
+ align:start position:0%
+this triangular Ripple falling the only
+ 
+
+ align:start position:0%
+this triangular Ripple falling the only
+thing that would have happened had I
+
+ align:start position:0%
+thing that would have happened had I
+ 
+
+ align:start position:0%
+thing that would have happened had I
+included that is that I would have had a
+
+ align:start position:0%
+included that is that I would have had a
+ 
+
+ align:start position:0%
+included that is that I would have had a
+little Ripple
+
+ align:start position:0%
+little Ripple
+ 
+
+ align:start position:0%
+little Ripple
+here okay and if I included that and
+
+ align:start position:0%
+here okay and if I included that and
+ 
+
+ align:start position:0%
+here okay and if I included that and
+then I calculated the voltage
+
+ align:start position:0%
+then I calculated the voltage
+ 
+
+ align:start position:0%
+then I calculated the voltage
+characteristic from that all that would
+
+ align:start position:0%
+characteristic from that all that would
+ 
+
+ align:start position:0%
+characteristic from that all that would
+have happened is instead of getting
+
+ align:start position:0%
+have happened is instead of getting
+ 
+
+ align:start position:0%
+have happened is instead of getting
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+slope or instead of getting a ripple
+
+ align:start position:0%
+slope or instead of getting a ripple
+ 
+
+ align:start position:0%
+slope or instead of getting a ripple
+wave form that looked like a perfect
+
+ align:start position:0%
+wave form that looked like a perfect
+ 
+
+ align:start position:0%
+wave form that looked like a perfect
+triangle wave like I drew here um all
+
+ align:start position:0%
+triangle wave like I drew here um all
+ 
+
+ align:start position:0%
+triangle wave like I drew here um all
+that would have happened is I would have
+
+ align:start position:0%
+that would have happened is I would have
+ 
+
+ align:start position:0%
+that would have happened is I would have
+gotten a different version with a
+
+ align:start position:0%
+gotten a different version with a
+ 
+
+ align:start position:0%
+gotten a different version with a
+slightly different curvature and the
+
+ align:start position:0%
+slightly different curvature and the
+ 
+
+ align:start position:0%
+slightly different curvature and the
+peak to Peak Ripple would have been
+
+ align:start position:0%
+peak to Peak Ripple would have been
+ 
+
+ align:start position:0%
+peak to Peak Ripple would have been
+exactly the same thing okay so I can
+
+ align:start position:0%
+exactly the same thing okay so I can
+ 
+
+ align:start position:0%
+exactly the same thing okay so I can
+make these approximations ignore the
+
+ align:start position:0%
+make these approximations ignore the
+ 
+
+ align:start position:0%
+make these approximations ignore the
+inductor current Ripple for calculating
+
+ align:start position:0%
+inductor current Ripple for calculating
+ 
+
+ align:start position:0%
+inductor current Ripple for calculating
+the capacitor bolt to Ripple and vice
+
+ align:start position:0%
+the capacitor bolt to Ripple and vice
+ 
+
+ align:start position:0%
+the capacitor bolt to Ripple and vice
+versa and I still get the right
+
+ align:start position:0%
+versa and I still get the right
+ 
+
+ align:start position:0%
+versa and I still get the right
+answer okay and what those have given me
+
+ align:start position:0%
+answer okay and what those have given me
+ 
+
+ align:start position:0%
+answer okay and what those have given me
+is a means to get to how big a capacitor
+
+ align:start position:0%
+is a means to get to how big a capacitor
+ 
+
+ align:start position:0%
+is a means to get to how big a capacitor
+do I need to get to a certain capacitor
+
+ align:start position:0%
+do I need to get to a certain capacitor
+ 
+
+ align:start position:0%
+do I need to get to a certain capacitor
+voltage Ripple and how big an inductor
+
+ align:start position:0%
+voltage Ripple and how big an inductor
+ 
+
+ align:start position:0%
+voltage Ripple and how big an inductor
+do I need to get to a certain inductor
+
+ align:start position:0%
+do I need to get to a certain inductor
+ 
+
+ align:start position:0%
+do I need to get to a certain inductor
+current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ripple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions so I would say that you know
+
+ align:start position:0%
+questions so I would say that you know
+ 
+
+ align:start position:0%
+questions so I would say that you know
+if I was going to sit down and design a
+
+ align:start position:0%
+if I was going to sit down and design a
+ 
+
+ align:start position:0%
+if I was going to sit down and design a
+converter I might start to think about
+
+ align:start position:0%
+converter I might start to think about
+ 
+
+ align:start position:0%
+converter I might start to think about
+hey um
+
+ align:start position:0%
+hey um
+ 
+
+ align:start position:0%
+hey um
+how much Ripple is tolerable right
+
+ align:start position:0%
+how much Ripple is tolerable right
+ 
+
+ align:start position:0%
+how much Ripple is tolerable right
+that's sort of an application thing
+
+ align:start position:0%
+that's sort of an application thing
+ 
+
+ align:start position:0%
+that's sort of an application thing
+right I'm building this boost converter
+
+ align:start position:0%
+right I'm building this boost converter
+ 
+
+ align:start position:0%
+right I'm building this boost converter
+to power some thing or other and perhaps
+
+ align:start position:0%
+to power some thing or other and perhaps
+ 
+
+ align:start position:0%
+to power some thing or other and perhaps
+my the specifications I'm giving you for
+
+ align:start position:0%
+my the specifications I'm giving you for
+ 
+
+ align:start position:0%
+my the specifications I'm giving you for
+the system is oh you're allowed you know
+
+ align:start position:0%
+the system is oh you're allowed you know
+ 
+
+ align:start position:0%
+the system is oh you're allowed you know
+100 Mill volts of Ripple on top of
+
+ align:start position:0%
+100 Mill volts of Ripple on top of
+ 
+
+ align:start position:0%
+100 Mill volts of Ripple on top of
+whatever your you know 50 volts of
+
+ align:start position:0%
+whatever your you know 50 volts of
+ 
+
+ align:start position:0%
+whatever your you know 50 volts of
+output is or something right somebody's
+
+ align:start position:0%
+output is or something right somebody's
+ 
+
+ align:start position:0%
+output is or something right somebody's
+going to tell you you're going to have
+
+ align:start position:0%
+going to tell you you're going to have
+ 
+
+ align:start position:0%
+going to tell you you're going to have
+this much voltage
+
+ align:start position:0%
+this much voltage
+ 
+
+ align:start position:0%
+this much voltage
+Ripple or this much current Ripple
+
+ align:start position:0%
+Ripple or this much current Ripple
+ 
+
+ align:start position:0%
+Ripple or this much current Ripple
+allowed into the input okay now one way
+
+ align:start position:0%
+allowed into the input okay now one way
+ 
+
+ align:start position:0%
+allowed into the input okay now one way
+to get those is just to make these
+
+ align:start position:0%
+to get those is just to make these
+ 
+
+ align:start position:0%
+to get those is just to make these
+components bigger we'll see other ways
+
+ align:start position:0%
+components bigger we'll see other ways
+ 
+
+ align:start position:0%
+components bigger we'll see other ways
+to reduce those by adding higher order
+
+ align:start position:0%
+to reduce those by adding higher order
+ 
+
+ align:start position:0%
+to reduce those by adding higher order
+filters and that kind of thing but this
+
+ align:start position:0%
+filters and that kind of thing but this
+ 
+
+ align:start position:0%
+filters and that kind of thing but this
+is a pretty good place to start to get L
+
+ align:start position:0%
+is a pretty good place to start to get L
+ 
+
+ align:start position:0%
+is a pretty good place to start to get L
+and C
+
+ align:start position:0%
+and C
+ 
+
+ align:start position:0%
+and C
+values okay and you notice in either
+
+ align:start position:0%
+values okay and you notice in either
+ 
+
+ align:start position:0%
+values okay and you notice in either
+case what I ended up with is triangular
+
+ align:start position:0%
+case what I ended up with is triangular
+ 
+
+ align:start position:0%
+case what I ended up with is triangular
+shaped
+
+ align:start position:0%
+shaped
+ 
+
+ align:start position:0%
+shaped
+ripples okay because essentially we're
+
+ align:start position:0%
+ripples okay because essentially we're
+ 
+
+ align:start position:0%
+ripples okay because essentially we're
+assuming that the currents just go the
+
+ align:start position:0%
+assuming that the currents just go the
+ 
+
+ align:start position:0%
+assuming that the currents just go the
+Ripple currents just going into the
+
+ align:start position:0%
+Ripple currents just going into the
+ 
+
+ align:start position:0%
+Ripple currents just going into the
+corresponding passive component a
+
+ align:start position:0%
+corresponding passive component a
+ 
+
+ align:start position:0%
+corresponding passive component a
+constant current is going to a passive
+
+ align:start position:0%
+constant current is going to a passive
+ 
+
+ align:start position:0%
+constant current is going to a passive
+component I get a triangular Ripple
+
+ align:start position:0%
+component I get a triangular Ripple
+ 
+
+ align:start position:0%
+component I get a triangular Ripple
+waveform okay well we can actually use
+
+ align:start position:0%
+waveform okay well we can actually use
+ 
+
+ align:start position:0%
+waveform okay well we can actually use
+that to our advantage we can kind of say
+
+ align:start position:0%
+that to our advantage we can kind of say
+ 
+
+ align:start position:0%
+that to our advantage we can kind of say
+okay any such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+component you know suppose I have some
+
+ align:start position:0%
+component you know suppose I have some
+ 
+
+ align:start position:0%
+component you know suppose I have some
+waveform I'm going to call X of
+
+ align:start position:0%
+waveform I'm going to call X of
+ 
+
+ align:start position:0%
+waveform I'm going to call X of
+T okay and maybe it has some DC value
+
+ align:start position:0%
+T okay and maybe it has some DC value
+ 
+
+ align:start position:0%
+T okay and maybe it has some DC value
+X that I'll call capital x this could be
+
+ align:start position:0%
+X that I'll call capital x this could be
+ 
+
+ align:start position:0%
+X that I'll call capital x this could be
+a Capac fter voltage or an inductor
+
+ align:start position:0%
+a Capac fter voltage or an inductor
+ 
+
+ align:start position:0%
+a Capac fter voltage or an inductor
+current and then maybe it has some
+
+ align:start position:0%
+current and then maybe it has some
+ 
+
+ align:start position:0%
+current and then maybe it has some
+triangular Ripple on it like
+
+ align:start position:0%
+triangular Ripple on it like
+ 
+
+ align:start position:0%
+triangular Ripple on it like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so then I'll have
+
+ align:start position:0%
+okay and so then I'll have
+ 
+
+ align:start position:0%
+okay and so then I'll have
+some Peak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value I'll call this x
+
+ align:start position:0%
+value I'll call this x
+ 
+
+ align:start position:0%
+value I'll call this x
+Peak and I'll call
+
+ align:start position:0%
+Peak and I'll call
+ 
+
+ align:start position:0%
+Peak and I'll call
+this x
+
+ align:start position:0%
+this x
+ 
+
+ align:start position:0%
+this x
+Min okay
+
+ align:start position:0%
+Min okay
+ 
+
+ align:start position:0%
+Min okay
+and if this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is Delta X Peak to Peak okay it turns
+
+ align:start position:0%
+is Delta X Peak to Peak okay it turns
+ 
+
+ align:start position:0%
+is Delta X Peak to Peak okay it turns
+out that for triangular Ripple the any
+
+ align:start position:0%
+out that for triangular Ripple the any
+ 
+
+ align:start position:0%
+out that for triangular Ripple the any
+triangle wave like this the average is
+
+ align:start position:0%
+triangle wave like this the average is
+ 
+
+ align:start position:0%
+triangle wave like this the average is
+exactly halfway between the
+
+ align:start position:0%
+exactly halfway between the
+ 
+
+ align:start position:0%
+exactly halfway between the
+Peaks that means that this
+
+ align:start position:0%
+Peaks that means that this
+ 
+
+ align:start position:0%
+Peaks that means that this
+is Delta X Peak to Peak over two and
+
+ align:start position:0%
+is Delta X Peak to Peak over two and
+ 
+
+ align:start position:0%
+is Delta X Peak to Peak over two and
+this is Delta X Peak to Peak over 2 all
+
+ align:start position:0%
+this is Delta X Peak to Peak over 2 all
+ 
+
+ align:start position:0%
+this is Delta X Peak to Peak over 2 all
+right that's just a property of triangle
+
+ align:start position:0%
+right that's just a property of triangle
+ 
+
+ align:start position:0%
+right that's just a property of triangle
+waves
+
+ align:start position:0%
+waves
+ 
+
+ align:start position:0%
+waves
+okay why am I getting to that because we
+
+ align:start position:0%
+okay why am I getting to that because we
+ 
+
+ align:start position:0%
+okay why am I getting to that because we
+might Define the Ripple ratio
+
+ align:start position:0%
+might Define the Ripple ratio
+ 
+
+ align:start position:0%
+might Define the Ripple ratio
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and I'm going to call this script R
+
+ align:start position:0%
+um and I'm going to call this script R
+ 
+
+ align:start position:0%
+um and I'm going to call this script R
+subx and I'm going to Define this to be
+
+ align:start position:0%
+subx and I'm going to Define this to be
+ 
+
+ align:start position:0%
+subx and I'm going to Define this to be
+equal to Delta X Peak to Peak / two
+
+ align:start position:0%
+equal to Delta X Peak to Peak / two
+ 
+
+ align:start position:0%
+equal to Delta X Peak to Peak / two
+that's the sort of the mean middle the
+
+ align:start position:0%
+that's the sort of the mean middle the
+ 
+
+ align:start position:0%
+that's the sort of the mean middle the
+average to the peak normalized to
+
+ align:start position:0%
+average to the peak normalized to
+ 
+
+ align:start position:0%
+average to the peak normalized to
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+right so this is sort of you might think
+
+ align:start position:0%
+right so this is sort of you might think
+ 
+
+ align:start position:0%
+right so this is sort of you might think
+of this as being like a percentage
+
+ align:start position:0%
+of this as being like a percentage
+ 
+
+ align:start position:0%
+of this as being like a percentage
+Ripple or a fraction Ripple okay why am
+
+ align:start position:0%
+Ripple or a fraction Ripple okay why am
+ 
+
+ align:start position:0%
+Ripple or a fraction Ripple okay why am
+I interested in that I'm interested in
+
+ align:start position:0%
+I interested in that I'm interested in
+ 
+
+ align:start position:0%
+I interested in that I'm interested in
+that because you know 100 molts a ripple
+
+ align:start position:0%
+that because you know 100 molts a ripple
+ 
+
+ align:start position:0%
+that because you know 100 molts a ripple
+on top of half a volt is a lot 100 Mill
+
+ align:start position:0%
+on top of half a volt is a lot 100 Mill
+ 
+
+ align:start position:0%
+on top of half a volt is a lot 100 Mill
+volts a ripple on top of 100 volts maybe
+
+ align:start position:0%
+volts a ripple on top of 100 volts maybe
+ 
+
+ align:start position:0%
+volts a ripple on top of 100 volts maybe
+it's not so big right so we might want
+
+ align:start position:0%
+it's not so big right so we might want
+ 
+
+ align:start position:0%
+it's not so big right so we might want
+to normally ize the Ripple we consider
+
+ align:start position:0%
+to normally ize the Ripple we consider
+ 
+
+ align:start position:0%
+to normally ize the Ripple we consider
+to the average value of any waveform
+
+ align:start position:0%
+to the average value of any waveform
+ 
+
+ align:start position:0%
+to the average value of any waveform
+inductor current or capacitor voltage
+
+ align:start position:0%
+inductor current or capacitor voltage
+ 
+
+ align:start position:0%
+inductor current or capacitor voltage
+okay so people often talk about the
+
+ align:start position:0%
+okay so people often talk about the
+ 
+
+ align:start position:0%
+okay so people often talk about the
+Ripple ratio of the waveforms or it's
+
+ align:start position:0%
+Ripple ratio of the waveforms or it's
+ 
+
+ align:start position:0%
+Ripple ratio of the waveforms or it's
+sort of a version of the percentage
+
+ align:start position:0%
+sort of a version of the percentage
+ 
+
+ align:start position:0%
+sort of a version of the percentage
+Ripple if you multiply by 100 okay um I
+
+ align:start position:0%
+Ripple if you multiply by 100 okay um I
+ 
+
+ align:start position:0%
+Ripple if you multiply by 100 okay um I
+will say that if you look in the
+
+ align:start position:0%
+will say that if you look in the
+ 
+
+ align:start position:0%
+will say that if you look in the
+literature there there's a skew in how
+
+ align:start position:0%
+literature there there's a skew in how
+ 
+
+ align:start position:0%
+literature there there's a skew in how
+people Define things some people Define
+
+ align:start position:0%
+people Define things some people Define
+ 
+
+ align:start position:0%
+people Define things some people Define
+the Ripple ratio as being Delta X Peak
+
+ align:start position:0%
+the Ripple ratio as being Delta X Peak
+ 
+
+ align:start position:0%
+the Ripple ratio as being Delta X Peak
+to Peak over X and some people Define it
+
+ align:start position:0%
+to Peak over X and some people Define it
+ 
+
+ align:start position:0%
+to Peak over X and some people Define it
+as Delta X Peak Peak over two overx you
+
+ align:start position:0%
+as Delta X Peak Peak over two overx you
+ 
+
+ align:start position:0%
+as Delta X Peak Peak over two overx you
+just got to be careful of what's being
+
+ align:start position:0%
+just got to be careful of what's being
+ 
+
+ align:start position:0%
+just got to be careful of what's being
+referred to when you read the literature
+
+ align:start position:0%
+referred to when you read the literature
+ 
+
+ align:start position:0%
+referred to when you read the literature
+um I kind of like this definition a
+
+ align:start position:0%
+um I kind of like this definition a
+ 
+
+ align:start position:0%
+um I kind of like this definition a
+because what it it's what is used in the
+
+ align:start position:0%
+because what it it's what is used in the
+ 
+
+ align:start position:0%
+because what it it's what is used in the
+text but the one of the nice things
+
+ align:start position:0%
+text but the one of the nice things
+ 
+
+ align:start position:0%
+text but the one of the nice things
+about it is you can then say x a
+
+ align:start position:0%
+about it is you can then say x a
+ 
+
+ align:start position:0%
+about it is you can then say x a
+peak is just simply equal to the DC
+
+ align:start position:0%
+peak is just simply equal to the DC
+ 
+
+ align:start position:0%
+peak is just simply equal to the DC
+value times 1 plus the Ripple ratio of
+
+ align:start position:0%
+value times 1 plus the Ripple ratio of
+ 
+
+ align:start position:0%
+value times 1 plus the Ripple ratio of
+X all
+
+ align:start position:0%
+X all
+ 
+
+ align:start position:0%
+X all
+right and so it's convenient to use this
+
+ align:start position:0%
+right and so it's convenient to use this
+ 
+
+ align:start position:0%
+right and so it's convenient to use this
+form of the definition of Ripple
+
+ align:start position:0%
+form of the definition of Ripple
+ 
+
+ align:start position:0%
+form of the definition of Ripple
+ratio any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so
+
+ align:start position:0%
+that okay so
+ 
+
+ align:start position:0%
+that okay so
+um how might I think about using this
+
+ align:start position:0%
+um how might I think about using this
+ 
+
+ align:start position:0%
+um how might I think about using this
+kind of definition well I might talk
+
+ align:start position:0%
+kind of definition well I might talk
+ 
+
+ align:start position:0%
+kind of definition well I might talk
+about um sort of V I might talk about
+
+ align:start position:0%
+about um sort of V I might talk about
+ 
+
+ align:start position:0%
+about um sort of V I might talk about
+the Ripple ratio in the capacitor
+
+ align:start position:0%
+the Ripple ratio in the capacitor
+ 
+
+ align:start position:0%
+the Ripple ratio in the capacitor
+voltage as being uh you know Delta VC
+
+ align:start position:0%
+voltage as being uh you know Delta VC
+ 
+
+ align:start position:0%
+voltage as being uh you know Delta VC
+Peak to Peak over two / VC and the
+
+ align:start position:0%
+Peak to Peak over two / VC and the
+ 
+
+ align:start position:0%
+Peak to Peak over two / VC and the
+Ripple ratio and the inductor current is
+
+ align:start position:0%
+Ripple ratio and the inductor current is
+ 
+
+ align:start position:0%
+Ripple ratio and the inductor current is
+being Delta I Peak to Peak over 2 / the
+
+ align:start position:0%
+being Delta I Peak to Peak over 2 / the
+ 
+
+ align:start position:0%
+being Delta I Peak to Peak over 2 / the
+DC inductor current
+
+ align:start position:0%
+DC inductor current
+ 
+
+ align:start position:0%
+DC inductor current
+okay and we can then use the Ripple
+
+ align:start position:0%
+okay and we can then use the Ripple
+ 
+
+ align:start position:0%
+okay and we can then use the Ripple
+ratio that I'm talking about to
+
+ align:start position:0%
+ratio that I'm talking about to
+ 
+
+ align:start position:0%
+ratio that I'm talking about to
+relate um sort of average values to
+
+ align:start position:0%
+relate um sort of average values to
+ 
+
+ align:start position:0%
+relate um sort of average values to
+actual Peak values because we know the
+
+ align:start position:0%
+actual Peak values because we know the
+ 
+
+ align:start position:0%
+actual Peak values because we know the
+Ripple's triangular okay there's another
+
+ align:start position:0%
+Ripple's triangular okay there's another
+ 
+
+ align:start position:0%
+Ripple's triangular okay there's another
+way we can use this too is a way to
+
+ align:start position:0%
+way we can use this too is a way to
+ 
+
+ align:start position:0%
+way we can use this too is a way to
+start thinking about as I ch change the
+
+ align:start position:0%
+start thinking about as I ch change the
+ 
+
+ align:start position:0%
+start thinking about as I ch change the
+Ripple ratio of my converter how much
+
+ align:start position:0%
+Ripple ratio of my converter how much
+ 
+
+ align:start position:0%
+Ripple ratio of my converter how much
+Ripple is allowed in my converter how
+
+ align:start position:0%
+Ripple is allowed in my converter how
+ 
+
+ align:start position:0%
+Ripple is allowed in my converter how
+big does the converter get okay I've
+
+ align:start position:0%
+big does the converter get okay I've
+ 
+
+ align:start position:0%
+big does the converter get okay I've
+come up with Expressions I need this big
+
+ align:start position:0%
+come up with Expressions I need this big
+ 
+
+ align:start position:0%
+come up with Expressions I need this big
+an inductor or this big a capacitor if I
+
+ align:start position:0%
+an inductor or this big a capacitor if I
+ 
+
+ align:start position:0%
+an inductor or this big a capacitor if I
+knew those factors but it might be nice
+
+ align:start position:0%
+knew those factors but it might be nice
+ 
+
+ align:start position:0%
+knew those factors but it might be nice
+to be able to express that a little bit
+
+ align:start position:0%
+to be able to express that a little bit
+ 
+
+ align:start position:0%
+to be able to express that a little bit
+better H how does that relate to the
+
+ align:start position:0%
+better H how does that relate to the
+ 
+
+ align:start position:0%
+better H how does that relate to the
+size of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+component that's a very complicated
+
+ align:start position:0%
+component that's a very complicated
+ 
+
+ align:start position:0%
+component that's a very complicated
+question in general right saying you
+
+ align:start position:0%
+question in general right saying you
+ 
+
+ align:start position:0%
+question in general right saying you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+how physically big is my inductor or
+
+ align:start position:0%
+how physically big is my inductor or
+ 
+
+ align:start position:0%
+how physically big is my inductor or
+capacitor going to be that that's a hard
+
+ align:start position:0%
+capacitor going to be that that's a hard
+ 
+
+ align:start position:0%
+capacitor going to be that that's a hard
+question to answer because and we're
+
+ align:start position:0%
+question to answer because and we're
+ 
+
+ align:start position:0%
+question to answer because and we're
+going to see that when we design we
+
+ align:start position:0%
+going to see that when we design we
+ 
+
+ align:start position:0%
+going to see that when we design we
+start to design the components
+
+ align:start position:0%
+start to design the components
+ 
+
+ align:start position:0%
+start to design the components
+themselves but it's reasonable to expect
+
+ align:start position:0%
+themselves but it's reasonable to expect
+ 
+
+ align:start position:0%
+themselves but it's reasonable to expect
+that to first
+
+ align:start position:0%
+that to first
+ 
+
+ align:start position:0%
+that to first
+order the size of your component the
+
+ align:start position:0%
+order the size of your component the
+ 
+
+ align:start position:0%
+order the size of your component the
+physical size of your component ought to
+
+ align:start position:0%
+physical size of your component ought to
+ 
+
+ align:start position:0%
+physical size of your component ought to
+be related to the amount of energy it
+
+ align:start position:0%
+be related to the amount of energy it
+ 
+
+ align:start position:0%
+be related to the amount of energy it
+stores right if I if I have to store
+
+ align:start position:0%
+stores right if I if I have to store
+ 
+
+ align:start position:0%
+stores right if I if I have to store
+twice as much energy and I get a certain
+
+ align:start position:0%
+twice as much energy and I get a certain
+ 
+
+ align:start position:0%
+twice as much energy and I get a certain
+energy density if you imagine
+
+ align:start position:0%
+energy density if you imagine
+ 
+
+ align:start position:0%
+energy density if you imagine
+of storage then twice as much energy
+
+ align:start position:0%
+of storage then twice as much energy
+ 
+
+ align:start position:0%
+of storage then twice as much energy
+storage ought to be twice as much size
+
+ align:start position:0%
+storage ought to be twice as much size
+ 
+
+ align:start position:0%
+storage ought to be twice as much size
+to first order right
+
+ align:start position:0%
+to first order right
+ 
+
+ align:start position:0%
+to first order right
+so Engineers often
+
+ align:start position:0%
+so Engineers often
+ 
+
+ align:start position:0%
+so Engineers often
+use energy storage of the components as
+
+ align:start position:0%
+use energy storage of the components as
+ 
+
+ align:start position:0%
+use energy storage of the components as
+a very crude standing for how physically
+
+ align:start position:0%
+a very crude standing for how physically
+ 
+
+ align:start position:0%
+a very crude standing for how physically
+big the components are going to be and I
+
+ align:start position:0%
+big the components are going to be and I
+ 
+
+ align:start position:0%
+big the components are going to be and I
+want to emphasize it's a very crude
+
+ align:start position:0%
+want to emphasize it's a very crude
+ 
+
+ align:start position:0%
+want to emphasize it's a very crude
+standing it's not true necessarily that
+
+ align:start position:0%
+standing it's not true necessarily that
+ 
+
+ align:start position:0%
+standing it's not true necessarily that
+it's a you know it's exactly
+
+ align:start position:0%
+it's a you know it's exactly
+ 
+
+ align:start position:0%
+it's a you know it's exactly
+proportional relationship or something
+
+ align:start position:0%
+proportional relationship or something
+ 
+
+ align:start position:0%
+proportional relationship or something
+like that it's not but it's at least a
+
+ align:start position:0%
+like that it's not but it's at least a
+ 
+
+ align:start position:0%
+like that it's not but it's at least a
+rough measure that you can get your
+
+ align:start position:0%
+rough measure that you can get your
+ 
+
+ align:start position:0%
+rough measure that you can get your
+hands
+
+ align:start position:0%
+hands
+ 
+
+ align:start position:0%
+hands
+around okay so let's think about what
+
+ align:start position:0%
+around okay so let's think about what
+ 
+
+ align:start position:0%
+around okay so let's think about what
+that might mean
+
+ align:start position:0%
+that might mean
+ 
+
+ align:start position:0%
+that might mean
+okay well um let's think about um the
+
+ align:start position:0%
+okay well um let's think about um the
+ 
+
+ align:start position:0%
+okay well um let's think about um the
+energy storage of the capacitor right
+
+ align:start position:0%
+energy storage of the capacitor right
+ 
+
+ align:start position:0%
+energy storage of the capacitor right
+I've got an expression here for the
+
+ align:start position:0%
+I've got an expression here for the
+ 
+
+ align:start position:0%
+I've got an expression here for the
+energy storage of the
+
+ align:start position:0%
+energy storage of the
+ 
+
+ align:start position:0%
+energy storage of the
+capacitor okay um so we said that
+
+ align:start position:0%
+capacitor okay um so we said that
+ 
+
+ align:start position:0%
+capacitor okay um so we said that
+c has to be of this size
+
+ align:start position:0%
+c has to be of this size
+ 
+
+ align:start position:0%
+c has to be of this size
+okay and in my Boost converter iil is
+
+ align:start position:0%
+okay and in my Boost converter iil is
+ 
+
+ align:start position:0%
+okay and in my Boost converter iil is
+the same thing as
+
+ align:start position:0%
+the same thing as
+ 
+
+ align:start position:0%
+the same thing as
+i1
+
+ align:start position:0%
+i1
+ 
+
+ align:start position:0%
+i1
+right so um what I get is for a boost
+
+ align:start position:0%
+right so um what I get is for a boost
+ 
+
+ align:start position:0%
+right so um what I get is for a boost
+converter then I get C is greater than
+
+ align:start position:0%
+converter then I get C is greater than
+ 
+
+ align:start position:0%
+converter then I get C is greater than
+or equal to
+
+ align:start position:0%
+or equal to
+ 
+
+ align:start position:0%
+or equal to
+D * 1us d i is the same thing as I
+
+ align:start position:0%
+D * 1us d i is the same thing as I
+ 
+
+ align:start position:0%
+D * 1us d i is the same thing as I
+Capital
+
+ align:start position:0%
+Capital
+ 
+
+ align:start position:0%
+Capital
+i1 uh this is the switching period
+
+ align:start position:0%
+i1 uh this is the switching period
+ 
+
+ align:start position:0%
+i1 uh this is the switching period
+divided by Delta VC Peak to Peak over
+
+ align:start position:0%
+divided by Delta VC Peak to Peak over
+ 
+
+ align:start position:0%
+divided by Delta VC Peak to Peak over
+two I'm sorry Delta VC Peak to Peak okay
+
+ align:start position:0%
+two I'm sorry Delta VC Peak to Peak okay
+ 
+
+ align:start position:0%
+two I'm sorry Delta VC Peak to Peak okay
+let me substitute this
+
+ align:start position:0%
+let me substitute this
+ 
+
+ align:start position:0%
+let me substitute this
+in so that means C is got to be greater
+
+ align:start position:0%
+in so that means C is got to be greater
+ 
+
+ align:start position:0%
+in so that means C is got to be greater
+than or equal to D * 1us d i1
+
+ align:start position:0%
+than or equal to D * 1us d i1
+ 
+
+ align:start position:0%
+than or equal to D * 1us d i1
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+uh divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 DC which is also equal to
+
+ align:start position:0%
+2 DC which is also equal to
+ 
+
+ align:start position:0%
+2 DC which is also equal to
+V2 uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RC Ripple ratio of the capacitor okay so
+
+ align:start position:0%
+RC Ripple ratio of the capacitor okay so
+ 
+
+ align:start position:0%
+RC Ripple ratio of the capacitor okay so
+this is the same thing just expressed in
+
+ align:start position:0%
+this is the same thing just expressed in
+ 
+
+ align:start position:0%
+this is the same thing just expressed in
+terms of input and output
+
+ align:start position:0%
+terms of input and output
+ 
+
+ align:start position:0%
+terms of input and output
+quantities and uh the Ripple ratio on
+
+ align:start position:0%
+quantities and uh the Ripple ratio on
+ 
+
+ align:start position:0%
+quantities and uh the Ripple ratio on
+the capacitor how much percentage Ripple
+
+ align:start position:0%
+the capacitor how much percentage Ripple
+ 
+
+ align:start position:0%
+the capacitor how much percentage Ripple
+am I going to allow in the capacitor
+
+ align:start position:0%
+am I going to allow in the capacitor
+ 
+
+ align:start position:0%
+am I going to allow in the capacitor
+everybody buy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if I then came back and said okay
+
+ align:start position:0%
+that if I then came back and said okay
+ 
+
+ align:start position:0%
+that if I then came back and said okay
+how much energy is stored in the
+
+ align:start position:0%
+how much energy is stored in the
+ 
+
+ align:start position:0%
+how much energy is stored in the
+capacitor energy in the capacitor is
+
+ align:start position:0%
+capacitor energy in the capacitor is
+ 
+
+ align:start position:0%
+capacitor energy in the capacitor is
+simply equal to 12 C VC Peak squared
+
+ align:start position:0%
+simply equal to 12 C VC Peak squared
+ 
+
+ align:start position:0%
+simply equal to 12 C VC Peak squared
+right if I got to go buy a capacitor and
+
+ align:start position:0%
+right if I got to go buy a capacitor and
+ 
+
+ align:start position:0%
+right if I got to go buy a capacitor and
+I want to know how much energy it stores
+
+ align:start position:0%
+I want to know how much energy it stores
+ 
+
+ align:start position:0%
+I want to know how much energy it stores
+I care about the peak voltage I'm going
+
+ align:start position:0%
+I care about the peak voltage I'm going
+ 
+
+ align:start position:0%
+I care about the peak voltage I'm going
+to put on the capacitor because that's
+
+ align:start position:0%
+to put on the capacitor because that's
+ 
+
+ align:start position:0%
+to put on the capacitor because that's
+what the capacitor is rated for and I
+
+ align:start position:0%
+what the capacitor is rated for and I
+ 
+
+ align:start position:0%
+what the capacitor is rated for and I
+care about the capacitance value I'm
+
+ align:start position:0%
+care about the capacitance value I'm
+ 
+
+ align:start position:0%
+care about the capacitance value I'm
+using and that's energy is2 cv^ s
+
+ align:start position:0%
+using and that's energy is2 cv^ s
+ 
+
+ align:start position:0%
+using and that's energy is2 cv^ s
+everybody buy
+
+ align:start position:0%
+everybody buy
+ 
+
+ align:start position:0%
+everybody buy
+that so what is that going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be all that's going to be is
+
+ align:start position:0%
+be all that's going to be is
+ 
+
+ align:start position:0%
+be all that's going to be is
+EC is equal to 12 I'm just going to
+
+ align:start position:0%
+EC is equal to 12 I'm just going to
+ 
+
+ align:start position:0%
+EC is equal to 12 I'm just going to
+substitute in this here so it's going to
+
+ align:start position:0%
+substitute in this here so it's going to
+ 
+
+ align:start position:0%
+substitute in this here so it's going to
+be D * 1 - d i1 t over
+
+ align:start position:0%
+be D * 1 - d i1 t over
+ 
+
+ align:start position:0%
+be D * 1 - d i1 t over
+2 V2
+
+ align:start position:0%
+2 V2
+ 
+
+ align:start position:0%
+2 V2
+RC and v v Peak squar on the capacitor
+
+ align:start position:0%
+RC and v v Peak squar on the capacitor
+ 
+
+ align:start position:0%
+RC and v v Peak squar on the capacitor
+is simply equal to V2
+
+ align:start position:0%
+is simply equal to V2
+ 
+
+ align:start position:0%
+is simply equal to V2
+Time 1 plus the Ripple ratio on the
+
+ align:start position:0%
+Time 1 plus the Ripple ratio on the
+ 
+
+ align:start position:0%
+Time 1 plus the Ripple ratio on the
+capacitor quantity
+
+ align:start position:0%
+capacitor quantity
+ 
+
+ align:start position:0%
+capacitor quantity
+squared right this is V Peak it's V2 * 1
+
+ align:start position:0%
+squared right this is V Peak it's V2 * 1
+ 
+
+ align:start position:0%
+squared right this is V Peak it's V2 * 1
+ratio okay if I were then to rewrite
+
+ align:start position:0%
+ratio okay if I were then to rewrite
+ 
+
+ align:start position:0%
+ratio okay if I were then to rewrite
+this what I would get is
+
+ align:start position:0%
+this what I would get is
+ 
+
+ align:start position:0%
+this what I would get is
+D time if I look at this by the
+
+ align:start position:0%
+D time if I look at this by the
+ 
+
+ align:start position:0%
+D time if I look at this by the
+way uh d d * 1 uh 1us di
+
+ align:start position:0%
+way uh d d * 1 uh 1us di
+ 
+
+ align:start position:0%
+way uh d d * 1 uh 1us di
+i1 is
+
+ align:start position:0%
+i1 is
+ 
+
+ align:start position:0%
+i1 is
+I2 right this is the same thing as
+
+ align:start position:0%
+I2 right this is the same thing as
+ 
+
+ align:start position:0%
+I2 right this is the same thing as
+I2
+
+ align:start position:0%
+I2
+ 
+
+ align:start position:0%
+I2
+T over
+
+ align:start position:0%
+T over
+ 
+
+ align:start position:0%
+T over
+two I'm sorry over four 2 * 2 is over 4
+
+ align:start position:0%
+two I'm sorry over four 2 * 2 is over 4
+ 
+
+ align:start position:0%
+two I'm sorry over four 2 * 2 is over 4
+then this is going to be v2^ 2 / V2 is
+
+ align:start position:0%
+then this is going to be v2^ 2 / V2 is
+ 
+
+ align:start position:0%
+then this is going to be v2^ 2 / V2 is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+V2 and then times 1 plus the Ripple
+
+ align:start position:0%
+V2 and then times 1 plus the Ripple
+ 
+
+ align:start position:0%
+V2 and then times 1 plus the Ripple
+ratio squar over the Ripple
+
+ align:start position:0%
+ratio squar over the Ripple
+ 
+
+ align:start position:0%
+ratio squar over the Ripple
+ratio okay and I'll rewrite one more
+
+ align:start position:0%
+ratio okay and I'll rewrite one more
+ 
+
+ align:start position:0%
+ratio okay and I'll rewrite one more
+thing V2 * I2 is just the output power
+
+ align:start position:0%
+thing V2 * I2 is just the output power
+ 
+
+ align:start position:0%
+thing V2 * I2 is just the output power
+right so this is going to be D * P
+
+ align:start position:0%
+right so this is going to be D * P
+ 
+
+ align:start position:0%
+right so this is going to be D * P
+out time T / 4
+
+ align:start position:0%
+out time T / 4
+ 
+
+ align:start position:0%
+out time T / 4
+Time 1 plus the Ripple ratio s over the
+
+ align:start position:0%
+Time 1 plus the Ripple ratio s over the
+ 
+
+ align:start position:0%
+Time 1 plus the Ripple ratio s over the
+Ripple ratio all right I apologize for
+
+ align:start position:0%
+Ripple ratio all right I apologize for
+ 
+
+ align:start position:0%
+Ripple ratio all right I apologize for
+all the math um this is the energy
+
+ align:start position:0%
+all the math um this is the energy
+ 
+
+ align:start position:0%
+all the math um this is the energy
+stored in the
+
+ align:start position:0%
+stored in the
+ 
+
+ align:start position:0%
+stored in the
+capacitor okay so why am I telling you
+
+ align:start position:0%
+capacitor okay so why am I telling you
+ 
+
+ align:start position:0%
+capacitor okay so why am I telling you
+this this tells
+
+ align:start position:0%
+this this tells
+ 
+
+ align:start position:0%
+this this tells
+me as a very broad function of Ripple
+
+ align:start position:0%
+me as a very broad function of Ripple
+ 
+
+ align:start position:0%
+me as a very broad function of Ripple
+and operating power and everything how
+
+ align:start position:0%
+and operating power and everything how
+ 
+
+ align:start position:0%
+and operating power and everything how
+much energy do I have to go put in that
+
+ align:start position:0%
+much energy do I have to go put in that
+ 
+
+ align:start position:0%
+much energy do I have to go put in that
+capacitor which I can use as a crude
+
+ align:start position:0%
+capacitor which I can use as a crude
+ 
+
+ align:start position:0%
+capacitor which I can use as a crude
+measure of how big and expensive that
+
+ align:start position:0%
+measure of how big and expensive that
+ 
+
+ align:start position:0%
+measure of how big and expensive that
+capacitor is going to be okay so what
+
+ align:start position:0%
+capacitor is going to be okay so what
+ 
+
+ align:start position:0%
+capacitor is going to be okay so what
+makes my capacitor requirement
+
+ align:start position:0%
+makes my capacitor requirement
+ 
+
+ align:start position:0%
+makes my capacitor requirement
+bigger it's proportion the energy
+
+ align:start position:0%
+bigger it's proportion the energy
+ 
+
+ align:start position:0%
+bigger it's proportion the energy
+storage which I'm claiming ought to be
+
+ align:start position:0%
+storage which I'm claiming ought to be
+ 
+
+ align:start position:0%
+storage which I'm claiming ought to be
+proportional to the size is proportional
+
+ align:start position:0%
+proportional to the size is proportional
+ 
+
+ align:start position:0%
+proportional to the size is proportional
+to the output power that's sort of
+
+ align:start position:0%
+to the output power that's sort of
+ 
+
+ align:start position:0%
+to the output power that's sort of
+physically reasonable right if I double
+
+ align:start position:0%
+physically reasonable right if I double
+ 
+
+ align:start position:0%
+physically reasonable right if I double
+the power maybe I need twice as much
+
+ align:start position:0%
+the power maybe I need twice as much
+ 
+
+ align:start position:0%
+the power maybe I need twice as much
+energy storage to do the same conversion
+
+ align:start position:0%
+energy storage to do the same conversion
+ 
+
+ align:start position:0%
+energy storage to do the same conversion
+function okay it's proportional to D
+
+ align:start position:0%
+function okay it's proportional to D
+ 
+
+ align:start position:0%
+function okay it's proportional to D
+well keep in mind the bigger D is the
+
+ align:start position:0%
+well keep in mind the bigger D is the
+ 
+
+ align:start position:0%
+well keep in mind the bigger D is the
+bigger the voltage conversion ratio is
+
+ align:start position:0%
+bigger the voltage conversion ratio is
+ 
+
+ align:start position:0%
+bigger the voltage conversion ratio is
+right because V2 is V1 over 1 minus D so
+
+ align:start position:0%
+right because V2 is V1 over 1 minus D so
+ 
+
+ align:start position:0%
+right because V2 is V1 over 1 minus D so
+the more I'm stepping up voltage the
+
+ align:start position:0%
+the more I'm stepping up voltage the
+ 
+
+ align:start position:0%
+the more I'm stepping up voltage the
+bigger D I need so if I want to do a
+
+ align:start position:0%
+bigger D I need so if I want to do a
+ 
+
+ align:start position:0%
+bigger D I need so if I want to do a
+bigger Step Up conversion that means I
+
+ align:start position:0%
+bigger Step Up conversion that means I
+ 
+
+ align:start position:0%
+bigger Step Up conversion that means I
+need more energy storage in my
+
+ align:start position:0%
+need more energy storage in my
+ 
+
+ align:start position:0%
+need more energy storage in my
+capacitor
+
+ align:start position:0%
+capacitor
+ 
+
+ align:start position:0%
+capacitor
+okay also notice that this function over
+
+ align:start position:0%
+okay also notice that this function over
+ 
+
+ align:start position:0%
+okay also notice that this function over
+here is some function of the Ripple
+
+ align:start position:0%
+here is some function of the Ripple
+ 
+
+ align:start position:0%
+here is some function of the Ripple
+ratio it turns out for most ranges of
+
+ align:start position:0%
+ratio it turns out for most ranges of
+ 
+
+ align:start position:0%
+ratio it turns out for most ranges of
+Ripple ratio which I care about which
+
+ align:start position:0%
+Ripple ratio which I care about which
+ 
+
+ align:start position:0%
+Ripple ratio which I care about which
+are much less than one making Ripple
+
+ align:start position:0%
+are much less than one making Ripple
+ 
+
+ align:start position:0%
+are much less than one making Ripple
+ratio smaller Mak this fraction
+
+ align:start position:0%
+ratio smaller Mak this fraction
+ 
+
+ align:start position:0%
+ratio smaller Mak this fraction
+bigger okay so if I tell you I need less
+
+ align:start position:0%
+bigger okay so if I tell you I need less
+ 
+
+ align:start position:0%
+bigger okay so if I tell you I need less
+Ripple smaller Ripple ratio suddenly my
+
+ align:start position:0%
+Ripple smaller Ripple ratio suddenly my
+ 
+
+ align:start position:0%
+Ripple smaller Ripple ratio suddenly my
+energy storage got bigger all right so
+
+ align:start position:0%
+energy storage got bigger all right so
+ 
+
+ align:start position:0%
+energy storage got bigger all right so
+that says if I want really nice input
+
+ align:start position:0%
+that says if I want really nice input
+ 
+
+ align:start position:0%
+that says if I want really nice input
+and output waveforms I'm going to need
+
+ align:start position:0%
+and output waveforms I'm going to need
+ 
+
+ align:start position:0%
+and output waveforms I'm going to need
+more energy storage okay lastly notice
+
+ align:start position:0%
+more energy storage okay lastly notice
+ 
+
+ align:start position:0%
+more energy storage okay lastly notice
+that this is the switching period here
+
+ align:start position:0%
+that this is the switching period here
+ 
+
+ align:start position:0%
+that this is the switching period here
+or one over the switching frequency the
+
+ align:start position:0%
+or one over the switching frequency the
+ 
+
+ align:start position:0%
+or one over the switching frequency the
+energy storage I need is proportional to
+
+ align:start position:0%
+energy storage I need is proportional to
+ 
+
+ align:start position:0%
+energy storage I need is proportional to
+the switching period or one over the
+
+ align:start position:0%
+the switching period or one over the
+ 
+
+ align:start position:0%
+the switching period or one over the
+switching frequency that means if I
+
+ align:start position:0%
+switching frequency that means if I
+ 
+
+ align:start position:0%
+switching frequency that means if I
+switch slowly
+
+ align:start position:0%
+switch slowly
+ 
+
+ align:start position:0%
+switch slowly
+I need very big capacitors and I showed
+
+ align:start position:0%
+I need very big capacitors and I showed
+ 
+
+ align:start position:0%
+I need very big capacitors and I showed
+you this for the capacitor in the
+
+ align:start position:0%
+you this for the capacitor in the
+ 
+
+ align:start position:0%
+you this for the capacitor in the
+lecture notes I put the equivalent
+
+ align:start position:0%
+lecture notes I put the equivalent
+ 
+
+ align:start position:0%
+lecture notes I put the equivalent
+expression for the inductor basically if
+
+ align:start position:0%
+expression for the inductor basically if
+ 
+
+ align:start position:0%
+expression for the inductor basically if
+you just substitute Ripple ratio of the
+
+ align:start position:0%
+you just substitute Ripple ratio of the
+ 
+
+ align:start position:0%
+you just substitute Ripple ratio of the
+inductor for capacitor you get the same
+
+ align:start position:0%
+inductor for capacitor you get the same
+ 
+
+ align:start position:0%
+inductor for capacitor you get the same
+result okay so what that says is either
+
+ align:start position:0%
+result okay so what that says is either
+ 
+
+ align:start position:0%
+result okay so what that says is either
+the inductor or capacitor going to get
+
+ align:start position:0%
+the inductor or capacitor going to get
+ 
+
+ align:start position:0%
+the inductor or capacitor going to get
+bigger and bigger and bigger if I either
+
+ align:start position:0%
+bigger and bigger and bigger if I either
+ 
+
+ align:start position:0%
+bigger and bigger and bigger if I either
+um reduce my switching frequency or
+
+ align:start position:0%
+um reduce my switching frequency or
+ 
+
+ align:start position:0%
+um reduce my switching frequency or
+reduce the amount of
+
+ align:start position:0%
+reduce the amount of
+ 
+
+ align:start position:0%
+reduce the amount of
+Ripple okay and that's what gives me a
+
+ align:start position:0%
+Ripple okay and that's what gives me a
+ 
+
+ align:start position:0%
+Ripple okay and that's what gives me a
+means to start saying gez I better limit
+
+ align:start position:0%
+means to start saying gez I better limit
+ 
+
+ align:start position:0%
+means to start saying gez I better limit
+if I want to limit the physical size or
+
+ align:start position:0%
+if I want to limit the physical size or
+ 
+
+ align:start position:0%
+if I want to limit the physical size or
+the cost of this thing I'm going to have
+
+ align:start position:0%
+the cost of this thing I'm going to have
+ 
+
+ align:start position:0%
+the cost of this thing I'm going to have
+to start making some decisions about how
+
+ align:start position:0%
+to start making some decisions about how
+ 
+
+ align:start position:0%
+to start making some decisions about how
+I pick my
+
+ align:start position:0%
+I pick my
+ 
+
+ align:start position:0%
+I pick my
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that just gives you a A first order
+
+ align:start position:0%
+and that just gives you a A first order
+ 
+
+ align:start position:0%
+and that just gives you a A first order
+place to be in terms of picking
+
+ align:start position:0%
+place to be in terms of picking
+ 
+
+ align:start position:0%
+place to be in terms of picking
+component values okay and this is only
+
+ align:start position:0%
+component values okay and this is only
+ 
+
+ align:start position:0%
+component values okay and this is only
+one thing this is based on Ripple we're
+
+ align:start position:0%
+one thing this is based on Ripple we're
+ 
+
+ align:start position:0%
+one thing this is based on Ripple we're
+also going to talk about based on things
+
+ align:start position:0%
+also going to talk about based on things
+ 
+
+ align:start position:0%
+also going to talk about based on things
+like transient performance and that kind
+
+ align:start position:0%
+like transient performance and that kind
+ 
+
+ align:start position:0%
+like transient performance and that kind
+of thing but this gives you at least a
+
+ align:start position:0%
+of thing but this gives you at least a
+ 
+
+ align:start position:0%
+of thing but this gives you at least a
+place to start for picking component
+
+ align:start position:0%
+place to start for picking component
+ 
+
+ align:start position:0%
+place to start for picking component
+values to get down to certain allowed
+
+ align:start position:0%
+values to get down to certain allowed
+ 
+
+ align:start position:0%
+values to get down to certain allowed
+levels of
+
+ align:start position:0%
+levels of
+ 
+
+ align:start position:0%
+levels of
+Ripple any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that these results are all for the Boost
+
+ align:start position:0%
+that these results are all for the Boost
+ 
+
+ align:start position:0%
+that these results are all for the Boost
+converter these results for the Boost
+
+ align:start position:0%
+converter these results for the Boost
+ 
+
+ align:start position:0%
+converter these results for the Boost
+converter um you can derive exactly
+
+ align:start position:0%
+converter um you can derive exactly
+ 
+
+ align:start position:0%
+converter um you can derive exactly
+equivalent results for the buck
+
+ align:start position:0%
+equivalent results for the buck
+ 
+
+ align:start position:0%
+equivalent results for the buck
+converter or any other converter you
+
+ align:start position:0%
+converter or any other converter you
+ 
+
+ align:start position:0%
+converter or any other converter you
+want and people often do um I will say
+
+ align:start position:0%
+want and people often do um I will say
+ 
+
+ align:start position:0%
+want and people often do um I will say
+that if I said how much EC or eel is
+
+ align:start position:0%
+that if I said how much EC or eel is
+ 
+
+ align:start position:0%
+that if I said how much EC or eel is
+required for a boost converter at a
+
+ align:start position:0%
+required for a boost converter at a
+ 
+
+ align:start position:0%
+required for a boost converter at a
+certain conversion ratio and I went back
+
+ align:start position:0%
+certain conversion ratio and I went back
+ 
+
+ align:start position:0%
+certain conversion ratio and I went back
+and did it for the buck boost converter
+
+ align:start position:0%
+and did it for the buck boost converter
+ 
+
+ align:start position:0%
+and did it for the buck boost converter
+that we started with it' be
+
+ align:start position:0%
+that we started with it' be
+ 
+
+ align:start position:0%
+that we started with it' be
+significantly
+
+ align:start position:0%
+significantly
+ 
+
+ align:start position:0%
+significantly
+worse much more energy storage and what
+
+ align:start position:0%
+worse much more energy storage and what
+ 
+
+ align:start position:0%
+worse much more energy storage and what
+that would mean is I'm going to end up
+
+ align:start position:0%
+that would mean is I'm going to end up
+ 
+
+ align:start position:0%
+that would mean is I'm going to end up
+with a bigger more expensive converter
+
+ align:start position:0%
+with a bigger more expensive converter
+ 
+
+ align:start position:0%
+with a bigger more expensive converter
+and what what this comes down to is you
+
+ align:start position:0%
+and what what this comes down to is you
+ 
+
+ align:start position:0%
+and what what this comes down to is you
+know you're competing right like the
+
+ align:start position:0%
+know you're competing right like the
+ 
+
+ align:start position:0%
+know you're competing right like the
+other guy's designing something you're
+
+ align:start position:0%
+other guy's designing something you're
+ 
+
+ align:start position:0%
+other guy's designing something you're
+designing something and yours is smaller
+
+ align:start position:0%
+designing something and yours is smaller
+ 
+
+ align:start position:0%
+designing something and yours is smaller
+and more efficient because you've used
+
+ align:start position:0%
+and more efficient because you've used
+ 
+
+ align:start position:0%
+and more efficient because you've used
+less energy storage to do the same
+
+ align:start position:0%
+less energy storage to do the same
+ 
+
+ align:start position:0%
+less energy storage to do the same
+conversion function you know
+
+ align:start position:0%
+conversion function you know
+ 
+
+ align:start position:0%
+conversion function you know
+you can win or lose based on those
+
+ align:start position:0%
+you can win or lose based on those
+ 
+
+ align:start position:0%
+you can win or lose based on those
+decisions but yes you can derive similar
+
+ align:start position:0%
+decisions but yes you can derive similar
+ 
+
+ align:start position:0%
+decisions but yes you can derive similar
+results and the typical thing is true
+
+ align:start position:0%
+results and the typical thing is true
+ 
+
+ align:start position:0%
+results and the typical thing is true
+the more conversion transformation
+
+ align:start position:0%
+the more conversion transformation
+ 
+
+ align:start position:0%
+the more conversion transformation
+you're doing you tend to require more
+
+ align:start position:0%
+you're doing you tend to require more
+ 
+
+ align:start position:0%
+you're doing you tend to require more
+energy storage the lower the Ripple you
+
+ align:start position:0%
+energy storage the lower the Ripple you
+ 
+
+ align:start position:0%
+energy storage the lower the Ripple you
+need you require more energy storage the
+
+ align:start position:0%
+need you require more energy storage the
+ 
+
+ align:start position:0%
+need you require more energy storage the
+slower you switch or the higher the
+
+ align:start position:0%
+slower you switch or the higher the
+ 
+
+ align:start position:0%
+slower you switch or the higher the
+power you require more energy
+
+ align:start position:0%
+power you require more energy
+ 
+
+ align:start position:0%
+power you require more energy
+storage any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay next time we'll start
+
+ align:start position:0%
+questions okay next time we'll start
+ 
+
+ align:start position:0%
+questions okay next time we'll start
+thinking a little bit more about
+
+ align:start position:0%
+thinking a little bit more about
+ 
+
+ align:start position:0%
+thinking a little bit more about
+conversion Ripple and what can happen in
+
+ align:start position:0%
+conversion Ripple and what can happen in
+ 
+
+ align:start position:0%
+conversion Ripple and what can happen in
+extreme cases have a great day
\ No newline at end of file
diff --git a/Q8SoG1OIveU.txt b/Q8SoG1OIveU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6038d3efa565d97367db88b426552bfdad66b34a
--- /dev/null
+++ b/Q8SoG1OIveU.txt
@@ -0,0 +1,2725 @@
+OPERATOR: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Last lecture we were
+talking about classes,
+
+and object-oriented programming,
+and we're going
+
+to come back to it today.
+
+I'm going to remind you, we were
+talking about it because
+
+we suggested it is a really
+powerful way of structuring
+
+systems, and that's really why
+we want to use it, It's a very
+
+common way of structuring
+systems. So today I'm going to
+
+pick up on a bunch of more
+nuanced, or more complex if
+
+you like, ways of leveraging
+the power of classes.
+
+But we're going to see a bunch
+of examples that are going to
+
+give us a sense.
+
+I'm going to talk about
+inheritance, we're going to
+
+talk about shadowing, we're
+going to talk about iterators.
+
+But before get to it, I want to
+start by just highlighting,
+
+sort of, what was the
+point of classes?
+
+So I'll remind you.
+
+A class, I said, was basically
+a template for an
+
+abstract data type.
+
+And this was really to drive
+home this idea of modularity.
+
+I want the ability to say, I've
+got a set of things that
+
+naturally belong together,
+I'm going to cluster them
+
+together, I want to treat it
+like it's a primitive, I want
+
+to treat it like it's a float
+or an int or a string.
+
+Is this going to be a point
+or a segment or something
+
+different like that.
+
+So it's really a way, as I
+said, of just trying to
+
+cluster data together.
+
+And this is a notion of
+modularity slash abstraction
+
+where I'm treating them
+as primitives.
+
+But the second thing we talked
+about is that we also have a
+
+set of methods, using the
+special name method because
+
+we're talking classes.
+
+But basically functions that are
+designed to deal with this
+
+data structure.
+
+We're trying to group those
+together as well.
+
+So we cluster data
+and methods.
+
+Second key thing we said was,
+in the ideal case, which
+
+unfortunately Python isn't, but
+we'll come back to that,
+
+in the ideal case, we would have
+data hiding, and by data
+
+hiding, which is sort of a
+version of encapsulation, what
+
+we meant was that you could
+only get to the internal
+
+pieces of that data structure
+through a proscribed method.
+
+Proscribed meaning it's
+something I set up.
+
+So data hiding saying, you would
+only access the parts
+
+through a method.
+
+And as we said, unfortunately
+Python does not enforce this.
+
+Meaning that I could create one
+of these data structures,
+
+ideally I'd have a method, that
+I'm going to see some
+
+examples of that I used to get
+the parts out, unfortunately
+
+in Python you could take the
+name the instance dot some
+
+internal variable you'll
+get it back.
+
+It is exposed.
+
+And this is actually just
+not a good idea.
+
+So I suggested in my very bad
+humor, that you practice
+
+computational hygiene and you
+only use appropriate methods
+
+to get the parts out.
+
+OK didn't laugh the joke last
+time, you're not going to
+
+laugh at it this time,
+I don't blame you.
+
+All right, and then the last
+piece of this is that we said
+
+the class is a template.
+
+When we call that class,
+it makes an instance.
+
+So class is used to make
+instances, meaning particular
+
+versions, of that structure,
+and we said inside the
+
+instances we have a
+set of attributes.
+
+Internal variables, methods,
+that are going to belong to
+
+that structure.
+
+OK, so with that in mind, here's
+what I want to do.
+
+I'm going to show you a set of
+examples, and I want to warn
+
+you ahead of time, the code
+handout today is a little
+
+longer than normal because we
+want to build essentially an
+
+extended example of a sequence
+of examples of classes.
+
+We're going to see the idea,
+of which we're gonna talk
+
+about, of inheritance or
+hierarchy, in which we can
+
+have classes that are
+
+specializations of other classes.
+
+We're gonna see how we can
+inherit methods, how we can
+
+shadow methods, how we can use
+methods in a variety of ways.
+
+So this is a way of suggesting
+you may find it more
+
+convenient to put notes on the
+code handout rather than in
+
+your own notes.
+
+Do whatever you like, but I
+just wanted to alert you,
+
+we're going to go through a
+little more code than normal.
+
+So, the little environment
+I'm going to build is an
+
+environment of people.
+
+I'll build a simple little
+simulation of people.
+
+So I'm going to start off with
+the first class, which I've
+
+got up on the screen, and it's
+on your handout as well, which
+
+is I'm going to build an
+instance, or a class rather,
+
+of persons.
+
+I'm going to draw a diagram,
+which I'm gonna try and see if
+
+I can do well, over here, of
+the different objects we're
+
+going to have. So I've got, a
+class, and by the way a class
+
+is an object.
+
+Instances are also objects,
+but classes are objects.
+
+We're gonna see why we want
+that in a second.
+
+Because I'm gonna build
+an object, sorry a
+
+class, called a person.
+
+Now, let's walk through some
+of the pieces here.
+
+The first one is, there's
+something a little different.
+
+Remember last time we had that
+keyword class and then a name,
+
+that name, in this case, person
+says this is the name
+
+for the class, and then we
+would have just had the
+
+semicolon and a bunch
+of internal things.
+
+Here I've got something in
+parens, and I want to stress
+
+this is not a variable.
+
+All right, this is not a
+def, this is a class.
+
+I'm going to come back to it,
+but what this is basically
+
+saying is that the person class
+is going to inherit from
+
+another class, which in this
+case is just the built-in
+
+Python object class.
+
+Hold on to that thought, it's
+going to make more sense when
+
+we look at a little more
+interesting example, but I
+
+want to highlight that.
+
+All right now, if we do this,
+as I said before, we can
+
+create a version of a
+person, let me just
+
+call it per, person.
+
+OK?
+
+And what we said last time is,
+when we wanted to create an
+
+instance inside of this class
+definition, we've got one of
+
+those built-in things
+called init.
+
+I'm gonna again remind you, some
+of the methods we have,
+
+Underbar underbar init is going
+to be the thing that
+
+creates the instance.
+
+Actually slightly misspeaking,
+actually Python creates the
+
+instance, but it's one thing
+that fills it in.
+
+So in this case, I'm going to
+give it 2 arguments: Frank
+
+Foobar Now, you might have said,
+wait a minute, init here
+
+has 3 arguments: self, family
+name, and first name.
+
+So again, just to remind you,
+what we said happens here is
+
+that when I call this
+class, person,
+
+I'm creating an instance.
+
+We'll draw a little instance
+diagram down here.
+
+I'm going to give
+it the name per.
+
+And I should have said inside
+of person, we've
+
+got a set of things.
+
+We've got our underbar underbar
+init, we've got, what
+
+else do I have up there?
+
+Family name.
+
+And a bunch of other methods,
+down to say.
+
+What happens inside of Python
+is, when we called the class
+
+definition, person, it creates
+an instance, there it is.
+
+Think of it as a pointer to a
+spot in memory, and then what
+
+we do is, we call, or find, that
+init method, up here, and
+
+we apply it.
+
+And the first argument self,
+points to the instance.
+
+So this object here is
+what self looks at.
+
+Now you can see what
+init's going to do.
+
+It says, oh, inside of self,
+which is pointing to here, let
+
+me bind a variable, which was,
+can read that very carefully,
+
+it's family underbar name,
+to the value I passed
+
+in, which was 4.
+
+Same thing with first name.
+
+OK, so the reason I'm stressing
+this is, self we do
+
+not supply explicitly, it is
+supplied as pointing to the
+
+instance, it's giving us
+that piece of memory.
+
+And that is what then
+gets created.
+
+So here's, now, the
+instance for per.
+
+OK, and I put a little label
+on there, I'm going to call
+
+that an isALink, because it is
+an instance of that class.
+
+God bless you.
+
+All right, so once we got this,
+let's look at what we
+
+can do with person.
+
+That's why I built
+person here.
+
+And as I said, I've
+already bound
+
+basically, those two pieces.
+
+If I want to get a value out,
+I can give person, or per,
+
+rather, this instance,
+a messaging.
+
+In this case I want to get
+family, what did I say, family
+
+name out, now, again I want to
+stress, what is happening
+
+here? per is an instance,
+it's this thing here.
+
+When I say per dot family
+name, I'm sending it a
+
+message, in essence what that
+does is, it says, from here
+
+it's going to go up the chain to
+this class object and find
+
+the appropriate method,
+which was family name.
+
+It is then going to apply
+that to self, which
+
+points to this instance.
+
+And that allows it, therefore,
+is you can see on the code, to
+
+look up under self, what's the
+binding for family name, and
+
+print it back up.
+
+So self is always going to point
+to the instance I want
+
+and I can use it.
+
+OK what else do we
+have in here?
+
+We can get the first name,
+that's not particularly
+
+interesting.
+
+We've got 2 other special
+methods: that's cmp and str.
+
+All right, cmp is our
+comparison method.
+
+And since I, I was about to
+say I blew it last time, I
+
+misspoke last time, a wonderful
+phrase that
+
+politicians like to use,
+I misspoke last time.
+
+Let me clarify again
+what cmp will do.
+
+Underbar underbar cmp is going
+to be the method you're going
+
+to use to compare two instances
+of an object.
+
+Now, let's back up for second.
+
+If I wanted to test equality,
+in fact I could use underbar
+
+underbar eq, under under.
+
+It's natural to think about an
+equality tester as returning a
+
+Boolean, it's either gonna
+be true or false, because
+
+something's either
+equal to or not.
+
+In many languages, comparisons
+also return Booleans, which is
+
+why I went down this
+slippery slope.
+
+For many languages, either it's
+greater than or it's not.
+
+But Python is different.
+
+Python use cmp, in fact it has
+a built in cmp, which is what
+
+we're relying on here.
+
+Where am I, right there.
+
+And what cmp returns
+is 1 of 3 values.
+
+Given 2 objects, it says if the
+first one is less than the
+
+second one, it returns -1, if
+it's equal it returns 0, if
+
+it's greater than,
+it returns 1.
+
+So it allows you this broader
+range of comparisons.
+
+And if you think about it,
+cmp, you could apply on
+
+integers, you could apply it on
+
+floats, apply it on strings.
+
+So it's overloaded, it has the
+ability to do all of those.
+
+And in this case what we're
+saying is, given 2 objects,
+
+let's create a tuple of the
+first, sorry, family and first
+
+name of ourselves, and other is
+another object, family and
+
+first name of that, and then
+just use cmp to compare them.
+
+All right, so it's going
+to use the base pieces.
+
+OK, so it gives me a way
+of doing comparisons.
+
+And str we saw last time as
+well, this is cmp does
+
+comparison, and str is our
+printed representation.
+
+OK.
+
+So what we've got now, is
+a simple little class.
+
+We've also got two
+methods there.
+
+I want to look at them, we're
+gonna come back to them, but
+
+they start to highlight things
+we can do with our classes.
+
+So I've built one simple
+version of it
+
+here, which is per.
+
+And notice I've got another
+method, right up
+
+here, called say.
+
+And say takes two arguments,
+for the moment the second
+
+argument, or the first
+argument's, not going to make
+
+a lot of sense, but say takes
+two arguments besides itself.
+
+It's going to take another
+object to which it's saying
+
+something and the
+thing to say.
+
+Since I only have one object
+here, I'm going to have person
+
+talk to himself.
+
+You may have met a few
+other undergraduates
+
+who have this behavior.
+
+I'll have him talk to himself
+and say, just some random
+
+message the faculty members
+occasionally worry about.
+
+OK, what does this thing do?
+
+Now you're going to see some
+of the power of this.
+
+Again, remember, I'm down here,
+I'm sending this the
+
+message say, it's going to go
+up the chain to find the say
+
+message in person.
+
+And what does say do, it says
+given another object and some
+
+string, it's going to return,
+oh, and interesting things,
+
+part of which you can't
+see on the screen.
+
+First what it does, is it
+gets first name of self.
+
+Remember self is pointing to
+this instance, so it's simply
+
+looks up that binding,
+which is Frank.
+
+It's going to create a string
+in which it adds to that the
+
+family name of self, and then
+another thing that says to,
+
+and then ah, I'm now going to
+send a message to the other
+
+object, saying give me
+your first name.
+
+Going to add that to the second
+piece, and you can see
+
+in this case it happens
+to be the same
+
+first and family name.
+
+And then at the end of it, which
+you can't see here but
+
+you can see in your handout, I
+just append the whole string,
+
+so it spits it out.
+
+What's the point of this,
+other than I can
+
+get it to say things?
+
+Notice, I can now reference
+values of the instance.
+
+But I can also get values
+of other instances, by
+
+sending in a message.
+
+And that's why we have that
+form right there.
+
+And then it glued
+all together.
+
+If you think about this for a
+second, you might say, wait a
+
+minute, actually you might
+have said wait a minute a
+
+while ago, why am I just using
+the variable name there in the
+
+function over here?
+
+Well in fact, I could've used
+the function here, first name
+
+open close, right?
+
+It would have done
+the same thing.
+
+But because I know I'm inside
+the instance, it's perfectly
+
+reasonable to just look
+up the value.
+
+OK, I could have, although I
+don't want you to do it, have
+
+done the same thing there and
+used underbar, sorry, first
+
+name underbar, sorry, first
+underbar name, but that's
+
+really breaking this contract
+that I want to happen.
+
+I should send the message to
+get the method back out.
+
+So again the standard practices
+is if you know
+
+you're inside the object, you
+can just access the values.
+
+If you're doing it with any
+other objects, send it a
+
+message to get it out.
+
+OK, now, that gives you an
+ability to say, let's look at
+
+one more example here, and
+then we're going to start
+
+building our hierarchy,
+which is, that this
+
+person can also sing.
+
+And we've got a little
+sing method here.
+
+And notice what it does, it's
+going to sing to somebody, I
+
+guess you're part of
+the Chorallaries.
+
+You're going to sing something,
+and notice what it
+
+does, it's simply going to use
+its say method, but add at the
+
+end of whatever's being said,
+just tra la la at the end.
+
+So this is now an example of a
+method using another method.
+
+Why would you want that?
+
+It's nice modularly.
+
+I have one method that's doing
+saying, I have another method
+
+that's just building on it.
+
+So if I have is person sing to
+themselves, not a highly
+
+recommended activity, it would
+help if I had it sing to
+
+itself, not sing to sing,
+sorry about that.
+
+Notice what it does.
+
+Looks like exactly like a say
+method, except it's got tra la
+
+la at the end.
+
+Don't worry I'm not going
+to sing to you.
+
+I'll simply say the words.
+
+Power of this, other than
+the silly examples.
+
+You see how I can access
+variables of the instance, how
+
+I can access variables of other
+instances, going to come
+
+back to that, and how I can use
+versions of my own methods
+
+to implement other methods.
+
+In this case sing is using
+say as part of what it
+
+wants to get out.
+
+OK, so we got a simple
+little example.
+
+Now, let's start adding some
+other pieces to this.
+
+OK, and what do I want to add.
+
+Find my spot here.
+
+OK, we're going to add
+an MIT person.
+
+Sorry, machine is -- do
+this, let's go down.
+
+OK so I'm going to add
+an MIT person.
+
+Look at the code for second.
+
+Aha!
+
+Notice what this says.
+
+MIT person says it inherits
+from person.
+
+That is, that's the first thing
+in parens up there.
+
+It says, you know, class of
+MIT person is person.
+
+What that is saying is, that
+this is a specialization of
+
+the person class.
+
+Or another way of saying it is,
+we have a super class, in
+
+this case it's person.
+
+And we have a subclass, in
+this case its MIT person.
+
+And we're going to walk through
+some examples, but
+
+what it says is that that
+subclass of MIT person can
+
+inherit the attributes
+of the person class.
+
+Can inherit the methods, it
+can inherit variables.
+
+OK, what does MIT person do?
+
+Well, here's 1 of the
+new things it does.
+
+It has a local variable called
+next id num, which is
+
+initially set to 0.
+
+See that up there.
+
+And then it's got some methods,
+it's got an init
+
+method, a get id method,
+a few other things.
+
+OK, let's run this.
+
+In particular, I go back
+down to this one.
+
+Let me just uncomment
+this and do it here.
+
+Assuming my machine will do what
+I want it to do, which it
+
+really doesn't seem to
+want to do today.
+
+Try one more time.
+
+Thank you, yep.
+
+Still not doing it
+for me, John.
+
+OK, we type it.
+
+No idea what Python doesn't like
+me today, but it doesn't.
+
+So we're gonna define p 1, I've
+lost my keyboard, indeed
+
+I have. Try one more time. p 1
+MIT person, see how fast I can
+
+type here --
+
+OK, now, let's look at what the
+code does, because again
+
+it's going to highlight
+some things.
+
+I called MIT person, push this
+up slightly, it's going to
+
+create an instance down
+here, I called p 1.
+
+And when I would do that,
+I'm gonna initialize it.
+
+So I've got, right up here, an
+initializer, init for MIT
+
+person, takes in the family
+name and the first name.
+
+Notice what it does.
+
+Huh.
+
+It says, if I'm sitting here at
+MIT person, I'm going to go
+
+up and inherit from person its
+init function and call it.
+
+And what am I calling it on?
+
+I'm calling it on self, which is
+pointing to this object, so
+
+I've still got it, and then I'm
+then going to apply the
+
+base initialization.
+
+And that does exactly what you'd
+expect, which is just
+
+going to create a binding for
+family name down here.
+
+As well as some other things.
+
+So this is an example
+of inheritance.
+
+MIT person inherits the init
+method from person, can get
+
+access to by simply referring
+to it, and I
+
+refer to it right there.
+
+And it's take the person class,
+get its init and apply
+
+it to my instance plus
+those things.
+
+So I'm just using the
+same piece of code
+
+Notice the second
+thing it does.
+
+It says inside of self, I'm
+going to bind the local
+
+variable id name to the value of
+next id name in MIT person.
+
+Self is down here, id num,
+sorry, not id name.
+
+I'm going to bind that to the
+value that I find my going up
+
+to here, which is 0, and having
+done that, I simply
+
+increment that value.
+
+OK?
+
+So what has this done?
+
+It says I now have captured in
+the class, a local variable
+
+that I can keep track of.
+
+And when I use it, every time I
+generate an example, let me
+
+build another one.
+
+I make p 2 another MIT person.
+
+OK, I can do things like saying,
+what is the id number
+
+for each of these.
+
+First one is 0, second one is
+1, which makes sense, right?
+
+I'm just incrementing
+a global variable.
+
+Now, things I want you
+to see about this.
+
+Now that I've got a beginning
+of a hierarchy, I have this
+
+notion of inheritance.
+
+I can ask a function inside one
+class to use a function
+
+from a class that it can reach
+by going up the chain.
+
+I just did it there.
+
+I can ask it to go get values
+of variables, right, so that
+
+looks good.
+
+What else do we have in
+person or MIT person?
+
+Well, we can get the id
+number, we just did.
+
+We have a thing to do
+with this string.
+
+Notice it's going to print out
+something a little different.
+
+In fact, there's a kind
+of funky form there.
+
+Which just says, if I want to
+print it out, I'm gonna
+
+create, what this says to do is,
+I'm gonna create an output
+
+template that has that structure
+to it, but where I
+
+see that percent s I'm going to
+substitute this value for
+
+the first one, that value
+for the second.
+
+So if I say, what is p 1?
+
+It says ok, MIT person
+Fred Smith.
+
+On the other hand, if I said,
+what is per, which is that
+
+thing I build earlier, it had
+a different string method,
+
+which is just print out
+person, those pieces.
+
+All right, one last piece
+to this and we're
+
+going to add to it.
+
+Suppose I want Fred
+to say something.
+
+Say something to Jane.
+
+OK, he said it.
+
+Where's the say method?
+
+OK, Fred is an instance
+of an MIT person.
+
+where's the say method?
+
+Well, there isn't one there,
+but again, that's where the
+
+hierarchy comes in.
+
+Fred is this object here, I'm
+sending it the message say.
+
+That turns into going up the
+chain to this object, which is
+
+the class object, and saying
+find a say method and apply it
+
+to that instance.
+
+Fudge-knuckle, it ain't here.
+
+Don't worry about it, because
+it says if I can't find one
+
+there, I'm going to go up the
+chain to this method, sorry to
+
+this class, and look
+for a method there.
+
+Which there was one, I
+have a say method.
+
+It's going to use
+that say method.
+
+Apply to it.
+
+Well, you might say, OK, what
+happens if it isn't there?
+
+Well, that's where, remember
+I defined person to be an
+
+instance of an object, it will
+go up the chain one last time
+
+to the base object in Python
+to see is there a
+
+method there or not.
+
+Probably isn't a say method
+for an object, so at that
+
+point it's going to raise an
+exception or throw an error.
+
+But now you again see this idea
+that the inheritance lets
+
+you capture methods.
+
+Now you might say, why not just
+put a say method inside
+
+of MIT person?
+
+Well, if you wanted it to do
+something different, that
+
+would be the right
+thing to do.
+
+But the whole notion here's that
+I'm capturing modularity,
+
+I've got base methods
+up in my base class.
+
+If I just want to use them I'm
+just going to inherit them by
+
+following that chain, if you
+like, basically up the track.
+
+OK, so we've got an MIT person,
+we can use that.
+
+Let's add a little bit more
+to our hierarchy here.
+
+I'm going to create, if
+I can do this right, a
+
+specialization of an MIT
+person, which is an
+
+undergraduate.
+
+A special kind of MIT person.
+
+All right, so if I go back up
+here, even though my thing is
+
+not going to let me do it, let's
+build an undergraduate.
+
+OK, there's the class definition
+for an undergrad.
+
+We're just starting to see some
+of the pieces, right, so
+
+in an undergraduate, where am
+I here, an undergraduate.
+
+OK, it's also got an
+initialization function.
+
+So if I call undergrad, I'm
+gonna make an undergrad here,
+
+again let me go back down here,
+line ug 2 it's making
+
+undergrad, Jane Doe.
+
+Now, what happens when I do
+the initialization here?
+
+Notice what goes on.
+
+It simply calls the person
+initialization method.
+
+All right, so I'm down here.
+
+I'm going to call the person
+initialization
+
+method, what did do?
+
+Sorry, the MIT person method,
+it calls the person method.
+
+Just walking up the chain,
+that's going to do exactly
+
+what I did with all the other
+ones, so I now have a family
+
+name and a first name.
+
+So I can, for example,
+say family name
+
+and get it back out.
+
+All right?
+
+And then, other things that I
+can do, well I can set what
+
+year the person's in, I can
+figure out what year they're
+
+in, there's this unfortunate
+overflow error if you've hung
+
+around too long, but that's not
+going to happen to you.
+
+And I've now got a say method
+here, so let's look what
+
+happens if I ask the
+
+undergraduate to say something.
+
+OK, it's not a realistic
+dialogue I know, but, what did
+
+this method do?
+
+I asked this object
+to do a say.
+
+And notice what it does.
+
+It simply passes it back
+up to MIT person.
+
+There's that inheritance
+again.
+
+It's saying, I'm going
+to have my base
+
+say method say something.
+
+I'm going to say it to a person,
+but all I'm going to
+
+do because undergraduates in my
+experience, at least, are
+
+always very polite, I'm going to
+put "Excuse me but" at the
+
+front of it.
+
+OK, what am I trying
+to show you here?
+
+I know the jokes are awful,
+but what am I
+
+trying to show you here?
+
+That I can simply pass up
+the chain to get it.
+
+In fact, what method does
+the final say here?
+
+What class does it come from?
+
+Person class, yes, thank you.
+
+It goes all the way up to
+person, right, because MIT
+
+person didn't have a say.
+
+So I can simply walk up the
+chain until I find the method
+
+I want to have.
+
+Now this is an example
+of shadowing.
+
+Not a great example, but it's
+a beginning example of
+
+shadowing, in that this same
+method for an undergraduate,
+
+shadows the base say method, it
+happens to call it, but it
+
+changes it.
+
+It puts "Excuse me but" at
+the front, before it
+
+goes on to do something.
+
+Now again, I could have decided
+here to actually copy
+
+what the original say method
+did, stitch all the other
+
+things together.
+
+But again, that loses
+my modularity.
+
+I'd really to only have to
+change it in one place.
+
+So by putting my say method up
+in person, I can add these
+
+nuances to it, and it lets
+me have something
+
+that has that variation.
+
+If I decide I want to change
+what say does, I only have to
+
+change it in one place.
+
+It is in the person class
+definition, and everything
+
+else will follow through
+for free.
+
+OK, so now I've got an
+undergrad, right?
+
+Let's look at a couple
+of variations of
+
+what happens here.
+
+So first of all, I can -- yes?
+
+PROFESSOR 2: Shadowing here
+is often sometimes called
+
+overriding.
+
+PROFESSOR: Yes, thank you,
+because I'm going to do a pure
+
+example of shadowing in
+a second, John right.
+
+Also called overriding.
+
+Part of the reason I like the
+phrase shadow is, if you think
+
+about it as looking at it from
+this direction, you see this
+
+version of init before you see
+the other ones, or you see
+
+that version of say, but
+it is overriding
+
+the base say example.
+
+OK, so I can say, what does
+p 1, sorry, yes, what does
+
+undergrad look like?
+
+And I said wait a minute,
+MIT person, not
+
+undergrad, is that right?
+
+Well, where's the str method?
+
+I didn't define one in
+undergrad, so it again tracks
+
+up the chain and finds the str
+method here, so it's OK
+
+undergrads are MIT people
+most the time, so
+
+it's perfectly fine.
+
+OK, now, I have built into this
+also these cmp methods.
+
+So I've got two examples.
+
+I've got undergrad, or ug.
+
+And then I've got poor
+old Frank Foobar
+
+back there, per person.
+
+So suppose I want
+to compare them?
+
+What do you think
+happens here?
+
+Compare sounds weird,
+right, I compare an
+
+undergraduate to a person.
+
+I don't know what that's doing,
+some kind of weird
+
+psychological thing, but what do
+you think happens in terms
+
+of the code here
+if I run this.
+
+I know it's a little hard
+because you got a lot of code
+
+to look at.
+
+Do I have a cmp method
+defined somewhere?
+
+Yeah.
+
+So, it's hard to know what it's
+going to do, but let's
+
+look at it.
+
+Hmm.
+
+Now sometimes I type things
+and I got errors I don't
+
+expect, this one I did expect.
+
+So what happened here?
+
+Well let's talk about what
+happens if I do that
+
+comparison I was doing,
+what was I doing?
+
+Ug greater than per?
+
+What unwinds into is, I'm going
+to send to ug, that
+
+instance, a cmp method.
+
+This is really going to become
+something like ug dot under
+
+under cmp under under
+applied to per.
+
+I think that's close.
+
+What does that do?
+
+It says starting in ug, I'm
+going to look for the first
+
+cmp method I could find, which
+is actually sitting here.
+
+I had a cmp method
+in MIT person.
+
+If you look at your code,
+what does it do?
+
+It looks up the id numbers
+to compare them.
+
+Well the, ug has an id number
+because it was created along
+
+this chamber.
+
+Remember per over here was
+just created as a person.
+
+It doesn't have an id number,
+so that's why it complaints.
+
+Ok, happens if I do that?
+
+Compare per to ug.
+
+How many people think
+I get an error?
+
+Wow.
+
+How many people think I'm going
+to get either true or
+
+false out of this?
+
+A few brave hands.
+
+Why?
+
+Can I ask you, please?
+
+Why do you think I'm going to
+get a, doesn't matter whether
+
+it's true or false, why am I
+going to have something work
+
+this time that didn't
+work last time?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Yeah, exactly.
+
+And in case you didn't hear it,
+thank you, great answer,
+
+sorry, terrible throw.
+
+In this case I'm using per,
+that's the first part, so it's
+
+not symmetric.
+
+It's gonna use per to
+do the look up.
+
+And as it was said there, per
+over here goes up and finds a
+
+cmp method here which
+it can apply.
+
+In that case, it simply looked
+at, remember, it took the
+
+tuples of first and last name
+which are both defined here,
+
+and did some comparison
+on that.
+
+So this is a way of again
+pointing out to you that the
+
+things are not always symmetric,
+and I have to be
+
+careful about where do
+I find the methods as
+
+I want to use them.
+
+Ok?
+
+All right.
+
+Let's add, I'm gonna do
+two more classes here.
+
+Let's add one more class, some
+people debate whether these
+
+are really people or not, but
+we're going to add a class
+
+called a professor.
+
+OK.
+
+Now what am I doing?
+
+I'm creating another version
+of class down here.
+
+Which again is an instance, or
+a subclass, sorry, not an
+
+instance, a subclass
+of an MIT person.
+
+I see that because I built
+it to be there.
+
+Again I've got an initialization
+that's going to
+
+call the person initialization,
+which we know
+
+is going to go up --
+
+I keep saying that -- going
+to call the MIT person
+
+initialization, which is going
+to go up and call this one.
+
+So again I'm going to be
+able to find names.
+
+And I do a couple of other
+different things here.
+
+I'm gonna pass in a rank, full
+professor, associate
+
+professor, assistant professor,
+which I'm just
+
+going to bind locally.
+
+But I'm gonna add one other
+piece here, which is I'm gonna
+
+add a little dictionary
+on teaching.
+
+So when I create a professor,
+I'm gonna associate with it a
+
+dictionary that says, what
+have you been teaching?
+
+And then notice the
+methods I create.
+
+I've got a method here called
+add teaching, takes, obviously
+
+a pointer to the instance.
+
+A term, which will just be
+a string, and a subject.
+
+And let's look at what
+it does right here.
+
+OK.
+
+In fact the call I'm going to
+make, I'm not certain I'm
+
+going to be able to get away
+with it, my machine is still
+
+wonderfully broken, all right,
+it is, let me just show you
+
+what the calls would
+look like.
+
+As you can see here I'm not
+going to be able to do them.
+
+But I'm going to add teaching,
+as a method call with this
+
+with a string for term,
+and a subject number.
+
+What is this going to do?
+
+Yeah, I know I'm just worried if
+I restart Python, I may not
+
+be able to pull the thing back
+in, so I'm going to try and
+
+wing it, John, and see if
+I can make it happen.
+
+Right, what does that
+teaching do?
+
+It's got one of those
+try except methods.
+
+So what does it say
+it's going to do?
+
+It's going to go into the
+dictionary associated with
+
+teaching, under the value of
+term, and get out a list. And
+
+it's going to append
+to the end of the
+
+list the new subject.
+
+So it's going to be stored in
+there, is then going to be
+
+term, and a list of what I
+taught, in case I teach more
+
+than one thing each term.
+
+It's going to do that, but
+notice it's a try.
+
+If in fact there is no term
+currently in the dictionary,
+
+started out empty, it's going to
+throw an error, sorry, not
+
+throw an error, it's going
+to raise an exception.
+
+Which is a key error, in which
+case notice what I'm going to
+
+do, I'm not going to treat
+it as an error.
+
+I'm simply going to say, in that
+case, just start off with
+
+an empty, with an initial list
+with just that subject in and
+
+put it in the dictionary.
+
+As I add more things in, I'll
+just keep adding things to
+
+this dictionary under
+that term.
+
+And if I want to find out what
+I'm doing, well I can use get
+
+teaching, which says given the
+term, find the thing in the
+
+dictionary under that
+term and return it.
+
+If I get an error, I'm going to
+raise it, which says there
+
+is nothing for that term, and in
+that case I guess I'm just
+
+going to return none.
+
+OK?
+
+And then the other two pieces
+we're going to have here, and
+
+we want to look at a little more
+carefully, I just wanted
+
+to show you that example, is a
+professor can lecture, and a
+
+professor can say something.
+
+Look at the say method, because
+this now add one more
+
+nuance to what we
+want to do here.
+
+And I think in interest of
+making this go, let me
+
+actually, since I'm not going
+to get my machine to do this
+
+right, let me create a
+couple of professors.
+
+If I look at what that is, it's
+an MIT person because I
+
+didn't have any separate string
+thing there, and we
+
+will create a more important
+professor.
+
+What rank do you want, John?
+
+Do you want to stay full?
+
+PROFESSOR 2: Undergraduate.
+
+PROFESSOR: Undergraduate, right,
+a lot more fun I agree.
+
+Sorry about that, and we
+can again just see
+
+what that looks like.
+
+And that of course,
+we'll print out,
+
+he's also an MIT person.
+
+But now here's what
+I want to do.
+
+I want to say something
+to my good
+
+colleague Professor Guttag.
+
+Actually I'm going to
+start a separate --
+
+I'm going to say something
+to a smart undergraduate.
+
+So if I say, remember we
+have ug defined as an
+
+undergraduate, let
+me do something a
+
+little different here.
+
+Well let, me do it that way.
+
+It says, I don't understand
+why you say you
+
+were enjoying 6.00.
+
+Not a good thing to say, right,
+but if I say to my good
+
+colleague Professor Guttag.
+
+I have to spell say right, I
+know, I need help with this,
+
+what can I say?
+
+We flatter each other
+all the time.
+
+It's part of what makes us feel
+good about ourselves.
+
+Why is the sky blue?
+
+I enjoyed your paper, but
+why is the sky blue?
+
+OK, terrible examples, but
+what's going on here?
+
+One more piece that
+I want to add.
+
+Here's my say method for
+professor, and now I'm
+
+actually taking advantage of to
+whom I am saying something.
+
+Notice again, what does it do?
+
+There's the self argument,
+that's just pointing to the
+
+instance of me.
+
+I'm passing in another argument,
+going to call it to
+
+who, in one case it was ug,
+in one case it was Guttag.
+
+And then the thing I want to
+say, ah, look what it does, it
+
+says, check the type.
+
+And the type is going to take
+that instance, I had an
+
+instance, for example, of a
+professor down here, and it's
+
+going to pick up what type
+of object it is.
+
+So if the type of the person I'm
+speaking to is undergrad,
+
+let's pause for second.
+
+Remember I started away back
+saying we're building abstract
+
+data types.
+
+Well, here's a great example
+of how I'm using
+
+exactly that, right?
+
+I've got int, I've got float,
+I now have ug, it's a type.
+
+So it's says if the object to
+whom I'm speaking is an
+
+undergrad, then use the same
+method from person where I'm
+
+going to put this
+on the front.
+
+On the other hand, if the object
+to whom I'm speaking is
+
+a professor, then I'm going to
+tag this on the front and use
+
+the underlying say method.
+
+On the other hand, if I'm
+speaking to somebody else, I'm
+
+just going to go lecture.
+
+All right, and when a professor
+lectures, they just
+
+put it's obvious on the
+end of things, as
+
+you may have noticed.
+
+What's the point I want
+you to see here?
+
+I'm now using the instances
+to help me to find what
+
+the code should do.
+
+I'm looking at the type.
+
+If the type is this, do that.
+
+If the type is this, do
+something different, ok?
+
+And I can now sort of build
+those pieces up.
+
+OK, I said one more class.
+
+Notice what we're doing.
+
+I know they're silly examples,
+but, sorry, they are cleverly
+
+designed examples to highlight
+key points.
+
+What I'm trying to do is show
+you how we have methods
+
+inherit methods, how have
+message shadow methods, how we
+
+have methods override methods,
+how we can use instances as
+
+types to define what the
+method should do.
+
+Let me show you one last class,
+because I'm gonna have
+
+one more piece that
+we want to use.
+
+And the last class is, sort of,
+once you've got a set of
+
+professors, you can have
+an aggregate of them.
+
+And I don't know, if a group of
+geese are gaggle, I don't
+
+know what a set of professors
+are, John.
+
+Flamers?
+
+I, you know, we've got to figure
+out what the right
+
+collective noun here is.
+
+We're going to call them a
+faculty for lack of a better
+
+term, right?
+
+Now the reason I want to show
+you this example is, this
+
+class, notice, it only is going
+to inherit from object.
+
+It actually makes sense.
+
+This is going to be a collection
+of things, but it's
+
+not a subclass of a particular
+kind of person.
+
+And what I want the faculty to
+do, is to be able to gather
+
+together a set of faculty.
+
+So if I go down here, grab this
+for second, and pull it
+
+down so you can see it.
+
+It looks like I'm not going to
+be able to run this because my
+
+machine is broken, but basically
+I'm gonna define a
+
+set of professors, and then I'm
+gonna create a new class
+
+called faculty.
+
+There's the definition of it.
+
+It's got an init.
+
+You can kind of see
+what it does.
+
+It's going to set up an internal
+variable called
+
+names, which is initially an
+empty list, internal variable
+
+called ids, which is empty, an
+internal variable called
+
+members, which is empty, and
+another special variable
+
+called place, which we're going
+to come back to in a
+
+second, initially
+bound to none.
+
+OK, I've got a method called
+add which I'm going to use
+
+down here to add professors
+to the course 6 faculty.
+
+Here's what I want
+to add to do.
+
+First of all, notice I'm going
+to check the type.
+
+If this is not a professor, I'm
+gonna raise an error, a
+
+type error, it's the wrong type
+of object to pass in.
+
+The second thing I'm gonna do
+is say, if that's okay, then
+
+let me go off and get
+the id number.
+
+Now remember, that's right up
+here, so I'm asking the
+
+instance of the professor to go
+up and get the id number.
+
+And I want to make sure I only
+have one instance of each
+
+professor in my faculty, so if
+the id number is in the list
+
+of ids already, I'm going to
+raise an error, sorry, raise
+
+an exception as well, saying
+I've got a duplicate id.
+
+OK?
+
+And the reason that's
+going to come up is,
+
+notice what I do now.
+
+Inside of the instant self, I
+take the variable names and I
+
+add to it the family name of
+the person I just added.
+
+OK, notice the form.
+
+I'm using the method, there's
+the parens to get the family
+
+name of the person.
+
+I'm just adding it to the list.
+I've got the id number,
+
+I've added the ids,
+and I add the
+
+object itself into members.
+
+So as I do this, what
+am I doing?
+
+I'm creating a list, actually
+several lists: a list of ids,
+
+a list of the actual instances,
+and a list of the
+
+family names.
+
+And as a cost I want to add,
+that's why I can check and
+
+see, is this in here
+already or not?
+
+Now, the last reason I want to
+do this is, I want to be able
+
+to support things like that.
+
+This is now different, right,
+this instance is a collection.
+
+I want to be able to do things
+like, for all the things in
+
+that collection, do something,
+like print
+
+out the family names.
+
+And to do that, I need two
+special forms: iter and next.
+
+OK, now let me see if I
+can say this cleanly.
+
+Whenever I use a for, in
+structure, even if it was on
+
+just a normal list you built,
+what Python is doing is
+
+returning an, what is
+called an iterator.
+
+Which is something that
+we talked earlier.
+
+It's keeping track of where are
+you in the list, and how
+
+do I get to the next
+thing in the list?
+
+I'm going to do the same thing
+here, and I'm going to create
+
+it for this particular
+structure.
+
+So this little thing iter, when
+I call a for something
+
+in, one of these instances,
+it calls iter, and
+
+notice what it does.
+
+It initializes place to 0.
+
+That was that variable
+I had up there.
+
+That's basically saying I'm at
+the beginning of the list.
+
+It's a pointer to the beginning
+of the list, and it
+
+returns self.
+
+Just gives me back a pointer
+to the instance.
+
+That now allows me at
+each step in that
+
+loop to call next.
+
+And what does next do?
+
+Next says, check to see if that
+value is too long, if
+
+it's longer than, for example,
+the list of names, raise an
+
+exception called stop iteration,
+which the for loop
+
+will use to say OK, I'm done.
+
+I'm going to break out
+of the for loop.
+
+Otherwise, what am
+I going to do?
+
+I'll increment place by 1,
+that's going to move me to the
+
+next place in the list, and then
+in this case I'll just
+
+return the instance
+itself, right?
+
+Members is a list of instances,
+place I've
+
+incremented by 1, I take 1
+off of it, I get to it.
+
+So iter and next
+work together.
+
+Iter creates this method, that's
+going to give you a
+
+pointer to the place in the
+structure, and then next
+
+literally walks along the
+structure giving you the next
+
+element and returning elements
+in turn so you can do
+
+something with it.
+
+Right, so now what that says
+is, I can have classes that
+
+just have local variables.
+
+I can have classes that get
+methods from other variables,
+
+and I can also have classes
+that are collections.
+
+And I've supported that by
+adding in this last piece.
+
+OK once you have all of that,
+in principle we could start
+
+doing some fun things.
+
+So let's see what happens
+if we try and
+
+make all of this go.
+
+And let me, since I'm not going
+to be able to run it,
+
+let me simply do it this way.
+
+If I have my undergraduate,
+ug.
+
+I can -- sorry, let's not
+do it that way --
+
+I can have undergraduate say
+things like -- all right, what
+
+did I just do wrong here?
+
+Do I not have undergrad
+defined?
+
+I do.
+
+Oh, I didn't have Grimson,
+sorry, it's me, isn't it?
+
+Thank you.
+
+The undergraduate very politely
+asks why he didn't
+
+understand, you can have
+the professor respond.
+
+Again, it simply puts a
+different thing into there.
+
+On the other hand, if Professor
+Guttag asks me
+
+something about understanding, I
+say I really like this paper
+
+on, you do not understand,
+it's a deep paper on
+
+programming languages 5, I
+think, John, isn't it?
+
+What else can you do with
+this thing, right?
+
+You can have an undergraduate
+talk to an undergraduate, in
+
+which case they're
+still polite.
+
+Or you could have -- sorry, let
+me do that the other way
+
+-- you could also have an
+undergraduate simply talk to a
+
+normal person.
+
+All right, but the good news is
+you know eventually you get
+
+it done, and when you're really
+done you can have the
+
+undergraduate be really happy
+about this, and so she sings
+
+to herself.
+
+OK it's a little silly, but
+notice what we've just
+
+illustrated.
+
+And this is where I want
+to pull it together.
+
+With a simple set of classes,
+and the following abilities,
+
+an ability to inherit methods
+from subclasses, sorry from
+
+superclasses, that is having
+this hierarchy of things.
+
+I can create a fairly complex
+kind of interaction.
+
+I can take advantage of the
+types of the objects to help
+
+me decide what to do.
+
+And if you think about that,
+I know it sounds very
+
+straightforward, but you would
+do exactly that if you were
+
+writing earlier code to deal
+with some numerical problem.
+
+All right, if the thing is an
+integer, do this, if it's a
+
+float, do that, if it's a
+string, do something else.
+
+I'm now giving you exactly the
+same ability, but the types
+
+now can be things that
+you could create.
+
+And what I've also got is now
+the ability to inherit those
+
+methods as they go
+up the chain.
+
+So another way of saying it is,
+things that you want to
+
+come away from here, are, in
+terms of these classes.
+
+We now have this idea
+of encapsulation.
+
+I'm gathering together data that
+naturally belongs as a
+
+unit, and I'm gathering together
+with it methods that
+
+apply to that unit.
+
+Just like we would have done
+with float or int.
+
+Ideally, we data hide, we don't
+happen to do it here,
+
+which is too bad.
+
+Basically we've got the
+idea of encapsulation.
+
+The second thing we've got is
+this idea of inheritance.
+
+Inheritance both meaning
+I can inherit
+
+attributes or field values.
+
+I can inherit methods by
+moving up the chain.
+
+I can also the shadow or
+override methods, so that I
+
+can specialise.
+
+And I do all of that with this
+nice hierarchy of classes.
+
+So what hopefully you've seen,
+between these two lectures,
+
+and we're going to come back
+to it in some subsequent
+
+lectures, is that this is now
+a different way of just
+
+structuring a computational
+system.
+
+Now, you'll also get arguments,
+polite arguments
+
+from faculty members or other
+experts about which is a
+
+better way of doing it.
+
+So I'll give you my bias,
+Professor Guttag will give you
+
+his bias next time around.
+
+My view, object-oriented system
+are great when you're
+
+trying to model systems that
+consist of a large number of
+
+units that interact in
+very specific ways.
+
+So, modeling a system of
+people's a great idea.
+
+Modeling a system of molecules
+is probably a great idea.
+
+Modeling a system where it is
+natural to associate things
+
+together and where the number
+of interactions between them
+
+is very controlled.
+
+These systems work
+really well.
+
+And we'll see some examples
+of that next week.
+
+Thanks.
\ No newline at end of file
diff --git a/QkyiiMUYH2U.txt b/QkyiiMUYH2U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07246562dfae4bf3da309496397a4341d1b1a291
--- /dev/null
+++ b/QkyiiMUYH2U.txt
@@ -0,0 +1,10931 @@
+align:start position:0%
+ 
+I hope that without the coffee you can
+
+ align:start position:0%
+I hope that without the coffee you can
+ 
+
+ align:start position:0%
+I hope that without the coffee you can
+still stay awake for uh the next 90
+
+ align:start position:0%
+still stay awake for uh the next 90
+ 
+
+ align:start position:0%
+still stay awake for uh the next 90
+minutes especially the first 45 is going
+
+ align:start position:0%
+minutes especially the first 45 is going
+ 
+
+ align:start position:0%
+minutes especially the first 45 is going
+to be mine and I'm going to take it very
+
+ align:start position:0%
+to be mine and I'm going to take it very
+ 
+
+ align:start position:0%
+to be mine and I'm going to take it very
+personally if all deep so please don't
+
+ align:start position:0%
+personally if all deep so please don't
+ 
+
+ align:start position:0%
+personally if all deep so please don't
+do it um so in the first part of the
+
+ align:start position:0%
+do it um so in the first part of the
+ 
+
+ align:start position:0%
+do it um so in the first part of the
+course we've been talking a lot about
+
+ align:start position:0%
+course we've been talking a lot about
+ 
+
+ align:start position:0%
+course we've been talking a lot about
+mitigation basically how do we make
+
+ align:start position:0%
+mitigation basically how do we make
+ 
+
+ align:start position:0%
+mitigation basically how do we make
+investments in the build environment and
+
+ align:start position:0%
+investments in the build environment and
+ 
+
+ align:start position:0%
+investments in the build environment and
+how do we understand the business case
+
+ align:start position:0%
+how do we understand the business case
+ 
+
+ align:start position:0%
+how do we understand the business case
+of reducing emissions uh to reduce uh
+
+ align:start position:0%
+of reducing emissions uh to reduce uh
+ 
+
+ align:start position:0%
+of reducing emissions uh to reduce uh
+the chances of suffering climate change
+
+ align:start position:0%
+the chances of suffering climate change
+ 
+
+ align:start position:0%
+the chances of suffering climate change
+climate disasters and so forth that's
+
+ align:start position:0%
+climate disasters and so forth that's
+ 
+
+ align:start position:0%
+climate disasters and so forth that's
+been the whole first part of the of the
+
+ align:start position:0%
+been the whole first part of the of the
+ 
+
+ align:start position:0%
+been the whole first part of the of the
+block brainwashing you into emissions
+
+ align:start position:0%
+block brainwashing you into emissions
+ 
+
+ align:start position:0%
+block brainwashing you into emissions
+are bad don't do it is actually
+
+ align:start position:0%
+are bad don't do it is actually
+ 
+
+ align:start position:0%
+are bad don't do it is actually
+profitable if you do it in a proper way
+
+ align:start position:0%
+profitable if you do it in a proper way
+ 
+
+ align:start position:0%
+profitable if you do it in a proper way
+so please uh take action that's the
+
+ align:start position:0%
+so please uh take action that's the
+ 
+
+ align:start position:0%
+so please uh take action that's the
+first part now we're going to have three
+
+ align:start position:0%
+first part now we're going to have three
+ 
+
+ align:start position:0%
+first part now we're going to have three
+sessions into the consequences of
+
+ align:start position:0%
+sessions into the consequences of
+ 
+
+ align:start position:0%
+sessions into the consequences of
+climate change so once we put a lot of
+
+ align:start position:0%
+climate change so once we put a lot of
+ 
+
+ align:start position:0%
+climate change so once we put a lot of
+these emissions in the atmosphere a lot
+
+ align:start position:0%
+these emissions in the atmosphere a lot
+ 
+
+ align:start position:0%
+these emissions in the atmosphere a lot
+of we increase the likelihood of a lot
+
+ align:start position:0%
+of we increase the likelihood of a lot
+ 
+
+ align:start position:0%
+of we increase the likelihood of a lot
+of St bad stuffff to happen and we are
+
+ align:start position:0%
+of St bad stuffff to happen and we are
+ 
+
+ align:start position:0%
+of St bad stuffff to happen and we are
+going to learn what are the consequences
+
+ align:start position:0%
+going to learn what are the consequences
+ 
+
+ align:start position:0%
+going to learn what are the consequences
+for real estate markets we're going to
+
+ align:start position:0%
+for real estate markets we're going to
+ 
+
+ align:start position:0%
+for real estate markets we're going to
+do this in terms of what are the
+
+ align:start position:0%
+do this in terms of what are the
+ 
+
+ align:start position:0%
+do this in terms of what are the
+consequences for Real Estate Value real
+
+ align:start position:0%
+consequences for Real Estate Value real
+ 
+
+ align:start position:0%
+consequences for Real Estate Value real
+estate prices we are going to talk about
+
+ align:start position:0%
+estate prices we are going to talk about
+ 
+
+ align:start position:0%
+estate prices we are going to talk about
+the basics of climate science and we're
+
+ align:start position:0%
+the basics of climate science and we're
+ 
+
+ align:start position:0%
+the basics of climate science and we're
+going to start thinking about how to
+
+ align:start position:0%
+going to start thinking about how to
+ 
+
+ align:start position:0%
+going to start thinking about how to
+adapt and how to make resiliency uh
+
+ align:start position:0%
+adapt and how to make resiliency uh
+ 
+
+ align:start position:0%
+adapt and how to make resiliency uh
+investments into the buildt environment
+
+ align:start position:0%
+investments into the buildt environment
+ 
+
+ align:start position:0%
+investments into the buildt environment
+so three sessions today Thursday and
+
+ align:start position:0%
+so three sessions today Thursday and
+ 
+
+ align:start position:0%
+so three sessions today Thursday and
+Tuesday we are going to be very uh deep
+
+ align:start position:0%
+Tuesday we are going to be very uh deep
+ 
+
+ align:start position:0%
+Tuesday we are going to be very uh deep
+into that topic onto how real estate
+
+ align:start position:0%
+into that topic onto how real estate
+ 
+
+ align:start position:0%
+into that topic onto how real estate
+assets how real estate markets how Real
+
+ align:start position:0%
+assets how real estate markets how Real
+ 
+
+ align:start position:0%
+assets how real estate markets how Real
+Estate Investors are impacted by climate
+
+ align:start position:0%
+Estate Investors are impacted by climate
+ 
+
+ align:start position:0%
+Estate Investors are impacted by climate
+risk and climate uh disasters we are
+
+ align:start position:0%
+risk and climate uh disasters we are
+ 
+
+ align:start position:0%
+risk and climate uh disasters we are
+going to do it with the usual suspects
+
+ align:start position:0%
+going to do it with the usual suspects
+ 
+
+ align:start position:0%
+going to do it with the usual suspects
+CI and me are going to be here in front
+
+ align:start position:0%
+CI and me are going to be here in front
+ 
+
+ align:start position:0%
+CI and me are going to be here in front
+of you uh but we are also going to have
+
+ align:start position:0%
+of you uh but we are also going to have
+ 
+
+ align:start position:0%
+of you uh but we are also going to have
+a industry leaders that are will to come
+
+ align:start position:0%
+a industry leaders that are will to come
+ 
+
+ align:start position:0%
+a industry leaders that are will to come
+here to see how actually the action is
+
+ align:start position:0%
+here to see how actually the action is
+ 
+
+ align:start position:0%
+here to see how actually the action is
+being taken on the ground in the in the
+
+ align:start position:0%
+being taken on the ground in the in the
+ 
+
+ align:start position:0%
+being taken on the ground in the in the
+sector today h I'm going to talk for the
+
+ align:start position:0%
+sector today h I'm going to talk for the
+ 
+
+ align:start position:0%
+sector today h I'm going to talk for the
+first half but the second half is going
+
+ align:start position:0%
+first half but the second half is going
+ 
+
+ align:start position:0%
+first half but the second half is going
+to be by Kevin fan who was sitting here
+
+ align:start position:0%
+to be by Kevin fan who was sitting here
+ 
+
+ align:start position:0%
+to be by Kevin fan who was sitting here
+12 years ago 13 13 years ago Ms alarm
+
+ align:start position:0%
+12 years ago 13 13 years ago Ms alarm
+ 
+
+ align:start position:0%
+12 years ago 13 13 years ago Ms alarm
+that went one day to New York he was
+
+ align:start position:0%
+that went one day to New York he was
+ 
+
+ align:start position:0%
+that went one day to New York he was
+telling me and got an offer after one
+
+ align:start position:0%
+telling me and got an offer after one
+ 
+
+ align:start position:0%
+telling me and got an offer after one
+hour and a half interview and was good
+
+ align:start position:0%
+hour and a half interview and was good
+ 
+
+ align:start position:0%
+hour and a half interview and was good
+enough to keep him for 12 years he's at
+
+ align:start position:0%
+enough to keep him for 12 years he's at
+ 
+
+ align:start position:0%
+enough to keep him for 12 years he's at
+moodies the head of the CR unit there
+
+ align:start position:0%
+moodies the head of the CR unit there
+ 
+
+ align:start position:0%
+moodies the head of the CR unit there
+after being for many years in the
+
+ align:start position:0%
+after being for many years in the
+ 
+
+ align:start position:0%
+after being for many years in the
+climate in the in the credit risk uh
+
+ align:start position:0%
+climate in the in the credit risk uh
+ 
+
+ align:start position:0%
+climate in the in the credit risk uh
+Department one of the people that I
+
+ align:start position:0%
+Department one of the people that I
+ 
+
+ align:start position:0%
+Department one of the people that I
+encountered that knows the most about
+
+ align:start position:0%
+encountered that knows the most about
+ 
+
+ align:start position:0%
+encountered that knows the most about
+climate change climate risk also
+
+ align:start position:0%
+climate change climate risk also
+ 
+
+ align:start position:0%
+climate change climate risk also
+transition risk and uh real estate so if
+
+ align:start position:0%
+transition risk and uh real estate so if
+ 
+
+ align:start position:0%
+transition risk and uh real estate so if
+you want to learn about that he's one of
+
+ align:start position:0%
+you want to learn about that he's one of
+ 
+
+ align:start position:0%
+you want to learn about that he's one of
+the best people in the world to do it
+
+ align:start position:0%
+the best people in the world to do it
+ 
+
+ align:start position:0%
+the best people in the world to do it
+and he's going to be with us the whole
+
+ align:start position:0%
+and he's going to be with us the whole
+ 
+
+ align:start position:0%
+and he's going to be with us the whole
+day we do this lecture and also a
+
+ align:start position:0%
+day we do this lecture and also a
+ 
+
+ align:start position:0%
+day we do this lecture and also a
+reception afterwards so please come
+
+ align:start position:0%
+reception afterwards so please come
+ 
+
+ align:start position:0%
+reception afterwards so please come
+enjoy the coffee but also make sure that
+
+ align:start position:0%
+enjoy the coffee but also make sure that
+ 
+
+ align:start position:0%
+enjoy the coffee but also make sure that
+you talk to Kevin because he's one of
+
+ align:start position:0%
+you talk to Kevin because he's one of
+ 
+
+ align:start position:0%
+you talk to Kevin because he's one of
+the people that you can learn the most
+
+ align:start position:0%
+the people that you can learn the most
+ 
+
+ align:start position:0%
+the people that you can learn the most
+much more than with me but I'm you know
+
+ align:start position:0%
+much more than with me but I'm you know
+ 
+
+ align:start position:0%
+much more than with me but I'm you know
+you guys have tra with me what can you
+
+ align:start position:0%
+you guys have tra with me what can you
+ 
+
+ align:start position:0%
+you guys have tra with me what can you
+say um so let me give you a little bit
+
+ align:start position:0%
+say um so let me give you a little bit
+ 
+
+ align:start position:0%
+say um so let me give you a little bit
+of you see bad and good bad Brown
+
+ align:start position:0%
+of you see bad and good bad Brown
+ 
+
+ align:start position:0%
+of you see bad and good bad Brown
+buildings polluting bad okay so let me
+
+ align:start position:0%
+buildings polluting bad okay so let me
+ 
+
+ align:start position:0%
+buildings polluting bad okay so let me
+give you a little bit of a of an outline
+
+ align:start position:0%
+give you a little bit of a of an outline
+ 
+
+ align:start position:0%
+give you a little bit of a of an outline
+for today's lecture or at least for for
+
+ align:start position:0%
+for today's lecture or at least for for
+ 
+
+ align:start position:0%
+for today's lecture or at least for for
+my part we are going to talk about the
+
+ align:start position:0%
+my part we are going to talk about the
+ 
+
+ align:start position:0%
+my part we are going to talk about the
+basics of climates uh change and the
+
+ align:start position:0%
+basics of climates uh change and the
+ 
+
+ align:start position:0%
+basics of climates uh change and the
+idea is to give you the logic of what it
+
+ align:start position:0%
+idea is to give you the logic of what it
+ 
+
+ align:start position:0%
+idea is to give you the logic of what it
+is and how that is actually going to be
+
+ align:start position:0%
+is and how that is actually going to be
+ 
+
+ align:start position:0%
+is and how that is actually going to be
+here to stay and how actually climate
+
+ align:start position:0%
+here to stay and how actually climate
+ 
+
+ align:start position:0%
+here to stay and how actually climate
+scientists are talking about it and
+
+ align:start position:0%
+scientists are talking about it and
+ 
+
+ align:start position:0%
+scientists are talking about it and
+discussing about climate change and and
+
+ align:start position:0%
+discussing about climate change and and
+ 
+
+ align:start position:0%
+discussing about climate change and and
+change in climate in a way that is
+
+ align:start position:0%
+change in climate in a way that is
+ 
+
+ align:start position:0%
+change in climate in a way that is
+useful to understand how that will
+
+ align:start position:0%
+useful to understand how that will
+ 
+
+ align:start position:0%
+useful to understand how that will
+impact the build environment and and
+
+ align:start position:0%
+impact the build environment and and
+ 
+
+ align:start position:0%
+impact the build environment and and
+real estate uh markets so I'm not going
+
+ align:start position:0%
+real estate uh markets so I'm not going
+ 
+
+ align:start position:0%
+real estate uh markets so I'm not going
+to give you a very thorough uh
+
+ align:start position:0%
+to give you a very thorough uh
+ 
+
+ align:start position:0%
+to give you a very thorough uh
+discussion around deep science but just
+
+ align:start position:0%
+discussion around deep science but just
+ 
+
+ align:start position:0%
+discussion around deep science but just
+enough for you to understand what you
+
+ align:start position:0%
+enough for you to understand what you
+ 
+
+ align:start position:0%
+enough for you to understand what you
+are talking about and what for you to
+
+ align:start position:0%
+are talking about and what for you to
+ 
+
+ align:start position:0%
+are talking about and what for you to
+understand that when the United Nations
+
+ align:start position:0%
+understand that when the United Nations
+ 
+
+ align:start position:0%
+understand that when the United Nations
+comes out and puts out a uh the next
+
+ align:start position:0%
+comes out and puts out a uh the next
+ 
+
+ align:start position:0%
+comes out and puts out a uh the next
+report how that affects your investment
+
+ align:start position:0%
+report how that affects your investment
+ 
+
+ align:start position:0%
+report how that affects your investment
+your Holdings or your decision in the
+
+ align:start position:0%
+your Holdings or your decision in the
+ 
+
+ align:start position:0%
+your Holdings or your decision in the
+real estate market then we're going to
+
+ align:start position:0%
+real estate market then we're going to
+ 
+
+ align:start position:0%
+real estate market then we're going to
+get into the the the nuts and balls of
+
+ align:start position:0%
+get into the the the nuts and balls of
+ 
+
+ align:start position:0%
+get into the the the nuts and balls of
+this in the real estate market using the
+
+ align:start position:0%
+this in the real estate market using the
+ 
+
+ align:start position:0%
+this in the real estate market using the
+for Quadrant model I've been casting a
+
+ align:start position:0%
+for Quadrant model I've been casting a
+ 
+
+ align:start position:0%
+for Quadrant model I've been casting a
+little bit around and there are some
+
+ align:start position:0%
+little bit around and there are some
+ 
+
+ align:start position:0%
+little bit around and there are some
+people that are more nervous and other
+
+ align:start position:0%
+people that are more nervous and other
+ 
+
+ align:start position:0%
+people that are more nervous and other
+people are less nervous about four
+
+ align:start position:0%
+people are less nervous about four
+ 
+
+ align:start position:0%
+people are less nervous about four
+quadrant models and so for more so we
+
+ align:start position:0%
+quadrant models and so for more so we
+ 
+
+ align:start position:0%
+quadrant models and so for more so we
+are going to undust that toolbox to
+
+ align:start position:0%
+are going to undust that toolbox to
+ 
+
+ align:start position:0%
+are going to undust that toolbox to
+understand actually how when one side of
+
+ align:start position:0%
+understand actually how when one side of
+ 
+
+ align:start position:0%
+understand actually how when one side of
+the market is impacted how it's going to
+
+ align:start position:0%
+the market is impacted how it's going to
+ 
+
+ align:start position:0%
+the market is impacted how it's going to
+be impacting the the whole Market as a
+
+ align:start position:0%
+be impacting the the whole Market as a
+ 
+
+ align:start position:0%
+be impacting the the whole Market as a
+whole all the stakeholders um and then
+
+ align:start position:0%
+whole all the stakeholders um and then
+ 
+
+ align:start position:0%
+whole all the stakeholders um and then
+we're are going to talk about more
+
+ align:start position:0%
+we're are going to talk about more
+ 
+
+ align:start position:0%
+we're are going to talk about more
+empirical assessments of climate risk
+
+ align:start position:0%
+empirical assessments of climate risk
+ 
+
+ align:start position:0%
+empirical assessments of climate risk
+and so forth so we're going to connect
+
+ align:start position:0%
+and so forth so we're going to connect
+ 
+
+ align:start position:0%
+and so forth so we're going to connect
+it to a lot of the tools that we cover
+
+ align:start position:0%
+it to a lot of the tools that we cover
+ 
+
+ align:start position:0%
+it to a lot of the tools that we cover
+in in these uh settings and a big part
+
+ align:start position:0%
+in in these uh settings and a big part
+ 
+
+ align:start position:0%
+in in these uh settings and a big part
+of this is going to be when we are
+
+ align:start position:0%
+of this is going to be when we are
+ 
+
+ align:start position:0%
+of this is going to be when we are
+thinking about DCS or we are thinking
+
+ align:start position:0%
+thinking about DCS or we are thinking
+ 
+
+ align:start position:0%
+thinking about DCS or we are thinking
+about assessing climate is going to be
+
+ align:start position:0%
+about assessing climate is going to be
+ 
+
+ align:start position:0%
+about assessing climate is going to be
+about about the discount rate that we're
+
+ align:start position:0%
+about about the discount rate that we're
+ 
+
+ align:start position:0%
+about about the discount rate that we're
+going to assess to that how the cap rate
+
+ align:start position:0%
+going to assess to that how the cap rate
+ 
+
+ align:start position:0%
+going to assess to that how the cap rate
+how a lot of the risk measures that are
+
+ align:start position:0%
+how a lot of the risk measures that are
+ 
+
+ align:start position:0%
+how a lot of the risk measures that are
+impacted are are introduced into these
+
+ align:start position:0%
+impacted are are introduced into these
+ 
+
+ align:start position:0%
+impacted are are introduced into these
+valuations are going to be affected by
+
+ align:start position:0%
+valuations are going to be affected by
+ 
+
+ align:start position:0%
+valuations are going to be affected by
+by climate RIS so this is going to be a
+
+ align:start position:0%
+by climate RIS so this is going to be a
+ 
+
+ align:start position:0%
+by climate RIS so this is going to be a
+big discussion into what what is
+
+ align:start position:0%
+big discussion into what what is
+ 
+
+ align:start position:0%
+big discussion into what what is
+appropriate to Discount climate risk and
+
+ align:start position:0%
+appropriate to Discount climate risk and
+ 
+
+ align:start position:0%
+appropriate to Discount climate risk and
+so forth it's going to be today on
+
+ align:start position:0%
+so forth it's going to be today on
+ 
+
+ align:start position:0%
+so forth it's going to be today on
+Thursday we're going to cover a lot of
+
+ align:start position:0%
+Thursday we're going to cover a lot of
+ 
+
+ align:start position:0%
+Thursday we're going to cover a lot of
+this and C we're going to cover also the
+
+ align:start position:0%
+this and C we're going to cover also the
+ 
+
+ align:start position:0%
+this and C we're going to cover also the
+role of beliefs in all of these the RO
+
+ align:start position:0%
+role of beliefs in all of these the RO
+ 
+
+ align:start position:0%
+role of beliefs in all of these the RO
+of climate beliefs and also the role of
+
+ align:start position:0%
+of climate beliefs and also the role of
+ 
+
+ align:start position:0%
+of climate beliefs and also the role of
+uh the differences between commercial
+
+ align:start position:0%
+uh the differences between commercial
+ 
+
+ align:start position:0%
+uh the differences between commercial
+and residential real estate markets for
+
+ align:start position:0%
+and residential real estate markets for
+ 
+
+ align:start position:0%
+and residential real estate markets for
+everyone to see so some Basics basically
+
+ align:start position:0%
+everyone to see so some Basics basically
+ 
+
+ align:start position:0%
+everyone to see so some Basics basically
+this is what happens with climate change
+
+ align:start position:0%
+this is what happens with climate change
+ 
+
+ align:start position:0%
+this is what happens with climate change
+we are emitting a lot of CO2 all those
+
+ align:start position:0%
+we are emitting a lot of CO2 all those
+ 
+
+ align:start position:0%
+we are emitting a lot of CO2 all those
+things that we are uh saying that you
+
+ align:start position:0%
+things that we are uh saying that you
+ 
+
+ align:start position:0%
+things that we are uh saying that you
+shouldn't do and we should reduce in the
+
+ align:start position:0%
+shouldn't do and we should reduce in the
+ 
+
+ align:start position:0%
+shouldn't do and we should reduce in the
+build environment once we put a unit of
+
+ align:start position:0%
+build environment once we put a unit of
+ 
+
+ align:start position:0%
+build environment once we put a unit of
+CO2 in the out there by burning uh fuel
+
+ align:start position:0%
+CO2 in the out there by burning uh fuel
+ 
+
+ align:start position:0%
+CO2 in the out there by burning uh fuel
+that sticks into the atmosphere and it
+
+ align:start position:0%
+that sticks into the atmosphere and it
+ 
+
+ align:start position:0%
+that sticks into the atmosphere and it
+prevents the radiancy of the the the
+
+ align:start position:0%
+prevents the radiancy of the the the
+ 
+
+ align:start position:0%
+prevents the radiancy of the the the
+radian power of of sun to go back into
+
+ align:start position:0%
+radian power of of sun to go back into
+ 
+
+ align:start position:0%
+radian power of of sun to go back into
+the universe and basically get stra
+
+ align:start position:0%
+the universe and basically get stra
+ 
+
+ align:start position:0%
+the universe and basically get stra
+warming the the planet and warm in the
+
+ align:start position:0%
+warming the the planet and warm in the
+ 
+
+ align:start position:0%
+warming the the planet and warm in the
+atmosphere that's a very basic thing
+
+ align:start position:0%
+atmosphere that's a very basic thing
+ 
+
+ align:start position:0%
+atmosphere that's a very basic thing
+every time that we put an extra unit of
+
+ align:start position:0%
+every time that we put an extra unit of
+ 
+
+ align:start position:0%
+every time that we put an extra unit of
+uh CO2 in the atmosphere we create an
+
+ align:start position:0%
+uh CO2 in the atmosphere we create an
+ 
+
+ align:start position:0%
+uh CO2 in the atmosphere we create an
+extra layer out there that prevents the
+
+ align:start position:0%
+extra layer out there that prevents the
+ 
+
+ align:start position:0%
+extra layer out there that prevents the
+sun to go to come out into the universe
+
+ align:start position:0%
+sun to go to come out into the universe
+ 
+
+ align:start position:0%
+sun to go to come out into the universe
+and keeps warming up the planet and what
+
+ align:start position:0%
+and keeps warming up the planet and what
+ 
+
+ align:start position:0%
+and keeps warming up the planet and what
+happens with climate change and and and
+
+ align:start position:0%
+happens with climate change and and and
+ 
+
+ align:start position:0%
+happens with climate change and and and
+the whole discussion is that CO2 is
+
+ align:start position:0%
+the whole discussion is that CO2 is
+ 
+
+ align:start position:0%
+the whole discussion is that CO2 is
+nothing new it's nothing that we create
+
+ align:start position:0%
+nothing new it's nothing that we create
+ 
+
+ align:start position:0%
+nothing new it's nothing that we create
+as humans is is there in the atmosphere
+
+ align:start position:0%
+as humans is is there in the atmosphere
+ 
+
+ align:start position:0%
+as humans is is there in the atmosphere
+the plants the animals a lot of these
+
+ align:start position:0%
+the plants the animals a lot of these
+ 
+
+ align:start position:0%
+the plants the animals a lot of these
+things are creating a fluctuation to CO2
+
+ align:start position:0%
+things are creating a fluctuation to CO2
+ 
+
+ align:start position:0%
+things are creating a fluctuation to CO2
+if you see even like over 1 million
+
+ align:start position:0%
+if you see even like over 1 million
+ 
+
+ align:start position:0%
+if you see even like over 1 million
+years ago there's still a fluctuation
+
+ align:start position:0%
+years ago there's still a fluctuation
+ 
+
+ align:start position:0%
+years ago there's still a fluctuation
+going up and down of the levels of CO2
+
+ align:start position:0%
+going up and down of the levels of CO2
+ 
+
+ align:start position:0%
+going up and down of the levels of CO2
+in the atmosphere and you can actually
+
+ align:start position:0%
+in the atmosphere and you can actually
+ 
+
+ align:start position:0%
+in the atmosphere and you can actually
+do that in a very clever way with
+
+ align:start position:0%
+do that in a very clever way with
+ 
+
+ align:start position:0%
+do that in a very clever way with
+checking even like layers of old uh ice
+
+ align:start position:0%
+checking even like layers of old uh ice
+ 
+
+ align:start position:0%
+checking even like layers of old uh ice
+in the in the North Pole and so forth
+
+ align:start position:0%
+in the in the North Pole and so forth
+ 
+
+ align:start position:0%
+in the in the North Pole and so forth
+you can actually see how how the level
+
+ align:start position:0%
+you can actually see how how the level
+ 
+
+ align:start position:0%
+you can actually see how how the level
+of the of CO2 was back even 1 million
+
+ align:start position:0%
+of the of CO2 was back even 1 million
+ 
+
+ align:start position:0%
+of the of CO2 was back even 1 million
+years ago so you can actually based on
+
+ align:start position:0%
+years ago so you can actually based on
+ 
+
+ align:start position:0%
+years ago so you can actually based on
+those some clever physics models you can
+
+ align:start position:0%
+those some clever physics models you can
+ 
+
+ align:start position:0%
+those some clever physics models you can
+actually see how the level of CO2 was
+
+ align:start position:0%
+actually see how the level of CO2 was
+ 
+
+ align:start position:0%
+actually see how the level of CO2 was
+fluctuating but after the first
+
+ align:start position:0%
+fluctuating but after the first
+ 
+
+ align:start position:0%
+fluctuating but after the first
+Industrial Revolution this is what is
+
+ align:start position:0%
+Industrial Revolution this is what is
+ 
+
+ align:start position:0%
+Industrial Revolution this is what is
+started to happen so this is what we are
+
+ align:start position:0%
+started to happen so this is what we are
+ 
+
+ align:start position:0%
+started to happen so this is what we are
+now and that is around double the amount
+
+ align:start position:0%
+now and that is around double the amount
+ 
+
+ align:start position:0%
+now and that is around double the amount
+of CO2 in the atmosphere that has been
+
+ align:start position:0%
+of CO2 in the atmosphere that has been
+ 
+
+ align:start position:0%
+of CO2 in the atmosphere that has been
+for the last 1 million years so this is
+
+ align:start position:0%
+for the last 1 million years so this is
+ 
+
+ align:start position:0%
+for the last 1 million years so this is
+what what we are thinking about this
+
+ align:start position:0%
+what what we are thinking about this
+ 
+
+ align:start position:0%
+what what we are thinking about this
+might be a problem and the problem ends
+
+ align:start position:0%
+might be a problem and the problem ends
+ 
+
+ align:start position:0%
+might be a problem and the problem ends
+up being uh related to the amount of the
+
+ align:start position:0%
+up being uh related to the amount of the
+ 
+
+ align:start position:0%
+up being uh related to the amount of the
+the temperature levels into in the
+
+ align:start position:0%
+the temperature levels into in the
+ 
+
+ align:start position:0%
+the temperature levels into in the
+planet so this is what the again
+
+ align:start position:0%
+planet so this is what the again
+ 
+
+ align:start position:0%
+planet so this is what the again
+relative to 1980 this is how for the
+
+ align:start position:0%
+relative to 1980 this is how for the
+ 
+
+ align:start position:0%
+relative to 1980 this is how for the
+last decades and centuries it's been
+
+ align:start position:0%
+last decades and centuries it's been
+ 
+
+ align:start position:0%
+last decades and centuries it's been
+like the temperature
+
+ align:start position:0%
+like the temperature
+ 
+
+ align:start position:0%
+like the temperature
+in in the atmosphere and this is how it
+
+ align:start position:0%
+in in the atmosphere and this is how it
+ 
+
+ align:start position:0%
+in in the atmosphere and this is how it
+changed over the last year since we
+
+ align:start position:0%
+changed over the last year since we
+ 
+
+ align:start position:0%
+changed over the last year since we
+start burning fossil fuels to produce
+
+ align:start position:0%
+start burning fossil fuels to produce
+ 
+
+ align:start position:0%
+start burning fossil fuels to produce
+Goods to move to move and to do to heat
+
+ align:start position:0%
+Goods to move to move and to do to heat
+ 
+
+ align:start position:0%
+Goods to move to move and to do to heat
+our buildings and to do all sort of
+
+ align:start position:0%
+our buildings and to do all sort of
+ 
+
+ align:start position:0%
+our buildings and to do all sort of
+things so you see how the levels used to
+
+ align:start position:0%
+things so you see how the levels used to
+ 
+
+ align:start position:0%
+things so you see how the levels used to
+be something like here around
+
+ align:start position:0%
+be something like here around
+ 
+
+ align:start position:0%
+be something like here around
+fluctuating around zero and around the
+
+ align:start position:0%
+fluctuating around zero and around the
+ 
+
+ align:start position:0%
+fluctuating around zero and around the
+mid last century this starts to go all
+
+ align:start position:0%
+mid last century this starts to go all
+ 
+
+ align:start position:0%
+mid last century this starts to go all
+the way up to one one degree higher uh
+
+ align:start position:0%
+the way up to one one degree higher uh
+ 
+
+ align:start position:0%
+the way up to one one degree higher uh
+abnormally higher than that it used to
+
+ align:start position:0%
+abnormally higher than that it used to
+ 
+
+ align:start position:0%
+abnormally higher than that it used to
+be um this these are the Blue Line uh
+
+ align:start position:0%
+be um this these are the Blue Line uh
+ 
+
+ align:start position:0%
+be um this these are the Blue Line uh
+and how do we know or how do we think
+
+ align:start position:0%
+and how do we know or how do we think
+ 
+
+ align:start position:0%
+and how do we know or how do we think
+about the the role of humans in all of
+
+ align:start position:0%
+about the the role of humans in all of
+ 
+
+ align:start position:0%
+about the the role of humans in all of
+this is that if you model with some
+
+ align:start position:0%
+this is that if you model with some
+ 
+
+ align:start position:0%
+this is that if you model with some
+clever physics models where the
+
+ align:start position:0%
+clever physics models where the
+ 
+
+ align:start position:0%
+clever physics models where the
+temperatures will be using only physic
+
+ align:start position:0%
+temperatures will be using only physic
+ 
+
+ align:start position:0%
+temperatures will be using only physic
+physical parameters so different things
+
+ align:start position:0%
+physical parameters so different things
+ 
+
+ align:start position:0%
+physical parameters so different things
+of development of uh the uh the foresty
+
+ align:start position:0%
+of development of uh the uh the foresty
+ 
+
+ align:start position:0%
+of development of uh the uh the foresty
+development of animals and so forth uh
+
+ align:start position:0%
+development of animals and so forth uh
+ 
+
+ align:start position:0%
+development of animals and so forth uh
+using the blue modeling using 1,000 one
+
+ align:start position:0%
+using the blue modeling using 1,000 one
+ 
+
+ align:start position:0%
+using the blue modeling using 1,000 one
+million sorry multiple millions of
+
+ align:start position:0%
+million sorry multiple millions of
+ 
+
+ align:start position:0%
+million sorry multiple millions of
+simulations this is all where it should
+
+ align:start position:0%
+simulations this is all where it should
+ 
+
+ align:start position:0%
+simulations this is all where it should
+be without the the the influence of
+
+ align:start position:0%
+be without the the the influence of
+ 
+
+ align:start position:0%
+be without the the the influence of
+humankind so you can actually predict
+
+ align:start position:0%
+humankind so you can actually predict
+ 
+
+ align:start position:0%
+humankind so you can actually predict
+and forecast how the evolution of
+
+ align:start position:0%
+and forecast how the evolution of
+ 
+
+ align:start position:0%
+and forecast how the evolution of
+temperature will be and there any
+
+ align:start position:0%
+temperature will be and there any
+ 
+
+ align:start position:0%
+temperature will be and there any
+potential scenario that you can actually
+
+ align:start position:0%
+potential scenario that you can actually
+ 
+
+ align:start position:0%
+potential scenario that you can actually
+think of without human cane and you see
+
+ align:start position:0%
+think of without human cane and you see
+ 
+
+ align:start position:0%
+think of without human cane and you see
+that that is why way off of what the
+
+ align:start position:0%
+that that is why way off of what the
+ 
+
+ align:start position:0%
+that that is why way off of what the
+black line that is what we are observing
+
+ align:start position:0%
+black line that is what we are observing
+ 
+
+ align:start position:0%
+black line that is what we are observing
+the only way that you can really fit in
+
+ align:start position:0%
+the only way that you can really fit in
+ 
+
+ align:start position:0%
+the only way that you can really fit in
+that black line into simulations is if
+
+ align:start position:0%
+that black line into simulations is if
+ 
+
+ align:start position:0%
+that black line into simulations is if
+you introduce the idea that there are
+
+ align:start position:0%
+you introduce the idea that there are
+ 
+
+ align:start position:0%
+you introduce the idea that there are
+normally high levels of CO2 produce by
+
+ align:start position:0%
+normally high levels of CO2 produce by
+ 
+
+ align:start position:0%
+normally high levels of CO2 produce by
+man humankind so that's really the how
+
+ align:start position:0%
+man humankind so that's really the how
+ 
+
+ align:start position:0%
+man humankind so that's really the how
+the climate scientist and how all of the
+
+ align:start position:0%
+the climate scientist and how all of the
+ 
+
+ align:start position:0%
+the climate scientist and how all of the
+policy makers are thinking about the
+
+ align:start position:0%
+policy makers are thinking about the
+ 
+
+ align:start position:0%
+policy makers are thinking about the
+role of humans in all of this is that if
+
+ align:start position:0%
+role of humans in all of this is that if
+ 
+
+ align:start position:0%
+role of humans in all of this is that if
+you use any clever physics models here
+
+ align:start position:0%
+you use any clever physics models here
+ 
+
+ align:start position:0%
+you use any clever physics models here
+to predict the evolution of temperatures
+
+ align:start position:0%
+to predict the evolution of temperatures
+ 
+
+ align:start position:0%
+to predict the evolution of temperatures
+you can never fit what we are observing
+
+ align:start position:0%
+you can never fit what we are observing
+ 
+
+ align:start position:0%
+you can never fit what we are observing
+now in the in the atmosphere in terms of
+
+ align:start position:0%
+now in the in the atmosphere in terms of
+ 
+
+ align:start position:0%
+now in the in the atmosphere in terms of
+temperature the only way that you can
+
+ align:start position:0%
+temperature the only way that you can
+ 
+
+ align:start position:0%
+temperature the only way that you can
+fit this line if is you actually
+
+ align:start position:0%
+fit this line if is you actually
+ 
+
+ align:start position:0%
+fit this line if is you actually
+incorporate the man-made production of
+
+ align:start position:0%
+incorporate the man-made production of
+ 
+
+ align:start position:0%
+incorporate the man-made production of
+CO2 emissions in the atmosphere and
+
+ align:start position:0%
+CO2 emissions in the atmosphere and
+ 
+
+ align:start position:0%
+CO2 emissions in the atmosphere and
+that's why the scientists are saying
+
+ align:start position:0%
+that's why the scientists are saying
+ 
+
+ align:start position:0%
+that's why the scientists are saying
+that climate is changing and it's
+
+ align:start position:0%
+that climate is changing and it's
+ 
+
+ align:start position:0%
+that climate is changing and it's
+changing because of of man-made
+
+ align:start position:0%
+changing because of of man-made
+ 
+
+ align:start position:0%
+changing because of of man-made
+emissions and the the forecasting is not
+
+ align:start position:0%
+emissions and the the forecasting is not
+ 
+
+ align:start position:0%
+emissions and the the forecasting is not
+really uh helpful for us because if we
+
+ align:start position:0%
+really uh helpful for us because if we
+ 
+
+ align:start position:0%
+really uh helpful for us because if we
+keep producing CO2 in the amounts that
+
+ align:start position:0%
+keep producing CO2 in the amounts that
+ 
+
+ align:start position:0%
+keep producing CO2 in the amounts that
+we are producing no matter what the the
+
+ align:start position:0%
+we are producing no matter what the the
+ 
+
+ align:start position:0%
+we are producing no matter what the the
+scenario every line here is on a
+
+ align:start position:0%
+scenario every line here is on a
+ 
+
+ align:start position:0%
+scenario every line here is on a
+scenario you have millions of lines here
+
+ align:start position:0%
+scenario you have millions of lines here
+ 
+
+ align:start position:0%
+scenario you have millions of lines here
+no matter what the scenario you pick the
+
+ align:start position:0%
+no matter what the scenario you pick the
+ 
+
+ align:start position:0%
+no matter what the scenario you pick the
+the temperatures are going to keep going
+
+ align:start position:0%
+the temperatures are going to keep going
+ 
+
+ align:start position:0%
+the temperatures are going to keep going
+up and it's going to have a lot of bad
+
+ align:start position:0%
+up and it's going to have a lot of bad
+ 
+
+ align:start position:0%
+up and it's going to have a lot of bad
+stuff that we will
+
+ align:start position:0%
+stuff that we will
+ 
+
+ align:start position:0%
+stuff that we will
+see now in a
+
+ align:start position:0%
+see now in a
+ 
+
+ align:start position:0%
+see now in a
+bit uh this is one of the things that
+
+ align:start position:0%
+bit uh this is one of the things that
+ 
+
+ align:start position:0%
+bit uh this is one of the things that
+happens is not only that temperature
+
+ align:start position:0%
+happens is not only that temperature
+ 
+
+ align:start position:0%
+happens is not only that temperature
+this one degree uh here or two degrees
+
+ align:start position:0%
+this one degree uh here or two degrees
+ 
+
+ align:start position:0%
+this one degree uh here or two degrees
+is going to be just kind of like the
+
+ align:start position:0%
+is going to be just kind of like the
+ 
+
+ align:start position:0%
+is going to be just kind of like the
+average day is going to be one or two
+
+ align:start position:0%
+average day is going to be one or two
+ 
+
+ align:start position:0%
+average day is going to be one or two
+degrees hotter but it's also that the
+
+ align:start position:0%
+degrees hotter but it's also that the
+ 
+
+ align:start position:0%
+degrees hotter but it's also that the
+number especially here the number of
+
+ align:start position:0%
+number especially here the number of
+ 
+
+ align:start position:0%
+number especially here the number of
+days that are extremely hot are going to
+
+ align:start position:0%
+days that are extremely hot are going to
+ 
+
+ align:start position:0%
+days that are extremely hot are going to
+increase by a lot so this is not a a
+
+ align:start position:0%
+increase by a lot so this is not a a
+ 
+
+ align:start position:0%
+increase by a lot so this is not a a
+pleasant increase in the temperature
+
+ align:start position:0%
+pleasant increase in the temperature
+ 
+
+ align:start position:0%
+pleasant increase in the temperature
+especially in a place like Boston we can
+
+ align:start position:0%
+especially in a place like Boston we can
+ 
+
+ align:start position:0%
+especially in a place like Boston we can
+always appreciate this one or two uh
+
+ align:start position:0%
+always appreciate this one or two uh
+ 
+
+ align:start position:0%
+always appreciate this one or two uh
+degrees extra in the winter is this the
+
+ align:start position:0%
+degrees extra in the winter is this the
+ 
+
+ align:start position:0%
+degrees extra in the winter is this the
+number of heat WS the number of days
+
+ align:start position:0%
+number of heat WS the number of days
+ 
+
+ align:start position:0%
+number of heat WS the number of days
+that are extremely hot is going to
+
+ align:start position:0%
+that are extremely hot is going to
+ 
+
+ align:start position:0%
+that are extremely hot is going to
+increase by a lot and that is going to
+
+ align:start position:0%
+increase by a lot and that is going to
+ 
+
+ align:start position:0%
+increase by a lot and that is going to
+generate all of the problems that we
+
+ align:start position:0%
+generate all of the problems that we
+ 
+
+ align:start position:0%
+generate all of the problems that we
+also discuss in the healthy building
+
+ align:start position:0%
+also discuss in the healthy building
+ 
+
+ align:start position:0%
+also discuss in the healthy building
+lecture in terms of health and
+
+ align:start position:0%
+lecture in terms of health and
+ 
+
+ align:start position:0%
+lecture in terms of health and
+cardiovascular problems and so forth so
+
+ align:start position:0%
+cardiovascular problems and so forth so
+ 
+
+ align:start position:0%
+cardiovascular problems and so forth so
+this is this is the issue in terms of
+
+ align:start position:0%
+this is this is the issue in terms of
+ 
+
+ align:start position:0%
+this is this is the issue in terms of
+temperatures that the amount of days
+
+ align:start position:0%
+temperatures that the amount of days
+ 
+
+ align:start position:0%
+temperatures that the amount of days
+that are unbearably warm is going to
+
+ align:start position:0%
+that are unbearably warm is going to
+ 
+
+ align:start position:0%
+that are unbearably warm is going to
+increase disproportionally compared to
+
+ align:start position:0%
+increase disproportionally compared to
+ 
+
+ align:start position:0%
+increase disproportionally compared to
+the to the Past
+
+ align:start position:0%
+the to the Past
+ 
+
+ align:start position:0%
+the to the Past
+decades um and now beyond all of that we
+
+ align:start position:0%
+decades um and now beyond all of that we
+ 
+
+ align:start position:0%
+decades um and now beyond all of that we
+are going to cover now all of the
+
+ align:start position:0%
+are going to cover now all of the
+ 
+
+ align:start position:0%
+are going to cover now all of the
+disasters that are associated with with
+
+ align:start position:0%
+disasters that are associated with with
+ 
+
+ align:start position:0%
+disasters that are associated with with
+that but I want to make a distinction
+
+ align:start position:0%
+that but I want to make a distinction
+ 
+
+ align:start position:0%
+that but I want to make a distinction
+here when we are thinking about weather
+
+ align:start position:0%
+here when we are thinking about weather
+ 
+
+ align:start position:0%
+here when we are thinking about weather
+and when we are going to think about
+
+ align:start position:0%
+and when we are going to think about
+ 
+
+ align:start position:0%
+and when we are going to think about
+climate to each of these uh lines here
+
+ align:start position:0%
+climate to each of these uh lines here
+ 
+
+ align:start position:0%
+climate to each of these uh lines here
+if they're ultimately color is one day
+
+ align:start position:0%
+if they're ultimately color is one day
+ 
+
+ align:start position:0%
+if they're ultimately color is one day
+so it's one day here will be like this
+
+ align:start position:0%
+so it's one day here will be like this
+ 
+
+ align:start position:0%
+so it's one day here will be like this
+amount of this temperature like 30
+
+ align:start position:0%
+amount of this temperature like 30
+ 
+
+ align:start position:0%
+amount of this temperature like 30
+degrees or whatever it will be in the in
+
+ align:start position:0%
+degrees or whatever it will be in the in
+ 
+
+ align:start position:0%
+degrees or whatever it will be in the in
+exit the distribution here will tell you
+
+ align:start position:0%
+exit the distribution here will tell you
+ 
+
+ align:start position:0%
+exit the distribution here will tell you
+the climate so climate describes
+
+ align:start position:0%
+the climate so climate describes
+ 
+
+ align:start position:0%
+the climate so climate describes
+long-term pattern of weather so every
+
+ align:start position:0%
+long-term pattern of weather so every
+ 
+
+ align:start position:0%
+long-term pattern of weather so every
+day you have a certain weather the
+
+ align:start position:0%
+day you have a certain weather the
+ 
+
+ align:start position:0%
+day you have a certain weather the
+weather is cold the weather is warm
+
+ align:start position:0%
+weather is cold the weather is warm
+ 
+
+ align:start position:0%
+weather is cold the weather is warm
+climate is this long-term distribution
+
+ align:start position:0%
+climate is this long-term distribution
+ 
+
+ align:start position:0%
+climate is this long-term distribution
+of weather and that's what it's changing
+
+ align:start position:0%
+of weather and that's what it's changing
+ 
+
+ align:start position:0%
+of weather and that's what it's changing
+and that's what people are responding to
+
+ align:start position:0%
+and that's what people are responding to
+ 
+
+ align:start position:0%
+and that's what people are responding to
+because it is stupid to believe that
+
+ align:start position:0%
+because it is stupid to believe that
+ 
+
+ align:start position:0%
+because it is stupid to believe that
+people will make an investment in a
+
+ align:start position:0%
+people will make an investment in a
+ 
+
+ align:start position:0%
+people will make an investment in a
+building that are planning to hold for
+
+ align:start position:0%
+building that are planning to hold for
+ 
+
+ align:start position:0%
+building that are planning to hold for
+20 30 40 years based on today's weather
+
+ align:start position:0%
+20 30 40 years based on today's weather
+ 
+
+ align:start position:0%
+20 30 40 years based on today's weather
+they are going to be thinking about it
+
+ align:start position:0%
+they are going to be thinking about it
+ 
+
+ align:start position:0%
+they are going to be thinking about it
+in terms of what they expect the weather
+
+ align:start position:0%
+in terms of what they expect the weather
+ 
+
+ align:start position:0%
+in terms of what they expect the weather
+all the weather the daily weather to be
+
+ align:start position:0%
+all the weather the daily weather to be
+ 
+
+ align:start position:0%
+all the weather the daily weather to be
+over the period of 30 40 50 years that
+
+ align:start position:0%
+over the period of 30 40 50 years that
+ 
+
+ align:start position:0%
+over the period of 30 40 50 years that
+this asset is going to be in our hands
+
+ align:start position:0%
+this asset is going to be in our hands
+ 
+
+ align:start position:0%
+this asset is going to be in our hands
+so what we are interested here is about
+
+ align:start position:0%
+so what we are interested here is about
+ 
+
+ align:start position:0%
+so what we are interested here is about
+this long-term distribution this
+
+ align:start position:0%
+this long-term distribution this
+ 
+
+ align:start position:0%
+this long-term distribution this
+long-term climate these 30-year averages
+
+ align:start position:0%
+long-term climate these 30-year averages
+ 
+
+ align:start position:0%
+long-term climate these 30-year averages
+of temperature 30 year averages of
+
+ align:start position:0%
+of temperature 30 year averages of
+ 
+
+ align:start position:0%
+of temperature 30 year averages of
+rainfall 30-year averages of uh Cyclones
+
+ align:start position:0%
+rainfall 30-year averages of uh Cyclones
+ 
+
+ align:start position:0%
+rainfall 30-year averages of uh Cyclones
+hurricanes and so forth this is what we
+
+ align:start position:0%
+hurricanes and so forth this is what we
+ 
+
+ align:start position:0%
+hurricanes and so forth this is what we
+are going to discuss here today and this
+
+ align:start position:0%
+are going to discuss here today and this
+ 
+
+ align:start position:0%
+are going to discuss here today and this
+what we are going to discuss here over
+
+ align:start position:0%
+what we are going to discuss here over
+ 
+
+ align:start position:0%
+what we are going to discuss here over
+the next two three weeks we are not
+
+ align:start position:0%
+the next two three weeks we are not
+ 
+
+ align:start position:0%
+the next two three weeks we are not
+going to discuss how people are impacted
+
+ align:start position:0%
+going to discuss how people are impacted
+ 
+
+ align:start position:0%
+going to discuss how people are impacted
+or the decisions of people are impacted
+
+ align:start position:0%
+or the decisions of people are impacted
+ 
+
+ align:start position:0%
+or the decisions of people are impacted
+by this one day cold day one day that is
+
+ align:start position:0%
+by this one day cold day one day that is
+ 
+
+ align:start position:0%
+by this one day cold day one day that is
+warm one day that is rainy no we are
+
+ align:start position:0%
+warm one day that is rainy no we are
+ 
+
+ align:start position:0%
+warm one day that is rainy no we are
+thinking about over the last 10 decades
+
+ align:start position:0%
+thinking about over the last 10 decades
+ 
+
+ align:start position:0%
+thinking about over the last 10 decades
+the the average temperature has been uh
+
+ align:start position:0%
+the the average temperature has been uh
+ 
+
+ align:start position:0%
+the the average temperature has been uh
+20° C 80 degrees Fahrenheit and now
+
+ align:start position:0%
+20° C 80 degrees Fahrenheit and now
+ 
+
+ align:start position:0%
+20° C 80 degrees Fahrenheit and now
+actually our average temperature goes to
+
+ align:start position:0%
+actually our average temperature goes to
+ 
+
+ align:start position:0%
+actually our average temperature goes to
+90 degrees Fahrenheit and our average
+
+ align:start position:0%
+90 degrees Fahrenheit and our average
+ 
+
+ align:start position:0%
+90 degrees Fahrenheit and our average
+temperature goes to 30 deges celi that's
+
+ align:start position:0%
+temperature goes to 30 deges celi that's
+ 
+
+ align:start position:0%
+temperature goes to 30 deges celi that's
+what we are thinking we are thinking
+
+ align:start position:0%
+what we are thinking we are thinking
+ 
+
+ align:start position:0%
+what we are thinking we are thinking
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+
+ align:start position:0%
+about we are here in terms of
+ 
+
+ align:start position:0%
+about we are here in terms of
+temperatures and we go here in terms of
+
+ align:start position:0%
+temperatures and we go here in terms of
+ 
+
+ align:start position:0%
+temperatures and we go here in terms of
+temperatures and this is here to stay
+
+ align:start position:0%
+temperatures and this is here to stay
+ 
+
+ align:start position:0%
+temperatures and this is here to stay
+and this is nothing that is going to be
+
+ align:start position:0%
+and this is nothing that is going to be
+ 
+
+ align:start position:0%
+and this is nothing that is going to be
+a fluctuation from one day to the other
+
+ align:start position:0%
+a fluctuation from one day to the other
+ 
+
+ align:start position:0%
+a fluctuation from one day to the other
+because these long-term trends is going
+
+ align:start position:0%
+because these long-term trends is going
+ 
+
+ align:start position:0%
+because these long-term trends is going
+to change is going to shape the
+
+ align:start position:0%
+to change is going to shape the
+ 
+
+ align:start position:0%
+to change is going to shape the
+expectations or the forecast of a lot of
+
+ align:start position:0%
+expectations or the forecast of a lot of
+ 
+
+ align:start position:0%
+expectations or the forecast of a lot of
+our analysts that are going to consider
+
+ align:start position:0%
+our analysts that are going to consider
+ 
+
+ align:start position:0%
+our analysts that are going to consider
+what to make in terms of building an
+
+ align:start position:0%
+what to make in terms of building an
+ 
+
+ align:start position:0%
+what to make in terms of building an
+asset transforming an asset and so forth
+
+ align:start position:0%
+asset transforming an asset and so forth
+ 
+
+ align:start position:0%
+asset transforming an asset and so forth
+this is what really matters because this
+
+ align:start position:0%
+this is what really matters because this
+ 
+
+ align:start position:0%
+this is what really matters because this
+is going
+
+ align:start position:0%
+is going
+ 
+
+ align:start position:0%
+is going
+to shape all of our valuations in terms
+
+ align:start position:0%
+to shape all of our valuations in terms
+ 
+
+ align:start position:0%
+to shape all of our valuations in terms
+of uh considering what to do with an
+
+ align:start position:0%
+of uh considering what to do with an
+ 
+
+ align:start position:0%
+of uh considering what to do with an
+asset what to do with a portfolio what
+
+ align:start position:0%
+asset what to do with a portfolio what
+ 
+
+ align:start position:0%
+asset what to do with a portfolio what
+what we what matter for us is always the
+
+ align:start position:0%
+what we what matter for us is always the
+ 
+
+ align:start position:0%
+what we what matter for us is always the
+long-term expectations the long-term uh
+
+ align:start position:0%
+long-term expectations the long-term uh
+ 
+
+ align:start position:0%
+long-term expectations the long-term uh
+beliefs that we have there and this is
+
+ align:start position:0%
+beliefs that we have there and this is
+ 
+
+ align:start position:0%
+beliefs that we have there and this is
+what climate change is about is that
+
+ align:start position:0%
+what climate change is about is that
+ 
+
+ align:start position:0%
+what climate change is about is that
+those expectations in terms of how the
+
+ align:start position:0%
+those expectations in terms of how the
+ 
+
+ align:start position:0%
+those expectations in terms of how the
+amenities of a place how the asset the
+
+ align:start position:0%
+amenities of a place how the asset the
+ 
+
+ align:start position:0%
+amenities of a place how the asset the
+cost of an assets are going to be are
+
+ align:start position:0%
+cost of an assets are going to be are
+ 
+
+ align:start position:0%
+cost of an assets are going to be are
+going to change just because the climate
+
+ align:start position:0%
+going to change just because the climate
+ 
+
+ align:start position:0%
+going to change just because the climate
+that this asset is exposed to is
+
+ align:start position:0%
+that this asset is exposed to is
+ 
+
+ align:start position:0%
+that this asset is exposed to is
+changing all right they are not going to
+
+ align:start position:0%
+changing all right they are not going to
+ 
+
+ align:start position:0%
+changing all right they are not going to
+be shape by what happens today in Boston
+
+ align:start position:0%
+be shape by what happens today in Boston
+ 
+
+ align:start position:0%
+be shape by what happens today in Boston
+is going to be safe but with what we
+
+ align:start position:0%
+is going to be safe but with what we
+ 
+
+ align:start position:0%
+is going to be safe but with what we
+think that in the next 10 15 20 years is
+
+ align:start position:0%
+think that in the next 10 15 20 years is
+ 
+
+ align:start position:0%
+think that in the next 10 15 20 years is
+happening in Boston or in New York or
+
+ align:start position:0%
+happening in Boston or in New York or
+ 
+
+ align:start position:0%
+happening in Boston or in New York or
+whatever we are considering that Carlos
+
+ align:start position:0%
+whatever we are considering that Carlos
+ 
+
+ align:start position:0%
+whatever we are considering that Carlos
+good I I saw you a bit
+
+ align:start position:0%
+good I I saw you a bit
+ 
+
+ align:start position:0%
+good I I saw you a bit
+confused and and this is what is
+
+ align:start position:0%
+confused and and this is what is
+ 
+
+ align:start position:0%
+confused and and this is what is
+changing and this is what you see if you
+
+ align:start position:0%
+changing and this is what you see if you
+ 
+
+ align:start position:0%
+changing and this is what you see if you
+see the uh the UN ipcc reports they are
+
+ align:start position:0%
+see the uh the UN ipcc reports they are
+ 
+
+ align:start position:0%
+see the uh the UN ipcc reports they are
+the ones that are actually investigating
+
+ align:start position:0%
+the ones that are actually investigating
+ 
+
+ align:start position:0%
+the ones that are actually investigating
+how the climate is changing and the
+
+ align:start position:0%
+how the climate is changing and the
+ 
+
+ align:start position:0%
+how the climate is changing and the
+attribution of of that change to to
+
+ align:start position:0%
+attribution of of that change to to
+ 
+
+ align:start position:0%
+attribution of of that change to to
+humankind that's you is what you see
+
+ align:start position:0%
+humankind that's you is what you see
+ 
+
+ align:start position:0%
+humankind that's you is what you see
+that there is a change in beliefs and
+
+ align:start position:0%
+that there is a change in beliefs and
+ 
+
+ align:start position:0%
+that there is a change in beliefs and
+change in expectations of how the
+
+ align:start position:0%
+change in expectations of how the
+ 
+
+ align:start position:0%
+change in expectations of how the
+climate is going to be so you see that
+
+ align:start position:0%
+climate is going to be so you see that
+ 
+
+ align:start position:0%
+climate is going to be so you see that
+they started with saying that there is a
+
+ align:start position:0%
+they started with saying that there is a
+ 
+
+ align:start position:0%
+they started with saying that there is a
+a a relationship between greenhouse
+
+ align:start position:0%
+a a relationship between greenhouse
+ 
+
+ align:start position:0%
+a a relationship between greenhouse
+evisions and uh there's a change an
+
+ align:start position:0%
+evisions and uh there's a change an
+ 
+
+ align:start position:0%
+evisions and uh there's a change an
+abnormal uh abnormal levels of
+
+ align:start position:0%
+abnormal uh abnormal levels of
+ 
+
+ align:start position:0%
+abnormal uh abnormal levels of
+greenhouse emissions uh and then that
+
+ align:start position:0%
+greenhouse emissions uh and then that
+ 
+
+ align:start position:0%
+greenhouse emissions uh and then that
+started to connect it to to climate they
+
+ align:start position:0%
+started to connect it to to climate they
+ 
+
+ align:start position:0%
+started to connect it to to climate they
+started to use Wars that are stronger
+
+ align:start position:0%
+started to use Wars that are stronger
+ 
+
+ align:start position:0%
+started to use Wars that are stronger
+and stronger in terms of the probability
+
+ align:start position:0%
+and stronger in terms of the probability
+ 
+
+ align:start position:0%
+and stronger in terms of the probability
+of a climate change to be occurring so
+
+ align:start position:0%
+of a climate change to be occurring so
+ 
+
+ align:start position:0%
+of a climate change to be occurring so
+you see from 1995 they go from suggest
+
+ align:start position:0%
+you see from 1995 they go from suggest
+ 
+
+ align:start position:0%
+you see from 1995 they go from suggest
+20 20 2001 they go to likely very likely
+
+ align:start position:0%
+20 20 2001 they go to likely very likely
+ 
+
+ align:start position:0%
+20 20 2001 they go to likely very likely
+extremely likely all the way down to is
+
+ align:start position:0%
+extremely likely all the way down to is
+ 
+
+ align:start position:0%
+extremely likely all the way down to is
+already impacting us
+
+ align:start position:0%
+already impacting us
+ 
+
+ align:start position:0%
+already impacting us
+so this is something that when you are
+
+ align:start position:0%
+so this is something that when you are
+ 
+
+ align:start position:0%
+so this is something that when you are
+making decisions you see how the
+
+ align:start position:0%
+making decisions you see how the
+ 
+
+ align:start position:0%
+making decisions you see how the
+approach and the belief is changing over
+
+ align:start position:0%
+approach and the belief is changing over
+ 
+
+ align:start position:0%
+approach and the belief is changing over
+time and
+
+ align:start position:0%
+time and
+ 
+
+ align:start position:0%
+time and
+therefore that should have consequences
+
+ align:start position:0%
+therefore that should have consequences
+ 
+
+ align:start position:0%
+therefore that should have consequences
+into the decisions that people are
+
+ align:start position:0%
+into the decisions that people are
+ 
+
+ align:start position:0%
+into the decisions that people are
+making in terms of long-term uh
+
+ align:start position:0%
+making in terms of long-term uh
+ 
+
+ align:start position:0%
+making in terms of long-term uh
+allocations of capital long-terms decis
+
+ align:start position:0%
+allocations of capital long-terms decis
+ 
+
+ align:start position:0%
+allocations of capital long-terms decis
+investment decisions and especially when
+
+ align:start position:0%
+investment decisions and especially when
+ 
+
+ align:start position:0%
+investment decisions and especially when
+it comes to 50 years when it comes to
+
+ align:start position:0%
+it comes to 50 years when it comes to
+ 
+
+ align:start position:0%
+it comes to 50 years when it comes to
+things that are kind of two three uh
+
+ align:start position:0%
+things that are kind of two three uh
+ 
+
+ align:start position:0%
+things that are kind of two three uh
+decades ahead this is something that it
+
+ align:start position:0%
+decades ahead this is something that it
+ 
+
+ align:start position:0%
+decades ahead this is something that it
+is not anymore something that our next
+
+ align:start position:0%
+is not anymore something that our next
+ 
+
+ align:start position:0%
+is not anymore something that our next
+gener generation will be impacted but
+
+ align:start position:0%
+gener generation will be impacted but
+ 
+
+ align:start position:0%
+gener generation will be impacted but
+it's actually that our generation is
+
+ align:start position:0%
+it's actually that our generation is
+ 
+
+ align:start position:0%
+it's actually that our generation is
+impacted and especially when you think
+
+ align:start position:0%
+impacted and especially when you think
+ 
+
+ align:start position:0%
+impacted and especially when you think
+about insurance companies Pension funds
+
+ align:start position:0%
+about insurance companies Pension funds
+ 
+
+ align:start position:0%
+about insurance companies Pension funds
+and so forth those are already within
+
+ align:start position:0%
+and so forth those are already within
+ 
+
+ align:start position:0%
+and so forth those are already within
+the investment Horizon of those folks
+
+ align:start position:0%
+the investment Horizon of those folks
+ 
+
+ align:start position:0%
+the investment Horizon of those folks
+and when you're thinking about buying an
+
+ align:start position:0%
+and when you're thinking about buying an
+ 
+
+ align:start position:0%
+and when you're thinking about buying an
+asset to hold it uh for using purposes
+
+ align:start position:0%
+asset to hold it uh for using purposes
+ 
+
+ align:start position:0%
+asset to hold it uh for using purposes
+and so forth 20 30 years is something
+
+ align:start position:0%
+and so forth 20 30 years is something
+ 
+
+ align:start position:0%
+and so forth 20 30 years is something
+that it is not anymore the next guy that
+
+ align:start position:0%
+that it is not anymore the next guy that
+ 
+
+ align:start position:0%
+that it is not anymore the next guy that
+buys the building but is actually
+
+ align:start position:0%
+buys the building but is actually
+ 
+
+ align:start position:0%
+buys the building but is actually
+something that it is me the one that is
+
+ align:start position:0%
+something that it is me the one that is
+ 
+
+ align:start position:0%
+something that it is me the one that is
+going to suffer uh the expected damages
+
+ align:start position:0%
+going to suffer uh the expected damages
+ 
+
+ align:start position:0%
+going to suffer uh the expected damages
+of a hurricane or the expected cost
+
+ align:start position:0%
+of a hurricane or the expected cost
+ 
+
+ align:start position:0%
+of a hurricane or the expected cost
+associated with having an an AC running
+
+ align:start position:0%
+associated with having an an AC running
+ 
+
+ align:start position:0%
+associated with having an an AC running
+full power not 20 days a year but
+
+ align:start position:0%
+full power not 20 days a year but
+ 
+
+ align:start position:0%
+full power not 20 days a year but
+actually 40 days a year so this is
+
+ align:start position:0%
+actually 40 days a year so this is
+ 
+
+ align:start position:0%
+actually 40 days a year so this is
+exactly this is the key of climate
+
+ align:start position:0%
+exactly this is the key of climate
+ 
+
+ align:start position:0%
+exactly this is the key of climate
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+
+ align:start position:0%
+change this is actually what we have to
+ 
+
+ align:start position:0%
+change this is actually what we have to
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+
+ align:start position:0%
+think about how that changes as is going
+ 
+
+ align:start position:0%
+think about how that changes as is going
+to influence the real estate market is
+
+ align:start position:0%
+to influence the real estate market is
+ 
+
+ align:start position:0%
+to influence the real estate market is
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+
+ align:start position:0%
+going to influence the real estate
+ 
+
+ align:start position:0%
+going to influence the real estate
+investment decisions it is going from ah
+
+ align:start position:0%
+investment decisions it is going from ah
+ 
+
+ align:start position:0%
+investment decisions it is going from ah
+it seems nothing changes to oh it seems
+
+ align:start position:0%
+it seems nothing changes to oh it seems
+ 
+
+ align:start position:0%
+it seems nothing changes to oh it seems
+that there is a change here in in the
+
+ align:start position:0%
+that there is a change here in in the
+ 
+
+ align:start position:0%
+that there is a change here in in the
+atmosphere and actually it seems that
+
+ align:start position:0%
+atmosphere and actually it seems that
+ 
+
+ align:start position:0%
+atmosphere and actually it seems that
+it's actually something that is related
+
+ align:start position:0%
+it's actually something that is related
+ 
+
+ align:start position:0%
+it's actually something that is related
+to how we produce uh goods and how heat
+
+ align:start position:0%
+to how we produce uh goods and how heat
+ 
+
+ align:start position:0%
+to how we produce uh goods and how heat
+buildings the CO2 emissions that we
+
+ align:start position:0%
+buildings the CO2 emissions that we
+ 
+
+ align:start position:0%
+buildings the CO2 emissions that we
+produce that is also something that we
+
+ align:start position:0%
+produce that is also something that we
+ 
+
+ align:start position:0%
+produce that is also something that we
+know is not going to change in the next
+
+ align:start position:0%
+know is not going to change in the next
+ 
+
+ align:start position:0%
+know is not going to change in the next
+a few years and this actually something
+
+ align:start position:0%
+a few years and this actually something
+ 
+
+ align:start position:0%
+a few years and this actually something
+that hey it seems that we have enough
+
+ align:start position:0%
+that hey it seems that we have enough
+ 
+
+ align:start position:0%
+that hey it seems that we have enough
+evidence to see that the EM the the
+
+ align:start position:0%
+evidence to see that the EM the the
+ 
+
+ align:start position:0%
+evidence to see that the EM the the
+climate already changed when you compare
+
+ align:start position:0%
+climate already changed when you compare
+ 
+
+ align:start position:0%
+climate already changed when you compare
+it to the last 20 30 years uh beforehand
+
+ align:start position:0%
+it to the last 20 30 years uh beforehand
+ 
+
+ align:start position:0%
+it to the last 20 30 years uh beforehand
+okay how is it changing and where is it
+
+ align:start position:0%
+okay how is it changing and where is it
+ 
+
+ align:start position:0%
+okay how is it changing and where is it
+changing if you see uh so on the one
+
+ align:start position:0%
+changing if you see uh so on the one
+ 
+
+ align:start position:0%
+changing if you see uh so on the one
+hand as I said as we saw the weather is
+
+ align:start position:0%
+hand as I said as we saw the weather is
+ 
+
+ align:start position:0%
+hand as I said as we saw the weather is
+uh the climate is getting hot hotter and
+
+ align:start position:0%
+uh the climate is getting hot hotter and
+ 
+
+ align:start position:0%
+uh the climate is getting hot hotter and
+hotter the amount of heat waves are are
+
+ align:start position:0%
+hotter the amount of heat waves are are
+ 
+
+ align:start position:0%
+hotter the amount of heat waves are are
+increasing everywhere in the world so if
+
+ align:start position:0%
+increasing everywhere in the world so if
+ 
+
+ align:start position:0%
+increasing everywhere in the world so if
+you compare the differences with 1980s
+
+ align:start position:0%
+you compare the differences with 1980s
+ 
+
+ align:start position:0%
+you compare the differences with 1980s
+in temperature you see that everywhere
+
+ align:start position:0%
+in temperature you see that everywhere
+ 
+
+ align:start position:0%
+in temperature you see that everywhere
+in the world is getting hotter and that
+
+ align:start position:0%
+in the world is getting hotter and that
+ 
+
+ align:start position:0%
+in the world is getting hotter and that
+means that you know people are exposed
+
+ align:start position:0%
+means that you know people are exposed
+ 
+
+ align:start position:0%
+means that you know people are exposed
+to uncomfortably warm weather when it
+
+ align:start position:0%
+to uncomfortably warm weather when it
+ 
+
+ align:start position:0%
+to uncomfortably warm weather when it
+comes to selecting where to live much
+
+ align:start position:0%
+comes to selecting where to live much
+ 
+
+ align:start position:0%
+comes to selecting where to live much
+more than than they used to be
+
+ align:start position:0%
+more than than they used to be
+ 
+
+ align:start position:0%
+more than than they used to be
+especially in areas that were already
+
+ align:start position:0%
+especially in areas that were already
+ 
+
+ align:start position:0%
+especially in areas that were already
+warm um you have more problems with
+
+ align:start position:0%
+warm um you have more problems with
+ 
+
+ align:start position:0%
+warm um you have more problems with
+health more problems with different heat
+
+ align:start position:0%
+health more problems with different heat
+ 
+
+ align:start position:0%
+health more problems with different heat
+related disease with cardiovascular
+
+ align:start position:0%
+related disease with cardiovascular
+ 
+
+ align:start position:0%
+related disease with cardiovascular
+problems and so forth and then you also
+
+ align:start position:0%
+problems and so forth and then you also
+ 
+
+ align:start position:0%
+problems and so forth and then you also
+have a change in the in the distribution
+
+ align:start position:0%
+have a change in the in the distribution
+ 
+
+ align:start position:0%
+have a change in the in the distribution
+of precipitation so as the the
+
+ align:start position:0%
+of precipitation so as the the
+ 
+
+ align:start position:0%
+of precipitation so as the the
+atmosphere gets warmer it has a
+
+ align:start position:0%
+atmosphere gets warmer it has a
+ 
+
+ align:start position:0%
+atmosphere gets warmer it has a
+different capacity to absorb uh moisture
+
+ align:start position:0%
+different capacity to absorb uh moisture
+ 
+
+ align:start position:0%
+different capacity to absorb uh moisture
+and actually distribute that moisture so
+
+ align:start position:0%
+and actually distribute that moisture so
+ 
+
+ align:start position:0%
+and actually distribute that moisture so
+you see that on the one hand you get
+
+ align:start position:0%
+you see that on the one hand you get
+ 
+
+ align:start position:0%
+you see that on the one hand you get
+more uh problems with draws and people
+
+ align:start position:0%
+more uh problems with draws and people
+ 
+
+ align:start position:0%
+more uh problems with draws and people
+that have droughts and people that are
+
+ align:start position:0%
+that have droughts and people that are
+ 
+
+ align:start position:0%
+that have droughts and people that are
+coming from the area of California and
+
+ align:start position:0%
+coming from the area of California and
+ 
+
+ align:start position:0%
+coming from the area of California and
+so for can I speak to the idea that it
+
+ align:start position:0%
+so for can I speak to the idea that it
+ 
+
+ align:start position:0%
+so for can I speak to the idea that it
+is much more severe than it used to be
+
+ align:start position:0%
+is much more severe than it used to be
+ 
+
+ align:start position:0%
+is much more severe than it used to be
+10 15 20 years ago and also people I
+
+ align:start position:0%
+10 15 20 years ago and also people I
+ 
+
+ align:start position:0%
+10 15 20 years ago and also people I
+come from Spain
+
+ align:start position:0%
+come from Spain
+ 
+
+ align:start position:0%
+come from Spain
+uh we have like what it used to be a bad
+
+ align:start position:0%
+uh we have like what it used to be a bad
+ 
+
+ align:start position:0%
+uh we have like what it used to be a bad
+year in terms of having the Lakes almost
+
+ align:start position:0%
+year in terms of having the Lakes almost
+ 
+
+ align:start position:0%
+year in terms of having the Lakes almost
+empty now is sort of like the normal
+
+ align:start position:0%
+empty now is sort of like the normal
+ 
+
+ align:start position:0%
+empty now is sort of like the normal
+routine to see that the lakes are really
+
+ align:start position:0%
+routine to see that the lakes are really
+ 
+
+ align:start position:0%
+routine to see that the lakes are really
+being really empty and having problems
+
+ align:start position:0%
+being really empty and having problems
+ 
+
+ align:start position:0%
+being really empty and having problems
+for the Agriculture and having problems
+
+ align:start position:0%
+for the Agriculture and having problems
+ 
+
+ align:start position:0%
+for the Agriculture and having problems
+for H giving water to certain cities um
+
+ align:start position:0%
+for H giving water to certain cities um
+ 
+
+ align:start position:0%
+for H giving water to certain cities um
+and if you combine hot temperatures with
+
+ align:start position:0%
+and if you combine hot temperatures with
+ 
+
+ align:start position:0%
+and if you combine hot temperatures with
+dry temperatures you have the perfect
+
+ align:start position:0%
+dry temperatures you have the perfect
+ 
+
+ align:start position:0%
+dry temperatures you have the perfect
+scenario for wildfires so again if you
+
+ align:start position:0%
+scenario for wildfires so again if you
+ 
+
+ align:start position:0%
+scenario for wildfires so again if you
+say something from California you see
+
+ align:start position:0%
+say something from California you see
+ 
+
+ align:start position:0%
+say something from California you see
+that year after year you have in the
+
+ align:start position:0%
+that year after year you have in the
+ 
+
+ align:start position:0%
+that year after year you have in the
+news that there has been a a wildfire
+
+ align:start position:0%
+news that there has been a a wildfire
+ 
+
+ align:start position:0%
+news that there has been a a wildfire
+somewhere near a city and that has some
+
+ align:start position:0%
+somewhere near a city and that has some
+ 
+
+ align:start position:0%
+somewhere near a city and that has some
+infrastructure being destroyed some
+
+ align:start position:0%
+infrastructure being destroyed some
+ 
+
+ align:start position:0%
+infrastructure being destroyed some
+buildings being at the risk of fire and
+
+ align:start position:0%
+buildings being at the risk of fire and
+ 
+
+ align:start position:0%
+buildings being at the risk of fire and
+so forth so again something that used to
+
+ align:start position:0%
+so forth so again something that used to
+ 
+
+ align:start position:0%
+so forth so again something that used to
+happen once in a decade is now happening
+
+ align:start position:0%
+happen once in a decade is now happening
+ 
+
+ align:start position:0%
+happen once in a decade is now happening
+every year and that is again the
+
+ align:start position:0%
+every year and that is again the
+ 
+
+ align:start position:0%
+every year and that is again the
+probability change that we want to use
+
+ align:start position:0%
+probability change that we want to use
+ 
+
+ align:start position:0%
+probability change that we want to use
+in terms of how do people are responding
+
+ align:start position:0%
+in terms of how do people are responding
+ 
+
+ align:start position:0%
+in terms of how do people are responding
+in the real estate market and how that
+
+ align:start position:0%
+in the real estate market and how that
+ 
+
+ align:start position:0%
+in the real estate market and how that
+is affecting the value and the different
+
+ align:start position:0%
+is affecting the value and the different
+ 
+
+ align:start position:0%
+is affecting the value and the different
+decisions that are happening in the
+
+ align:start position:0%
+decisions that are happening in the
+ 
+
+ align:start position:0%
+decisions that are happening in the
+build
+
+ align:start position:0%
+build
+ 
+
+ align:start position:0%
+build
+environment and on the other hand you
+
+ align:start position:0%
+environment and on the other hand you
+ 
+
+ align:start position:0%
+environment and on the other hand you
+also have uh the of too much water in
+
+ align:start position:0%
+also have uh the of too much water in
+ 
+
+ align:start position:0%
+also have uh the of too much water in
+other places so if you see the the level
+
+ align:start position:0%
+other places so if you see the the level
+ 
+
+ align:start position:0%
+other places so if you see the the level
+of ice in in places like Antarctica in
+
+ align:start position:0%
+of ice in in places like Antarctica in
+ 
+
+ align:start position:0%
+of ice in in places like Antarctica in
+places like uh the North Pole or or
+
+ align:start position:0%
+places like uh the North Pole or or
+ 
+
+ align:start position:0%
+places like uh the North Pole or or
+Greenland you see that the amount of uh
+
+ align:start position:0%
+Greenland you see that the amount of uh
+ 
+
+ align:start position:0%
+Greenland you see that the amount of uh
+ice that is in there is much much lower
+
+ align:start position:0%
+ice that is in there is much much lower
+ 
+
+ align:start position:0%
+ice that is in there is much much lower
+than it used to be and it's not only the
+
+ align:start position:0%
+than it used to be and it's not only the
+ 
+
+ align:start position:0%
+than it used to be and it's not only the
+what the the ice that is generating from
+
+ align:start position:0%
+what the the ice that is generating from
+ 
+
+ align:start position:0%
+what the the ice that is generating from
+year to year but actually the ice that
+
+ align:start position:0%
+year to year but actually the ice that
+ 
+
+ align:start position:0%
+year to year but actually the ice that
+has been there for thousands of years is
+
+ align:start position:0%
+has been there for thousands of years is
+ 
+
+ align:start position:0%
+has been there for thousands of years is
+now being melted and it's going to take
+
+ align:start position:0%
+now being melted and it's going to take
+ 
+
+ align:start position:0%
+now being melted and it's going to take
+a lot of time if ever it's going to be
+
+ align:start position:0%
+a lot of time if ever it's going to be
+ 
+
+ align:start position:0%
+a lot of time if ever it's going to be
+recovered that is going to be more more
+
+ align:start position:0%
+recovered that is going to be more more
+ 
+
+ align:start position:0%
+recovered that is going to be more more
+water that is coming to the into the
+
+ align:start position:0%
+water that is coming to the into the
+ 
+
+ align:start position:0%
+water that is coming to the into the
+oceans and the season is going to make
+
+ align:start position:0%
+oceans and the season is going to make
+ 
+
+ align:start position:0%
+oceans and the season is going to make
+ultimately that the the coastal cities
+
+ align:start position:0%
+ultimately that the the coastal cities
+ 
+
+ align:start position:0%
+ultimately that the the coastal cities
+like Boston are going to have uh a sea
+
+ align:start position:0%
+like Boston are going to have uh a sea
+ 
+
+ align:start position:0%
+like Boston are going to have uh a sea
+level rise
+
+ align:start position:0%
+level rise
+ 
+
+ align:start position:0%
+level rise
+problem and not only that so even if you
+
+ align:start position:0%
+problem and not only that so even if you
+ 
+
+ align:start position:0%
+problem and not only that so even if you
+are not in the coastal areas what you
+
+ align:start position:0%
+are not in the coastal areas what you
+ 
+
+ align:start position:0%
+are not in the coastal areas what you
+see is that because of the distribution
+
+ align:start position:0%
+see is that because of the distribution
+ 
+
+ align:start position:0%
+see is that because of the distribution
+in moist or in the atmosphere you're not
+
+ align:start position:0%
+in moist or in the atmosphere you're not
+ 
+
+ align:start position:0%
+in moist or in the atmosphere you're not
+only having more problems with r but
+
+ align:start position:0%
+only having more problems with r but
+ 
+
+ align:start position:0%
+only having more problems with r but
+also you're having that when there is a
+
+ align:start position:0%
+also you're having that when there is a
+ 
+
+ align:start position:0%
+also you're having that when there is a
+rain is more likely to be a a big storm
+
+ align:start position:0%
+rain is more likely to be a a big storm
+ 
+
+ align:start position:0%
+rain is more likely to be a a big storm
+that you're going to discharge big
+
+ align:start position:0%
+that you're going to discharge big
+ 
+
+ align:start position:0%
+that you're going to discharge big
+amount of water in a given point often
+
+ align:start position:0%
+amount of water in a given point often
+ 
+
+ align:start position:0%
+amount of water in a given point often
+in a given region and it's going to make
+
+ align:start position:0%
+in a given region and it's going to make
+ 
+
+ align:start position:0%
+in a given region and it's going to make
+very difficult for that region to absorb
+
+ align:start position:0%
+very difficult for that region to absorb
+ 
+
+ align:start position:0%
+very difficult for that region to absorb
+the soil to absorb that that water is
+
+ align:start position:0%
+the soil to absorb that that water is
+ 
+
+ align:start position:0%
+the soil to absorb that that water is
+going to generate a lot of problems with
+
+ align:start position:0%
+going to generate a lot of problems with
+ 
+
+ align:start position:0%
+going to generate a lot of problems with
+with floods all over the place and
+
+ align:start position:0%
+with floods all over the place and
+ 
+
+ align:start position:0%
+with floods all over the place and
+especially next to to these big Rivers
+
+ align:start position:0%
+especially next to to these big Rivers
+ 
+
+ align:start position:0%
+especially next to to these big Rivers
+so there is no area that is not impacted
+
+ align:start position:0%
+so there is no area that is not impacted
+ 
+
+ align:start position:0%
+so there is no area that is not impacted
+by this risk in a lot of places like the
+
+ align:start position:0%
+by this risk in a lot of places like the
+ 
+
+ align:start position:0%
+by this risk in a lot of places like the
+United States not only the sea the the
+
+ align:start position:0%
+United States not only the sea the the
+ 
+
+ align:start position:0%
+United States not only the sea the the
+ones next to the sea but also all over
+
+ align:start position:0%
+ones next to the sea but also all over
+ 
+
+ align:start position:0%
+ones next to the sea but also all over
+all over the region you have the problem
+
+ align:start position:0%
+all over the region you have the problem
+ 
+
+ align:start position:0%
+all over the region you have the problem
+that you can have uh the chance to this
+
+ align:start position:0%
+that you can have uh the chance to this
+ 
+
+ align:start position:0%
+that you can have uh the chance to this
+biggest stor being being larger and
+
+ align:start position:0%
+biggest stor being being larger and
+ 
+
+ align:start position:0%
+biggest stor being being larger and
+therefore having big problems for water
+
+ align:start position:0%
+therefore having big problems for water
+ 
+
+ align:start position:0%
+therefore having big problems for water
+management and being able to cope with
+
+ align:start position:0%
+management and being able to cope with
+ 
+
+ align:start position:0%
+management and being able to cope with
+that amount of water in a very short
+
+ align:start position:0%
+that amount of water in a very short
+ 
+
+ align:start position:0%
+that amount of water in a very short
+term this will happens for example in
+
+ align:start position:0%
+term this will happens for example in
+ 
+
+ align:start position:0%
+term this will happens for example in
+Germany for those that are from Europe
+
+ align:start position:0%
+Germany for those that are from Europe
+ 
+
+ align:start position:0%
+Germany for those that are from Europe
+couple of years ago I was actually
+
+ align:start position:0%
+couple of years ago I was actually
+ 
+
+ align:start position:0%
+couple of years ago I was actually
+really nearby uh there out of the sudden
+
+ align:start position:0%
+really nearby uh there out of the sudden
+ 
+
+ align:start position:0%
+really nearby uh there out of the sudden
+there was a big storm and there was this
+
+ align:start position:0%
+there was a big storm and there was this
+ 
+
+ align:start position:0%
+there was a big storm and there was this
+one of the main rivers that got flooded
+
+ align:start position:0%
+one of the main rivers that got flooded
+ 
+
+ align:start position:0%
+one of the main rivers that got flooded
+and areas in Belgium in Germany and in
+
+ align:start position:0%
+and areas in Belgium in Germany and in
+ 
+
+ align:start position:0%
+and areas in Belgium in Germany and in
+in uh in the Netherlands got completely
+
+ align:start position:0%
+in uh in the Netherlands got completely
+ 
+
+ align:start position:0%
+in uh in the Netherlands got completely
+dilapidated by by the water and a lot of
+
+ align:start position:0%
+dilapidated by by the water and a lot of
+ 
+
+ align:start position:0%
+dilapidated by by the water and a lot of
+people died because especially in
+
+ align:start position:0%
+people died because especially in
+ 
+
+ align:start position:0%
+people died because especially in
+Germany people can't live in basements
+
+ align:start position:0%
+Germany people can't live in basements
+ 
+
+ align:start position:0%
+Germany people can't live in basements
+and they were worn too late they
+
+ align:start position:0%
+and they were worn too late they
+ 
+
+ align:start position:0%
+and they were worn too late they
+couldn't escape the basement and then
+
+ align:start position:0%
+couldn't escape the basement and then
+ 
+
+ align:start position:0%
+couldn't escape the basement and then
+the water came in into their their
+
+ align:start position:0%
+the water came in into their their
+ 
+
+ align:start position:0%
+the water came in into their their
+houses and then they died and at the
+
+ align:start position:0%
+houses and then they died and at the
+ 
+
+ align:start position:0%
+houses and then they died and at the
+same time Shi is originally from jeno at
+
+ align:start position:0%
+same time Shi is originally from jeno at
+ 
+
+ align:start position:0%
+same time Shi is originally from jeno at
+the very same time there was a big
+
+ align:start position:0%
+the very same time there was a big
+ 
+
+ align:start position:0%
+the very same time there was a big
+floating in in jeno for the exact same
+
+ align:start position:0%
+floating in in jeno for the exact same
+ 
+
+ align:start position:0%
+floating in in jeno for the exact same
+reason of big precipitation coming in
+
+ align:start position:0%
+reason of big precipitation coming in
+ 
+
+ align:start position:0%
+reason of big precipitation coming in
+and being unable to absorb all of that
+
+ align:start position:0%
+and being unable to absorb all of that
+ 
+
+ align:start position:0%
+and being unable to absorb all of that
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+so those events that again used to
+
+ align:start position:0%
+so those events that again used to
+ 
+
+ align:start position:0%
+so those events that again used to
+happen once in a lifetime now are
+
+ align:start position:0%
+happen once in a lifetime now are
+ 
+
+ align:start position:0%
+happen once in a lifetime now are
+happening more and more often and what
+
+ align:start position:0%
+happening more and more often and what
+ 
+
+ align:start position:0%
+happening more and more often and what
+it used to be something that you
+
+ align:start position:0%
+it used to be something that you
+ 
+
+ align:start position:0%
+it used to be something that you
+wouldn't care at all when you were
+
+ align:start position:0%
+wouldn't care at all when you were
+ 
+
+ align:start position:0%
+wouldn't care at all when you were
+underwriting any asset or making any
+
+ align:start position:0%
+underwriting any asset or making any
+ 
+
+ align:start position:0%
+underwriting any asset or making any
+decision now it comes to be very
+
+ align:start position:0%
+decision now it comes to be very
+ 
+
+ align:start position:0%
+decision now it comes to be very
+responsible if you you have no
+
+ align:start position:0%
+responsible if you you have no
+ 
+
+ align:start position:0%
+responsible if you you have no
+consideration for them because it's very
+
+ align:start position:0%
+consideration for them because it's very
+ 
+
+ align:start position:0%
+consideration for them because it's very
+very much more frequent than they used
+
+ align:start position:0%
+very much more frequent than they used
+ 
+
+ align:start position:0%
+very much more frequent than they used
+to be and this is again the probability
+
+ align:start position:0%
+to be and this is again the probability
+ 
+
+ align:start position:0%
+to be and this is again the probability
+that we want to think carefully about
+
+ align:start position:0%
+that we want to think carefully about
+ 
+
+ align:start position:0%
+that we want to think carefully about
+how that impact the the real estate
+
+ align:start position:0%
+how that impact the the real estate
+ 
+
+ align:start position:0%
+how that impact the the real estate
+markets and this is
+
+ align:start position:0%
+markets and this is
+ 
+
+ align:start position:0%
+markets and this is
+the overall trend this is the uh the
+
+ align:start position:0%
+the overall trend this is the uh the
+ 
+
+ align:start position:0%
+the overall trend this is the uh the
+number of uh every bar is the number of
+
+ align:start position:0%
+number of uh every bar is the number of
+ 
+
+ align:start position:0%
+number of uh every bar is the number of
+1 billion disasters across different
+
+ align:start position:0%
+1 billion disasters across different
+ 
+
+ align:start position:0%
+1 billion disasters across different
+type of uh events so draw droughts
+
+ align:start position:0%
+type of uh events so draw droughts
+ 
+
+ align:start position:0%
+type of uh events so draw droughts
+wildfires floting and so forth and if
+
+ align:start position:0%
+wildfires floting and so forth and if
+ 
+
+ align:start position:0%
+wildfires floting and so forth and if
+you see over the last decade there is a
+
+ align:start position:0%
+you see over the last decade there is a
+ 
+
+ align:start position:0%
+you see over the last decade there is a
+clear upward Trend into the number of
+
+ align:start position:0%
+clear upward Trend into the number of
+ 
+
+ align:start position:0%
+clear upward Trend into the number of
+events that are happening and these are
+
+ align:start position:0%
+events that are happening and these are
+ 
+
+ align:start position:0%
+events that are happening and these are
+events of1 billion dollar events these
+
+ align:start position:0%
+events of1 billion dollar events these
+ 
+
+ align:start position:0%
+events of1 billion dollar events these
+are not the smallest storms that you are
+
+ align:start position:0%
+are not the smallest storms that you are
+ 
+
+ align:start position:0%
+are not the smallest storms that you are
+seeing these are actually storms that
+
+ align:start position:0%
+seeing these are actually storms that
+ 
+
+ align:start position:0%
+seeing these are actually storms that
+are causing big damages and then you see
+
+ align:start position:0%
+are causing big damages and then you see
+ 
+
+ align:start position:0%
+are causing big damages and then you see
+in the in the
+
+ align:start position:0%
+in the in the
+ 
+
+ align:start position:0%
+in the in the
+how also
+
+ align:start position:0%
+how also
+ 
+
+ align:start position:0%
+how also
+the the amount of the cost in billions
+
+ align:start position:0%
+the the amount of the cost in billions
+ 
+
+ align:start position:0%
+the the amount of the cost in billions
+of the of those disasters are also going
+
+ align:start position:0%
+of the of those disasters are also going
+ 
+
+ align:start position:0%
+of the of those disasters are also going
+up so those are billions of dollars that
+
+ align:start position:0%
+up so those are billions of dollars that
+ 
+
+ align:start position:0%
+up so those are billions of dollars that
+are happening and they used to be just
+
+ align:start position:0%
+are happening and they used to be just
+ 
+
+ align:start position:0%
+are happening and they used to be just
+this much and they used to be this small
+
+ align:start position:0%
+this much and they used to be this small
+ 
+
+ align:start position:0%
+this much and they used to be this small
+here and now are going all the way up so
+
+ align:start position:0%
+here and now are going all the way up so
+ 
+
+ align:start position:0%
+here and now are going all the way up so
+those billions are being distributed
+
+ align:start position:0%
+those billions are being distributed
+ 
+
+ align:start position:0%
+those billions are being distributed
+ultimately among the public sector among
+
+ align:start position:0%
+ultimately among the public sector among
+ 
+
+ align:start position:0%
+ultimately among the public sector among
+the insurance companies and among the
+
+ align:start position:0%
+the insurance companies and among the
+ 
+
+ align:start position:0%
+the insurance companies and among the
+private sector but it's very clear
+
+ align:start position:0%
+private sector but it's very clear
+ 
+
+ align:start position:0%
+private sector but it's very clear
+that somehow we will all pay in one form
+
+ align:start position:0%
+that somehow we will all pay in one form
+ 
+
+ align:start position:0%
+that somehow we will all pay in one form
+or the other for it because the
+
+ align:start position:0%
+or the other for it because the
+ 
+
+ align:start position:0%
+or the other for it because the
+insurance are not going to keep
+
+ align:start position:0%
+insurance are not going to keep
+ 
+
+ align:start position:0%
+insurance are not going to keep
+absorbing billions and billions of
+
+ align:start position:0%
+absorbing billions and billions of
+ 
+
+ align:start position:0%
+absorbing billions and billions of
+dollars of climate disasters because
+
+ align:start position:0%
+dollars of climate disasters because
+ 
+
+ align:start position:0%
+dollars of climate disasters because
+there is just no way that you can
+
+ align:start position:0%
+there is just no way that you can
+ 
+
+ align:start position:0%
+there is just no way that you can
+actually keep making business sense of
+
+ align:start position:0%
+actually keep making business sense of
+ 
+
+ align:start position:0%
+actually keep making business sense of
+keep absorbing billions of dollars at
+
+ align:start position:0%
+keep absorbing billions of dollars at
+ 
+
+ align:start position:0%
+keep absorbing billions of dollars at
+that in places like Louisiana places
+
+ align:start position:0%
+that in places like Louisiana places
+ 
+
+ align:start position:0%
+that in places like Louisiana places
+like Florida and so forth Kevin uh and I
+
+ align:start position:0%
+like Florida and so forth Kevin uh and I
+ 
+
+ align:start position:0%
+like Florida and so forth Kevin uh and I
+and CI were talking about breakfast how
+
+ align:start position:0%
+and CI were talking about breakfast how
+ 
+
+ align:start position:0%
+and CI were talking about breakfast how
+insurance companies are exiting markets
+
+ align:start position:0%
+insurance companies are exiting markets
+ 
+
+ align:start position:0%
+insurance companies are exiting markets
+like Louisiana just because because
+
+ align:start position:0%
+like Louisiana just because because
+ 
+
+ align:start position:0%
+like Louisiana just because because
+there is just no financial model or no
+
+ align:start position:0%
+there is just no financial model or no
+ 
+
+ align:start position:0%
+there is just no financial model or no
+business sense to keep absorbing a lot
+
+ align:start position:0%
+business sense to keep absorbing a lot
+ 
+
+ align:start position:0%
+business sense to keep absorbing a lot
+of those damages if you have such a
+
+ align:start position:0%
+of those damages if you have such a
+ 
+
+ align:start position:0%
+of those damages if you have such a
+frequency of those disasters in in that
+
+ align:start position:0%
+frequency of those disasters in in that
+ 
+
+ align:start position:0%
+frequency of those disasters in in that
+region so you know for a while they can
+
+ align:start position:0%
+region so you know for a while they can
+ 
+
+ align:start position:0%
+region so you know for a while they can
+be a uh they can give you some bandwidth
+
+ align:start position:0%
+be a uh they can give you some bandwidth
+ 
+
+ align:start position:0%
+be a uh they can give you some bandwidth
+but if this becomes the systematic
+
+ align:start position:0%
+but if this becomes the systematic
+ 
+
+ align:start position:0%
+but if this becomes the systematic
+change there where every year you have
+
+ align:start position:0%
+change there where every year you have
+ 
+
+ align:start position:0%
+change there where every year you have
+to absorb all of those billions and even
+
+ align:start position:0%
+to absorb all of those billions and even
+ 
+
+ align:start position:0%
+to absorb all of those billions and even
+more because you see that the trend is
+
+ align:start position:0%
+more because you see that the trend is
+ 
+
+ align:start position:0%
+more because you see that the trend is
+going upward then ultimately you will go
+
+ align:start position:0%
+going upward then ultimately you will go
+ 
+
+ align:start position:0%
+going upward then ultimately you will go
+bankrupt or you will just decide to exit
+
+ align:start position:0%
+bankrupt or you will just decide to exit
+ 
+
+ align:start position:0%
+bankrupt or you will just decide to exit
+to make to keep making money out of your
+
+ align:start position:0%
+to make to keep making money out of your
+ 
+
+ align:start position:0%
+to make to keep making money out of your
+own business because if you keep just
+
+ align:start position:0%
+own business because if you keep just
+ 
+
+ align:start position:0%
+own business because if you keep just
+absorbing the punches eventually it just
+
+ align:start position:0%
+absorbing the punches eventually it just
+ 
+
+ align:start position:0%
+absorbing the punches eventually it just
+doesn't make any Financial sense so this
+
+ align:start position:0%
+doesn't make any Financial sense so this
+ 
+
+ align:start position:0%
+doesn't make any Financial sense so this
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+situation I hope that you are all
+
+ align:start position:0%
+situation I hope that you are all
+ 
+
+ align:start position:0%
+situation I hope that you are all
+depressed
+
+ align:start position:0%
+depressed
+ 
+
+ align:start position:0%
+depressed
+no When someone tells you that I hope
+
+ align:start position:0%
+no When someone tells you that I hope
+ 
+
+ align:start position:0%
+no When someone tells you that I hope
+that you be depressed you shouldn't
+
+ align:start position:0%
+that you be depressed you shouldn't
+ 
+
+ align:start position:0%
+that you be depressed you shouldn't
+laugh so I'm
+
+ align:start position:0%
+laugh so I'm
+ 
+
+ align:start position:0%
+laugh so I'm
+poite this will also bring bring us a
+
+ align:start position:0%
+poite this will also bring bring us a
+ 
+
+ align:start position:0%
+poite this will also bring bring us a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+job yeah for
+
+ align:start position:0%
+job yeah for
+ 
+
+ align:start position:0%
+job yeah for
+for for Rebuilders yeah exactly all the
+
+ align:start position:0%
+for for Rebuilders yeah exactly all the
+ 
+
+ align:start position:0%
+for for Rebuilders yeah exactly all the
+real companies they need
+
+ align:start position:0%
+real companies they need
+ 
+
+ align:start position:0%
+real companies they need
+us to start to to start the C the risks
+
+ align:start position:0%
+us to start to to start the C the risks
+ 
+
+ align:start position:0%
+us to start to to start the C the risks
+right yeah job opportunities for those
+
+ align:start position:0%
+right yeah job opportunities for those
+ 
+
+ align:start position:0%
+right yeah job opportunities for those
+that know and understand this yeah yeah
+
+ align:start position:0%
+that know and understand this yeah yeah
+ 
+
+ align:start position:0%
+that know and understand this yeah yeah
+only only from us we know yeah well
+
+ align:start position:0%
+only only from us we know yeah well
+ 
+
+ align:start position:0%
+only only from us we know yeah well
+definitely I mean there is a lot of
+
+ align:start position:0%
+definitely I mean there is a lot of
+ 
+
+ align:start position:0%
+definitely I mean there is a lot of
+people that never got these type of
+
+ align:start position:0%
+people that never got these type of
+ 
+
+ align:start position:0%
+people that never got these type of
+insights and they really they keep
+
+ align:start position:0%
+insights and they really they keep
+ 
+
+ align:start position:0%
+insights and they really they keep
+living in a they keep living and making
+
+ align:start position:0%
+living in a they keep living and making
+ 
+
+ align:start position:0%
+living in a they keep living and making
+decisions in a world that look like this
+
+ align:start position:0%
+decisions in a world that look like this
+ 
+
+ align:start position:0%
+decisions in a world that look like this
+while hopefully after these sessions and
+
+ align:start position:0%
+while hopefully after these sessions and
+ 
+
+ align:start position:0%
+while hopefully after these sessions and
+after this course you understand how to
+
+ align:start position:0%
+after this course you understand how to
+ 
+
+ align:start position:0%
+after this course you understand how to
+make decisions and how to uh think in a
+
+ align:start position:0%
+make decisions and how to uh think in a
+ 
+
+ align:start position:0%
+make decisions and how to uh think in a
+world that looks like
+
+ align:start position:0%
+world that looks like
+ 
+
+ align:start position:0%
+world that looks like
+present so that's where your job
+
+ align:start position:0%
+present so that's where your job
+ 
+
+ align:start position:0%
+present so that's where your job
+opportunities come thinking not like
+
+ align:start position:0%
+opportunities come thinking not like
+ 
+
+ align:start position:0%
+opportunities come thinking not like
+this but thinking like this and this is
+
+ align:start position:0%
+this but thinking like this and this is
+ 
+
+ align:start position:0%
+this but thinking like this and this is
+also one of the sessions Carlos you want
+
+ align:start position:0%
+also one of the sessions Carlos you want
+ 
+
+ align:start position:0%
+also one of the sessions Carlos you want
+to think like this I have a question
+
+ align:start position:0%
+to think like this I have a question
+ 
+
+ align:start position:0%
+to think like this I have a question
+sure looking into the graphs and seeing
+
+ align:start position:0%
+sure looking into the graphs and seeing
+ 
+
+ align:start position:0%
+sure looking into the graphs and seeing
+that the green component which is severe
+
+ align:start position:0%
+that the green component which is severe
+ 
+
+ align:start position:0%
+that the green component which is severe
+storm count is the one that has grown
+
+ align:start position:0%
+storm count is the one that has grown
+ 
+
+ align:start position:0%
+storm count is the one that has grown
+substantially and also looking at the
+
+ align:start position:0%
+substantially and also looking at the
+ 
+
+ align:start position:0%
+substantially and also looking at the
+five average cost line is there any
+
+ align:start position:0%
+five average cost line is there any
+ 
+
+ align:start position:0%
+five average cost line is there any
+correlation between how population has
+
+ align:start position:0%
+correlation between how population has
+ 
+
+ align:start position:0%
+correlation between how population has
+grown into big urban areas and how does
+
+ align:start position:0%
+grown into big urban areas and how does
+ 
+
+ align:start position:0%
+grown into big urban areas and how does
+that has affected indeed the costs of
+
+ align:start position:0%
+that has affected indeed the costs of
+ 
+
+ align:start position:0%
+that has affected indeed the costs of
+this this the the ongoing disasters that
+
+ align:start position:0%
+this this the the ongoing disasters that
+ 
+
+ align:start position:0%
+this this the the ongoing disasters that
+are related with at least with the
+
+ align:start position:0%
+are related with at least with the
+ 
+
+ align:start position:0%
+are related with at least with the
+storms and floodings yeah because I
+
+ align:start position:0%
+storms and floodings yeah because I
+ 
+
+ align:start position:0%
+storms and floodings yeah because I
+imagine I mean it's more costly if you
+
+ align:start position:0%
+imagine I mean it's more costly if you
+ 
+
+ align:start position:0%
+imagine I mean it's more costly if you
+have more people people living in dense
+
+ align:start position:0%
+have more people people living in dense
+ 
+
+ align:start position:0%
+have more people people living in dense
+areas that maybe separated small rural
+
+ align:start position:0%
+areas that maybe separated small rural
+ 
+
+ align:start position:0%
+areas that maybe separated small rural
+suburban concentration of people I don't
+
+ align:start position:0%
+suburban concentration of people I don't
+ 
+
+ align:start position:0%
+suburban concentration of people I don't
+know if it has any anything any
+
+ align:start position:0%
+know if it has any anything any
+ 
+
+ align:start position:0%
+know if it has any anything any
+correlation with the ongoing growing of
+
+ align:start position:0%
+correlation with the ongoing growing of
+ 
+
+ align:start position:0%
+correlation with the ongoing growing of
+costs yeah yeah it will not no that's a
+
+ align:start position:0%
+costs yeah yeah it will not no that's a
+ 
+
+ align:start position:0%
+costs yeah yeah it will not no that's a
+very good point and that's a very good
+
+ align:start position:0%
+very good point and that's a very good
+ 
+
+ align:start position:0%
+very good point and that's a very good
+question so it it will not explain the
+
+ align:start position:0%
+question so it it will not explain the
+ 
+
+ align:start position:0%
+question so it it will not explain the
+the the total amount of Damages but it
+
+ align:start position:0%
+the the total amount of Damages but it
+ 
+
+ align:start position:0%
+the the total amount of Damages but it
+is true that one of the failures of
+
+ align:start position:0%
+is true that one of the failures of
+ 
+
+ align:start position:0%
+is true that one of the failures of
+market failures that are creating that
+
+ align:start position:0%
+market failures that are creating that
+ 
+
+ align:start position:0%
+market failures that are creating that
+the that the damages are more sever here
+
+ align:start position:0%
+the that the damages are more sever here
+ 
+
+ align:start position:0%
+the that the damages are more sever here
+is that we keep letting people develop
+
+ align:start position:0%
+is that we keep letting people develop
+ 
+
+ align:start position:0%
+is that we keep letting people develop
+in areas that we know are at risk of
+
+ align:start position:0%
+in areas that we know are at risk of
+ 
+
+ align:start position:0%
+in areas that we know are at risk of
+floating we know that are at risk of
+
+ align:start position:0%
+floating we know that are at risk of
+ 
+
+ align:start position:0%
+floating we know that are at risk of
+suffering some of those uh events so it
+
+ align:start position:0%
+suffering some of those uh events so it
+ 
+
+ align:start position:0%
+suffering some of those uh events so it
+doesn't make sense that if you think
+
+ align:start position:0%
+doesn't make sense that if you think
+ 
+
+ align:start position:0%
+doesn't make sense that if you think
+about areas that are at very high risk
+
+ align:start position:0%
+about areas that are at very high risk
+ 
+
+ align:start position:0%
+about areas that are at very high risk
+of um of suffering a wildfire or
+
+ align:start position:0%
+of um of suffering a wildfire or
+ 
+
+ align:start position:0%
+of um of suffering a wildfire or
+suffering a storm that you keep letting
+
+ align:start position:0%
+suffering a storm that you keep letting
+ 
+
+ align:start position:0%
+suffering a storm that you keep letting
+people develop in those areas and you
+
+ align:start position:0%
+people develop in those areas and you
+ 
+
+ align:start position:0%
+people develop in those areas and you
+have for example the United State you
+
+ align:start position:0%
+have for example the United State you
+ 
+
+ align:start position:0%
+have for example the United State you
+have the FEMA Maps where you have a very
+
+ align:start position:0%
+have the FEMA Maps where you have a very
+ 
+
+ align:start position:0%
+have the FEMA Maps where you have a very
+accurate uh view on what are risky areas
+
+ align:start position:0%
+accurate uh view on what are risky areas
+ 
+
+ align:start position:0%
+accurate uh view on what are risky areas
+where are not risky areas and in a lot
+
+ align:start position:0%
+where are not risky areas and in a lot
+ 
+
+ align:start position:0%
+where are not risky areas and in a lot
+of places we let people develop as that
+
+ align:start position:0%
+of places we let people develop as that
+ 
+
+ align:start position:0%
+of places we let people develop as that
+risk is not there and we let people
+
+ align:start position:0%
+risk is not there and we let people
+ 
+
+ align:start position:0%
+risk is not there and we let people
+develop in areas where we know that
+
+ align:start position:0%
+develop in areas where we know that
+ 
+
+ align:start position:0%
+develop in areas where we know that
+sooner than later there will be
+
+ align:start position:0%
+sooner than later there will be
+ 
+
+ align:start position:0%
+sooner than later there will be
+something that will blow away uh those
+
+ align:start position:0%
+something that will blow away uh those
+ 
+
+ align:start position:0%
+something that will blow away uh those
+houses and therefore the damages and the
+
+ align:start position:0%
+houses and therefore the damages and the
+ 
+
+ align:start position:0%
+houses and therefore the damages and the
+human lives that are involved in that
+
+ align:start position:0%
+human lives that are involved in that
+ 
+
+ align:start position:0%
+human lives that are involved in that
+are at are at risk so we definitely need
+
+ align:start position:0%
+are at are at risk so we definitely need
+ 
+
+ align:start position:0%
+are at are at risk so we definitely need
+to rethink about different zoning areas
+
+ align:start position:0%
+to rethink about different zoning areas
+ 
+
+ align:start position:0%
+to rethink about different zoning areas
+that are um helping to mitigate those
+
+ align:start position:0%
+that are um helping to mitigate those
+ 
+
+ align:start position:0%
+that are um helping to mitigate those
+Risk by a avoiding that people are
+
+ align:start position:0%
+Risk by a avoiding that people are
+ 
+
+ align:start position:0%
+Risk by a avoiding that people are
+exposed to certain things in certain
+
+ align:start position:0%
+exposed to certain things in certain
+ 
+
+ align:start position:0%
+exposed to certain things in certain
+areas that we know are at
+
+ align:start position:0%
+areas that we know are at
+ 
+
+ align:start position:0%
+areas that we know are at
+disproportionately high risk of
+
+ align:start position:0%
+disproportionately high risk of
+ 
+
+ align:start position:0%
+disproportionately high risk of
+suffering a wildfire uh floating and so
+
+ align:start position:0%
+suffering a wildfire uh floating and so
+ 
+
+ align:start position:0%
+suffering a wildfire uh floating and so
+forth so this is part of the problem
+
+ align:start position:0%
+forth so this is part of the problem
+ 
+
+ align:start position:0%
+forth so this is part of the problem
+that we let people keep developing next
+
+ align:start position:0%
+that we let people keep developing next
+ 
+
+ align:start position:0%
+that we let people keep developing next
+to the coastal line we need to people
+
+ align:start position:0%
+to the coastal line we need to people
+ 
+
+ align:start position:0%
+to the coastal line we need to people
+and while we don't put infrastructure in
+
+ align:start position:0%
+and while we don't put infrastructure in
+ 
+
+ align:start position:0%
+and while we don't put infrastructure in
+place to to prevent the floting we let
+
+ align:start position:0%
+place to to prevent the floting we let
+ 
+
+ align:start position:0%
+place to to prevent the floting we let
+people to be uh leing next to River
+
+ align:start position:0%
+people to be uh leing next to River
+ 
+
+ align:start position:0%
+people to be uh leing next to River
+Flows that are at risk of floating when
+
+ align:start position:0%
+Flows that are at risk of floating when
+ 
+
+ align:start position:0%
+Flows that are at risk of floating when
+there the severe storms happening uh but
+
+ align:start position:0%
+there the severe storms happening uh but
+ 
+
+ align:start position:0%
+there the severe storms happening uh but
+part A lot of it is that as you see uh
+
+ align:start position:0%
+part A lot of it is that as you see uh
+ 
+
+ align:start position:0%
+part A lot of it is that as you see uh
+in the uh let me go back as you see in
+
+ align:start position:0%
+in the uh let me go back as you see in
+ 
+
+ align:start position:0%
+in the uh let me go back as you see in
+this map those events this is only for
+
+ align:start position:0%
+this map those events this is only for
+ 
+
+ align:start position:0%
+this map those events this is only for
+heat WS but that happens everywhere in
+
+ align:start position:0%
+heat WS but that happens everywhere in
+ 
+
+ align:start position:0%
+heat WS but that happens everywhere in
+in a lot of those events too those
+
+ align:start position:0%
+in a lot of those events too those
+ 
+
+ align:start position:0%
+in a lot of those events too those
+events are being more and more
+
+ align:start position:0%
+events are being more and more
+ 
+
+ align:start position:0%
+events are being more and more
+widespread and they are going more and
+
+ align:start position:0%
+widespread and they are going more and
+ 
+
+ align:start position:0%
+widespread and they are going more and
+more and they are more and more
+
+ align:start position:0%
+more and they are more and more
+ 
+
+ align:start position:0%
+more and they are more and more
+damaging uh year after year so that is
+
+ align:start position:0%
+damaging uh year after year so that is
+ 
+
+ align:start position:0%
+damaging uh year after year so that is
+uh that is the big part of that graph
+
+ align:start position:0%
+uh that is the big part of that graph
+ 
+
+ align:start position:0%
+uh that is the big part of that graph
+that something that if you see here if
+
+ align:start position:0%
+that something that if you see here if
+ 
+
+ align:start position:0%
+that something that if you see here if
+you think about Latin America here you
+
+ align:start position:0%
+you think about Latin America here you
+ 
+
+ align:start position:0%
+you think about Latin America here you
+see that it used to be it starts in blue
+
+ align:start position:0%
+see that it used to be it starts in blue
+ 
+
+ align:start position:0%
+see that it used to be it starts in blue
+and it's really nothing there but as you
+
+ align:start position:0%
+and it's really nothing there but as you
+ 
+
+ align:start position:0%
+and it's really nothing there but as you
+go on you see that it starts to be part
+
+ align:start position:0%
+go on you see that it starts to be part
+ 
+
+ align:start position:0%
+go on you see that it starts to be part
+of Latin America and now as as the graph
+
+ align:start position:0%
+of Latin America and now as as the graph
+ 
+
+ align:start position:0%
+of Latin America and now as as the graph
+goes on is the entire Latin America that
+
+ align:start position:0%
+goes on is the entire Latin America that
+ 
+
+ align:start position:0%
+goes on is the entire Latin America that
+is affected by heat waves so it is going
+
+ align:start position:0%
+is affected by heat waves so it is going
+ 
+
+ align:start position:0%
+is affected by heat waves so it is going
+more and more widespread and it's going
+
+ align:start position:0%
+more and more widespread and it's going
+ 
+
+ align:start position:0%
+more and more widespread and it's going
+more and more damaging and that is what
+
+ align:start position:0%
+more and more damaging and that is what
+ 
+
+ align:start position:0%
+more and more damaging and that is what
+is causing this uh this TR to go up
+
+ align:start position:0%
+is causing this uh this TR to go up
+ 
+
+ align:start position:0%
+is causing this uh this TR to go up
+together with the idea that we don't let
+
+ align:start position:0%
+together with the idea that we don't let
+ 
+
+ align:start position:0%
+together with the idea that we don't let
+people be protected given that we seems
+
+ align:start position:0%
+people be protected given that we seems
+ 
+
+ align:start position:0%
+people be protected given that we seems
+that we don't learn from the past and
+
+ align:start position:0%
+that we don't learn from the past and
+ 
+
+ align:start position:0%
+that we don't learn from the past and
+then we keep letting them leave whatever
+
+ align:start position:0%
+then we keep letting them leave whatever
+ 
+
+ align:start position:0%
+then we keep letting them leave whatever
+a developer decides them to to leave or
+
+ align:start position:0%
+a developer decides them to to leave or
+ 
+
+ align:start position:0%
+a developer decides them to to leave or
+then themselves decide to build up a
+
+ align:start position:0%
+then themselves decide to build up a
+ 
+
+ align:start position:0%
+then themselves decide to build up a
+partiel of land and we will talk about
+
+ align:start position:0%
+partiel of land and we will talk about
+ 
+
+ align:start position:0%
+partiel of land and we will talk about
+resiliency and we will talk about those
+
+ align:start position:0%
+resiliency and we will talk about those
+ 
+
+ align:start position:0%
+resiliency and we will talk about those
+things later too Bill that point and if
+
+ align:start position:0%
+things later too Bill that point and if
+ 
+
+ align:start position:0%
+things later too Bill that point and if
+you're going to touch on it later um
+
+ align:start position:0%
+you're going to touch on it later um
+ 
+
+ align:start position:0%
+you're going to touch on it later um
+then feel free to just
+
+ align:start position:0%
+then feel free to just
+ 
+
+ align:start position:0%
+then feel free to just
+skip we're dealing with finite amounts
+
+ align:start position:0%
+skip we're dealing with finite amounts
+ 
+
+ align:start position:0%
+skip we're dealing with finite amounts
+of public funds private sector funds and
+
+ align:start position:0%
+of public funds private sector funds and
+ 
+
+ align:start position:0%
+of public funds private sector funds and
+like you said there's already people
+
+ align:start position:0%
+like you said there's already people
+ 
+
+ align:start position:0%
+like you said there's already people
+living next to that River that's going
+
+ align:start position:0%
+living next to that River that's going
+ 
+
+ align:start position:0%
+living next to that River that's going
+to start overflowing
+
+ align:start position:0%
+to start overflowing
+ 
+
+ align:start position:0%
+to start overflowing
+five years rather than every 100 years
+
+ align:start position:0%
+five years rather than every 100 years
+ 
+
+ align:start position:0%
+five years rather than every 100 years
+where do you put money into adaptation
+
+ align:start position:0%
+where do you put money into adaptation
+ 
+
+ align:start position:0%
+where do you put money into adaptation
+and where do you put money into
+
+ align:start position:0%
+and where do you put money into
+ 
+
+ align:start position:0%
+and where do you put money into
+mitigation is that is it context context
+
+ align:start position:0%
+mitigation is that is it context context
+ 
+
+ align:start position:0%
+mitigation is that is it context context
+specific yeah that's a very good point a
+
+ align:start position:0%
+specific yeah that's a very good point a
+ 
+
+ align:start position:0%
+specific yeah that's a very good point a
+lot of it this comes down to political
+
+ align:start position:0%
+lot of it this comes down to political
+ 
+
+ align:start position:0%
+lot of it this comes down to political
+decision of what do you want to do and a
+
+ align:start position:0%
+decision of what do you want to do and a
+ 
+
+ align:start position:0%
+decision of what do you want to do and a
+lot of it we will talk about beliefs
+
+ align:start position:0%
+lot of it we will talk about beliefs
+ 
+
+ align:start position:0%
+lot of it we will talk about beliefs
+about climate change and so forth so
+
+ align:start position:0%
+about climate change and so forth so
+ 
+
+ align:start position:0%
+about climate change and so forth so
+then there is also some belief story
+
+ align:start position:0%
+then there is also some belief story
+ 
+
+ align:start position:0%
+then there is also some belief story
+there uh we will talk about uh later
+
+ align:start position:0%
+there uh we will talk about uh later
+ 
+
+ align:start position:0%
+there uh we will talk about uh later
+today or early on um on Thursday I think
+
+ align:start position:0%
+today or early on um on Thursday I think
+ 
+
+ align:start position:0%
+today or early on um on Thursday I think
+it will be early on Thursday given the
+
+ align:start position:0%
+it will be early on Thursday given the
+ 
+
+ align:start position:0%
+it will be early on Thursday given the
+the data and I want to give Kevin enough
+
+ align:start position:0%
+the data and I want to give Kevin enough
+ 
+
+ align:start position:0%
+the data and I want to give Kevin enough
+time to talk about resiliency investment
+
+ align:start position:0%
+time to talk about resiliency investment
+ 
+
+ align:start position:0%
+time to talk about resiliency investment
+so we will talk we will go through the
+
+ align:start position:0%
+so we will talk we will go through the
+ 
+
+ align:start position:0%
+so we will talk we will go through the
+case of Boston Seaport and how do we
+
+ align:start position:0%
+case of Boston Seaport and how do we
+ 
+
+ align:start position:0%
+case of Boston Seaport and how do we
+make those decisions uh all going down
+
+ align:start position:0%
+make those decisions uh all going down
+ 
+
+ align:start position:0%
+make those decisions uh all going down
+to the valuation of of those disasters
+
+ align:start position:0%
+to the valuation of of those disasters
+ 
+
+ align:start position:0%
+to the valuation of of those disasters
+and the valuation of uh the
+
+ align:start position:0%
+and the valuation of uh the
+ 
+
+ align:start position:0%
+and the valuation of uh the
+spected uh
+
+ align:start position:0%
+spected uh
+ 
+
+ align:start position:0%
+spected uh
+defensive uh effectiveness of the
+
+ align:start position:0%
+defensive uh effectiveness of the
+ 
+
+ align:start position:0%
+defensive uh effectiveness of the
+effectiveness of defensive Investments
+
+ align:start position:0%
+effectiveness of defensive Investments
+ 
+
+ align:start position:0%
+effectiveness of defensive Investments
+that we are going to do with different
+
+ align:start position:0%
+that we are going to do with different
+ 
+
+ align:start position:0%
+that we are going to do with different
+city walls and so forth and then you are
+
+ align:start position:0%
+city walls and so forth and then you are
+ 
+
+ align:start position:0%
+city walls and so forth and then you are
+going to see how those decisions are
+
+ align:start position:0%
+going to see how those decisions are
+ 
+
+ align:start position:0%
+going to see how those decisions are
+being influenced by mitigation versus
+
+ align:start position:0%
+being influenced by mitigation versus
+ 
+
+ align:start position:0%
+being influenced by mitigation versus
+adaptation preferences and also your
+
+ align:start position:0%
+adaptation preferences and also your
+ 
+
+ align:start position:0%
+adaptation preferences and also your
+beliefs about different risk associated
+
+ align:start position:0%
+beliefs about different risk associated
+ 
+
+ align:start position:0%
+beliefs about different risk associated
+with it and so forth and there we can we
+
+ align:start position:0%
+with it and so forth and there we can we
+ 
+
+ align:start position:0%
+with it and so forth and there we can we
+can talk more about it with those
+
+ align:start position:0%
+can talk more about it with those
+ 
+
+ align:start position:0%
+can talk more about it with those
+numbers in front of it anyone else
+
+ align:start position:0%
+numbers in front of it anyone else
+ 
+
+ align:start position:0%
+numbers in front of it anyone else
+David
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh7 yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pretty 1 was either Harvey Orma but
+
+ align:start position:0%
+pretty 1 was either Harvey Orma but
+ 
+
+ align:start position:0%
+pretty 1 was either Harvey Orma but
+there was of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wild great so one of the things that I
+
+ align:start position:0%
+wild great so one of the things that I
+ 
+
+ align:start position:0%
+wild great so one of the things that I
+want to do uh now is all of
+
+ align:start position:0%
+want to do uh now is all of
+ 
+
+ align:start position:0%
+want to do uh now is all of
+those disasters have some implications
+
+ align:start position:0%
+those disasters have some implications
+ 
+
+ align:start position:0%
+those disasters have some implications
+for real estate and now what we are
+
+ align:start position:0%
+for real estate and now what we are
+ 
+
+ align:start position:0%
+for real estate and now what we are
+going to do is also thinking about uh
+
+ align:start position:0%
+going to do is also thinking about uh
+ 
+
+ align:start position:0%
+going to do is also thinking about uh
+how those type of disasters are going to
+
+ align:start position:0%
+how those type of disasters are going to
+ 
+
+ align:start position:0%
+how those type of disasters are going to
+translate Ely to the bottom line one of
+
+ align:start position:0%
+translate Ely to the bottom line one of
+ 
+
+ align:start position:0%
+translate Ely to the bottom line one of
+the first steps is to start classifying
+
+ align:start position:0%
+the first steps is to start classifying
+ 
+
+ align:start position:0%
+the first steps is to start classifying
+those disasters it's not the same for uh
+
+ align:start position:0%
+those disasters it's not the same for uh
+ 
+
+ align:start position:0%
+those disasters it's not the same for uh
+a for the buil environment and for an
+
+ align:start position:0%
+a for the buil environment and for an
+ 
+
+ align:start position:0%
+a for the buil environment and for an
+investment in real estate to be thinking
+
+ align:start position:0%
+investment in real estate to be thinking
+ 
+
+ align:start position:0%
+investment in real estate to be thinking
+about exposure to a heat wve to being
+
+ align:start position:0%
+about exposure to a heat wve to being
+ 
+
+ align:start position:0%
+about exposure to a heat wve to being
+exposed to a wildfire or to being
+
+ align:start position:0%
+exposed to a wildfire or to being
+ 
+
+ align:start position:0%
+exposed to a wildfire or to being
+exposed to uh sea level rise or floting
+
+ align:start position:0%
+exposed to uh sea level rise or floting
+ 
+
+ align:start position:0%
+exposed to uh sea level rise or floting
+some of them have direct risk of uh
+
+ align:start position:0%
+some of them have direct risk of uh
+ 
+
+ align:start position:0%
+some of them have direct risk of uh
+destroying our properties some of them
+
+ align:start position:0%
+destroying our properties some of them
+ 
+
+ align:start position:0%
+destroying our properties some of them
+will have uh implications for the cost
+
+ align:start position:0%
+will have uh implications for the cost
+ 
+
+ align:start position:0%
+will have uh implications for the cost
+operating cost of that property some of
+
+ align:start position:0%
+operating cost of that property some of
+ 
+
+ align:start position:0%
+operating cost of that property some of
+them are actually things that are uh
+
+ align:start position:0%
+them are actually things that are uh
+ 
+
+ align:start position:0%
+them are actually things that are uh
+related to to risk and some of them are
+
+ align:start position:0%
+related to to risk and some of them are
+ 
+
+ align:start position:0%
+related to to risk and some of them are
+thinking related to um um to
+
+ align:start position:0%
+thinking related to um um to
+ 
+
+ align:start position:0%
+thinking related to um um to
+experiencing this amenities and this
+
+ align:start position:0%
+experiencing this amenities and this
+ 
+
+ align:start position:0%
+experiencing this amenities and this
+utility of being in that place uh if you
+
+ align:start position:0%
+utility of being in that place uh if you
+ 
+
+ align:start position:0%
+utility of being in that place uh if you
+look at the the classification that is
+
+ align:start position:0%
+look at the the classification that is
+ 
+
+ align:start position:0%
+look at the the classification that is
+usually taken in the real estate
+
+ align:start position:0%
+usually taken in the real estate
+ 
+
+ align:start position:0%
+usually taken in the real estate
+industry and if you see the reports of
+
+ align:start position:0%
+industry and if you see the reports of
+ 
+
+ align:start position:0%
+industry and if you see the reports of
+Uli and other other big thing tanks you
+
+ align:start position:0%
+Uli and other other big thing tanks you
+ 
+
+ align:start position:0%
+Uli and other other big thing tanks you
+will see that you have a classification
+
+ align:start position:0%
+will see that you have a classification
+ 
+
+ align:start position:0%
+will see that you have a classification
+of physical risk that is divided into
+
+ align:start position:0%
+of physical risk that is divided into
+ 
+
+ align:start position:0%
+of physical risk that is divided into
+two you have acute climate risk that is
+
+ align:start position:0%
+two you have acute climate risk that is
+ 
+
+ align:start position:0%
+two you have acute climate risk that is
+basically all of these catastrophic
+
+ align:start position:0%
+basically all of these catastrophic
+ 
+
+ align:start position:0%
+basically all of these catastrophic
+events these one billion dollar events
+
+ align:start position:0%
+events these one billion dollar events
+ 
+
+ align:start position:0%
+events these one billion dollar events
+that I showed you in the previous slide
+
+ align:start position:0%
+that I showed you in the previous slide
+ 
+
+ align:start position:0%
+that I showed you in the previous slide
+but you also have more chronic climate
+
+ align:start position:0%
+but you also have more chronic climate
+ 
+
+ align:start position:0%
+but you also have more chronic climate
+risk that are basically this disamenity
+
+ align:start position:0%
+risk that are basically this disamenity
+ 
+
+ align:start position:0%
+risk that are basically this disamenity
+like the increasing heat waves and also
+
+ align:start position:0%
+like the increasing heat waves and also
+ 
+
+ align:start position:0%
+like the increasing heat waves and also
+sea level rise those things that are not
+
+ align:start position:0%
+sea level rise those things that are not
+ 
+
+ align:start position:0%
+sea level rise those things that are not
+necessarily things that will generate a
+
+ align:start position:0%
+necessarily things that will generate a
+ 
+
+ align:start position:0%
+necessarily things that will generate a
+an impact as of now but it's actually
+
+ align:start position:0%
+an impact as of now but it's actually
+ 
+
+ align:start position:0%
+an impact as of now but it's actually
+increasing the risk of a lot of other
+
+ align:start position:0%
+increasing the risk of a lot of other
+ 
+
+ align:start position:0%
+increasing the risk of a lot of other
+stuff to happen so that's a big
+
+ align:start position:0%
+stuff to happen so that's a big
+ 
+
+ align:start position:0%
+stuff to happen so that's a big
+different then we have the transition
+
+ align:start position:0%
+different then we have the transition
+ 
+
+ align:start position:0%
+different then we have the transition
+risk that is a lot of the things that we
+
+ align:start position:0%
+risk that is a lot of the things that we
+ 
+
+ align:start position:0%
+risk that is a lot of the things that we
+also cover in the first block uh
+
+ align:start position:0%
+also cover in the first block uh
+ 
+
+ align:start position:0%
+also cover in the first block uh
+regulatory changes Market changes that
+
+ align:start position:0%
+regulatory changes Market changes that
+ 
+
+ align:start position:0%
+regulatory changes Market changes that
+will actually make those assets be less
+
+ align:start position:0%
+will actually make those assets be less
+ 
+
+ align:start position:0%
+will actually make those assets be less
+attractive so it's not only here we have
+
+ align:start position:0%
+attractive so it's not only here we have
+ 
+
+ align:start position:0%
+attractive so it's not only here we have
+like kind of the physical race is sort
+
+ align:start position:0%
+like kind of the physical race is sort
+ 
+
+ align:start position:0%
+like kind of the physical race is sort
+of risk is sort of the first order
+
+ align:start position:0%
+of risk is sort of the first order
+ 
+
+ align:start position:0%
+of risk is sort of the first order
+effect so once my asset is hit by that
+
+ align:start position:0%
+effect so once my asset is hit by that
+ 
+
+ align:start position:0%
+effect so once my asset is hit by that
+event how will that respond but also you
+
+ align:start position:0%
+event how will that respond but also you
+ 
+
+ align:start position:0%
+event how will that respond but also you
+have all the market responses associated
+
+ align:start position:0%
+have all the market responses associated
+ 
+
+ align:start position:0%
+have all the market responses associated
+with people believing that that uh heat
+
+ align:start position:0%
+with people believing that that uh heat
+ 
+
+ align:start position:0%
+with people believing that that uh heat
+will happen more often and will be more
+
+ align:start position:0%
+will happen more often and will be more
+ 
+
+ align:start position:0%
+will happen more often and will be more
+severe these are the two things that we
+
+ align:start position:0%
+severe these are the two things that we
+ 
+
+ align:start position:0%
+severe these are the two things that we
+are going to cover in the course and
+
+ align:start position:0%
+are going to cover in the course and
+ 
+
+ align:start position:0%
+are going to cover in the course and
+especially actually thinking about the
+
+ align:start position:0%
+especially actually thinking about the
+ 
+
+ align:start position:0%
+especially actually thinking about the
+market risk and transition RIS so before
+
+ align:start position:0%
+market risk and transition RIS so before
+ 
+
+ align:start position:0%
+market risk and transition RIS so before
+we want to be preventive here and we
+
+ align:start position:0%
+we want to be preventive here and we
+ 
+
+ align:start position:0%
+we want to be preventive here and we
+want to actually teach you how to avoid
+
+ align:start position:0%
+want to actually teach you how to avoid
+ 
+
+ align:start position:0%
+want to actually teach you how to avoid
+the punches so we actually want to teach
+
+ align:start position:0%
+the punches so we actually want to teach
+ 
+
+ align:start position:0%
+the punches so we actually want to teach
+you how to be ahead of of those severe
+
+ align:start position:0%
+you how to be ahead of of those severe
+ 
+
+ align:start position:0%
+you how to be ahead of of those severe
+events and actually how to cope with
+
+ align:start position:0%
+events and actually how to cope with
+ 
+
+ align:start position:0%
+events and actually how to cope with
+them using Market signals and Market
+
+ align:start position:0%
+them using Market signals and Market
+ 
+
+ align:start position:0%
+them using Market signals and Market
+strategies um there are few things here
+
+ align:start position:0%
+strategies um there are few things here
+ 
+
+ align:start position:0%
+strategies um there are few things here
+that you you want to uh think about it's
+
+ align:start position:0%
+that you you want to uh think about it's
+ 
+
+ align:start position:0%
+that you you want to uh think about it's
+a lot of the the things of raising sea
+
+ align:start position:0%
+a lot of the the things of raising sea
+ 
+
+ align:start position:0%
+a lot of the the things of raising sea
+levels raising average temperatures have
+
+ align:start position:0%
+levels raising average temperatures have
+ 
+
+ align:start position:0%
+levels raising average temperatures have
+to do with things that are happening on
+
+ align:start position:0%
+to do with things that are happening on
+ 
+
+ align:start position:0%
+to do with things that are happening on
+on a very continuous basis day year
+
+ align:start position:0%
+on a very continuous basis day year
+ 
+
+ align:start position:0%
+on a very continuous basis day year
+after years you have more higher
+
+ align:start position:0%
+after years you have more higher
+ 
+
+ align:start position:0%
+after years you have more higher
+temperatures year after years you have
+
+ align:start position:0%
+temperatures year after years you have
+ 
+
+ align:start position:0%
+temperatures year after years you have
+also a higher level of sea rise those
+
+ align:start position:0%
+also a higher level of sea rise those
+ 
+
+ align:start position:0%
+also a higher level of sea rise those
+are things that we are experiencing we
+
+ align:start position:0%
+are things that we are experiencing we
+ 
+
+ align:start position:0%
+are things that we are experiencing we
+can actually almost continuously
+
+ align:start position:0%
+can actually almost continuously
+ 
+
+ align:start position:0%
+can actually almost continuously
+incorporate it into this and then you
+
+ align:start position:0%
+incorporate it into this and then you
+ 
+
+ align:start position:0%
+incorporate it into this and then you
+have a lot of things that are
+
+ align:start position:0%
+have a lot of things that are
+ 
+
+ align:start position:0%
+have a lot of things that are
+catastrophic events that will happen
+
+ align:start position:0%
+catastrophic events that will happen
+ 
+
+ align:start position:0%
+catastrophic events that will happen
+every 10 years every 15 years and those
+
+ align:start position:0%
+every 10 years every 15 years and those
+ 
+
+ align:start position:0%
+every 10 years every 15 years and those
+are thinkings are those are events that
+
+ align:start position:0%
+are thinkings are those are events that
+ 
+
+ align:start position:0%
+are thinkings are those are events that
+are related to to risk you don't
+
+ align:start position:0%
+are related to to risk you don't
+ 
+
+ align:start position:0%
+are related to to risk you don't
+experience them on a daily basis you
+
+ align:start position:0%
+experience them on a daily basis you
+ 
+
+ align:start position:0%
+experience them on a daily basis you
+don't experience them on an hour bases
+
+ align:start position:0%
+don't experience them on an hour bases
+ 
+
+ align:start position:0%
+don't experience them on an hour bases
+those are things that are the risk to
+
+ align:start position:0%
+those are things that are the risk to
+ 
+
+ align:start position:0%
+those are things that are the risk to
+happen a very severe bad things in 10 15
+
+ align:start position:0%
+happen a very severe bad things in 10 15
+ 
+
+ align:start position:0%
+happen a very severe bad things in 10 15
+20 years
+
+ align:start position:0%
+20 years
+ 
+
+ align:start position:0%
+20 years
+um let me skip this and now we want to
+
+ align:start position:0%
+um let me skip this and now we want to
+ 
+
+ align:start position:0%
+um let me skip this and now we want to
+do in the last 10 minutes of of of this
+
+ align:start position:0%
+do in the last 10 minutes of of of this
+ 
+
+ align:start position:0%
+do in the last 10 minutes of of of this
+I want to
+
+ align:start position:0%
+I want to
+ 
+
+ align:start position:0%
+I want to
+actually use one of the key tools that
+
+ align:start position:0%
+actually use one of the key tools that
+ 
+
+ align:start position:0%
+actually use one of the key tools that
+you learn in real estate economics to
+
+ align:start position:0%
+you learn in real estate economics to
+ 
+
+ align:start position:0%
+you learn in real estate economics to
+understand how all of these translates
+
+ align:start position:0%
+understand how all of these translates
+ 
+
+ align:start position:0%
+understand how all of these translates
+into real estate markets and real estate
+
+ align:start position:0%
+into real estate markets and real estate
+ 
+
+ align:start position:0%
+into real estate markets and real estate
+uh building and asset values um there is
+
+ align:start position:0%
+uh building and asset values um there is
+ 
+
+ align:start position:0%
+uh building and asset values um there is
+a lot of and the reason why this is
+
+ align:start position:0%
+a lot of and the reason why this is
+ 
+
+ align:start position:0%
+a lot of and the reason why this is
+important is that there is a lot of
+
+ align:start position:0%
+important is that there is a lot of
+ 
+
+ align:start position:0%
+important is that there is a lot of
+literature every year every month you
+
+ align:start position:0%
+literature every year every month you
+ 
+
+ align:start position:0%
+literature every year every month you
+get a new paper showing that there is
+
+ align:start position:0%
+get a new paper showing that there is
+ 
+
+ align:start position:0%
+get a new paper showing that there is
+this climate event or This Disaster that
+
+ align:start position:0%
+this climate event or This Disaster that
+ 
+
+ align:start position:0%
+this climate event or This Disaster that
+is linked to a drop in value and so
+
+ align:start position:0%
+is linked to a drop in value and so
+ 
+
+ align:start position:0%
+is linked to a drop in value and so
+forth so there is a lot of different
+
+ align:start position:0%
+forth so there is a lot of different
+ 
+
+ align:start position:0%
+forth so there is a lot of different
+scatter pieces out there and it will
+
+ align:start position:0%
+scatter pieces out there and it will
+ 
+
+ align:start position:0%
+scatter pieces out there and it will
+happen more and more over the years so
+
+ align:start position:0%
+happen more and more over the years so
+ 
+
+ align:start position:0%
+happen more and more over the years so
+when you graduate and when you need to
+
+ align:start position:0%
+when you graduate and when you need to
+ 
+
+ align:start position:0%
+when you graduate and when you need to
+incorporate those things there will be a
+
+ align:start position:0%
+incorporate those things there will be a
+ 
+
+ align:start position:0%
+incorporate those things there will be a
+tons of new papers and what we need to
+
+ align:start position:0%
+tons of new papers and what we need to
+ 
+
+ align:start position:0%
+tons of new papers and what we need to
+do here is to give you a good framework
+
+ align:start position:0%
+do here is to give you a good framework
+ 
+
+ align:start position:0%
+do here is to give you a good framework
+and a good way to understand how those
+
+ align:start position:0%
+and a good way to understand how those
+ 
+
+ align:start position:0%
+and a good way to understand how those
+translates ultimately into asset values
+
+ align:start position:0%
+translates ultimately into asset values
+ 
+
+ align:start position:0%
+translates ultimately into asset values
+and how those actually connect with each
+
+ align:start position:0%
+and how those actually connect with each
+ 
+
+ align:start position:0%
+and how those actually connect with each
+other and in a way that if you see that
+
+ align:start position:0%
+other and in a way that if you see that
+ 
+
+ align:start position:0%
+other and in a way that if you see that
+on the one side tenants are affected how
+
+ align:start position:0%
+on the one side tenants are affected how
+ 
+
+ align:start position:0%
+on the one side tenants are affected how
+you actually think from your developer
+
+ align:start position:0%
+you actually think from your developer
+ 
+
+ align:start position:0%
+you actually think from your developer
+chair about the consequences of of your
+
+ align:start position:0%
+chair about the consequences of of your
+ 
+
+ align:start position:0%
+chair about the consequences of of your
+decisions so one of the things that I
+
+ align:start position:0%
+decisions so one of the things that I
+ 
+
+ align:start position:0%
+decisions so one of the things that I
+want to do is get someone to help me
+
+ align:start position:0%
+want to do is get someone to help me
+ 
+
+ align:start position:0%
+want to do is get someone to help me
+understand the four quadrant model so
+
+ align:start position:0%
+understand the four quadrant model so
+ 
+
+ align:start position:0%
+understand the four quadrant model so
+who can tell me what it is and who can
+
+ align:start position:0%
+who can tell me what it is and who can
+ 
+
+ align:start position:0%
+who can tell me what it is and who can
+tell me who is in each of the spaces so
+
+ align:start position:0%
+tell me who is in each of the spaces so
+ 
+
+ align:start position:0%
+tell me who is in each of the spaces so
+who is in in this space you start here
+
+ align:start position:0%
+who is in in this space you start here
+ 
+
+ align:start position:0%
+who is in in this space you start here
+from the top right who is in this space
+
+ align:start position:0%
+from the top right who is in this space
+ 
+
+ align:start position:0%
+from the top right who is in this space
+who meets in this space the developer
+
+ align:start position:0%
+who meets in this space the developer
+ 
+
+ align:start position:0%
+who meets in this space the developer
+the construction company the tenants the
+
+ align:start position:0%
+the construction company the tenants the
+ 
+
+ align:start position:0%
+the construction company the tenants the
+banks landlords and tenants all right
+
+ align:start position:0%
+banks landlords and tenants all right
+ 
+
+ align:start position:0%
+banks landlords and tenants all right
+and how do they relate to each other
+
+ align:start position:0%
+and how do they relate to each other
+ 
+
+ align:start position:0%
+and how do they relate to each other
+Julio what are they doing here what is
+
+ align:start position:0%
+Julio what are they doing here what is
+ 
+
+ align:start position:0%
+Julio what are they doing here what is
+this curve telling me I see a stock I
+
+ align:start position:0%
+this curve telling me I see a stock I
+ 
+
+ align:start position:0%
+this curve telling me I see a stock I
+see rent who decides what that's a
+
+ align:start position:0%
+see rent who decides what that's a
+ 
+
+ align:start position:0%
+see rent who decides what that's a
+demand curve now have it's showing the
+
+ align:start position:0%
+demand curve now have it's showing the
+ 
+
+ align:start position:0%
+demand curve now have it's showing the
+but you also have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+supp so the supply the way that we
+
+ align:start position:0%
+supp so the supply the way that we
+ 
+
+ align:start position:0%
+supp so the supply the way that we
+usually start is that the supply is
+
+ align:start position:0%
+usually start is that the supply is
+ 
+
+ align:start position:0%
+usually start is that the supply is
+fixed right we don't move they building
+
+ align:start position:0%
+fixed right we don't move they building
+ 
+
+ align:start position:0%
+fixed right we don't move they building
+a stock from year to year it takes some
+
+ align:start position:0%
+a stock from year to year it takes some
+ 
+
+ align:start position:0%
+a stock from year to year it takes some
+time to build housing to build buildings
+
+ align:start position:0%
+time to build housing to build buildings
+ 
+
+ align:start position:0%
+time to build housing to build buildings
+so this s0 is a starting point and then
+
+ align:start position:0%
+so this s0 is a starting point and then
+ 
+
+ align:start position:0%
+so this s0 is a starting point and then
+given the the demand for a space of
+
+ align:start position:0%
+given the the demand for a space of
+ 
+
+ align:start position:0%
+given the the demand for a space of
+tenants this is the amount of rent that
+
+ align:start position:0%
+tenants this is the amount of rent that
+ 
+
+ align:start position:0%
+tenants this is the amount of rent that
+they will
+
+ align:start position:0%
+they will
+ 
+
+ align:start position:0%
+they will
+pay if the if the if the tenants want
+
+ align:start position:0%
+pay if the if the if the tenants want
+ 
+
+ align:start position:0%
+pay if the if the if the tenants want
+more space then this this line will go
+
+ align:start position:0%
+more space then this this line will go
+ 
+
+ align:start position:0%
+more space then this this line will go
+to the right if the tenants will go less
+
+ align:start position:0%
+to the right if the tenants will go less
+ 
+
+ align:start position:0%
+to the right if the tenants will go less
+will need less space this tenant this
+
+ align:start position:0%
+will need less space this tenant this
+ 
+
+ align:start position:0%
+will need less space this tenant this
+Curve will move inwards so if you think
+
+ align:start position:0%
+Curve will move inwards so if you think
+ 
+
+ align:start position:0%
+Curve will move inwards so if you think
+about now this working from home and so
+
+ align:start position:0%
+about now this working from home and so
+ 
+
+ align:start position:0%
+about now this working from home and so
+forth these tenants will actually demand
+
+ align:start position:0%
+forth these tenants will actually demand
+ 
+
+ align:start position:0%
+forth these tenants will actually demand
+less space so this Curve will go inward
+
+ align:start position:0%
+less space so this Curve will go inward
+ 
+
+ align:start position:0%
+less space so this Curve will go inward
+so forever for whatever the amount of
+
+ align:start position:0%
+so forever for whatever the amount of
+ 
+
+ align:start position:0%
+so forever for whatever the amount of
+buildings are in a city like New York I
+
+ align:start position:0%
+buildings are in a city like New York I
+ 
+
+ align:start position:0%
+buildings are in a city like New York I
+will need less space that I used to be
+
+ align:start position:0%
+will need less space that I used to be
+ 
+
+ align:start position:0%
+will need less space that I used to be
+okay so now we have a supplying meeting
+
+ align:start position:0%
+okay so now we have a supplying meeting
+ 
+
+ align:start position:0%
+okay so now we have a supplying meeting
+the tenants what about the asset
+
+ align:start position:0%
+the tenants what about the asset
+ 
+
+ align:start position:0%
+the tenants what about the asset
+Market what who meets there it's uh
+
+ align:start position:0%
+Market what who meets there it's uh
+ 
+
+ align:start position:0%
+Market what who meets there it's uh
+buyers and sellers so given that level
+
+ align:start position:0%
+buyers and sellers so given that level
+ 
+
+ align:start position:0%
+buyers and sellers so given that level
+we just established you then determ what
+
+ align:start position:0%
+we just established you then determ what
+ 
+
+ align:start position:0%
+we just established you then determ what
+the market prices for transactions so if
+
+ align:start position:0%
+the market prices for transactions so if
+ 
+
+ align:start position:0%
+the market prices for transactions so if
+you're like you said if your rent
+
+ align:start position:0%
+you're like you said if your rent
+ 
+
+ align:start position:0%
+you're like you said if your rent
+increases the price increases but if
+
+ align:start position:0%
+increases the price increases but if
+ 
+
+ align:start position:0%
+increases the price increases but if
+it's decreasing the price will decrease
+
+ align:start position:0%
+it's decreasing the price will decrease
+ 
+
+ align:start position:0%
+it's decreasing the price will decrease
+fewer transactions and how do we think
+
+ align:start position:0%
+fewer transactions and how do we think
+ 
+
+ align:start position:0%
+fewer transactions and how do we think
+about movements in these curve what
+
+ align:start position:0%
+about movements in these curve what
+ 
+
+ align:start position:0%
+about movements in these curve what
+makes that
+
+ align:start position:0%
+makes that
+ 
+
+ align:start position:0%
+makes that
+move here movees that curve stronger
+
+ align:start position:0%
+move here movees that curve stronger
+ 
+
+ align:start position:0%
+move here movees that curve stronger
+stronger fundamentals in the market so
+
+ align:start position:0%
+stronger fundamentals in the market so
+ 
+
+ align:start position:0%
+stronger fundamentals in the market so
+higher rents me higher value or lower
+
+ align:start position:0%
+higher rents me higher value or lower
+ 
+
+ align:start position:0%
+higher rents me higher value or lower
+rent be lower value yeah but that will
+
+ align:start position:0%
+rent be lower value yeah but that will
+ 
+
+ align:start position:0%
+rent be lower value yeah but that will
+be movements along the curve right so if
+
+ align:start position:0%
+be movements along the curve right so if
+ 
+
+ align:start position:0%
+be movements along the curve right so if
+this rent will be here then that price
+
+ align:start position:0%
+this rent will be here then that price
+ 
+
+ align:start position:0%
+this rent will be here then that price
+will be there but how should we think
+
+ align:start position:0%
+will be there but how should we think
+ 
+
+ align:start position:0%
+will be there but how should we think
+about movements in this curve What would
+
+ align:start position:0%
+about movements in this curve What would
+ 
+
+ align:start position:0%
+about movements in this curve What would
+make that for a given rent the price
+
+ align:start position:0%
+make that for a given rent the price
+ 
+
+ align:start position:0%
+make that for a given rent the price
+will be higher or for a given rent the
+
+ align:start position:0%
+will be higher or for a given rent the
+ 
+
+ align:start position:0%
+will be higher or for a given rent the
+price will be lower changes in Cates
+
+ align:start position:0%
+price will be lower changes in Cates
+ 
+
+ align:start position:0%
+price will be lower changes in Cates
+okay and what generates changes in C
+
+ align:start position:0%
+okay and what generates changes in C
+ 
+
+ align:start position:0%
+okay and what generates changes in C
+Rate underly
+
+ align:start position:0%
+Rate underly
+ 
+
+ align:start position:0%
+Rate underly
+Financial systems
+
+ align:start position:0%
+Financial systems
+ 
+
+ align:start position:0%
+Financial systems
+economics interest rates okay so and
+
+ align:start position:0%
+economics interest rates okay so and
+ 
+
+ align:start position:0%
+economics interest rates okay so and
+what about asset a
+
+ align:start position:0%
+what about asset a
+ 
+
+ align:start position:0%
+what about asset a
+specific uh
+
+ align:start position:0%
+specific uh
+ 
+
+ align:start position:0%
+specific uh
+perception risk what happens if the risk
+
+ align:start position:0%
+perception risk what happens if the risk
+ 
+
+ align:start position:0%
+perception risk what happens if the risk
+of an asset is
+
+ align:start position:0%
+of an asset is
+ 
+
+ align:start position:0%
+of an asset is
+higher or perceive as higher rate would
+
+ align:start position:0%
+higher or perceive as higher rate would
+ 
+
+ align:start position:0%
+higher or perceive as higher rate would
+increase and that means that the this
+
+ align:start position:0%
+increase and that means that the this
+ 
+
+ align:start position:0%
+increase and that means that the this
+guy will be here right because for a
+
+ align:start position:0%
+guy will be here right because for a
+ 
+
+ align:start position:0%
+guy will be here right because for a
+given rent the high the risk will be
+
+ align:start position:0%
+given rent the high the risk will be
+ 
+
+ align:start position:0%
+given rent the high the risk will be
+higher and therefore the more reluctant
+
+ align:start position:0%
+higher and therefore the more reluctant
+ 
+
+ align:start position:0%
+higher and therefore the more reluctant
+I will be to hold that asset because at
+
+ align:start position:0%
+I will be to hold that asset because at
+ 
+
+ align:start position:0%
+I will be to hold that asset because at
+the end of the day as a as an investor
+
+ align:start position:0%
+the end of the day as a as an investor
+ 
+
+ align:start position:0%
+the end of the day as a as an investor
+what I care about is not how beautiful
+
+ align:start position:0%
+what I care about is not how beautiful
+ 
+
+ align:start position:0%
+what I care about is not how beautiful
+is the building or anything like that
+
+ align:start position:0%
+is the building or anything like that
+ 
+
+ align:start position:0%
+is the building or anything like that
+what I care is about my chances to get
+
+ align:start position:0%
+what I care is about my chances to get
+ 
+
+ align:start position:0%
+what I care is about my chances to get
+to retrieve back cash flows so as those
+
+ align:start position:0%
+to retrieve back cash flows so as those
+ 
+
+ align:start position:0%
+to retrieve back cash flows so as those
+cash flows are getting riskier then my
+
+ align:start position:0%
+cash flows are getting riskier then my
+ 
+
+ align:start position:0%
+cash flows are getting riskier then my
+willingness to pay for that asset is
+
+ align:start position:0%
+willingness to pay for that asset is
+ 
+
+ align:start position:0%
+willingness to pay for that asset is
+going to be lower because you know it
+
+ align:start position:0%
+going to be lower because you know it
+ 
+
+ align:start position:0%
+going to be lower because you know it
+might be that the tenants go away if you
+
+ align:start position:0%
+might be that the tenants go away if you
+ 
+
+ align:start position:0%
+might be that the tenants go away if you
+think about holding the same asset
+
+ align:start position:0%
+think about holding the same asset
+ 
+
+ align:start position:0%
+think about holding the same asset
+before and after covid or before and
+
+ align:start position:0%
+before and after covid or before and
+ 
+
+ align:start position:0%
+before and after covid or before and
+after the war work from home uh changes
+
+ align:start position:0%
+after the war work from home uh changes
+ 
+
+ align:start position:0%
+after the war work from home uh changes
+in New York it is probably the same
+
+ align:start position:0%
+in New York it is probably the same
+ 
+
+ align:start position:0%
+in New York it is probably the same
+Leist structure and so for in a lot of
+
+ align:start position:0%
+Leist structure and so for in a lot of
+ 
+
+ align:start position:0%
+Leist structure and so for in a lot of
+assets but now I'm way more worried that
+
+ align:start position:0%
+assets but now I'm way more worried that
+ 
+
+ align:start position:0%
+assets but now I'm way more worried that
+those tenants will leave and even though
+
+ align:start position:0%
+those tenants will leave and even though
+ 
+
+ align:start position:0%
+those tenants will leave and even though
+I'm buying the same set of contracts my
+
+ align:start position:0%
+I'm buying the same set of contracts my
+ 
+
+ align:start position:0%
+I'm buying the same set of contracts my
+expectation that those leases will stop
+
+ align:start position:0%
+expectation that those leases will stop
+ 
+
+ align:start position:0%
+expectation that those leases will stop
+is much higher so for whatever the
+
+ align:start position:0%
+is much higher so for whatever the
+ 
+
+ align:start position:0%
+is much higher so for whatever the
+rental value is as of now I'm going to
+
+ align:start position:0%
+rental value is as of now I'm going to
+ 
+
+ align:start position:0%
+rental value is as of now I'm going to
+pay much lower price because i'm way
+
+ align:start position:0%
+pay much lower price because i'm way
+ 
+
+ align:start position:0%
+pay much lower price because i'm way
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+worried okay who can help me with the
+
+ align:start position:0%
+worried okay who can help me with the
+ 
+
+ align:start position:0%
+worried okay who can help me with the
+top with the bottom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bill as prices increase for
+
+ align:start position:0%
+bill as prices increase for
+ 
+
+ align:start position:0%
+bill as prices increase for
+assets developers resp build more MH
+
+ align:start position:0%
+assets developers resp build more MH
+ 
+
+ align:start position:0%
+assets developers resp build more MH
+okay and uh what about this why is not
+
+ align:start position:0%
+okay and uh what about this why is not
+ 
+
+ align:start position:0%
+okay and uh what about this why is not
+like the rest of the lines start
+
+ align:start position:0%
+like the rest of the lines start
+ 
+
+ align:start position:0%
+like the rest of the lines start
+here in the in the cross of the two axis
+
+ align:start position:0%
+here in the in the cross of the two axis
+ 
+
+ align:start position:0%
+here in the in the cross of the two axis
+why is that one started only here um I'm
+
+ align:start position:0%
+why is that one started only here um I'm
+ 
+
+ align:start position:0%
+why is that one started only here um I'm
+assuming because you already have a
+
+ align:start position:0%
+assuming because you already have a
+ 
+
+ align:start position:0%
+assuming because you already have a
+certain amount of MH you're not going to
+
+ align:start position:0%
+certain amount of MH you're not going to
+ 
+
+ align:start position:0%
+certain amount of MH you're not going to
+go to zero like you're going to always
+
+ align:start position:0%
+go to zero like you're going to always
+ 
+
+ align:start position:0%
+go to zero like you're going to always
+have some square footage some stock and
+
+ align:start position:0%
+have some square footage some stock and
+ 
+
+ align:start position:0%
+have some square footage some stock and
+that's why it doesn't start from
+
+ align:start position:0%
+that's why it doesn't start from
+ 
+
+ align:start position:0%
+that's why it doesn't start from
+zero any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thought make any money so certain price
+
+ align:start position:0%
+thought make any money so certain price
+ 
+
+ align:start position:0%
+thought make any money so certain price
+it started to make and that's where it
+
+ align:start position:0%
+it started to make and that's where it
+ 
+
+ align:start position:0%
+it started to make and that's where it
+yeah so you can think about this as the
+
+ align:start position:0%
+yeah so you can think about this as the
+ 
+
+ align:start position:0%
+yeah so you can think about this as the
+number of square feet that are built if
+
+ align:start position:0%
+number of square feet that are built if
+ 
+
+ align:start position:0%
+number of square feet that are built if
+you don't reach certain amount you will
+
+ align:start position:0%
+you don't reach certain amount you will
+ 
+
+ align:start position:0%
+you don't reach certain amount you will
+be at all you will not have make any
+
+ align:start position:0%
+be at all you will not have make any
+ 
+
+ align:start position:0%
+be at all you will not have make any
+sense of building a building at all uh
+
+ align:start position:0%
+sense of building a building at all uh
+ 
+
+ align:start position:0%
+sense of building a building at all uh
+what makes this curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+move here we have like preferences of
+
+ align:start position:0%
+move here we have like preferences of
+ 
+
+ align:start position:0%
+move here we have like preferences of
+tenants here we have the cap rates and
+
+ align:start position:0%
+tenants here we have the cap rates and
+ 
+
+ align:start position:0%
+tenants here we have the cap rates and
+the assessment of risk of an asset what
+
+ align:start position:0%
+the assessment of risk of an asset what
+ 
+
+ align:start position:0%
+the assessment of risk of an asset what
+do we have
+
+ align:start position:0%
+do we have
+ 
+
+ align:start position:0%
+do we have
+here Julio construction prices and
+
+ align:start position:0%
+here Julio construction prices and
+ 
+
+ align:start position:0%
+here Julio construction prices and
+construction cost yeah yeah and
+
+ align:start position:0%
+construction cost yeah yeah and
+ 
+
+ align:start position:0%
+construction cost yeah yeah and
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+else it doesn't change a lot let's say
+
+ align:start position:0%
+else it doesn't change a lot let's say
+ 
+
+ align:start position:0%
+else it doesn't change a lot let's say
+permitting and yeah so those are costs
+
+ align:start position:0%
+permitting and yeah so those are costs
+ 
+
+ align:start position:0%
+permitting and yeah so those are costs
+of building that that asset uh material
+
+ align:start position:0%
+of building that that asset uh material
+ 
+
+ align:start position:0%
+of building that that asset uh material
+cost and other things so Carlos you were
+
+ align:start position:0%
+cost and other things so Carlos you were
+ 
+
+ align:start position:0%
+cost and other things so Carlos you were
+saying maybe we shouldn't let people
+
+ align:start position:0%
+saying maybe we shouldn't let people
+ 
+
+ align:start position:0%
+saying maybe we shouldn't let people
+live in areas that are going to be hit
+
+ align:start position:0%
+live in areas that are going to be hit
+ 
+
+ align:start position:0%
+live in areas that are going to be hit
+by certain disasters if we make those
+
+ align:start position:0%
+by certain disasters if we make those
+ 
+
+ align:start position:0%
+by certain disasters if we make those
+things more difficult if we make the
+
+ align:start position:0%
+things more difficult if we make the
+ 
+
+ align:start position:0%
+things more difficult if we make the
+requirements the resiliency uh
+
+ align:start position:0%
+requirements the resiliency uh
+ 
+
+ align:start position:0%
+requirements the resiliency uh
+requirements for assets to be higher it
+
+ align:start position:0%
+requirements for assets to be higher it
+ 
+
+ align:start position:0%
+requirements for assets to be higher it
+is great on the one on the hand that the
+
+ align:start position:0%
+is great on the one on the hand that the
+ 
+
+ align:start position:0%
+is great on the one on the hand that the
+the assets that are going to be built
+
+ align:start position:0%
+the assets that are going to be built
+ 
+
+ align:start position:0%
+the assets that are going to be built
+are going to be safer but on the other
+
+ align:start position:0%
+are going to be safer but on the other
+ 
+
+ align:start position:0%
+are going to be safer but on the other
+hand there will be some assets that will
+
+ align:start position:0%
+hand there will be some assets that will
+ 
+
+ align:start position:0%
+hand there will be some assets that will
+not be built because are the the cost of
+
+ align:start position:0%
+not be built because are the the cost of
+ 
+
+ align:start position:0%
+not be built because are the the cost of
+construction are going up so then you
+
+ align:start position:0%
+construction are going up so then you
+ 
+
+ align:start position:0%
+construction are going up so then you
+need prices to be high up higher up to
+
+ align:start position:0%
+need prices to be high up higher up to
+ 
+
+ align:start position:0%
+need prices to be high up higher up to
+make sure that you compensate for the
+
+ align:start position:0%
+make sure that you compensate for the
+ 
+
+ align:start position:0%
+make sure that you compensate for the
+increase requirements in in uh in
+
+ align:start position:0%
+increase requirements in in uh in
+ 
+
+ align:start position:0%
+increase requirements in in uh in
+building uh certain buildings uh and
+
+ align:start position:0%
+building uh certain buildings uh and
+ 
+
+ align:start position:0%
+building uh certain buildings uh and
+what about the last one this one relates
+
+ align:start position:0%
+what about the last one this one relates
+ 
+
+ align:start position:0%
+what about the last one this one relates
+the amount of buildings that are
+
+ align:start position:0%
+the amount of buildings that are
+ 
+
+ align:start position:0%
+the amount of buildings that are
+constructed with the amount of buildings
+
+ align:start position:0%
+constructed with the amount of buildings
+ 
+
+ align:start position:0%
+constructed with the amount of buildings
+that are EST stand in in the uh in the
+
+ align:start position:0%
+that are EST stand in in the uh in the
+ 
+
+ align:start position:0%
+that are EST stand in in the uh in the
+market and um in the market there's the
+
+ align:start position:0%
+market and um in the market there's the
+ 
+
+ align:start position:0%
+market and um in the market there's the
+existing assets and there's a
+
+ align:start position:0%
+existing assets and there's a
+ 
+
+ align:start position:0%
+existing assets and there's a
+depreciation of the existing stock and
+
+ align:start position:0%
+depreciation of the existing stock and
+ 
+
+ align:start position:0%
+depreciation of the existing stock and
+the new amount of construction that
+
+ align:start position:0%
+the new amount of construction that
+ 
+
+ align:start position:0%
+the new amount of construction that
+comes in from the third quadrant will
+
+ align:start position:0%
+comes in from the third quadrant will
+ 
+
+ align:start position:0%
+comes in from the third quadrant will
+increase that value but if construction
+
+ align:start position:0%
+increase that value but if construction
+ 
+
+ align:start position:0%
+increase that value but if construction
+slows down you already have the existing
+
+ align:start position:0%
+slows down you already have the existing
+ 
+
+ align:start position:0%
+slows down you already have the existing
+stock but that's decreasing at the
+
+ align:start position:0%
+stock but that's decreasing at the
+ 
+
+ align:start position:0%
+stock but that's decreasing at the
+appreciation
+
+ align:start position:0%
+appreciation
+ 
+
+ align:start position:0%
+appreciation
+rate so new stock feeds that higher and
+
+ align:start position:0%
+rate so new stock feeds that higher and
+ 
+
+ align:start position:0%
+rate so new stock feeds that higher and
+then a stall in construction means that
+
+ align:start position:0%
+then a stall in construction means that
+ 
+
+ align:start position:0%
+then a stall in construction means that
+the number comes down great what can
+
+ align:start position:0%
+the number comes down great what can
+ 
+
+ align:start position:0%
+the number comes down great what can
+move that curve the depreciation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M yeah so if um if things like for
+
+ align:start position:0%
+M yeah so if um if things like for
+ 
+
+ align:start position:0%
+M yeah so if um if things like for
+example the amount of uh how harsh is
+
+ align:start position:0%
+example the amount of uh how harsh is
+ 
+
+ align:start position:0%
+example the amount of uh how harsh is
+the place in terms of the depreciation
+
+ align:start position:0%
+the place in terms of the depreciation
+ 
+
+ align:start position:0%
+the place in terms of the depreciation
+of that assets or maybe even when it
+
+ align:start position:0%
+of that assets or maybe even when it
+ 
+
+ align:start position:0%
+of that assets or maybe even when it
+comes to equipment the requirements for
+
+ align:start position:0%
+comes to equipment the requirements for
+ 
+
+ align:start position:0%
+comes to equipment the requirements for
+that equipment to be full power all the
+
+ align:start position:0%
+that equipment to be full power all the
+ 
+
+ align:start position:0%
+that equipment to be full power all the
+time in terms of temperature and so
+
+ align:start position:0%
+time in terms of temperature and so
+ 
+
+ align:start position:0%
+time in terms of temperature and so
+forth then the amount of depreciation
+
+ align:start position:0%
+forth then the amount of depreciation
+ 
+
+ align:start position:0%
+forth then the amount of depreciation
+will be higher but also if you have the
+
+ align:start position:0%
+will be higher but also if you have the
+ 
+
+ align:start position:0%
+will be higher but also if you have the
+risk of these assets to be banish every
+
+ align:start position:0%
+risk of these assets to be banish every
+ 
+
+ align:start position:0%
+risk of these assets to be banish every
+other decade then you also have somehow
+
+ align:start position:0%
+other decade then you also have somehow
+ 
+
+ align:start position:0%
+other decade then you also have somehow
+there a probability that whatever you're
+
+ align:start position:0%
+there a probability that whatever you're
+ 
+
+ align:start position:0%
+there a probability that whatever you're
+are building is going to be destroyed at
+
+ align:start position:0%
+are building is going to be destroyed at
+ 
+
+ align:start position:0%
+are building is going to be destroyed at
+some point and the stock is not going to
+
+ align:start position:0%
+some point and the stock is not going to
+ 
+
+ align:start position:0%
+some point and the stock is not going to
+translate one1 to uh to the construction
+
+ align:start position:0%
+translate one1 to uh to the construction
+ 
+
+ align:start position:0%
+translate one1 to uh to the construction
+okay so we are going to use those things
+
+ align:start position:0%
+okay so we are going to use those things
+ 
+
+ align:start position:0%
+okay so we are going to use those things
+and and the important thing is that
+
+ align:start position:0%
+and and the important thing is that
+ 
+
+ align:start position:0%
+and and the important thing is that
+everything is ultimately connected so if
+
+ align:start position:0%
+everything is ultimately connected so if
+ 
+
+ align:start position:0%
+everything is ultimately connected so if
+something is happening to to our tenants
+
+ align:start position:0%
+something is happening to to our tenants
+ 
+
+ align:start position:0%
+something is happening to to our tenants
+it's going to shift this curve and it's
+
+ align:start position:0%
+it's going to shift this curve and it's
+ 
+
+ align:start position:0%
+it's going to shift this curve and it's
+going to ultimately shift the prices of
+
+ align:start position:0%
+going to ultimately shift the prices of
+ 
+
+ align:start position:0%
+going to ultimately shift the prices of
+of uh of Assets in the market and it's
+
+ align:start position:0%
+of uh of Assets in the market and it's
+ 
+
+ align:start position:0%
+of uh of Assets in the market and it's
+going to shift the construction rate and
+
+ align:start position:0%
+going to shift the construction rate and
+ 
+
+ align:start position:0%
+going to shift the construction rate and
+it's going to shift ultimately the
+
+ align:start position:0%
+it's going to shift ultimately the
+ 
+
+ align:start position:0%
+it's going to shift ultimately the
+supply of assets in in the market so
+
+ align:start position:0%
+supply of assets in in the market so
+ 
+
+ align:start position:0%
+supply of assets in in the market so
+everything is connected so whenever we
+
+ align:start position:0%
+everything is connected so whenever we
+ 
+
+ align:start position:0%
+everything is connected so whenever we
+have a report wherever we have a study
+
+ align:start position:0%
+have a report wherever we have a study
+ 
+
+ align:start position:0%
+have a report wherever we have a study
+that will tell us that this quadrant is
+
+ align:start position:0%
+that will tell us that this quadrant is
+ 
+
+ align:start position:0%
+that will tell us that this quadrant is
+affected or that quadrant is affected
+
+ align:start position:0%
+affected or that quadrant is affected
+ 
+
+ align:start position:0%
+affected or that quadrant is affected
+ultimately the whole market and everyone
+
+ align:start position:0%
+ultimately the whole market and everyone
+ 
+
+ align:start position:0%
+ultimately the whole market and everyone
+in that market is affected and and the
+
+ align:start position:0%
+in that market is affected and and the
+ 
+
+ align:start position:0%
+in that market is affected and and the
+key is that if we don't have that view
+
+ align:start position:0%
+key is that if we don't have that view
+ 
+
+ align:start position:0%
+key is that if we don't have that view
+we will have a very myopic view of the
+
+ align:start position:0%
+we will have a very myopic view of the
+ 
+
+ align:start position:0%
+we will have a very myopic view of the
+of the whole climate change because we
+
+ align:start position:0%
+of the whole climate change because we
+ 
+
+ align:start position:0%
+of the whole climate change because we
+will only think about this partial view
+
+ align:start position:0%
+will only think about this partial view
+ 
+
+ align:start position:0%
+will only think about this partial view
+of okay yeah rains will change but yeah
+
+ align:start position:0%
+of okay yeah rains will change but yeah
+ 
+
+ align:start position:0%
+of okay yeah rains will change but yeah
+if rain changes then the investors will
+
+ align:start position:0%
+if rain changes then the investors will
+ 
+
+ align:start position:0%
+if rain changes then the investors will
+will act differently and then the
+
+ align:start position:0%
+will act differently and then the
+ 
+
+ align:start position:0%
+will act differently and then the
+contractor construction companies will
+
+ align:start position:0%
+contractor construction companies will
+ 
+
+ align:start position:0%
+contractor construction companies will
+act differently and ultimately the
+
+ align:start position:0%
+act differently and ultimately the
+ 
+
+ align:start position:0%
+act differently and ultimately the
+supply will be different so all of these
+
+ align:start position:0%
+supply will be different so all of these
+ 
+
+ align:start position:0%
+supply will be different so all of these
+long-term short-term effects is
+
+ align:start position:0%
+long-term short-term effects is
+ 
+
+ align:start position:0%
+long-term short-term effects is
+something that we have to be very
+
+ align:start position:0%
+something that we have to be very
+ 
+
+ align:start position:0%
+something that we have to be very
+present uh when we are analyzing the
+
+ align:start position:0%
+present uh when we are analyzing the
+ 
+
+ align:start position:0%
+present uh when we are analyzing the
+consequences of climate change in the
+
+ align:start position:0%
+consequences of climate change in the
+ 
+
+ align:start position:0%
+consequences of climate change in the
+real estate industry and that's where
+
+ align:start position:0%
+real estate industry and that's where
+ 
+
+ align:start position:0%
+real estate industry and that's where
+one of the the key values of knowing
+
+ align:start position:0%
+one of the the key values of knowing
+ 
+
+ align:start position:0%
+one of the the key values of knowing
+real estate economics when we are
+
+ align:start position:0%
+real estate economics when we are
+ 
+
+ align:start position:0%
+real estate economics when we are
+thinking about this and that's the value
+
+ align:start position:0%
+thinking about this and that's the value
+ 
+
+ align:start position:0%
+thinking about this and that's the value
+for those that are doing the mid program
+
+ align:start position:0%
+for those that are doing the mid program
+ 
+
+ align:start position:0%
+for those that are doing the mid program
+to come from that course all the way
+
+ align:start position:0%
+to come from that course all the way
+ 
+
+ align:start position:0%
+to come from that course all the way
+into here so if you think about the
+
+ align:start position:0%
+into here so if you think about the
+ 
+
+ align:start position:0%
+into here so if you think about the
+demand side Leah I just have a quick
+
+ align:start position:0%
+demand side Leah I just have a quick
+ 
+
+ align:start position:0%
+demand side Leah I just have a quick
+question sure
+
+ align:start position:0%
+question sure
+ 
+
+ align:start position:0%
+question sure
+this is for the Ral Market how does it
+
+ align:start position:0%
+this is for the Ral Market how does it
+ 
+
+ align:start position:0%
+this is for the Ral Market how does it
+work for own yeah so here we are
+
+ align:start position:0%
+work for own yeah so here we are
+ 
+
+ align:start position:0%
+work for own yeah so here we are
+thinking about uh commercial real estate
+
+ align:start position:0%
+thinking about uh commercial real estate
+ 
+
+ align:start position:0%
+thinking about uh commercial real estate
+properties in in uh this Center we have
+
+ align:start position:0%
+properties in in uh this Center we have
+ 
+
+ align:start position:0%
+properties in in uh this Center we have
+uh thanks to David gner that kind of
+
+ align:start position:0%
+uh thanks to David gner that kind of
+ 
+
+ align:start position:0%
+uh thanks to David gner that kind of
+brainwash us we think about commercial
+
+ align:start position:0%
+brainwash us we think about commercial
+ 
+
+ align:start position:0%
+brainwash us we think about commercial
+real estate as any income generating
+
+ align:start position:0%
+real estate as any income generating
+ 
+
+ align:start position:0%
+real estate as any income generating
+property so you can think also here as
+
+ align:start position:0%
+property so you can think also here as
+ 
+
+ align:start position:0%
+property so you can think also here as
+res as a multif family and kind of if
+
+ align:start position:0%
+res as a multif family and kind of if
+ 
+
+ align:start position:0%
+res as a multif family and kind of if
+you will rent a an apartment it will be
+
+ align:start position:0%
+you will rent a an apartment it will be
+ 
+
+ align:start position:0%
+you will rent a an apartment it will be
+part of this uh if you think about home
+
+ align:start position:0%
+part of this uh if you think about home
+ 
+
+ align:start position:0%
+part of this uh if you think about home
+ownership that will be basically you
+
+ align:start position:0%
+ownership that will be basically you
+ 
+
+ align:start position:0%
+ownership that will be basically you
+will not have this but you will have
+
+ align:start position:0%
+will not have this but you will have
+ 
+
+ align:start position:0%
+will not have this but you will have
+some sort of utility of living in that
+
+ align:start position:0%
+some sort of utility of living in that
+ 
+
+ align:start position:0%
+some sort of utility of living in that
+place so you will have a monetization in
+
+ align:start position:0%
+place so you will have a monetization in
+ 
+
+ align:start position:0%
+place so you will have a monetization in
+your head of what it is what it meant
+
+ align:start position:0%
+your head of what it is what it meant
+ 
+
+ align:start position:0%
+your head of what it is what it meant
+means for you to live in that place we
+
+ align:start position:0%
+means for you to live in that place we
+ 
+
+ align:start position:0%
+means for you to live in that place we
+will see some graph now also in in the
+
+ align:start position:0%
+will see some graph now also in in the
+ 
+
+ align:start position:0%
+will see some graph now also in in the
+uh from the empirical studies on how
+
+ align:start position:0%
+uh from the empirical studies on how
+ 
+
+ align:start position:0%
+uh from the empirical studies on how
+home owners and and home buyers are
+
+ align:start position:0%
+home owners and and home buyers are
+ 
+
+ align:start position:0%
+home owners and and home buyers are
+actually changing uh their willingness
+
+ align:start position:0%
+actually changing uh their willingness
+ 
+
+ align:start position:0%
+actually changing uh their willingness
+to pay to live in a certain place
+
+ align:start position:0%
+to pay to live in a certain place
+ 
+
+ align:start position:0%
+to pay to live in a certain place
+depending on the temperature of those
+
+ align:start position:0%
+depending on the temperature of those
+ 
+
+ align:start position:0%
+depending on the temperature of those
+places so there will be some that's how
+
+ align:start position:0%
+places so there will be some that's how
+ 
+
+ align:start position:0%
+places so there will be some that's how
+we use it in economics we will translate
+
+ align:start position:0%
+we use it in economics we will translate
+ 
+
+ align:start position:0%
+we use it in economics we will translate
+your happiness or utility to live in a
+
+ align:start position:0%
+your happiness or utility to live in a
+ 
+
+ align:start position:0%
+your happiness or utility to live in a
+place into willingness to pay or any
+
+ align:start position:0%
+place into willingness to pay or any
+ 
+
+ align:start position:0%
+place into willingness to pay or any
+kind of monetary value that will
+
+ align:start position:0%
+kind of monetary value that will
+ 
+
+ align:start position:0%
+kind of monetary value that will
+translate that into some sort of demand
+
+ align:start position:0%
+translate that into some sort of demand
+ 
+
+ align:start position:0%
+translate that into some sort of demand
+curve okay and then there will be some
+
+ align:start position:0%
+curve okay and then there will be some
+ 
+
+ align:start position:0%
+curve okay and then there will be some
+investors that it is on the one hand
+
+ align:start position:0%
+investors that it is on the one hand
+ 
+
+ align:start position:0%
+investors that it is on the one hand
+that Equity investor so someone that is
+
+ align:start position:0%
+that Equity investor so someone that is
+ 
+
+ align:start position:0%
+that Equity investor so someone that is
+buying or co- buying that property with
+
+ align:start position:0%
+buying or co- buying that property with
+ 
+
+ align:start position:0%
+buying or co- buying that property with
+you but it's also here that is someone
+
+ align:start position:0%
+you but it's also here that is someone
+ 
+
+ align:start position:0%
+you but it's also here that is someone
+important here that are the banks and
+
+ align:start position:0%
+important here that are the banks and
+ 
+
+ align:start position:0%
+important here that are the banks and
+the and the Deb providers so they are
+
+ align:start position:0%
+the and the Deb providers so they are
+ 
+
+ align:start position:0%
+the and the Deb providers so they are
+going to be here even if you're a
+
+ align:start position:0%
+going to be here even if you're a
+ 
+
+ align:start position:0%
+going to be here even if you're a
+homeowner and that will be applying a
+
+ align:start position:0%
+homeowner and that will be applying a
+ 
+
+ align:start position:0%
+homeowner and that will be applying a
+lot of the logic to to that for Quadrant
+
+ align:start position:0%
+lot of the logic to to that for Quadrant
+ 
+
+ align:start position:0%
+lot of the logic to to that for Quadrant
+model tooo
+
+ align:start position:0%
+model tooo
+ 
+
+ align:start position:0%
+model tooo
+okay um so what do we what can we expect
+
+ align:start position:0%
+okay um so what do we what can we expect
+ 
+
+ align:start position:0%
+okay um so what do we what can we expect
+in terms of climate change impacts on
+
+ align:start position:0%
+in terms of climate change impacts on
+ 
+
+ align:start position:0%
+in terms of climate change impacts on
+the space Market what do we think do we
+
+ align:start position:0%
+the space Market what do we think do we
+ 
+
+ align:start position:0%
+the space Market what do we think do we
+think that people are going to be more
+
+ align:start position:0%
+think that people are going to be more
+ 
+
+ align:start position:0%
+think that people are going to be more
+happy to live in places that are going
+
+ align:start position:0%
+happy to live in places that are going
+ 
+
+ align:start position:0%
+happy to live in places that are going
+to be at risk of wildfires so let's
+
+ align:start position:0%
+to be at risk of wildfires so let's
+ 
+
+ align:start position:0%
+to be at risk of wildfires so let's
+think about California or are we going
+
+ align:start position:0%
+think about California or are we going
+ 
+
+ align:start position:0%
+think about California or are we going
+to think that people are less happy to
+
+ align:start position:0%
+to think that people are less happy to
+ 
+
+ align:start position:0%
+to think that people are less happy to
+live there and how are we going to see
+
+ align:start position:0%
+live there and how are we going to see
+ 
+
+ align:start position:0%
+live there and how are we going to see
+that in the
+
+ align:start position:0%
+that in the
+ 
+
+ align:start position:0%
+that in the
+market um some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah and that will have a direct
+
+ align:start position:0%
+yeah yeah and that will have a direct
+ 
+
+ align:start position:0%
+yeah yeah and that will have a direct
+impact on the rents But ultimately
+
+ align:start position:0%
+impact on the rents But ultimately
+ 
+
+ align:start position:0%
+impact on the rents But ultimately
+because the rents now are lower in that
+
+ align:start position:0%
+because the rents now are lower in that
+ 
+
+ align:start position:0%
+because the rents now are lower in that
+market prices and ultimately the
+
+ align:start position:0%
+market prices and ultimately the
+ 
+
+ align:start position:0%
+market prices and ultimately the
+construction activity so that's how that
+
+ align:start position:0%
+construction activity so that's how that
+ 
+
+ align:start position:0%
+construction activity so that's how that
+uh that shifts the whole whole idea so
+
+ align:start position:0%
+uh that shifts the whole whole idea so
+ 
+
+ align:start position:0%
+uh that shifts the whole whole idea so
+and that if we want to put it into what
+
+ align:start position:0%
+and that if we want to put it into what
+ 
+
+ align:start position:0%
+and that if we want to put it into what
+will determine that it will be the the
+
+ align:start position:0%
+will determine that it will be the the
+ 
+
+ align:start position:0%
+will determine that it will be the the
+attractiveness of that space so if you
+
+ align:start position:0%
+attractiveness of that space so if you
+ 
+
+ align:start position:0%
+attractiveness of that space so if you
+are exposed not only to to couple of
+
+ align:start position:0%
+are exposed not only to to couple of
+ 
+
+ align:start position:0%
+are exposed not only to to couple of
+days of heat waves a year but actually
+
+ align:start position:0%
+days of heat waves a year but actually
+ 
+
+ align:start position:0%
+days of heat waves a year but actually
+now it starts to be like two weeks three
+
+ align:start position:0%
+now it starts to be like two weeks three
+ 
+
+ align:start position:0%
+now it starts to be like two weeks three
+weeks a year of heat waves then as a
+
+ align:start position:0%
+weeks a year of heat waves then as a
+ 
+
+ align:start position:0%
+weeks a year of heat waves then as a
+resident of that place you're going to
+
+ align:start position:0%
+resident of that place you're going to
+ 
+
+ align:start position:0%
+resident of that place you're going to
+be uh less keen on living in that in
+
+ align:start position:0%
+be uh less keen on living in that in
+ 
+
+ align:start position:0%
+be uh less keen on living in that in
+that place yeah H that could also work
+
+ align:start position:0%
+that place yeah H that could also work
+ 
+
+ align:start position:0%
+that place yeah H that could also work
+the other way around right when you have
+
+ align:start position:0%
+the other way around right when you have
+ 
+
+ align:start position:0%
+the other way around right when you have
+people moving from one place to the
+
+ align:start position:0%
+people moving from one place to the
+ 
+
+ align:start position:0%
+people moving from one place to the
+other because climate change correct
+
+ align:start position:0%
+other because climate change correct
+ 
+
+ align:start position:0%
+other because climate change correct
+have effect correct here we are thinking
+
+ align:start position:0%
+have effect correct here we are thinking
+ 
+
+ align:start position:0%
+have effect correct here we are thinking
+about areas that are uh badly impacted
+
+ align:start position:0%
+about areas that are uh badly impacted
+ 
+
+ align:start position:0%
+about areas that are uh badly impacted
+by that so more heat
+
+ align:start position:0%
+by that so more heat
+ 
+
+ align:start position:0%
+by that so more heat
+waves cities like New York City like
+
+ align:start position:0%
+waves cities like New York City like
+ 
+
+ align:start position:0%
+waves cities like New York City like
+Boston that are experiencing more and
+
+ align:start position:0%
+Boston that are experiencing more and
+ 
+
+ align:start position:0%
+Boston that are experiencing more and
+more heat waves uh and so forth uh also
+
+ align:start position:0%
+more heat waves uh and so forth uh also
+ 
+
+ align:start position:0%
+more heat waves uh and so forth uh also
+impacts of occupants so these are for
+
+ align:start position:0%
+impacts of occupants so these are for
+ 
+
+ align:start position:0%
+impacts of occupants so these are for
+people that want to live there but
+
+ align:start position:0%
+people that want to live there but
+ 
+
+ align:start position:0%
+people that want to live there but
+companies that are renting a space to
+
+ align:start position:0%
+companies that are renting a space to
+ 
+
+ align:start position:0%
+companies that are renting a space to
+work there they will be worried about
+
+ align:start position:0%
+work there they will be worried about
+ 
+
+ align:start position:0%
+work there they will be worried about
+performance changes they will be worried
+
+ align:start position:0%
+performance changes they will be worried
+ 
+
+ align:start position:0%
+performance changes they will be worried
+about Behavior change of consumers so
+
+ align:start position:0%
+about Behavior change of consumers so
+ 
+
+ align:start position:0%
+about Behavior change of consumers so
+people are actually less likely to go to
+
+ align:start position:0%
+people are actually less likely to go to
+ 
+
+ align:start position:0%
+people are actually less likely to go to
+the shopping mall because it's in uh uh
+
+ align:start position:0%
+the shopping mall because it's in uh uh
+ 
+
+ align:start position:0%
+the shopping mall because it's in uh uh
+attactive for more severe storms for
+
+ align:start position:0%
+attactive for more severe storms for
+ 
+
+ align:start position:0%
+attactive for more severe storms for
+more heat waves and so so forth they are
+
+ align:start position:0%
+more heat waves and so so forth they are
+ 
+
+ align:start position:0%
+more heat waves and so so forth they are
+all going to beat lower in their leasing
+
+ align:start position:0%
+all going to beat lower in their leasing
+ 
+
+ align:start position:0%
+all going to beat lower in their leasing
+uh beats than they used to be and then
+
+ align:start position:0%
+uh beats than they used to be and then
+ 
+
+ align:start position:0%
+uh beats than they used to be and then
+also ultimately the impact of on on
+
+ align:start position:0%
+also ultimately the impact of on on
+ 
+
+ align:start position:0%
+also ultimately the impact of on on
+amenities and also the climate risk
+
+ align:start position:0%
+amenities and also the climate risk
+ 
+
+ align:start position:0%
+amenities and also the climate risk
+discloser uh this is what you see so
+
+ align:start position:0%
+discloser uh this is what you see so
+ 
+
+ align:start position:0%
+discloser uh this is what you see so
+here this is translated into this model
+
+ align:start position:0%
+here this is translated into this model
+ 
+
+ align:start position:0%
+here this is translated into this model
+of uh R robot model where you say well
+
+ align:start position:0%
+of uh R robot model where you say well
+ 
+
+ align:start position:0%
+of uh R robot model where you say well
+the amount of money that you're going to
+
+ align:start position:0%
+the amount of money that you're going to
+ 
+
+ align:start position:0%
+the amount of money that you're going to
+to pay for living a place of rent is
+
+ align:start position:0%
+to pay for living a place of rent is
+ 
+
+ align:start position:0%
+to pay for living a place of rent is
+going to be affected by the amount of
+
+ align:start position:0%
+going to be affected by the amount of
+ 
+
+ align:start position:0%
+going to be affected by the amount of
+money that you earn as a uh in the labor
+
+ align:start position:0%
+money that you earn as a uh in the labor
+ 
+
+ align:start position:0%
+money that you earn as a uh in the labor
+market and also your appreciation for
+
+ align:start position:0%
+market and also your appreciation for
+ 
+
+ align:start position:0%
+market and also your appreciation for
+that place so you can actually uh be
+
+ align:start position:0%
+that place so you can actually uh be
+ 
+
+ align:start position:0%
+that place so you can actually uh be
+willing to earn less if you are in a
+
+ align:start position:0%
+willing to earn less if you are in a
+ 
+
+ align:start position:0%
+willing to earn less if you are in a
+place that really gives you a lot of
+
+ align:start position:0%
+place that really gives you a lot of
+ 
+
+ align:start position:0%
+place that really gives you a lot of
+utility a lot of nice place so you know
+
+ align:start position:0%
+utility a lot of nice place so you know
+ 
+
+ align:start position:0%
+utility a lot of nice place so you know
+if you are living in a very uh bad place
+
+ align:start position:0%
+if you are living in a very uh bad place
+ 
+
+ align:start position:0%
+if you are living in a very uh bad place
+like think about a very bad with low
+
+ align:start position:0%
+like think about a very bad with low
+ 
+
+ align:start position:0%
+like think about a very bad with low
+amenities industrial area in the middle
+
+ align:start position:0%
+amenities industrial area in the middle
+ 
+
+ align:start position:0%
+amenities industrial area in the middle
+of nowhere they really need to pay you a
+
+ align:start position:0%
+of nowhere they really need to pay you a
+ 
+
+ align:start position:0%
+of nowhere they really need to pay you a
+lot to attract someone as talented as
+
+ align:start position:0%
+lot to attract someone as talented as
+ 
+
+ align:start position:0%
+lot to attract someone as talented as
+you guys to be on working there but if
+
+ align:start position:0%
+you guys to be on working there but if
+ 
+
+ align:start position:0%
+you guys to be on working there but if
+someone has a little bit lower payche
+
+ align:start position:0%
+someone has a little bit lower payche
+ 
+
+ align:start position:0%
+someone has a little bit lower payche
+but is in an area next to a nice Lake
+
+ align:start position:0%
+but is in an area next to a nice Lake
+ 
+
+ align:start position:0%
+but is in an area next to a nice Lake
+mountains whatever you are going to be
+
+ align:start position:0%
+mountains whatever you are going to be
+ 
+
+ align:start position:0%
+mountains whatever you are going to be
+less uh less greedy when it comes to
+
+ align:start position:0%
+less uh less greedy when it comes to
+ 
+
+ align:start position:0%
+less uh less greedy when it comes to
+negotiating those terms because you
+
+ align:start position:0%
+negotiating those terms because you
+ 
+
+ align:start position:0%
+negotiating those terms because you
+really want to live there or if you have
+
+ align:start position:0%
+really want to live there or if you have
+ 
+
+ align:start position:0%
+really want to live there or if you have
+the family next to you or whatever you
+
+ align:start position:0%
+the family next to you or whatever you
+ 
+
+ align:start position:0%
+the family next to you or whatever you
+want to gives you a quality of life so
+
+ align:start position:0%
+want to gives you a quality of life so
+ 
+
+ align:start position:0%
+want to gives you a quality of life so
+as the quality of life reduces the
+
+ align:start position:0%
+as the quality of life reduces the
+ 
+
+ align:start position:0%
+as the quality of life reduces the
+people will have the companies will have
+
+ align:start position:0%
+people will have the companies will have
+ 
+
+ align:start position:0%
+people will have the companies will have
+to pay you more or you have or the
+
+ align:start position:0%
+to pay you more or you have or the
+ 
+
+ align:start position:0%
+to pay you more or you have or the
+landlords will have to ask you less rent
+
+ align:start position:0%
+landlords will have to ask you less rent
+ 
+
+ align:start position:0%
+landlords will have to ask you less rent
+because you are less attractive to live
+
+ align:start position:0%
+because you are less attractive to live
+ 
+
+ align:start position:0%
+because you are less attractive to live
+in that area so as climate change is
+
+ align:start position:0%
+in that area so as climate change is
+ 
+
+ align:start position:0%
+in that area so as climate change is
+actually uh or temperature if for
+
+ align:start position:0%
+actually uh or temperature if for
+ 
+
+ align:start position:0%
+actually uh or temperature if for
+example temperature exposure will
+
+ align:start position:0%
+example temperature exposure will
+ 
+
+ align:start position:0%
+example temperature exposure will
+actually reduce that quality of life
+
+ align:start position:0%
+actually reduce that quality of life
+ 
+
+ align:start position:0%
+actually reduce that quality of life
+that will mean that either you are
+
+ align:start position:0%
+that will mean that either you are
+ 
+
+ align:start position:0%
+that will mean that either you are
+required to pay less to be in that place
+
+ align:start position:0%
+required to pay less to be in that place
+ 
+
+ align:start position:0%
+required to pay less to be in that place
+or the employers will have to pay you
+
+ align:start position:0%
+or the employers will have to pay you
+ 
+
+ align:start position:0%
+or the employers will have to pay you
+more but basically the rent the real
+
+ align:start position:0%
+more but basically the rent the real
+ 
+
+ align:start position:0%
+more but basically the rent the real
+rents will actually need to go down yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure people comp to
+
+ align:start position:0%
+sure people comp to
+ 
+
+ align:start position:0%
+sure people comp to
+Adreas construction yeah that is also
+
+ align:start position:0%
+Adreas construction yeah that is also
+ 
+
+ align:start position:0%
+Adreas construction yeah that is also
+something that will be there so that
+
+ align:start position:0%
+something that will be there so that
+ 
+
+ align:start position:0%
+something that will be there so that
+will be the other quadrant this is more
+
+ align:start position:0%
+will be the other quadrant this is more
+ 
+
+ align:start position:0%
+will be the other quadrant this is more
+for the uh for the demand the demand for
+
+ align:start position:0%
+for the uh for the demand the demand for
+ 
+
+ align:start position:0%
+for the uh for the demand the demand for
+a space so there is not the adaptation
+
+ align:start position:0%
+a space so there is not the adaptation
+ 
+
+ align:start position:0%
+a space so there is not the adaptation
+but it's more like kind of there is a
+
+ align:start position:0%
+but it's more like kind of there is a
+ 
+
+ align:start position:0%
+but it's more like kind of there is a
+set of buildings that are built for you
+
+ align:start position:0%
+set of buildings that are built for you
+ 
+
+ align:start position:0%
+set of buildings that are built for you
+and where do you choose to leave and how
+
+ align:start position:0%
+and where do you choose to leave and how
+ 
+
+ align:start position:0%
+and where do you choose to leave and how
+much are you choosing to pay for those
+
+ align:start position:0%
+much are you choosing to pay for those
+ 
+
+ align:start position:0%
+much are you choosing to pay for those
+buildings and then there will be the
+
+ align:start position:0%
+buildings and then there will be the
+ 
+
+ align:start position:0%
+buildings and then there will be the
+construction company that is trying to
+
+ align:start position:0%
+construction company that is trying to
+ 
+
+ align:start position:0%
+construction company that is trying to
+to match those preferences to the
+
+ align:start position:0%
+to match those preferences to the
+ 
+
+ align:start position:0%
+to match those preferences to the
+characteristics of those of those places
+
+ align:start position:0%
+characteristics of those of those places
+ 
+
+ align:start position:0%
+characteristics of those of those places
+and indeed if now you required to live
+
+ align:start position:0%
+and indeed if now you required to live
+ 
+
+ align:start position:0%
+and indeed if now you required to live
+in a place or to work in a place that
+
+ align:start position:0%
+in a place or to work in a place that
+ 
+
+ align:start position:0%
+in a place or to work in a place that
+are that are that needs an
+
+ align:start position:0%
+are that are that needs an
+ 
+
+ align:start position:0%
+are that are that needs an
+infrastructure upgrade because now you
+
+ align:start position:0%
+infrastructure upgrade because now you
+ 
+
+ align:start position:0%
+infrastructure upgrade because now you
+need to have a fancier easy unit you
+
+ align:start position:0%
+need to have a fancier easy unit you
+ 
+
+ align:start position:0%
+need to have a fancier easy unit you
+need to have a a a stronger seaw wall
+
+ align:start position:0%
+need to have a a a stronger seaw wall
+ 
+
+ align:start position:0%
+need to have a a a stronger seaw wall
+around the property then that will
+
+ align:start position:0%
+around the property then that will
+ 
+
+ align:start position:0%
+around the property then that will
+increase the construction cost and that
+
+ align:start position:0%
+increase the construction cost and that
+ 
+
+ align:start position:0%
+increase the construction cost and that
+will have H an ultimate effect on the
+
+ align:start position:0%
+will have H an ultimate effect on the
+ 
+
+ align:start position:0%
+will have H an ultimate effect on the
+supply and the cost and the and the
+
+ align:start position:0%
+supply and the cost and the and the
+ 
+
+ align:start position:0%
+supply and the cost and the and the
+price for those
+
+ align:start position:0%
+price for those
+ 
+
+ align:start position:0%
+price for those
+properties and this is what you see in
+
+ align:start position:0%
+properties and this is what you see in
+ 
+
+ align:start position:0%
+properties and this is what you see in
+the empirical data so you see that
+
+ align:start position:0%
+the empirical data so you see that
+ 
+
+ align:start position:0%
+the empirical data so you see that
+people actually this is the the amount
+
+ align:start position:0%
+people actually this is the the amount
+ 
+
+ align:start position:0%
+people actually this is the the amount
+of money that people are willing to pay
+
+ align:start position:0%
+of money that people are willing to pay
+ 
+
+ align:start position:0%
+of money that people are willing to pay
+per square feet and this is the winter
+
+ align:start position:0%
+per square feet and this is the winter
+ 
+
+ align:start position:0%
+per square feet and this is the winter
+temperature in fahrenheit so you see
+
+ align:start position:0%
+temperature in fahrenheit so you see
+ 
+
+ align:start position:0%
+temperature in fahrenheit so you see
+that people want to live in places
+
+ align:start position:0%
+that people want to live in places
+ 
+
+ align:start position:0%
+that people want to live in places
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+um warmer in winter and also cooler in
+
+ align:start position:0%
+um warmer in winter and also cooler in
+ 
+
+ align:start position:0%
+um warmer in winter and also cooler in
+in summer for any any region in the in
+
+ align:start position:0%
+in summer for any any region in the in
+ 
+
+ align:start position:0%
+in summer for any any region in the in
+the United States and these are the
+
+ align:start position:0%
+the United States and these are the
+ 
+
+ align:start position:0%
+the United States and these are the
+effects of on behavior and so forth what
+
+ align:start position:0%
+effects of on behavior and so forth what
+ 
+
+ align:start position:0%
+effects of on behavior and so forth what
+about the asset
+
+ align:start position:0%
+about the asset
+ 
+
+ align:start position:0%
+about the asset
+Market what happens there what do we
+
+ align:start position:0%
+Market what happens there what do we
+ 
+
+ align:start position:0%
+Market what happens there what do we
+think about climate risk is there any
+
+ align:start position:0%
+think about climate risk is there any
+ 
+
+ align:start position:0%
+think about climate risk is there any
+impact of climate risk on the asset
+
+ align:start position:0%
+impact of climate risk on the asset
+ 
+
+ align:start position:0%
+impact of climate risk on the asset
+Market or
+
+ align:start position:0%
+Market or
+ 
+
+ align:start position:0%
+Market or
+no I keep pressing twice and then I keep
+
+ align:start position:0%
+no I keep pressing twice and then I keep
+ 
+
+ align:start position:0%
+no I keep pressing twice and then I keep
+giveing the answer but but what I like
+
+ align:start position:0%
+giveing the answer but but what I like
+ 
+
+ align:start position:0%
+giveing the answer but but what I like
+is the is the logic not so much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ashleyk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wild yes that is true that is not the
+
+ align:start position:0%
+wild yes that is true that is not the
+ 
+
+ align:start position:0%
+wild yes that is true that is not the
+space Market but is the asset the
+
+ align:start position:0%
+space Market but is the asset the
+ 
+
+ align:start position:0%
+space Market but is the asset the
+construction Market uh because that will
+
+ align:start position:0%
+construction Market uh because that will
+ 
+
+ align:start position:0%
+construction Market uh because that will
+ultimately impact the price of Timber
+
+ align:start position:0%
+ultimately impact the price of Timber
+ 
+
+ align:start position:0%
+ultimately impact the price of Timber
+and that will ultimately impact how much
+
+ align:start position:0%
+and that will ultimately impact how much
+ 
+
+ align:start position:0%
+and that will ultimately impact how much
+it cost to build a a building Andy
+
+ align:start position:0%
+it cost to build a a building Andy
+ 
+
+ align:start position:0%
+it cost to build a a building Andy
+before we were talking about shifts on
+
+ align:start position:0%
+before we were talking about shifts on
+ 
+
+ align:start position:0%
+before we were talking about shifts on
+the curve uh given a current rent level
+
+ align:start position:0%
+the curve uh given a current rent level
+ 
+
+ align:start position:0%
+the curve uh given a current rent level
+if there's perceived higher risk or
+
+ align:start position:0%
+if there's perceived higher risk or
+ 
+
+ align:start position:0%
+if there's perceived higher risk or
+future higher cost to maintaining the
+
+ align:start position:0%
+future higher cost to maintaining the
+ 
+
+ align:start position:0%
+future higher cost to maintaining the
+property yeah the curve's going to shift
+
+ align:start position:0%
+property yeah the curve's going to shift
+ 
+
+ align:start position:0%
+property yeah the curve's going to shift
+in so that at that current rent level
+
+ align:start position:0%
+in so that at that current rent level
+ 
+
+ align:start position:0%
+in so that at that current rent level
+there's a lower price Market can we
+
+ align:start position:0%
+there's a lower price Market can we
+ 
+
+ align:start position:0%
+there's a lower price Market can we
+think on a specific U event that will
+
+ align:start position:0%
+think on a specific U event that will
+ 
+
+ align:start position:0%
+think on a specific U event that will
+make that curve shift yeah or that will
+
+ align:start position:0%
+make that curve shift yeah or that will
+ 
+
+ align:start position:0%
+make that curve shift yeah or that will
+increase the perception of risk um
+
+ align:start position:0%
+increase the perception of risk um
+ 
+
+ align:start position:0%
+increase the perception of risk um
+insurance premiums double or triple in
+
+ align:start position:0%
+insurance premiums double or triple in
+ 
+
+ align:start position:0%
+insurance premiums double or triple in
+theur given Market your operating
+
+ align:start position:0%
+theur given Market your operating
+ 
+
+ align:start position:0%
+theur given Market your operating
+expenses are that much higher corre so
+
+ align:start position:0%
+expenses are that much higher corre so
+ 
+
+ align:start position:0%
+expenses are that much higher corre so
+you're going to pay a lower price to
+
+ align:start position:0%
+you're going to pay a lower price to
+ 
+
+ align:start position:0%
+you're going to pay a lower price to
+adjust for that at of cost correct
+
+ align:start position:0%
+adjust for that at of cost correct
+ 
+
+ align:start position:0%
+adjust for that at of cost correct
+correct so the rents will what you don't
+
+ align:start position:0%
+correct so the rents will what you don't
+ 
+
+ align:start position:0%
+correct so the rents will what you don't
+what you get is not actually the rents
+
+ align:start position:0%
+what you get is not actually the rents
+ 
+
+ align:start position:0%
+what you get is not actually the rents
+what you get is the ultimate profit of
+
+ align:start position:0%
+what you get is the ultimate profit of
+ 
+
+ align:start position:0%
+what you get is the ultimate profit of
+of holding that asset every year as a as
+
+ align:start position:0%
+of holding that asset every year as a as
+ 
+
+ align:start position:0%
+of holding that asset every year as a as
+a as an owner of that asset so that is
+
+ align:start position:0%
+a as an owner of that asset so that is
+ 
+
+ align:start position:0%
+a as an owner of that asset so that is
+one and there will be also so you have
+
+ align:start position:0%
+one and there will be also so you have
+ 
+
+ align:start position:0%
+one and there will be also so you have
+it here and also great aware greater
+
+ align:start position:0%
+it here and also great aware greater
+ 
+
+ align:start position:0%
+it here and also great aware greater
+awareness of investors that will
+
+ align:start position:0%
+awareness of investors that will
+ 
+
+ align:start position:0%
+awareness of investors that will
+actually adjust the the risk Kevin I
+
+ align:start position:0%
+actually adjust the the risk Kevin I
+ 
+
+ align:start position:0%
+actually adjust the the risk Kevin I
+I'll give you the floor in one minute um
+
+ align:start position:0%
+I'll give you the floor in one minute um
+ 
+
+ align:start position:0%
+I'll give you the floor in one minute um
+and these are there are things like the
+
+ align:start position:0%
+and these are there are things like the
+ 
+
+ align:start position:0%
+and these are there are things like the
+the TV SD the the task force for on
+
+ align:start position:0%
+the TV SD the the task force for on
+ 
+
+ align:start position:0%
+the TV SD the the task force for on
+climate related Financial disclosure
+
+ align:start position:0%
+climate related Financial disclosure
+ 
+
+ align:start position:0%
+climate related Financial disclosure
+where major Banks and investors are
+
+ align:start position:0%
+where major Banks and investors are
+ 
+
+ align:start position:0%
+where major Banks and investors are
+actually forcing uh companies to
+
+ align:start position:0%
+actually forcing uh companies to
+ 
+
+ align:start position:0%
+actually forcing uh companies to
+disclose the climate risk associated
+
+ align:start position:0%
+disclose the climate risk associated
+ 
+
+ align:start position:0%
+disclose the climate risk associated
+with their assets so they can actually
+
+ align:start position:0%
+with their assets so they can actually
+ 
+
+ align:start position:0%
+with their assets so they can actually
+price it in in their in their conditions
+
+ align:start position:0%
+price it in in their in their conditions
+ 
+
+ align:start position:0%
+price it in in their in their conditions
+and terms where they are giving depth to
+
+ align:start position:0%
+and terms where they are giving depth to
+ 
+
+ align:start position:0%
+and terms where they are giving depth to
+uh to building owners so all of this
+
+ align:start position:0%
+uh to building owners so all of this
+ 
+
+ align:start position:0%
+uh to building owners so all of this
+will make that for whatever rent tenants
+
+ align:start position:0%
+will make that for whatever rent tenants
+ 
+
+ align:start position:0%
+will make that for whatever rent tenants
+are willing to pay ultimately the price
+
+ align:start position:0%
+are willing to pay ultimately the price
+ 
+
+ align:start position:0%
+are willing to pay ultimately the price
+for those assets are going to be lower
+
+ align:start position:0%
+for those assets are going to be lower
+ 
+
+ align:start position:0%
+for those assets are going to be lower
+that is going to impact the construction
+
+ align:start position:0%
+that is going to impact the construction
+ 
+
+ align:start position:0%
+that is going to impact the construction
+too and it's going to impact the the
+
+ align:start position:0%
+too and it's going to impact the the
+ 
+
+ align:start position:0%
+too and it's going to impact the the
+long-term Supply in the market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I have it here and that is also
+
+ align:start position:0%
+and I have it here and that is also
+ 
+
+ align:start position:0%
+and I have it here and that is also
+something that if you see and I'll I'll
+
+ align:start position:0%
+something that if you see and I'll I'll
+ 
+
+ align:start position:0%
+something that if you see and I'll I'll
+discuss this next week in in more detail
+
+ align:start position:0%
+discuss this next week in in more detail
+ 
+
+ align:start position:0%
+discuss this next week in in more detail
+but what you see is that actually when
+
+ align:start position:0%
+but what you see is that actually when
+ 
+
+ align:start position:0%
+but what you see is that actually when
+you see the empirical data you see that
+
+ align:start position:0%
+you see the empirical data you see that
+ 
+
+ align:start position:0%
+you see the empirical data you see that
+a lot of the changes in property prices
+
+ align:start position:0%
+a lot of the changes in property prices
+ 
+
+ align:start position:0%
+a lot of the changes in property prices
+are not coming by changes in noi and
+
+ align:start position:0%
+are not coming by changes in noi and
+ 
+
+ align:start position:0%
+are not coming by changes in noi and
+rents but actually coming from increases
+
+ align:start position:0%
+rents but actually coming from increases
+ 
+
+ align:start position:0%
+rents but actually coming from increases
+in C rate is coming from the perception
+
+ align:start position:0%
+in C rate is coming from the perception
+ 
+
+ align:start position:0%
+in C rate is coming from the perception
+of risk of those properties so for any
+
+ align:start position:0%
+of risk of those properties so for any
+ 
+
+ align:start position:0%
+of risk of those properties so for any
+given rent uh that is out there actually
+
+ align:start position:0%
+given rent uh that is out there actually
+ 
+
+ align:start position:0%
+given rent uh that is out there actually
+now uh owners and investors are willing
+
+ align:start position:0%
+now uh owners and investors are willing
+ 
+
+ align:start position:0%
+now uh owners and investors are willing
+to pay less because because they have a
+
+ align:start position:0%
+to pay less because because they have a
+ 
+
+ align:start position:0%
+to pay less because because they have a
+higher perception of risk on those
+
+ align:start position:0%
+higher perception of risk on those
+ 
+
+ align:start position:0%
+higher perception of risk on those
+properties and it makes sense because
+
+ align:start position:0%
+properties and it makes sense because
+ 
+
+ align:start position:0%
+properties and it makes sense because
+those are the ones that have a long-term
+
+ align:start position:0%
+those are the ones that have a long-term
+ 
+
+ align:start position:0%
+those are the ones that have a long-term
+Horizon versus the ones that are making
+
+ align:start position:0%
+Horizon versus the ones that are making
+ 
+
+ align:start position:0%
+Horizon versus the ones that are making
+a leas for two three five years uh time
+
+ align:start position:0%
+a leas for two three five years uh time
+ 
+
+ align:start position:0%
+a leas for two three five years uh time
+and finally the just as a recap finally
+
+ align:start position:0%
+and finally the just as a recap finally
+ 
+
+ align:start position:0%
+and finally the just as a recap finally
+the the construction what you see is
+
+ align:start position:0%
+the the construction what you see is
+ 
+
+ align:start position:0%
+the the construction what you see is
+that as the cost of materials and the
+
+ align:start position:0%
+that as the cost of materials and the
+ 
+
+ align:start position:0%
+that as the cost of materials and the
+different requirements of companies to
+
+ align:start position:0%
+different requirements of companies to
+ 
+
+ align:start position:0%
+different requirements of companies to
+to uh to construct in certain places you
+
+ align:start position:0%
+to uh to construct in certain places you
+ 
+
+ align:start position:0%
+to uh to construct in certain places you
+see that the the amount of uh
+
+ align:start position:0%
+see that the the amount of uh
+ 
+
+ align:start position:0%
+see that the the amount of uh
+construction is going to go down the the
+
+ align:start position:0%
+construction is going to go down the the
+ 
+
+ align:start position:0%
+construction is going to go down the the
+the price is going to also reflect that
+
+ align:start position:0%
+the price is going to also reflect that
+ 
+
+ align:start position:0%
+the price is going to also reflect that
+and the RS are also going to reflect
+
+ align:start position:0%
+and the RS are also going to reflect
+ 
+
+ align:start position:0%
+and the RS are also going to reflect
+those and finally as the the likelihood
+
+ align:start position:0%
+those and finally as the the likelihood
+ 
+
+ align:start position:0%
+those and finally as the the likelihood
+of the stock to be destroyed increases
+
+ align:start position:0%
+of the stock to be destroyed increases
+ 
+
+ align:start position:0%
+of the stock to be destroyed increases
+then for whatever unit of uh whatever
+
+ align:start position:0%
+then for whatever unit of uh whatever
+ 
+
+ align:start position:0%
+then for whatever unit of uh whatever
+amount of construction is happening now
+
+ align:start position:0%
+amount of construction is happening now
+ 
+
+ align:start position:0%
+amount of construction is happening now
+it's going to survive less and that is
+
+ align:start position:0%
+it's going to survive less and that is
+ 
+
+ align:start position:0%
+it's going to survive less and that is
+going to decrease the supply and have
+
+ align:start position:0%
+going to decrease the supply and have
+ 
+
+ align:start position:0%
+going to decrease the supply and have
+all the bad consequences for rents and
+
+ align:start position:0%
+all the bad consequences for rents and
+ 
+
+ align:start position:0%
+all the bad consequences for rents and
+so forth and remember that at the same
+
+ align:start position:0%
+so forth and remember that at the same
+ 
+
+ align:start position:0%
+so forth and remember that at the same
+time that we have the climate crisis we
+
+ align:start position:0%
+time that we have the climate crisis we
+ 
+
+ align:start position:0%
+time that we have the climate crisis we
+have in a lot of places affordability
+
+ align:start position:0%
+have in a lot of places affordability
+ 
+
+ align:start position:0%
+have in a lot of places affordability
+crisis so we really don't want Supply to
+
+ align:start position:0%
+crisis so we really don't want Supply to
+ 
+
+ align:start position:0%
+crisis so we really don't want Supply to
+be even more constrained uh especially
+
+ align:start position:0%
+be even more constrained uh especially
+ 
+
+ align:start position:0%
+be even more constrained uh especially
+when it comes to the to the housing
+
+ align:start position:0%
+when it comes to the to the housing
+ 
+
+ align:start position:0%
+when it comes to the to the housing
+market market so all of these things is
+
+ align:start position:0%
+market market so all of these things is
+ 
+
+ align:start position:0%
+market market so all of these things is
+going to put a lot of stress into
+
+ align:start position:0%
+going to put a lot of stress into
+ 
+
+ align:start position:0%
+going to put a lot of stress into
+markets and it's going to make a lot of
+
+ align:start position:0%
+markets and it's going to make a lot of
+ 
+
+ align:start position:0%
+markets and it's going to make a lot of
+the lives of a lot of people even more
+
+ align:start position:0%
+the lives of a lot of people even more
+ 
+
+ align:start position:0%
+the lives of a lot of people even more
+miserable
\ No newline at end of file
diff --git a/RrZ8-1w7iok.txt b/RrZ8-1w7iok.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ad55ba026ff972561376164e625ec6fa057424b5
--- /dev/null
+++ b/RrZ8-1w7iok.txt
@@ -0,0 +1,232 @@
+Let's review what happens when the CPU accesses
+a non-resident virtual page, i.e., a page
+
+with its resident bit set to 0.
+
+In the example shown here, the CPU is trying
+to access virtual page 5.
+
+In this case, the MMU signals a page fault
+exception, causing the CPU to suspend execution
+
+of the program and switch to the page fault
+handler, which is code that deals with the
+
+page fault.
+
+The handler starts by either finding an unused
+physical page or, if necessary, creating an
+
+unused page by selecting an in-use page and
+making it available.
+
+In our example, the handler has chosen virtual
+page 1 for reuse.
+
+If the selected page is dirty, i.e., its D
+bit is 1 indicating that its contents have
+
+changed since being read from secondary storage,
+write it back to secondary storage.
+
+Finally, mark the selected virtual page as
+no longer resident.
+
+In the "after" figure, we see that the R bit
+for virtual page 1 has been set to 0.
+
+Now physical page 4 is available for re-use.
+
+Are there any restrictions on which page we
+can select?
+
+Obviously, we can't select the page that holds
+the code for the page fault handler.
+
+Pages immune from selection are called "wired"
+pages.
+
+And it would very inefficient to choose the
+page that holds the code that made the initial
+
+memory access, since we expect to start executing
+that code as soon as we finish handling the
+
+page fault.
+
+The optimal strategy would be to choose the
+page whose next use will occur farthest in
+
+the future.
+
+But, of course, this involves knowledge of
+future execution paths and so isn't a realizable
+
+strategy.
+
+Wikipedia provides a nice description of the
+many strategies for choosing a replacement
+
+page, with their various tradeoffs between
+ease of implementation and impact on the rate
+
+of page faults -
+see the URL given at the bottom of the slide.
+
+The aging algorithm they describe is frequently
+used since it offers near optimal performance
+
+at a moderate implementation cost.
+
+Next, the desired virtual page is read from
+secondary storage into the selected physical
+
+page.
+
+In our example, virtual page 5 is now loaded
+into physical page 4.
+
+Then the R bit and PPN fields in the page
+table entry for virtual page 5 are updated
+
+to indicate that the contents of that virtual
+page now reside in physical page 4.
+
+Finally the handler is finished and execution
+of the original program is resumed, re-executing
+
+the instruction that caused the page fault.
+
+Since the page map has been updated, this
+time the access succeeds and execution continues.
+
+To double-check our understanding of page
+faults, let's run through an example.
+
+Here's the same setup as in our previous example,
+but this time consider a store instruction
+
+that's making an access to virtual address
+0x600, which is located on virtual page 6.
+
+Checking the page table entry for VPN 6, we
+see that its R bit 0 indicating that it is
+
+NOT resident in main memory, which causes
+a page fault exception.
+
+The page fault handler selects VPN 0xE for
+replacement since we've been told in the setup
+
+that it's the least-recently-used page.
+
+The page table entry for VPN 0xE has D=1 so
+the handler writes the contents of VPN 0xE,
+
+which is found in PPN 0x5, to secondary storage.
+
+Then it updates the page table to indicate
+that VPN 0xE is no longer resident.
+
+Next, the contents of VPN 0x6 are read from
+secondary storage into the now available PPN
+
+0x5.
+
+Now the handler updates the page table entry
+for VPN 0x6 to indicate that it's resident
+
+in PPN 0x5.
+
+The page fault handler has completed its work,
+so program execution resumes and the ST instruction
+
+is re-executed.
+
+This time the MMU is able to translate virtual
+address 0x600 to physical address 0x500.
+
+And since the ST instruction modifies the
+contents of VPN 0x6, its D bit is set to 1.
+
+Whew!
+
+We're done :)
+We can think of the work of the MMU as being
+
+divided into two tasks, which as computer
+scientists, we would think of as two procedures.
+
+In this formulation the information in the
+page map is held in several arrays: the R
+
+array holds the resident bits,
+the D array holds the dirty bits, the PPN
+
+array holds the physical page numbers,
+and the DiskAdr array holds the location in
+
+secondary storage for each virtual page.
+
+The VtoP procedure is invoked on each memory
+access to translate the virtual address into
+
+a physical address.
+
+If the requested virtual page is not resident,
+the PageFault procedure is invoked to make
+
+the page resident.
+
+Once the requested page is resident, the VPN
+is used as an index to lookup the corresponding
+
+PPN, which is then concatenated with the page
+offset to form the physical address.
+
+The PageFault routine starts by selecting
+a virtual page to be replaced, writing out
+
+its contents if it's dirty.
+
+The selected page is then marked as not resident.
+
+Finally the desired virtual page is read from
+secondary storage and the page map information
+
+updated to reflect that it's now resident
+in the newly filled physical page.
+
+We'll use hardware to implement the VtoP functionality
+since it's needed for every memory access.
+
+The call to the PageFault procedure is accomplished
+via a page fault exception, which directs
+
+the CPU to execute the appropriate handler
+software that contains the PageFault procedure.
+
+This is a good strategy to pursue in all our
+implementation choices: use hardware for the
+
+operations that need to be fast, but use exceptions
+to handle the (hopefully infrequent) exceptional
+
+cases in software.
+
+Since the software is executed by the CPU,
+which is itself a piece of hardware, what
+
+we're really doing is making the tradeoff
+between using special-purpose hardware (e.g.,
+
+the MMU) or using general-purpose hardware
+(e.g., the CPU).
+
+In general, one should be skeptical of proposals
+to use special-purpose hardware, reserving
+
+that choice for operations that truly are
+commonplace and whose performance is critical
+
+to the overall performance of the system.
\ No newline at end of file
diff --git a/SP21-5q2uzw.txt b/SP21-5q2uzw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..08c1dd9448c0249500a22372e10dce7874734580
--- /dev/null
+++ b/SP21-5q2uzw.txt
@@ -0,0 +1,6699 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's talk about processes and
+
+ align:start position:0%
+so let's talk about processes and
+ 
+
+ align:start position:0%
+so let's talk about processes and
+thermodynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so we talked about Thermo being
+
+ align:start position:0%
+right so we talked about Thermo being
+ 
+
+ align:start position:0%
+right so we talked about Thermo being
+this weird thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can tell you about
+
+ align:start position:0%
+that can tell you about
+ 
+
+ align:start position:0%
+that can tell you about
+the starting state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the final state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+doesn't really have a clue as to the
+
+ align:start position:0%
+doesn't really have a clue as to the
+ 
+
+ align:start position:0%
+doesn't really have a clue as to the
+process that takes you from one to the
+
+ align:start position:0%
+process that takes you from one to the
+ 
+
+ align:start position:0%
+process that takes you from one to the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+that is Thermo
+
+ align:start position:0%
+that is Thermo
+ 
+
+ align:start position:0%
+that is Thermo
+doesn't describe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+real world processes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but that doesn't mean it's useless the
+
+ align:start position:0%
+but that doesn't mean it's useless the
+ 
+
+ align:start position:0%
+but that doesn't mean it's useless the
+concept of State functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which are history independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allows us to make predictions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so for example if someone told you
+
+ align:start position:0%
+right so for example if someone told you
+ 
+
+ align:start position:0%
+right so for example if someone told you
+the pressure temperature and volume of
+
+ align:start position:0%
+the pressure temperature and volume of
+ 
+
+ align:start position:0%
+the pressure temperature and volume of
+the system at the beginning
+
+ align:start position:0%
+the system at the beginning
+ 
+
+ align:start position:0%
+the system at the beginning
+and then totally do the pressure and
+
+ align:start position:0%
+and then totally do the pressure and
+ 
+
+ align:start position:0%
+and then totally do the pressure and
+temperature of the system at the end
+
+ align:start position:0%
+temperature of the system at the end
+ 
+
+ align:start position:0%
+temperature of the system at the end
+with that information you could
+
+ align:start position:0%
+with that information you could
+ 
+
+ align:start position:0%
+with that information you could
+calculate the volume without knowing
+
+ align:start position:0%
+calculate the volume without knowing
+ 
+
+ align:start position:0%
+calculate the volume without knowing
+the process that took it from A to B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's the property of State
+
+ align:start position:0%
+so here's the property of State
+ 
+
+ align:start position:0%
+so here's the property of State
+functions any process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+connecting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A to B will give same results
+
+ align:start position:0%
+A to B will give same results
+ 
+
+ align:start position:0%
+A to B will give same results
+it's like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the final state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the final State variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because they are State variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you want to calculate something
+
+ align:start position:0%
+so you want to calculate something
+ 
+
+ align:start position:0%
+so you want to calculate something
+you want to do the easiest calculation
+
+ align:start position:0%
+you want to do the easiest calculation
+ 
+
+ align:start position:0%
+you want to do the easiest calculation
+you can conceptualize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the simplest process to calculate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the same way that we choose a
+
+ align:start position:0%
+so in the same way that we choose a
+ 
+
+ align:start position:0%
+so in the same way that we choose a
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+components and its boundaries out of
+
+ align:start position:0%
+components and its boundaries out of
+ 
+
+ align:start position:0%
+components and its boundaries out of
+convenience
+
+ align:start position:0%
+convenience
+ 
+
+ align:start position:0%
+convenience
+depending on the problem we're trying to
+
+ align:start position:0%
+depending on the problem we're trying to
+ 
+
+ align:start position:0%
+depending on the problem we're trying to
+solve you
+
+ align:start position:0%
+solve you
+ 
+
+ align:start position:0%
+solve you
+calculate the simplest process
+
+ align:start position:0%
+calculate the simplest process
+ 
+
+ align:start position:0%
+calculate the simplest process
+to calculate out of convenience not
+
+ align:start position:0%
+to calculate out of convenience not
+ 
+
+ align:start position:0%
+to calculate out of convenience not
+necessarily the process that nature
+
+ align:start position:0%
+necessarily the process that nature
+ 
+
+ align:start position:0%
+necessarily the process that nature
+actually takes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the simplest process is to calculate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are reversible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so reversible process that's that's a
+
+ align:start position:0%
+so reversible process that's that's a
+ 
+
+ align:start position:0%
+so reversible process that's that's a
+New Concept
+
+ align:start position:0%
+New Concept
+ 
+
+ align:start position:0%
+New Concept
+That's A New Concept for us and it has a
+
+ align:start position:0%
+That's A New Concept for us and it has a
+ 
+
+ align:start position:0%
+That's A New Concept for us and it has a
+very deep and important thermodynamic
+
+ align:start position:0%
+very deep and important thermodynamic
+ 
+
+ align:start position:0%
+very deep and important thermodynamic
+meaning it means a process that does not
+
+ align:start position:0%
+meaning it means a process that does not
+ 
+
+ align:start position:0%
+meaning it means a process that does not
+change the entropy of the universe that
+
+ align:start position:0%
+change the entropy of the universe that
+ 
+
+ align:start position:0%
+change the entropy of the universe that
+is a system plus its surroundings
+
+ align:start position:0%
+is a system plus its surroundings
+ 
+
+ align:start position:0%
+is a system plus its surroundings
+and we'll see that in the next couple of
+
+ align:start position:0%
+and we'll see that in the next couple of
+ 
+
+ align:start position:0%
+and we'll see that in the next couple of
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+reversible processes have these
+
+ align:start position:0%
+reversible processes have these
+ 
+
+ align:start position:0%
+reversible processes have these
+properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the system plus surroundings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are in equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at all times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's an assumption
+
+ align:start position:0%
+that's an assumption
+ 
+
+ align:start position:0%
+that's an assumption
+all right this violates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our day
+
+ align:start position:0%
+our day
+ 
+
+ align:start position:0%
+our day
+to day notion of an arrow of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's really inconsistent with most of
+
+ align:start position:0%
+it's really inconsistent with most of
+ 
+
+ align:start position:0%
+it's really inconsistent with most of
+our experience
+
+ align:start position:0%
+our experience
+ 
+
+ align:start position:0%
+our experience
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in practice a reversible process would
+
+ align:start position:0%
+in practice a reversible process would
+ 
+
+ align:start position:0%
+in practice a reversible process would
+take forever
+
+ align:start position:0%
+take forever
+ 
+
+ align:start position:0%
+take forever
+so we're imagining a process which
+
+ align:start position:0%
+so we're imagining a process which
+ 
+
+ align:start position:0%
+so we're imagining a process which
+doesn't actually exist but it makes a
+
+ align:start position:0%
+doesn't actually exist but it makes a
+ 
+
+ align:start position:0%
+doesn't actually exist but it makes a
+calculation easier
+
+ align:start position:0%
+calculation easier
+ 
+
+ align:start position:0%
+calculation easier
+so in order for a process to be in
+
+ align:start position:0%
+so in order for a process to be in
+ 
+
+ align:start position:0%
+so in order for a process to be in
+equilibrium at all times it has to go
+
+ align:start position:0%
+equilibrium at all times it has to go
+ 
+
+ align:start position:0%
+equilibrium at all times it has to go
+arbitrarily slowly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order for a process to be able to go
+
+ align:start position:0%
+in order for a process to be able to go
+ 
+
+ align:start position:0%
+in order for a process to be able to go
+forwards or backwards we need to be able
+
+ align:start position:0%
+forwards or backwards we need to be able
+ 
+
+ align:start position:0%
+forwards or backwards we need to be able
+to play the movie
+
+ align:start position:0%
+to play the movie
+ 
+
+ align:start position:0%
+to play the movie
+forwards or backwards
+
+ align:start position:0%
+forwards or backwards
+ 
+
+ align:start position:0%
+forwards or backwards
+without being able to tell
+
+ align:start position:0%
+without being able to tell
+ 
+
+ align:start position:0%
+without being able to tell
+which one is forwards and which one is
+
+ align:start position:0%
+which one is forwards and which one is
+ 
+
+ align:start position:0%
+which one is forwards and which one is
+backwards that violates our day-to-day
+
+ align:start position:0%
+backwards that violates our day-to-day
+ 
+
+ align:start position:0%
+backwards that violates our day-to-day
+notion of the arrow of time
+
+ align:start position:0%
+notion of the arrow of time
+ 
+
+ align:start position:0%
+notion of the arrow of time
+and the requirement to go arbitrarily
+
+ align:start position:0%
+and the requirement to go arbitrarily
+ 
+
+ align:start position:0%
+and the requirement to go arbitrarily
+slowly means that in practice and a
+
+ align:start position:0%
+slowly means that in practice and a
+ 
+
+ align:start position:0%
+slowly means that in practice and a
+reversible process would take forever
+
+ align:start position:0%
+reversible process would take forever
+ 
+
+ align:start position:0%
+reversible process would take forever
+but it makes calculations really easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that surprising to anybody
+
+ align:start position:0%
+is that surprising to anybody
+ 
+
+ align:start position:0%
+is that surprising to anybody
+or we're comfortable with the concept of
+
+ align:start position:0%
+or we're comfortable with the concept of
+ 
+
+ align:start position:0%
+or we're comfortable with the concept of
+a reversible process
+
+ align:start position:0%
+a reversible process
+ 
+
+ align:start position:0%
+a reversible process
+none of your day-to-day processes are
+
+ align:start position:0%
+none of your day-to-day processes are
+ 
+
+ align:start position:0%
+none of your day-to-day processes are
+reversible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you think you you think of one
+
+ align:start position:0%
+if you think you you think of one
+ 
+
+ align:start position:0%
+if you think you you think of one
+um let's toss it out and we can try to
+
+ align:start position:0%
+um let's toss it out and we can try to
+ 
+
+ align:start position:0%
+um let's toss it out and we can try to
+figure out why it's not those are kind
+
+ align:start position:0%
+figure out why it's not those are kind
+ 
+
+ align:start position:0%
+figure out why it's not those are kind
+of fun thought experiments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's describe processes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the last lecture we described systems
+
+ align:start position:0%
+in the last lecture we described systems
+ 
+
+ align:start position:0%
+in the last lecture we described systems
+now we're going to describe processes
+
+ align:start position:0%
+now we're going to describe processes
+ 
+
+ align:start position:0%
+now we're going to describe processes
+all right so things you can do to a
+
+ align:start position:0%
+all right so things you can do to a
+ 
+
+ align:start position:0%
+all right so things you can do to a
+system you can work on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+you can heat it
+
+ align:start position:0%
+you can heat it
+ 
+
+ align:start position:0%
+you can heat it
+or you could add
+
+ align:start position:0%
+or you could add
+ 
+
+ align:start position:0%
+or you could add
+or subtract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay these are things you can do
+
+ align:start position:0%
+okay these are things you can do
+ 
+
+ align:start position:0%
+okay these are things you can do
+these are
+
+ align:start position:0%
+these are
+ 
+
+ align:start position:0%
+these are
+verbs in thermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of these are verbs in thermal
+
+ align:start position:0%
+all of these are verbs in thermal
+ 
+
+ align:start position:0%
+all of these are verbs in thermal
+they're actions that you do on a system
+
+ align:start position:0%
+they're actions that you do on a system
+ 
+
+ align:start position:0%
+they're actions that you do on a system
+okay work what is work
+
+ align:start position:0%
+okay work what is work
+ 
+
+ align:start position:0%
+okay work what is work
+it's a mechanical way of exchanging
+
+ align:start position:0%
+it's a mechanical way of exchanging
+ 
+
+ align:start position:0%
+it's a mechanical way of exchanging
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+mechanical
+
+ align:start position:0%
+mechanical
+ 
+
+ align:start position:0%
+mechanical
+Exchange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we use w
+
+ align:start position:0%
+so we use w
+ 
+
+ align:start position:0%
+so we use w
+and what's that
+
+ align:start position:0%
+and what's that
+ 
+
+ align:start position:0%
+and what's that
+kilogram meters squared per second
+
+ align:start position:0%
+kilogram meters squared per second
+ 
+
+ align:start position:0%
+kilogram meters squared per second
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+as the units of
+
+ align:start position:0%
+as the units of
+ 
+
+ align:start position:0%
+as the units of
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+right just a little bit of dimensional
+
+ align:start position:0%
+right just a little bit of dimensional
+ 
+
+ align:start position:0%
+right just a little bit of dimensional
+analysis you guys flip separate that out
+
+ align:start position:0%
+analysis you guys flip separate that out
+ 
+
+ align:start position:0%
+analysis you guys flip separate that out
+it's kilogram meter per second squared
+
+ align:start position:0%
+it's kilogram meter per second squared
+ 
+
+ align:start position:0%
+it's kilogram meter per second squared
+per meter right
+
+ align:start position:0%
+per meter right
+ 
+
+ align:start position:0%
+per meter right
+equals fourths times distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's Force
+
+ align:start position:0%
+right that's Force
+ 
+
+ align:start position:0%
+right that's Force
+and that's distance that's fine
+
+ align:start position:0%
+and that's distance that's fine
+ 
+
+ align:start position:0%
+and that's distance that's fine
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in thermo we we normally separate that
+
+ align:start position:0%
+in thermo we we normally separate that
+ 
+
+ align:start position:0%
+in thermo we we normally separate that
+out a little bit differently
+
+ align:start position:0%
+out a little bit differently
+ 
+
+ align:start position:0%
+out a little bit differently
+we grab kilogram
+
+ align:start position:0%
+we grab kilogram
+ 
+
+ align:start position:0%
+we grab kilogram
+per meter
+
+ align:start position:0%
+per meter
+ 
+
+ align:start position:0%
+per meter
+per second squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what do I need what do I need to
+
+ align:start position:0%
+okay what do I need what do I need to
+ 
+
+ align:start position:0%
+okay what do I need what do I need to
+multiply this by in order to get the
+
+ align:start position:0%
+multiply this by in order to get the
+ 
+
+ align:start position:0%
+multiply this by in order to get the
+same units
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do I need
+
+ align:start position:0%
+what do I need
+ 
+
+ align:start position:0%
+what do I need
+volume meters volume
+
+ align:start position:0%
+volume meters volume
+ 
+
+ align:start position:0%
+volume meters volume
+yeah meters cubed
+
+ align:start position:0%
+yeah meters cubed
+ 
+
+ align:start position:0%
+yeah meters cubed
+so what's this this is a pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the volume
+
+ align:start position:0%
+times the volume
+ 
+
+ align:start position:0%
+times the volume
+so when you take intro mechanics let's
+
+ align:start position:0%
+so when you take intro mechanics let's
+ 
+
+ align:start position:0%
+so when you take intro mechanics let's
+say in a physics class you normally do
+
+ align:start position:0%
+say in a physics class you normally do
+ 
+
+ align:start position:0%
+say in a physics class you normally do
+force times distance work
+
+ align:start position:0%
+force times distance work
+ 
+
+ align:start position:0%
+force times distance work
+but when you take into a thermodynamics
+
+ align:start position:0%
+but when you take into a thermodynamics
+ 
+
+ align:start position:0%
+but when you take into a thermodynamics
+you normally do pressure volume work
+
+ align:start position:0%
+you normally do pressure volume work
+ 
+
+ align:start position:0%
+you normally do pressure volume work
+of course the units work out the same
+
+ align:start position:0%
+of course the units work out the same
+ 
+
+ align:start position:0%
+of course the units work out the same
+but this is p pdv work we call it okay
+
+ align:start position:0%
+but this is p pdv work we call it okay
+ 
+
+ align:start position:0%
+but this is p pdv work we call it okay
+let's work
+
+ align:start position:0%
+let's work
+ 
+
+ align:start position:0%
+let's work
+what about heat
+
+ align:start position:0%
+what about heat
+ 
+
+ align:start position:0%
+what about heat
+today all right well he is kind of
+
+ align:start position:0%
+today all right well he is kind of
+ 
+
+ align:start position:0%
+today all right well he is kind of
+difficult to ex to Define actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he is a process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that exchanges energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+without
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mechanical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or mass Exchange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so heat is defined by what it's not
+
+ align:start position:0%
+so heat is defined by what it's not
+ 
+
+ align:start position:0%
+so heat is defined by what it's not
+it's kind of a weird thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for heat we're going to use Q yes I
+
+ align:start position:0%
+and for heat we're going to use Q yes I
+ 
+
+ align:start position:0%
+and for heat we're going to use Q yes I
+work as W heat is Q they both have units
+
+ align:start position:0%
+work as W heat is Q they both have units
+ 
+
+ align:start position:0%
+work as W heat is Q they both have units
+of energy joules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we have described State
+
+ align:start position:0%
+all right so we have described State
+ 
+
+ align:start position:0%
+all right so we have described State
+variables which are history independent
+
+ align:start position:0%
+variables which are history independent
+ 
+
+ align:start position:0%
+variables which are history independent
+but we also have process variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+process dependent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so infinitesimal increments
+
+ align:start position:0%
+so infinitesimal increments
+ 
+
+ align:start position:0%
+so infinitesimal increments
+infinitesimal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of process variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are denoted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+I'm going to put this in in quotes
+
+ align:start position:0%
+I'm going to put this in in quotes
+ 
+
+ align:start position:0%
+I'm going to put this in in quotes
+inexact differentials
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is DQ
+
+ align:start position:0%
+that is DQ
+ 
+
+ align:start position:0%
+that is DQ
+D work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+D not
+
+ align:start position:0%
+D not
+ 
+
+ align:start position:0%
+D not
+d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is annoying don't blame don't shoot
+
+ align:start position:0%
+this is annoying don't blame don't shoot
+ 
+
+ align:start position:0%
+this is annoying don't blame don't shoot
+the messenger this is one really key
+
+ align:start position:0%
+the messenger this is one really key
+ 
+
+ align:start position:0%
+the messenger this is one really key
+area where Thermo deviates from
+
+ align:start position:0%
+area where Thermo deviates from
+ 
+
+ align:start position:0%
+area where Thermo deviates from
+multivariable calculus
+
+ align:start position:0%
+multivariable calculus
+ 
+
+ align:start position:0%
+multivariable calculus
+so um try not to get confused because it
+
+ align:start position:0%
+so um try not to get confused because it
+ 
+
+ align:start position:0%
+so um try not to get confused because it
+is confusing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a mini lecture I recorded it's
+
+ align:start position:0%
+there's a mini lecture I recorded it's
+ 
+
+ align:start position:0%
+there's a mini lecture I recorded it's
+up on the website called the 3DS of
+
+ align:start position:0%
+up on the website called the 3DS of
+ 
+
+ align:start position:0%
+up on the website called the 3DS of
+thermodynamics because it gets kind of
+
+ align:start position:0%
+thermodynamics because it gets kind of
+ 
+
+ align:start position:0%
+thermodynamics because it gets kind of
+harried we use a lot of Deeds
+
+ align:start position:0%
+harried we use a lot of Deeds
+ 
+
+ align:start position:0%
+harried we use a lot of Deeds
+to denote differences so hopefully
+
+ align:start position:0%
+to denote differences so hopefully
+ 
+
+ align:start position:0%
+to denote differences so hopefully
+that's useful at some point if not now
+
+ align:start position:0%
+that's useful at some point if not now
+ 
+
+ align:start position:0%
+that's useful at some point if not now
+then maybe in a week or two in the quest
+
+ align:start position:0%
+then maybe in a week or two in the quest
+ 
+
+ align:start position:0%
+then maybe in a week or two in the quest
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in thermodynamics this Greek d
+
+ align:start position:0%
+in thermodynamics this Greek d
+ 
+
+ align:start position:0%
+in thermodynamics this Greek d
+means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path dependent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what it means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is a process variable if you
+
+ align:start position:0%
+so what is a process variable if you
+ 
+
+ align:start position:0%
+so what is a process variable if you
+have a state a
+
+ align:start position:0%
+have a state a
+ 
+
+ align:start position:0%
+have a state a
+State B
+
+ align:start position:0%
+State B
+ 
+
+ align:start position:0%
+State B
+a process variable
+
+ align:start position:0%
+a process variable
+ 
+
+ align:start position:0%
+a process variable
+is a variable which depends on the
+
+ align:start position:0%
+is a variable which depends on the
+ 
+
+ align:start position:0%
+is a variable which depends on the
+process it takes to get from A to B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so you might have path one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with work one and heat one
+
+ align:start position:0%
+with work one and heat one
+ 
+
+ align:start position:0%
+with work one and heat one
+and path two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with work to
+
+ align:start position:0%
+with work to
+ 
+
+ align:start position:0%
+with work to
+and heat too and those are different
+
+ align:start position:0%
+and heat too and those are different
+ 
+
+ align:start position:0%
+and heat too and those are different
+because they're not State variables
+
+ align:start position:0%
+because they're not State variables
+ 
+
+ align:start position:0%
+because they're not State variables
+they're process variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we were on campus you know the the
+
+ align:start position:0%
+if we were on campus you know the the
+ 
+
+ align:start position:0%
+if we were on campus you know the the
+nice analogy to use is the amount of
+
+ align:start position:0%
+nice analogy to use is the amount of
+ 
+
+ align:start position:0%
+nice analogy to use is the amount of
+work you need to get from the second
+
+ align:start position:0%
+work you need to get from the second
+ 
+
+ align:start position:0%
+work you need to get from the second
+floor of building one to the fifth floor
+
+ align:start position:0%
+floor of building one to the fifth floor
+ 
+
+ align:start position:0%
+floor of building one to the fifth floor
+of building 32. or just pick a pair like
+
+ align:start position:0%
+of building 32. or just pick a pair like
+ 
+
+ align:start position:0%
+of building 32. or just pick a pair like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um there's Myriad ways of connecting
+
+ align:start position:0%
+um there's Myriad ways of connecting
+ 
+
+ align:start position:0%
+um there's Myriad ways of connecting
+those here because campus is connected
+
+ align:start position:0%
+those here because campus is connected
+ 
+
+ align:start position:0%
+those here because campus is connected
+you can go upstairs and downstairs you
+
+ align:start position:0%
+you can go upstairs and downstairs you
+ 
+
+ align:start position:0%
+you can go upstairs and downstairs you
+can take elevators you could you could
+
+ align:start position:0%
+can take elevators you could you could
+ 
+
+ align:start position:0%
+can take elevators you could you could
+get between those two points um in a
+
+ align:start position:0%
+get between those two points um in a
+ 
+
+ align:start position:0%
+get between those two points um in a
+very large number of different
+
+ align:start position:0%
+very large number of different
+ 
+
+ align:start position:0%
+very large number of different
+combinations
+
+ align:start position:0%
+combinations
+ 
+
+ align:start position:0%
+combinations
+and the amount of mechanical work you
+
+ align:start position:0%
+and the amount of mechanical work you
+ 
+
+ align:start position:0%
+and the amount of mechanical work you
+need to do
+
+ align:start position:0%
+need to do
+ 
+
+ align:start position:0%
+need to do
+will vary with combination
+
+ align:start position:0%
+will vary with combination
+ 
+
+ align:start position:0%
+will vary with combination
+but the change in your gravitational
+
+ align:start position:0%
+but the change in your gravitational
+ 
+
+ align:start position:0%
+but the change in your gravitational
+potential energy
+
+ align:start position:0%
+potential energy
+ 
+
+ align:start position:0%
+potential energy
+between the starting and final Point
+
+ align:start position:0%
+between the starting and final Point
+ 
+
+ align:start position:0%
+between the starting and final Point
+that's a fixed change
+
+ align:start position:0%
+that's a fixed change
+ 
+
+ align:start position:0%
+that's a fixed change
+that's an example of uh process
+
+ align:start position:0%
+that's an example of uh process
+ 
+
+ align:start position:0%
+that's an example of uh process
+variables versus State variables
+
+ align:start position:0%
+variables versus State variables
+ 
+
+ align:start position:0%
+variables versus State variables
+but we're not on campus it's so sad
+
+ align:start position:0%
+but we're not on campus it's so sad
+ 
+
+ align:start position:0%
+but we're not on campus it's so sad
+you're just going to have to imagine all
+
+ align:start position:0%
+you're just going to have to imagine all
+ 
+
+ align:start position:0%
+you're just going to have to imagine all
+the work you'd have to do to get from
+
+ align:start position:0%
+the work you'd have to do to get from
+ 
+
+ align:start position:0%
+the work you'd have to do to get from
+building one to building 32.
+
+ align:start position:0%
+building one to building 32.
+ 
+
+ align:start position:0%
+building one to building 32.
+okay so this is infinitesimal increments
+
+ align:start position:0%
+okay so this is infinitesimal increments
+ 
+
+ align:start position:0%
+okay so this is infinitesimal increments
+and process variables
+
+ align:start position:0%
+and process variables
+ 
+
+ align:start position:0%
+and process variables
+infinitesimal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think I need new markers
+
+ align:start position:0%
+I think I need new markers
+ 
+
+ align:start position:0%
+I think I need new markers
+and state variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are denoted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as exact differentials
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example d t
+
+ align:start position:0%
+so for example d t
+ 
+
+ align:start position:0%
+so for example d t
+d p
+
+ align:start position:0%
+d p
+ 
+
+ align:start position:0%
+d p
+d v
+
+ align:start position:0%
+d v
+ 
+
+ align:start position:0%
+d v
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+right using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+irregular lowercase D agent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a total differential in calculus okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so all I can do is tell you that
+
+ align:start position:0%
+so all I can do is tell you that
+ 
+
+ align:start position:0%
+so all I can do is tell you that
+um understanding that will can only come
+
+ align:start position:0%
+um understanding that will can only come
+ 
+
+ align:start position:0%
+um understanding that will can only come
+through practice
+
+ align:start position:0%
+through practice
+ 
+
+ align:start position:0%
+through practice
+but towards the beginning of the class
+
+ align:start position:0%
+but towards the beginning of the class
+ 
+
+ align:start position:0%
+but towards the beginning of the class
+so all I can do is tell you I think I'm
+
+ align:start position:0%
+so all I can do is tell you I think I'm
+ 
+
+ align:start position:0%
+so all I can do is tell you I think I'm
+going to try to switch to purple so
+
+ align:start position:0%
+going to try to switch to purple so
+ 
+
+ align:start position:0%
+going to try to switch to purple so
+things show up a little better
+
+ align:start position:0%
+things show up a little better
+ 
+
+ align:start position:0%
+things show up a little better
+all right so let's talk about how we
+
+ align:start position:0%
+all right so let's talk about how we
+ 
+
+ align:start position:0%
+all right so let's talk about how we
+classify processes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so an isothermal process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a process at fixed temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about an adiabatic process anybody
+
+ align:start position:0%
+what about an adiabatic process anybody
+ 
+
+ align:start position:0%
+what about an adiabatic process anybody
+know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not very fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I had a couple things which are
+
+ align:start position:0%
+I had a couple things which are
+ 
+
+ align:start position:0%
+I had a couple things which are
+equivalent actually somebody said very
+
+ align:start position:0%
+equivalent actually somebody said very
+ 
+
+ align:start position:0%
+equivalent actually somebody said very
+fast
+
+ align:start position:0%
+fast
+ 
+
+ align:start position:0%
+fast
+somebody else said no heat flow across
+
+ align:start position:0%
+somebody else said no heat flow across
+ 
+
+ align:start position:0%
+somebody else said no heat flow across
+the boundary
+
+ align:start position:0%
+the boundary
+ 
+
+ align:start position:0%
+the boundary
+so the strict definition is no heating
+
+ align:start position:0%
+so the strict definition is no heating
+ 
+
+ align:start position:0%
+so the strict definition is no heating
+across the boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in reality heat will always flow
+
+ align:start position:0%
+okay in reality heat will always flow
+ 
+
+ align:start position:0%
+okay in reality heat will always flow
+from a hot object to a cold object
+
+ align:start position:0%
+from a hot object to a cold object
+ 
+
+ align:start position:0%
+from a hot object to a cold object
+but if you've insulated your system
+
+ align:start position:0%
+but if you've insulated your system
+ 
+
+ align:start position:0%
+but if you've insulated your system
+whether it's your house
+
+ align:start position:0%
+whether it's your house
+ 
+
+ align:start position:0%
+whether it's your house
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+or a beaker
+
+ align:start position:0%
+or a beaker
+ 
+
+ align:start position:0%
+or a beaker
+in the lab
+
+ align:start position:0%
+in the lab
+ 
+
+ align:start position:0%
+in the lab
+then that slow that heat flow could be
+
+ align:start position:0%
+then that slow that heat flow could be
+ 
+
+ align:start position:0%
+then that slow that heat flow could be
+slowed down
+
+ align:start position:0%
+slowed down
+ 
+
+ align:start position:0%
+slowed down
+so one way of approximating an
+
+ align:start position:0%
+so one way of approximating an
+ 
+
+ align:start position:0%
+so one way of approximating an
+adiabiotic process is to run it quickly
+
+ align:start position:0%
+adiabiotic process is to run it quickly
+ 
+
+ align:start position:0%
+adiabiotic process is to run it quickly
+if you run a process very quickly
+
+ align:start position:0%
+if you run a process very quickly
+ 
+
+ align:start position:0%
+if you run a process very quickly
+the entire process can run before an
+
+ align:start position:0%
+the entire process can run before an
+ 
+
+ align:start position:0%
+the entire process can run before an
+appreciable amount of heat flows across
+
+ align:start position:0%
+appreciable amount of heat flows across
+ 
+
+ align:start position:0%
+appreciable amount of heat flows across
+the boundary
+
+ align:start position:0%
+the boundary
+ 
+
+ align:start position:0%
+the boundary
+so so that's why a fast process can be
+
+ align:start position:0%
+so so that's why a fast process can be
+ 
+
+ align:start position:0%
+so so that's why a fast process can be
+equivalent so I like both of those
+
+ align:start position:0%
+equivalent so I like both of those
+ 
+
+ align:start position:0%
+equivalent so I like both of those
+answers
+
+ align:start position:0%
+answers
+ 
+
+ align:start position:0%
+answers
+all right isobaric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isobaric process is at fixed p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um isocoric
+
+ align:start position:0%
+and um isocoric
+ 
+
+ align:start position:0%
+and um isocoric
+we don't use as much
+
+ align:start position:0%
+we don't use as much
+ 
+
+ align:start position:0%
+we don't use as much
+is fixed B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll see that means that there can
+
+ align:start position:0%
+and we'll see that means that there can
+ 
+
+ align:start position:0%
+and we'll see that means that there can
+be no work done on the system if the
+
+ align:start position:0%
+be no work done on the system if the
+ 
+
+ align:start position:0%
+be no work done on the system if the
+volume is fixed
+
+ align:start position:0%
+volume is fixed
+ 
+
+ align:start position:0%
+volume is fixed
+all right and then there is
+
+ align:start position:0%
+all right and then there is
+ 
+
+ align:start position:0%
+all right and then there is
+classifying
+
+ align:start position:0%
+classifying
+ 
+
+ align:start position:0%
+classifying
+boundaries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've seen this a little bit so far
+
+ align:start position:0%
+we've seen this a little bit so far
+ 
+
+ align:start position:0%
+we've seen this a little bit so far
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+as a practical matter
+
+ align:start position:0%
+as a practical matter
+ 
+
+ align:start position:0%
+as a practical matter
+the way that we set up processes are by
+
+ align:start position:0%
+the way that we set up processes are by
+ 
+
+ align:start position:0%
+the way that we set up processes are by
+defining boundaries
+
+ align:start position:0%
+defining boundaries
+ 
+
+ align:start position:0%
+defining boundaries
+so for example an insulating boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a no or a say slow heat flow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+diathermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+no Mass transfer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+open or closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is Mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transfer allowed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or disallowed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and rigid
+
+ align:start position:0%
+and rigid
+ 
+
+ align:start position:0%
+and rigid
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so when we run processes we can
+
+ align:start position:0%
+okay so when we run processes we can
+ 
+
+ align:start position:0%
+okay so when we run processes we can
+somewhat determine what kind of process
+
+ align:start position:0%
+somewhat determine what kind of process
+ 
+
+ align:start position:0%
+somewhat determine what kind of process
+we're going to run by setting up the
+
+ align:start position:0%
+we're going to run by setting up the
+ 
+
+ align:start position:0%
+we're going to run by setting up the
+boundary conditions
+
+ align:start position:0%
+boundary conditions
+ 
+
+ align:start position:0%
+boundary conditions
+and this is a practical thing this is a
+
+ align:start position:0%
+and this is a practical thing this is a
+ 
+
+ align:start position:0%
+and this is a practical thing this is a
+practical matter and all of us who run
+
+ align:start position:0%
+practical matter and all of us who run
+ 
+
+ align:start position:0%
+practical matter and all of us who run
+Labs
+
+ align:start position:0%
+Labs
+ 
+
+ align:start position:0%
+Labs
+um we do this every day in various ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so classifying processes
+
+ align:start position:0%
+all right so classifying processes
+ 
+
+ align:start position:0%
+all right so classifying processes
+classifying boundaries and so forth okay
+
+ align:start position:0%
+classifying boundaries and so forth okay
+ 
+
+ align:start position:0%
+classifying boundaries and so forth okay
+let's talk about other things associated
+
+ align:start position:0%
+let's talk about other things associated
+ 
+
+ align:start position:0%
+let's talk about other things associated
+with processes what about heat capacity
+
+ align:start position:0%
+with processes what about heat capacity
+ 
+
+ align:start position:0%
+with processes what about heat capacity
+most folks have encountered heat
+
+ align:start position:0%
+most folks have encountered heat
+ 
+
+ align:start position:0%
+most folks have encountered heat
+capacity before heat capacity we're
+
+ align:start position:0%
+capacity before heat capacity we're
+ 
+
+ align:start position:0%
+capacity before heat capacity we're
+going to use C
+
+ align:start position:0%
+going to use C
+ 
+
+ align:start position:0%
+going to use C
+and it is
+
+ align:start position:0%
+and it is
+ 
+
+ align:start position:0%
+and it is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+change in
+
+ align:start position:0%
+change in
+ 
+
+ align:start position:0%
+change in
+heat an incremental amount of heat
+
+ align:start position:0%
+heat an incremental amount of heat
+ 
+
+ align:start position:0%
+heat an incremental amount of heat
+for an incremental change of temperature
+
+ align:start position:0%
+for an incremental change of temperature
+ 
+
+ align:start position:0%
+for an incremental change of temperature
+heat increments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temp increment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+is heat capacity a state variable or a
+
+ align:start position:0%
+is heat capacity a state variable or a
+ 
+
+ align:start position:0%
+is heat capacity a state variable or a
+process variable
+
+ align:start position:0%
+process variable
+ 
+
+ align:start position:0%
+process variable
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+the process is right why is it a process
+
+ align:start position:0%
+the process is right why is it a process
+ 
+
+ align:start position:0%
+the process is right why is it a process
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+um because the first like the DQ is path
+
+ align:start position:0%
+um because the first like the DQ is path
+ 
+
+ align:start position:0%
+um because the first like the DQ is path
+dependent yeah exactly it's a process
+
+ align:start position:0%
+dependent yeah exactly it's a process
+ 
+
+ align:start position:0%
+dependent yeah exactly it's a process
+variable because it depends on a process
+
+ align:start position:0%
+variable because it depends on a process
+ 
+
+ align:start position:0%
+variable because it depends on a process
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+one corollary of the postula that there
+
+ align:start position:0%
+one corollary of the postula that there
+ 
+
+ align:start position:0%
+one corollary of the postula that there
+exist State functions is that state
+
+ align:start position:0%
+exist State functions is that state
+ 
+
+ align:start position:0%
+exist State functions is that state
+functions can only depend on other state
+
+ align:start position:0%
+functions can only depend on other state
+ 
+
+ align:start position:0%
+functions can only depend on other state
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+so if something depends on a process
+
+ align:start position:0%
+so if something depends on a process
+ 
+
+ align:start position:0%
+so if something depends on a process
+variable it itself is a process variable
+
+ align:start position:0%
+variable it itself is a process variable
+ 
+
+ align:start position:0%
+variable it itself is a process variable
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+C is path dependent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DQ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's useful
+
+ align:start position:0%
+it's useful
+ 
+
+ align:start position:0%
+it's useful
+to Define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+common processes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should say Define four common
+
+ align:start position:0%
+I should say Define four common
+ 
+
+ align:start position:0%
+I should say Define four common
+processes and the ones that we encounter
+
+ align:start position:0%
+processes and the ones that we encounter
+ 
+
+ align:start position:0%
+processes and the ones that we encounter
+in this class are CV
+
+ align:start position:0%
+in this class are CV
+ 
+
+ align:start position:0%
+in this class are CV
+equals DQ
+
+ align:start position:0%
+equals DQ
+ 
+
+ align:start position:0%
+equals DQ
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+at fixed volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and CP
+
+ align:start position:0%
+and CP
+ 
+
+ align:start position:0%
+and CP
+which is d q
+
+ align:start position:0%
+which is d q
+ 
+
+ align:start position:0%
+which is d q
+d t
+
+ align:start position:0%
+d t
+ 
+
+ align:start position:0%
+d t
+at fixed pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason these are what you
+
+ align:start position:0%
+and the reason these are what you
+ 
+
+ align:start position:0%
+and the reason these are what you
+encounter is because these are the most
+
+ align:start position:0%
+encounter is because these are the most
+ 
+
+ align:start position:0%
+encounter is because these are the most
+useful
+
+ align:start position:0%
+useful
+ 
+
+ align:start position:0%
+useful
+you could how do you keep a system with
+
+ align:start position:0%
+you could how do you keep a system with
+ 
+
+ align:start position:0%
+you could how do you keep a system with
+fixed pressure let's say you want to
+
+ align:start position:0%
+fixed pressure let's say you want to
+ 
+
+ align:start position:0%
+fixed pressure let's say you want to
+keep a system at atmospheric pressure
+
+ align:start position:0%
+keep a system at atmospheric pressure
+ 
+
+ align:start position:0%
+keep a system at atmospheric pressure
+what's the easiest way to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use like a piston
+
+ align:start position:0%
+use like a piston
+ 
+
+ align:start position:0%
+use like a piston
+that's actually I would think the
+
+ align:start position:0%
+that's actually I would think the
+ 
+
+ align:start position:0%
+that's actually I would think the
+opposite it expose it to the atmosphere
+
+ align:start position:0%
+opposite it expose it to the atmosphere
+ 
+
+ align:start position:0%
+opposite it expose it to the atmosphere
+remove the piston
+
+ align:start position:0%
+remove the piston
+ 
+
+ align:start position:0%
+remove the piston
+because if a system is exposed to the
+
+ align:start position:0%
+because if a system is exposed to the
+ 
+
+ align:start position:0%
+because if a system is exposed to the
+atmosphere
+
+ align:start position:0%
+atmosphere
+ 
+
+ align:start position:0%
+atmosphere
+it can exchange volume with the
+
+ align:start position:0%
+it can exchange volume with the
+ 
+
+ align:start position:0%
+it can exchange volume with the
+atmosphere you can get bigger or get
+
+ align:start position:0%
+atmosphere you can get bigger or get
+ 
+
+ align:start position:0%
+atmosphere you can get bigger or get
+smaller if it's higher pressure in
+
+ align:start position:0%
+smaller if it's higher pressure in
+ 
+
+ align:start position:0%
+smaller if it's higher pressure in
+atmosphere it'll push against the
+
+ align:start position:0%
+atmosphere it'll push against the
+ 
+
+ align:start position:0%
+atmosphere it'll push against the
+atmosphere and return back to
+
+ align:start position:0%
+atmosphere and return back to
+ 
+
+ align:start position:0%
+atmosphere and return back to
+atmospheric pressure if it's at lower
+
+ align:start position:0%
+atmospheric pressure if it's at lower
+ 
+
+ align:start position:0%
+atmospheric pressure if it's at lower
+pressure it will get compressed by the
+
+ align:start position:0%
+pressure it will get compressed by the
+ 
+
+ align:start position:0%
+pressure it will get compressed by the
+atmosphere and return back atmospheric
+
+ align:start position:0%
+atmosphere and return back atmospheric
+ 
+
+ align:start position:0%
+atmosphere and return back atmospheric
+pressure so the existence of a free
+
+ align:start position:0%
+pressure so the existence of a free
+ 
+
+ align:start position:0%
+pressure so the existence of a free
+surface regulates the pressure
+
+ align:start position:0%
+surface regulates the pressure
+ 
+
+ align:start position:0%
+surface regulates the pressure
+constant volume that would be a case
+
+ align:start position:0%
+constant volume that would be a case
+ 
+
+ align:start position:0%
+constant volume that would be a case
+like a piston where you have a something
+
+ align:start position:0%
+like a piston where you have a something
+ 
+
+ align:start position:0%
+like a piston where you have a something
+rigid a really rigid container you can
+
+ align:start position:0%
+rigid a really rigid container you can
+ 
+
+ align:start position:0%
+rigid a really rigid container you can
+fix the volume and then run the process
+
+ align:start position:0%
+fix the volume and then run the process
+ 
+
+ align:start position:0%
+fix the volume and then run the process
+you know the volume is not going to
+
+ align:start position:0%
+you know the volume is not going to
+ 
+
+ align:start position:0%
+you know the volume is not going to
+change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which one of these is bigger
+
+ align:start position:0%
+which one of these is bigger
+ 
+
+ align:start position:0%
+which one of these is bigger
+that requires a little more thought
+
+ align:start position:0%
+that requires a little more thought
+ 
+
+ align:start position:0%
+that requires a little more thought
+we're going to increase the energy of
+
+ align:start position:0%
+we're going to increase the energy of
+ 
+
+ align:start position:0%
+we're going to increase the energy of
+the system by heating it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right we're going to increase the
+
+ align:start position:0%
+all right we're going to increase the
+ 
+
+ align:start position:0%
+all right we're going to increase the
+energy by heating it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a given increase in temperature
+
+ align:start position:0%
+for a given increase in temperature
+ 
+
+ align:start position:0%
+for a given increase in temperature
+right do I need to heat it more for
+
+ align:start position:0%
+right do I need to heat it more for
+ 
+
+ align:start position:0%
+right do I need to heat it more for
+fixed volume or fixed depression
+
+ align:start position:0%
+fixed volume or fixed depression
+ 
+
+ align:start position:0%
+fixed volume or fixed depression
+we haven't really gotten there yet but
+
+ align:start position:0%
+we haven't really gotten there yet but
+ 
+
+ align:start position:0%
+we haven't really gotten there yet but
+I'm wondering if somebody wants to
+
+ align:start position:0%
+I'm wondering if somebody wants to
+ 
+
+ align:start position:0%
+I'm wondering if somebody wants to
+Venture a guess with an explanation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh maybe fixed pressure
+
+ align:start position:0%
+uh maybe fixed pressure
+ 
+
+ align:start position:0%
+uh maybe fixed pressure
+expression how do you figure uh I mean I
+
+ align:start position:0%
+expression how do you figure uh I mean I
+ 
+
+ align:start position:0%
+expression how do you figure uh I mean I
+think like if the system is like half
+
+ align:start position:0%
+think like if the system is like half
+ 
+
+ align:start position:0%
+think like if the system is like half
+fixed volume it would wouldn't be able
+
+ align:start position:0%
+fixed volume it would wouldn't be able
+ 
+
+ align:start position:0%
+fixed volume it would wouldn't be able
+to use the heat as well
+
+ align:start position:0%
+to use the heat as well
+ 
+
+ align:start position:0%
+to use the heat as well
+but to fix pressure that can expand
+
+ align:start position:0%
+but to fix pressure that can expand
+ 
+
+ align:start position:0%
+but to fix pressure that can expand
+yeah so so your reasoning is right but
+
+ align:start position:0%
+yeah so so your reasoning is right but
+ 
+
+ align:start position:0%
+yeah so so your reasoning is right but
+your answer is wrong so I'm glad the
+
+ align:start position:0%
+your answer is wrong so I'm glad the
+ 
+
+ align:start position:0%
+your answer is wrong so I'm glad the
+reason there is when when you have a
+
+ align:start position:0%
+reason there is when when you have a
+ 
+
+ align:start position:0%
+reason there is when when you have a
+system that's a fixed volume it can't do
+
+ align:start position:0%
+system that's a fixed volume it can't do
+ 
+
+ align:start position:0%
+system that's a fixed volume it can't do
+any work on the surroundings right it's
+
+ align:start position:0%
+any work on the surroundings right it's
+ 
+
+ align:start position:0%
+any work on the surroundings right it's
+hemmed in
+
+ align:start position:0%
+hemmed in
+ 
+
+ align:start position:0%
+hemmed in
+so all the thermal energy you put in
+
+ align:start position:0%
+so all the thermal energy you put in
+ 
+
+ align:start position:0%
+so all the thermal energy you put in
+will go into a change in the internal
+
+ align:start position:0%
+will go into a change in the internal
+ 
+
+ align:start position:0%
+will go into a change in the internal
+energy of the system increase in
+
+ align:start position:0%
+energy of the system increase in
+ 
+
+ align:start position:0%
+energy of the system increase in
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+whereas if you have a system that's
+
+ align:start position:0%
+whereas if you have a system that's
+ 
+
+ align:start position:0%
+whereas if you have a system that's
+fixed pressure
+
+ align:start position:0%
+fixed pressure
+ 
+
+ align:start position:0%
+fixed pressure
+it can do work it can expand against its
+
+ align:start position:0%
+it can do work it can expand against its
+ 
+
+ align:start position:0%
+it can do work it can expand against its
+surroundings
+
+ align:start position:0%
+surroundings
+ 
+
+ align:start position:0%
+surroundings
+so as you pour energy in in the form of
+
+ align:start position:0%
+so as you pour energy in in the form of
+ 
+
+ align:start position:0%
+so as you pour energy in in the form of
+heat
+
+ align:start position:0%
+heat
+ 
+
+ align:start position:0%
+heat
+it can lose energy in the form of doing
+
+ align:start position:0%
+it can lose energy in the form of doing
+ 
+
+ align:start position:0%
+it can lose energy in the form of doing
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+so it's like filling up a leaky Cup
+
+ align:start position:0%
+so it's like filling up a leaky Cup
+ 
+
+ align:start position:0%
+so it's like filling up a leaky Cup
+right you have to pour more water in
+
+ align:start position:0%
+right you have to pour more water in
+ 
+
+ align:start position:0%
+right you have to pour more water in
+because there's stuff leaking out the
+
+ align:start position:0%
+because there's stuff leaking out the
+ 
+
+ align:start position:0%
+because there's stuff leaking out the
+bottom of the cup in this case the stuff
+
+ align:start position:0%
+bottom of the cup in this case the stuff
+ 
+
+ align:start position:0%
+bottom of the cup in this case the stuff
+leaking out is energy in the form of
+
+ align:start position:0%
+leaking out is energy in the form of
+ 
+
+ align:start position:0%
+leaking out is energy in the form of
+work on the surroundings
+
+ align:start position:0%
+work on the surroundings
+ 
+
+ align:start position:0%
+work on the surroundings
+so CV is is is smaller CP is larger but
+
+ align:start position:0%
+so CV is is is smaller CP is larger but
+ 
+
+ align:start position:0%
+so CV is is is smaller CP is larger but
+you're you're thinking about work was
+
+ align:start position:0%
+you're you're thinking about work was
+ 
+
+ align:start position:0%
+you're you're thinking about work was
+correct okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right C
+
+ align:start position:0%
+all right C
+ 
+
+ align:start position:0%
+all right C
+is an empirical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recorded in databases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's really important maybe you know
+
+ align:start position:0%
+that's really important maybe you know
+ 
+
+ align:start position:0%
+that's really important maybe you know
+that maybe you don't but the heat
+
+ align:start position:0%
+that maybe you don't but the heat
+ 
+
+ align:start position:0%
+that maybe you don't but the heat
+capacity of a system
+
+ align:start position:0%
+capacity of a system
+ 
+
+ align:start position:0%
+capacity of a system
+um tells you so much about that system
+
+ align:start position:0%
+um tells you so much about that system
+ 
+
+ align:start position:0%
+um tells you so much about that system
+but most of those things you can't
+
+ align:start position:0%
+but most of those things you can't
+ 
+
+ align:start position:0%
+but most of those things you can't
+calculate from first principles
+
+ align:start position:0%
+calculate from first principles
+ 
+
+ align:start position:0%
+calculate from first principles
+we need to be measured and then reported
+
+ align:start position:0%
+we need to be measured and then reported
+ 
+
+ align:start position:0%
+we need to be measured and then reported
+so for example
+
+ align:start position:0%
+so for example
+ 
+
+ align:start position:0%
+so for example
+what has larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right here's some okay here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay entry level what has a bigger heat
+
+ align:start position:0%
+okay entry level what has a bigger heat
+ 
+
+ align:start position:0%
+okay entry level what has a bigger heat
+capacity a big pot of water or a small
+
+ align:start position:0%
+capacity a big pot of water or a small
+ 
+
+ align:start position:0%
+capacity a big pot of water or a small
+pot of water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have the same
+
+ align:start position:0%
+you have the same
+ 
+
+ align:start position:0%
+you have the same
+well yeah it depends Your Capacity could
+
+ align:start position:0%
+well yeah it depends Your Capacity could
+ 
+
+ align:start position:0%
+well yeah it depends Your Capacity could
+be extensive or intensive
+
+ align:start position:0%
+be extensive or intensive
+ 
+
+ align:start position:0%
+be extensive or intensive
+right so I think I I know what you're
+
+ align:start position:0%
+right so I think I I know what you're
+ 
+
+ align:start position:0%
+right so I think I I know what you're
+saying water is water but when we want
+
+ align:start position:0%
+saying water is water but when we want
+ 
+
+ align:start position:0%
+saying water is water but when we want
+to regulate the temperature of something
+
+ align:start position:0%
+to regulate the temperature of something
+ 
+
+ align:start position:0%
+to regulate the temperature of something
+we want to prevent a temperature change
+
+ align:start position:0%
+we want to prevent a temperature change
+ 
+
+ align:start position:0%
+we want to prevent a temperature change
+it helps to have a large heat capacity
+
+ align:start position:0%
+it helps to have a large heat capacity
+ 
+
+ align:start position:0%
+it helps to have a large heat capacity
+object nearby
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a large thermal Reservoir
+
+ align:start position:0%
+a large thermal Reservoir
+ 
+
+ align:start position:0%
+a large thermal Reservoir
+that's one reasons why the temperatures
+
+ align:start position:0%
+that's one reasons why the temperatures
+ 
+
+ align:start position:0%
+that's one reasons why the temperatures
+are more moderate on the coasts of
+
+ align:start position:0%
+are more moderate on the coasts of
+ 
+
+ align:start position:0%
+are more moderate on the coasts of
+continents than Inland right our
+
+ align:start position:0%
+continents than Inland right our
+ 
+
+ align:start position:0%
+continents than Inland right our
+temperature in Boston doesn't swing
+
+ align:start position:0%
+temperature in Boston doesn't swing
+ 
+
+ align:start position:0%
+temperature in Boston doesn't swing
+nearly as much as it does in Iowa
+
+ align:start position:0%
+nearly as much as it does in Iowa
+ 
+
+ align:start position:0%
+nearly as much as it does in Iowa
+um you could say the same about any
+
+ align:start position:0%
+um you could say the same about any
+ 
+
+ align:start position:0%
+um you could say the same about any
+Inland versus Coastal Community in the
+
+ align:start position:0%
+Inland versus Coastal Community in the
+ 
+
+ align:start position:0%
+Inland versus Coastal Community in the
+world and the reason is that the oceans
+
+ align:start position:0%
+world and the reason is that the oceans
+ 
+
+ align:start position:0%
+world and the reason is that the oceans
+are a big thermal Reservoir they have a
+
+ align:start position:0%
+are a big thermal Reservoir they have a
+ 
+
+ align:start position:0%
+are a big thermal Reservoir they have a
+larger heat capacity than the Great
+
+ align:start position:0%
+larger heat capacity than the Great
+ 
+
+ align:start position:0%
+larger heat capacity than the Great
+Lakes do
+
+ align:start position:0%
+Lakes do
+ 
+
+ align:start position:0%
+Lakes do
+so our temperature swings are less okay
+
+ align:start position:0%
+so our temperature swings are less okay
+ 
+
+ align:start position:0%
+so our temperature swings are less okay
+what about bread
+
+ align:start position:0%
+what about bread
+ 
+
+ align:start position:0%
+what about bread
+or cheese
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same same quantity now same mess bread
+
+ align:start position:0%
+same same quantity now same mess bread
+ 
+
+ align:start position:0%
+same same quantity now same mess bread
+or cheese
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bread
+
+ align:start position:0%
+bread
+ 
+
+ align:start position:0%
+bread
+cheese I think it's cheese when you eat
+
+ align:start position:0%
+cheese I think it's cheese when you eat
+ 
+
+ align:start position:0%
+cheese I think it's cheese when you eat
+pizza the bread's not the one that burns
+
+ align:start position:0%
+pizza the bread's not the one that burns
+ 
+
+ align:start position:0%
+pizza the bread's not the one that burns
+the top of your mouth it's the cheese it
+
+ align:start position:0%
+the top of your mouth it's the cheese it
+ 
+
+ align:start position:0%
+the top of your mouth it's the cheese it
+has a larger heat capacity
+
+ align:start position:0%
+has a larger heat capacity
+ 
+
+ align:start position:0%
+has a larger heat capacity
+cheese has a large degree capacity it
+
+ align:start position:0%
+cheese has a large degree capacity it
+ 
+
+ align:start position:0%
+cheese has a large degree capacity it
+has to do with of course the chemistry
+
+ align:start position:0%
+has to do with of course the chemistry
+ 
+
+ align:start position:0%
+has to do with of course the chemistry
+big pot of water has a larger heat
+
+ align:start position:0%
+big pot of water has a larger heat
+ 
+
+ align:start position:0%
+big pot of water has a larger heat
+capacity what about aluminum foil or a
+
+ align:start position:0%
+capacity what about aluminum foil or a
+ 
+
+ align:start position:0%
+capacity what about aluminum foil or a
+potato
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right sorry isn't
+
+ align:start position:0%
+all right sorry isn't
+ 
+
+ align:start position:0%
+all right sorry isn't
+isn't a larger heat capacity and ability
+
+ align:start position:0%
+isn't a larger heat capacity and ability
+ 
+
+ align:start position:0%
+isn't a larger heat capacity and ability
+to absorb more thermal energy without
+
+ align:start position:0%
+to absorb more thermal energy without
+ 
+
+ align:start position:0%
+to absorb more thermal energy without
+changing temperature though yes exactly
+
+ align:start position:0%
+changing temperature though yes exactly
+ 
+
+ align:start position:0%
+changing temperature though yes exactly
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so isn't the isn't the cheese like
+
+ align:start position:0%
+so isn't the isn't the cheese like
+ 
+
+ align:start position:0%
+so isn't the isn't the cheese like
+changing more in temperature than the
+
+ align:start position:0%
+changing more in temperature than the
+ 
+
+ align:start position:0%
+changing more in temperature than the
+bread no what it means is that you have
+
+ align:start position:0%
+bread no what it means is that you have
+ 
+
+ align:start position:0%
+bread no what it means is that you have
+to put in more energy from your mouth to
+
+ align:start position:0%
+to put in more energy from your mouth to
+ 
+
+ align:start position:0%
+to put in more energy from your mouth to
+cool down the cheese than you do to cool
+
+ align:start position:0%
+cool down the cheese than you do to cool
+ 
+
+ align:start position:0%
+cool down the cheese than you do to cool
+down the bread
+
+ align:start position:0%
+down the bread
+ 
+
+ align:start position:0%
+down the bread
+so here's another example which should
+
+ align:start position:0%
+so here's another example which should
+ 
+
+ align:start position:0%
+so here's another example which should
+help aluminum foil versus potato you
+
+ align:start position:0%
+help aluminum foil versus potato you
+ 
+
+ align:start position:0%
+help aluminum foil versus potato you
+bake a potato that's wrapped in foil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potato
+
+ align:start position:0%
+potato
+ 
+
+ align:start position:0%
+potato
+you take it out of the oven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+someone said potato the answer is going
+
+ align:start position:0%
+someone said potato the answer is going
+ 
+
+ align:start position:0%
+someone said potato the answer is going
+to be the foil when you take something
+
+ align:start position:0%
+to be the foil when you take something
+ 
+
+ align:start position:0%
+to be the foil when you take something
+out of the oven it's wrapped in foil you
+
+ align:start position:0%
+out of the oven it's wrapped in foil you
+ 
+
+ align:start position:0%
+out of the oven it's wrapped in foil you
+can often open the foil even if the oven
+
+ align:start position:0%
+can often open the foil even if the oven
+ 
+
+ align:start position:0%
+can often open the foil even if the oven
+was at 400 degrees you can you can open
+
+ align:start position:0%
+was at 400 degrees you can you can open
+ 
+
+ align:start position:0%
+was at 400 degrees you can you can open
+the foil without burning your fingers
+
+ align:start position:0%
+the foil without burning your fingers
+ 
+
+ align:start position:0%
+the foil without burning your fingers
+you have to avoid the steam right but
+
+ align:start position:0%
+you have to avoid the steam right but
+ 
+
+ align:start position:0%
+you have to avoid the steam right but
+you could you could grab that foil and
+
+ align:start position:0%
+you could you could grab that foil and
+ 
+
+ align:start position:0%
+you could you could grab that foil and
+very quickly bring that foil down to
+
+ align:start position:0%
+very quickly bring that foil down to
+ 
+
+ align:start position:0%
+very quickly bring that foil down to
+room temperature
+
+ align:start position:0%
+room temperature
+ 
+
+ align:start position:0%
+room temperature
+without burning your fingers
+
+ align:start position:0%
+without burning your fingers
+ 
+
+ align:start position:0%
+without burning your fingers
+but if you grab the potato you're gonna
+
+ align:start position:0%
+but if you grab the potato you're gonna
+ 
+
+ align:start position:0%
+but if you grab the potato you're gonna
+burn your hands because it takes more
+
+ align:start position:0%
+burn your hands because it takes more
+ 
+
+ align:start position:0%
+burn your hands because it takes more
+energy out of you in this case to cool
+
+ align:start position:0%
+energy out of you in this case to cool
+ 
+
+ align:start position:0%
+energy out of you in this case to cool
+the potato than it does to cool the soil
+
+ align:start position:0%
+the potato than it does to cool the soil
+ 
+
+ align:start position:0%
+the potato than it does to cool the soil
+doesn't that mean the potato is actually
+
+ align:start position:0%
+doesn't that mean the potato is actually
+ 
+
+ align:start position:0%
+doesn't that mean the potato is actually
+the one with high seeds
+
+ align:start position:0%
+the one with high seeds
+ 
+
+ align:start position:0%
+the one with high seeds
+uh larger c yeah sorry sorry yeah
+
+ align:start position:0%
+uh larger c yeah sorry sorry yeah
+ 
+
+ align:start position:0%
+uh larger c yeah sorry sorry yeah
+everything I said but reverse right
+
+ align:start position:0%
+everything I said but reverse right
+ 
+
+ align:start position:0%
+everything I said but reverse right
+exactly it's easier to bring down
+
+ align:start position:0%
+exactly it's easier to bring down
+ 
+
+ align:start position:0%
+exactly it's easier to bring down
+all right and this is lots of examples
+
+ align:start position:0%
+all right and this is lots of examples
+ 
+
+ align:start position:0%
+all right and this is lots of examples
+here that are every day right why
+
+ align:start position:0%
+here that are every day right why
+ 
+
+ align:start position:0%
+here that are every day right why
+certain surfaces outside feel colder or
+
+ align:start position:0%
+certain surfaces outside feel colder or
+ 
+
+ align:start position:0%
+certain surfaces outside feel colder or
+hotter than other surfaces on a very
+
+ align:start position:0%
+hotter than other surfaces on a very
+ 
+
+ align:start position:0%
+hotter than other surfaces on a very
+cold or a very hot day lots of examples
+
+ align:start position:0%
+cold or a very hot day lots of examples
+ 
+
+ align:start position:0%
+cold or a very hot day lots of examples
+like this okay
+
+ align:start position:0%
+like this okay
+ 
+
+ align:start position:0%
+like this okay
+so um so uh uh
+
+ align:start position:0%
+so um so uh uh
+ 
+
+ align:start position:0%
+so um so uh uh
+what do I mean to say here um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C can be calculated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for simple
+
+ align:start position:0%
+for simple
+ 
+
+ align:start position:0%
+for simple
+we call toy problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in most cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+especially cases that we rely on as
+
+ align:start position:0%
+especially cases that we rely on as
+ 
+
+ align:start position:0%
+especially cases that we rely on as
+engineers
+
+ align:start position:0%
+engineers
+ 
+
+ align:start position:0%
+engineers
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+measurements are necessary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I actually did record some numbers
+
+ align:start position:0%
+and I actually did record some numbers
+ 
+
+ align:start position:0%
+and I actually did record some numbers
+here so heat capacity in joules per gram
+
+ align:start position:0%
+here so heat capacity in joules per gram
+ 
+
+ align:start position:0%
+here so heat capacity in joules per gram
+Kelvin
+
+ align:start position:0%
+Kelvin
+ 
+
+ align:start position:0%
+Kelvin
+let's say water
+
+ align:start position:0%
+let's say water
+ 
+
+ align:start position:0%
+let's say water
+has a large heat capacity
+
+ align:start position:0%
+has a large heat capacity
+ 
+
+ align:start position:0%
+has a large heat capacity
+has to do with all of the vibrational
+
+ align:start position:0%
+has to do with all of the vibrational
+ 
+
+ align:start position:0%
+has to do with all of the vibrational
+degrees of freedom and water
+
+ align:start position:0%
+degrees of freedom and water
+ 
+
+ align:start position:0%
+degrees of freedom and water
+aluminum is very small 0.897
+
+ align:start position:0%
+aluminum is very small 0.897
+ 
+
+ align:start position:0%
+aluminum is very small 0.897
+so this right here is why you can touch
+
+ align:start position:0%
+so this right here is why you can touch
+ 
+
+ align:start position:0%
+so this right here is why you can touch
+the aluminum foil but you have to avoid
+
+ align:start position:0%
+the aluminum foil but you have to avoid
+ 
+
+ align:start position:0%
+the aluminum foil but you have to avoid
+getting a steam burn
+
+ align:start position:0%
+getting a steam burn
+ 
+
+ align:start position:0%
+getting a steam burn
+right when you open up the food you've
+
+ align:start position:0%
+right when you open up the food you've
+ 
+
+ align:start position:0%
+right when you open up the food you've
+you've packed and foil potatoes actually
+
+ align:start position:0%
+you've packed and foil potatoes actually
+ 
+
+ align:start position:0%
+you've packed and foil potatoes actually
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+large it's close to water
+
+ align:start position:0%
+large it's close to water
+ 
+
+ align:start position:0%
+large it's close to water
+because anything that's food related
+
+ align:start position:0%
+because anything that's food related
+ 
+
+ align:start position:0%
+because anything that's food related
+basically is set by the water content
+
+ align:start position:0%
+basically is set by the water content
+ 
+
+ align:start position:0%
+basically is set by the water content
+all right cheese
+
+ align:start position:0%
+all right cheese
+ 
+
+ align:start position:0%
+all right cheese
+has a lower water content than potato I
+
+ align:start position:0%
+has a lower water content than potato I
+ 
+
+ align:start position:0%
+has a lower water content than potato I
+grabbed the number 3.15 if you are a
+
+ align:start position:0%
+grabbed the number 3.15 if you are a
+ 
+
+ align:start position:0%
+grabbed the number 3.15 if you are a
+Gourmet Chef you have a table of heat
+
+ align:start position:0%
+Gourmet Chef you have a table of heat
+ 
+
+ align:start position:0%
+Gourmet Chef you have a table of heat
+capacities of things like cheese
+
+ align:start position:0%
+capacities of things like cheese
+ 
+
+ align:start position:0%
+capacities of things like cheese
+and um and uh and and 2.15 is just one
+
+ align:start position:0%
+and um and uh and and 2.15 is just one
+ 
+
+ align:start position:0%
+and um and uh and and 2.15 is just one
+number right I mean that's I don't know
+
+ align:start position:0%
+number right I mean that's I don't know
+ 
+
+ align:start position:0%
+number right I mean that's I don't know
+Cheddars but anyway
+
+ align:start position:0%
+Cheddars but anyway
+ 
+
+ align:start position:0%
+Cheddars but anyway
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so let's move on
+
+ align:start position:0%
+so let's move on
+ 
+
+ align:start position:0%
+so let's move on
+let's move on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's talk about something really
+
+ align:start position:0%
+so let's talk about something really
+ 
+
+ align:start position:0%
+so let's talk about something really
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+the first law of thermodynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's the first law of thumb
+
+ align:start position:0%
+okay so here's the first law of thumb
+ 
+
+ align:start position:0%
+okay so here's the first law of thumb
+Dynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+you sometimes encounter it in a physics
+
+ align:start position:0%
+you sometimes encounter it in a physics
+ 
+
+ align:start position:0%
+you sometimes encounter it in a physics
+class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm here to tell you this is totally
+
+ align:start position:0%
+and I'm here to tell you this is totally
+ 
+
+ align:start position:0%
+and I'm here to tell you this is totally
+useless
+
+ align:start position:0%
+useless
+ 
+
+ align:start position:0%
+useless
+because if this is all it were
+
+ align:start position:0%
+because if this is all it were
+ 
+
+ align:start position:0%
+because if this is all it were
+who cares I mean it's interesting right
+
+ align:start position:0%
+who cares I mean it's interesting right
+ 
+
+ align:start position:0%
+who cares I mean it's interesting right
+but you can't use that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's not how we arrived at it
+
+ align:start position:0%
+and that's not how we arrived at it
+ 
+
+ align:start position:0%
+and that's not how we arrived at it
+intellectually it's sort of
+
+ align:start position:0%
+intellectually it's sort of
+ 
+
+ align:start position:0%
+intellectually it's sort of
+intellectually
+
+ align:start position:0%
+intellectually
+ 
+
+ align:start position:0%
+intellectually
+um being dishonest
+
+ align:start position:0%
+um being dishonest
+ 
+
+ align:start position:0%
+um being dishonest
+because this is very non-obvious right
+
+ align:start position:0%
+because this is very non-obvious right
+ 
+
+ align:start position:0%
+because this is very non-obvious right
+it's very non-obvious and rather hard to
+
+ align:start position:0%
+it's very non-obvious and rather hard to
+ 
+
+ align:start position:0%
+it's very non-obvious and rather hard to
+prove also
+
+ align:start position:0%
+prove also
+ 
+
+ align:start position:0%
+prove also
+how is this useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the answer
+
+ align:start position:0%
+the answer
+ 
+
+ align:start position:0%
+the answer
+is because it applies locally
+
+ align:start position:0%
+is because it applies locally
+ 
+
+ align:start position:0%
+is because it applies locally
+and this is where the real intellectual
+
+ align:start position:0%
+and this is where the real intellectual
+ 
+
+ align:start position:0%
+and this is where the real intellectual
+thread comes from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we talk about the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus the surroundings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system plus surroundings
+
+ align:start position:0%
+system plus surroundings
+ 
+
+ align:start position:0%
+system plus surroundings
+you could call universe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's kind of highfalutin language
+
+ align:start position:0%
+it's kind of highfalutin language
+ 
+
+ align:start position:0%
+it's kind of highfalutin language
+sometimes I'll flip and I'll say
+
+ align:start position:0%
+sometimes I'll flip and I'll say
+ 
+
+ align:start position:0%
+sometimes I'll flip and I'll say
+universe but I don't mean to systems for
+
+ align:start position:0%
+universe but I don't mean to systems for
+ 
+
+ align:start position:0%
+universe but I don't mean to systems for
+surroundings energy this isn't for
+
+ align:start position:0%
+surroundings energy this isn't for
+ 
+
+ align:start position:0%
+surroundings energy this isn't for
+surroundings is constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but here's where it gets useful
+
+ align:start position:0%
+but here's where it gets useful
+ 
+
+ align:start position:0%
+but here's where it gets useful
+we use
+
+ align:start position:0%
+we use
+ 
+
+ align:start position:0%
+we use
+the boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for bookkeeping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+like it or not a lot of thermo is
+
+ align:start position:0%
+like it or not a lot of thermo is
+ 
+
+ align:start position:0%
+like it or not a lot of thermo is
+bookkeeping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so we have a system
+
+ align:start position:0%
+right so we have a system
+ 
+
+ align:start position:0%
+right so we have a system
+we have a boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have
+
+ align:start position:0%
+and we have
+ 
+
+ align:start position:0%
+and we have
+flows of energy
+
+ align:start position:0%
+flows of energy
+ 
+
+ align:start position:0%
+flows of energy
+and we can keep track of them and we can
+
+ align:start position:0%
+and we can keep track of them and we can
+ 
+
+ align:start position:0%
+and we can keep track of them and we can
+keep track of the forms that energy can
+
+ align:start position:0%
+keep track of the forms that energy can
+ 
+
+ align:start position:0%
+keep track of the forms that energy can
+flow so there are three ways that energy
+
+ align:start position:0%
+flow so there are three ways that energy
+ 
+
+ align:start position:0%
+flow so there are three ways that energy
+can flow between a system and the
+
+ align:start position:0%
+can flow between a system and the
+ 
+
+ align:start position:0%
+can flow between a system and the
+surroundings in 3020
+
+ align:start position:0%
+surroundings in 3020
+ 
+
+ align:start position:0%
+surroundings in 3020
+we've encountered two of them so far uh
+
+ align:start position:0%
+we've encountered two of them so far uh
+ 
+
+ align:start position:0%
+we've encountered two of them so far uh
+about 20 minutes ago if somebody want to
+
+ align:start position:0%
+about 20 minutes ago if somebody want to
+ 
+
+ align:start position:0%
+about 20 minutes ago if somebody want to
+tell me what the three of them are all
+
+ align:start position:0%
+tell me what the three of them are all
+ 
+
+ align:start position:0%
+tell me what the three of them are all
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+action radiation and conduction
+
+ align:start position:0%
+action radiation and conduction
+ 
+
+ align:start position:0%
+action radiation and conduction
+nope sorry
+
+ align:start position:0%
+nope sorry
+ 
+
+ align:start position:0%
+nope sorry
+so those are those are forms of heat
+
+ align:start position:0%
+so those are those are forms of heat
+ 
+
+ align:start position:0%
+so those are those are forms of heat
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+we are not going to talk about fluid
+
+ align:start position:0%
+we are not going to talk about fluid
+ 
+
+ align:start position:0%
+we are not going to talk about fluid
+dynamics or uh or radiative processes in
+
+ align:start position:0%
+dynamics or uh or radiative processes in
+ 
+
+ align:start position:0%
+dynamics or uh or radiative processes in
+any detail in o2o so what you said was
+
+ align:start position:0%
+any detail in o2o so what you said was
+ 
+
+ align:start position:0%
+any detail in o2o so what you said was
+scientifically true it's it's not
+
+ align:start position:0%
+scientifically true it's it's not
+ 
+
+ align:start position:0%
+scientifically true it's it's not
+specifically what the three forms are in
+
+ align:start position:0%
+specifically what the three forms are in
+ 
+
+ align:start position:0%
+specifically what the three forms are in
+O2L we've talked about two of them so
+
+ align:start position:0%
+O2L we've talked about two of them so
+ 
+
+ align:start position:0%
+O2L we've talked about two of them so
+far
+
+ align:start position:0%
+far
+ 
+
+ align:start position:0%
+far
+um one is heat which is everything you
+
+ align:start position:0%
+um one is heat which is everything you
+ 
+
+ align:start position:0%
+um one is heat which is everything you
+just described
+
+ align:start position:0%
+just described
+ 
+
+ align:start position:0%
+just described
+what's another way energy can flow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work work okay cool he he works
+
+ align:start position:0%
+work work okay cool he he works
+ 
+
+ align:start position:0%
+work work okay cool he he works
+mechanical work and there's a third way
+
+ align:start position:0%
+mechanical work and there's a third way
+ 
+
+ align:start position:0%
+mechanical work and there's a third way
+that energy can can flow that we haven't
+
+ align:start position:0%
+that energy can can flow that we haven't
+ 
+
+ align:start position:0%
+that energy can can flow that we haven't
+introduced it yet would anyone like to
+
+ align:start position:0%
+introduced it yet would anyone like to
+ 
+
+ align:start position:0%
+introduced it yet would anyone like to
+venture our guests Mass transfer Mass
+
+ align:start position:0%
+venture our guests Mass transfer Mass
+ 
+
+ align:start position:0%
+venture our guests Mass transfer Mass
+transfer right matter has energy and so
+
+ align:start position:0%
+transfer right matter has energy and so
+ 
+
+ align:start position:0%
+transfer right matter has energy and so
+you can exchange matter
+
+ align:start position:0%
+you can exchange matter
+ 
+
+ align:start position:0%
+you can exchange matter
+and transfer energy that way so this is
+
+ align:start position:0%
+and transfer energy that way so this is
+ 
+
+ align:start position:0%
+and transfer energy that way so this is
+the bookkeeping that we're going to do
+
+ align:start position:0%
+the bookkeeping that we're going to do
+ 
+
+ align:start position:0%
+the bookkeeping that we're going to do
+in this class so this gets me to
+
+ align:start position:0%
+in this class so this gets me to
+ 
+
+ align:start position:0%
+in this class so this gets me to
+first law bookkeeper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I wish I had a week to teach the fluid
+
+ align:start position:0%
+I wish I had a week to teach the fluid
+ 
+
+ align:start position:0%
+I wish I had a week to teach the fluid
+dynamics and talk about
+
+ align:start position:0%
+dynamics and talk about
+ 
+
+ align:start position:0%
+dynamics and talk about
+convection and then talk about heat
+
+ align:start position:0%
+convection and then talk about heat
+ 
+
+ align:start position:0%
+convection and then talk about heat
+transfer talk about conduction and do
+
+ align:start position:0%
+transfer talk about conduction and do
+ 
+
+ align:start position:0%
+transfer talk about conduction and do
+radiative but um it goes well beyond
+
+ align:start position:0%
+radiative but um it goes well beyond
+ 
+
+ align:start position:0%
+radiative but um it goes well beyond
+this class
+
+ align:start position:0%
+this class
+ 
+
+ align:start position:0%
+this class
+you'll learn about those things in other
+
+ align:start position:0%
+you'll learn about those things in other
+ 
+
+ align:start position:0%
+you'll learn about those things in other
+classes or come to office hours we can
+
+ align:start position:0%
+classes or come to office hours we can
+ 
+
+ align:start position:0%
+classes or come to office hours we can
+talk about heat transfer first law
+
+ align:start position:0%
+talk about heat transfer first law
+ 
+
+ align:start position:0%
+talk about heat transfer first law
+bookkeeping okay this is where we
+
+ align:start position:0%
+bookkeeping okay this is where we
+ 
+
+ align:start position:0%
+bookkeeping okay this is where we
+hopefully
+
+ align:start position:0%
+hopefully
+ 
+
+ align:start position:0%
+hopefully
+resolve some ambiguity about o2o via V
+
+ align:start position:0%
+resolve some ambiguity about o2o via V
+ 
+
+ align:start position:0%
+resolve some ambiguity about o2o via V
+other classes you've taken so types of
+
+ align:start position:0%
+other classes you've taken so types of
+ 
+
+ align:start position:0%
+other classes you've taken so types of
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+include kinetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and internal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we use U
+
+ align:start position:0%
+which we use U
+ 
+
+ align:start position:0%
+which we use U
+so kinetic energy depends on how fast
+
+ align:start position:0%
+so kinetic energy depends on how fast
+ 
+
+ align:start position:0%
+so kinetic energy depends on how fast
+a system is moving right you know that
+
+ align:start position:0%
+a system is moving right you know that
+ 
+
+ align:start position:0%
+a system is moving right you know that
+so if your system is a baseball
+
+ align:start position:0%
+so if your system is a baseball
+ 
+
+ align:start position:0%
+so if your system is a baseball
+kinetic energy is how fast it's moving
+
+ align:start position:0%
+kinetic energy is how fast it's moving
+ 
+
+ align:start position:0%
+kinetic energy is how fast it's moving
+potential energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depends on where a system is
+
+ align:start position:0%
+depends on where a system is
+ 
+
+ align:start position:0%
+depends on where a system is
+in some reference frame so again if your
+
+ align:start position:0%
+in some reference frame so again if your
+ 
+
+ align:start position:0%
+in some reference frame so again if your
+system is a baseball the potential
+
+ align:start position:0%
+system is a baseball the potential
+ 
+
+ align:start position:0%
+system is a baseball the potential
+energy depends on where it is relative
+
+ align:start position:0%
+energy depends on where it is relative
+ 
+
+ align:start position:0%
+energy depends on where it is relative
+to the center of mass of the Earth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+internal energy is everything else
+
+ align:start position:0%
+internal energy is everything else
+ 
+
+ align:start position:0%
+internal energy is everything else
+all of the energy which is independent
+
+ align:start position:0%
+all of the energy which is independent
+ 
+
+ align:start position:0%
+all of the energy which is independent
+of the velocity of the system and
+
+ align:start position:0%
+of the velocity of the system and
+ 
+
+ align:start position:0%
+of the velocity of the system and
+independent of the location of the
+
+ align:start position:0%
+independent of the location of the
+ 
+
+ align:start position:0%
+independent of the location of the
+system so again if your system is the
+
+ align:start position:0%
+system so again if your system is the
+ 
+
+ align:start position:0%
+system so again if your system is the
+baseball the internal energy is all the
+
+ align:start position:0%
+baseball the internal energy is all the
+ 
+
+ align:start position:0%
+baseball the internal energy is all the
+molecular bonds that make up the
+
+ align:start position:0%
+molecular bonds that make up the
+ 
+
+ align:start position:0%
+molecular bonds that make up the
+baseball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus The Binding energy of the electrons
+
+ align:start position:0%
+plus The Binding energy of the electrons
+ 
+
+ align:start position:0%
+plus The Binding energy of the electrons
+to the nuclei okay so this is the one
+
+ align:start position:0%
+to the nuclei okay so this is the one
+ 
+
+ align:start position:0%
+to the nuclei okay so this is the one
+that we use in thermal
+
+ align:start position:0%
+that we use in thermal
+ 
+
+ align:start position:0%
+that we use in thermal
+this is the last time we'll talk about
+
+ align:start position:0%
+this is the last time we'll talk about
+ 
+
+ align:start position:0%
+this is the last time we'll talk about
+kinetic energy and the last time we'll
+
+ align:start position:0%
+kinetic energy and the last time we'll
+ 
+
+ align:start position:0%
+kinetic energy and the last time we'll
+talk about potential energy we might get
+
+ align:start position:0%
+talk about potential energy we might get
+ 
+
+ align:start position:0%
+talk about potential energy we might get
+to like 20 minutes of electrochemistry
+
+ align:start position:0%
+to like 20 minutes of electrochemistry
+ 
+
+ align:start position:0%
+to like 20 minutes of electrochemistry
+later in the term and then potential
+
+ align:start position:0%
+later in the term and then potential
+ 
+
+ align:start position:0%
+later in the term and then potential
+might sneak back in but basically this
+
+ align:start position:0%
+might sneak back in but basically this
+ 
+
+ align:start position:0%
+might sneak back in but basically this
+is where we are for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3020 okay what about processes
+
+ align:start position:0%
+3020 okay what about processes
+ 
+
+ align:start position:0%
+3020 okay what about processes
+please
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes that exchange energy so this
+
+ align:start position:0%
+processes that exchange energy so this
+ 
+
+ align:start position:0%
+processes that exchange energy so this
+week we just answer there's Heating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's Mass transfer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is some first lot
+
+ align:start position:0%
+okay so this is some first lot
+ 
+
+ align:start position:0%
+okay so this is some first lot
+bookkeeping I hope this helps a little
+
+ align:start position:0%
+bookkeeping I hope this helps a little
+ 
+
+ align:start position:0%
+bookkeeping I hope this helps a little
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+as we try to recall what what counts and
+
+ align:start position:0%
+as we try to recall what what counts and
+ 
+
+ align:start position:0%
+as we try to recall what what counts and
+what doesn't an equilibrium Therma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so so um
+
+ align:start position:0%
+all right so so um
+ 
+
+ align:start position:0%
+all right so so um
+we can do this mathematically
+
+ align:start position:0%
+we can do this mathematically
+ 
+
+ align:start position:0%
+we can do this mathematically
+energy is a state function but it's
+
+ align:start position:0%
+energy is a state function but it's
+ 
+
+ align:start position:0%
+energy is a state function but it's
+changed by processes
+
+ align:start position:0%
+changed by processes
+ 
+
+ align:start position:0%
+changed by processes
+so d u
+
+ align:start position:0%
+so d u
+ 
+
+ align:start position:0%
+so d u
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change in heat energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus change and mechanical work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus something new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a term which accounts for a change in
+
+ align:start position:0%
+a term which accounts for a change in
+ 
+
+ align:start position:0%
+a term which accounts for a change in
+mass
+
+ align:start position:0%
+mass
+ 
+
+ align:start position:0%
+mass
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+so d q equals heat
+
+ align:start position:0%
+so d q equals heat
+ 
+
+ align:start position:0%
+so d q equals heat
+applied
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the system is a sign convention here
+
+ align:start position:0%
+the system is a sign convention here
+ 
+
+ align:start position:0%
+the system is a sign convention here
+we're going to follow the sign
+
+ align:start position:0%
+we're going to follow the sign
+ 
+
+ align:start position:0%
+we're going to follow the sign
+convention in the dahas textbook
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you're heating a system
+
+ align:start position:0%
+so if you're heating a system
+ 
+
+ align:start position:0%
+so if you're heating a system
+let's say that's the endothermic
+
+ align:start position:0%
+let's say that's the endothermic
+ 
+
+ align:start position:0%
+let's say that's the endothermic
+reaction the instant cold pack then DQ
+
+ align:start position:0%
+reaction the instant cold pack then DQ
+ 
+
+ align:start position:0%
+reaction the instant cold pack then DQ
+is positive right
+
+ align:start position:0%
+is positive right
+ 
+
+ align:start position:0%
+is positive right
+d w is work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+performed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a consistent convention there
+
+ align:start position:0%
+so there's a consistent convention there
+ 
+
+ align:start position:0%
+so there's a consistent convention there
+these have the same sign
+
+ align:start position:0%
+these have the same sign
+ 
+
+ align:start position:0%
+these have the same sign
+right positive DQ increases the energy
+
+ align:start position:0%
+right positive DQ increases the energy
+ 
+
+ align:start position:0%
+right positive DQ increases the energy
+of the system positive DW increases the
+
+ align:start position:0%
+of the system positive DW increases the
+ 
+
+ align:start position:0%
+of the system positive DW increases the
+energy of the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for mechanical work that we encounter in
+
+ align:start position:0%
+for mechanical work that we encounter in
+ 
+
+ align:start position:0%
+for mechanical work that we encounter in
+this class
+
+ align:start position:0%
+this class
+ 
+
+ align:start position:0%
+this class
+ew equals p
+
+ align:start position:0%
+ew equals p
+ 
+
+ align:start position:0%
+ew equals p
+DV
+
+ align:start position:0%
+DV
+ 
+
+ align:start position:0%
+DV
+and here I'll ask is it positive or
+
+ align:start position:0%
+and here I'll ask is it positive or
+ 
+
+ align:start position:0%
+and here I'll ask is it positive or
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which one is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the pressure this is the change
+
+ align:start position:0%
+this is the pressure this is the change
+ 
+
+ align:start position:0%
+this is the pressure this is the change
+in volume of a system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a positive pdv means the system is
+
+ align:start position:0%
+so a positive pdv means the system is
+ 
+
+ align:start position:0%
+so a positive pdv means the system is
+doing work on the surroundings it's
+
+ align:start position:0%
+doing work on the surroundings it's
+ 
+
+ align:start position:0%
+doing work on the surroundings it's
+expanding against the surroundings
+
+ align:start position:0%
+expanding against the surroundings
+ 
+
+ align:start position:0%
+expanding against the surroundings
+so what should be the sign here to stick
+
+ align:start position:0%
+so what should be the sign here to stick
+ 
+
+ align:start position:0%
+so what should be the sign here to stick
+with our new convention
+
+ align:start position:0%
+with our new convention
+ 
+
+ align:start position:0%
+with our new convention
+negative negative right it's negative
+
+ align:start position:0%
+negative negative right it's negative
+ 
+
+ align:start position:0%
+negative negative right it's negative
+because the system is losing energy
+
+ align:start position:0%
+because the system is losing energy
+ 
+
+ align:start position:0%
+because the system is losing energy
+as it expands right negative so it
+
+ align:start position:0%
+as it expands right negative so it
+ 
+
+ align:start position:0%
+as it expands right negative so it
+equals minus p
+
+ align:start position:0%
+equals minus p
+ 
+
+ align:start position:0%
+equals minus p
+DV
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little mathematical note here this is
+
+ align:start position:0%
+a little mathematical note here this is
+ 
+
+ align:start position:0%
+a little mathematical note here this is
+a process
+
+ align:start position:0%
+a process
+ 
+
+ align:start position:0%
+a process
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this is a state
+
+ align:start position:0%
+this is a state
+ 
+
+ align:start position:0%
+this is a state
+variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is not an equation of State this is
+
+ align:start position:0%
+this is not an equation of State this is
+ 
+
+ align:start position:0%
+this is not an equation of State this is
+a differential form of an equation of
+
+ align:start position:0%
+a differential form of an equation of
+ 
+
+ align:start position:0%
+a differential form of an equation of
+state so it's not the same thing
+
+ align:start position:0%
+state so it's not the same thing
+ 
+
+ align:start position:0%
+state so it's not the same thing
+but it has this funny uh
+
+ align:start position:0%
+but it has this funny uh
+ 
+
+ align:start position:0%
+but it has this funny uh
+property that you have on the one hand
+
+ align:start position:0%
+property that you have on the one hand
+ 
+
+ align:start position:0%
+property that you have on the one hand
+process variable on the other hand of
+
+ align:start position:0%
+process variable on the other hand of
+ 
+
+ align:start position:0%
+process variable on the other hand of
+State variable this could be considered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an integration constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you don't care about that comment
+
+ align:start position:0%
+if you don't care about that comment
+ 
+
+ align:start position:0%
+if you don't care about that comment
+ignore that comment we don't really talk
+
+ align:start position:0%
+ignore that comment we don't really talk
+ 
+
+ align:start position:0%
+ignore that comment we don't really talk
+about integration constants in this
+
+ align:start position:0%
+about integration constants in this
+ 
+
+ align:start position:0%
+about integration constants in this
+class we don't have time but they are
+
+ align:start position:0%
+class we don't have time but they are
+ 
+
+ align:start position:0%
+class we don't have time but they are
+kind of hidden there in the structure of
+
+ align:start position:0%
+kind of hidden there in the structure of
+ 
+
+ align:start position:0%
+kind of hidden there in the structure of
+Therma
+
+ align:start position:0%
+Therma
+ 
+
+ align:start position:0%
+Therma
+all right so DQ DW
+
+ align:start position:0%
+all right so DQ DW
+ 
+
+ align:start position:0%
+all right so DQ DW
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu i d n i
+
+ align:start position:0%
+mu i d n i
+ 
+
+ align:start position:0%
+mu i d n i
+equals the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+D and I
+
+ align:start position:0%
+D and I
+ 
+
+ align:start position:0%
+D and I
+of moles
+
+ align:start position:0%
+of moles
+ 
+
+ align:start position:0%
+of moles
+of component I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where I has to run over all the
+
+ align:start position:0%
+where I has to run over all the
+ 
+
+ align:start position:0%
+where I has to run over all the
+different components of the system so n
+
+ align:start position:0%
+different components of the system so n
+ 
+
+ align:start position:0%
+different components of the system so n
+of I equals number moles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of component I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and mu of I is defined as
+
+ align:start position:0%
+and mu of I is defined as
+ 
+
+ align:start position:0%
+and mu of I is defined as
+partial U
+
+ align:start position:0%
+partial U
+ 
+
+ align:start position:0%
+partial U
+partial n of I
+
+ align:start position:0%
+partial n of I
+ 
+
+ align:start position:0%
+partial n of I
+for fixed and we'll get to this entropy
+
+ align:start position:0%
+for fixed and we'll get to this entropy
+ 
+
+ align:start position:0%
+for fixed and we'll get to this entropy
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+and moles of J not equal to I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I is a component label
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this whole thing is called the
+
+ align:start position:0%
+and this whole thing is called the
+ 
+
+ align:start position:0%
+and this whole thing is called the
+chemical potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is a really Central concept for
+
+ align:start position:0%
+which is a really Central concept for
+ 
+
+ align:start position:0%
+which is a really Central concept for
+Material Science and chemical
+
+ align:start position:0%
+Material Science and chemical
+ 
+
+ align:start position:0%
+Material Science and chemical
+engineering
+
+ align:start position:0%
+engineering
+ 
+
+ align:start position:0%
+engineering
+so we will go spending
+
+ align:start position:0%
+so we will go spending
+ 
+
+ align:start position:0%
+so we will go spending
+an entire term on the chemical potential
+
+ align:start position:0%
+an entire term on the chemical potential
+ 
+
+ align:start position:0%
+an entire term on the chemical potential
+okay that's where I wanted to get to
+
+ align:start position:0%
+okay that's where I wanted to get to
+ 
+
+ align:start position:0%
+okay that's where I wanted to get to
+today
\ No newline at end of file
diff --git a/T2n6fVybLcU.txt b/T2n6fVybLcU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..201ab6b58928ebc3858b9aa9599c8d2226cda3bc
--- /dev/null
+++ b/T2n6fVybLcU.txt
@@ -0,0 +1,9667 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so welcome back everybody we'll
+
+ align:start position:0%
+okay so welcome back everybody we'll
+ 
+
+ align:start position:0%
+okay so welcome back everybody we'll
+come back to a o3 today we are going to
+
+ align:start position:0%
+come back to a o3 today we are going to
+ 
+
+ align:start position:0%
+come back to a o3 today we are going to
+continue a discussion of the harmonic
+
+ align:start position:0%
+continue a discussion of the harmonic
+ 
+
+ align:start position:0%
+continue a discussion of the harmonic
+oscillators and also we will add 10 p.m.
+
+ align:start position:0%
+oscillators and also we will add 10 p.m.
+ 
+
+ align:start position:0%
+oscillators and also we will add 10 p.m.
+force into the game and see what will
+
+ align:start position:0%
+force into the game and see what will
+ 
+
+ align:start position:0%
+force into the game and see what will
+happen okay so this essentially what we
+
+ align:start position:0%
+happen okay so this essentially what we
+ 
+
+ align:start position:0%
+happen okay so this essentially what we
+have learned that time from this slide
+
+ align:start position:0%
+have learned that time from this slide
+ 
+
+ align:start position:0%
+have learned that time from this slide
+we have analyzed the physics of a
+
+ align:start position:0%
+we have analyzed the physics of a
+ 
+
+ align:start position:0%
+we have analyzed the physics of a
+harmonic oscillator so which we actually
+
+ align:start position:0%
+harmonic oscillator so which we actually
+ 
+
+ align:start position:0%
+harmonic oscillator so which we actually
+demonstrated last time and you can see
+
+ align:start position:0%
+demonstrated last time and you can see
+ 
+
+ align:start position:0%
+demonstrated last time and you can see
+the device still there and Hookes law
+
+ align:start position:0%
+the device still there and Hookes law
+ 
+
+ align:start position:0%
+the device still there and Hookes law
+actually Hookes law is actually far more
+
+ align:start position:0%
+actually Hookes law is actually far more
+ 
+
+ align:start position:0%
+actually Hookes law is actually far more
+general than what we saw before it works
+
+ align:start position:0%
+general than what we saw before it works
+ 
+
+ align:start position:0%
+general than what we saw before it works
+for all small oscillations run about a
+
+ align:start position:0%
+for all small oscillations run about a
+ 
+
+ align:start position:0%
+for all small oscillations run about a
+point of equilibrium position okay and
+
+ align:start position:0%
+point of equilibrium position okay and
+ 
+
+ align:start position:0%
+point of equilibrium position okay and
+that is it can be demonstrated by
+
+ align:start position:0%
+that is it can be demonstrated by
+ 
+
+ align:start position:0%
+that is it can be demonstrated by
+multiple different kind of physical
+
+ align:start position:0%
+multiple different kind of physical
+ 
+
+ align:start position:0%
+multiple different kind of physical
+systems for example here I have a mass
+
+ align:start position:0%
+systems for example here I have a mass
+ 
+
+ align:start position:0%
+systems for example here I have a mass
+which essentially can only move along
+
+ align:start position:0%
+which essentially can only move along
+ 
+
+ align:start position:0%
+which essentially can only move along
+this track here and if I put these maths
+
+ align:start position:0%
+this track here and if I put these maths
+ 
+
+ align:start position:0%
+this track here and if I put these maths
+set free and this thing is actually
+
+ align:start position:0%
+set free and this thing is actually
+ 
+
+ align:start position:0%
+set free and this thing is actually
+exercising harmonic oscillation okay we
+
+ align:start position:0%
+exercising harmonic oscillation okay we
+ 
+
+ align:start position:0%
+exercising harmonic oscillation okay we
+can do this with large amplitude with
+
+ align:start position:0%
+can do this with large amplitude with
+ 
+
+ align:start position:0%
+can do this with large amplitude with
+and also to it with small amplitude and
+
+ align:start position:0%
+and also to it with small amplitude and
+ 
+
+ align:start position:0%
+and also to it with small amplitude and
+you see that hi pretty it works
+
+ align:start position:0%
+you see that hi pretty it works
+ 
+
+ align:start position:0%
+you see that hi pretty it works
+Hookes law actually works and it
+
+ align:start position:0%
+Hookes law actually works and it
+ 
+
+ align:start position:0%
+Hookes law actually works and it
+predicts exactly the same motion as what
+
+ align:start position:0%
+predicts exactly the same motion as what
+ 
+
+ align:start position:0%
+predicts exactly the same motion as what
+you see on the slide okay and we also
+
+ align:start position:0%
+you see on the slide okay and we also
+ 
+
+ align:start position:0%
+you see on the slide okay and we also
+have a little bit more complicated
+
+ align:start position:0%
+have a little bit more complicated
+ 
+
+ align:start position:0%
+have a little bit more complicated
+system for example this is as your some
+
+ align:start position:0%
+system for example this is as your some
+ 
+
+ align:start position:0%
+system for example this is as your some
+kind of rod and you can actually fixed
+
+ align:start position:0%
+kind of rod and you can actually fixed
+ 
+
+ align:start position:0%
+kind of rod and you can actually fixed
+one point and make it oscillate and we
+
+ align:start position:0%
+one point and make it oscillate and we
+ 
+
+ align:start position:0%
+one point and make it oscillate and we
+see that ha he also does some kind of
+
+ align:start position:0%
+see that ha he also does some kind of
+ 
+
+ align:start position:0%
+see that ha he also does some kind of
+harmonic oscillation but now what is
+
+ align:start position:0%
+harmonic oscillation but now what is
+ 
+
+ align:start position:0%
+harmonic oscillation but now what is
+actually that oscillating is the
+
+ align:start position:0%
+actually that oscillating is the
+ 
+
+ align:start position:0%
+actually that oscillating is the
+amplitude the amplitude is actually the
+
+ align:start position:0%
+amplitude the amplitude is actually the
+ 
+
+ align:start position:0%
+amplitude the amplitude is actually the
+angle with respect to the to a downward
+
+ align:start position:0%
+angle with respect to the to a downward
+ 
+
+ align:start position:0%
+angle with respect to the to a downward
+direction and finally this is actually
+
+ align:start position:0%
+direction and finally this is actually
+ 
+
+ align:start position:0%
+direction and finally this is actually
+up the Lebert
+
+ align:start position:0%
+up the Lebert
+ 
+
+ align:start position:0%
+up the Lebert
+conversion of this spring-mass system
+
+ align:start position:0%
+conversion of this spring-mass system
+ 
+
+ align:start position:0%
+conversion of this spring-mass system
+which will be analyzing data yo your
+
+ align:start position:0%
+which will be analyzing data yo your
+ 
+
+ align:start position:0%
+which will be analyzing data yo your
+pset and you see that huh
+
+ align:start position:0%
+pset and you see that huh
+ 
+
+ align:start position:0%
+pset and you see that huh
+you actually also they up and down
+
+ align:start position:0%
+you actually also they up and down
+ 
+
+ align:start position:0%
+you actually also they up and down
+harmonically so that's all very nice and
+
+ align:start position:0%
+harmonically so that's all very nice and
+ 
+
+ align:start position:0%
+harmonically so that's all very nice and
+we also have learned one thing which is
+
+ align:start position:0%
+we also have learned one thing which is
+ 
+
+ align:start position:0%
+we also have learned one thing which is
+very very interesting is that complete a
+
+ align:start position:0%
+very very interesting is that complete a
+ 
+
+ align:start position:0%
+very very interesting is that complete a
+complex exponential is actually a pretty
+
+ align:start position:0%
+complex exponential is actually a pretty
+ 
+
+ align:start position:0%
+complex exponential is actually a pretty
+beautiful way to present the solution
+
+ align:start position:0%
+beautiful way to present the solution
+ 
+
+ align:start position:0%
+beautiful way to present the solution
+and you se it works also in describing
+
+ align:start position:0%
+and you se it works also in describing
+ 
+
+ align:start position:0%
+and you se it works also in describing
+the temped oscillators and we will we
+
+ align:start position:0%
+the temped oscillators and we will we
+ 
+
+ align:start position:0%
+the temped oscillators and we will we
+will see how it works in the lecture
+
+ align:start position:0%
+will see how it works in the lecture
+ 
+
+ align:start position:0%
+will see how it works in the lecture
+today I'd receive several questions
+
+ align:start position:0%
+today I'd receive several questions
+ 
+
+ align:start position:0%
+today I'd receive several questions
+during my office hour and and through
+
+ align:start position:0%
+during my office hour and and through
+ 
+
+ align:start position:0%
+during my office hour and and through
+email or Piazza there were some
+
+ align:start position:0%
+email or Piazza there were some
+ 
+
+ align:start position:0%
+email or Piazza there were some
+confusions about doing a Taylor
+
+ align:start position:0%
+confusions about doing a Taylor
+ 
+
+ align:start position:0%
+confusions about doing a Taylor
+expansion okay so in in the lecture last
+
+ align:start position:0%
+expansion okay so in in the lecture last
+ 
+
+ align:start position:0%
+expansion okay so in in the lecture last
+time the equilibrium position is at X
+
+ align:start position:0%
+time the equilibrium position is at X
+ 
+
+ align:start position:0%
+time the equilibrium position is at X
+equal to zero therefore I do Taylor
+
+ align:start position:0%
+equal to zero therefore I do Taylor
+ 
+
+ align:start position:0%
+equal to zero therefore I do Taylor
+expansion around 0 okay but in this case
+
+ align:start position:0%
+expansion around 0 okay but in this case
+ 
+
+ align:start position:0%
+expansion around 0 okay but in this case
+if the equilibrium position or the
+
+ align:start position:0%
+if the equilibrium position or the
+ 
+
+ align:start position:0%
+if the equilibrium position or the
+minimum of the potential is at X equal
+
+ align:start position:0%
+minimum of the potential is at X equal
+ 
+
+ align:start position:0%
+minimum of the potential is at X equal
+to L then what you need to do is to do a
+
+ align:start position:0%
+to L then what you need to do is to do a
+ 
+
+ align:start position:0%
+to L then what you need to do is to do a
+Taylor expansion around X equal to L
+
+ align:start position:0%
+Taylor expansion around X equal to L
+ 
+
+ align:start position:0%
+Taylor expansion around X equal to L
+okay just to make that really really
+
+ align:start position:0%
+okay just to make that really really
+ 
+
+ align:start position:0%
+okay just to make that really really
+clear
+
+ align:start position:0%
+clear
+ 
+
+ align:start position:0%
+clear
+okay okay I hope that will help you with
+
+ align:start position:0%
+okay okay I hope that will help you with
+ 
+
+ align:start position:0%
+okay okay I hope that will help you with
+the pset question okay so that's get
+
+ align:start position:0%
+the pset question okay so that's get
+ 
+
+ align:start position:0%
+the pset question okay so that's get
+started immediately so let's continue
+
+ align:start position:0%
+started immediately so let's continue
+ 
+
+ align:start position:0%
+started immediately so let's continue
+the discussion of the equation of motion
+
+ align:start position:0%
+the discussion of the equation of motion
+ 
+
+ align:start position:0%
+the discussion of the equation of motion
+we arrived last time so we have n X
+
+ align:start position:0%
+we arrived last time so we have n X
+ 
+
+ align:start position:0%
+we arrived last time so we have n X
+double dot and this is equal to minus K
+
+ align:start position:0%
+double dot and this is equal to minus K
+ 
+
+ align:start position:0%
+double dot and this is equal to minus K
+X okay that's this issue the formula
+
+ align:start position:0%
+X okay that's this issue the formula
+ 
+
+ align:start position:0%
+X okay that's this issue the formula
+from last time and we can actually
+
+ align:start position:0%
+from last time and we can actually
+ 
+
+ align:start position:0%
+from last time and we can actually
+calculate the kinetic energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this spring-mass system and basically
+
+ align:start position:0%
+of this spring-mass system and basically
+ 
+
+ align:start position:0%
+of this spring-mass system and basically
+we will arrive this is going to be equal
+
+ align:start position:0%
+we will arrive this is going to be equal
+ 
+
+ align:start position:0%
+we will arrive this is going to be equal
+to 1 1 / 2 and times X dot square okay
+
+ align:start position:0%
+to 1 1 / 2 and times X dot square okay
+ 
+
+ align:start position:0%
+to 1 1 / 2 and times X dot square okay
+and we can also calculate the potential
+
+ align:start position:0%
+and we can also calculate the potential
+ 
+
+ align:start position:0%
+and we can also calculate the potential
+energy of with the of the spring
+
+ align:start position:0%
+energy of with the of the spring
+ 
+
+ align:start position:0%
+energy of with the of the spring
+potential energy and that is equal to
+
+ align:start position:0%
+potential energy and that is equal to
+ 
+
+ align:start position:0%
+potential energy and that is equal to
+1/2 K x squared we also know what would
+
+ align:start position:0%
+1/2 K x squared we also know what would
+ 
+
+ align:start position:0%
+1/2 K x squared we also know what would
+be the total energy the total energy
+
+ align:start position:0%
+be the total energy the total energy
+ 
+
+ align:start position:0%
+be the total energy the total energy
+will be a sum of the kinetic energy and
+
+ align:start position:0%
+will be a sum of the kinetic energy and
+ 
+
+ align:start position:0%
+will be a sum of the kinetic energy and
+the potential basically you get this
+
+ align:start position:0%
+the potential basically you get this
+ 
+
+ align:start position:0%
+the potential basically you get this
+formula one half and X dot squared plus
+
+ align:start position:0%
+formula one half and X dot squared plus
+ 
+
+ align:start position:0%
+formula one half and X dot squared plus
+one-half KX squared for last time we
+
+ align:start position:0%
+one-half KX squared for last time we
+ 
+
+ align:start position:0%
+one-half KX squared for last time we
+have solved this equation of motion
+
+ align:start position:0%
+have solved this equation of motion
+ 
+
+ align:start position:0%
+have solved this equation of motion
+right so that the solution we got is X
+
+ align:start position:0%
+right so that the solution we got is X
+ 
+
+ align:start position:0%
+right so that the solution we got is X
+equal to a cosine Omega 0 T plus Phi
+
+ align:start position:0%
+equal to a cosine Omega 0 T plus Phi
+ 
+
+ align:start position:0%
+equal to a cosine Omega 0 T plus Phi
+while Omega zero is equal to square root
+
+ align:start position:0%
+while Omega zero is equal to square root
+ 
+
+ align:start position:0%
+while Omega zero is equal to square root
+of K over m therefore we can actually
+
+ align:start position:0%
+of K over m therefore we can actually
+ 
+
+ align:start position:0%
+of K over m therefore we can actually
+calculate what would be the total energy
+
+ align:start position:0%
+calculate what would be the total energy
+ 
+
+ align:start position:0%
+calculate what would be the total energy
+as a function of time right so if we
+
+ align:start position:0%
+as a function of time right so if we
+ 
+
+ align:start position:0%
+as a function of time right so if we
+calculate that you'll get e will be
+
+ align:start position:0%
+calculate that you'll get e will be
+ 
+
+ align:start position:0%
+calculate that you'll get e will be
+equal to n over 2 n is square Omega 0
+
+ align:start position:0%
+equal to n over 2 n is square Omega 0
+ 
+
+ align:start position:0%
+equal to n over 2 n is square Omega 0
+square sine squared Omega 0 T plus Phi
+
+ align:start position:0%
+square sine squared Omega 0 T plus Phi
+ 
+
+ align:start position:0%
+square sine squared Omega 0 T plus Phi
+so this is actually the first time ok
+
+ align:start position:0%
+so this is actually the first time ok
+ 
+
+ align:start position:0%
+so this is actually the first time ok
+here plus 1 over 2k a squared cosine
+
+ align:start position:0%
+here plus 1 over 2k a squared cosine
+ 
+
+ align:start position:0%
+here plus 1 over 2k a squared cosine
+squared Omega 0 T plus Phi ok
+
+ align:start position:0%
+squared Omega 0 T plus Phi ok
+ 
+
+ align:start position:0%
+squared Omega 0 T plus Phi ok
+and we also know that this this turn
+
+ align:start position:0%
+and we also know that this this turn
+ 
+
+ align:start position:0%
+and we also know that this this turn
+this issue a coefficient here is just
+
+ align:start position:0%
+this issue a coefficient here is just
+ 
+
+ align:start position:0%
+this issue a coefficient here is just
+ka square right because Omega zero is
+
+ align:start position:0%
+ka square right because Omega zero is
+ 
+
+ align:start position:0%
+ka square right because Omega zero is
+actually equal to square root of K over
+
+ align:start position:0%
+actually equal to square root of K over
+ 
+
+ align:start position:0%
+actually equal to square root of K over
+m and if you replace this Omega 0 square
+
+ align:start position:0%
+m and if you replace this Omega 0 square
+ 
+
+ align:start position:0%
+m and if you replace this Omega 0 square
+by by ko and then you actually arrive K
+
+ align:start position:0%
+by by ko and then you actually arrive K
+ 
+
+ align:start position:0%
+by by ko and then you actually arrive K
+a square okay so that is actually very
+
+ align:start position:0%
+a square okay so that is actually very
+ 
+
+ align:start position:0%
+a square okay so that is actually very
+good so that means I can simplify the
+
+ align:start position:0%
+good so that means I can simplify the
+ 
+
+ align:start position:0%
+good so that means I can simplify the
+total energy and what we are going to
+
+ align:start position:0%
+total energy and what we are going to
+ 
+
+ align:start position:0%
+total energy and what we are going to
+get is 1 over 2 ka square I can take
+
+ align:start position:0%
+get is 1 over 2 ka square I can take
+ 
+
+ align:start position:0%
+get is 1 over 2 ka square I can take
+this factor out and that will give me
+
+ align:start position:0%
+this factor out and that will give me
+ 
+
+ align:start position:0%
+this factor out and that will give me
+inside this bracket I will get sine
+
+ align:start position:0%
+inside this bracket I will get sine
+ 
+
+ align:start position:0%
+inside this bracket I will get sine
+square Omega 0 T plus Phi plus cosine
+
+ align:start position:0%
+square Omega 0 T plus Phi plus cosine
+ 
+
+ align:start position:0%
+square Omega 0 T plus Phi plus cosine
+square Omega 0 T plus Phi and this is
+
+ align:start position:0%
+square Omega 0 T plus Phi and this is
+ 
+
+ align:start position:0%
+square Omega 0 T plus Phi and this is
+actually equal to 1 right just a
+
+ align:start position:0%
+actually equal to 1 right just a
+ 
+
+ align:start position:0%
+actually equal to 1 right just a
+reminder sine squared theta plus cosine
+
+ align:start position:0%
+reminder sine squared theta plus cosine
+ 
+
+ align:start position:0%
+reminder sine squared theta plus cosine
+square theta is always equal to 1 so
+
+ align:start position:0%
+square theta is always equal to 1 so
+ 
+
+ align:start position:0%
+square theta is always equal to 1 so
+that give me this result this is a 1
+
+ align:start position:0%
+that give me this result this is a 1
+ 
+
+ align:start position:0%
+that give me this result this is a 1
+over 2k
+
+ align:start position:0%
+over 2k
+ 
+
+ align:start position:0%
+over 2k
+a square ok so that is actually the
+
+ align:start position:0%
+a square ok so that is actually the
+ 
+
+ align:start position:0%
+a square ok so that is actually the
+result what does that mean that means if
+
+ align:start position:0%
+result what does that mean that means if
+ 
+
+ align:start position:0%
+result what does that mean that means if
+I actually put this mass harder okay so
+
+ align:start position:0%
+I actually put this mass harder okay so
+ 
+
+ align:start position:0%
+I actually put this mass harder okay so
+that the initial de has larger amplitude
+
+ align:start position:0%
+that the initial de has larger amplitude
+ 
+
+ align:start position:0%
+that the initial de has larger amplitude
+then the total energy is actually
+
+ align:start position:0%
+then the total energy is actually
+ 
+
+ align:start position:0%
+then the total energy is actually
+proportional to amplitude squared okay
+
+ align:start position:0%
+proportional to amplitude squared okay
+ 
+
+ align:start position:0%
+proportional to amplitude squared okay
+so I am storing more and more energy if
+
+ align:start position:0%
+so I am storing more and more energy if
+ 
+
+ align:start position:0%
+so I am storing more and more energy if
+I increase the temperature increase the
+
+ align:start position:0%
+I increase the temperature increase the
+ 
+
+ align:start position:0%
+I increase the temperature increase the
+amplitude even more than I'm storing the
+
+ align:start position:0%
+amplitude even more than I'm storing the
+ 
+
+ align:start position:0%
+amplitude even more than I'm storing the
+energy in this system and it's
+
+ align:start position:0%
+energy in this system and it's
+ 
+
+ align:start position:0%
+energy in this system and it's
+proportional to a square and also if the
+
+ align:start position:0%
+proportional to a square and also if the
+ 
+
+ align:start position:0%
+proportional to a square and also if the
+spring constant is larger the same
+
+ align:start position:0%
+spring constant is larger the same
+ 
+
+ align:start position:0%
+spring constant is larger the same
+amplitude will give you more energy so
+
+ align:start position:0%
+amplitude will give you more energy so
+ 
+
+ align:start position:0%
+amplitude will give you more energy so
+that means you can store more energy if
+
+ align:start position:0%
+that means you can store more energy if
+ 
+
+ align:start position:0%
+that means you can store more energy if
+you have larger spring constant okay the
+
+ align:start position:0%
+you have larger spring constant okay the
+ 
+
+ align:start position:0%
+you have larger spring constant okay the
+most surprising thing is that actually
+
+ align:start position:0%
+most surprising thing is that actually
+ 
+
+ align:start position:0%
+most surprising thing is that actually
+this is actually a constant right what
+
+ align:start position:0%
+this is actually a constant right what
+ 
+
+ align:start position:0%
+this is actually a constant right what
+does that mean the total energy is
+
+ align:start position:0%
+does that mean the total energy is
+ 
+
+ align:start position:0%
+does that mean the total energy is
+actually not varying as a function of
+
+ align:start position:0%
+actually not varying as a function of
+ 
+
+ align:start position:0%
+actually not varying as a function of
+time you see so total energy is
+
+ align:start position:0%
+time you see so total energy is
+ 
+
+ align:start position:0%
+time you see so total energy is
+conserved
+
+ align:start position:0%
+conserved
+ 
+
+ align:start position:0%
+conserved
+okay so you can see from this slide the
+
+ align:start position:0%
+okay so you can see from this slide the
+ 
+
+ align:start position:0%
+okay so you can see from this slide the
+total energy is actually shown as the
+
+ align:start position:0%
+total energy is actually shown as the
+ 
+
+ align:start position:0%
+total energy is actually shown as the
+sum which is the green curve and the
+
+ align:start position:0%
+sum which is the green curve and the
+ 
+
+ align:start position:0%
+sum which is the green curve and the
+kinetic energy and potential energy are
+
+ align:start position:0%
+kinetic energy and potential energy are
+ 
+
+ align:start position:0%
+kinetic energy and potential energy are
+shown as red and blue curves you can see
+
+ align:start position:0%
+shown as red and blue curves you can see
+ 
+
+ align:start position:0%
+shown as red and blue curves you can see
+that they are energy the total energy is
+
+ align:start position:0%
+that they are energy the total energy is
+ 
+
+ align:start position:0%
+that they are energy the total energy is
+actually constant but this system is
+
+ align:start position:0%
+actually constant but this system is
+ 
+
+ align:start position:0%
+actually constant but this system is
+very diamonique oh you see so the energy
+
+ align:start position:0%
+very diamonique oh you see so the energy
+ 
+
+ align:start position:0%
+very diamonique oh you see so the energy
+is actually going back and forth between
+
+ align:start position:0%
+is actually going back and forth between
+ 
+
+ align:start position:0%
+is actually going back and forth between
+the spring and a mass okay in the form
+
+ align:start position:0%
+the spring and a mass okay in the form
+ 
+
+ align:start position:0%
+the spring and a mass okay in the form
+of kinetic energy and in the form of
+
+ align:start position:0%
+of kinetic energy and in the form of
+ 
+
+ align:start position:0%
+of kinetic energy and in the form of
+potential energy but they are doing this
+
+ align:start position:0%
+potential energy but they are doing this
+ 
+
+ align:start position:0%
+potential energy but they are doing this
+so well such that the sum is actually a
+
+ align:start position:0%
+so well such that the sum is actually a
+ 
+
+ align:start position:0%
+so well such that the sum is actually a
+constant so energy is conserved okay so
+
+ align:start position:0%
+constant so energy is conserved okay so
+ 
+
+ align:start position:0%
+constant so energy is conserved okay so
+that is actually pretty beautiful and
+
+ align:start position:0%
+that is actually pretty beautiful and
+ 
+
+ align:start position:0%
+that is actually pretty beautiful and
+and can be described by very well about
+
+ align:start position:0%
+and can be described by very well about
+ 
+
+ align:start position:0%
+and can be described by very well about
+this mathematics any questions from here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I would like to say simple
+
+ align:start position:0%
+okay so I would like to say simple
+ 
+
+ align:start position:0%
+okay so I would like to say simple
+harmonic motion actually what you are
+
+ align:start position:0%
+harmonic motion actually what you are
+ 
+
+ align:start position:0%
+harmonic motion actually what you are
+going to get is the energy is as you can
+
+ align:start position:0%
+going to get is the energy is as you can
+ 
+
+ align:start position:0%
+going to get is the energy is as you can
+serve and independent that time and
+
+ align:start position:0%
+serve and independent that time and
+ 
+
+ align:start position:0%
+serve and independent that time and
+later you will see an example with
+
+ align:start position:0%
+later you will see an example with
+ 
+
+ align:start position:0%
+later you will see an example with
+stamping and you will see that energy
+
+ align:start position:0%
+stamping and you will see that energy
+ 
+
+ align:start position:0%
+stamping and you will see that energy
+conservation is no longer the case
+
+ align:start position:0%
+conservation is no longer the case
+ 
+
+ align:start position:0%
+conservation is no longer the case
+okay so that's immediately jump to
+
+ align:start position:0%
+okay so that's immediately jump to
+ 
+
+ align:start position:0%
+okay so that's immediately jump to
+another example which is a should be
+
+ align:start position:0%
+another example which is a should be
+ 
+
+ align:start position:0%
+another example which is a should be
+involving simple harmonic motion so
+
+ align:start position:0%
+involving simple harmonic motion so
+ 
+
+ align:start position:0%
+involving simple harmonic motion so
+let's take this rod and a nail system as
+
+ align:start position:0%
+let's take this rod and a nail system as
+ 
+
+ align:start position:0%
+let's take this rod and a nail system as
+an example if I actually slightly move
+
+ align:start position:0%
+an example if I actually slightly move
+ 
+
+ align:start position:0%
+an example if I actually slightly move
+this rod and then I release that then it
+
+ align:start position:0%
+this rod and then I release that then it
+ 
+
+ align:start position:0%
+this rod and then I release that then it
+was actually us see a simple harmonic
+
+ align:start position:0%
+was actually us see a simple harmonic
+ 
+
+ align:start position:0%
+was actually us see a simple harmonic
+motion okay also consistent so that's
+
+ align:start position:0%
+motion okay also consistent so that's
+ 
+
+ align:start position:0%
+motion okay also consistent so that's
+actually do the calculation as another
+
+ align:start position:0%
+actually do the calculation as another
+ 
+
+ align:start position:0%
+actually do the calculation as another
+example so this is actually my system I
+
+ align:start position:0%
+example so this is actually my system I
+ 
+
+ align:start position:0%
+example so this is actually my system I
+have this rod okay now I assume that
+
+ align:start position:0%
+have this rod okay now I assume that
+ 
+
+ align:start position:0%
+have this rod okay now I assume that
+that the mass is uniformly distributed
+
+ align:start position:0%
+that the mass is uniformly distributed
+ 
+
+ align:start position:0%
+that the mass is uniformly distributed
+and this rod and the snail down the war
+
+ align:start position:0%
+and this rod and the snail down the war
+ 
+
+ align:start position:0%
+and this rod and the snail down the war
+okay and the length of this rod is that
+
+ align:start position:0%
+okay and the length of this rod is that
+ 
+
+ align:start position:0%
+okay and the length of this rod is that
+you the L so that means the center of
+
+ align:start position:0%
+you the L so that means the center of
+ 
+
+ align:start position:0%
+you the L so that means the center of
+mass is actually at L over 2 with
+
+ align:start position:0%
+mass is actually at L over 2 with
+ 
+
+ align:start position:0%
+mass is actually at L over 2 with
+respect to the nail okay
+
+ align:start position:0%
+respect to the nail okay
+ 
+
+ align:start position:0%
+respect to the nail okay
+and also this whole system is set up and
+
+ align:start position:0%
+and also this whole system is set up and
+ 
+
+ align:start position:0%
+and also this whole system is set up and
+on earth right therefore there will be
+
+ align:start position:0%
+on earth right therefore there will be
+ 
+
+ align:start position:0%
+on earth right therefore there will be
+gravitational force pointing downward
+
+ align:start position:0%
+gravitational force pointing downward
+ 
+
+ align:start position:0%
+gravitational force pointing downward
+okay so that means you have rotational
+
+ align:start position:0%
+okay so that means you have rotational
+ 
+
+ align:start position:0%
+okay so that means you have rotational
+force FG pointing downward okay so this
+
+ align:start position:0%
+force FG pointing downward okay so this
+ 
+
+ align:start position:0%
+force FG pointing downward okay so this
+is actually the system which I would
+
+ align:start position:0%
+is actually the system which I would
+ 
+
+ align:start position:0%
+is actually the system which I would
+like to understand and that just a
+
+ align:start position:0%
+like to understand and that just a
+ 
+
+ align:start position:0%
+like to understand and that just a
+reminder what that we're going to do
+
+ align:start position:0%
+reminder what that we're going to do
+ 
+
+ align:start position:0%
+reminder what that we're going to do
+afterwards in order to turn the whole
+
+ align:start position:0%
+afterwards in order to turn the whole
+ 
+
+ align:start position:0%
+afterwards in order to turn the whole
+system into a language we will now
+
+ align:start position:0%
+system into a language we will now
+ 
+
+ align:start position:0%
+system into a language we will now
+describe the nature what is going to why
+
+ align:start position:0%
+describe the nature what is going to why
+ 
+
+ align:start position:0%
+describe the nature what is going to why
+we're going to do anybody we are going
+
+ align:start position:0%
+we're going to do anybody we are going
+ 
+
+ align:start position:0%
+we're going to do anybody we are going
+to define the coordinate system right so
+
+ align:start position:0%
+to define the coordinate system right so
+ 
+
+ align:start position:0%
+to define the coordinate system right so
+that I can translate everything into
+
+ align:start position:0%
+that I can translate everything into
+ 
+
+ align:start position:0%
+that I can translate everything into
+mathematics right so that's actually
+
+ align:start position:0%
+mathematics right so that's actually
+ 
+
+ align:start position:0%
+mathematics right so that's actually
+what we are always doing and you will
+
+ align:start position:0%
+what we are always doing and you will
+ 
+
+ align:start position:0%
+what we are always doing and you will
+see that we are always doing this in
+
+ align:start position:0%
+see that we are always doing this in
+ 
+
+ align:start position:0%
+see that we are always doing this in
+this class okay so how what is actually
+
+ align:start position:0%
+this class okay so how what is actually
+ 
+
+ align:start position:0%
+this class okay so how what is actually
+the coordinate system which I would like
+
+ align:start position:0%
+the coordinate system which I would like
+ 
+
+ align:start position:0%
+the coordinate system which I would like
+to use since this system is going to be
+
+ align:start position:0%
+to use since this system is going to be
+ 
+
+ align:start position:0%
+to use since this system is going to be
+rotating back and forth okay therefore I
+
+ align:start position:0%
+rotating back and forth okay therefore I
+ 
+
+ align:start position:0%
+rotating back and forth okay therefore I
+would like to define theta to be the
+
+ align:start position:0%
+would like to define theta to be the
+ 
+
+ align:start position:0%
+would like to define theta to be the
+angle with respect to axis which is
+
+ align:start position:0%
+angle with respect to axis which is
+ 
+
+ align:start position:0%
+angle with respect to axis which is
+actually pointing downward okay so the
+
+ align:start position:0%
+actually pointing downward okay so the
+ 
+
+ align:start position:0%
+actually pointing downward okay so the
+origin of this coordinate system is
+
+ align:start position:0%
+origin of this coordinate system is
+ 
+
+ align:start position:0%
+origin of this coordinate system is
+theta equal to zero this means that I'm
+
+ align:start position:0%
+theta equal to zero this means that I'm
+ 
+
+ align:start position:0%
+theta equal to zero this means that I'm
+pointing that okay that's rad is a ship
+
+ align:start position:0%
+pointing that okay that's rad is a ship
+ 
+
+ align:start position:0%
+pointing that okay that's rad is a ship
+pointing tango okay and also I need to
+
+ align:start position:0%
+pointing tango okay and also I need to
+ 
+
+ align:start position:0%
+pointing tango okay and also I need to
+define what is actually the positive
+
+ align:start position:0%
+define what is actually the positive
+ 
+
+ align:start position:0%
+define what is actually the positive
+what is actually the positive value of
+
+ align:start position:0%
+what is actually the positive value of
+ 
+
+ align:start position:0%
+what is actually the positive value of
+the theta right
+
+ align:start position:0%
+the theta right
+ 
+
+ align:start position:0%
+the theta right
+so I define anti-clockwise direction
+
+ align:start position:0%
+so I define anti-clockwise direction
+ 
+
+ align:start position:0%
+so I define anti-clockwise direction
+to be positive okay so it is actually
+
+ align:start position:0%
+to be positive okay so it is actually
+ 
+
+ align:start position:0%
+to be positive okay so it is actually
+important to say to h we first defined
+
+ align:start position:0%
+important to say to h we first defined
+ 
+
+ align:start position:0%
+important to say to h we first defined
+that then actually then actually to
+
+ align:start position:0%
+that then actually then actually to
+ 
+
+ align:start position:0%
+that then actually then actually to
+translate everything into mathematics
+
+ align:start position:0%
+translate everything into mathematics
+ 
+
+ align:start position:0%
+translate everything into mathematics
+okay so the initial condition is the
+
+ align:start position:0%
+okay so the initial condition is the
+ 
+
+ align:start position:0%
+okay so the initial condition is the
+following so I actually move this thing
+
+ align:start position:0%
+following so I actually move this thing
+ 
+
+ align:start position:0%
+following so I actually move this thing
+rotate this inside D then I actually
+
+ align:start position:0%
+rotate this inside D then I actually
+ 
+
+ align:start position:0%
+rotate this inside D then I actually
+reduce that really carefully without
+
+ align:start position:0%
+reduce that really carefully without
+ 
+
+ align:start position:0%
+reduce that really carefully without
+introducing any initial velocity okay
+
+ align:start position:0%
+introducing any initial velocity okay
+ 
+
+ align:start position:0%
+introducing any initial velocity okay
+therefore I have two initial conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay at T equal to zero there are two
+
+ align:start position:0%
+okay at T equal to zero there are two
+ 
+
+ align:start position:0%
+okay at T equal to zero there are two
+initial conditions
+
+ align:start position:0%
+initial conditions
+ 
+
+ align:start position:0%
+initial conditions
+the first one is theta equal to theta 0
+
+ align:start position:0%
+the first one is theta equal to theta 0
+ 
+
+ align:start position:0%
+the first one is theta equal to theta 0
+this equal to theta initial the second
+
+ align:start position:0%
+this equal to theta initial the second
+ 
+
+ align:start position:0%
+this equal to theta initial the second
+condition is the same as what we have
+
+ align:start position:0%
+condition is the same as what we have
+ 
+
+ align:start position:0%
+condition is the same as what we have
+been doing last time the initial
+
+ align:start position:0%
+been doing last time the initial
+ 
+
+ align:start position:0%
+been doing last time the initial
+velocity or angular velocity is actually
+
+ align:start position:0%
+velocity or angular velocity is actually
+ 
+
+ align:start position:0%
+velocity or angular velocity is actually
+equal to 0 so that gives you theta dot
+
+ align:start position:0%
+equal to 0 so that gives you theta dot
+ 
+
+ align:start position:0%
+equal to 0 so that gives you theta dot
+equal to 0 okay now we have actually
+
+ align:start position:0%
+equal to 0 okay now we have actually
+ 
+
+ align:start position:0%
+equal to 0 okay now we have actually
+define the coordinate system then now we
+
+ align:start position:0%
+define the coordinate system then now we
+ 
+
+ align:start position:0%
+define the coordinate system then now we
+can issue the draw a force diagram right
+
+ align:start position:0%
+can issue the draw a force diagram right
+ 
+
+ align:start position:0%
+can issue the draw a force diagram right
+so that we can actually use the null our
+
+ align:start position:0%
+so that we can actually use the null our
+ 
+
+ align:start position:0%
+so that we can actually use the null our
+knowledge about the physics and to
+
+ align:start position:0%
+knowledge about the physics and to
+ 
+
+ align:start position:0%
+knowledge about the physics and to
+obtain the equation of motion right so
+
+ align:start position:0%
+obtain the equation of motion right so
+ 
+
+ align:start position:0%
+obtain the equation of motion right so
+now the force diagram looks like this so
+
+ align:start position:0%
+now the force diagram looks like this so
+ 
+
+ align:start position:0%
+now the force diagram looks like this so
+this is actually the center of mass of
+
+ align:start position:0%
+this is actually the center of mass of
+ 
+
+ align:start position:0%
+this is actually the center of mass of
+this rod and you have a force pointing
+
+ align:start position:0%
+this rod and you have a force pointing
+ 
+
+ align:start position:0%
+this rod and you have a force pointing
+downward which is due to the
+
+ align:start position:0%
+downward which is due to the
+ 
+
+ align:start position:0%
+downward which is due to the
+gravitational force FG is equal to mg
+
+ align:start position:0%
+gravitational force FG is equal to mg
+ 
+
+ align:start position:0%
+gravitational force FG is equal to mg
+okay is pointing downward okay the
+
+ align:start position:0%
+okay is pointing downward okay the
+ 
+
+ align:start position:0%
+okay is pointing downward okay the
+magnitude is actually equal to mg and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and also we know the R vector this
+
+ align:start position:0%
+and also we know the R vector this
+ 
+
+ align:start position:0%
+and also we know the R vector this
+vector have a length of L over 2
+
+ align:start position:0%
+vector have a length of L over 2
+ 
+
+ align:start position:0%
+vector have a length of L over 2
+pointing from the center of mass of this
+
+ align:start position:0%
+pointing from the center of mass of this
+ 
+
+ align:start position:0%
+pointing from the center of mass of this
+rod to the tuna net okay and also we
+
+ align:start position:0%
+rod to the tuna net okay and also we
+ 
+
+ align:start position:0%
+rod to the tuna net okay and also we
+know the angle between this vector
+
+ align:start position:0%
+know the angle between this vector
+ 
+
+ align:start position:0%
+know the angle between this vector
+pointing from the center of mass to the
+
+ align:start position:0%
+pointing from the center of mass to the
+ 
+
+ align:start position:0%
+pointing from the center of mass to the
+nail and the vertical direction which we
+
+ align:start position:0%
+nail and the vertical direction which we
+ 
+
+ align:start position:0%
+nail and the vertical direction which we
+have already defined which is actually
+
+ align:start position:0%
+have already defined which is actually
+ 
+
+ align:start position:0%
+have already defined which is actually
+called Sita therefore now we can
+
+ align:start position:0%
+called Sita therefore now we can
+ 
+
+ align:start position:0%
+called Sita therefore now we can
+actually calculate wobbler the torque
+
+ align:start position:0%
+actually calculate wobbler the torque
+ 
+
+ align:start position:0%
+actually calculate wobbler the torque
+tau will be equal to this R vector plus
+
+ align:start position:0%
+tau will be equal to this R vector plus
+ 
+
+ align:start position:0%
+tau will be equal to this R vector plus
+the force the total force acting on the
+
+ align:start position:0%
+the force the total force acting on the
+ 
+
+ align:start position:0%
+the force the total force acting on the
+the center of mass in this case is just
+
+ align:start position:0%
+the center of mass in this case is just
+ 
+
+ align:start position:0%
+the center of mass in this case is just
+F G okay so now we can actually write
+
+ align:start position:0%
+F G okay so now we can actually write
+ 
+
+ align:start position:0%
+F G okay so now we can actually write
+this explicitly since the whole system
+
+ align:start position:0%
+this explicitly since the whole system
+ 
+
+ align:start position:0%
+this explicitly since the whole system
+is actually rotating on a single plane
+
+ align:start position:0%
+is actually rotating on a single plane
+ 
+
+ align:start position:0%
+is actually rotating on a single plane
+right so there's only one plan this rod
+
+ align:start position:0%
+right so there's only one plan this rod
+ 
+
+ align:start position:0%
+right so there's only one plan this rod
+is sitting up and it's actually going
+
+ align:start position:0%
+is sitting up and it's actually going
+ 
+
+ align:start position:0%
+is sitting up and it's actually going
+back and forth only on this prep okay
+
+ align:start position:0%
+back and forth only on this prep okay
+ 
+
+ align:start position:0%
+back and forth only on this prep okay
+therefore actually I can drop all the
+
+ align:start position:0%
+therefore actually I can drop all the
+ 
+
+ align:start position:0%
+therefore actually I can drop all the
+arrows and write it down the magnitude
+
+ align:start position:0%
+arrows and write it down the magnitude
+ 
+
+ align:start position:0%
+arrows and write it down the magnitude
+of the Tau directly and this will be
+
+ align:start position:0%
+of the Tau directly and this will be
+ 
+
+ align:start position:0%
+of the Tau directly and this will be
+equal to minus and G L over 2 sine theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we have the talk and the
+
+ align:start position:0%
+okay so now we have the talk and the
+ 
+
+ align:start position:0%
+okay so now we have the talk and the
+weekend you make use the rotational
+
+ align:start position:0%
+weekend you make use the rotational
+ 
+
+ align:start position:0%
+weekend you make use the rotational
+version of Newton's law to obtain the
+
+ align:start position:0%
+version of Newton's law to obtain the
+ 
+
+ align:start position:0%
+version of Newton's law to obtain the
+equation of motion right so that should
+
+ align:start position:0%
+equation of motion right so that should
+ 
+
+ align:start position:0%
+equation of motion right so that should
+be pretty straightforward tau will be
+
+ align:start position:0%
+be pretty straightforward tau will be
+ 
+
+ align:start position:0%
+be pretty straightforward tau will be
+equal to I which is smooth the moment of
+
+ align:start position:0%
+equal to I which is smooth the moment of
+ 
+
+ align:start position:0%
+equal to I which is smooth the moment of
+inertia of the system and times alpha
+
+ align:start position:0%
+inertia of the system and times alpha
+ 
+
+ align:start position:0%
+inertia of the system and times alpha
+okay and there's just for your
+
+ align:start position:0%
+okay and there's just for your
+ 
+
+ align:start position:0%
+okay and there's just for your
+information I already calculated the AI
+
+ align:start position:0%
+information I already calculated the AI
+ 
+
+ align:start position:0%
+information I already calculated the AI
+for you I is equal to 1/3 and l squared
+
+ align:start position:0%
+for you I is equal to 1/3 and l squared
+ 
+
+ align:start position:0%
+for you I is equal to 1/3 and l squared
+okay so you can actually go back home
+
+ align:start position:0%
+okay so you can actually go back home
+ 
+
+ align:start position:0%
+okay so you can actually go back home
+and that actually to a check to see if I
+
+ align:start position:0%
+and that actually to a check to see if I
+ 
+
+ align:start position:0%
+and that actually to a check to see if I
+entered in the tools and if you trust me
+
+ align:start position:0%
+entered in the tools and if you trust me
+ 
+
+ align:start position:0%
+entered in the tools and if you trust me
+and that's and the answer which is
+
+ align:start position:0%
+and that's and the answer which is
+ 
+
+ align:start position:0%
+and that's and the answer which is
+actually 1 over 3 and L square if the
+
+ align:start position:0%
+actually 1 over 3 and L square if the
+ 
+
+ align:start position:0%
+actually 1 over 3 and L square if the
+mass is uniformly distributed on this
+
+ align:start position:0%
+mass is uniformly distributed on this
+ 
+
+ align:start position:0%
+mass is uniformly distributed on this
+rod okay so that will give me minus n 2
+
+ align:start position:0%
+rod okay so that will give me minus n 2
+ 
+
+ align:start position:0%
+rod okay so that will give me minus n 2
+L divided by 2 sine theta ok so that is
+
+ align:start position:0%
+L divided by 2 sine theta ok so that is
+ 
+
+ align:start position:0%
+L divided by 2 sine theta ok so that is
+actually coming from from this side okay
+
+ align:start position:0%
+actually coming from from this side okay
+ 
+
+ align:start position:0%
+actually coming from from this side okay
+so now I can actually simplify this
+
+ align:start position:0%
+so now I can actually simplify this
+ 
+
+ align:start position:0%
+so now I can actually simplify this
+expression I can now practice the I
+
+ align:start position:0%
+expression I can now practice the I
+ 
+
+ align:start position:0%
+expression I can now practice the I
+value into this equation and I will get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 over 3 and L square theta double dot P
+
+ align:start position:0%
+1 over 3 and L square theta double dot P
+ 
+
+ align:start position:0%
+1 over 3 and L square theta double dot P
+which is actually alpha okay I now
+
+ align:start position:0%
+which is actually alpha okay I now
+ 
+
+ align:start position:0%
+which is actually alpha okay I now
+dreaded as a seat at about dot and that
+
+ align:start position:0%
+dreaded as a seat at about dot and that
+ 
+
+ align:start position:0%
+dreaded as a seat at about dot and that
+will be equal to minus and G L over 2
+
+ align:start position:0%
+will be equal to minus and G L over 2
+ 
+
+ align:start position:0%
+will be equal to minus and G L over 2
+sine theta okay I can move all the
+
+ align:start position:0%
+sine theta okay I can move all the
+ 
+
+ align:start position:0%
+sine theta okay I can move all the
+constant to the right hand side
+
+ align:start position:0%
+constant to the right hand side
+ 
+
+ align:start position:0%
+constant to the right hand side
+therefore I get theta double dot T this
+
+ align:start position:0%
+therefore I get theta double dot T this
+ 
+
+ align:start position:0%
+therefore I get theta double dot T this
+is equal to minus and gee L okay
+
+ align:start position:0%
+is equal to minus and gee L okay
+ 
+
+ align:start position:0%
+is equal to minus and gee L okay
+actually I can - you already simplify
+
+ align:start position:0%
+actually I can - you already simplify
+ 
+
+ align:start position:0%
+actually I can - you already simplify
+this right
+
+ align:start position:0%
+this right
+ 
+
+ align:start position:0%
+this right
+this says you cancel and why one of the
+
+ align:start position:0%
+this says you cancel and why one of the
+ 
+
+ align:start position:0%
+this says you cancel and why one of the
+L as you can so so therefore I get - 3G
+
+ align:start position:0%
+L as you can so so therefore I get - 3G
+ 
+
+ align:start position:0%
+L as you can so so therefore I get - 3G
+over 2 sine theta ok as judo we actually
+
+ align:start position:0%
+over 2 sine theta ok as judo we actually
+ 
+
+ align:start position:0%
+over 2 sine theta ok as judo we actually
+define a Omega to repress this kind of
+
+ align:start position:0%
+define a Omega to repress this kind of
+ 
+
+ align:start position:0%
+define a Omega to repress this kind of
+this constant to make our life easier
+
+ align:start position:0%
+this constant to make our life easier
+ 
+
+ align:start position:0%
+this constant to make our life easier
+so I can now define Omega 0 equal to
+
+ align:start position:0%
+so I can now define Omega 0 equal to
+ 
+
+ align:start position:0%
+so I can now define Omega 0 equal to
+square root of 3G over 2l okay and that
+
+ align:start position:0%
+square root of 3G over 2l okay and that
+ 
+
+ align:start position:0%
+square root of 3G over 2l okay and that
+will give you CPAP double dot e equal to
+
+ align:start position:0%
+will give you CPAP double dot e equal to
+ 
+
+ align:start position:0%
+will give you CPAP double dot e equal to
+minus Omega 0 square sine theta any
+
+ align:start position:0%
+minus Omega 0 square sine theta any
+ 
+
+ align:start position:0%
+minus Omega 0 square sine theta any
+questions so far a lot of calculation
+
+ align:start position:0%
+questions so far a lot of calculation
+ 
+
+ align:start position:0%
+questions so far a lot of calculation
+but I should be all pretty
+
+ align:start position:0%
+but I should be all pretty
+ 
+
+ align:start position:0%
+but I should be all pretty
+straightforward and HD we are done no we
+
+ align:start position:0%
+straightforward and HD we are done no we
+ 
+
+ align:start position:0%
+straightforward and HD we are done no we
+are done because we have the equation of
+
+ align:start position:0%
+are done because we have the equation of
+ 
+
+ align:start position:0%
+are done because we have the equation of
+motion and the rest of the job is to
+
+ align:start position:0%
+motion and the rest of the job is to
+ 
+
+ align:start position:0%
+motion and the rest of the job is to
+just solve it so this is actually now
+
+ align:start position:0%
+just solve it so this is actually now
+ 
+
+ align:start position:0%
+just solve it so this is actually now
+the the problem of the maths Department
+
+ align:start position:0%
+the the problem of the maths Department
+ 
+
+ align:start position:0%
+the the problem of the maths Department
+so can anybody as you tell me the
+
+ align:start position:0%
+so can anybody as you tell me the
+ 
+
+ align:start position:0%
+so can anybody as you tell me the
+solution of the seat of t anybody so
+
+ align:start position:0%
+solution of the seat of t anybody so
+ 
+
+ align:start position:0%
+solution of the seat of t anybody so
+that now we are facing a very difficult
+
+ align:start position:0%
+that now we are facing a very difficult
+ 
+
+ align:start position:0%
+that now we are facing a very difficult
+situation we don't know how to solve
+
+ align:start position:0%
+situation we don't know how to solve
+ 
+
+ align:start position:0%
+situation we don't know how to solve
+this equation in front of you I I don't
+
+ align:start position:0%
+this equation in front of you I I don't
+ 
+
+ align:start position:0%
+this equation in front of you I I don't
+know okay of course you can easily solve
+
+ align:start position:0%
+know okay of course you can easily solve
+ 
+
+ align:start position:0%
+know okay of course you can easily solve
+it with a computer ok or you want to go
+
+ align:start position:0%
+it with a computer ok or you want to go
+ 
+
+ align:start position:0%
+it with a computer ok or you want to go
+fancy solve it with your cellphone
+
+ align:start position:0%
+fancy solve it with your cellphone
+ 
+
+ align:start position:0%
+fancy solve it with your cellphone
+if we turn X Pro but it's not very nice
+
+ align:start position:0%
+if we turn X Pro but it's not very nice
+ 
+
+ align:start position:0%
+if we turn X Pro but it's not very nice
+to do this in front of you yeah we don't
+
+ align:start position:0%
+to do this in front of you yeah we don't
+ 
+
+ align:start position:0%
+to do this in front of you yeah we don't
+learn too much ok so what are we going
+
+ align:start position:0%
+learn too much ok so what are we going
+ 
+
+ align:start position:0%
+learn too much ok so what are we going
+to do so what we can do is actually to
+
+ align:start position:0%
+to do so what we can do is actually to
+ 
+
+ align:start position:0%
+to do so what we can do is actually to
+consider a special case
+
+ align:start position:0%
+consider a special case
+ 
+
+ align:start position:0%
+consider a special case
+so we know that this equation of motion
+
+ align:start position:0%
+so we know that this equation of motion
+ 
+
+ align:start position:0%
+so we know that this equation of motion
+is exact okay so if you solve it it
+
+ align:start position:0%
+is exact okay so if you solve it it
+ 
+
+ align:start position:0%
+is exact okay so if you solve it it
+would describe the motion of this this
+
+ align:start position:0%
+would describe the motion of this this
+ 
+
+ align:start position:0%
+would describe the motion of this this
+rod the motion of this the same even
+
+ align:start position:0%
+rod the motion of this the same even
+ 
+
+ align:start position:0%
+rod the motion of this the same even
+with slash angle it works okay and now
+
+ align:start position:0%
+with slash angle it works okay and now
+ 
+
+ align:start position:0%
+with slash angle it works okay and now
+in order to actually to show you the
+
+ align:start position:0%
+in order to actually to show you the
+ 
+
+ align:start position:0%
+in order to actually to show you the
+mass if in the class therefore actually
+
+ align:start position:0%
+mass if in the class therefore actually
+ 
+
+ align:start position:0%
+mass if in the class therefore actually
+I were to a small approximation so I
+
+ align:start position:0%
+I were to a small approximation so I
+ 
+
+ align:start position:0%
+I were to a small approximation so I
+should I would only work on the case
+
+ align:start position:0%
+should I would only work on the case
+ 
+
+ align:start position:0%
+should I would only work on the case
+that when the amplitude is very small
+
+ align:start position:0%
+that when the amplitude is very small
+ 
+
+ align:start position:0%
+that when the amplitude is very small
+and see what is going to happen so now
+
+ align:start position:0%
+and see what is going to happen so now
+ 
+
+ align:start position:0%
+and see what is going to happen so now
+I'm considered in a special case up to
+
+ align:start position:0%
+I'm considered in a special case up to
+ 
+
+ align:start position:0%
+I'm considered in a special case up to
+now everything is exact and now I'm now
+
+ align:start position:0%
+now everything is exact and now I'm now
+ 
+
+ align:start position:0%
+now everything is exact and now I'm now
+going to a special case see top T goes
+
+ align:start position:0%
+going to a special case see top T goes
+ 
+
+ align:start position:0%
+going to a special case see top T goes
+to 0 okay then we can actually get this
+
+ align:start position:0%
+to 0 okay then we can actually get this
+ 
+
+ align:start position:0%
+to 0 okay then we can actually get this
+sine theta P is roughly C Turkey okay
+
+ align:start position:0%
+sine theta P is roughly C Turkey okay
+ 
+
+ align:start position:0%
+sine theta P is roughly C Turkey okay
+based on the Tyler expansion you can
+
+ align:start position:0%
+based on the Tyler expansion you can
+ 
+
+ align:start position:0%
+based on the Tyler expansion you can
+actually verify this okay so in this
+
+ align:start position:0%
+actually verify this okay so in this
+ 
+
+ align:start position:0%
+actually verify this okay so in this
+case if we take Sita equal to one degree
+
+ align:start position:0%
+case if we take Sita equal to one degree
+ 
+
+ align:start position:0%
+case if we take Sita equal to one degree
+okay then the ratio of the sine theta
+
+ align:start position:0%
+okay then the ratio of the sine theta
+ 
+
+ align:start position:0%
+okay then the ratio of the sine theta
+and the Sita is actually equal to 99.99%
+
+ align:start position:0%
+and the Sita is actually equal to 99.99%
+ 
+
+ align:start position:0%
+and the Sita is actually equal to 99.99%
+which is very good if I take it as like
+
+ align:start position:0%
+which is very good if I take it as like
+ 
+
+ align:start position:0%
+which is very good if I take it as like
+five percent then I get ninety nine so
+
+ align:start position:0%
+five percent then I get ninety nine so
+ 
+
+ align:start position:0%
+five percent then I get ninety nine so
+at five degree okay and this issue in
+
+ align:start position:0%
+at five degree okay and this issue in
+ 
+
+ align:start position:0%
+at five degree okay and this issue in
+nineteen ninety nine percent even a tank
+
+ align:start position:0%
+nineteen ninety nine percent even a tank
+ 
+
+ align:start position:0%
+nineteen ninety nine percent even a tank
+degree okay it says should be 99.5
+
+ align:start position:0%
+degree okay it says should be 99.5
+ 
+
+ align:start position:0%
+degree okay it says should be 99.5
+percent that shows you that science it
+
+ align:start position:0%
+percent that shows you that science it
+ 
+
+ align:start position:0%
+percent that shows you that science it
+has so close to Sita okay we are pretty
+
+ align:start position:0%
+has so close to Sita okay we are pretty
+ 
+
+ align:start position:0%
+has so close to Sita okay we are pretty
+safe because the difference is smaller
+
+ align:start position:0%
+safe because the difference is smaller
+ 
+
+ align:start position:0%
+safe because the difference is smaller
+than one percent okay so that's really
+
+ align:start position:0%
+than one percent okay so that's really
+ 
+
+ align:start position:0%
+than one percent okay so that's really
+nice after this approximation okay I get
+
+ align:start position:0%
+nice after this approximation okay I get
+ 
+
+ align:start position:0%
+nice after this approximation okay I get
+my final equation of motion Sita double
+
+ align:start position:0%
+my final equation of motion Sita double
+ 
+
+ align:start position:0%
+my final equation of motion Sita double
+dot T equal to minus Omega 0 square
+
+ align:start position:0%
+dot T equal to minus Omega 0 square
+ 
+
+ align:start position:0%
+dot T equal to minus Omega 0 square
+Sita just a reminder Omega zero is equal
+
+ align:start position:0%
+Sita just a reminder Omega zero is equal
+ 
+
+ align:start position:0%
+Sita just a reminder Omega zero is equal
+to square root of 3G over 2l okay we
+
+ align:start position:0%
+to square root of 3G over 2l okay we
+ 
+
+ align:start position:0%
+to square root of 3G over 2l okay we
+have solved this equation last time last
+
+ align:start position:0%
+have solved this equation last time last
+ 
+
+ align:start position:0%
+have solved this equation last time last
+lecture right it's exactly the same
+
+ align:start position:0%
+lecture right it's exactly the same
+ 
+
+ align:start position:0%
+lecture right it's exactly the same
+okay happen to be exactly the same
+
+ align:start position:0%
+okay happen to be exactly the same
+ 
+
+ align:start position:0%
+okay happen to be exactly the same
+therefore I know the solution will be
+
+ align:start position:0%
+therefore I know the solution will be
+ 
+
+ align:start position:0%
+therefore I know the solution will be
+Sita with T equal to a cosine Omega 0 T
+
+ align:start position:0%
+Sita with T equal to a cosine Omega 0 T
+ 
+
+ align:start position:0%
+Sita with T equal to a cosine Omega 0 T
+transfer from the initial conditions
+
+ align:start position:0%
+transfer from the initial conditions
+ 
+
+ align:start position:0%
+transfer from the initial conditions
+which I have one and the two okay I'm
+
+ align:start position:0%
+which I have one and the two okay I'm
+ 
+
+ align:start position:0%
+which I have one and the two okay I'm
+not going to go over this calculation
+
+ align:start position:0%
+not going to go over this calculation
+ 
+
+ align:start position:0%
+not going to go over this calculation
+again but again we can actually plug in
+
+ align:start position:0%
+again but again we can actually plug in
+ 
+
+ align:start position:0%
+again but again we can actually plug in
+1 and 2 to solve the unknown a and Phi
+
+ align:start position:0%
+1 and 2 to solve the unknown a and Phi
+ 
+
+ align:start position:0%
+1 and 2 to solve the unknown a and Phi
+if you do this exercise you will
+
+ align:start position:0%
+if you do this exercise you will
+ 
+
+ align:start position:0%
+if you do this exercise you will
+conclude that a is equal to theta
+
+ align:start position:0%
+conclude that a is equal to theta
+ 
+
+ align:start position:0%
+conclude that a is equal to theta
+initial and Phi is equal to zero okay so
+
+ align:start position:0%
+initial and Phi is equal to zero okay so
+ 
+
+ align:start position:0%
+initial and Phi is equal to zero okay so
+what the solution will be seated with T
+
+ align:start position:0%
+what the solution will be seated with T
+ 
+
+ align:start position:0%
+what the solution will be seated with T
+equal to a ok so n is now replaced by
+
+ align:start position:0%
+equal to a ok so n is now replaced by
+ 
+
+ align:start position:0%
+equal to a ok so n is now replaced by
+theta initial cosine Omega 0 you can see
+
+ align:start position:0%
+theta initial cosine Omega 0 you can see
+ 
+
+ align:start position:0%
+theta initial cosine Omega 0 you can see
+that this actually works for this system
+
+ align:start position:0%
+that this actually works for this system
+ 
+
+ align:start position:0%
+that this actually works for this system
+simple harmonic oscillation actually
+
+ align:start position:0%
+simple harmonic oscillation actually
+ 
+
+ align:start position:0%
+simple harmonic oscillation actually
+described this the motion of this system
+
+ align:start position:0%
+described this the motion of this system
+ 
+
+ align:start position:0%
+described this the motion of this system
+as a function of time you can also see a
+
+ align:start position:0%
+as a function of time you can also see a
+ 
+
+ align:start position:0%
+as a function of time you can also see a
+few more example showing here to obtain
+
+ align:start position:0%
+few more example showing here to obtain
+ 
+
+ align:start position:0%
+few more example showing here to obtain
+you are going to actually work on in
+
+ align:start position:0%
+you are going to actually work on in
+ 
+
+ align:start position:0%
+you are going to actually work on in
+your pset and also another one involving
+
+ align:start position:0%
+your pset and also another one involving
+ 
+
+ align:start position:0%
+your pset and also another one involving
+circuit if you have a capacitor and you
+
+ align:start position:0%
+circuit if you have a capacitor and you
+ 
+
+ align:start position:0%
+circuit if you have a capacitor and you
+have a daughter actually the the current
+
+ align:start position:0%
+have a daughter actually the the current
+ 
+
+ align:start position:0%
+have a daughter actually the the current
+the size of the current is also doing a
+
+ align:start position:0%
+the size of the current is also doing a
+ 
+
+ align:start position:0%
+the size of the current is also doing a
+simple harmonic motion okay and as we
+
+ align:start position:0%
+simple harmonic motion okay and as we
+ 
+
+ align:start position:0%
+simple harmonic motion okay and as we
+actually discussed before the energy is
+
+ align:start position:0%
+actually discussed before the energy is
+ 
+
+ align:start position:0%
+actually discussed before the energy is
+always conserved
+
+ align:start position:0%
+always conserved
+ 
+
+ align:start position:0%
+always conserved
+and it's actually stored in different
+
+ align:start position:0%
+and it's actually stored in different
+ 
+
+ align:start position:0%
+and it's actually stored in different
+components of the systems okay so we
+
+ align:start position:0%
+components of the systems okay so we
+ 
+
+ align:start position:0%
+components of the systems okay so we
+have done this what is actually new
+
+ align:start position:0%
+have done this what is actually new
+ 
+
+ align:start position:0%
+have done this what is actually new
+today what we are going to do today is
+
+ align:start position:0%
+today what we are going to do today is
+ 
+
+ align:start position:0%
+today what we are going to do today is
+that's actually observe this phenomena
+
+ align:start position:0%
+that's actually observe this phenomena
+ 
+
+ align:start position:0%
+that's actually observe this phenomena
+here so this thing is actually going to
+
+ align:start position:0%
+here so this thing is actually going to
+ 
+
+ align:start position:0%
+here so this thing is actually going to
+go back and forth but it's actually not
+
+ align:start position:0%
+go back and forth but it's actually not
+ 
+
+ align:start position:0%
+go back and forth but it's actually not
+going to do that forever right
+
+ align:start position:0%
+going to do that forever right
+ 
+
+ align:start position:0%
+going to do that forever right
+something is happening which I should
+
+ align:start position:0%
+something is happening which I should
+ 
+
+ align:start position:0%
+something is happening which I should
+slow the motion damn I can also you make
+
+ align:start position:0%
+slow the motion damn I can also you make
+ 
+
+ align:start position:0%
+slow the motion damn I can also you make
+use of this system okay I start from
+
+ align:start position:0%
+use of this system okay I start from
+ 
+
+ align:start position:0%
+use of this system okay I start from
+from here and I not worried that this
+
+ align:start position:0%
+from here and I not worried that this
+ 
+
+ align:start position:0%
+from here and I not worried that this
+issue goes out of the of this track
+
+ align:start position:0%
+issue goes out of the of this track
+ 
+
+ align:start position:0%
+issue goes out of the of this track
+because I know for sure you will stop
+
+ align:start position:0%
+because I know for sure you will stop
+ 
+
+ align:start position:0%
+because I know for sure you will stop
+there why because the initial amplitude
+
+ align:start position:0%
+there why because the initial amplitude
+ 
+
+ align:start position:0%
+there why because the initial amplitude
+okay it's not going to okay so the mp2
+
+ align:start position:0%
+okay it's not going to okay so the mp2
+ 
+
+ align:start position:0%
+okay it's not going to okay so the mp2
+is not going to be larger than the
+
+ align:start position:0%
+is not going to be larger than the
+ 
+
+ align:start position:0%
+is not going to be larger than the
+initial amplitude right so I'm now
+
+ align:start position:0%
+initial amplitude right so I'm now
+ 
+
+ align:start position:0%
+initial amplitude right so I'm now
+worried at all okay but you can see that
+
+ align:start position:0%
+worried at all okay but you can see that
+ 
+
+ align:start position:0%
+worried at all okay but you can see that
+the amplitude is changing as a function
+
+ align:start position:0%
+the amplitude is changing as a function
+ 
+
+ align:start position:0%
+the amplitude is changing as a function
+of time apparently something is missing
+
+ align:start position:0%
+of time apparently something is missing
+ 
+
+ align:start position:0%
+of time apparently something is missing
+and that is actually a drag force work
+
+ align:start position:0%
+and that is actually a drag force work
+ 
+
+ align:start position:0%
+and that is actually a drag force work
+or friction which is actually not
+
+ align:start position:0%
+or friction which is actually not
+ 
+
+ align:start position:0%
+or friction which is actually not
+including in included in our calculation
+
+ align:start position:0%
+including in included in our calculation
+ 
+
+ align:start position:0%
+including in included in our calculation
+so that actually try to make the
+
+ align:start position:0%
+so that actually try to make the
+ 
+
+ align:start position:0%
+so that actually try to make the
+calculation more realistic and see what
+
+ align:start position:0%
+calculation more realistic and see what
+ 
+
+ align:start position:0%
+calculation more realistic and see what
+is going to happen so now I will
+
+ align:start position:0%
+is going to happen so now I will
+ 
+
+ align:start position:0%
+is going to happen so now I will
+introduce a drag force okay which I
+
+ align:start position:0%
+introduce a drag force okay which I
+ 
+
+ align:start position:0%
+introduce a drag force okay which I
+should introduce a torque tau drag T
+
+ align:start position:0%
+should introduce a torque tau drag T
+ 
+
+ align:start position:0%
+should introduce a torque tau drag T
+which is equal to minus P P is a some
+
+ align:start position:0%
+which is equal to minus P P is a some
+ 
+
+ align:start position:0%
+which is equal to minus P P is a some
+kind of constant which is given to you
+
+ align:start position:0%
+kind of constant which is given to you
+ 
+
+ align:start position:0%
+kind of constant which is given to you
+Seeta thought he which is actually
+
+ align:start position:0%
+Seeta thought he which is actually
+ 
+
+ align:start position:0%
+Seeta thought he which is actually
+proportional to the angular velocity of
+
+ align:start position:0%
+proportional to the angular velocity of
+ 
+
+ align:start position:0%
+proportional to the angular velocity of
+that rod okay and also of course I keep
+
+ align:start position:0%
+that rod okay and also of course I keep
+ 
+
+ align:start position:0%
+that rod okay and also of course I keep
+the original approximation the CETA is
+
+ align:start position:0%
+the original approximation the CETA is
+ 
+
+ align:start position:0%
+the original approximation the CETA is
+very small such that I don't have to
+
+ align:start position:0%
+very small such that I don't have to
+ 
+
+ align:start position:0%
+very small such that I don't have to
+tell with the integration of science
+
+ align:start position:0%
+tell with the integration of science
+ 
+
+ align:start position:0%
+tell with the integration of science
+system okay so being this out about
+
+ align:start position:0%
+system okay so being this out about
+ 
+
+ align:start position:0%
+system okay so being this out about
+dot equal to minus Omega 0 square sine
+
+ align:start position:0%
+dot equal to minus Omega 0 square sine
+ 
+
+ align:start position:0%
+dot equal to minus Omega 0 square sine
+theta this complicated function okay you
+
+ align:start position:0%
+theta this complicated function okay you
+ 
+
+ align:start position:0%
+theta this complicated function okay you
+may ask why do I actually introduce a
+
+ align:start position:0%
+may ask why do I actually introduce a
+ 
+
+ align:start position:0%
+may ask why do I actually introduce a
+drag force proportional to the velocity
+
+ align:start position:0%
+drag force proportional to the velocity
+ 
+
+ align:start position:0%
+drag force proportional to the velocity
+okay and why do we put a minus sign
+
+ align:start position:0%
+okay and why do we put a minus sign
+ 
+
+ align:start position:0%
+okay and why do we put a minus sign
+there okay that is essentially because
+
+ align:start position:0%
+there okay that is essentially because
+ 
+
+ align:start position:0%
+there okay that is essentially because
+if you have a minus sign okay that means
+
+ align:start position:0%
+if you have a minus sign okay that means
+ 
+
+ align:start position:0%
+if you have a minus sign okay that means
+when this mass or that rod is actually
+
+ align:start position:0%
+when this mass or that rod is actually
+ 
+
+ align:start position:0%
+when this mass or that rod is actually
+for example it's actually going downward
+
+ align:start position:0%
+for example it's actually going downward
+ 
+
+ align:start position:0%
+for example it's actually going downward
+then the track force is really tracking
+
+ align:start position:0%
+then the track force is really tracking
+ 
+
+ align:start position:0%
+then the track force is really tracking
+it because it's actually in the opposite
+
+ align:start position:0%
+it because it's actually in the opposite
+ 
+
+ align:start position:0%
+it because it's actually in the opposite
+direction of the velocity of the mass or
+
+ align:start position:0%
+direction of the velocity of the mass or
+ 
+
+ align:start position:0%
+direction of the velocity of the mass or
+the angular velocity of the rod okay so
+
+ align:start position:0%
+the angular velocity of the rod okay so
+ 
+
+ align:start position:0%
+the angular velocity of the rod okay so
+I need a minus sign there okay otherwise
+
+ align:start position:0%
+I need a minus sign there okay otherwise
+ 
+
+ align:start position:0%
+I need a minus sign there okay otherwise
+sign it's not a track force anymore it's
+
+ align:start position:0%
+sign it's not a track force anymore it's
+ 
+
+ align:start position:0%
+sign it's not a track force anymore it's
+actually accelerating the whole thing
+
+ align:start position:0%
+actually accelerating the whole thing
+ 
+
+ align:start position:0%
+actually accelerating the whole thing
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+secondly why is that why do I choose
+
+ align:start position:0%
+secondly why is that why do I choose
+ 
+
+ align:start position:0%
+secondly why is that why do I choose
+that to be proportional to sit a dot
+
+ align:start position:0%
+that to be proportional to sit a dot
+ 
+
+ align:start position:0%
+that to be proportional to sit a dot
+over velocity okay
+
+ align:start position:0%
+over velocity okay
+ 
+
+ align:start position:0%
+over velocity okay
+there's really no much deeper reason I
+
+ align:start position:0%
+there's really no much deeper reason I
+ 
+
+ align:start position:0%
+there's really no much deeper reason I
+choose this form because I can actually
+
+ align:start position:0%
+choose this form because I can actually
+ 
+
+ align:start position:0%
+choose this form because I can actually
+solve it in front of you
+
+ align:start position:0%
+solve it in front of you
+ 
+
+ align:start position:0%
+solve it in front of you
+okay the reality is actually between
+
+ align:start position:0%
+okay the reality is actually between
+ 
+
+ align:start position:0%
+okay the reality is actually between
+proportional to theta dot and theta dot
+
+ align:start position:0%
+proportional to theta dot and theta dot
+ 
+
+ align:start position:0%
+proportional to theta dot and theta dot
+square for example okay
+
+ align:start position:0%
+square for example okay
+ 
+
+ align:start position:0%
+square for example okay
+this is your model which I introduce
+
+ align:start position:0%
+this is your model which I introduce
+ 
+
+ align:start position:0%
+this is your model which I introduce
+here which I can actually solve it in
+
+ align:start position:0%
+here which I can actually solve it in
+ 
+
+ align:start position:0%
+here which I can actually solve it in
+front of you okay on the other hand you
+
+ align:start position:0%
+front of you okay on the other hand you
+ 
+
+ align:start position:0%
+front of you okay on the other hand you
+will see that it's actually not bad at
+
+ align:start position:0%
+will see that it's actually not bad at
+ 
+
+ align:start position:0%
+will see that it's actually not bad at
+all okay it actually works and the
+
+ align:start position:0%
+all okay it actually works and the
+ 
+
+ align:start position:0%
+all okay it actually works and the
+describe the system which we actually
+
+ align:start position:0%
+describe the system which we actually
+ 
+
+ align:start position:0%
+describe the system which we actually
+work perform the demo here okay and once
+
+ align:start position:0%
+work perform the demo here okay and once
+ 
+
+ align:start position:0%
+work perform the demo here okay and once
+we have introduced this okay the
+
+ align:start position:0%
+we have introduced this okay the
+ 
+
+ align:start position:0%
+we have introduced this okay the
+equation of motion will be modified okay
+
+ align:start position:0%
+equation of motion will be modified okay
+ 
+
+ align:start position:0%
+equation of motion will be modified okay
+so that's come back to the equation of
+
+ align:start position:0%
+so that's come back to the equation of
+ 
+
+ align:start position:0%
+so that's come back to the equation of
+motion so you have theta double dot he
+
+ align:start position:0%
+motion so you have theta double dot he
+ 
+
+ align:start position:0%
+motion so you have theta double dot he
+originally will be equal to tau Toto P
+
+ align:start position:0%
+originally will be equal to tau Toto P
+ 
+
+ align:start position:0%
+originally will be equal to tau Toto P
+/ I okay and now this will become tau t
+
+ align:start position:0%
+/ I okay and now this will become tau t
+ 
+
+ align:start position:0%
+/ I okay and now this will become tau t
+plus tau drag T / app there's additional
+
+ align:start position:0%
+plus tau drag T / app there's additional
+ 
+
+ align:start position:0%
+plus tau drag T / app there's additional
+time here okay if I simplify this whole
+
+ align:start position:0%
+time here okay if I simplify this whole
+ 
+
+ align:start position:0%
+time here okay if I simplify this whole
+equation then I get minus mg L / - okay
+
+ align:start position:0%
+equation then I get minus mg L / - okay
+ 
+
+ align:start position:0%
+equation then I get minus mg L / - okay
+signs theta and this is actually roughly
+
+ align:start position:0%
+signs theta and this is actually roughly
+ 
+
+ align:start position:0%
+signs theta and this is actually roughly
+Sita okay - P Sita dot divided by
+
+ align:start position:0%
+Sita okay - P Sita dot divided by
+ 
+
+ align:start position:0%
+Sita okay - P Sita dot divided by
+one-third of M L square okay so you can
+
+ align:start position:0%
+one-third of M L square okay so you can
+ 
+
+ align:start position:0%
+one-third of M L square okay so you can
+see that I still make this approximation
+
+ align:start position:0%
+see that I still make this approximation
+ 
+
+ align:start position:0%
+see that I still make this approximation
+sine theta roughly equal to Sita okay
+
+ align:start position:0%
+sine theta roughly equal to Sita okay
+ 
+
+ align:start position:0%
+sine theta roughly equal to Sita okay
+then I can actually write this equation
+
+ align:start position:0%
+then I can actually write this equation
+ 
+
+ align:start position:0%
+then I can actually write this equation
+in a small angle case okay I get minus
+
+ align:start position:0%
+in a small angle case okay I get minus
+ 
+
+ align:start position:0%
+in a small angle case okay I get minus
+3G over 2l Sita
+
+ align:start position:0%
+3G over 2l Sita
+ 
+
+ align:start position:0%
+3G over 2l Sita
+t minus 3b over and L square theta dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and now I as usual I define Omega 0
+
+ align:start position:0%
+okay and now I as usual I define Omega 0
+ 
+
+ align:start position:0%
+okay and now I as usual I define Omega 0
+square equal to 3G over 2l and I can
+
+ align:start position:0%
+square equal to 3G over 2l and I can
+ 
+
+ align:start position:0%
+square equal to 3G over 2l and I can
+also define gamma is equal to CP / ml
+
+ align:start position:0%
+also define gamma is equal to CP / ml
+ 
+
+ align:start position:0%
+also define gamma is equal to CP / ml
+squared okay just to make my life easier
+
+ align:start position:0%
+squared okay just to make my life easier
+ 
+
+ align:start position:0%
+squared okay just to make my life easier
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+finally we will arrive this expression
+
+ align:start position:0%
+finally we will arrive this expression
+ 
+
+ align:start position:0%
+finally we will arrive this expression
+sheet a double dot plus gamma theta dot
+
+ align:start position:0%
+sheet a double dot plus gamma theta dot
+ 
+
+ align:start position:0%
+sheet a double dot plus gamma theta dot
+plus Omega 0 square theta and that is
+
+ align:start position:0%
+plus Omega 0 square theta and that is
+ 
+
+ align:start position:0%
+plus Omega 0 square theta and that is
+equal to 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what you can see from here is that we
+
+ align:start position:0%
+so what you can see from here is that we
+ 
+
+ align:start position:0%
+so what you can see from here is that we
+have actually arrived and derive the
+
+ align:start position:0%
+have actually arrived and derive the
+ 
+
+ align:start position:0%
+have actually arrived and derive the
+equation of motion
+
+ align:start position:0%
+equation of motion
+ 
+
+ align:start position:0%
+equation of motion
+okay we have described that this
+
+ align:start position:0%
+okay we have described that this
+ 
+
+ align:start position:0%
+okay we have described that this
+equation of motion and what is really
+
+ align:start position:0%
+equation of motion and what is really
+ 
+
+ align:start position:0%
+equation of motion and what is really
+the rest part of the world is actually
+
+ align:start position:0%
+the rest part of the world is actually
+ 
+
+ align:start position:0%
+the rest part of the world is actually
+ready to solve this equation of motion
+
+ align:start position:0%
+ready to solve this equation of motion
+ 
+
+ align:start position:0%
+ready to solve this equation of motion
+and you don't really have to solve it
+
+ align:start position:0%
+and you don't really have to solve it
+ 
+
+ align:start position:0%
+and you don't really have to solve it
+because you already get the result from
+
+ align:start position:0%
+because you already get the result from
+ 
+
+ align:start position:0%
+because you already get the result from
+1803 HD you will remember and we are
+
+ align:start position:0%
+1803 HD you will remember and we are
+ 
+
+ align:start position:0%
+1803 HD you will remember and we are
+going to discuss the result but before
+
+ align:start position:0%
+going to discuss the result but before
+ 
+
+ align:start position:0%
+going to discuss the result but before
+that before I really try to solve this
+
+ align:start position:0%
+that before I really try to solve this
+ 
+
+ align:start position:0%
+that before I really try to solve this
+equation I would like to take a vote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here I have two different two
+
+ align:start position:0%
+okay so here I have two different two
+ 
+
+ align:start position:0%
+okay so here I have two different two
+system okay they have equal amount of
+
+ align:start position:0%
+system okay they have equal amount of
+ 
+
+ align:start position:0%
+system okay they have equal amount of
+mass okay they are attached to a spring
+
+ align:start position:0%
+mass okay they are attached to a spring
+ 
+
+ align:start position:0%
+mass okay they are attached to a spring
+okay if you do the same equation motion
+
+ align:start position:0%
+okay if you do the same equation motion
+ 
+
+ align:start position:0%
+okay if you do the same equation motion
+simulation you will actually get exactly
+
+ align:start position:0%
+simulation you will actually get exactly
+ 
+
+ align:start position:0%
+simulation you will actually get exactly
+the same solution so it exactly the same
+
+ align:start position:0%
+the same solution so it exactly the same
+ 
+
+ align:start position:0%
+the same solution so it exactly the same
+equation of motion in in that form
+
+ align:start position:0%
+equation of motion in in that form
+ 
+
+ align:start position:0%
+equation of motion in in that form
+format okay so the form of the equation
+
+ align:start position:0%
+format okay so the form of the equation
+ 
+
+ align:start position:0%
+format okay so the form of the equation
+of motion will be the same between this
+
+ align:start position:0%
+of motion will be the same between this
+ 
+
+ align:start position:0%
+of motion will be the same between this
+system and that system okay I would like
+
+ align:start position:0%
+system and that system okay I would like
+ 
+
+ align:start position:0%
+system and that system okay I would like
+to ask you a question about the
+
+ align:start position:0%
+to ask you a question about the
+ 
+
+ align:start position:0%
+to ask you a question about the
+oscillation frequency so you can see
+
+ align:start position:0%
+oscillation frequency so you can see
+ 
+
+ align:start position:0%
+oscillation frequency so you can see
+that one one of them is as you have a
+
+ align:start position:0%
+that one one of them is as you have a
+ 
+
+ align:start position:0%
+that one one of them is as you have a
+mass like a point-like particle and the
+
+ align:start position:0%
+mass like a point-like particle and the
+ 
+
+ align:start position:0%
+mass like a point-like particle and the
+other one where the ahead okay what is
+
+ align:start position:0%
+other one where the ahead okay what is
+ 
+
+ align:start position:0%
+other one where the ahead okay what is
+going to happen is that this Mexican hat
+
+ align:start position:0%
+going to happen is that this Mexican hat
+ 
+
+ align:start position:0%
+going to happen is that this Mexican hat
+is going to be trying to push the air
+
+ align:start position:0%
+is going to be trying to push the air
+ 
+
+ align:start position:0%
+is going to be trying to push the air
+away right then you may sing okay this
+
+ align:start position:0%
+away right then you may sing okay this
+ 
+
+ align:start position:0%
+away right then you may sing okay this
+Mexican stream is not really very
+
+ align:start position:0%
+Mexican stream is not really very
+ 
+
+ align:start position:0%
+Mexican stream is not really very
+important therefore the oscillation
+
+ align:start position:0%
+important therefore the oscillation
+ 
+
+ align:start position:0%
+important therefore the oscillation
+frequency may be the same right how many
+
+ align:start position:0%
+frequency may be the same right how many
+ 
+
+ align:start position:0%
+frequency may be the same right how many
+of you think the oscillation frequency
+
+ align:start position:0%
+of you think the oscillation frequency
+ 
+
+ align:start position:0%
+of you think the oscillation frequency
+if I actually try to protect this two
+
+ align:start position:0%
+if I actually try to protect this two
+ 
+
+ align:start position:0%
+if I actually try to protect this two
+system will be the same help raise your
+
+ align:start position:0%
+system will be the same help raise your
+ 
+
+ align:start position:0%
+system will be the same help raise your
+hand one two three four five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you have 11 so the Omega the
+
+ align:start position:0%
+okay you have 11 so the Omega the
+ 
+
+ align:start position:0%
+okay you have 11 so the Omega the
+predate Omega will be equal to Omega how
+
+ align:start position:0%
+predate Omega will be equal to Omega how
+ 
+
+ align:start position:0%
+predate Omega will be equal to Omega how
+many of you were seeing that okay
+
+ align:start position:0%
+many of you were seeing that okay
+ 
+
+ align:start position:0%
+many of you were seeing that okay
+because of this hat okay
+
+ align:start position:0%
+because of this hat okay
+ 
+
+ align:start position:0%
+because of this hat okay
+this is pushing this air away you know
+
+ align:start position:0%
+this is pushing this air away you know
+ 
+
+ align:start position:0%
+this is pushing this air away you know
+it's a lot of work to be done and
+
+ align:start position:0%
+it's a lot of work to be done and
+ 
+
+ align:start position:0%
+it's a lot of work to be done and
+therefore this is going to slow down the
+
+ align:start position:0%
+therefore this is going to slow down the
+ 
+
+ align:start position:0%
+therefore this is going to slow down the
+oscillation how many of you think that
+
+ align:start position:0%
+oscillation how many of you think that
+ 
+
+ align:start position:0%
+oscillation how many of you think that
+is going to happen one two three okay
+
+ align:start position:0%
+is going to happen one two three okay
+ 
+
+ align:start position:0%
+is going to happen one two three okay
+seventeen okay it may it may happen to
+
+ align:start position:0%
+seventeen okay it may it may happen to
+ 
+
+ align:start position:0%
+seventeen okay it may it may happen to
+you that you think this idea of know
+
+ align:start position:0%
+you that you think this idea of know
+ 
+
+ align:start position:0%
+you that you think this idea of know
+where Dena Headlee is really fashionable
+
+ align:start position:0%
+where Dena Headlee is really fashionable
+ 
+
+ align:start position:0%
+where Dena Headlee is really fashionable
+know therefore it got really exciting
+
+ align:start position:0%
+know therefore it got really exciting
+ 
+
+ align:start position:0%
+know therefore it got really exciting
+and also the faster cannot happen how
+
+ align:start position:0%
+and also the faster cannot happen how
+ 
+
+ align:start position:0%
+and also the faster cannot happen how
+many of you as you think that is going
+
+ align:start position:0%
+many of you as you think that is going
+ 
+
+ align:start position:0%
+many of you as you think that is going
+to happen okay one do you think so too
+
+ align:start position:0%
+to happen okay one do you think so too
+ 
+
+ align:start position:0%
+to happen okay one do you think so too
+very good we have to what what do you
+
+ align:start position:0%
+very good we have to what what do you
+ 
+
+ align:start position:0%
+very good we have to what what do you
+think what are the rest
+
+ align:start position:0%
+think what are the rest
+ 
+
+ align:start position:0%
+think what are the rest
+the only 30 of you as you think that is
+
+ align:start position:0%
+the only 30 of you as you think that is
+ 
+
+ align:start position:0%
+the only 30 of you as you think that is
+going to happen okay all the rest think
+
+ align:start position:0%
+going to happen okay all the rest think
+ 
+
+ align:start position:0%
+going to happen okay all the rest think
+all the rest of the class think that
+
+ align:start position:0%
+all the rest of the class think that
+ 
+
+ align:start position:0%
+all the rest of the class think that
+this is going to to disappear to the
+
+ align:start position:0%
+this is going to to disappear to the
+ 
+
+ align:start position:0%
+this is going to to disappear to the
+moon okay so that is as real opinion and
+
+ align:start position:0%
+moon okay so that is as real opinion and
+ 
+
+ align:start position:0%
+moon okay so that is as real opinion and
+we have completed the poll and what we
+
+ align:start position:0%
+we have completed the poll and what we
+ 
+
+ align:start position:0%
+we have completed the poll and what we
+are we are going to do is that we are
+
+ align:start position:0%
+are we are going to do is that we are
+ 
+
+ align:start position:0%
+are we are going to do is that we are
+going to solve this system and see what
+
+ align:start position:0%
+going to solve this system and see what
+ 
+
+ align:start position:0%
+going to solve this system and see what
+is going to happen and we will do the
+
+ align:start position:0%
+is going to happen and we will do the
+ 
+
+ align:start position:0%
+is going to happen and we will do the
+experiment in front of you okay all
+
+ align:start position:0%
+experiment in front of you okay all
+ 
+
+ align:start position:0%
+experiment in front of you okay all
+right so that's very nice so now we have
+
+ align:start position:0%
+right so that's very nice so now we have
+ 
+
+ align:start position:0%
+right so that's very nice so now we have
+this equation of motion and now I will
+
+ align:start position:0%
+this equation of motion and now I will
+ 
+
+ align:start position:0%
+this equation of motion and now I will
+pretend that I'm from the math
+
+ align:start position:0%
+pretend that I'm from the math
+ 
+
+ align:start position:0%
+pretend that I'm from the math
+department for a bit and help you guide
+
+ align:start position:0%
+department for a bit and help you guide
+ 
+
+ align:start position:0%
+department for a bit and help you guide
+you through the solution
+
+ align:start position:0%
+you through the solution
+ 
+
+ align:start position:0%
+you through the solution
+so now I can use this trick okay the
+
+ align:start position:0%
+so now I can use this trick okay the
+ 
+
+ align:start position:0%
+so now I can use this trick okay the
+CETA I can actually say Sita is actually
+
+ align:start position:0%
+CETA I can actually say Sita is actually
+ 
+
+ align:start position:0%
+CETA I can actually say Sita is actually
+the real part of the Z is a complex
+
+ align:start position:0%
+the real part of the Z is a complex
+ 
+
+ align:start position:0%
+the real part of the Z is a complex
+function and as we learned before the T
+
+ align:start position:0%
+function and as we learned before the T
+ 
+
+ align:start position:0%
+function and as we learned before the T
+and I assume that to be exponential I
+
+ align:start position:0%
+and I assume that to be exponential I
+ 
+
+ align:start position:0%
+and I assume that to be exponential I
+alpha so alpha is actually some kind of
+
+ align:start position:0%
+alpha so alpha is actually some kind of
+ 
+
+ align:start position:0%
+alpha so alpha is actually some kind of
+constant which we I I don't really know
+
+ align:start position:0%
+constant which we I I don't really know
+ 
+
+ align:start position:0%
+constant which we I I don't really know
+what is the constant yet okay now I can
+
+ align:start position:0%
+what is the constant yet okay now I can
+ 
+
+ align:start position:0%
+what is the constant yet okay now I can
+now actually write the equation of
+
+ align:start position:0%
+now actually write the equation of
+ 
+
+ align:start position:0%
+now actually write the equation of
+motion okay in the form of Z then
+
+ align:start position:0%
+motion okay in the form of Z then
+ 
+
+ align:start position:0%
+motion okay in the form of Z then
+basically what I get is Z double dot T
+
+ align:start position:0%
+basically what I get is Z double dot T
+ 
+
+ align:start position:0%
+basically what I get is Z double dot T
+plus gamma the dot T plus Omega 0 square
+
+ align:start position:0%
+plus gamma the dot T plus Omega 0 square
+ 
+
+ align:start position:0%
+plus gamma the dot T plus Omega 0 square
+the e of T and this is equal to 0 okay
+
+ align:start position:0%
+the e of T and this is equal to 0 okay
+ 
+
+ align:start position:0%
+the e of T and this is equal to 0 okay
+so remember explanation function cannot
+
+ align:start position:0%
+so remember explanation function cannot
+ 
+
+ align:start position:0%
+so remember explanation function cannot
+be killed by differentiation right
+
+ align:start position:0%
+be killed by differentiation right
+ 
+
+ align:start position:0%
+be killed by differentiation right
+therefore it's really convenient you can
+
+ align:start position:0%
+therefore it's really convenient you can
+ 
+
+ align:start position:0%
+therefore it's really convenient you can
+see from here now I can plug in this
+
+ align:start position:0%
+see from here now I can plug in this
+ 
+
+ align:start position:0%
+see from here now I can plug in this
+expression which I did some guests and
+
+ align:start position:0%
+expression which I did some guests and
+ 
+
+ align:start position:0%
+expression which I did some guests and
+two to this equation of motion then what
+
+ align:start position:0%
+two to this equation of motion then what
+ 
+
+ align:start position:0%
+two to this equation of motion then what
+I am going to get this minus alpha
+
+ align:start position:0%
+I am going to get this minus alpha
+ 
+
+ align:start position:0%
+I am going to get this minus alpha
+square okay because I you take I offer I
+
+ align:start position:0%
+square okay because I you take I offer I
+ 
+
+ align:start position:0%
+square okay because I you take I offer I
+have out of this exponential function
+
+ align:start position:0%
+have out of this exponential function
+ 
+
+ align:start position:0%
+have out of this exponential function
+right because you do to double
+
+ align:start position:0%
+right because you do to double
+ 
+
+ align:start position:0%
+right because you do to double
+differentiation okay so you get minus
+
+ align:start position:0%
+differentiation okay so you get minus
+ 
+
+ align:start position:0%
+differentiation okay so you get minus
+alpha square plus I gamma alpha right
+
+ align:start position:0%
+alpha square plus I gamma alpha right
+ 
+
+ align:start position:0%
+alpha square plus I gamma alpha right
+because this is only differentiate at
+
+ align:start position:0%
+because this is only differentiate at
+ 
+
+ align:start position:0%
+because this is only differentiate at
+one time plus Omega 0 Square and that is
+
+ align:start position:0%
+one time plus Omega 0 Square and that is
+ 
+
+ align:start position:0%
+one time plus Omega 0 Square and that is
+actually all those things as you is
+
+ align:start position:0%
+actually all those things as you is
+ 
+
+ align:start position:0%
+actually all those things as you is
+multiplying this exponential function
+
+ align:start position:0%
+multiplying this exponential function
+ 
+
+ align:start position:0%
+multiplying this exponential function
+exponential I have ax equal to zero okay
+
+ align:start position:0%
+exponential I have ax equal to zero okay
+ 
+
+ align:start position:0%
+exponential I have ax equal to zero okay
+so we will write this expression that is
+
+ align:start position:0%
+so we will write this expression that is
+ 
+
+ align:start position:0%
+so we will write this expression that is
+very nice and we also know that this
+
+ align:start position:0%
+very nice and we also know that this
+ 
+
+ align:start position:0%
+very nice and we also know that this
+expression is going to be bad it all the
+
+ align:start position:0%
+expression is going to be bad it all the
+ 
+
+ align:start position:0%
+expression is going to be bad it all the
+time no matter what
+
+ align:start position:0%
+time no matter what
+ 
+
+ align:start position:0%
+time no matter what
+what T you put in it should be bad right
+
+ align:start position:0%
+what T you put in it should be bad right
+ 
+
+ align:start position:0%
+what T you put in it should be bad right
+because this is the equation of motion
+
+ align:start position:0%
+because this is the equation of motion
+ 
+
+ align:start position:0%
+because this is the equation of motion
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that we hope that this solution will
+
+ align:start position:0%
+that we hope that this solution will
+ 
+
+ align:start position:0%
+that we hope that this solution will
+survive this test right okay
+
+ align:start position:0%
+survive this test right okay
+ 
+
+ align:start position:0%
+survive this test right okay
+so I can easily conclude that this one
+
+ align:start position:0%
+so I can easily conclude that this one
+ 
+
+ align:start position:0%
+so I can easily conclude that this one
+is actually not equal to zero okay it
+
+ align:start position:0%
+is actually not equal to zero okay it
+ 
+
+ align:start position:0%
+is actually not equal to zero okay it
+can be some value nonzero so what is
+
+ align:start position:0%
+can be some value nonzero so what is
+ 
+
+ align:start position:0%
+can be some value nonzero so what is
+actually equal to zero this first term
+
+ align:start position:0%
+actually equal to zero this first term
+ 
+
+ align:start position:0%
+actually equal to zero this first term
+is actually equal to zero okay therefore
+
+ align:start position:0%
+is actually equal to zero okay therefore
+ 
+
+ align:start position:0%
+is actually equal to zero okay therefore
+I can now solve this equation minus
+
+ align:start position:0%
+I can now solve this equation minus
+ 
+
+ align:start position:0%
+I can now solve this equation minus
+alpha squared plus I gamma alpha plus
+
+ align:start position:0%
+alpha squared plus I gamma alpha plus
+ 
+
+ align:start position:0%
+alpha squared plus I gamma alpha plus
+Omega 0 square equal to zero I can solve
+
+ align:start position:0%
+Omega 0 square equal to zero I can solve
+ 
+
+ align:start position:0%
+Omega 0 square equal to zero I can solve
+it ok if I do that then I will get alpha
+
+ align:start position:0%
+it ok if I do that then I will get alpha
+ 
+
+ align:start position:0%
+it ok if I do that then I will get alpha
+is equal to I gamma plus minus square
+
+ align:start position:0%
+is equal to I gamma plus minus square
+ 
+
+ align:start position:0%
+is equal to I gamma plus minus square
+root of 4 Omega 0 square minus gamma
+
+ align:start position:0%
+root of 4 Omega 0 square minus gamma
+ 
+
+ align:start position:0%
+root of 4 Omega 0 square minus gamma
+square divided by 2 this is actually a
+
+ align:start position:0%
+square divided by 2 this is actually a
+ 
+
+ align:start position:0%
+square divided by 2 this is actually a
+second-order polynomial and you can
+
+ align:start position:0%
+second-order polynomial and you can
+ 
+
+ align:start position:0%
+second-order polynomial and you can
+actually add that this issue equal to 0
+
+ align:start position:0%
+actually add that this issue equal to 0
+ 
+
+ align:start position:0%
+actually add that this issue equal to 0
+therefore you can actually solve in Z
+
+ align:start position:0%
+therefore you can actually solve in Z
+ 
+
+ align:start position:0%
+therefore you can actually solve in Z
+and this is actually the solution and I
+
+ align:start position:0%
+and this is actually the solution and I
+ 
+
+ align:start position:0%
+and this is actually the solution and I
+can write it down you know slightly
+
+ align:start position:0%
+can write it down you know slightly
+ 
+
+ align:start position:0%
+can write it down you know slightly
+different form I gamma over 2 plus minus
+
+ align:start position:0%
+different form I gamma over 2 plus minus
+ 
+
+ align:start position:0%
+different form I gamma over 2 plus minus
+square root of Omega 0 square minus
+
+ align:start position:0%
+square root of Omega 0 square minus
+ 
+
+ align:start position:0%
+square root of Omega 0 square minus
+gamma square over 4 okay
+
+ align:start position:0%
+gamma square over 4 okay
+ 
+
+ align:start position:0%
+gamma square over 4 okay
+any questions so far and not going too
+
+ align:start position:0%
+any questions so far and not going too
+ 
+
+ align:start position:0%
+any questions so far and not going too
+fast no everything so ok ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can see that half is equal to
+
+ align:start position:0%
+so you can see that half is equal to
+ 
+
+ align:start position:0%
+so you can see that half is equal to
+this expression and I would like to
+
+ align:start position:0%
+this expression and I would like to
+ 
+
+ align:start position:0%
+this expression and I would like to
+consider a situation where Omega zero is
+
+ align:start position:0%
+consider a situation where Omega zero is
+ 
+
+ align:start position:0%
+consider a situation where Omega zero is
+much much larger than gamma okay
+
+ align:start position:0%
+much much larger than gamma okay
+ 
+
+ align:start position:0%
+much much larger than gamma okay
+that means just a reminder of what is
+
+ align:start position:0%
+that means just a reminder of what is
+ 
+
+ align:start position:0%
+that means just a reminder of what is
+gamma okay
+
+ align:start position:0%
+gamma okay
+ 
+
+ align:start position:0%
+gamma okay
+maybe you got already a bit confused
+
+ align:start position:0%
+maybe you got already a bit confused
+ 
+
+ align:start position:0%
+maybe you got already a bit confused
+what is gamma gamma is related to the
+
+ align:start position:0%
+what is gamma gamma is related to the
+ 
+
+ align:start position:0%
+what is gamma gamma is related to the
+strength of the drag force right it's
+
+ align:start position:0%
+strength of the drag force right it's
+ 
+
+ align:start position:0%
+strength of the drag force right it's
+actually three P over N squared okay P
+
+ align:start position:0%
+actually three P over N squared okay P
+ 
+
+ align:start position:0%
+actually three P over N squared okay P
+is actually giving you the portion okay
+
+ align:start position:0%
+is actually giving you the portion okay
+ 
+
+ align:start position:0%
+is actually giving you the portion okay
+it's actually determining the size of
+
+ align:start position:0%
+it's actually determining the size of
+ 
+
+ align:start position:0%
+it's actually determining the size of
+the drag force okay so I would like to
+
+ align:start position:0%
+the drag force okay so I would like to
+ 
+
+ align:start position:0%
+the drag force okay so I would like to
+consider a situation the first situation
+
+ align:start position:0%
+consider a situation the first situation
+ 
+
+ align:start position:0%
+consider a situation the first situation
+is if Omega 0 square is larger than
+
+ align:start position:0%
+is if Omega 0 square is larger than
+ 
+
+ align:start position:0%
+is if Omega 0 square is larger than
+gamma square over 4 okay so it not limit
+
+ align:start position:0%
+gamma square over 4 okay so it not limit
+ 
+
+ align:start position:0%
+gamma square over 4 okay so it not limit
+it so in that case the drag force okay
+
+ align:start position:0%
+it so in that case the drag force okay
+ 
+
+ align:start position:0%
+it so in that case the drag force okay
+it is small okay it's not huge okay
+
+ align:start position:0%
+it is small okay it's not huge okay
+ 
+
+ align:start position:0%
+it is small okay it's not huge okay
+small okay if that is the case this is
+
+ align:start position:0%
+small okay if that is the case this is
+ 
+
+ align:start position:0%
+small okay if that is the case this is
+actually real right because Omega 0
+
+ align:start position:0%
+actually real right because Omega 0
+ 
+
+ align:start position:0%
+actually real right because Omega 0
+square is larger than gamma square over
+
+ align:start position:0%
+square is larger than gamma square over
+ 
+
+ align:start position:0%
+square is larger than gamma square over
+4 therefore this is real okay so now I
+
+ align:start position:0%
+4 therefore this is real okay so now I
+ 
+
+ align:start position:0%
+4 therefore this is real okay so now I
+can actually define Omega square define
+
+ align:start position:0%
+can actually define Omega square define
+ 
+
+ align:start position:0%
+can actually define Omega square define
+that as Omega 0 square minus gamma
+
+ align:start position:0%
+that as Omega 0 square minus gamma
+ 
+
+ align:start position:0%
+that as Omega 0 square minus gamma
+square over 4 ok and this will become
+
+ align:start position:0%
+square over 4 ok and this will become
+ 
+
+ align:start position:0%
+square over 4 ok and this will become
+and this will become hi gamma over 2
+
+ align:start position:0%
+and this will become hi gamma over 2
+ 
+
+ align:start position:0%
+and this will become hi gamma over 2
+plus minus Omega okay so that means I
+
+ align:start position:0%
+plus minus Omega okay so that means I
+ 
+
+ align:start position:0%
+plus minus Omega okay so that means I
+will have two solutions coming from this
+
+ align:start position:0%
+will have two solutions coming from this
+ 
+
+ align:start position:0%
+will have two solutions coming from this
+exercise the pass of T is equal to
+
+ align:start position:0%
+exercise the pass of T is equal to
+ 
+
+ align:start position:0%
+exercise the pass of T is equal to
+exponential minus gamma over 2 T
+
+ align:start position:0%
+exponential minus gamma over 2 T
+ 
+
+ align:start position:0%
+exponential minus gamma over 2 T
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+I Omega okay and the - the second
+
+ align:start position:0%
+I Omega okay and the - the second
+ 
+
+ align:start position:0%
+I Omega okay and the - the second
+solution okay if I take one of the plus
+
+ align:start position:0%
+solution okay if I take one of the plus
+ 
+
+ align:start position:0%
+solution okay if I take one of the plus
+sign that was a minus sign solution then
+
+ align:start position:0%
+sign that was a minus sign solution then
+ 
+
+ align:start position:0%
+sign that was a minus sign solution then
+the second solution will be explanation
+
+ align:start position:0%
+the second solution will be explanation
+ 
+
+ align:start position:0%
+the second solution will be explanation
+minus I gamma over 2t explanation - hi
+
+ align:start position:0%
+minus I gamma over 2t explanation - hi
+ 
+
+ align:start position:0%
+minus I gamma over 2t explanation - hi
+oh my gosh okay any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we would like to go back to Sita
+
+ align:start position:0%
+okay so we would like to go back to Sita
+ 
+
+ align:start position:0%
+okay so we would like to go back to Sita
+right so so what would be the Sita so
+
+ align:start position:0%
+right so so what would be the Sita so
+ 
+
+ align:start position:0%
+right so so what would be the Sita so
+that means I will have a theta 1 of T
+
+ align:start position:0%
+that means I will have a theta 1 of T
+ 
+
+ align:start position:0%
+that means I will have a theta 1 of T
+which is actually taking the real part
+
+ align:start position:0%
+which is actually taking the real part
+ 
+
+ align:start position:0%
+which is actually taking the real part
+so I see the price maybe okay
+
+ align:start position:0%
+so I see the price maybe okay
+ 
+
+ align:start position:0%
+so I see the price maybe okay
+taking the real part of the Z press and
+
+ align:start position:0%
+taking the real part of the Z press and
+ 
+
+ align:start position:0%
+taking the real part of the Z press and
+now we'll give you exponential minus
+
+ align:start position:0%
+now we'll give you exponential minus
+ 
+
+ align:start position:0%
+now we'll give you exponential minus
+gamma over 2t cosine Omega okay I'm just
+
+ align:start position:0%
+gamma over 2t cosine Omega okay I'm just
+ 
+
+ align:start position:0%
+gamma over 2t cosine Omega okay I'm just
+plugging in the solution to this
+
+ align:start position:0%
+plugging in the solution to this
+ 
+
+ align:start position:0%
+plugging in the solution to this
+equation okay theta minus T will be
+
+ align:start position:0%
+equation okay theta minus T will be
+ 
+
+ align:start position:0%
+equation okay theta minus T will be
+equal to exponential and come over to T
+
+ align:start position:0%
+equal to exponential and come over to T
+ 
+
+ align:start position:0%
+equal to exponential and come over to T
+sine Omega T okay finally the full
+
+ align:start position:0%
+sine Omega T okay finally the full
+ 
+
+ align:start position:0%
+sine Omega T okay finally the full
+solution of theta of T will be a linear
+
+ align:start position:0%
+solution of theta of T will be a linear
+ 
+
+ align:start position:0%
+solution of theta of T will be a linear
+combination of this two solution right
+
+ align:start position:0%
+combination of this two solution right
+ 
+
+ align:start position:0%
+combination of this two solution right
+therefore you will get set of t equal to
+
+ align:start position:0%
+therefore you will get set of t equal to
+ 
+
+ align:start position:0%
+therefore you will get set of t equal to
+exponential minus gamma over 2t a is
+
+ align:start position:0%
+exponential minus gamma over 2t a is
+ 
+
+ align:start position:0%
+exponential minus gamma over 2t a is
+some kind of constant times cosine Omega
+
+ align:start position:0%
+some kind of constant times cosine Omega
+ 
+
+ align:start position:0%
+some kind of constant times cosine Omega
+T plus P sine Omega T okay
+
+ align:start position:0%
+T plus P sine Omega T okay
+ 
+
+ align:start position:0%
+T plus P sine Omega T okay
+and of course from the last time as you
+
+ align:start position:0%
+and of course from the last time as you
+ 
+
+ align:start position:0%
+and of course from the last time as you
+we know that this can also be written as
+
+ align:start position:0%
+we know that this can also be written as
+ 
+
+ align:start position:0%
+we know that this can also be written as
+a cosine Omega T plus five
+
+ align:start position:0%
+a cosine Omega T plus five
+ 
+
+ align:start position:0%
+a cosine Omega T plus five
+okay any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay very good so we have actually
+
+ align:start position:0%
+okay very good so we have actually
+ 
+
+ align:start position:0%
+okay very good so we have actually
+already solved this equation and of
+
+ align:start position:0%
+already solved this equation and of
+ 
+
+ align:start position:0%
+already solved this equation and of
+course we can actually practice a back
+
+ align:start position:0%
+course we can actually practice a back
+ 
+
+ align:start position:0%
+course we can actually practice a back
+into this equation of motion and you
+
+ align:start position:0%
+into this equation of motion and you
+ 
+
+ align:start position:0%
+into this equation of motion and you
+will see that it really works and I'm
+
+ align:start position:0%
+will see that it really works and I'm
+ 
+
+ align:start position:0%
+will see that it really works and I'm
+not going to do that now but you can
+
+ align:start position:0%
+not going to do that now but you can
+ 
+
+ align:start position:0%
+not going to do that now but you can
+easily go back home and check and you
+
+ align:start position:0%
+easily go back home and check and you
+ 
+
+ align:start position:0%
+easily go back home and check and you
+will be deep me it works and also at the
+
+ align:start position:0%
+will be deep me it works and also at the
+ 
+
+ align:start position:0%
+will be deep me it works and also at the
+same time you got to undetermined
+
+ align:start position:0%
+same time you got to undetermined
+ 
+
+ align:start position:0%
+same time you got to undetermined
+constants since this is a second order
+
+ align:start position:0%
+constants since this is a second order
+ 
+
+ align:start position:0%
+constants since this is a second order
+differential equation therefore ha this
+
+ align:start position:0%
+differential equation therefore ha this
+ 
+
+ align:start position:0%
+differential equation therefore ha this
+thing as you works have two arbitrary
+
+ align:start position:0%
+thing as you works have two arbitrary
+ 
+
+ align:start position:0%
+thing as you works have two arbitrary
+constant therefore that is actually one
+
+ align:start position:0%
+constant therefore that is actually one
+ 
+
+ align:start position:0%
+constant therefore that is actually one
+and the only one solution in a universe
+
+ align:start position:0%
+and the only one solution in a universe
+ 
+
+ align:start position:0%
+and the only one solution in a universe
+which satisfy the equation of motion or
+
+ align:start position:0%
+which satisfy the equation of motion or
+ 
+
+ align:start position:0%
+which satisfy the equation of motion or
+to satisfy that equation equation
+
+ align:start position:0%
+to satisfy that equation equation
+ 
+
+ align:start position:0%
+to satisfy that equation equation
+differential equation okay so this thing
+
+ align:start position:0%
+differential equation okay so this thing
+ 
+
+ align:start position:0%
+differential equation okay so this thing
+actually have dramatical consequence the
+
+ align:start position:0%
+actually have dramatical consequence the
+ 
+
+ align:start position:0%
+actually have dramatical consequence the
+first thing which we learn is that as a
+
+ align:start position:0%
+first thing which we learn is that as a
+ 
+
+ align:start position:0%
+first thing which we learn is that as a
+function of time what is going to happen
+
+ align:start position:0%
+function of time what is going to happen
+ 
+
+ align:start position:0%
+function of time what is going to happen
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the amplitude is now becoming
+
+ align:start position:0%
+the amplitude is now becoming
+ 
+
+ align:start position:0%
+the amplitude is now becoming
+exponential minus gamma over 2t times a
+
+ align:start position:0%
+exponential minus gamma over 2t times a
+ 
+
+ align:start position:0%
+exponential minus gamma over 2t times a
+this is actually the amplitude the
+
+ align:start position:0%
+this is actually the amplitude the
+ 
+
+ align:start position:0%
+this is actually the amplitude the
+amplitude is decreasing exponentially so
+
+ align:start position:0%
+amplitude is decreasing exponentially so
+ 
+
+ align:start position:0%
+amplitude is decreasing exponentially so
+that is actually the first partition
+
+ align:start position:0%
+that is actually the first partition
+ 
+
+ align:start position:0%
+that is actually the first partition
+coming from this exercise okay the
+
+ align:start position:0%
+coming from this exercise okay the
+ 
+
+ align:start position:0%
+coming from this exercise okay the
+second prediction is that this C is
+
+ align:start position:0%
+second prediction is that this C is
+ 
+
+ align:start position:0%
+second prediction is that this C is
+still oscillating because we've got the
+
+ align:start position:0%
+still oscillating because we've got the
+ 
+
+ align:start position:0%
+still oscillating because we've got the
+cosine Omega T plus Phi there you see so
+
+ align:start position:0%
+cosine Omega T plus Phi there you see so
+ 
+
+ align:start position:0%
+cosine Omega T plus Phi there you see so
+the resulting motion is going to be like
+
+ align:start position:0%
+the resulting motion is going to be like
+ 
+
+ align:start position:0%
+the resulting motion is going to be like
+going up and down I'll be done and got
+
+ align:start position:0%
+going up and down I'll be done and got
+ 
+
+ align:start position:0%
+going up and down I'll be done and got
+tired
+
+ align:start position:0%
+tired
+ 
+
+ align:start position:0%
+tired
+therefore the amplitude because small
+
+ align:start position:0%
+therefore the amplitude because small
+ 
+
+ align:start position:0%
+therefore the amplitude because small
+Ernst
+
+ align:start position:0%
+Ernst
+ 
+
+ align:start position:0%
+Ernst
+and modern but it's never zero right
+
+ align:start position:0%
+and modern but it's never zero right
+ 
+
+ align:start position:0%
+and modern but it's never zero right
+it's never a zero okay it's actually
+
+ align:start position:0%
+it's never a zero okay it's actually
+ 
+
+ align:start position:0%
+it's never a zero okay it's actually
+going to be a living down so small I
+
+ align:start position:0%
+going to be a living down so small I
+ 
+
+ align:start position:0%
+going to be a living down so small I
+couldn't see it but it's still
+
+ align:start position:0%
+couldn't see it but it's still
+ 
+
+ align:start position:0%
+couldn't see it but it's still
+oscillating okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finally we actually have also the answer
+
+ align:start position:0%
+finally we actually have also the answer
+ 
+
+ align:start position:0%
+finally we actually have also the answer
+to the original question we post okay so
+
+ align:start position:0%
+to the original question we post okay so
+ 
+
+ align:start position:0%
+to the original question we post okay so
+now you can see that the oscillation
+
+ align:start position:0%
+now you can see that the oscillation
+ 
+
+ align:start position:0%
+now you can see that the oscillation
+frequency is omega okay originally
+
+ align:start position:0%
+frequency is omega okay originally
+ 
+
+ align:start position:0%
+frequency is omega okay originally
+before we introduced the drag force
+
+ align:start position:0%
+before we introduced the drag force
+ 
+
+ align:start position:0%
+before we introduced the drag force
+Omega 0 which is the oscillation
+
+ align:start position:0%
+Omega 0 which is the oscillation
+ 
+
+ align:start position:0%
+Omega 0 which is the oscillation
+frequency it should be like your
+
+ align:start position:0%
+frequency it should be like your
+ 
+
+ align:start position:0%
+frequency it should be like your
+frequency is a square root of 3G over 2l
+
+ align:start position:0%
+frequency is a square root of 3G over 2l
+ 
+
+ align:start position:0%
+frequency is a square root of 3G over 2l
+and you can see that the Omega okay that
+
+ align:start position:0%
+and you can see that the Omega okay that
+ 
+
+ align:start position:0%
+and you can see that the Omega okay that
+the new Omega the oscillation frequency
+
+ align:start position:0%
+the new Omega the oscillation frequency
+ 
+
+ align:start position:0%
+the new Omega the oscillation frequency
+with drag force essentially Omega 0
+
+ align:start position:0%
+with drag force essentially Omega 0
+ 
+
+ align:start position:0%
+with drag force essentially Omega 0
+square square root of this Omega 0
+
+ align:start position:0%
+square square root of this Omega 0
+ 
+
+ align:start position:0%
+square square root of this Omega 0
+square minus gamma squared over 4 so
+
+ align:start position:0%
+square minus gamma squared over 4 so
+ 
+
+ align:start position:0%
+square minus gamma squared over 4 so
+that what this tells she tells us is
+
+ align:start position:0%
+that what this tells she tells us is
+ 
+
+ align:start position:0%
+that what this tells she tells us is
+that this is going to be smaller right
+
+ align:start position:0%
+that this is going to be smaller right
+ 
+
+ align:start position:0%
+that this is going to be smaller right
+because of the drag force okay so that's
+
+ align:start position:0%
+because of the drag force okay so that's
+ 
+
+ align:start position:0%
+because of the drag force okay so that's
+the prediction ok let's do the
+
+ align:start position:0%
+the prediction ok let's do the
+ 
+
+ align:start position:0%
+the prediction ok let's do the
+experiment and see what is going to
+
+ align:start position:0%
+experiment and see what is going to
+ 
+
+ align:start position:0%
+experiment and see what is going to
+happen so let's take a look at this two
+
+ align:start position:0%
+happen so let's take a look at this two
+ 
+
+ align:start position:0%
+happen so let's take a look at this two
+system they have the identical mass
+
+ align:start position:0%
+system they have the identical mass
+ 
+
+ align:start position:0%
+system they have the identical mass
+which our instructor taking her
+
+ align:start position:0%
+which our instructor taking her
+ 
+
+ align:start position:0%
+which our instructor taking her
+instructor H we kept for the prepare
+
+ align:start position:0%
+instructor H we kept for the prepare
+ 
+
+ align:start position:0%
+instructor H we kept for the prepare
+okay they have the same mass even though
+
+ align:start position:0%
+okay they have the same mass even though
+ 
+
+ align:start position:0%
+okay they have the same mass even though
+one is actually do go Tiffany the other
+
+ align:start position:0%
+one is actually do go Tiffany the other
+ 
+
+ align:start position:0%
+one is actually do go Tiffany the other
+one looks normal okay now what I'm going
+
+ align:start position:0%
+one looks normal okay now what I'm going
+ 
+
+ align:start position:0%
+one looks normal okay now what I'm going
+to do is to really try and and see which
+
+ align:start position:0%
+to do is to really try and and see which
+ 
+
+ align:start position:0%
+to do is to really try and and see which
+one is actually isolating faster okay so
+
+ align:start position:0%
+one is actually isolating faster okay so
+ 
+
+ align:start position:0%
+one is actually isolating faster okay so
+let's see I drew this then at the same
+
+ align:start position:0%
+let's see I drew this then at the same
+ 
+
+ align:start position:0%
+let's see I drew this then at the same
+time and you can see that originally
+
+ align:start position:0%
+time and you can see that originally
+ 
+
+ align:start position:0%
+time and you can see that originally
+they seem to be oscillating at the same
+
+ align:start position:0%
+they seem to be oscillating at the same
+ 
+
+ align:start position:0%
+they seem to be oscillating at the same
+frequency but you can see very clearly
+
+ align:start position:0%
+frequency but you can see very clearly
+ 
+
+ align:start position:0%
+frequency but you can see very clearly
+that the one with the head is actually
+
+ align:start position:0%
+that the one with the head is actually
+ 
+
+ align:start position:0%
+that the one with the head is actually
+oscillating slower okay so you can see
+
+ align:start position:0%
+oscillating slower okay so you can see
+ 
+
+ align:start position:0%
+oscillating slower okay so you can see
+that okay seventeen of you actually have
+
+ align:start position:0%
+that okay seventeen of you actually have
+ 
+
+ align:start position:0%
+that okay seventeen of you actually have
+the correct answer gather courage and
+
+ align:start position:0%
+the correct answer gather courage and
+ 
+
+ align:start position:0%
+the correct answer gather courage and
+and the most important thing is that you
+
+ align:start position:0%
+and the most important thing is that you
+ 
+
+ align:start position:0%
+and the most important thing is that you
+can see that this simple mask actually
+
+ align:start position:0%
+can see that this simple mask actually
+ 
+
+ align:start position:0%
+can see that this simple mask actually
+describe and predict what is going to
+
+ align:start position:0%
+describe and predict what is going to
+ 
+
+ align:start position:0%
+describe and predict what is going to
+happen in my little experiment so that
+
+ align:start position:0%
+happen in my little experiment so that
+ 
+
+ align:start position:0%
+happen in my little experiment so that
+is actually really cool and I think it's
+
+ align:start position:0%
+is actually really cool and I think it's
+ 
+
+ align:start position:0%
+is actually really cool and I think it's
+time to take a little break and they
+
+ align:start position:0%
+time to take a little break and they
+ 
+
+ align:start position:0%
+time to take a little break and they
+will come come back and and look at
+
+ align:start position:0%
+will come come back and and look at
+ 
+
+ align:start position:0%
+will come come back and and look at
+other solutions and of course you are
+
+ align:start position:0%
+other solutions and of course you are
+ 
+
+ align:start position:0%
+other solutions and of course you are
+welcome to come to the front to pray
+
+ align:start position:0%
+welcome to come to the front to pray
+ 
+
+ align:start position:0%
+welcome to come to the front to pray
+with those demonstrations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are two small issues which were
+
+ align:start position:0%
+so there are two small issues which were
+ 
+
+ align:start position:0%
+so there are two small issues which were
+raised by during the break so the first
+
+ align:start position:0%
+raised by during the break so the first
+ 
+
+ align:start position:0%
+raised by during the break so the first
+one is that if you actually calculate
+
+ align:start position:0%
+one is that if you actually calculate
+ 
+
+ align:start position:0%
+one is that if you actually calculate
+the torque okay
+
+ align:start position:0%
+the torque okay
+ 
+
+ align:start position:0%
+the torque okay
+from this fund this equation so I made a
+
+ align:start position:0%
+from this fund this equation so I made a
+ 
+
+ align:start position:0%
+from this fund this equation so I made a
+mistake
+
+ align:start position:0%
+mistake
+ 
+
+ align:start position:0%
+mistake
+the R vector should be actually pointing
+
+ align:start position:0%
+the R vector should be actually pointing
+ 
+
+ align:start position:0%
+the R vector should be actually pointing
+from the nail to the center of mass okay
+
+ align:start position:0%
+from the nail to the center of mass okay
+ 
+
+ align:start position:0%
+from the nail to the center of mass okay
+so I think that's a trivial a mistake so
+
+ align:start position:0%
+so I think that's a trivial a mistake so
+ 
+
+ align:start position:0%
+so I think that's a trivial a mistake so
+if you do this okay
+
+ align:start position:0%
+if you do this okay
+ 
+
+ align:start position:0%
+if you do this okay
+then you can get you a care today the
+
+ align:start position:0%
+then you can get you a care today the
+ 
+
+ align:start position:0%
+then you can get you a care today the
+tau equal to R cross F then you actually
+
+ align:start position:0%
+tau equal to R cross F then you actually
+ 
+
+ align:start position:0%
+tau equal to R cross F then you actually
+get this minus sign okay so so if I if I
+
+ align:start position:0%
+get this minus sign okay so so if I if I
+ 
+
+ align:start position:0%
+get this minus sign okay so so if I if I
+make a mistake and pointing toward the
+
+ align:start position:0%
+make a mistake and pointing toward the
+ 
+
+ align:start position:0%
+make a mistake and pointing toward the
+nail okay then you will get no minus
+
+ align:start position:0%
+nail okay then you will get no minus
+ 
+
+ align:start position:0%
+nail okay then you will get no minus
+sign okay they're not really work okay
+
+ align:start position:0%
+sign okay they're not really work okay
+ 
+
+ align:start position:0%
+sign okay they're not really work okay
+so so very good I'm very happy that you
+
+ align:start position:0%
+so so very good I'm very happy that you
+ 
+
+ align:start position:0%
+so so very good I'm very happy that you
+are actually paying very much attention
+
+ align:start position:0%
+are actually paying very much attention
+ 
+
+ align:start position:0%
+are actually paying very much attention
+to capture those the the second issue is
+
+ align:start position:0%
+to capture those the the second issue is
+ 
+
+ align:start position:0%
+to capture those the the second issue is
+that okay so now I'm saying that okay
+
+ align:start position:0%
+that okay so now I'm saying that okay
+ 
+
+ align:start position:0%
+that okay so now I'm saying that okay
+now I have the solution in the complex
+
+ align:start position:0%
+now I have the solution in the complex
+ 
+
+ align:start position:0%
+now I have the solution in the complex
+form format so I can have a G+ and I
+
+ align:start position:0%
+form format so I can have a G+ and I
+ 
+
+ align:start position:0%
+form format so I can have a G+ and I
+have the Z - okay
+
+ align:start position:0%
+have the Z - okay
+ 
+
+ align:start position:0%
+have the Z - okay
+and then I would like to go to the real
+
+ align:start position:0%
+and then I would like to go to the real
+ 
+
+ align:start position:0%
+and then I would like to go to the real
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+right because imaginary thing is
+
+ align:start position:0%
+right because imaginary thing is
+ 
+
+ align:start position:0%
+right because imaginary thing is
+actually hidden in some kind of you know
+
+ align:start position:0%
+actually hidden in some kind of you know
+ 
+
+ align:start position:0%
+actually hidden in some kind of you know
+motion in the actual dimension and etc I
+
+ align:start position:0%
+motion in the actual dimension and etc I
+ 
+
+ align:start position:0%
+motion in the actual dimension and etc I
+would like to go back to reality okay
+
+ align:start position:0%
+would like to go back to reality okay
+ 
+
+ align:start position:0%
+would like to go back to reality okay
+and and what I said in the class is that
+
+ align:start position:0%
+and and what I said in the class is that
+ 
+
+ align:start position:0%
+and and what I said in the class is that
+I take a real part of one of the
+
+ align:start position:0%
+I take a real part of one of the
+ 
+
+ align:start position:0%
+I take a real part of one of the
+solution and I can also take the real
+
+ align:start position:0%
+solution and I can also take the real
+ 
+
+ align:start position:0%
+solution and I can also take the real
+part of I times one of the solution but
+
+ align:start position:0%
+part of I times one of the solution but
+ 
+
+ align:start position:0%
+part of I times one of the solution but
+of course you can also do this by doing
+
+ align:start position:0%
+of course you can also do this by doing
+ 
+
+ align:start position:0%
+of course you can also do this by doing
+a linear combination of the solution
+
+ align:start position:0%
+a linear combination of the solution
+ 
+
+ align:start position:0%
+a linear combination of the solution
+right as we actually discussed last time
+
+ align:start position:0%
+right as we actually discussed last time
+ 
+
+ align:start position:0%
+right as we actually discussed last time
+linear combination of the solutions is
+
+ align:start position:0%
+linear combination of the solutions is
+ 
+
+ align:start position:0%
+linear combination of the solutions is
+also a solution to this the same
+
+ align:start position:0%
+also a solution to this the same
+ 
+
+ align:start position:0%
+also a solution to this the same
+equation of motion right since this one
+
+ align:start position:0%
+equation of motion right since this one
+ 
+
+ align:start position:0%
+equation of motion right since this one
+is a linear therefore what I actually do
+
+ align:start position:0%
+is a linear therefore what I actually do
+ 
+
+ align:start position:0%
+is a linear therefore what I actually do
+is actually to to sum the two solution
+
+ align:start position:0%
+is actually to to sum the two solution
+ 
+
+ align:start position:0%
+is actually to to sum the two solution
+the press and D - and / - or actually I
+
+ align:start position:0%
+the press and D - and / - or actually I
+ 
+
+ align:start position:0%
+the press and D - and / - or actually I
+attended to the two minus I over 2 times
+
+ align:start position:0%
+attended to the two minus I over 2 times
+ 
+
+ align:start position:0%
+attended to the two minus I over 2 times
+the price - the the - okay then I can
+
+ align:start position:0%
+the price - the the - okay then I can
+ 
+
+ align:start position:0%
+the price - the the - okay then I can
+also extract this sign
+
+ align:start position:0%
+also extract this sign
+ 
+
+ align:start position:0%
+also extract this sign
+here okay so that is that should be the
+
+ align:start position:0%
+here okay so that is that should be the
+ 
+
+ align:start position:0%
+here okay so that is that should be the
+correct explanation of the two solution
+
+ align:start position:0%
+correct explanation of the two solution
+ 
+
+ align:start position:0%
+correct explanation of the two solution
+in real axis okay any questions so far
+
+ align:start position:0%
+in real axis okay any questions so far
+ 
+
+ align:start position:0%
+in real axis okay any questions so far
+thank you very much for protection
+
+ align:start position:0%
+thank you very much for protection
+ 
+
+ align:start position:0%
+thank you very much for protection
+during those okay so now you can see
+
+ align:start position:0%
+during those okay so now you can see
+ 
+
+ align:start position:0%
+during those okay so now you can see
+that we have been discussing the
+
+ align:start position:0%
+that we have been discussing the
+ 
+
+ align:start position:0%
+that we have been discussing the
+equation of motion of this functional
+
+ align:start position:0%
+equation of motion of this functional
+ 
+
+ align:start position:0%
+equation of motion of this functional
+form and the one thing which is really
+
+ align:start position:0%
+form and the one thing which is really
+ 
+
+ align:start position:0%
+form and the one thing which is really
+interesting is that the solution when we
+
+ align:start position:0%
+interesting is that the solution when we
+ 
+
+ align:start position:0%
+interesting is that the solution when we
+take small track force limit actually we
+
+ align:start position:0%
+take small track force limit actually we
+ 
+
+ align:start position:0%
+take small track force limit actually we
+arrive a beautiful solution looks like
+
+ align:start position:0%
+arrive a beautiful solution looks like
+ 
+
+ align:start position:0%
+arrive a beautiful solution looks like
+this a exponential minus gamma over 2t
+
+ align:start position:0%
+this a exponential minus gamma over 2t
+ 
+
+ align:start position:0%
+this a exponential minus gamma over 2t
+cosine Omega T plus Phi
+
+ align:start position:0%
+cosine Omega T plus Phi
+ 
+
+ align:start position:0%
+cosine Omega T plus Phi
+that I should predict the oscillation
+
+ align:start position:0%
+that I should predict the oscillation
+ 
+
+ align:start position:0%
+that I should predict the oscillation
+okay at the same time he also says that
+
+ align:start position:0%
+okay at the same time he also says that
+ 
+
+ align:start position:0%
+okay at the same time he also says that
+the amplitude is actually going to drop
+
+ align:start position:0%
+the amplitude is actually going to drop
+ 
+
+ align:start position:0%
+the amplitude is actually going to drop
+exponentially but never zero okay
+
+ align:start position:0%
+exponentially but never zero okay
+ 
+
+ align:start position:0%
+exponentially but never zero okay
+finally we also know that this solution
+
+ align:start position:0%
+finally we also know that this solution
+ 
+
+ align:start position:0%
+finally we also know that this solution
+actually tells us that if we have a
+
+ align:start position:0%
+actually tells us that if we have a
+ 
+
+ align:start position:0%
+actually tells us that if we have a
+spring mass system oscillating up and
+
+ align:start position:0%
+spring mass system oscillating up and
+ 
+
+ align:start position:0%
+spring mass system oscillating up and
+down if we have a rod like what we
+
+ align:start position:0%
+down if we have a rod like what we
+ 
+
+ align:start position:0%
+down if we have a rod like what we
+actually solving in in a class this
+
+ align:start position:0%
+actually solving in in a class this
+ 
+
+ align:start position:0%
+actually solving in in a class this
+object is going to pass through zero the
+
+ align:start position:0%
+object is going to pass through zero the
+ 
+
+ align:start position:0%
+object is going to pass through zero the
+equilibrium position infinite number of
+
+ align:start position:0%
+equilibrium position infinite number of
+ 
+
+ align:start position:0%
+equilibrium position infinite number of
+times right because the the cosine is
+
+ align:start position:0%
+times right because the the cosine is
+ 
+
+ align:start position:0%
+times right because the the cosine is
+always there therefore although the mp2
+
+ align:start position:0%
+always there therefore although the mp2
+ 
+
+ align:start position:0%
+always there therefore although the mp2
+become very small they still oscillating
+
+ align:start position:0%
+become very small they still oscillating
+ 
+
+ align:start position:0%
+become very small they still oscillating
+forever until the end of the universe
+
+ align:start position:0%
+forever until the end of the universe
+ 
+
+ align:start position:0%
+forever until the end of the universe
+okay all right so that's actually what
+
+ align:start position:0%
+okay all right so that's actually what
+ 
+
+ align:start position:0%
+okay all right so that's actually what
+we have learned and also one thing which
+
+ align:start position:0%
+we have learned and also one thing which
+ 
+
+ align:start position:0%
+we have learned and also one thing which
+we learned that time is that simple
+
+ align:start position:0%
+we learned that time is that simple
+ 
+
+ align:start position:0%
+we learned that time is that simple
+harmonic motion okay like this one which
+
+ align:start position:0%
+harmonic motion okay like this one which
+ 
+
+ align:start position:0%
+harmonic motion okay like this one which
+was shown here or this one which is a
+
+ align:start position:0%
+was shown here or this one which is a
+ 
+
+ align:start position:0%
+was shown here or this one which is a
+mass oscillating back and forth on the
+
+ align:start position:0%
+mass oscillating back and forth on the
+ 
+
+ align:start position:0%
+mass oscillating back and forth on the
+track essentially just a projection of a
+
+ align:start position:0%
+track essentially just a projection of a
+ 
+
+ align:start position:0%
+track essentially just a projection of a
+circular motion right in the complex
+
+ align:start position:0%
+circular motion right in the complex
+ 
+
+ align:start position:0%
+circular motion right in the complex
+plane okay and what we are really seeing
+
+ align:start position:0%
+plane okay and what we are really seeing
+ 
+
+ align:start position:0%
+plane okay and what we are really seeing
+here in front of in front of you is
+
+ align:start position:0%
+here in front of in front of you is
+ 
+
+ align:start position:0%
+here in front of in front of you is
+actually a projection to the real axis
+
+ align:start position:0%
+actually a projection to the real axis
+ 
+
+ align:start position:0%
+actually a projection to the real axis
+okay so that's actually really
+
+ align:start position:0%
+okay so that's actually really
+ 
+
+ align:start position:0%
+okay so that's actually really
+remarkable
+
+ align:start position:0%
+remarkable
+ 
+
+ align:start position:0%
+remarkable
+result and the beautiful picture and of
+
+ align:start position:0%
+result and the beautiful picture and of
+ 
+
+ align:start position:0%
+result and the beautiful picture and of
+course we can actually also practice the
+
+ align:start position:0%
+course we can actually also practice the
+ 
+
+ align:start position:0%
+course we can actually also practice the
+solution with Tempe so what is actually
+
+ align:start position:0%
+solution with Tempe so what is actually
+ 
+
+ align:start position:0%
+solution with Tempe so what is actually
+the picture in this language in in this
+
+ align:start position:0%
+the picture in this language in in this
+ 
+
+ align:start position:0%
+the picture in this language in in this
+exactly the same language if we actually
+
+ align:start position:0%
+exactly the same language if we actually
+ 
+
+ align:start position:0%
+exactly the same language if we actually
+follow the locus and basically what you
+
+ align:start position:0%
+follow the locus and basically what you
+ 
+
+ align:start position:0%
+follow the locus and basically what you
+are going to see is that this thing as
+
+ align:start position:0%
+are going to see is that this thing as
+ 
+
+ align:start position:0%
+are going to see is that this thing as
+you spiral okay and the amplitude is
+
+ align:start position:0%
+you spiral okay and the amplitude is
+ 
+
+ align:start position:0%
+you spiral okay and the amplitude is
+actually getting smaller and smaller and
+
+ align:start position:0%
+actually getting smaller and smaller and
+ 
+
+ align:start position:0%
+actually getting smaller and smaller and
+they sucked into this black hole in the
+
+ align:start position:0%
+they sucked into this black hole in the
+ 
+
+ align:start position:0%
+they sucked into this black hole in the
+zero zero okay so you can see that now
+
+ align:start position:0%
+zero zero okay so you can see that now
+ 
+
+ align:start position:0%
+zero zero okay so you can see that now
+the the the picture looks as if there is
+
+ align:start position:0%
+the the the picture looks as if there is
+ 
+
+ align:start position:0%
+the the the picture looks as if there is
+something really rotating in the complex
+
+ align:start position:0%
+something really rotating in the complex
+ 
+
+ align:start position:0%
+something really rotating in the complex
+plane and they essentially approaching
+
+ align:start position:0%
+plane and they essentially approaching
+ 
+
+ align:start position:0%
+plane and they essentially approaching
+zero because the amplitude is casually
+
+ align:start position:0%
+zero because the amplitude is casually
+ 
+
+ align:start position:0%
+zero because the amplitude is casually
+getting smaller and smaller but this
+
+ align:start position:0%
+getting smaller and smaller but this
+ 
+
+ align:start position:0%
+getting smaller and smaller but this
+whole thing is still rotating okay okay
+
+ align:start position:0%
+whole thing is still rotating okay okay
+ 
+
+ align:start position:0%
+whole thing is still rotating okay okay
+that's pretty nice
+
+ align:start position:0%
+that's pretty nice
+ 
+
+ align:start position:0%
+that's pretty nice
+alright so now this is actually a
+
+ align:start position:0%
+alright so now this is actually a
+ 
+
+ align:start position:0%
+alright so now this is actually a
+special case when we actually assume
+
+ align:start position:0%
+special case when we actually assume
+ 
+
+ align:start position:0%
+special case when we actually assume
+that gamma is actually pretty small so
+
+ align:start position:0%
+that gamma is actually pretty small so
+ 
+
+ align:start position:0%
+that gamma is actually pretty small so
+you have very small tract force okay so
+
+ align:start position:0%
+you have very small tract force okay so
+ 
+
+ align:start position:0%
+you have very small tract force okay so
+that's actually check what will happen
+
+ align:start position:0%
+that's actually check what will happen
+ 
+
+ align:start position:0%
+that's actually check what will happen
+if I now start to increase the drag
+
+ align:start position:0%
+if I now start to increase the drag
+ 
+
+ align:start position:0%
+if I now start to increase the drag
+force make this hat larger larger and
+
+ align:start position:0%
+force make this hat larger larger and
+ 
+
+ align:start position:0%
+force make this hat larger larger and
+larger okay introducing more and more
+
+ align:start position:0%
+larger okay introducing more and more
+ 
+
+ align:start position:0%
+larger okay introducing more and more
+track okay what is going to happen okay
+
+ align:start position:0%
+track okay what is going to happen okay
+ 
+
+ align:start position:0%
+track okay what is going to happen okay
+so now I consider the situation the
+
+ align:start position:0%
+so now I consider the situation the
+ 
+
+ align:start position:0%
+so now I consider the situation the
+second situation Omega 0 square equal to
+
+ align:start position:0%
+second situation Omega 0 square equal to
+ 
+
+ align:start position:0%
+second situation Omega 0 square equal to
+gamma square over 4 okay okay so when
+
+ align:start position:0%
+gamma square over 4 okay okay so when
+ 
+
+ align:start position:0%
+gamma square over 4 okay okay so when
+when the gamma is very small what we see
+
+ align:start position:0%
+when the gamma is very small what we see
+ 
+
+ align:start position:0%
+when the gamma is very small what we see
+is that this is actually under damped
+
+ align:start position:0%
+is that this is actually under damped
+ 
+
+ align:start position:0%
+is that this is actually under damped
+right so so the damping is really small
+
+ align:start position:0%
+right so so the damping is really small
+ 
+
+ align:start position:0%
+right so so the damping is really small
+but if I increase the gamma to a
+
+ align:start position:0%
+but if I increase the gamma to a
+ 
+
+ align:start position:0%
+but if I increase the gamma to a
+critical value now Omega 0 square happen
+
+ align:start position:0%
+critical value now Omega 0 square happen
+ 
+
+ align:start position:0%
+critical value now Omega 0 square happen
+to be equal to gamma square over 4 okay
+
+ align:start position:0%
+to be equal to gamma square over 4 okay
+ 
+
+ align:start position:0%
+to be equal to gamma square over 4 okay
+I call this critically
+
+ align:start position:0%
+I call this critically
+ 
+
+ align:start position:0%
+I call this critically
+damn oscillate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what does that mean that means Omega
+
+ align:start position:0%
+so what does that mean that means Omega
+ 
+
+ align:start position:0%
+so what does that mean that means Omega
+is equal to zero
+
+ align:start position:0%
+is equal to zero
+ 
+
+ align:start position:0%
+is equal to zero
+you see this is our definition of Omega
+
+ align:start position:0%
+you see this is our definition of Omega
+ 
+
+ align:start position:0%
+you see this is our definition of Omega
+right if Omega zero equal square equal
+
+ align:start position:0%
+right if Omega zero equal square equal
+ 
+
+ align:start position:0%
+right if Omega zero equal square equal
+to gamma square over 4 then Omega is
+
+ align:start position:0%
+to gamma square over 4 then Omega is
+ 
+
+ align:start position:0%
+to gamma square over 4 then Omega is
+equal to zero
+
+ align:start position:0%
+equal to zero
+ 
+
+ align:start position:0%
+equal to zero
+the artisans with the critical moment
+
+ align:start position:0%
+the artisans with the critical moment
+ 
+
+ align:start position:0%
+the artisans with the critical moment
+the cistern stop oscillating okay so it
+
+ align:start position:0%
+the cistern stop oscillating okay so it
+ 
+
+ align:start position:0%
+the cistern stop oscillating okay so it
+is not absolutely any more okay so now I
+
+ align:start position:0%
+is not absolutely any more okay so now I
+ 
+
+ align:start position:0%
+is not absolutely any more okay so now I
+can actually start from from the
+
+ align:start position:0%
+can actually start from from the
+ 
+
+ align:start position:0%
+can actually start from from the
+solution where I obtained from one one
+
+ align:start position:0%
+solution where I obtained from one one
+ 
+
+ align:start position:0%
+solution where I obtained from one one
+okay and I can actually how you make
+
+ align:start position:0%
+okay and I can actually how you make
+ 
+
+ align:start position:0%
+okay and I can actually how you make
+make use of this this two solution
+
+ align:start position:0%
+make use of this this two solution
+ 
+
+ align:start position:0%
+make use of this this two solution
+cheetara's in the city minus theta plus
+
+ align:start position:0%
+cheetara's in the city minus theta plus
+ 
+
+ align:start position:0%
+cheetara's in the city minus theta plus
+P will be equal to exponential minus
+
+ align:start position:0%
+P will be equal to exponential minus
+ 
+
+ align:start position:0%
+P will be equal to exponential minus
+gamma over 2t cosine Omega T when Omega
+
+ align:start position:0%
+gamma over 2t cosine Omega T when Omega
+ 
+
+ align:start position:0%
+gamma over 2t cosine Omega T when Omega
+goes to 0 okay what is going to happen
+
+ align:start position:0%
+goes to 0 okay what is going to happen
+ 
+
+ align:start position:0%
+goes to 0 okay what is going to happen
+is that this is actually becoming which
+
+ align:start position:0%
+is that this is actually becoming which
+ 
+
+ align:start position:0%
+is that this is actually becoming which
+value anybody know if Omega C 0 what is
+
+ align:start position:0%
+value anybody know if Omega C 0 what is
+ 
+
+ align:start position:0%
+value anybody know if Omega C 0 what is
+going to happen one yeah okay one right
+
+ align:start position:0%
+going to happen one yeah okay one right
+ 
+
+ align:start position:0%
+going to happen one yeah okay one right
+so that will give me exponential minus
+
+ align:start position:0%
+so that will give me exponential minus
+ 
+
+ align:start position:0%
+so that will give me exponential minus
+gamma over 2t see top minus T okay I can
+
+ align:start position:0%
+gamma over 2t see top minus T okay I can
+ 
+
+ align:start position:0%
+gamma over 2t see top minus T okay I can
+do the same trick and see what will
+
+ align:start position:0%
+do the same trick and see what will
+ 
+
+ align:start position:0%
+do the same trick and see what will
+happen so I take sin theta minus T okay
+
+ align:start position:0%
+happen so I take sin theta minus T okay
+ 
+
+ align:start position:0%
+happen so I take sin theta minus T okay
+which is as you obtained it from the
+
+ align:start position:0%
+which is as you obtained it from the
+ 
+
+ align:start position:0%
+which is as you obtained it from the
+exercise number one when we discuss on
+
+ align:start position:0%
+exercise number one when we discuss on
+ 
+
+ align:start position:0%
+exercise number one when we discuss on
+the template system then you in case you
+
+ align:start position:0%
+the template system then you in case you
+ 
+
+ align:start position:0%
+the template system then you in case you
+get exponential minus gamma over 2t sine
+
+ align:start position:0%
+get exponential minus gamma over 2t sine
+ 
+
+ align:start position:0%
+get exponential minus gamma over 2t sine
+Omega T Omega goes to 0 I should I get 0
+
+ align:start position:0%
+Omega T Omega goes to 0 I should I get 0
+ 
+
+ align:start position:0%
+Omega T Omega goes to 0 I should I get 0
+it's time okay so that don't really
+
+ align:start position:0%
+it's time okay so that don't really
+ 
+
+ align:start position:0%
+it's time okay so that don't really
+right because if I have a solution which
+
+ align:start position:0%
+right because if I have a solution which
+ 
+
+ align:start position:0%
+right because if I have a solution which
+is zero then it's not describing
+
+ align:start position:0%
+is zero then it's not describing
+ 
+
+ align:start position:0%
+is zero then it's not describing
+anything right I can always add zero to
+
+ align:start position:0%
+anything right I can always add zero to
+ 
+
+ align:start position:0%
+anything right I can always add zero to
+to the solution but that help you okay
+
+ align:start position:0%
+to the solution but that help you okay
+ 
+
+ align:start position:0%
+to the solution but that help you okay
+so instead of taking the limit of this
+
+ align:start position:0%
+so instead of taking the limit of this
+ 
+
+ align:start position:0%
+so instead of taking the limit of this
+this function actually we choose to
+
+ align:start position:0%
+this function actually we choose to
+ 
+
+ align:start position:0%
+this function actually we choose to
+actually to Sita minus T divided by
+
+ align:start position:0%
+actually to Sita minus T divided by
+ 
+
+ align:start position:0%
+actually to Sita minus T divided by
+Omega and that we actually make this
+
+ align:start position:0%
+Omega and that we actually make this
+ 
+
+ align:start position:0%
+Omega and that we actually make this
+approaching Omega approaching zero then
+
+ align:start position:0%
+approaching Omega approaching zero then
+ 
+
+ align:start position:0%
+approaching Omega approaching zero then
+basically I get exponential minus gamma
+
+ align:start position:0%
+basically I get exponential minus gamma
+ 
+
+ align:start position:0%
+basically I get exponential minus gamma
+over 2t sine Omega T divided by Omega
+
+ align:start position:0%
+over 2t sine Omega T divided by Omega
+ 
+
+ align:start position:0%
+over 2t sine Omega T divided by Omega
+okay if I have this approaching Omega
+
+ align:start position:0%
+okay if I have this approaching Omega
+ 
+
+ align:start position:0%
+okay if I have this approaching Omega
+approaching to 0 and this is HD roughly
+
+ align:start position:0%
+approaching to 0 and this is HD roughly
+ 
+
+ align:start position:0%
+approaching to 0 and this is HD roughly
+just explanation of minus gamma over 2t
+
+ align:start position:0%
+just explanation of minus gamma over 2t
+ 
+
+ align:start position:0%
+just explanation of minus gamma over 2t
+Omega T Omega and this is actually
+
+ align:start position:0%
+Omega T Omega and this is actually
+ 
+
+ align:start position:0%
+Omega T Omega and this is actually
+keeping you ki times exponential minus
+
+ align:start position:0%
+keeping you ki times exponential minus
+ 
+
+ align:start position:0%
+keeping you ki times exponential minus
+gamma over 2t any questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at this one yeah so it should be okay
+
+ align:start position:0%
+at this one yeah so it should be okay
+ 
+
+ align:start position:0%
+at this one yeah so it should be okay
+yeah yes this is a negative sign
+
+ align:start position:0%
+yeah yes this is a negative sign
+ 
+
+ align:start position:0%
+yeah yes this is a negative sign
+yes okay any other questions okay so you
+
+ align:start position:0%
+yes okay any other questions okay so you
+ 
+
+ align:start position:0%
+yes okay any other questions okay so you
+can see that now I arrived to solution
+
+ align:start position:0%
+can see that now I arrived to solution
+ 
+
+ align:start position:0%
+can see that now I arrived to solution
+one is actually proportional to
+
+ align:start position:0%
+one is actually proportional to
+ 
+
+ align:start position:0%
+one is actually proportional to
+exponential minus gamma over 2t the
+
+ align:start position:0%
+exponential minus gamma over 2t the
+ 
+
+ align:start position:0%
+exponential minus gamma over 2t the
+other one is actually proportional to T
+
+ align:start position:0%
+other one is actually proportional to T
+ 
+
+ align:start position:0%
+other one is actually proportional to T
+times exponential minus gamma over 2t
+
+ align:start position:0%
+times exponential minus gamma over 2t
+ 
+
+ align:start position:0%
+times exponential minus gamma over 2t
+okay so you can see that the cosine or
+
+ align:start position:0%
+okay so you can see that the cosine or
+ 
+
+ align:start position:0%
+okay so you can see that the cosine or
+sine turn disappeared right so that
+
+ align:start position:0%
+sine turn disappeared right so that
+ 
+
+ align:start position:0%
+sine turn disappeared right so that
+means you were never oscillating okay so
+
+ align:start position:0%
+means you were never oscillating okay so
+ 
+
+ align:start position:0%
+means you were never oscillating okay so
+this is actually what we see in this
+
+ align:start position:0%
+this is actually what we see in this
+ 
+
+ align:start position:0%
+this is actually what we see in this
+slide this so-called critically damped
+
+ align:start position:0%
+slide this so-called critically damped
+ 
+
+ align:start position:0%
+slide this so-called critically damped
+okay when actually Omega zero squared is
+
+ align:start position:0%
+okay when actually Omega zero squared is
+ 
+
+ align:start position:0%
+okay when actually Omega zero squared is
+equal to gamma square over 4 and you can
+
+ align:start position:0%
+equal to gamma square over 4 and you can
+ 
+
+ align:start position:0%
+equal to gamma square over 4 and you can
+see that what is going to happen is that
+
+ align:start position:0%
+see that what is going to happen is that
+ 
+
+ align:start position:0%
+see that what is going to happen is that
+this mass okay or this rod is going to
+
+ align:start position:0%
+this mass okay or this rod is going to
+ 
+
+ align:start position:0%
+this mass okay or this rod is going to
+pass 0 only one time at most okay and it
+
+ align:start position:0%
+pass 0 only one time at most okay and it
+ 
+
+ align:start position:0%
+pass 0 only one time at most okay and it
+could actually never pass 0 if you
+
+ align:start position:0%
+could actually never pass 0 if you
+ 
+
+ align:start position:0%
+could actually never pass 0 if you
+actually set up the initial condition
+
+ align:start position:0%
+actually set up the initial condition
+ 
+
+ align:start position:0%
+actually set up the initial condition
+correcting okay so so one thing which I
+
+ align:start position:0%
+correcting okay so so one thing which I
+ 
+
+ align:start position:0%
+correcting okay so so one thing which I
+can do is I shoot this mass really
+
+ align:start position:0%
+can do is I shoot this mass really
+ 
+
+ align:start position:0%
+can do is I shoot this mass really
+really very forcefully so that I have a
+
+ align:start position:0%
+really very forcefully so that I have a
+ 
+
+ align:start position:0%
+really very forcefully so that I have a
+very large initial velocity and what it
+
+ align:start position:0%
+very large initial velocity and what it
+ 
+
+ align:start position:0%
+very large initial velocity and what it
+really is going to do like the
+
+ align:start position:0%
+really is going to do like the
+ 
+
+ align:start position:0%
+really is going to do like the
+right-hand side diagram
+
+ align:start position:0%
+right-hand side diagram
+ 
+
+ align:start position:0%
+right-hand side diagram
+oh you will overshoot the row a bit then
+
+ align:start position:0%
+oh you will overshoot the row a bit then
+ 
+
+ align:start position:0%
+oh you will overshoot the row a bit then
+close back it almost like exponentially
+
+ align:start position:0%
+close back it almost like exponentially
+ 
+
+ align:start position:0%
+close back it almost like exponentially
+okay so at most you can only pass to
+
+ align:start position:0%
+okay so at most you can only pass to
+ 
+
+ align:start position:0%
+okay so at most you can only pass to
+zero one time if you do this kind of
+
+ align:start position:0%
+zero one time if you do this kind of
+ 
+
+ align:start position:0%
+zero one time if you do this kind of
+initial condition okay so that is
+
+ align:start position:0%
+initial condition okay so that is
+ 
+
+ align:start position:0%
+initial condition okay so that is
+actually pretty interesting and there
+
+ align:start position:0%
+actually pretty interesting and there
+ 
+
+ align:start position:0%
+actually pretty interesting and there
+are practical application of this poncho
+
+ align:start position:0%
+are practical application of this poncho
+ 
+
+ align:start position:0%
+are practical application of this poncho
+it is a solution actually so for example
+
+ align:start position:0%
+it is a solution actually so for example
+ 
+
+ align:start position:0%
+it is a solution actually so for example
+we have the door closed
+
+ align:start position:0%
+we have the door closed
+ 
+
+ align:start position:0%
+we have the door closed
+so it's also here right the toad clothes
+
+ align:start position:0%
+so it's also here right the toad clothes
+ 
+
+ align:start position:0%
+so it's also here right the toad clothes
+you would like to have the tour go back
+
+ align:start position:0%
+you would like to have the tour go back
+ 
+
+ align:start position:0%
+you would like to have the tour go back
+to the original clothes the mode the
+
+ align:start position:0%
+to the original clothes the mode the
+ 
+
+ align:start position:0%
+to the original clothes the mode the
+position of equilibrium position is
+
+ align:start position:0%
+position of equilibrium position is
+ 
+
+ align:start position:0%
+position of equilibrium position is
+really fast ok so what you can do is
+
+ align:start position:0%
+really fast ok so what you can do is
+ 
+
+ align:start position:0%
+really fast ok so what you can do is
+really design this toad course so that
+
+ align:start position:0%
+really design this toad course so that
+ 
+
+ align:start position:0%
+really design this toad course so that
+issue is actually match with critical
+
+ align:start position:0%
+issue is actually match with critical
+ 
+
+ align:start position:0%
+issue is actually match with critical
+tempter situation ok a good condition so
+
+ align:start position:0%
+tempter situation ok a good condition so
+ 
+
+ align:start position:0%
+tempter situation ok a good condition so
+that actually you go back to zero really
+
+ align:start position:0%
+that actually you go back to zero really
+ 
+
+ align:start position:0%
+that actually you go back to zero really
+quick ok any questions ok so now what we
+
+ align:start position:0%
+quick ok any questions ok so now what we
+ 
+
+ align:start position:0%
+quick ok any questions ok so now what we
+could do is that instead of having a
+
+ align:start position:0%
+could do is that instead of having a
+ 
+
+ align:start position:0%
+could do is that instead of having a
+very small drag force were worse a
+
+ align:start position:0%
+very small drag force were worse a
+ 
+
+ align:start position:0%
+very small drag force were worse a
+slightly larger track for so that
+
+ align:start position:0%
+slightly larger track for so that
+ 
+
+ align:start position:0%
+slightly larger track for so that
+actually reach critical tempt situation
+
+ align:start position:0%
+actually reach critical tempt situation
+ 
+
+ align:start position:0%
+actually reach critical tempt situation
+what we could do is that we put the
+
+ align:start position:0%
+what we could do is that we put the
+ 
+
+ align:start position:0%
+what we could do is that we put the
+whole system into water right the end of
+
+ align:start position:0%
+whole system into water right the end of
+ 
+
+ align:start position:0%
+whole system into water right the end of
+track force will be very big okay and we
+
+ align:start position:0%
+track force will be very big okay and we
+ 
+
+ align:start position:0%
+track force will be very big okay and we
+would like to see what is going to
+
+ align:start position:0%
+would like to see what is going to
+ 
+
+ align:start position:0%
+would like to see what is going to
+happen ok so in this case is the third
+
+ align:start position:0%
+happen ok so in this case is the third
+ 
+
+ align:start position:0%
+happen ok so in this case is the third
+situation ok the third situation is that
+
+ align:start position:0%
+situation ok the third situation is that
+ 
+
+ align:start position:0%
+situation ok the third situation is that
+Omega 0 square is actually smoother than
+
+ align:start position:0%
+Omega 0 square is actually smoother than
+ 
+
+ align:start position:0%
+Omega 0 square is actually smoother than
+gamma square over 4 so you have huge
+
+ align:start position:0%
+gamma square over 4 so you have huge
+ 
+
+ align:start position:0%
+gamma square over 4 so you have huge
+drag force okay so that will give you a
+
+ align:start position:0%
+drag force okay so that will give you a
+ 
+
+ align:start position:0%
+drag force okay so that will give you a
+situation which is called over damped
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscillator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I have again alpha is equal to I
+
+ align:start position:0%
+now I have again alpha is equal to I
+ 
+
+ align:start position:0%
+now I have again alpha is equal to I
+gamma over 2
+
+ align:start position:0%
+gamma over 2
+ 
+
+ align:start position:0%
+gamma over 2
+okay price minus square root of Omega 0
+
+ align:start position:0%
+okay price minus square root of Omega 0
+ 
+
+ align:start position:0%
+okay price minus square root of Omega 0
+square minus gamma square over 4 right
+
+ align:start position:0%
+square minus gamma square over 4 right
+ 
+
+ align:start position:0%
+square minus gamma square over 4 right
+I'm just copying from here okay and that
+
+ align:start position:0%
+I'm just copying from here okay and that
+ 
+
+ align:start position:0%
+I'm just copying from here okay and that
+will be equal to I I can take out the I
+
+ align:start position:0%
+will be equal to I I can take out the I
+ 
+
+ align:start position:0%
+will be equal to I I can take out the I
+ok gamma over 2 plus minus square root
+
+ align:start position:0%
+ok gamma over 2 plus minus square root
+ 
+
+ align:start position:0%
+ok gamma over 2 plus minus square root
+of gamma squared over 4 minus Omega 0
+
+ align:start position:0%
+of gamma squared over 4 minus Omega 0
+ 
+
+ align:start position:0%
+of gamma squared over 4 minus Omega 0
+square now I can easily define gamma
+
+ align:start position:0%
+square now I can easily define gamma
+ 
+
+ align:start position:0%
+square now I can easily define gamma
+plus minus equal to gamma over 2 plus
+
+ align:start position:0%
+plus minus equal to gamma over 2 plus
+ 
+
+ align:start position:0%
+plus minus equal to gamma over 2 plus
+minus square root of gamma square over 4
+
+ align:start position:0%
+minus square root of gamma square over 4
+ 
+
+ align:start position:0%
+minus square root of gamma square over 4
+minus Omega 0 square ok then basically
+
+ align:start position:0%
+minus Omega 0 square ok then basically
+ 
+
+ align:start position:0%
+minus Omega 0 square ok then basically
+the solution okay I this is actually now
+
+ align:start position:0%
+the solution okay I this is actually now
+ 
+
+ align:start position:0%
+the solution okay I this is actually now
+I already have the solution so basically
+
+ align:start position:0%
+I already have the solution so basically
+ 
+
+ align:start position:0%
+I already have the solution so basically
+the two solution will be looking like
+
+ align:start position:0%
+the two solution will be looking like
+ 
+
+ align:start position:0%
+the two solution will be looking like
+this Sita of T will be equal to a plus
+
+ align:start position:0%
+this Sita of T will be equal to a plus
+ 
+
+ align:start position:0%
+this Sita of T will be equal to a plus
+some kind of constant exponential minus
+
+ align:start position:0%
+some kind of constant exponential minus
+ 
+
+ align:start position:0%
+some kind of constant exponential minus
+gamma plus T plus a minus exponential
+
+ align:start position:0%
+gamma plus T plus a minus exponential
+ 
+
+ align:start position:0%
+gamma plus T plus a minus exponential
+minus gamma minus T ok because this is
+
+ align:start position:0%
+minus gamma minus T ok because this is
+ 
+
+ align:start position:0%
+minus gamma minus T ok because this is
+actually becoming already ok
+
+ align:start position:0%
+actually becoming already ok
+ 
+
+ align:start position:0%
+actually becoming already ok
+so alpha is actually I times gamma plus
+
+ align:start position:0%
+so alpha is actually I times gamma plus
+ 
+
+ align:start position:0%
+so alpha is actually I times gamma plus
+minus right there for you if you put the
+
+ align:start position:0%
+minus right there for you if you put the
+ 
+
+ align:start position:0%
+minus right there for you if you put the
+back into this then basically what you
+
+ align:start position:0%
+back into this then basically what you
+ 
+
+ align:start position:0%
+back into this then basically what you
+are getting is explanation plus gamma
+
+ align:start position:0%
+are getting is explanation plus gamma
+ 
+
+ align:start position:0%
+are getting is explanation plus gamma
+exponential minus gamma plus T or
+
+ align:start position:0%
+exponential minus gamma plus T or
+ 
+
+ align:start position:0%
+exponential minus gamma plus T or
+explanation of minus gamma minus T ok so
+
+ align:start position:0%
+explanation of minus gamma minus T ok so
+ 
+
+ align:start position:0%
+explanation of minus gamma minus T ok so
+that's already a real function and
+
+ align:start position:0%
+that's already a real function and
+ 
+
+ align:start position:0%
+that's already a real function and
+linear combination of these two solution
+
+ align:start position:0%
+linear combination of these two solution
+ 
+
+ align:start position:0%
+linear combination of these two solution
+is our final four solution to the
+
+ align:start position:0%
+is our final four solution to the
+ 
+
+ align:start position:0%
+is our final four solution to the
+equation of motion
+
+ align:start position:0%
+equation of motion
+ 
+
+ align:start position:0%
+equation of motion
+okay again what we are going to see is
+
+ align:start position:0%
+okay again what we are going to see is
+ 
+
+ align:start position:0%
+okay again what we are going to see is
+that this is actually the drag force is
+
+ align:start position:0%
+that this is actually the drag force is
+ 
+
+ align:start position:0%
+that this is actually the drag force is
+huge I just throw the whole system into
+
+ align:start position:0%
+huge I just throw the whole system into
+ 
+
+ align:start position:0%
+huge I just throw the whole system into
+water and the water is really stopped
+
+ align:start position:0%
+water and the water is really stopped
+ 
+
+ align:start position:0%
+water and the water is really stopped
+trying to stop the oscillation really
+
+ align:start position:0%
+trying to stop the oscillation really
+ 
+
+ align:start position:0%
+trying to stop the oscillation really
+very much therefore you can see that huh
+
+ align:start position:0%
+very much therefore you can see that huh
+ 
+
+ align:start position:0%
+very much therefore you can see that huh
+again I don't have any oscillation okay
+
+ align:start position:0%
+again I don't have any oscillation okay
+ 
+
+ align:start position:0%
+again I don't have any oscillation okay
+if I am very very strong start this
+
+ align:start position:0%
+if I am very very strong start this
+ 
+
+ align:start position:0%
+if I am very very strong start this
+thing 3d 3d start the initial velocity
+
+ align:start position:0%
+thing 3d 3d start the initial velocity
+ 
+
+ align:start position:0%
+thing 3d 3d start the initial velocity
+or initial angular velocity really high
+
+ align:start position:0%
+or initial angular velocity really high
+ 
+
+ align:start position:0%
+or initial angular velocity really high
+you have I have actually give a huge
+
+ align:start position:0%
+you have I have actually give a huge
+ 
+
+ align:start position:0%
+you have I have actually give a huge
+amount of energy into this system then
+
+ align:start position:0%
+amount of energy into this system then
+ 
+
+ align:start position:0%
+amount of energy into this system then
+at most again I can actually have that
+
+ align:start position:0%
+at most again I can actually have that
+ 
+
+ align:start position:0%
+at most again I can actually have that
+system to pass through the equilibrium
+
+ align:start position:0%
+system to pass through the equilibrium
+ 
+
+ align:start position:0%
+system to pass through the equilibrium
+position only one time then this whole
+
+ align:start position:0%
+position only one time then this whole
+ 
+
+ align:start position:0%
+position only one time then this whole
+this system will slow the grid paper
+
+ align:start position:0%
+this system will slow the grid paper
+ 
+
+ align:start position:0%
+this system will slow the grid paper
+okay because the gamma because of the
+
+ align:start position:0%
+okay because the gamma because of the
+ 
+
+ align:start position:0%
+okay because the gamma because of the
+exponential function we see here the
+
+ align:start position:0%
+exponential function we see here the
+ 
+
+ align:start position:0%
+exponential function we see here the
+amplitude is going to be decaying
+
+ align:start position:0%
+amplitude is going to be decaying
+ 
+
+ align:start position:0%
+amplitude is going to be decaying
+exponentially okay any questions so
+
+ align:start position:0%
+exponentially okay any questions so
+ 
+
+ align:start position:0%
+exponentially okay any questions so
+that's actually do a quick demonstration
+
+ align:start position:0%
+that's actually do a quick demonstration
+ 
+
+ align:start position:0%
+that's actually do a quick demonstration
+here okay so here this is actually the
+
+ align:start position:0%
+here okay so here this is actually the
+ 
+
+ align:start position:0%
+here okay so here this is actually the
+original bit little pore here metal one
+
+ align:start position:0%
+original bit little pore here metal one
+ 
+
+ align:start position:0%
+original bit little pore here metal one
+which is actually you can see that this
+
+ align:start position:0%
+which is actually you can see that this
+ 
+
+ align:start position:0%
+which is actually you can see that this
+is going to go back and forth really
+
+ align:start position:0%
+is going to go back and forth really
+ 
+
+ align:start position:0%
+is going to go back and forth really
+nicely and you can see that because of
+
+ align:start position:0%
+nicely and you can see that because of
+ 
+
+ align:start position:0%
+nicely and you can see that because of
+the friction okay actually the amplitude
+
+ align:start position:0%
+the friction okay actually the amplitude
+ 
+
+ align:start position:0%
+the friction okay actually the amplitude
+is becoming smaller and smaller okay so
+
+ align:start position:0%
+is becoming smaller and smaller okay so
+ 
+
+ align:start position:0%
+is becoming smaller and smaller okay so
+that actually match with this situation
+
+ align:start position:0%
+that actually match with this situation
+ 
+
+ align:start position:0%
+that actually match with this situation
+right so it's actually under damped the
+
+ align:start position:0%
+right so it's actually under damped the
+ 
+
+ align:start position:0%
+right so it's actually under damped the
+situation this ball is going to if in
+
+ align:start position:0%
+situation this ball is going to if in
+ 
+
+ align:start position:0%
+situation this ball is going to if in
+idealized situation it's going to go
+
+ align:start position:0%
+idealized situation it's going to go
+ 
+
+ align:start position:0%
+idealized situation it's going to go
+through zero infinite number of times
+
+ align:start position:0%
+through zero infinite number of times
+ 
+
+ align:start position:0%
+through zero infinite number of times
+okay so now what I'm going to do is how
+
+ align:start position:0%
+okay so now what I'm going to do is how
+ 
+
+ align:start position:0%
+okay so now what I'm going to do is how
+I change this ball to something which is
+
+ align:start position:0%
+I change this ball to something which is
+ 
+
+ align:start position:0%
+I change this ball to something which is
+different okay this is actually made of
+
+ align:start position:0%
+different okay this is actually made of
+ 
+
+ align:start position:0%
+different okay this is actually made of
+Mac Magna knee okay and let's see what
+
+ align:start position:0%
+Mac Magna knee okay and let's see what
+ 
+
+ align:start position:0%
+Mac Magna knee okay and let's see what
+is going to happen
+
+ align:start position:0%
+is going to happen
+ 
+
+ align:start position:0%
+is going to happen
+so now you can see that because this is
+
+ align:start position:0%
+so now you can see that because this is
+ 
+
+ align:start position:0%
+so now you can see that because this is
+actually made of magnet
+
+ align:start position:0%
+actually made of magnet
+ 
+
+ align:start position:0%
+actually made of magnet
+therefore the drag force will be kolosso
+
+ align:start position:0%
+therefore the drag force will be kolosso
+ 
+
+ align:start position:0%
+therefore the drag force will be kolosso
+will be very very big and let's see what
+
+ align:start position:0%
+will be very very big and let's see what
+ 
+
+ align:start position:0%
+will be very very big and let's see what
+happen you see that that the track force
+
+ align:start position:0%
+happen you see that that the track force
+ 
+
+ align:start position:0%
+happen you see that that the track force
+is huge
+
+ align:start position:0%
+is huge
+ 
+
+ align:start position:0%
+is huge
+therefore you see I put it here so that
+
+ align:start position:0%
+therefore you see I put it here so that
+ 
+
+ align:start position:0%
+therefore you see I put it here so that
+ie has big initial velocity the only
+
+ align:start position:0%
+ie has big initial velocity the only
+ 
+
+ align:start position:0%
+ie has big initial velocity the only
+path to zero once right
+
+ align:start position:0%
+path to zero once right
+ 
+
+ align:start position:0%
+path to zero once right
+of course it now is actually approaching
+
+ align:start position:0%
+of course it now is actually approaching
+ 
+
+ align:start position:0%
+of course it now is actually approaching
+the zero already really slowly
+
+ align:start position:0%
+the zero already really slowly
+ 
+
+ align:start position:0%
+the zero already really slowly
+exponentially but it's not zero okay so
+
+ align:start position:0%
+exponentially but it's not zero okay so
+ 
+
+ align:start position:0%
+exponentially but it's not zero okay so
+you know the pass through the zero you
+
+ align:start position:0%
+you know the pass through the zero you
+ 
+
+ align:start position:0%
+you know the pass through the zero you
+feel free diplomats only once
+
+ align:start position:0%
+feel free diplomats only once
+ 
+
+ align:start position:0%
+feel free diplomats only once
+okay just to show that this is a real
+
+ align:start position:0%
+okay just to show that this is a real
+ 
+
+ align:start position:0%
+okay just to show that this is a real
+deal okay right oh I'm not trying to
+
+ align:start position:0%
+deal okay right oh I'm not trying to
+ 
+
+ align:start position:0%
+deal okay right oh I'm not trying to
+destroy the whole cause ruin okay okay
+
+ align:start position:0%
+destroy the whole cause ruin okay okay
+ 
+
+ align:start position:0%
+destroy the whole cause ruin okay okay
+so you can actually pray with this
+
+ align:start position:0%
+so you can actually pray with this
+ 
+
+ align:start position:0%
+so you can actually pray with this
+after we initial lecture okay I would
+
+ align:start position:0%
+after we initial lecture okay I would
+ 
+
+ align:start position:0%
+after we initial lecture okay I would
+like to ask you a question after we
+
+ align:start position:0%
+like to ask you a question after we
+ 
+
+ align:start position:0%
+like to ask you a question after we
+learn this front is a lecture okay there
+
+ align:start position:0%
+learn this front is a lecture okay there
+ 
+
+ align:start position:0%
+learn this front is a lecture okay there
+are three situation under damped
+
+ align:start position:0%
+are three situation under damped
+ 
+
+ align:start position:0%
+are three situation under damped
+critically damped and the over damped
+
+ align:start position:0%
+critically damped and the over damped
+ 
+
+ align:start position:0%
+critically damped and the over damped
+okay I would like to ask you two
+
+ align:start position:0%
+okay I would like to ask you two
+ 
+
+ align:start position:0%
+okay I would like to ask you two
+questions the first one is through this
+
+ align:start position:0%
+questions the first one is through this
+ 
+
+ align:start position:0%
+questions the first one is through this
+demonstration okay so now I have a
+
+ align:start position:0%
+demonstration okay so now I have a
+ 
+
+ align:start position:0%
+demonstration okay so now I have a
+system which is nicely constructed I
+
+ align:start position:0%
+system which is nicely constructed I
+ 
+
+ align:start position:0%
+system which is nicely constructed I
+hope you can see it okay that's it and
+
+ align:start position:0%
+hope you can see it okay that's it and
+ 
+
+ align:start position:0%
+hope you can see it okay that's it and
+this system is made of a torsional
+
+ align:start position:0%
+this system is made of a torsional
+ 
+
+ align:start position:0%
+this system is made of a torsional
+spring and also there's a pad here which
+
+ align:start position:0%
+spring and also there's a pad here which
+ 
+
+ align:start position:0%
+spring and also there's a pad here which
+is connected to a spring okay if I
+
+ align:start position:0%
+is connected to a spring okay if I
+ 
+
+ align:start position:0%
+is connected to a spring okay if I
+actually perturb this thing it's going
+
+ align:start position:0%
+actually perturb this thing it's going
+ 
+
+ align:start position:0%
+actually perturb this thing it's going
+to be oscillating back and forth before
+
+ align:start position:0%
+to be oscillating back and forth before
+ 
+
+ align:start position:0%
+to be oscillating back and forth before
+I turn on the power so that you know the
+
+ align:start position:0%
+I turn on the power so that you know the
+ 
+
+ align:start position:0%
+I turn on the power so that you know the
+lower part is actually you have magnet
+
+ align:start position:0%
+lower part is actually you have magnet
+ 
+
+ align:start position:0%
+lower part is actually you have magnet
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+is not turned on yet okay and this
+
+ align:start position:0%
+is not turned on yet okay and this
+ 
+
+ align:start position:0%
+is not turned on yet okay and this
+magnet is going to provide a drag force
+
+ align:start position:0%
+magnet is going to provide a drag force
+ 
+
+ align:start position:0%
+magnet is going to provide a drag force
+to actually change the behavior of this
+
+ align:start position:0%
+to actually change the behavior of this
+ 
+
+ align:start position:0%
+to actually change the behavior of this
+system okay so you can see that before I
+
+ align:start position:0%
+system okay so you can see that before I
+ 
+
+ align:start position:0%
+system okay so you can see that before I
+turn on the magnetic field the whole
+
+ align:start position:0%
+turn on the magnetic field the whole
+ 
+
+ align:start position:0%
+turn on the magnetic field the whole
+system is actually oscillating back and
+
+ align:start position:0%
+system is actually oscillating back and
+ 
+
+ align:start position:0%
+system is actually oscillating back and
+forth really nicely as we predict smoke
+
+ align:start position:0%
+forth really nicely as we predict smoke
+ 
+
+ align:start position:0%
+forth really nicely as we predict smoke
+amplitude vibration is harmonic
+
+ align:start position:0%
+amplitude vibration is harmonic
+ 
+
+ align:start position:0%
+amplitude vibration is harmonic
+oscillation okay so that's very nice so
+
+ align:start position:0%
+oscillation okay so that's very nice so
+ 
+
+ align:start position:0%
+oscillation okay so that's very nice so
+now what I'm going to do is to turn on
+
+ align:start position:0%
+now what I'm going to do is to turn on
+ 
+
+ align:start position:0%
+now what I'm going to do is to turn on
+the power and see what is going to
+
+ align:start position:0%
+the power and see what is going to
+ 
+
+ align:start position:0%
+the power and see what is going to
+happen after I turn on the power there's
+
+ align:start position:0%
+happen after I turn on the power there's
+ 
+
+ align:start position:0%
+happen after I turn on the power there's
+a there's a electric field okay and and
+
+ align:start position:0%
+a there's a electric field okay and and
+ 
+
+ align:start position:0%
+a there's a electric field okay and and
+this is you're going to be okay so the
+
+ align:start position:0%
+this is you're going to be okay so the
+ 
+
+ align:start position:0%
+this is you're going to be okay so the
+magnet when the magnetic field is I
+
+ align:start position:0%
+magnet when the magnetic field is I
+ 
+
+ align:start position:0%
+magnet when the magnetic field is I
+should turn down therefore this is
+
+ align:start position:0%
+should turn down therefore this is
+ 
+
+ align:start position:0%
+should turn down therefore this is
+actually acting like a drag force a
+
+ align:start position:0%
+actually acting like a drag force a
+ 
+
+ align:start position:0%
+actually acting like a drag force a
+tooth to this system okay so that's
+
+ align:start position:0%
+tooth to this system okay so that's
+ 
+
+ align:start position:0%
+tooth to this system okay so that's
+actually see what is going to happen now
+
+ align:start position:0%
+actually see what is going to happen now
+ 
+
+ align:start position:0%
+actually see what is going to happen now
+I drew this this makes this the behavior
+
+ align:start position:0%
+I drew this this makes this the behavior
+ 
+
+ align:start position:0%
+I drew this this makes this the behavior
+of the system looks like this you first
+
+ align:start position:0%
+of the system looks like this you first
+ 
+
+ align:start position:0%
+of the system looks like this you first
+oscillate and then it stops so the
+
+ align:start position:0%
+oscillate and then it stops so the
+ 
+
+ align:start position:0%
+oscillate and then it stops so the
+question is is this critical tent under
+
+ align:start position:0%
+question is is this critical tent under
+ 
+
+ align:start position:0%
+question is is this critical tent under
+damped over over damped system anybody
+
+ align:start position:0%
+damped over over damped system anybody
+ 
+
+ align:start position:0%
+damped over over damped system anybody
+knows yeah yes this is under damped how
+
+ align:start position:0%
+knows yeah yes this is under damped how
+ 
+
+ align:start position:0%
+knows yeah yes this is under damped how
+do I see that that is because when I do
+
+ align:start position:0%
+do I see that that is because when I do
+ 
+
+ align:start position:0%
+do I see that that is because when I do
+this experiment you will pass through
+
+ align:start position:0%
+this experiment you will pass through
+ 
+
+ align:start position:0%
+this experiment you will pass through
+zeros multiple times
+
+ align:start position:0%
+zeros multiple times
+ 
+
+ align:start position:0%
+zeros multiple times
+therefore there are oscillations trying
+
+ align:start position:0%
+therefore there are oscillations trying
+ 
+
+ align:start position:0%
+therefore there are oscillations trying
+into prey
+
+ align:start position:0%
+into prey
+ 
+
+ align:start position:0%
+into prey
+therefore I can conclude that the drag
+
+ align:start position:0%
+therefore I can conclude that the drag
+ 
+
+ align:start position:0%
+therefore I can conclude that the drag
+force is not large enough so that is
+
+ align:start position:0%
+force is not large enough so that is
+ 
+
+ align:start position:0%
+force is not large enough so that is
+actually a ton on the template situation
+
+ align:start position:0%
+actually a ton on the template situation
+ 
+
+ align:start position:0%
+actually a ton on the template situation
+okay and the next time we are going to
+
+ align:start position:0%
+okay and the next time we are going to
+ 
+
+ align:start position:0%
+okay and the next time we are going to
+drive this system I have a second
+
+ align:start position:0%
+drive this system I have a second
+ 
+
+ align:start position:0%
+drive this system I have a second
+question for you so now your friends
+
+ align:start position:0%
+question for you so now your friends
+ 
+
+ align:start position:0%
+question for you so now your friends
+know that you take took arrow 3
+
+ align:start position:0%
+know that you take took arrow 3
+ 
+
+ align:start position:0%
+know that you take took arrow 3
+therefore they were wondering if you can
+
+ align:start position:0%
+therefore they were wondering if you can
+ 
+
+ align:start position:0%
+therefore they were wondering if you can
+actually design a car suspension system
+
+ align:start position:0%
+actually design a car suspension system
+ 
+
+ align:start position:0%
+actually design a car suspension system
+okay to see if you can actually make the
+
+ align:start position:0%
+okay to see if you can actually make the
+ 
+
+ align:start position:0%
+okay to see if you can actually make the
+design for them when you design this car
+
+ align:start position:0%
+design for them when you design this car
+ 
+
+ align:start position:0%
+design for them when you design this car
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+condition will you consider to set up
+
+ align:start position:0%
+condition will you consider to set up
+ 
+
+ align:start position:0%
+condition will you consider to set up
+the car where you set it up as a under
+
+ align:start position:0%
+the car where you set it up as a under
+ 
+
+ align:start position:0%
+the car where you set it up as a under
+damped critically damped or over damped
+
+ align:start position:0%
+damped critically damped or over damped
+ 
+
+ align:start position:0%
+damped critically damped or over damped
+how many of you actually think you
+
+ align:start position:0%
+how many of you actually think you
+ 
+
+ align:start position:0%
+how many of you actually think you
+should be under damped no nobody
+
+ align:start position:0%
+should be under damped no nobody
+ 
+
+ align:start position:0%
+should be under damped no nobody
+how many of you as you think it should
+
+ align:start position:0%
+how many of you as you think it should
+ 
+
+ align:start position:0%
+how many of you as you think it should
+be over damped one two three four okay
+
+ align:start position:0%
+be over damped one two three four okay
+ 
+
+ align:start position:0%
+be over damped one two three four okay
+how many of you as you think you should
+
+ align:start position:0%
+how many of you as you think you should
+ 
+
+ align:start position:0%
+how many of you as you think you should
+be critically damped okay but jority of
+
+ align:start position:0%
+be critically damped okay but jority of
+ 
+
+ align:start position:0%
+be critically damped okay but jority of
+you think that should be the correct
+
+ align:start position:0%
+you think that should be the correct
+ 
+
+ align:start position:0%
+you think that should be the correct
+design so if you have the car design as
+
+ align:start position:0%
+design so if you have the car design as
+ 
+
+ align:start position:0%
+design so if you have the car design as
+an under damped situation then when you
+
+ align:start position:0%
+an under damped situation then when you
+ 
+
+ align:start position:0%
+an under damped situation then when you
+drive the car you are going to have very
+
+ align:start position:0%
+drive the car you are going to have very
+ 
+
+ align:start position:0%
+drive the car you are going to have very
+funny style you're going to have this
+
+ align:start position:0%
+funny style you're going to have this
+ 
+
+ align:start position:0%
+funny style you're going to have this
+now this is the style so that your car
+
+ align:start position:0%
+now this is the style so that your car
+ 
+
+ align:start position:0%
+now this is the style so that your car
+is going to be oscillating all the time
+
+ align:start position:0%
+is going to be oscillating all the time
+ 
+
+ align:start position:0%
+is going to be oscillating all the time
+okay because it's going to be there and
+
+ align:start position:0%
+okay because it's going to be there and
+ 
+
+ align:start position:0%
+okay because it's going to be there and
+it's really tempting really slowly okay
+
+ align:start position:0%
+it's really tempting really slowly okay
+ 
+
+ align:start position:0%
+it's really tempting really slowly okay
+if you design that to be over damped it
+
+ align:start position:0%
+if you design that to be over damped it
+ 
+
+ align:start position:0%
+if you design that to be over damped it
+would be become very bumpy right so so
+
+ align:start position:0%
+would be become very bumpy right so so
+ 
+
+ align:start position:0%
+would be become very bumpy right so so
+let's take a limit of infinitely large
+
+ align:start position:0%
+let's take a limit of infinitely large
+ 
+
+ align:start position:0%
+let's take a limit of infinitely large
+drug force constant okay then it's like
+
+ align:start position:0%
+drug force constant okay then it's like
+ 
+
+ align:start position:0%
+drug force constant okay then it's like
+when you heat some boundary oh it
+
+ align:start position:0%
+when you heat some boundary oh it
+ 
+
+ align:start position:0%
+when you heat some boundary oh it
+doesn't really help you to reduce the
+
+ align:start position:0%
+doesn't really help you to reduce the
+ 
+
+ align:start position:0%
+doesn't really help you to reduce the
+amplitude okay so the correct answer is
+
+ align:start position:0%
+amplitude okay so the correct answer is
+ 
+
+ align:start position:0%
+amplitude okay so the correct answer is
+you would choose your give the device
+
+ align:start position:0%
+you would choose your give the device
+ 
+
+ align:start position:0%
+you would choose your give the device
+that you will do it critically damped
+
+ align:start position:0%
+that you will do it critically damped
+ 
+
+ align:start position:0%
+that you will do it critically damped
+okay so before we end the section today
+
+ align:start position:0%
+okay so before we end the section today
+ 
+
+ align:start position:0%
+okay so before we end the section today
+I would like to post a question to you
+
+ align:start position:0%
+I would like to post a question to you
+ 
+
+ align:start position:0%
+I would like to post a question to you
+the first the thing with which we have
+
+ align:start position:0%
+the first the thing with which we have
+ 
+
+ align:start position:0%
+the first the thing with which we have
+learned from simple harmonic motion is
+
+ align:start position:0%
+learned from simple harmonic motion is
+ 
+
+ align:start position:0%
+learned from simple harmonic motion is
+that the energy is conserved in the
+
+ align:start position:0%
+that the energy is conserved in the
+ 
+
+ align:start position:0%
+that the energy is conserved in the
+simple harmonic motion okay I have the
+
+ align:start position:0%
+simple harmonic motion okay I have the
+ 
+
+ align:start position:0%
+simple harmonic motion okay I have the
+FS the spring force proportional to
+
+ align:start position:0%
+FS the spring force proportional to
+ 
+
+ align:start position:0%
+FS the spring force proportional to
+minus K times X and that energy is
+
+ align:start position:0%
+minus K times X and that energy is
+ 
+
+ align:start position:0%
+minus K times X and that energy is
+conserved okay but if I add a drag force
+
+ align:start position:0%
+conserved okay but if I add a drag force
+ 
+
+ align:start position:0%
+conserved okay but if I add a drag force
+in the form of minus P times V energy is
+
+ align:start position:0%
+in the form of minus P times V energy is
+ 
+
+ align:start position:0%
+in the form of minus P times V energy is
+not conserved right okay
+
+ align:start position:0%
+not conserved right okay
+ 
+
+ align:start position:0%
+not conserved right okay
+see that he was to issue a sedating now
+
+ align:start position:0%
+see that he was to issue a sedating now
+ 
+
+ align:start position:0%
+see that he was to issue a sedating now
+it's now oscillating right this scene is
+
+ align:start position:0%
+it's now oscillating right this scene is
+ 
+
+ align:start position:0%
+it's now oscillating right this scene is
+stop absolutely okay why you start the
+
+ align:start position:0%
+stop absolutely okay why you start the
+ 
+
+ align:start position:0%
+stop absolutely okay why you start the
+case mathematically okay we know what is
+
+ align:start position:0%
+case mathematically okay we know what is
+ 
+
+ align:start position:0%
+case mathematically okay we know what is
+happening physically because in this
+
+ align:start position:0%
+happening physically because in this
+ 
+
+ align:start position:0%
+happening physically because in this
+physical system because okay this a
+
+ align:start position:0%
+physical system because okay this a
+ 
+
+ align:start position:0%
+physical system because okay this a
+Mexican Hat is trying to push the air
+
+ align:start position:0%
+Mexican Hat is trying to push the air
+ 
+
+ align:start position:0%
+Mexican Hat is trying to push the air
+away so what is going to happen is that
+
+ align:start position:0%
+away so what is going to happen is that
+ 
+
+ align:start position:0%
+away so what is going to happen is that
+it's transferring the energy from the
+
+ align:start position:0%
+it's transferring the energy from the
+ 
+
+ align:start position:0%
+it's transferring the energy from the
+system to the to alemannic use of air
+
+ align:start position:0%
+system to the to alemannic use of air
+ 
+
+ align:start position:0%
+system to the to alemannic use of air
+okay so it's a separating the air so the
+
+ align:start position:0%
+okay so it's a separating the air so the
+ 
+
+ align:start position:0%
+okay so it's a separating the air so the
+energy goes away but why the
+
+ align:start position:0%
+energy goes away but why the
+ 
+
+ align:start position:0%
+energy goes away but why the
+mathematical form looks so similar and
+
+ align:start position:0%
+mathematical form looks so similar and
+ 
+
+ align:start position:0%
+mathematical form looks so similar and
+it does different thing and think about
+
+ align:start position:0%
+it does different thing and think about
+ 
+
+ align:start position:0%
+it does different thing and think about
+it and I'm not going to talk talk about
+
+ align:start position:0%
+it and I'm not going to talk talk about
+ 
+
+ align:start position:0%
+it and I'm not going to talk talk about
+the answer today and thank you Matt
+
+ align:start position:0%
+the answer today and thank you Matt
+ 
+
+ align:start position:0%
+the answer today and thank you Matt
+thank you very much and we will continue
+
+ align:start position:0%
+thank you very much and we will continue
+ 
+
+ align:start position:0%
+thank you very much and we will continue
+next time to see what we can learn if I
+
+ align:start position:0%
+next time to see what we can learn if I
+ 
+
+ align:start position:0%
+next time to see what we can learn if I
+start to type the oscillation back
\ No newline at end of file
diff --git a/TgPcNnUrE24.txt b/TgPcNnUrE24.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6a281edf84adee147a93eec86dcff6668b13248f
--- /dev/null
+++ b/TgPcNnUrE24.txt
@@ -0,0 +1,9307 @@
+align:start position:0%
+ 
+so we spend the last few lectures
+
+ align:start position:0%
+so we spend the last few lectures
+ 
+
+ align:start position:0%
+so we spend the last few lectures
+discussing similarities regularity lemma
+
+ align:start position:0%
+discussing similarities regularity lemma
+ 
+
+ align:start position:0%
+discussing similarities regularity lemma
+so we saw that this is an important tool
+
+ align:start position:0%
+so we saw that this is an important tool
+ 
+
+ align:start position:0%
+so we saw that this is an important tool
+with important applications allowing you
+
+ align:start position:0%
+with important applications allowing you
+ 
+
+ align:start position:0%
+with important applications allowing you
+to do things like a proof of roster via
+
+ align:start position:0%
+to do things like a proof of roster via
+ 
+
+ align:start position:0%
+to do things like a proof of roster via
+graph theory one of the concepts that
+
+ align:start position:0%
+graph theory one of the concepts that
+ 
+
+ align:start position:0%
+graph theory one of the concepts that
+came up when we were discussing this
+
+ align:start position:0%
+came up when we were discussing this
+ 
+
+ align:start position:0%
+came up when we were discussing this
+statement of summary destroy clarity
+
+ align:start position:0%
+statement of summary destroy clarity
+ 
+
+ align:start position:0%
+statement of summary destroy clarity
+lemma it's that of pseudo randomness so
+
+ align:start position:0%
+lemma it's that of pseudo randomness so
+ 
+
+ align:start position:0%
+lemma it's that of pseudo randomness so
+the statement of some Redis graph
+
+ align:start position:0%
+the statement of some Redis graph
+ 
+
+ align:start position:0%
+the statement of some Redis graph
+regularity lemma is that you can
+
+ align:start position:0%
+regularity lemma is that you can
+ 
+
+ align:start position:0%
+regularity lemma is that you can
+partition an arbitrary graph into a
+
+ align:start position:0%
+partition an arbitrary graph into a
+ 
+
+ align:start position:0%
+partition an arbitrary graph into a
+bounded number of pieces so that the
+
+ align:start position:0%
+bounded number of pieces so that the
+ 
+
+ align:start position:0%
+bounded number of pieces so that the
+graph looks random like as we call it
+
+ align:start position:0%
+graph looks random like as we call it
+ 
+
+ align:start position:0%
+graph looks random like as we call it
+between most pairs of parts okay so what
+
+ align:start position:0%
+between most pairs of parts okay so what
+ 
+
+ align:start position:0%
+between most pairs of parts okay so what
+does random like me so that's something
+
+ align:start position:0%
+does random like me so that's something
+ 
+
+ align:start position:0%
+does random like me so that's something
+that I want to discuss the next couple
+
+ align:start position:0%
+that I want to discuss the next couple
+ 
+
+ align:start position:0%
+that I want to discuss the next couple
+of lectures and this is the idea of
+
+ align:start position:0%
+of lectures and this is the idea of
+ 
+
+ align:start position:0%
+of lectures and this is the idea of
+pseudo randomness which is a it's a
+
+ align:start position:0%
+pseudo randomness which is a it's a
+ 
+
+ align:start position:0%
+pseudo randomness which is a it's a
+concept that it's really prevalent in
+
+ align:start position:0%
+concept that it's really prevalent in
+ 
+
+ align:start position:0%
+concept that it's really prevalent in
+combinatorics in the radical computer
+
+ align:start position:0%
+combinatorics in the radical computer
+ 
+
+ align:start position:0%
+combinatorics in the radical computer
+science and in many different areas and
+
+ align:start position:0%
+science and in many different areas and
+ 
+
+ align:start position:0%
+science and in many different areas and
+what pseudo randomness tries to capture
+
+ align:start position:0%
+what pseudo randomness tries to capture
+ 
+
+ align:start position:0%
+what pseudo randomness tries to capture
+is in what ways can a non random object
+
+ align:start position:0%
+is in what ways can a non random object
+ 
+
+ align:start position:0%
+is in what ways can a non random object
+look random
+
+ align:start position:0%
+look random
+ 
+
+ align:start position:0%
+look random
+alright so before diving into some
+
+ align:start position:0%
+alright so before diving into some
+ 
+
+ align:start position:0%
+alright so before diving into some
+specific mathematics I want to offer
+
+ align:start position:0%
+specific mathematics I want to offer
+ 
+
+ align:start position:0%
+specific mathematics I want to offer
+some philosophical remarks and so you
+
+ align:start position:0%
+some philosophical remarks and so you
+ 
+
+ align:start position:0%
+some philosophical remarks and so you
+might know that you know income on a
+
+ align:start position:0%
+might know that you know income on a
+ 
+
+ align:start position:0%
+might know that you know income on a
+computer you want to generate a random
+
+ align:start position:0%
+computer you want to generate a random
+ 
+
+ align:start position:0%
+computer you want to generate a random
+number while you type in a Rand and it
+
+ align:start position:0%
+number while you type in a Rand and it
+ 
+
+ align:start position:0%
+number while you type in a Rand and it
+gives you a random number but of course
+
+ align:start position:0%
+gives you a random number but of course
+ 
+
+ align:start position:0%
+gives you a random number but of course
+you know that it's not necessarily true
+
+ align:start position:0%
+you know that it's not necessarily true
+ 
+
+ align:start position:0%
+you know that it's not necessarily true
+randomness it came from some
+
+ align:start position:0%
+randomness it came from some
+ 
+
+ align:start position:0%
+randomness it came from some
+pseudo-random generator
+
+ align:start position:0%
+pseudo-random generator
+ 
+
+ align:start position:0%
+pseudo-random generator
+probably there's some seed and some
+
+ align:start position:0%
+probably there's some seed and some
+ 
+
+ align:start position:0%
+probably there's some seed and some
+complex looking function and output
+
+ align:start position:0%
+complex looking function and output
+ 
+
+ align:start position:0%
+complex looking function and output
+something that you couldn't distinguish
+
+ align:start position:0%
+something that you couldn't distinguish
+ 
+
+ align:start position:0%
+something that you couldn't distinguish
+from random but it might not actually be
+
+ align:start position:0%
+from random but it might not actually be
+ 
+
+ align:start position:0%
+from random but it might not actually be
+random it's just something that looks in
+
+ align:start position:0%
+random it's just something that looks in
+ 
+
+ align:start position:0%
+random it's just something that looks in
+many different ways like random so there
+
+ align:start position:0%
+many different ways like random so there
+ 
+
+ align:start position:0%
+many different ways like random so there
+is this concept of randomness you can
+
+ align:start position:0%
+is this concept of randomness you can
+ 
+
+ align:start position:0%
+is this concept of randomness you can
+think about a random graph right
+
+ align:start position:0%
+think about a random graph right
+ 
+
+ align:start position:0%
+think about a random graph right
+generate this address writing a random
+
+ align:start position:0%
+generate this address writing a random
+ 
+
+ align:start position:0%
+generate this address writing a random
+graph every edge occurs independently
+
+ align:start position:0%
+graph every edge occurs independently
+ 
+
+ align:start position:0%
+graph every edge occurs independently
+with some probability but I can also
+
+ align:start position:0%
+with some probability but I can also
+ 
+
+ align:start position:0%
+with some probability but I can also
+show you some graph some specific graph
+
+ align:start position:0%
+show you some graph some specific graph
+ 
+
+ align:start position:0%
+show you some graph some specific graph
+which I say well it's
+
+ align:start position:0%
+which I say well it's
+ 
+
+ align:start position:0%
+which I say well it's
+just for all intents and purposes just
+
+ align:start position:0%
+just for all intents and purposes just
+ 
+
+ align:start position:0%
+just for all intents and purposes just
+as good as a random graph so in what
+
+ align:start position:0%
+as good as a random graph so in what
+ 
+
+ align:start position:0%
+as good as a random graph so in what
+ways can we capture that concept so
+
+ align:start position:0%
+ways can we capture that concept so
+ 
+
+ align:start position:0%
+ways can we capture that concept so
+that's what I want to discuss and that's
+
+ align:start position:0%
+that's what I want to discuss and that's
+ 
+
+ align:start position:0%
+that's what I want to discuss and that's
+the topic of pseudo randomness and of
+
+ align:start position:0%
+the topic of pseudo randomness and of
+ 
+
+ align:start position:0%
+the topic of pseudo randomness and of
+course well you know this idea extends
+
+ align:start position:0%
+course well you know this idea extends
+ 
+
+ align:start position:0%
+course well you know this idea extends
+to in the many areas number theory and
+
+ align:start position:0%
+to in the many areas number theory and
+ 
+
+ align:start position:0%
+to in the many areas number theory and
+whatnot but we'll stick with graph
+
+ align:start position:0%
+whatnot but we'll stick with graph
+ 
+
+ align:start position:0%
+whatnot but we'll stick with graph
+theory in particular I want to explore
+
+ align:start position:0%
+theory in particular I want to explore
+ 
+
+ align:start position:0%
+theory in particular I want to explore
+today just one specific notion of pseudo
+
+ align:start position:0%
+today just one specific notion of pseudo
+ 
+
+ align:start position:0%
+today just one specific notion of pseudo
+randomness and this is comes from an
+
+ align:start position:0%
+randomness and this is comes from an
+ 
+
+ align:start position:0%
+randomness and this is comes from an
+important paper called quasi random
+
+ align:start position:0%
+important paper called quasi random
+ 
+
+ align:start position:0%
+important paper called quasi random
+graphs and this concept is due to Chung
+
+ align:start position:0%
+graphs and this concept is due to Chung
+ 
+
+ align:start position:0%
+graphs and this concept is due to Chung
+Graham and Wilson back in the late 80s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so they defined various notions of
+
+ align:start position:0%
+so they defined various notions of
+ 
+
+ align:start position:0%
+so they defined various notions of
+pseudo randomness and I want to state
+
+ align:start position:0%
+pseudo randomness and I want to state
+ 
+
+ align:start position:0%
+pseudo randomness and I want to state
+them and what it turns out and the
+
+ align:start position:0%
+them and what it turns out and the
+ 
+
+ align:start position:0%
+them and what it turns out and the
+surprising part is that these notions
+
+ align:start position:0%
+surprising part is that these notions
+ 
+
+ align:start position:0%
+surprising part is that these notions
+these definitions although they look
+
+ align:start position:0%
+these definitions although they look
+ 
+
+ align:start position:0%
+these definitions although they look
+superficially different they're actually
+
+ align:start position:0%
+superficially different they're actually
+ 
+
+ align:start position:0%
+superficially different they're actually
+only equivalent to each other so let's
+
+ align:start position:0%
+only equivalent to each other so let's
+ 
+
+ align:start position:0%
+only equivalent to each other so let's
+see what the theorem says so the set up
+
+ align:start position:0%
+see what the theorem says so the set up
+ 
+
+ align:start position:0%
+see what the theorem says so the set up
+of this theorem is that you have some
+
+ align:start position:0%
+of this theorem is that you have some
+ 
+
+ align:start position:0%
+of this theorem is that you have some
+fixed real P between 0 & 1
+
+ align:start position:0%
+fixed real P between 0 & 1
+ 
+
+ align:start position:0%
+fixed real P between 0 & 1
+and this is going to be your graph edge
+
+ align:start position:0%
+and this is going to be your graph edge
+ 
+
+ align:start position:0%
+and this is going to be your graph edge
+density so for any sequence of graphs GN
+
+ align:start position:0%
+density so for any sequence of graphs GN
+ 
+
+ align:start position:0%
+density so for any sequence of graphs GN
+so with so from now I'm going to drop
+
+ align:start position:0%
+so with so from now I'm going to drop
+ 
+
+ align:start position:0%
+so with so from now I'm going to drop
+the subscript G so subscript n so G will
+
+ align:start position:0%
+the subscript G so subscript n so G will
+ 
+
+ align:start position:0%
+the subscript G so subscript n so G will
+just be G n such that the number of
+
+ align:start position:0%
+just be G n such that the number of
+ 
+
+ align:start position:0%
+just be G n such that the number of
+vertices so to genius and vertex with
+
+ align:start position:0%
+vertices so to genius and vertex with
+ 
+
+ align:start position:0%
+vertices so to genius and vertex with
+extensity basically peep okay so this is
+
+ align:start position:0%
+extensity basically peep okay so this is
+ 
+
+ align:start position:0%
+extensity basically peep okay so this is
+your sequence of graphs and the claim is
+
+ align:start position:0%
+your sequence of graphs and the claim is
+ 
+
+ align:start position:0%
+your sequence of graphs and the claim is
+that we're going to state some set of
+
+ align:start position:0%
+that we're going to state some set of
+ 
+
+ align:start position:0%
+that we're going to state some set of
+properties and these properties are all
+
+ align:start position:0%
+properties and these properties are all
+ 
+
+ align:start position:0%
+properties and these properties are all
+going to be equivalent to each other
+
+ align:start position:0%
+going to be equivalent to each other
+ 
+
+ align:start position:0%
+going to be equivalent to each other
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so all of these properties capture
+
+ align:start position:0%
+okay so all of these properties capture
+ 
+
+ align:start position:0%
+okay so all of these properties capture
+some notion of pseudo randomness in what
+
+ align:start position:0%
+some notion of pseudo randomness in what
+ 
+
+ align:start position:0%
+some notion of pseudo randomness in what
+ways does this graph G or really a
+
+ align:start position:0%
+ways does this graph G or really a
+ 
+
+ align:start position:0%
+ways does this graph G or really a
+sequence of graphs or you can talk about
+
+ align:start position:0%
+sequence of graphs or you can talk about
+ 
+
+ align:start position:0%
+sequence of graphs or you can talk about
+a specific graph and have some error
+
+ align:start position:0%
+a specific graph and have some error
+ 
+
+ align:start position:0%
+a specific graph and have some error
+parameters and error balance they're all
+
+ align:start position:0%
+parameters and error balance they're all
+ 
+
+ align:start position:0%
+parameters and error balance they're all
+roughly the same ideas so in what ways
+
+ align:start position:0%
+roughly the same ideas so in what ways
+ 
+
+ align:start position:0%
+roughly the same ideas so in what ways
+can we talk about this graph G being
+
+ align:start position:0%
+can we talk about this graph G being
+ 
+
+ align:start position:0%
+can we talk about this graph G being
+random like well we already saw one
+
+ align:start position:0%
+random like well we already saw one
+ 
+
+ align:start position:0%
+random like well we already saw one
+notion when we discussed similarities
+
+ align:start position:0%
+notion when we discussed similarities
+ 
+
+ align:start position:0%
+notion when we discussed similarities
+regularity lemma and let's see that here
+
+ align:start position:0%
+regularity lemma and let's see that here
+ 
+
+ align:start position:0%
+regularity lemma and let's see that here
+so this notion is known as discrepancy
+
+ align:start position:0%
+so this notion is known as discrepancy
+ 
+
+ align:start position:0%
+so this notion is known as discrepancy
+and it says that if I restrict my graph
+
+ align:start position:0%
+and it says that if I restrict my graph
+ 
+
+ align:start position:0%
+and it says that if I restrict my graph
+to looking only at edges between some
+
+ align:start position:0%
+to looking only at edges between some
+ 
+
+ align:start position:0%
+to looking only at edges between some
+pair of vertex sets then the number of
+
+ align:start position:0%
+pair of vertex sets then the number of
+ 
+
+ align:start position:0%
+pair of vertex sets then the number of
+edges should be roughly what you expect
+
+ align:start position:0%
+edges should be roughly what you expect
+ 
+
+ align:start position:0%
+edges should be roughly what you expect
+based on density along so this is
+
+ align:start position:0%
+based on density along so this is
+ 
+
+ align:start position:0%
+based on density along so this is
+basically the notion that came up in
+
+ align:start position:0%
+basically the notion that came up in
+ 
+
+ align:start position:0%
+basically the notion that came up in
+epsilon regularity this is essentially
+
+ align:start position:0%
+epsilon regularity this is essentially
+ 
+
+ align:start position:0%
+epsilon regularity this is essentially
+the same as saying that G is epsilon
+
+ align:start position:0%
+the same as saying that G is epsilon
+ 
+
+ align:start position:0%
+the same as saying that G is epsilon
+regular with itself for this epsilon now
+
+ align:start position:0%
+regular with itself for this epsilon now
+ 
+
+ align:start position:0%
+regular with itself for this epsilon now
+hidden in this little old parameter so
+
+ align:start position:0%
+hidden in this little old parameter so
+ 
+
+ align:start position:0%
+hidden in this little old parameter so
+that's one notion of pseudo randomness
+
+ align:start position:0%
+that's one notion of pseudo randomness
+ 
+
+ align:start position:0%
+that's one notion of pseudo randomness
+okay so here's another notion which is
+
+ align:start position:0%
+okay so here's another notion which is
+ 
+
+ align:start position:0%
+okay so here's another notion which is
+very similar so it's almost just a
+
+ align:start position:0%
+very similar so it's almost just a
+ 
+
+ align:start position:0%
+very similar so it's almost just a
+semantic difference okay so I have to do
+
+ align:start position:0%
+semantic difference okay so I have to do
+ 
+
+ align:start position:0%
+semantic difference okay so I have to do
+a little bit of work so let me call this
+
+ align:start position:0%
+a little bit of work so let me call this
+ 
+
+ align:start position:0%
+a little bit of work so let me call this
+this prime so it says that if you look
+
+ align:start position:0%
+this prime so it says that if you look
+ 
+
+ align:start position:0%
+this prime so it says that if you look
+at only edges within a set so instead of
+
+ align:start position:0%
+at only edges within a set so instead of
+ 
+
+ align:start position:0%
+at only edges within a set so instead of
+taking two sets I only look at one set
+
+ align:start position:0%
+taking two sets I only look at one set
+ 
+
+ align:start position:0%
+taking two sets I only look at one set
+and then look at how many edges are in
+
+ align:start position:0%
+and then look at how many edges are in
+ 
+
+ align:start position:0%
+and then look at how many edges are in
+there versus how many you should expect
+
+ align:start position:0%
+there versus how many you should expect
+ 
+
+ align:start position:0%
+there versus how many you should expect
+based on density alone
+
+ align:start position:0%
+based on density alone
+ 
+
+ align:start position:0%
+based on density alone
+these two numbers are also very similar
+
+ align:start position:0%
+these two numbers are also very similar
+ 
+
+ align:start position:0%
+these two numbers are also very similar
+to each other so let's get to something
+
+ align:start position:0%
+to each other so let's get to something
+ 
+
+ align:start position:0%
+to each other so let's get to something
+that looks dramatically different the
+
+ align:start position:0%
+that looks dramatically different the
+ 
+
+ align:start position:0%
+that looks dramatically different the
+next one I'm going to call count so
+
+ align:start position:0%
+next one I'm going to call count so
+ 
+
+ align:start position:0%
+next one I'm going to call count so
+count says that for every graph H the
+
+ align:start position:0%
+count says that for every graph H the
+ 
+
+ align:start position:0%
+count says that for every graph H the
+number of labeled copies of H in G okay
+
+ align:start position:0%
+number of labeled copies of H in G okay
+ 
+
+ align:start position:0%
+number of labeled copies of H in G okay
+so labeled copies I mean that the
+
+ align:start position:0%
+so labeled copies I mean that the
+ 
+
+ align:start position:0%
+so labeled copies I mean that the
+vertices of H are labeled so for every
+
+ align:start position:0%
+vertices of H are labeled so for every
+ 
+
+ align:start position:0%
+vertices of H are labeled so for every
+triangle there are six labeled triangles
+
+ align:start position:0%
+triangle there are six labeled triangles
+ 
+
+ align:start position:0%
+triangle there are six labeled triangles
+that correspond to that triangle in the
+
+ align:start position:0%
+that correspond to that triangle in the
+ 
+
+ align:start position:0%
+that correspond to that triangle in the
+graph the number of labeled copies of H
+
+ align:start position:0%
+graph the number of labeled copies of H
+ 
+
+ align:start position:0%
+graph the number of labeled copies of H
+is okay so what should you expect if
+
+ align:start position:0%
+is okay so what should you expect if
+ 
+
+ align:start position:0%
+is okay so what should you expect if
+this graph will truly random you expect
+
+ align:start position:0%
+this graph will truly random you expect
+ 
+
+ align:start position:0%
+this graph will truly random you expect
+P raised to the number of edges of h
+
+ align:start position:0%
+P raised to the number of edges of h
+ 
+
+ align:start position:0%
+P raised to the number of edges of h
+plus small error times n number raised
+
+ align:start position:0%
+plus small error times n number raised
+ 
+
+ align:start position:0%
+plus small error times n number raised
+to the number of vertices of H and just
+
+ align:start position:0%
+to the number of vertices of H and just
+ 
+
+ align:start position:0%
+to the number of vertices of H and just
+as a remark this little old term one
+
+ align:start position:0%
+as a remark this little old term one
+ 
+
+ align:start position:0%
+as a remark this little old term one
+term may depend on H so this condition
+
+ align:start position:0%
+term may depend on H so this condition
+ 
+
+ align:start position:0%
+term may depend on H so this condition
+count says for every graph H this is
+
+ align:start position:0%
+count says for every graph H this is
+ 
+
+ align:start position:0%
+count says for every graph H this is
+true and by that I mean for every H
+
+ align:start position:0%
+true and by that I mean for every H
+ 
+
+ align:start position:0%
+true and by that I mean for every H
+there's some sequence of decaying errors
+
+ align:start position:0%
+there's some sequence of decaying errors
+ 
+
+ align:start position:0%
+there's some sequence of decaying errors
+but that sequence of the K nares may
+
+ align:start position:0%
+but that sequence of the K nares may
+ 
+
+ align:start position:0%
+but that sequence of the K nares may
+depend on your graph H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the next one is almost a special case of
+
+ align:start position:0%
+the next one is almost a special case of
+ 
+
+ align:start position:0%
+the next one is almost a special case of
+count
+
+ align:start position:0%
+count
+ 
+
+ align:start position:0%
+count
+it's called c4 and it says that the
+
+ align:start position:0%
+it's called c4 and it says that the
+ 
+
+ align:start position:0%
+it's called c4 and it says that the
+number of labelled copies of c-4 to the
+
+ align:start position:0%
+number of labelled copies of c-4 to the
+ 
+
+ align:start position:0%
+number of labelled copies of c-4 to the
+four cycle yes at most P raised to power
+
+ align:start position:0%
+four cycle yes at most P raised to power
+ 
+
+ align:start position:0%
+four cycle yes at most P raised to power
+4 ok so again what you should expect in
+
+ align:start position:0%
+4 ok so again what you should expect in
+ 
+
+ align:start position:0%
+4 ok so again what you should expect in
+a random setting just for cycle count
+
+ align:start position:0%
+a random setting just for cycle count
+ 
+
+ align:start position:0%
+a random setting just for cycle count
+alone I see already some of you are
+
+ align:start position:0%
+alone I see already some of you are
+ 
+
+ align:start position:0%
+alone I see already some of you are
+surprised and we'll discuss that you
+
+ align:start position:0%
+surprised and we'll discuss that you
+ 
+
+ align:start position:0%
+surprised and we'll discuss that you
+know this is an important constraint it
+
+ align:start position:0%
+know this is an important constraint it
+ 
+
+ align:start position:0%
+know this is an important constraint it
+turns out that alone implies everything
+
+ align:start position:0%
+turns out that alone implies everything
+ 
+
+ align:start position:0%
+turns out that alone implies everything
+just having the correct c4 count the
+
+ align:start position:0%
+just having the correct c4 count the
+ 
+
+ align:start position:0%
+just having the correct c4 count the
+next one we'll call Co degree and the co
+
+ align:start position:0%
+next one we'll call Co degree and the co
+ 
+
+ align:start position:0%
+next one we'll call Co degree and the co
+degree condition says that if you look
+
+ align:start position:0%
+degree condition says that if you look
+ 
+
+ align:start position:0%
+degree condition says that if you look
+at a pair of vertices and look at their
+
+ align:start position:0%
+at a pair of vertices and look at their
+ 
+
+ align:start position:0%
+at a pair of vertices and look at their
+number of common neighbors in other
+
+ align:start position:0%
+number of common neighbors in other
+ 
+
+ align:start position:0%
+number of common neighbors in other
+words their Co degree then what should
+
+ align:start position:0%
+words their Co degree then what should
+ 
+
+ align:start position:0%
+words their Co degree then what should
+you expect this quantity to be and
+
+ align:start position:0%
+you expect this quantity to be and
+ 
+
+ align:start position:0%
+you expect this quantity to be and
+vertices that possibly could be common
+
+ align:start position:0%
+vertices that possibly could be common
+ 
+
+ align:start position:0%
+vertices that possibly could be common
+neighbors and each one of them if this
+
+ align:start position:0%
+neighbors and each one of them if this
+ 
+
+ align:start position:0%
+neighbors and each one of them if this
+were a random graph with edge
+
+ align:start position:0%
+were a random graph with edge
+ 
+
+ align:start position:0%
+were a random graph with edge
+probability P then you expect the number
+
+ align:start position:0%
+probability P then you expect the number
+ 
+
+ align:start position:0%
+probability P then you expect the number
+of common neighbors to be around pqube a
+
+ align:start position:0%
+of common neighbors to be around pqube a
+ 
+
+ align:start position:0%
+of common neighbors to be around pqube a
+p squared n so the co degree condition
+
+ align:start position:0%
+p squared n so the co degree condition
+ 
+
+ align:start position:0%
+p squared n so the co degree condition
+is that this sum is small so most pairs
+
+ align:start position:0%
+is that this sum is small so most pairs
+ 
+
+ align:start position:0%
+is that this sum is small so most pairs
+of vertices have roughly the correct
+
+ align:start position:0%
+of vertices have roughly the correct
+ 
+
+ align:start position:0%
+of vertices have roughly the correct
+number of common neighbors degree yes
+
+ align:start position:0%
+number of common neighbors degree yes
+ 
+
+ align:start position:0%
+number of common neighbors degree yes
+number of common neighbors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next in the last one certainly not the
+
+ align:start position:0%
+next in the last one certainly not the
+ 
+
+ align:start position:0%
+next in the last one certainly not the
+least is I can value condition so here
+
+ align:start position:0%
+least is I can value condition so here
+ 
+
+ align:start position:0%
+least is I can value condition so here
+we are going to denote by lambda 1
+
+ align:start position:0%
+we are going to denote by lambda 1
+ 
+
+ align:start position:0%
+we are going to denote by lambda 1
+through lambda G the eigenvalues of the
+
+ align:start position:0%
+through lambda G the eigenvalues of the
+ 
+
+ align:start position:0%
+through lambda G the eigenvalues of the
+adjacency matrix of G okay so we saw
+
+ align:start position:0%
+adjacency matrix of G okay so we saw
+ 
+
+ align:start position:0%
+adjacency matrix of G okay so we saw
+this object in the last lecture I
+
+ align:start position:0%
+this object in the last lecture I
+ 
+
+ align:start position:0%
+this object in the last lecture I
+include multiplicities if some
+
+ align:start position:0%
+include multiplicities if some
+ 
+
+ align:start position:0%
+include multiplicities if some
+eigenvalue occurs with multiple times
+
+ align:start position:0%
+eigenvalue occurs with multiple times
+ 
+
+ align:start position:0%
+eigenvalue occurs with multiple times
+that included multiple times so the
+
+ align:start position:0%
+that included multiple times so the
+ 
+
+ align:start position:0%
+that included multiple times so the
+eigenvalue condition says that the top
+
+ align:start position:0%
+eigenvalue condition says that the top
+ 
+
+ align:start position:0%
+eigenvalue condition says that the top
+eigenvalue is around pn and that more
+
+ align:start position:0%
+eigenvalue is around pn and that more
+ 
+
+ align:start position:0%
+eigenvalue is around pn and that more
+importantly the other eigenvalues are
+
+ align:start position:0%
+importantly the other eigenvalues are
+ 
+
+ align:start position:0%
+importantly the other eigenvalues are
+all quite small now for D regular graph
+
+ align:start position:0%
+all quite small now for D regular graph
+ 
+
+ align:start position:0%
+all quite small now for D regular graph
+the top I can value it's fine to think
+
+ align:start position:0%
+the top I can value it's fine to think
+ 
+
+ align:start position:0%
+the top I can value it's fine to think
+about D regular graphs you know if you
+
+ align:start position:0%
+about D regular graphs you know if you
+ 
+
+ align:start position:0%
+about D regular graphs you know if you
+want to get some intuition out of this
+
+ align:start position:0%
+want to get some intuition out of this
+ 
+
+ align:start position:0%
+want to get some intuition out of this
+term for D regular graph the top I can
+
+ align:start position:0%
+term for D regular graph the top I can
+ 
+
+ align:start position:0%
+term for D regular graph the top I can
+value is equal to D because the top
+
+ align:start position:0%
+value is equal to D because the top
+ 
+
+ align:start position:0%
+value is equal to D because the top
+eigenvector is there's the old one
+
+ align:start position:0%
+eigenvector is there's the old one
+ 
+
+ align:start position:0%
+eigenvector is there's the old one
+vector so top eigenvector is a one
+
+ align:start position:0%
+vector so top eigenvector is a one
+ 
+
+ align:start position:0%
+vector so top eigenvector is a one
+vector which has eigen value T and what
+
+ align:start position:0%
+vector which has eigen value T and what
+ 
+
+ align:start position:0%
+vector which has eigen value T and what
+I can value condition says is that all
+
+ align:start position:0%
+I can value condition says is that all
+ 
+
+ align:start position:0%
+I can value condition says is that all
+the other eigen values are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much smaller right so here I'm thinking
+
+ align:start position:0%
+much smaller right so here I'm thinking
+ 
+
+ align:start position:0%
+much smaller right so here I'm thinking
+of des on the same order of SN okay so
+
+ align:start position:0%
+of des on the same order of SN okay so
+ 
+
+ align:start position:0%
+of des on the same order of SN okay so
+this is the theorem so that's what we'll
+
+ align:start position:0%
+this is the theorem so that's what we'll
+ 
+
+ align:start position:0%
+this is the theorem so that's what we'll
+do today well prove that all of these
+
+ align:start position:0%
+do today well prove that all of these
+ 
+
+ align:start position:0%
+do today well prove that all of these
+properties are equivalent to each other
+
+ align:start position:0%
+properties are equivalent to each other
+ 
+
+ align:start position:0%
+properties are equivalent to each other
+and all of these properties you should
+
+ align:start position:0%
+and all of these properties you should
+ 
+
+ align:start position:0%
+and all of these properties you should
+think of as characterizations of pseudo
+
+ align:start position:0%
+think of as characterizations of pseudo
+ 
+
+ align:start position:0%
+think of as characterizations of pseudo
+randomness and of course this theorem
+
+ align:start position:0%
+randomness and of course this theorem
+ 
+
+ align:start position:0%
+randomness and of course this theorem
+guarantees us that it doesn't matter
+
+ align:start position:0%
+guarantees us that it doesn't matter
+ 
+
+ align:start position:0%
+guarantees us that it doesn't matter
+which one you use their own equivalent
+
+ align:start position:0%
+which one you use their own equivalent
+ 
+
+ align:start position:0%
+which one you use their own equivalent
+to each other and you know our proofs
+
+ align:start position:0%
+to each other and you know our proofs
+ 
+
+ align:start position:0%
+to each other and you know our proofs
+are actually going to be I mean I'm
+
+ align:start position:0%
+are actually going to be I mean I'm
+ 
+
+ align:start position:0%
+are actually going to be I mean I'm
+going to try to do everything fairly
+
+ align:start position:0%
+going to try to do everything fairly
+ 
+
+ align:start position:0%
+going to try to do everything fairly
+slowly but none of these proofs are
+
+ align:start position:0%
+slowly but none of these proofs are
+ 
+
+ align:start position:0%
+slowly but none of these proofs are
+difficult we're not going to use any
+
+ align:start position:0%
+difficult we're not going to use any
+ 
+
+ align:start position:0%
+difficult we're not going to use any
+fancy tools like some radix regularity
+
+ align:start position:0%
+fancy tools like some radix regularity
+ 
+
+ align:start position:0%
+fancy tools like some radix regularity
+lemma and in particular all of these
+
+ align:start position:0%
+lemma and in particular all of these
+ 
+
+ align:start position:0%
+lemma and in particular all of these
+quantitative errors are reasonably
+
+ align:start position:0%
+quantitative errors are reasonably
+ 
+
+ align:start position:0%
+quantitative errors are reasonably
+dependent on each other so I've stated
+
+ align:start position:0%
+dependent on each other so I've stated
+ 
+
+ align:start position:0%
+dependent on each other so I've stated
+this theorem so far in this form where
+
+ align:start position:0%
+this theorem so far in this form where
+ 
+
+ align:start position:0%
+this theorem so far in this form where
+there's a little one error but
+
+ align:start position:0%
+there's a little one error but
+ 
+
+ align:start position:0%
+there's a little one error but
+equivalent ly so can equivalently state
+
+ align:start position:0%
+equivalent ly so can equivalently state
+ 
+
+ align:start position:0%
+equivalent ly so can equivalently state
+them State theorem for example disk with
+
+ align:start position:0%
+them State theorem for example disk with
+ 
+
+ align:start position:0%
+them State theorem for example disk with
+an epsilon error which is that some
+
+ align:start position:0%
+an epsilon error which is that some
+ 
+
+ align:start position:0%
+an epsilon error which is that some
+inequality is true with a most epsilon
+
+ align:start position:0%
+inequality is true with a most epsilon
+ 
+
+ align:start position:0%
+inequality is true with a most epsilon
+error instead of oh and you have a
+
+ align:start position:0%
+error instead of oh and you have a
+ 
+
+ align:start position:0%
+error instead of oh and you have a
+different epsilon for each one of them
+
+ align:start position:0%
+different epsilon for each one of them
+ 
+
+ align:start position:0%
+different epsilon for each one of them
+and the theorem turns out that okay so
+
+ align:start position:0%
+and the theorem turns out that okay so
+ 
+
+ align:start position:0%
+and the theorem turns out that okay so
+the proof of this theorem will be that
+
+ align:start position:0%
+the proof of this theorem will be that
+ 
+
+ align:start position:0%
+the proof of this theorem will be that
+these conditions are true so all
+
+ align:start position:0%
+these conditions are true so all
+ 
+
+ align:start position:0%
+these conditions are true so all
+equivalent up to at most a polynomial
+
+ align:start position:0%
+equivalent up to at most a polynomial
+ 
+
+ align:start position:0%
+equivalent up to at most a polynomial
+change in the epsilon in other words so
+
+ align:start position:0%
+change in the epsilon in other words so
+ 
+
+ align:start position:0%
+change in the epsilon in other words so
+property one is true for epsilon implies
+
+ align:start position:0%
+property one is true for epsilon implies
+ 
+
+ align:start position:0%
+property one is true for epsilon implies
+that property two is true for some
+
+ align:start position:0%
+that property two is true for some
+ 
+
+ align:start position:0%
+that property two is true for some
+epsilon raised to a constant so the
+
+ align:start position:0%
+epsilon raised to a constant so the
+ 
+
+ align:start position:0%
+epsilon raised to a constant so the
+changes in parameters are quite
+
+ align:start position:0%
+changes in parameters are quite
+ 
+
+ align:start position:0%
+changes in parameters are quite
+reasonable and we'll see this from the
+
+ align:start position:0%
+reasonable and we'll see this from the
+ 
+
+ align:start position:0%
+reasonable and we'll see this from the
+proof but I won't say it again
+
+ align:start position:0%
+proof but I won't say it again
+ 
+
+ align:start position:0%
+proof but I won't say it again
+explicitly any
+
+ align:start position:0%
+explicitly any
+ 
+
+ align:start position:0%
+explicitly any
+questions so far about the statement of
+
+ align:start position:0%
+questions so far about the statement of
+ 
+
+ align:start position:0%
+questions so far about the statement of
+this theorem so as I mentioned just now
+
+ align:start position:0%
+this theorem so as I mentioned just now
+ 
+
+ align:start position:0%
+this theorem so as I mentioned just now
+the most surprising part of this theorem
+
+ align:start position:0%
+the most surprising part of this theorem
+ 
+
+ align:start position:0%
+the most surprising part of this theorem
+and the one that I want you to pay the
+
+ align:start position:0%
+and the one that I want you to pay the
+ 
+
+ align:start position:0%
+and the one that I want you to pay the
+most attention to is the c4 condition
+
+ align:start position:0%
+most attention to is the c4 condition
+ 
+
+ align:start position:0%
+most attention to is the c4 condition
+this seems at least at face value the
+
+ align:start position:0%
+this seems at least at face value the
+ 
+
+ align:start position:0%
+this seems at least at face value the
+weakest condition among all of them it
+
+ align:start position:0%
+weakest condition among all of them it
+ 
+
+ align:start position:0%
+weakest condition among all of them it
+just says the correct c4 count but it
+
+ align:start position:0%
+just says the correct c4 count but it
+ 
+
+ align:start position:0%
+just says the correct c4 count but it
+turns out to be equivalent to everything
+
+ align:start position:0%
+turns out to be equivalent to everything
+ 
+
+ align:start position:0%
+turns out to be equivalent to everything
+else and there's something special about
+
+ align:start position:0%
+else and there's something special about
+ 
+
+ align:start position:0%
+else and there's something special about
+c-4 right if I replace c-4 by c3 by just
+
+ align:start position:0%
+c-4 right if I replace c-4 by c3 by just
+ 
+
+ align:start position:0%
+c-4 right if I replace c-4 by c3 by just
+triangles then that's not true so I want
+
+ align:start position:0%
+triangles then that's not true so I want
+ 
+
+ align:start position:0%
+triangles then that's not true so I want
+you to think about you know where the
+
+ align:start position:0%
+you to think about you know where the
+ 
+
+ align:start position:0%
+you to think about you know where the
+c-4 played this important role how does
+
+ align:start position:0%
+c-4 played this important role how does
+ 
+
+ align:start position:0%
+c-4 played this important role how does
+it play this important role okay so
+
+ align:start position:0%
+it play this important role okay so
+ 
+
+ align:start position:0%
+it play this important role okay so
+let's get started with the proof but
+
+ align:start position:0%
+let's get started with the proof but
+ 
+
+ align:start position:0%
+let's get started with the proof but
+before that let me so in this proof one
+
+ align:start position:0%
+before that let me so in this proof one
+ 
+
+ align:start position:0%
+before that let me so in this proof one
+recurring theme is that we're going to
+
+ align:start position:0%
+recurring theme is that we're going to
+ 
+
+ align:start position:0%
+recurring theme is that we're going to
+be using the Cauchy Schwarz inequality
+
+ align:start position:0%
+be using the Cauchy Schwarz inequality
+ 
+
+ align:start position:0%
+be using the Cauchy Schwarz inequality
+many times and I want to just begin with
+
+ align:start position:0%
+many times and I want to just begin with
+ 
+
+ align:start position:0%
+many times and I want to just begin with
+an exercise that gets you some
+
+ align:start position:0%
+an exercise that gets you some
+ 
+
+ align:start position:0%
+an exercise that gets you some
+familiarity with applying the Cauchy
+
+ align:start position:0%
+familiarity with applying the Cauchy
+ 
+
+ align:start position:0%
+familiarity with applying the Cauchy
+Schwarz inequality and this simple tool
+
+ align:start position:0%
+Schwarz inequality and this simple tool
+ 
+
+ align:start position:0%
+Schwarz inequality and this simple tool
+but it's extremely powerful and
+
+ align:start position:0%
+but it's extremely powerful and
+ 
+
+ align:start position:0%
+but it's extremely powerful and
+worthwhile to you know master how to use
+
+ align:start position:0%
+worthwhile to you know master how to use
+ 
+
+ align:start position:0%
+worthwhile to you know master how to use
+the Cauchy Schwarz inequality okay so
+
+ align:start position:0%
+the Cauchy Schwarz inequality okay so
+ 
+
+ align:start position:0%
+the Cauchy Schwarz inequality okay so
+let's let's get some practice let me
+
+ align:start position:0%
+let's let's get some practice let me
+ 
+
+ align:start position:0%
+let's let's get some practice let me
+prove a claim which is not directly
+
+ align:start position:0%
+prove a claim which is not directly
+ 
+
+ align:start position:0%
+prove a claim which is not directly
+related to the proof of the theorem but
+
+ align:start position:0%
+related to the proof of the theorem but
+ 
+
+ align:start position:0%
+related to the proof of the theorem but
+it's indirectly in that explains
+
+ align:start position:0%
+it's indirectly in that explains
+ 
+
+ align:start position:0%
+it's indirectly in that explains
+somewhat the c-4 condition why we have
+
+ align:start position:0%
+somewhat the c-4 condition why we have
+ 
+
+ align:start position:0%
+somewhat the c-4 condition why we have
+less than or equal to over there okay so
+
+ align:start position:0%
+less than or equal to over there okay so
+ 
+
+ align:start position:0%
+less than or equal to over there okay so
+the lemma is that if you have a graph on
+
+ align:start position:0%
+the lemma is that if you have a graph on
+ 
+
+ align:start position:0%
+the lemma is that if you have a graph on
+n vertices such that the number of edges
+
+ align:start position:0%
+n vertices such that the number of edges
+ 
+
+ align:start position:0%
+n vertices such that the number of edges
+is at least P and squared over 2 so edge
+
+ align:start position:0%
+is at least P and squared over 2 so edge
+ 
+
+ align:start position:0%
+is at least P and squared over 2 so edge
+density basically P then the number of
+
+ align:start position:0%
+density basically P then the number of
+ 
+
+ align:start position:0%
+density basically P then the number of
+labeled copies of c-4 is at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e to the 4 - little one and so if you
+
+ align:start position:0%
+e to the 4 - little one and so if you
+ 
+
+ align:start position:0%
+e to the 4 - little one and so if you
+have a graph with edge density P P is a
+
+ align:start position:0%
+have a graph with edge density P P is a
+ 
+
+ align:start position:0%
+have a graph with edge density P P is a
+constant then the number of C forces are
+
+ align:start position:0%
+constant then the number of C forces are
+ 
+
+ align:start position:0%
+constant then the number of C forces are
+at least roughly what you would expect
+
+ align:start position:0%
+at least roughly what you would expect
+ 
+
+ align:start position:0%
+at least roughly what you would expect
+in a random graph alright so let's see
+
+ align:start position:0%
+in a random graph alright so let's see
+ 
+
+ align:start position:0%
+in a random graph alright so let's see
+how to do this and I want to show this
+
+ align:start position:0%
+how to do this and I want to show this
+ 
+
+ align:start position:0%
+how to do this and I want to show this
+inequality as a me I'll show you how to
+
+ align:start position:0%
+inequality as a me I'll show you how to
+ 
+
+ align:start position:0%
+inequality as a me I'll show you how to
+prove this inequality but I also want to
+
+ align:start position:0%
+prove this inequality but I also want to
+ 
+
+ align:start position:0%
+prove this inequality but I also want to
+draw sequence of pictures that at least
+
+ align:start position:0%
+draw sequence of pictures that at least
+ 
+
+ align:start position:0%
+draw sequence of pictures that at least
+to explain how I think about
+
+ align:start position:0%
+to explain how I think about
+ 
+
+ align:start position:0%
+to explain how I think about
+applications of the Cauchy Schwarz
+
+ align:start position:0%
+applications of the Cauchy Schwarz
+ 
+
+ align:start position:0%
+applications of the Cauchy Schwarz
+inequality ok so the first thing is that
+
+ align:start position:0%
+inequality ok so the first thing is that
+ 
+
+ align:start position:0%
+inequality ok so the first thing is that
+we are counting labelled copies of c4
+
+ align:start position:0%
+we are counting labelled copies of c4
+ 
+
+ align:start position:0%
+we are counting labelled copies of c4
+and this is basically but not exactly
+
+ align:start position:0%
+and this is basically but not exactly
+ 
+
+ align:start position:0%
+and this is basically but not exactly
+the same as number of homomorphic copies
+
+ align:start position:0%
+the same as number of homomorphic copies
+ 
+
+ align:start position:0%
+the same as number of homomorphic copies
+of c-4 in g so by this guy here i really
+
+ align:start position:0%
+of c-4 in g so by this guy here i really
+ 
+
+ align:start position:0%
+of c-4 in g so by this guy here i really
+just mean you are mapping vertices of
+
+ align:start position:0%
+just mean you are mapping vertices of
+ 
+
+ align:start position:0%
+just mean you are mapping vertices of
+c-4 to g so that the edges all map to
+
+ align:start position:0%
+c-4 to g so that the edges all map to
+ 
+
+ align:start position:0%
+c-4 to g so that the edges all map to
+edges but we are allowing not
+
+ align:start position:0%
+edges but we are allowing not
+ 
+
+ align:start position:0%
+edges but we are allowing not
+necessarily injective maps c4 to 2g but
+
+ align:start position:0%
+necessarily injective maps c4 to 2g but
+ 
+
+ align:start position:0%
+necessarily injective maps c4 to 2g but
+that's okay so the number of non
+
+ align:start position:0%
+that's okay so the number of non
+ 
+
+ align:start position:0%
+that's okay so the number of non
+injective maps yes most cubic so we're
+
+ align:start position:0%
+injective maps yes most cubic so we're
+ 
+
+ align:start position:0%
+injective maps yes most cubic so we're
+not really affecting our account so it's
+
+ align:start position:0%
+not really affecting our account so it's
+ 
+
+ align:start position:0%
+not really affecting our account so it's
+enough to think about homomorphic copies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what's going on here
+
+ align:start position:0%
+okay so what's going on here
+ 
+
+ align:start position:0%
+okay so what's going on here
+so let me draw a sequence of pictures
+
+ align:start position:0%
+so let me draw a sequence of pictures
+ 
+
+ align:start position:0%
+so let me draw a sequence of pictures
+illustrating this calculation so first
+
+ align:start position:0%
+illustrating this calculation so first
+ 
+
+ align:start position:0%
+illustrating this calculation so first
+we are thinking about counting c4 c4 I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can rewrite the c-4 count as a sum over
+
+ align:start position:0%
+can rewrite the c-4 count as a sum over
+ 
+
+ align:start position:0%
+can rewrite the c-4 count as a sum over
+pairs of vertices of G as the squared Co
+
+ align:start position:0%
+pairs of vertices of G as the squared Co
+ 
+
+ align:start position:0%
+pairs of vertices of G as the squared Co
+degree and what happens here so this is
+
+ align:start position:0%
+degree and what happens here so this is
+ 
+
+ align:start position:0%
+degree and what happens here so this is
+true mean it's not hard to see why this
+
+ align:start position:0%
+true mean it's not hard to see why this
+ 
+
+ align:start position:0%
+true mean it's not hard to see why this
+is true but I want to draw this in
+
+ align:start position:0%
+is true but I want to draw this in
+ 
+
+ align:start position:0%
+is true but I want to draw this in
+pictures because you know we have larger
+
+ align:start position:0%
+pictures because you know we have larger
+ 
+
+ align:start position:0%
+pictures because you know we have larger
+and bigger graphs may be more difficult
+
+ align:start position:0%
+and bigger graphs may be more difficult
+ 
+
+ align:start position:0%
+and bigger graphs may be more difficult
+to think about the algebra unless you
+
+ align:start position:0%
+to think about the algebra unless you
+ 
+
+ align:start position:0%
+to think about the algebra unless you
+have some visualization so what happens
+
+ align:start position:0%
+have some visualization so what happens
+ 
+
+ align:start position:0%
+have some visualization so what happens
+here is that I noticed that this c4 has
+
+ align:start position:0%
+here is that I noticed that this c4 has
+ 
+
+ align:start position:0%
+here is that I noticed that this c4 has
+a certain reflection namely it has a
+
+ align:start position:0%
+a certain reflection namely it has a
+ 
+
+ align:start position:0%
+a certain reflection namely it has a
+reflection along this horizontal line
+
+ align:start position:0%
+reflection along this horizontal line
+ 
+
+ align:start position:0%
+reflection along this horizontal line
+and so if I put these two vertices as U
+
+ align:start position:0%
+and so if I put these two vertices as U
+ 
+
+ align:start position:0%
+and so if I put these two vertices as U
+and D then this reflection tells you
+
+ align:start position:0%
+and D then this reflection tells you
+ 
+
+ align:start position:0%
+and D then this reflection tells you
+that you can write this homomorphic
+
+ align:start position:0%
+that you can write this homomorphic
+ 
+
+ align:start position:0%
+that you can write this homomorphic
+number who more copies as the sum of
+
+ align:start position:0%
+number who more copies as the sum of
+ 
+
+ align:start position:0%
+number who more copies as the sum of
+squares but once you have this
+
+ align:start position:0%
+squares but once you have this
+ 
+
+ align:start position:0%
+squares but once you have this
+reflection and reflections are super
+
+ align:start position:0%
+reflection and reflections are super
+ 
+
+ align:start position:0%
+reflection and reflections are super
+useful because they allow us to get
+
+ align:start position:0%
+useful because they allow us to get
+ 
+
+ align:start position:0%
+useful because they allow us to get
+something into a square and then right
+
+ align:start position:0%
+something into a square and then right
+ 
+
+ align:start position:0%
+something into a square and then right
+after apply the Cauchy Schwarz
+
+ align:start position:0%
+after apply the Cauchy Schwarz
+ 
+
+ align:start position:0%
+after apply the Cauchy Schwarz
+inequality so we apply Cauchy Schwarz
+
+ align:start position:0%
+inequality so we apply Cauchy Schwarz
+ 
+
+ align:start position:0%
+inequality so we apply Cauchy Schwarz
+here and we obtain that this sum is at
+
+ align:start position:0%
+here and we obtain that this sum is at
+ 
+
+ align:start position:0%
+here and we obtain that this sum is at
+most where I can pull the square out and
+
+ align:start position:0%
+most where I can pull the square out and
+ 
+
+ align:start position:0%
+most where I can pull the square out and
+I need to think about what is the
+
+ align:start position:0%
+I need to think about what is the
+ 
+
+ align:start position:0%
+I need to think about what is the
+correct factor to put out here and that
+
+ align:start position:0%
+correct factor to put out here and that
+ 
+
+ align:start position:0%
+correct factor to put out here and that
+should be okay so what's the correct
+
+ align:start position:0%
+should be okay so what's the correct
+ 
+
+ align:start position:0%
+should be okay so what's the correct
+factor that I should put out there okay
+
+ align:start position:0%
+factor that I should put out there okay
+ 
+
+ align:start position:0%
+factor that I should put out there okay
+so 1 over N squared so I don't actually
+
+ align:start position:0%
+so 1 over N squared so I don't actually
+ 
+
+ align:start position:0%
+so 1 over N squared so I don't actually
+like doing this kind of calculations
+
+ align:start position:0%
+like doing this kind of calculations
+ 
+
+ align:start position:0%
+like doing this kind of calculations
+which sums because then you have to keep
+
+ align:start position:0%
+which sums because then you have to keep
+ 
+
+ align:start position:0%
+which sums because then you have to keep
+keep track of these normalizing factors
+
+ align:start position:0%
+keep track of these normalizing factors
+ 
+
+ align:start position:0%
+keep track of these normalizing factors
+one of the upcoming chapters when we
+
+ align:start position:0%
+one of the upcoming chapters when we
+ 
+
+ align:start position:0%
+one of the upcoming chapters when we
+discuss graph limits or in fact you can
+
+ align:start position:0%
+discuss graph limits or in fact you can
+ 
+
+ align:start position:0%
+discuss graph limits or in fact you can
+even do this instead of taking sums if
+
+ align:start position:0%
+even do this instead of taking sums if
+ 
+
+ align:start position:0%
+even do this instead of taking sums if
+you take an average if you take an
+
+ align:start position:0%
+you take an average if you take an
+ 
+
+ align:start position:0%
+you take an average if you take an
+expectation then it turns out you never
+
+ align:start position:0%
+expectation then it turns out you never
+ 
+
+ align:start position:0%
+expectation then it turns out you never
+have to worry about these normalizing
+
+ align:start position:0%
+have to worry about these normalizing
+ 
+
+ align:start position:0%
+have to worry about these normalizing
+factors and so on somehow normalizing
+
+ align:start position:0%
+factors and so on somehow normalizing
+ 
+
+ align:start position:0%
+factors and so on somehow normalizing
+factor should never bother you if you do
+
+ align:start position:0%
+factor should never bother you if you do
+ 
+
+ align:start position:0%
+factor should never bother you if you do
+it correctly but just to make sure
+
+ align:start position:0%
+it correctly but just to make sure
+ 
+
+ align:start position:0%
+it correctly but just to make sure
+things are correct
+
+ align:start position:0%
+things are correct
+ 
+
+ align:start position:0%
+things are correct
+this keep me in check all right so what
+
+ align:start position:0%
+this keep me in check all right so what
+ 
+
+ align:start position:0%
+this keep me in check all right so what
+happened in this step in this step we
+
+ align:start position:0%
+happened in this step in this step we
+ 
+
+ align:start position:0%
+happened in this step in this step we
+pulled out that square and pictorially
+
+ align:start position:0%
+pulled out that square and pictorially
+ 
+
+ align:start position:0%
+pulled out that square and pictorially
+what happens is that we got rid of half
+
+ align:start position:0%
+what happens is that we got rid of half
+ 
+
+ align:start position:0%
+what happens is that we got rid of half
+of this picture so we used
+
+ align:start position:0%
+of this picture so we used
+ 
+
+ align:start position:0%
+of this picture so we used
+cauchy-schwarz and we wiped out half of
+
+ align:start position:0%
+cauchy-schwarz and we wiped out half of
+ 
+
+ align:start position:0%
+cauchy-schwarz and we wiped out half of
+the picture and now what we can do is
+
+ align:start position:0%
+the picture and now what we can do is
+ 
+
+ align:start position:0%
+the picture and now what we can do is
+while we're counting these guys these
+
+ align:start position:0%
+while we're counting these guys these
+ 
+
+ align:start position:0%
+while we're counting these guys these
+paths of length two but I can
+
+ align:start position:0%
+paths of length two but I can
+ 
+
+ align:start position:0%
+paths of length two but I can
+reprioritize this picture so that it
+
+ align:start position:0%
+reprioritize this picture so that it
+ 
+
+ align:start position:0%
+reprioritize this picture so that it
+looks like that and now I notice that
+
+ align:start position:0%
+looks like that and now I notice that
+ 
+
+ align:start position:0%
+looks like that and now I notice that
+there is one more reflection all right
+
+ align:start position:0%
+there is one more reflection all right
+ 
+
+ align:start position:0%
+there is one more reflection all right
+so there's one more reflection and
+
+ align:start position:0%
+so there's one more reflection and
+ 
+
+ align:start position:0%
+so there's one more reflection and
+that's the reflection around the
+
+ align:start position:0%
+that's the reflection around the
+ 
+
+ align:start position:0%
+that's the reflection around the
+vertical axis so let me call this top
+
+ align:start position:0%
+vertical axis so let me call this top
+ 
+
+ align:start position:0%
+vertical axis so let me call this top
+vertex X and I can rewrite the sum okay
+
+ align:start position:0%
+vertex X and I can rewrite the sum okay
+ 
+
+ align:start position:0%
+vertex X and I can rewrite the sum okay
+so once more with your cauchy-schwarz
+
+ align:start position:0%
+so once more with your cauchy-schwarz
+ 
+
+ align:start position:0%
+so once more with your cauchy-schwarz
+which allows us to get rid of half of
+
+ align:start position:0%
+which allows us to get rid of half of
+ 
+
+ align:start position:0%
+which allows us to get rid of half of
+the picture and now I'm going to draw
+
+ align:start position:0%
+the picture and now I'm going to draw
+ 
+
+ align:start position:0%
+the picture and now I'm going to draw
+the picture first Stan you see that what
+
+ align:start position:0%
+the picture first Stan you see that what
+ 
+
+ align:start position:0%
+the picture first Stan you see that what
+we should be left with it's just a
+
+ align:start position:0%
+we should be left with it's just a
+ 
+
+ align:start position:0%
+we should be left with it's just a
+single edge and then you write down the
+
+ align:start position:0%
+single edge and then you write down the
+ 
+
+ align:start position:0%
+single edge and then you write down the
+correct sum making sure that all the
+
+ align:start position:0%
+correct sum making sure that all the
+ 
+
+ align:start position:0%
+correct sum making sure that all the
+parentheses and normalizations are
+
+ align:start position:0%
+parentheses and normalizations are
+ 
+
+ align:start position:0%
+parentheses and normalizations are
+correct but somehow that doesn't worry
+
+ align:start position:0%
+correct but somehow that doesn't worry
+ 
+
+ align:start position:0%
+correct but somehow that doesn't worry
+me so much because I know this what that
+
+ align:start position:0%
+me so much because I know this what that
+ 
+
+ align:start position:0%
+me so much because I know this what that
+means the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but whatever it is were just summing the
+
+ align:start position:0%
+but whatever it is were just summing the
+ 
+
+ align:start position:0%
+but whatever it is were just summing the
+number of edges so that's just a number
+
+ align:start position:0%
+number of edges so that's just a number
+ 
+
+ align:start position:0%
+number of edges so that's just a number
+of edges and okay so we put everything
+
+ align:start position:0%
+of edges and okay so we put everything
+ 
+
+ align:start position:0%
+of edges and okay so we put everything
+in and we find that the final quantity
+
+ align:start position:0%
+in and we find that the final quantity
+ 
+
+ align:start position:0%
+in and we find that the final quantity
+is at least P raised to 4 and 2 4 ok so
+
+ align:start position:0%
+is at least P raised to 4 and 2 4 ok so
+ 
+
+ align:start position:0%
+is at least P raised to 4 and 2 4 ok so
+I did this quite slowly but and also
+
+ align:start position:0%
+I did this quite slowly but and also
+ 
+
+ align:start position:0%
+I did this quite slowly but and also
+emphasizing the sequence of pictures
+
+ align:start position:0%
+emphasizing the sequence of pictures
+ 
+
+ align:start position:0%
+emphasizing the sequence of pictures
+on and party to tell you like how I
+
+ align:start position:0%
+on and party to tell you like how I
+ 
+
+ align:start position:0%
+on and party to tell you like how I
+think about these inequalities because
+
+ align:start position:0%
+think about these inequalities because
+ 
+
+ align:start position:0%
+think about these inequalities because
+for other similar looking inequalities
+
+ align:start position:0%
+for other similar looking inequalities
+ 
+
+ align:start position:0%
+for other similar looking inequalities
+in fact there is something called
+
+ align:start position:0%
+in fact there is something called
+ 
+
+ align:start position:0%
+in fact there is something called
+sidorenko's conjecture which I may
+
+ align:start position:0%
+sidorenko's conjecture which I may
+ 
+
+ align:start position:0%
+sidorenko's conjecture which I may
+discuss more in a future lecture that
+
+ align:start position:0%
+discuss more in a future lecture that
+ 
+
+ align:start position:0%
+discuss more in a future lecture that
+says that this kind of inequality should
+
+ align:start position:0%
+says that this kind of inequality should
+ 
+
+ align:start position:0%
+says that this kind of inequality should
+be true whenever you replace c4 by any
+
+ align:start position:0%
+be true whenever you replace c4 by any
+ 
+
+ align:start position:0%
+be true whenever you replace c4 by any
+bipartite graph and that's a major open
+
+ align:start position:0%
+bipartite graph and that's a major open
+ 
+
+ align:start position:0%
+bipartite graph and that's a major open
+problem in combinatorics it's kind of
+
+ align:start position:0%
+problem in combinatorics it's kind of
+ 
+
+ align:start position:0%
+problem in combinatorics it's kind of
+hard to keep track of these calculations
+
+ align:start position:0%
+hard to keep track of these calculations
+ 
+
+ align:start position:0%
+hard to keep track of these calculations
+unless you have a visual anchor and this
+
+ align:start position:0%
+unless you have a visual anchor and this
+ 
+
+ align:start position:0%
+unless you have a visual anchor and this
+is my visual anchor which I'm trying to
+
+ align:start position:0%
+is my visual anchor which I'm trying to
+ 
+
+ align:start position:0%
+is my visual anchor which I'm trying to
+explain
+
+ align:start position:0%
+explain
+ 
+
+ align:start position:0%
+explain
+of course it's down-to-earth it's just
+
+ align:start position:0%
+of course it's down-to-earth it's just
+ 
+
+ align:start position:0%
+of course it's down-to-earth it's just
+the sequence of inequalities and this is
+
+ align:start position:0%
+the sequence of inequalities and this is
+ 
+
+ align:start position:0%
+the sequence of inequalities and this is
+also some practice with cauchy-schwarz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright any questions so but one thing
+
+ align:start position:0%
+alright any questions so but one thing
+ 
+
+ align:start position:0%
+alright any questions so but one thing
+in this calculation told us is that if
+
+ align:start position:0%
+in this calculation told us is that if
+ 
+
+ align:start position:0%
+in this calculation told us is that if
+you have edge density P then you
+
+ align:start position:0%
+you have edge density P then you
+ 
+
+ align:start position:0%
+you have edge density P then you
+necessarily have c4 density at least P
+
+ align:start position:0%
+necessarily have c4 density at least P
+ 
+
+ align:start position:0%
+necessarily have c4 density at least P
+to the fourth so that party explains why
+
+ align:start position:0%
+to the fourth so that party explains why
+ 
+
+ align:start position:0%
+to the fourth so that party explains why
+you have at most n here so you always
+
+ align:start position:0%
+you have at most n here so you always
+ 
+
+ align:start position:0%
+you have at most n here so you always
+know that it is at least this quantity
+
+ align:start position:0%
+know that it is at least this quantity
+ 
+
+ align:start position:0%
+know that it is at least this quantity
+so the c-4 quasi randomness condition
+
+ align:start position:0%
+so the c-4 quasi randomness condition
+ 
+
+ align:start position:0%
+so the c-4 quasi randomness condition
+it's really the equivalent to replacing
+
+ align:start position:0%
+it's really the equivalent to replacing
+ 
+
+ align:start position:0%
+it's really the equivalent to replacing
+this less than or equal to u by an equal
+
+ align:start position:0%
+this less than or equal to u by an equal
+ 
+
+ align:start position:0%
+this less than or equal to u by an equal
+sign ok so let's get started with
+
+ align:start position:0%
+sign ok so let's get started with
+ 
+
+ align:start position:0%
+sign ok so let's get started with
+proving the chunk um Wilson theorem so
+
+ align:start position:0%
+proving the chunk um Wilson theorem so
+ 
+
+ align:start position:0%
+proving the chunk um Wilson theorem so
+the first place that we'll look at is
+
+ align:start position:0%
+the first place that we'll look at is
+ 
+
+ align:start position:0%
+the first place that we'll look at is
+the two versions of disk disk stands for
+
+ align:start position:0%
+the two versions of disk disk stands for
+ 
+
+ align:start position:0%
+the two versions of disk disk stands for
+discrepancy okay so first fact that disk
+
+ align:start position:0%
+discrepancy okay so first fact that disk
+ 
+
+ align:start position:0%
+discrepancy okay so first fact that disk
+implies this prime I mean this is pretty
+
+ align:start position:0%
+implies this prime I mean this is pretty
+ 
+
+ align:start position:0%
+implies this prime I mean this is pretty
+easy you take Y 2 equal to X be slightly
+
+ align:start position:0%
+easy you take Y 2 equal to X be slightly
+ 
+
+ align:start position:0%
+easy you take Y 2 equal to X be slightly
+careful about the definitions but you're
+
+ align:start position:0%
+careful about the definitions but you're
+ 
+
+ align:start position:0%
+careful about the definitions but you're
+okay not much to do that
+
+ align:start position:0%
+okay not much to do that
+ 
+
+ align:start position:0%
+okay not much to do that
+the other direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where you only have discrepancies for
+
+ align:start position:0%
+where you only have discrepancies for
+ 
+
+ align:start position:0%
+where you only have discrepancies for
+single sets and you want to produce
+
+ align:start position:0%
+single sets and you want to produce
+ 
+
+ align:start position:0%
+single sets and you want to produce
+discrepancies four pairs of sets ok so
+
+ align:start position:0%
+discrepancies four pairs of sets ok so
+ 
+
+ align:start position:0%
+discrepancies four pairs of sets ok so
+this is actually a fairly common
+
+ align:start position:0%
+this is actually a fairly common
+ 
+
+ align:start position:0%
+this is actually a fairly common
+technique in algebra that allows you to
+
+ align:start position:0%
+technique in algebra that allows you to
+ 
+
+ align:start position:0%
+technique in algebra that allows you to
+go from bilinear forms to quadratic
+
+ align:start position:0%
+go from bilinear forms to quadratic
+ 
+
+ align:start position:0%
+go from bilinear forms to quadratic
+forms and vice versa it's that kind of
+
+ align:start position:0%
+forms and vice versa it's that kind of
+ 
+
+ align:start position:0%
+forms and vice versa it's that kind of
+calculation so let me do it here
+
+ align:start position:0%
+calculation so let me do it here
+ 
+
+ align:start position:0%
+calculation so let me do it here
+concretely in this setting so here what
+
+ align:start position:0%
+concretely in this setting so here what
+ 
+
+ align:start position:0%
+concretely in this setting so here what
+you should think of is that you have two
+
+ align:start position:0%
+you should think of is that you have two
+ 
+
+ align:start position:0%
+you should think of is that you have two
+sets x and y and they might overlap and
+
+ align:start position:0%
+sets x and y and they might overlap and
+ 
+
+ align:start position:0%
+sets x and y and they might overlap and
+what they correspond to in the and you
+
+ align:start position:0%
+what they correspond to in the and you
+ 
+
+ align:start position:0%
+what they correspond to in the and you
+think about the corresponding Venn
+
+ align:start position:0%
+think about the corresponding Venn
+ 
+
+ align:start position:0%
+think about the corresponding Venn
+diagram where I am looking at ways that
+
+ align:start position:0%
+diagram where I am looking at ways that
+ 
+
+ align:start position:0%
+diagram where I am looking at ways that
+a vertex and fall in pair of vertices
+
+ align:start position:0%
+a vertex and fall in pair of vertices
+ 
+
+ align:start position:0%
+a vertex and fall in pair of vertices
+can fall in X and/or Y so if you have x
+
+ align:start position:0%
+can fall in X and/or Y so if you have x
+ 
+
+ align:start position:0%
+can fall in X and/or Y so if you have x
+and y and so it's useful to keep track
+
+ align:start position:0%
+and y and so it's useful to keep track
+ 
+
+ align:start position:0%
+and y and so it's useful to keep track
+of which vertices are in which set but
+
+ align:start position:0%
+of which vertices are in which set but
+ 
+
+ align:start position:0%
+of which vertices are in which set but
+what the thing finally comes down to is
+
+ align:start position:0%
+what the thing finally comes down to is
+ 
+
+ align:start position:0%
+what the thing finally comes down to is
+that the number of edges with one vertex
+
+ align:start position:0%
+that the number of edges with one vertex
+ 
+
+ align:start position:0%
+that the number of edges with one vertex
+in X on one vertex in Y I can write this
+
+ align:start position:0%
+in X on one vertex in Y I can write this
+ 
+
+ align:start position:0%
+in X on one vertex in Y I can write this
+bilinear form type quantity as a course
+
+ align:start position:0%
+bilinear form type quantity as a course
+ 
+
+ align:start position:0%
+bilinear form type quantity as a course
+as an appropriate some just number of
+
+ align:start position:0%
+as an appropriate some just number of
+ 
+
+ align:start position:0%
+as an appropriate some just number of
+edges in single sets okay so there are
+
+ align:start position:0%
+edges in single sets okay so there are
+ 
+
+ align:start position:0%
+edges in single sets okay so there are
+several ways to check that this is true
+
+ align:start position:0%
+several ways to check that this is true
+ 
+
+ align:start position:0%
+several ways to check that this is true
+one way is to just tally and keep track
+
+ align:start position:0%
+one way is to just tally and keep track
+ 
+
+ align:start position:0%
+one way is to just tally and keep track
+of how many edges are you counting in
+
+ align:start position:0%
+of how many edges are you counting in
+ 
+
+ align:start position:0%
+of how many edges are you counting in
+each step so if you are trying to count
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the number of edges in yeah so let's say
+
+ align:start position:0%
+the number of edges in yeah so let's say
+ 
+
+ align:start position:0%
+the number of edges in yeah so let's say
+if you're trying to count the number of
+
+ align:start position:0%
+if you're trying to count the number of
+ 
+
+ align:start position:0%
+if you're trying to count the number of
+edges in with one vertex in x one vertex
+
+ align:start position:0%
+edges in with one vertex in x one vertex
+ 
+
+ align:start position:0%
+edges in with one vertex in x one vertex
+in Y then what this corresponds to is
+
+ align:start position:0%
+in Y then what this corresponds to is
+ 
+
+ align:start position:0%
+in Y then what this corresponds to is
+that count but let me do a reflection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you see that you can write this
+
+ align:start position:0%
+and then you see that you can write this
+ 
+
+ align:start position:0%
+and then you see that you can write this
+some say alternating sum of principal
+
+ align:start position:0%
+some say alternating sum of principal
+ 
+
+ align:start position:0%
+some say alternating sum of principal
+squares so this one big square plus the
+
+ align:start position:0%
+squares so this one big square plus the
+ 
+
+ align:start position:0%
+squares so this one big square plus the
+middle square and minus the 2 side
+
+ align:start position:0%
+middle square and minus the 2 side
+ 
+
+ align:start position:0%
+middle square and minus the 2 side
+squares which is what that sum comes to
+
+ align:start position:0%
+squares which is what that sum comes to
+ 
+
+ align:start position:0%
+squares which is what that sum comes to
+alright so if we assume this prime then
+
+ align:start position:0%
+alright so if we assume this prime then
+ 
+
+ align:start position:0%
+alright so if we assume this prime then
+I know that all of these individual sets
+
+ align:start position:0%
+I know that all of these individual sets
+ 
+
+ align:start position:0%
+I know that all of these individual sets
+have roughly the correct number of edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up to a little o of n squared error and
+
+ align:start position:0%
+up to a little o of n squared error and
+ 
+
+ align:start position:0%
+up to a little o of n squared error and
+again like I don't have to do this
+
+ align:start position:0%
+again like I don't have to do this
+ 
+
+ align:start position:0%
+again like I don't have to do this
+calculation again because it's the same
+
+ align:start position:0%
+calculation again because it's the same
+ 
+
+ align:start position:0%
+calculation again because it's the same
+calculation so the final thing should be
+
+ align:start position:0%
+calculation so the final thing should be
+ 
+
+ align:start position:0%
+calculation so the final thing should be
+P times the sizes of x and y together
+
+ align:start position:0%
+P times the sizes of x and y together
+ 
+
+ align:start position:0%
+P times the sizes of x and y together
+Plus this same error ok so that shows
+
+ align:start position:0%
+Plus this same error ok so that shows
+ 
+
+ align:start position:0%
+Plus this same error ok so that shows
+you this prime implies disk so the self
+
+ align:start position:0%
+you this prime implies disk so the self
+ 
+
+ align:start position:0%
+you this prime implies disk so the self
+version of discrepancy implies the pair
+
+ align:start position:0%
+version of discrepancy implies the pair
+ 
+
+ align:start position:0%
+version of discrepancy implies the pair
+version and discrepancy so let's move on
+
+ align:start position:0%
+version and discrepancy so let's move on
+ 
+
+ align:start position:0%
+version and discrepancy so let's move on
+to count
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to show that disk implies count actually
+
+ align:start position:0%
+to show that disk implies count actually
+ 
+
+ align:start position:0%
+to show that disk implies count actually
+we already did this so this is the
+
+ align:start position:0%
+we already did this so this is the
+ 
+
+ align:start position:0%
+we already did this so this is the
+counting lemma so the counting lemma
+
+ align:start position:0%
+counting lemma so the counting lemma
+ 
+
+ align:start position:0%
+counting lemma so the counting lemma
+tells us how to count labelled copies if
+
+ align:start position:0%
+tells us how to count labelled copies if
+ 
+
+ align:start position:0%
+tells us how to count labelled copies if
+you have these epsilon regularity
+
+ align:start position:0%
+you have these epsilon regularity
+ 
+
+ align:start position:0%
+you have these epsilon regularity
+conditions which is exactly what this
+
+ align:start position:0%
+conditions which is exactly what this
+ 
+
+ align:start position:0%
+conditions which is exactly what this
+case so so count is good
+
+ align:start position:0%
+case so so count is good
+ 
+
+ align:start position:0%
+case so so count is good
+another easy implication
+
+ align:start position:0%
+another easy implication
+ 
+
+ align:start position:0%
+another easy implication
+yes can implies c4 or this is actually
+
+ align:start position:0%
+yes can implies c4 or this is actually
+ 
+
+ align:start position:0%
+yes can implies c4 or this is actually
+just tautological c4 condition is a
+
+ align:start position:0%
+just tautological c4 condition is a
+ 
+
+ align:start position:0%
+just tautological c4 condition is a
+special case of of the count hypothesis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's move on to some
+
+ align:start position:0%
+all right so let's move on to some
+ 
+
+ align:start position:0%
+all right so let's move on to some
+additional implications that require a
+
+ align:start position:0%
+additional implications that require a
+ 
+
+ align:start position:0%
+additional implications that require a
+bit more work so what about c4 implies
+
+ align:start position:0%
+bit more work so what about c4 implies
+ 
+
+ align:start position:0%
+bit more work so what about c4 implies
+Co degree so this is where we need to do
+
+ align:start position:0%
+Co degree so this is where we need to do
+ 
+
+ align:start position:0%
+Co degree so this is where we need to do
+this kind of Cauchy Schwarz exercise so
+
+ align:start position:0%
+this kind of Cauchy Schwarz exercise so
+ 
+
+ align:start position:0%
+this kind of Cauchy Schwarz exercise so
+let's start with c4 so assume the c-4
+
+ align:start position:0%
+let's start with c4 so assume the c-4
+ 
+
+ align:start position:0%
+let's start with c4 so assume the c-4
+condition and suppose you have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's so I want to deduce that
+
+ align:start position:0%
+okay so let's so I want to deduce that
+ 
+
+ align:start position:0%
+okay so let's so I want to deduce that
+the co degree condition is true but
+
+ align:start position:0%
+the co degree condition is true but
+ 
+
+ align:start position:0%
+the co degree condition is true but
+first let's think about just what is the
+
+ align:start position:0%
+first let's think about just what is the
+ 
+
+ align:start position:0%
+first let's think about just what is the
+sum of these Co degrees as I vary U and
+
+ align:start position:0%
+sum of these Co degrees as I vary U and
+ 
+
+ align:start position:0%
+sum of these Co degrees as I vary U and
+V over all pairs of vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the a picture so that is
+
+ align:start position:0%
+so this is the a picture so that is
+ 
+
+ align:start position:0%
+so this is the a picture so that is
+equal to the sums of degrees squared
+
+ align:start position:0%
+equal to the sums of degrees squared
+ 
+
+ align:start position:0%
+equal to the sums of degrees squared
+which now by cauchy-schwarz you can
+
+ align:start position:0%
+which now by cauchy-schwarz you can
+ 
+
+ align:start position:0%
+which now by cauchy-schwarz you can
+reduce to be at least n times 2 raised
+
+ align:start position:0%
+reduce to be at least n times 2 raised
+ 
+
+ align:start position:0%
+reduce to be at least n times 2 raised
+to the number of edges namely the sum of
+
+ align:start position:0%
+to the number of edges namely the sum of
+ 
+
+ align:start position:0%
+to the number of edges namely the sum of
+the degrees
+
+ align:start position:0%
+the degrees
+ 
+
+ align:start position:0%
+the degrees
+I think squared so now we assumed the
+
+ align:start position:0%
+I think squared so now we assumed the
+ 
+
+ align:start position:0%
+I think squared so now we assumed the
+c-4 condition actually we assume that G
+
+ align:start position:0%
+c-4 condition actually we assume that G
+ 
+
+ align:start position:0%
+c-4 condition actually we assume that G
+has the density yes written up there so
+
+ align:start position:0%
+has the density yes written up there so
+ 
+
+ align:start position:0%
+has the density yes written up there so
+this quantity is P squared plus Pluto 1
+
+ align:start position:0%
+this quantity is P squared plus Pluto 1
+ 
+
+ align:start position:0%
+this quantity is P squared plus Pluto 1
+times n which is what you should expect
+
+ align:start position:0%
+times n which is what you should expect
+ 
+
+ align:start position:0%
+times n which is what you should expect
+in a random graph of GMP okay so that's
+
+ align:start position:0%
+in a random graph of GMP okay so that's
+ 
+
+ align:start position:0%
+in a random graph of GMP okay so that's
+but that's not quite what we're looking
+
+ align:start position:0%
+but that's not quite what we're looking
+ 
+
+ align:start position:0%
+but that's not quite what we're looking
+for okay so this is just the sum of the
+
+ align:start position:0%
+for okay so this is just the sum of the
+ 
+
+ align:start position:0%
+for okay so this is just the sum of the
+co degrees what we actually want is the
+
+ align:start position:0%
+co degrees what we actually want is the
+ 
+
+ align:start position:0%
+co degrees what we actually want is the
+deviation of co degrees from its
+
+ align:start position:0%
+deviation of co degrees from its
+ 
+
+ align:start position:0%
+deviation of co degrees from its
+expectation so to speak you know here's
+
+ align:start position:0%
+expectation so to speak you know here's
+ 
+
+ align:start position:0%
+expectation so to speak you know here's
+a important technique from probabilistic
+
+ align:start position:0%
+a important technique from probabilistic
+ 
+
+ align:start position:0%
+a important technique from probabilistic
+component works is that if you want to
+
+ align:start position:0%
+component works is that if you want to
+ 
+
+ align:start position:0%
+component works is that if you want to
+control the deviation of a random
+
+ align:start position:0%
+control the deviation of a random
+ 
+
+ align:start position:0%
+control the deviation of a random
+variable one thing should look at is the
+
+ align:start position:0%
+variable one thing should look at is the
+ 
+
+ align:start position:0%
+variable one thing should look at is the
+variance so if you can control the
+
+ align:start position:0%
+variance so if you can control the
+ 
+
+ align:start position:0%
+variance so if you can control the
+variance then you can control the
+
+ align:start position:0%
+variance then you can control the
+ 
+
+ align:start position:0%
+variance then you can control the
+deviation and this is a method known as
+
+ align:start position:0%
+deviation and this is a method known as
+ 
+
+ align:start position:0%
+deviation and this is a method known as
+the second moment method and that's what
+
+ align:start position:0%
+the second moment method and that's what
+ 
+
+ align:start position:0%
+the second moment method and that's what
+we're going to do here so what we'll try
+
+ align:start position:0%
+we're going to do here so what we'll try
+ 
+
+ align:start position:0%
+we're going to do here so what we'll try
+to show is that the second moment of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this code agrees a meter
+
+ align:start position:0%
+this code agrees a meter
+ 
+
+ align:start position:0%
+this code agrees a meter
+sum of their squares it's also what you
+
+ align:start position:0%
+sum of their squares it's also what you
+ 
+
+ align:start position:0%
+sum of their squares it's also what you
+should expect as if the random setting
+
+ align:start position:0%
+should expect as if the random setting
+ 
+
+ align:start position:0%
+should expect as if the random setting
+and then you can put them together to
+
+ align:start position:0%
+and then you can put them together to
+ 
+
+ align:start position:0%
+and then you can put them together to
+show what you want so this quantity here
+
+ align:start position:0%
+show what you want so this quantity here
+ 
+
+ align:start position:0%
+show what you want so this quantity here
+well what is this we just saw see up
+
+ align:start position:0%
+well what is this we just saw see up
+ 
+
+ align:start position:0%
+well what is this we just saw see up
+there it's also called degree square
+
+ align:start position:0%
+there it's also called degree square
+ 
+
+ align:start position:0%
+there it's also called degree square
+squared so this quantity is also the
+
+ align:start position:0%
+squared so this quantity is also the
+ 
+
+ align:start position:0%
+squared so this quantity is also the
+number of labeled copies of c4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not quite because you might have two
+
+ align:start position:0%
+not quite because you might have two
+ 
+
+ align:start position:0%
+not quite because you might have two
+vertices and the amber at the same
+
+ align:start position:0%
+vertices and the amber at the same
+ 
+
+ align:start position:0%
+vertices and the amber at the same
+vertex so I incorporate a small error so
+
+ align:start position:0%
+vertex so I incorporate a small error so
+ 
+
+ align:start position:0%
+vertex so I incorporate a small error so
+it's really a sub it's a cubic error but
+
+ align:start position:0%
+it's really a sub it's a cubic error but
+ 
+
+ align:start position:0%
+it's really a sub it's a cubic error but
+certainly sub n to the fourth and we
+
+ align:start position:0%
+certainly sub n to the fourth and we
+ 
+
+ align:start position:0%
+certainly sub n to the fourth and we
+assume that the number of labeled copies
+
+ align:start position:0%
+assume that the number of labeled copies
+ 
+
+ align:start position:0%
+assume that the number of labeled copies
+of c-4 by the support condition is no
+
+ align:start position:0%
+of c-4 by the support condition is no
+ 
+
+ align:start position:0%
+of c-4 by the support condition is no
+more than basically P to the 4 times and
+
+ align:start position:0%
+more than basically P to the 4 times and
+ 
+
+ align:start position:0%
+more than basically P to the 4 times and
+raise to the power 4 okay so now you
+
+ align:start position:0%
+raise to the power 4 okay so now you
+ 
+
+ align:start position:0%
+raise to the power 4 okay so now you
+have a first moment for some average and
+
+ align:start position:0%
+have a first moment for some average and
+ 
+
+ align:start position:0%
+have a first moment for some average and
+you have some control in the second
+
+ align:start position:0%
+you have some control in the second
+ 
+
+ align:start position:0%
+you have some control in the second
+moment I can put them together to bound
+
+ align:start position:0%
+moment I can put them together to bound
+ 
+
+ align:start position:0%
+moment I can put them together to bound
+the deviation using this idea of
+
+ align:start position:0%
+the deviation using this idea of
+ 
+
+ align:start position:0%
+the deviation using this idea of
+controlling variance code degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deviation is upper bounded by okay so
+
+ align:start position:0%
+deviation is upper bounded by okay so
+ 
+
+ align:start position:0%
+deviation is upper bounded by okay so
+here using Cauchy Schwartz it's upper
+
+ align:start position:0%
+here using Cauchy Schwartz it's upper
+ 
+
+ align:start position:0%
+here using Cauchy Schwartz it's upper
+bounded by basically the same sum except
+
+ align:start position:0%
+bounded by basically the same sum except
+ 
+
+ align:start position:0%
+bounded by basically the same sum except
+I want to square the summoned this also
+
+ align:start position:0%
+I want to square the summoned this also
+ 
+
+ align:start position:0%
+I want to square the summoned this also
+gets rid of the pesky absolute value
+
+ align:start position:0%
+gets rid of the pesky absolute value
+ 
+
+ align:start position:0%
+gets rid of the pesky absolute value
+sign which is not nicely algebraically
+
+ align:start position:0%
+sign which is not nicely algebraically
+ 
+
+ align:start position:0%
+sign which is not nicely algebraically
+behaved now at the square and I can
+
+ align:start position:0%
+behaved now at the square and I can
+ 
+
+ align:start position:0%
+behaved now at the square and I can
+expand the square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I expand the square into these
+
+ align:start position:0%
+okay so I expand the square into these
+ 
+
+ align:start position:0%
+okay so I expand the square into these
+terms and the final term here it's P 2 4
+
+ align:start position:0%
+terms and the final term here it's P 2 4
+ 
+
+ align:start position:0%
+terms and the final term here it's P 2 4
+& 6 all right but I have controlled
+
+ align:start position:0%
+& 6 all right but I have controlled
+ 
+
+ align:start position:0%
+& 6 all right but I have controlled
+individual terms from the calculations
+
+ align:start position:0%
+individual terms from the calculations
+ 
+
+ align:start position:0%
+individual terms from the calculations
+above so I can upper bound this
+
+ align:start position:0%
+above so I can upper bound this
+ 
+
+ align:start position:0%
+above so I can upper bound this
+expression by what I'm writing down now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and basically you should expect that
+
+ align:start position:0%
+and basically you should expect that
+ 
+
+ align:start position:0%
+and basically you should expect that
+everything should cancel out because
+
+ align:start position:0%
+everything should cancel out because
+ 
+
+ align:start position:0%
+everything should cancel out because
+they do cancel all in a random case but
+
+ align:start position:0%
+they do cancel all in a random case but
+ 
+
+ align:start position:0%
+they do cancel all in a random case but
+of course it's a sin if you check it's
+
+ align:start position:0%
+of course it's a sin if you check it's
+ 
+
+ align:start position:0%
+of course it's a sin if you check it's
+it's important to write down this
+
+ align:start position:0%
+it's important to write down this
+ 
+
+ align:start position:0%
+it's important to write down this
+calculation so if everything works all
+
+ align:start position:0%
+calculation so if everything works all
+ 
+
+ align:start position:0%
+calculation so if everything works all
+right everything should cancel out and
+
+ align:start position:0%
+right everything should cancel out and
+ 
+
+ align:start position:0%
+right everything should cancel out and
+indeed it you cancel out and you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so everything should cancel out and
+
+ align:start position:0%
+this so everything should cancel out and
+ 
+
+ align:start position:0%
+this so everything should cancel out and
+you get a little o of n cubed I have to
+
+ align:start position:0%
+you get a little o of n cubed I have to
+ 
+
+ align:start position:0%
+you get a little o of n cubed I have to
+summarize in this implication from c42
+
+ align:start position:0%
+summarize in this implication from c42
+ 
+
+ align:start position:0%
+summarize in this implication from c42
+to Co degree what we're doing is were
+
+ align:start position:0%
+to Co degree what we're doing is were
+ 
+
+ align:start position:0%
+to Co degree what we're doing is were
+controlling the variance of Co degrees
+
+ align:start position:0%
+controlling the variance of Co degrees
+ 
+
+ align:start position:0%
+controlling the variance of Co degrees
+using the c4 condition and a second
+
+ align:start position:0%
+using the c4 condition and a second
+ 
+
+ align:start position:0%
+using the c4 condition and a second
+moment bound showing that the c-4
+
+ align:start position:0%
+moment bound showing that the c-4
+ 
+
+ align:start position:0%
+moment bound showing that the c-4
+condition you know trumps over to a col
+
+ align:start position:0%
+condition you know trumps over to a col
+ 
+
+ align:start position:0%
+condition you know trumps over to a col
+degree condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions so far okay so I'll let
+
+ align:start position:0%
+any questions so far okay so I'll let
+ 
+
+ align:start position:0%
+any questions so far okay so I'll let
+you ponder in this calculation the next
+
+ align:start position:0%
+you ponder in this calculation the next
+ 
+
+ align:start position:0%
+you ponder in this calculation the next
+one that will do is Co degree implies
+
+ align:start position:0%
+one that will do is Co degree implies
+ 
+
+ align:start position:0%
+one that will do is Co degree implies
+disk okay and that will be a calculation
+
+ align:start position:0%
+disk okay and that will be a calculation
+ 
+
+ align:start position:0%
+disk okay and that will be a calculation
+in a very similar flavor but it will be
+
+ align:start position:0%
+in a very similar flavor but it will be
+ 
+
+ align:start position:0%
+in a very similar flavor but it will be
+a slightly longer by a similar flavor
+
+ align:start position:0%
+a slightly longer by a similar flavor
+ 
+
+ align:start position:0%
+a slightly longer by a similar flavor
+calculation so let me do that after the
+
+ align:start position:0%
+calculation so let me do that after the
+ 
+
+ align:start position:0%
+calculation so let me do that after the
+break alright so what we've done so far
+
+ align:start position:0%
+break alright so what we've done so far
+ 
+
+ align:start position:0%
+break alright so what we've done so far
+so let's summarize the chain of
+
+ align:start position:0%
+so let's summarize the chain of
+ 
+
+ align:start position:0%
+so let's summarize the chain of
+implications that we have already proved
+
+ align:start position:0%
+implications that we have already proved
+ 
+
+ align:start position:0%
+implications that we have already proved
+so first we started with showing that
+
+ align:start position:0%
+so first we started with showing that
+ 
+
+ align:start position:0%
+so first we started with showing that
+the two versions of disk are equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we also noticed that disk
+
+ align:start position:0%
+and then we also noticed that disk
+ 
+
+ align:start position:0%
+and then we also noticed that disk
+implies count through the counting lemma
+
+ align:start position:0%
+implies count through the counting lemma
+ 
+
+ align:start position:0%
+implies count through the counting lemma
+so we also observe that count implies c4
+
+ align:start position:0%
+so we also observe that count implies c4
+ 
+
+ align:start position:0%
+so we also observe that count implies c4
+tautologically and c-4 implies code
+
+ align:start position:0%
+tautologically and c-4 implies code
+ 
+
+ align:start position:0%
+tautologically and c-4 implies code
+agree okay so the next natural thing to
+
+ align:start position:0%
+agree okay so the next natural thing to
+ 
+
+ align:start position:0%
+agree okay so the next natural thing to
+do is to complete this circuit and show
+
+ align:start position:0%
+do is to complete this circuit and show
+ 
+
+ align:start position:0%
+do is to complete this circuit and show
+that the code agree condition implies
+
+ align:start position:0%
+that the code agree condition implies
+ 
+
+ align:start position:0%
+that the code agree condition implies
+that the discrepancy condition so that's
+
+ align:start position:0%
+that the discrepancy condition so that's
+ 
+
+ align:start position:0%
+that the discrepancy condition so that's
+what we do next and in some sense you
+
+ align:start position:0%
+what we do next and in some sense you
+ 
+
+ align:start position:0%
+what we do next and in some sense you
+know these two steps you should think of
+
+ align:start position:0%
+know these two steps you should think of
+ 
+
+ align:start position:0%
+know these two steps you should think of
+them as going in this natural chain
+
+ align:start position:0%
+them as going in this natural chain
+ 
+
+ align:start position:0%
+them as going in this natural chain
+where C 4 so C 4 is 4 like this C 4 code
+
+ align:start position:0%
+where C 4 so C 4 is 4 like this C 4 code
+ 
+
+ align:start position:0%
+where C 4 so C 4 is 4 like this C 4 code
+agree condition is really about that and
+
+ align:start position:0%
+agree condition is really about that and
+ 
+
+ align:start position:0%
+agree condition is really about that and
+disk it's really about single edges as
+
+ align:start position:0%
+disk it's really about single edges as
+ 
+
+ align:start position:0%
+disk it's really about single edges as
+you can go from top if you you have you
+
+ align:start position:0%
+you can go from top if you you have you
+ 
+
+ align:start position:0%
+you can go from top if you you have you
+you get much more power so it's going in
+
+ align:start position:0%
+you get much more power so it's going in
+ 
+
+ align:start position:0%
+you get much more power so it's going in
+the right direction going downstream so
+
+ align:start position:0%
+the right direction going downstream so
+ 
+
+ align:start position:0%
+the right direction going downstream so
+to speak so that's what we're doing now
+
+ align:start position:0%
+to speak so that's what we're doing now
+ 
+
+ align:start position:0%
+to speak so that's what we're doing now
+going downstream and then you go
+
+ align:start position:0%
+going downstream and then you go
+ 
+
+ align:start position:0%
+going downstream and then you go
+upstream via the counting number all
+
+ align:start position:0%
+upstream via the counting number all
+ 
+
+ align:start position:0%
+upstream via the counting number all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+let's do code degree implies disk so we
+
+ align:start position:0%
+let's do code degree implies disk so we
+ 
+
+ align:start position:0%
+let's do code degree implies disk so we
+want to show the discrepancy condition
+
+ align:start position:0%
+want to show the discrepancy condition
+ 
+
+ align:start position:0%
+want to show the discrepancy condition
+which is one written up there but before
+
+ align:start position:0%
+which is one written up there but before
+ 
+
+ align:start position:0%
+which is one written up there but before
+that let me first show you that the
+
+ align:start position:0%
+that let me first show you that the
+ 
+
+ align:start position:0%
+that let me first show you that the
+degrees do not vary too much so that the
+
+ align:start position:0%
+degrees do not vary too much so that the
+ 
+
+ align:start position:0%
+degrees do not vary too much so that the
+degrees are fairly well distributed
+
+ align:start position:0%
+degrees are fairly well distributed
+ 
+
+ align:start position:0%
+degrees are fairly well distributed
+which is what you should expect in a
+
+ align:start position:0%
+which is what you should expect in a
+ 
+
+ align:start position:0%
+which is what you should expect in a
+pseudo random graph right so you don't
+
+ align:start position:0%
+pseudo random graph right so you don't
+ 
+
+ align:start position:0%
+pseudo random graph right so you don't
+expect a half the vertices half into
+
+ align:start position:0%
+expect a half the vertices half into
+ 
+
+ align:start position:0%
+expect a half the vertices half into
+Greece twice the other half so that's
+
+ align:start position:0%
+Greece twice the other half so that's
+ 
+
+ align:start position:0%
+Greece twice the other half so that's
+the first thing I want to establish if
+
+ align:start position:0%
+the first thing I want to establish if
+ 
+
+ align:start position:0%
+the first thing I want to establish if
+you look at degrees this variant this
+
+ align:start position:0%
+you look at degrees this variant this
+ 
+
+ align:start position:0%
+you look at degrees this variant this
+this deviation is it's not too big okay
+
+ align:start position:0%
+this deviation is it's not too big okay
+ 
+
+ align:start position:0%
+this deviation is it's not too big okay
+so like before we've seen absolute value
+
+ align:start position:0%
+so like before we've seen absolute value
+ 
+
+ align:start position:0%
+so like before we've seen absolute value
+sign we see some so what do you coffee
+
+ align:start position:0%
+sign we see some so what do you coffee
+ 
+
+ align:start position:0%
+sign we see some so what do you coffee
+shorts coffee Schwartz allows us to
+
+ align:start position:0%
+shorts coffee Schwartz allows us to
+ 
+
+ align:start position:0%
+shorts coffee Schwartz allows us to
+bound this quantity replacing the
+
+ align:start position:0%
+bound this quantity replacing the
+ 
+
+ align:start position:0%
+bound this quantity replacing the
+summoned by a sum of squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a square so I can expand the square so
+
+ align:start position:0%
+a square so I can expand the square so
+ 
+
+ align:start position:0%
+a square so I can expand the square so
+let me expand the square I get that
+
+ align:start position:0%
+let me expand the square I get that
+ 
+
+ align:start position:0%
+let me expand the square I get that
+so just expanding this square inside and
+
+ align:start position:0%
+so just expanding this square inside and
+ 
+
+ align:start position:0%
+so just expanding this square inside and
+you see this degree squared is that
+
+ align:start position:0%
+you see this degree squared is that
+ 
+
+ align:start position:0%
+you see this degree squared is that
+picture so that's some of code degrees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and some of the degrees is just a number
+
+ align:start position:0%
+and some of the degrees is just a number
+ 
+
+ align:start position:0%
+and some of the degrees is just a number
+of edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but we now assume the code agree
+
+ align:start position:0%
+okay but we now assume the code agree
+ 
+
+ align:start position:0%
+okay but we now assume the code agree
+condition which in particular implies
+
+ align:start position:0%
+condition which in particular implies
+ 
+
+ align:start position:0%
+condition which in particular implies
+that the sum the code agrees is roughly
+
+ align:start position:0%
+that the sum the code agrees is roughly
+ 
+
+ align:start position:0%
+that the sum the code agrees is roughly
+what you expect so the sum of the code
+
+ align:start position:0%
+what you expect so the sum of the code
+ 
+
+ align:start position:0%
+what you expect so the sum of the code
+agrees should be P Square and cubed plus
+
+ align:start position:0%
+agrees should be P Square and cubed plus
+ 
+
+ align:start position:0%
+agrees should be P Square and cubed plus
+a little ol and cube error at the end
+
+ align:start position:0%
+a little ol and cube error at the end
+ 
+
+ align:start position:0%
+a little ol and cube error at the end
+likewise the number of edges is by
+
+ align:start position:0%
+likewise the number of edges is by
+ 
+
+ align:start position:0%
+likewise the number of edges is by
+assumption what you would expect in a
+
+ align:start position:0%
+assumption what you would expect in a
+ 
+
+ align:start position:0%
+assumption what you would expect in a
+random graph and then a final term and
+
+ align:start position:0%
+random graph and then a final term and
+ 
+
+ align:start position:0%
+random graph and then a final term and
+like before of course it's good to do it
+
+ align:start position:0%
+like before of course it's good to do it
+ 
+
+ align:start position:0%
+like before of course it's good to do it
+since then if you check everything
+
+ align:start position:0%
+since then if you check everything
+ 
+
+ align:start position:0%
+since then if you check everything
+should cancel out so what you end up
+
+ align:start position:0%
+should cancel out so what you end up
+ 
+
+ align:start position:0%
+should cancel out so what you end up
+with is little o of N squared showing
+
+ align:start position:0%
+with is little o of N squared showing
+ 
+
+ align:start position:0%
+with is little o of N squared showing
+that the degrees do not vary too much
+
+ align:start position:0%
+that the degrees do not vary too much
+ 
+
+ align:start position:0%
+that the degrees do not vary too much
+and once you have that promise then we
+
+ align:start position:0%
+and once you have that promise then we
+ 
+
+ align:start position:0%
+and once you have that promise then we
+move on to the actual discrepancy
+
+ align:start position:0%
+move on to the actual discrepancy
+ 
+
+ align:start position:0%
+move on to the actual discrepancy
+condition so this discrepancy is can be
+
+ align:start position:0%
+condition so this discrepancy is can be
+ 
+
+ align:start position:0%
+condition so this discrepancy is can be
+rewritten as the sum over vertices
+
+ align:start position:0%
+rewritten as the sum over vertices
+ 
+
+ align:start position:0%
+rewritten as the sum over vertices
+little X in big x degree from little X
+
+ align:start position:0%
+little X in big x degree from little X
+ 
+
+ align:start position:0%
+little X in big x degree from little X
+to Y minus key times the size of y okay
+
+ align:start position:0%
+to Y minus key times the size of y okay
+ 
+
+ align:start position:0%
+to Y minus key times the size of y okay
+so rewriting this sum of course what
+
+ align:start position:0%
+so rewriting this sum of course what
+ 
+
+ align:start position:0%
+so rewriting this sum of course what
+should we do next
+
+ align:start position:0%
+should we do next
+ 
+
+ align:start position:0%
+should we do next
+Cosi sorts great so what do you call
+
+ align:start position:0%
+Cosi sorts great so what do you call
+ 
+
+ align:start position:0%
+Cosi sorts great so what do you call
+shorts okay so here's a here's a
+
+ align:start position:0%
+shorts okay so here's a here's a
+ 
+
+ align:start position:0%
+shorts okay so here's a here's a
+important step or a trick if you will so
+
+ align:start position:0%
+important step or a trick if you will so
+ 
+
+ align:start position:0%
+important step or a trick if you will so
+what do you coach is shorts and
+
+ align:start position:0%
+what do you coach is shorts and
+ 
+
+ align:start position:0%
+what do you coach is shorts and
+something very nice happens we need your
+
+ align:start position:0%
+something very nice happens we need your
+ 
+
+ align:start position:0%
+something very nice happens we need your
+coffee shorts here instead okay so you
+
+ align:start position:0%
+coffee shorts here instead okay so you
+ 
+
+ align:start position:0%
+coffee shorts here instead okay so you
+can write down the expression that you
+
+ align:start position:0%
+can write down the expression that you
+ 
+
+ align:start position:0%
+can write down the expression that you
+obtain when you do coffee shorts so we
+
+ align:start position:0%
+obtain when you do coffee shorts so we
+ 
+
+ align:start position:0%
+obtain when you do coffee shorts so we
+do that first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's a step which is very easy
+
+ align:start position:0%
+okay so here's a step which is very easy
+ 
+
+ align:start position:0%
+okay so here's a step which is very easy
+to cross over but I want to pause and
+
+ align:start position:0%
+to cross over but I want to pause and
+ 
+
+ align:start position:0%
+to cross over but I want to pause and
+emphasize this step because this is
+
+ align:start position:0%
+emphasize this step because this is
+ 
+
+ align:start position:0%
+emphasize this step because this is
+actually really important what I'm going
+
+ align:start position:0%
+actually really important what I'm going
+ 
+
+ align:start position:0%
+actually really important what I'm going
+to do now is to observe that the summon
+
+ align:start position:0%
+to do now is to observe that the summon
+ 
+
+ align:start position:0%
+to do now is to observe that the summon
+is always non-negative therefore I can
+
+ align:start position:0%
+is always non-negative therefore I can
+ 
+
+ align:start position:0%
+is always non-negative therefore I can
+enlarge the sum from just little X in X
+
+ align:start position:0%
+enlarge the sum from just little X in X
+ 
+
+ align:start position:0%
+enlarge the sum from just little X in X
+to the entire vertex set and this is
+
+ align:start position:0%
+to the entire vertex set and this is
+ 
+
+ align:start position:0%
+to the entire vertex set and this is
+important right so this is important
+
+ align:start position:0%
+important right so this is important
+ 
+
+ align:start position:0%
+important right so this is important
+that we had to do coffee shorts first to
+
+ align:start position:0%
+that we had to do coffee shorts first to
+ 
+
+ align:start position:0%
+that we had to do coffee shorts first to
+get a non negative someone you couldn't
+
+ align:start position:0%
+get a non negative someone you couldn't
+ 
+
+ align:start position:0%
+get a non negative someone you couldn't
+do this in the beginning so you do that
+
+ align:start position:0%
+do this in the beginning so you do that
+ 
+
+ align:start position:0%
+do this in the beginning so you do that
+and okay so I have this sum of squares
+
+ align:start position:0%
+and okay so I have this sum of squares
+ 
+
+ align:start position:0%
+and okay so I have this sum of squares
+so I expand expand I write out all these
+
+ align:start position:0%
+so I expand expand I write out all these
+ 
+
+ align:start position:0%
+so I expand expand I write out all these
+expressions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now the little x-range over the
+
+ align:start position:0%
+and now the little x-range over the
+ 
+
+ align:start position:0%
+and now the little x-range over the
+entire vertex set all right so what was
+
+ align:start position:0%
+entire vertex set all right so what was
+ 
+
+ align:start position:0%
+entire vertex set all right so what was
+the point of all of that so you see this
+
+ align:start position:0%
+the point of all of that so you see this
+ 
+
+ align:start position:0%
+the point of all of that so you see this
+expression here the degree of from
+
+ align:start position:0%
+expression here the degree of from
+ 
+
+ align:start position:0%
+expression here the degree of from
+little X to big Y squared okay so what
+
+ align:start position:0%
+little X to big Y squared okay so what
+ 
+
+ align:start position:0%
+little X to big Y squared okay so what
+is that how can we rewrite this
+
+ align:start position:0%
+is that how can we rewrite this
+ 
+
+ align:start position:0%
+is that how can we rewrite this
+expression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+honey little X Y squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so some of code degree of two
+
+ align:start position:0%
+yeah so some of code degree of two
+ 
+
+ align:start position:0%
+yeah so some of code degree of two
+vertices in Y so Y Y prime in Y code
+
+ align:start position:0%
+vertices in Y so Y Y prime in Y code
+ 
+
+ align:start position:0%
+vertices in Y so Y Y prime in Y code
+degree of little Y little Y Prime and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likewise the next expression can be
+
+ align:start position:0%
+likewise the next expression can be
+ 
+
+ align:start position:0%
+likewise the next expression can be
+written as the sum of the degrees of
+
+ align:start position:0%
+written as the sum of the degrees of
+ 
+
+ align:start position:0%
+written as the sum of the degrees of
+vertices in Y and the third term I leave
+
+ align:start position:0%
+vertices in Y and the third term I leave
+ 
+
+ align:start position:0%
+vertices in Y and the third term I leave
+unchanged so now we've gotten rid of
+
+ align:start position:0%
+unchanged so now we've gotten rid of
+ 
+
+ align:start position:0%
+unchanged so now we've gotten rid of
+these funny expressions we're just
+
+ align:start position:0%
+these funny expressions we're just
+ 
+
+ align:start position:0%
+these funny expressions we're just
+degree from the vertex to a set and we
+
+ align:start position:0%
+degree from the vertex to a set and we
+ 
+
+ align:start position:0%
+degree from the vertex to a set and we
+could do this because of this relaxation
+
+ align:start position:0%
+could do this because of this relaxation
+ 
+
+ align:start position:0%
+could do this because of this relaxation
+up here so that was that was the point
+
+ align:start position:0%
+up here so that was that was the point
+ 
+
+ align:start position:0%
+up here so that was that was the point
+we had to use this relaxation so now we
+
+ align:start position:0%
+we had to use this relaxation so now we
+ 
+
+ align:start position:0%
+we had to use this relaxation so now we
+get these Co degree terms but now
+
+ align:start position:0%
+get these Co degree terms but now
+ 
+
+ align:start position:0%
+get these Co degree terms but now
+because you have the Co degree terms and
+
+ align:start position:0%
+because you have the Co degree terms and
+ 
+
+ align:start position:0%
+because you have the Co degree terms and
+we assume the Co degree hypothesis we
+
+ align:start position:0%
+we assume the Co degree hypothesis we
+ 
+
+ align:start position:0%
+we assume the Co degree hypothesis we
+obtained that the sum is roughly what
+
+ align:start position:0%
+obtained that the sum is roughly what
+ 
+
+ align:start position:0%
+obtained that the sum is roughly what
+you expect as a random case because all
+
+ align:start position:0%
+you expect as a random case because all
+ 
+
+ align:start position:0%
+you expect as a random case because all
+the individual deviations do not add up
+
+ align:start position:0%
+the individual deviations do not add up
+ 
+
+ align:start position:0%
+the individual deviations do not add up
+to more than little and cubed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that could agree some so what you expect
+
+ align:start position:0%
+that could agree some so what you expect
+ 
+
+ align:start position:0%
+that could agree some so what you expect
+and the next term is some of the grease
+
+ align:start position:0%
+and the next term is some of the grease
+ 
+
+ align:start position:0%
+and the next term is some of the grease
+it's also by what we did up there what
+
+ align:start position:0%
+it's also by what we did up there what
+ 
+
+ align:start position:0%
+it's also by what we did up there what
+you expect and finally third term and as
+
+ align:start position:0%
+you expect and finally third term and as
+ 
+
+ align:start position:0%
+you expect and finally third term and as
+earlier if you did everything correctly
+
+ align:start position:0%
+earlier if you did everything correctly
+ 
+
+ align:start position:0%
+earlier if you did everything correctly
+everything should cancel and they do and
+
+ align:start position:0%
+everything should cancel and they do and
+ 
+
+ align:start position:0%
+everything should cancel and they do and
+so what you get at the end is total of n
+
+ align:start position:0%
+so what you get at the end is total of n
+ 
+
+ align:start position:0%
+so what you get at the end is total of n
+square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this completes this 4-cycle any
+
+ align:start position:0%
+okay this completes this 4-cycle any
+ 
+
+ align:start position:0%
+okay this completes this 4-cycle any
+questions so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're missing one more condition
+
+ align:start position:0%
+okay so we're missing one more condition
+ 
+
+ align:start position:0%
+okay so we're missing one more condition
+and that's the eigenvalue condition so
+
+ align:start position:0%
+and that's the eigenvalue condition so
+ 
+
+ align:start position:0%
+and that's the eigenvalue condition so
+so far everything had to deal with
+
+ align:start position:0%
+so far everything had to deal with
+ 
+
+ align:start position:0%
+so far everything had to deal with
+counting various things all right so
+
+ align:start position:0%
+counting various things all right so
+ 
+
+ align:start position:0%
+counting various things all right so
+what does eigenvalue have to do with
+
+ align:start position:0%
+what does eigenvalue have to do with
+ 
+
+ align:start position:0%
+what does eigenvalue have to do with
+anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the eigenvalue condition is actually
+
+ align:start position:0%
+so the eigenvalue condition is actually
+ 
+
+ align:start position:0%
+so the eigenvalue condition is actually
+a particularly important one and we'll
+
+ align:start position:0%
+a particularly important one and we'll
+ 
+
+ align:start position:0%
+a particularly important one and we'll
+see more of this in the next lecture but
+
+ align:start position:0%
+see more of this in the next lecture but
+ 
+
+ align:start position:0%
+see more of this in the next lecture but
+let me first show you the equivalent
+
+ align:start position:0%
+let me first show you the equivalent
+ 
+
+ align:start position:0%
+let me first show you the equivalent
+implications so what we'll show is that
+
+ align:start position:0%
+implications so what we'll show is that
+ 
+
+ align:start position:0%
+implications so what we'll show is that
+the eigen gallery condition is the
+
+ align:start position:0%
+the eigen gallery condition is the
+ 
+
+ align:start position:0%
+the eigen gallery condition is the
+equivalent to the c-4 condition so
+
+ align:start position:0%
+equivalent to the c-4 condition so
+ 
+
+ align:start position:0%
+equivalent to the c-4 condition so
+that's that's the goal I'll show you
+
+ align:start position:0%
+that's that's the goal I'll show you
+ 
+
+ align:start position:0%
+that's that's the goal I'll show you
+covalent between I and c4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first implies the c-4 condition
+
+ align:start position:0%
+so first implies the c-4 condition
+ 
+
+ align:start position:0%
+so first implies the c-4 condition
+because up to so instead of counting
+
+ align:start position:0%
+because up to so instead of counting
+ 
+
+ align:start position:0%
+because up to so instead of counting
+cforce which is a little bit actually
+
+ align:start position:0%
+cforce which is a little bit actually
+ 
+
+ align:start position:0%
+cforce which is a little bit actually
+not it's been annoying to do actual
+
+ align:start position:0%
+not it's been annoying to do actual
+ 
+
+ align:start position:0%
+not it's been annoying to do actual
+cforce just like earlier we want to
+
+ align:start position:0%
+cforce just like earlier we want to
+ 
+
+ align:start position:0%
+cforce just like earlier we want to
+consider homomorphic copies which are
+
+ align:start position:0%
+consider homomorphic copies which are
+ 
+
+ align:start position:0%
+consider homomorphic copies which are
+also labeled walks so closed walks of
+
+ align:start position:0%
+also labeled walks so closed walks of
+ 
+
+ align:start position:0%
+also labeled walks so closed walks of
+length 4 so up to a cubic error the
+
+ align:start position:0%
+length 4 so up to a cubic error the
+ 
+
+ align:start position:0%
+length 4 so up to a cubic error the
+number of labeled C force is given by
+
+ align:start position:0%
+number of labeled C force is given by
+ 
+
+ align:start position:0%
+number of labeled C force is given by
+the number of closed walks of length 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is equal to the trace of the
+
+ align:start position:0%
+which is equal to the trace of the
+ 
+
+ align:start position:0%
+which is equal to the trace of the
+fourth power of the adjacency matrix of
+
+ align:start position:0%
+fourth power of the adjacency matrix of
+ 
+
+ align:start position:0%
+fourth power of the adjacency matrix of
+this graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the next thing is super
+
+ align:start position:0%
+okay and the next thing is super
+ 
+
+ align:start position:0%
+okay and the next thing is super
+important so the next thing is this is
+
+ align:start position:0%
+important so the next thing is this is
+ 
+
+ align:start position:0%
+important so the next thing is this is
+sometimes called the trace method that
+
+ align:start position:0%
+sometimes called the trace method that
+ 
+
+ align:start position:0%
+sometimes called the trace method that
+one important way that the eigenvalues
+
+ align:start position:0%
+one important way that the eigenvalues
+ 
+
+ align:start position:0%
+one important way that the eigenvalues
+of the spectrum of a graph or matrix
+
+ align:start position:0%
+of the spectrum of a graph or matrix
+ 
+
+ align:start position:0%
+of the spectrum of a graph or matrix
+relates to other combinatorial
+
+ align:start position:0%
+relates to other combinatorial
+ 
+
+ align:start position:0%
+relates to other combinatorial
+quantities is via this trace so we know
+
+ align:start position:0%
+quantities is via this trace so we know
+ 
+
+ align:start position:0%
+quantities is via this trace so we know
+that the trace of the fourth power is
+
+ align:start position:0%
+that the trace of the fourth power is
+ 
+
+ align:start position:0%
+that the trace of the fourth power is
+equal to the fourth moment of the
+
+ align:start position:0%
+equal to the fourth moment of the
+ 
+
+ align:start position:0%
+equal to the fourth moment of the
+eigenvalues okay so if you haven't seen
+
+ align:start position:0%
+eigenvalues okay so if you haven't seen
+ 
+
+ align:start position:0%
+eigenvalues okay so if you haven't seen
+a proof of this before I encourage you
+
+ align:start position:0%
+a proof of this before I encourage you
+ 
+
+ align:start position:0%
+a proof of this before I encourage you
+to go home and think about it so this is
+
+ align:start position:0%
+to go home and think about it so this is
+ 
+
+ align:start position:0%
+to go home and think about it so this is
+this is an important identity of course
+
+ align:start position:0%
+this is an important identity of course
+ 
+
+ align:start position:0%
+this is an important identity of course
+4 can be replaced by any number up here
+
+ align:start position:0%
+4 can be replaced by any number up here
+ 
+
+ align:start position:0%
+4 can be replaced by any number up here
+and well now you have the eigenvalue
+
+ align:start position:0%
+and well now you have the eigenvalue
+ 
+
+ align:start position:0%
+and well now you have the eigenvalue
+condition so i can estimate this sum
+
+ align:start position:0%
+condition so i can estimate this sum
+ 
+
+ align:start position:0%
+condition so i can estimate this sum
+there's a principal term namely lambda 1
+
+ align:start position:0%
+there's a principal term namely lambda 1
+ 
+
+ align:start position:0%
+there's a principal term namely lambda 1
+right so that's the big term everything
+
+ align:start position:0%
+right so that's the big term everything
+ 
+
+ align:start position:0%
+right so that's the big term everything
+else is small and the smallness is
+
+ align:start position:0%
+else is small and the smallness is
+ 
+
+ align:start position:0%
+else is small and the smallness is
+supposed to capture pseudo randomness
+
+ align:start position:0%
+supposed to capture pseudo randomness
+ 
+
+ align:start position:0%
+supposed to capture pseudo randomness
+but the big term you have to analyze
+
+ align:start position:0%
+but the big term you have to analyze
+ 
+
+ align:start position:0%
+but the big term you have to analyze
+separately so the big term okay so let
+
+ align:start position:0%
+separately so the big term okay so let
+ 
+
+ align:start position:0%
+separately so the big term okay so let
+me write it out so the big term you know
+
+ align:start position:0%
+me write it out so the big term you know
+ 
+
+ align:start position:0%
+me write it out so the big term you know
+that it is P to the 4n to the 4 plus
+
+ align:start position:0%
+that it is P to the 4n to the 4 plus
+ 
+
+ align:start position:0%
+that it is P to the 4n to the 4 plus
+total of 4 ok so the next thing is what
+
+ align:start position:0%
+total of 4 ok so the next thing is what
+ 
+
+ align:start position:0%
+total of 4 ok so the next thing is what
+to do with the middle terms so we want
+
+ align:start position:0%
+to do with the middle terms so we want
+ 
+
+ align:start position:0%
+to do with the middle terms so we want
+to show that the contribution in total
+
+ align:start position:0%
+to show that the contribution in total
+ 
+
+ align:start position:0%
+to show that the contribution in total
+is not too big so what can we do well so
+
+ align:start position:0%
+is not too big so what can we do well so
+ 
+
+ align:start position:0%
+is not too big so what can we do well so
+let me first try something
+
+ align:start position:0%
+let me first try something
+ 
+
+ align:start position:0%
+let me first try something
+so first well see that each one of these
+
+ align:start position:0%
+so first well see that each one of these
+ 
+
+ align:start position:0%
+so first well see that each one of these
+guys is not too big so maybe let's pound
+
+ align:start position:0%
+guys is not too big so maybe let's pound
+ 
+
+ align:start position:0%
+guys is not too big so maybe let's pound
+each one of them by go to all of em so
+
+ align:start position:0%
+each one of them by go to all of em so
+ 
+
+ align:start position:0%
+each one of them by go to all of em so
+raise to 4 but then there n of them so
+
+ align:start position:0%
+raise to 4 but then there n of them so
+ 
+
+ align:start position:0%
+raise to 4 but then there n of them so
+you have to multiply by an extra n and
+
+ align:start position:0%
+you have to multiply by an extra n and
+ 
+
+ align:start position:0%
+you have to multiply by an extra n and
+that's too much that's not good enough
+
+ align:start position:0%
+that's too much that's not good enough
+ 
+
+ align:start position:0%
+that's too much that's not good enough
+so we cannot individually pound each one
+
+ align:start position:0%
+so we cannot individually pound each one
+ 
+
+ align:start position:0%
+so we cannot individually pound each one
+of them and this is a this is a novice
+
+ align:start position:0%
+of them and this is a this is a novice
+ 
+
+ align:start position:0%
+of them and this is a this is a novice
+mistake so this is something that will
+
+ align:start position:0%
+mistake so this is something that will
+ 
+
+ align:start position:0%
+mistake so this is something that will
+actually we'll see this type of
+
+ align:start position:0%
+actually we'll see this type of
+ 
+
+ align:start position:0%
+actually we'll see this type of
+calculation later on in the term when we
+
+ align:start position:0%
+calculation later on in the term when we
+ 
+
+ align:start position:0%
+calculation later on in the term when we
+discussed Roth theorem but you're not
+
+ align:start position:0%
+discussed Roth theorem but you're not
+ 
+
+ align:start position:0%
+discussed Roth theorem but you're not
+supposed to bound these terms individual
+
+ align:start position:0%
+supposed to bound these terms individual
+ 
+
+ align:start position:0%
+supposed to bound these terms individual
+the better way to do this or the correct
+
+ align:start position:0%
+the better way to do this or the correct
+ 
+
+ align:start position:0%
+the better way to do this or the correct
+way to do this is to pull out just a
+
+ align:start position:0%
+way to do this is to pull out just a
+ 
+
+ align:start position:0%
+way to do this is to pull out just a
+couple you know some but not all of
+
+ align:start position:0%
+couple you know some but not all of
+ 
+
+ align:start position:0%
+couple you know some but not all of
+these factors so it is upper bounded by
+
+ align:start position:0%
+these factors so it is upper bounded by
+ 
+
+ align:start position:0%
+these factors so it is upper bounded by
+you take max off in this case you can
+
+ align:start position:0%
+you take max off in this case you can
+ 
+
+ align:start position:0%
+you take max off in this case you can
+take out with one or two but you take
+
+ align:start position:0%
+take out with one or two but you take
+ 
+
+ align:start position:0%
+take out with one or two but you take
+out let's say in two factors and then
+
+ align:start position:0%
+out let's say in two factors and then
+ 
+
+ align:start position:0%
+out let's say in two factors and then
+you leave the remaining sum intact in
+
+ align:start position:0%
+you leave the remaining sum intact in
+ 
+
+ align:start position:0%
+you leave the remaining sum intact in
+fact I can leave I can even put lambda
+
+ align:start position:0%
+fact I can leave I can even put lambda
+ 
+
+ align:start position:0%
+fact I can leave I can even put lambda
+one back into the remaining so so so
+
+ align:start position:0%
+one back into the remaining so so so
+ 
+
+ align:start position:0%
+one back into the remaining so so so
+that is true so what I've written down
+
+ align:start position:0%
+that is true so what I've written down
+ 
+
+ align:start position:0%
+that is true so what I've written down
+is just true as inequality and now I
+
+ align:start position:0%
+is just true as inequality and now I
+ 
+
+ align:start position:0%
+is just true as inequality and now I
+apply the hypothesis on the sizes of the
+
+ align:start position:0%
+apply the hypothesis on the sizes of the
+ 
+
+ align:start position:0%
+apply the hypothesis on the sizes of the
+other lambdas so one I pulled out is
+
+ align:start position:0%
+other lambdas so one I pulled out is
+ 
+
+ align:start position:0%
+other lambdas so one I pulled out is
+little Olaf N squared and now what's the
+
+ align:start position:0%
+little Olaf N squared and now what's the
+ 
+
+ align:start position:0%
+little Olaf N squared and now what's the
+second sum that sum is the trace of a
+
+ align:start position:0%
+second sum that sum is the trace of a
+ 
+
+ align:start position:0%
+second sum that sum is the trace of a
+squared which is just the twice the
+
+ align:start position:0%
+squared which is just the twice the
+ 
+
+ align:start position:0%
+squared which is just the twice the
+number of edges of the graph so that's
+
+ align:start position:0%
+number of edges of the graph so that's
+ 
+
+ align:start position:0%
+number of edges of the graph so that's
+also at most N squared so combining
+
+ align:start position:0%
+also at most N squared so combining
+ 
+
+ align:start position:0%
+also at most N squared so combining
+everything you have the desired bound on
+
+ align:start position:0%
+everything you have the desired bound on
+ 
+
+ align:start position:0%
+everything you have the desired bound on
+the C for count of course this gives you
+
+ align:start position:0%
+the C for count of course this gives you
+ 
+
+ align:start position:0%
+the C for count of course this gives you
+an upper bound but we also did a
+
+ align:start position:0%
+an upper bound but we also did a
+ 
+
+ align:start position:0%
+an upper bound but we also did a
+calculation before the break that shows
+
+ align:start position:0%
+calculation before the break that shows
+ 
+
+ align:start position:0%
+calculation before the break that shows
+you that the C for bound is a lower
+
+ align:start position:0%
+you that the C for bound is a lower
+ 
+
+ align:start position:0%
+you that the C for bound is a lower
+bound as well so really having the
+
+ align:start position:0%
+bound as well so really having the
+ 
+
+ align:start position:0%
+bound as well so really having the
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+I can value this already already shows
+
+ align:start position:0%
+I can value this already already shows
+ 
+
+ align:start position:0%
+I can value this already already shows
+you that the C for bound is correct in
+
+ align:start position:0%
+you that the C for bound is correct in
+ 
+
+ align:start position:0%
+you that the C for bound is correct in
+both directions but because we this is
+
+ align:start position:0%
+both directions but because we this is
+ 
+
+ align:start position:0%
+both directions but because we this is
+the main term and then everything else
+
+ align:start position:0%
+the main term and then everything else
+ 
+
+ align:start position:0%
+the main term and then everything else
+is small okay the final implication is C
+
+ align:start position:0%
+is small okay the final implication is C
+ 
+
+ align:start position:0%
+is small okay the final implication is C
+for implies eigen value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay for this one I need to explore this
+
+ align:start position:0%
+okay for this one I need to explore this
+ 
+
+ align:start position:0%
+okay for this one I need to explore this
+following important property of the top
+
+ align:start position:0%
+following important property of the top
+ 
+
+ align:start position:0%
+following important property of the top
+eigenvalue so this is something that we
+
+ align:start position:0%
+eigenvalue so this is something that we
+ 
+
+ align:start position:0%
+eigenvalue so this is something that we
+also saw last time which is the
+
+ align:start position:0%
+also saw last time which is the
+ 
+
+ align:start position:0%
+also saw last time which is the
+interpretation of the top eigen value of
+
+ align:start position:0%
+interpretation of the top eigen value of
+ 
+
+ align:start position:0%
+interpretation of the top eigen value of
+a matrix interpreted as so this is
+
+ align:start position:0%
+a matrix interpreted as so this is
+ 
+
+ align:start position:0%
+a matrix interpreted as so this is
+sometimes called the Kuran Fisher
+
+ align:start position:0%
+sometimes called the Kuran Fisher
+ 
+
+ align:start position:0%
+sometimes called the Kuran Fisher
+criterion or there actually this is a
+
+ align:start position:0%
+criterion or there actually this is a
+ 
+
+ align:start position:0%
+criterion or there actually this is a
+special case of Kuran Fisher okay this
+
+ align:start position:0%
+special case of Kuran Fisher okay this
+ 
+
+ align:start position:0%
+special case of Kuran Fisher okay this
+is a basic linear algebra fact if you
+
+ align:start position:0%
+is a basic linear algebra fact if you
+ 
+
+ align:start position:0%
+is a basic linear algebra fact if you
+are not familiar with it I recommend
+
+ align:start position:0%
+are not familiar with it I recommend
+ 
+
+ align:start position:0%
+are not familiar with it I recommend
+looking it up that the top eigen value
+
+ align:start position:0%
+looking it up that the top eigen value
+ 
+
+ align:start position:0%
+looking it up that the top eigen value
+of a matrix of a real symmetric matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is characterized by the maximum value of
+
+ align:start position:0%
+is characterized by the maximum value of
+ 
+
+ align:start position:0%
+is characterized by the maximum value of
+this quadratic form let's say if X is a
+
+ align:start position:0%
+this quadratic form let's say if X is a
+ 
+
+ align:start position:0%
+this quadratic form let's say if X is a
+non zero vector so in particular if I
+
+ align:start position:0%
+non zero vector so in particular if I
+ 
+
+ align:start position:0%
+non zero vector so in particular if I
+set X to be a specific vector I can
+
+ align:start position:0%
+set X to be a specific vector I can
+ 
+
+ align:start position:0%
+set X to be a specific vector I can
+lower bound lambda 1 so if we set this
+
+ align:start position:0%
+lower bound lambda 1 so if we set this
+ 
+
+ align:start position:0%
+lower bound lambda 1 so if we set this
+boldface one to be the oh one vector in
+
+ align:start position:0%
+boldface one to be the oh one vector in
+ 
+
+ align:start position:0%
+boldface one to be the oh one vector in
+R raised to the number of vertices of G
+
+ align:start position:0%
+R raised to the number of vertices of G
+ 
+
+ align:start position:0%
+R raised to the number of vertices of G
+then the lambda one of the graph is at
+
+ align:start position:0%
+then the lambda one of the graph is at
+ 
+
+ align:start position:0%
+then the lambda one of the graph is at
+least this quantity over here the
+
+ align:start position:0%
+least this quantity over here the
+ 
+
+ align:start position:0%
+least this quantity over here the
+numerator and denominators are all easy
+
+ align:start position:0%
+numerator and denominators are all easy
+ 
+
+ align:start position:0%
+numerator and denominators are all easy
+things to evaluate the numerator is just
+
+ align:start position:0%
+things to evaluate the numerator is just
+ 
+
+ align:start position:0%
+things to evaluate the numerator is just
+twice the number of edges because you
+
+ align:start position:0%
+twice the number of edges because you
+ 
+
+ align:start position:0%
+twice the number of edges because you
+are summing up all the entries of the
+
+ align:start position:0%
+are summing up all the entries of the
+ 
+
+ align:start position:0%
+are summing up all the entries of the
+matrix and the new denominator is just n
+
+ align:start position:0%
+matrix and the new denominator is just n
+ 
+
+ align:start position:0%
+matrix and the new denominator is just n
+so the top eigenvalue is at least
+
+ align:start position:0%
+so the top eigenvalue is at least
+ 
+
+ align:start position:0%
+so the top eigenvalue is at least
+roughly PM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what about the other eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or the other eigenvalues I can again
+
+ align:start position:0%
+or the other eigenvalues I can again
+ 
+
+ align:start position:0%
+or the other eigenvalues I can again
+refer back to this moment formula
+
+ align:start position:0%
+refer back to this moment formula
+ 
+
+ align:start position:0%
+refer back to this moment formula
+relating a trace and closed walks it is
+
+ align:start position:0%
+relating a trace and closed walks it is
+ 
+
+ align:start position:0%
+relating a trace and closed walks it is
+at most the trace of the fourth power
+
+ align:start position:0%
+at most the trace of the fourth power
+ 
+
+ align:start position:0%
+at most the trace of the fourth power
+minus the top eigenvalue raised to the
+
+ align:start position:0%
+minus the top eigenvalue raised to the
+ 
+
+ align:start position:0%
+minus the top eigenvalue raised to the
+fourth power some of the other
+
+ align:start position:0%
+fourth power some of the other
+ 
+
+ align:start position:0%
+fourth power some of the other
+eigenvalue raised to the fourth power
+
+ align:start position:0%
+eigenvalue raised to the fourth power
+ 
+
+ align:start position:0%
+eigenvalue raised to the fourth power
+and for here we're using the force an
+
+ align:start position:0%
+and for here we're using the force an
+ 
+
+ align:start position:0%
+and for here we're using the force an
+even number okay so you have this over
+
+ align:start position:0%
+even number okay so you have this over
+ 
+
+ align:start position:0%
+even number okay so you have this over
+here so having a c4 hypothesis and also
+
+ align:start position:0%
+here so having a c4 hypothesis and also
+ 
+
+ align:start position:0%
+here so having a c4 hypothesis and also
+knowing what lambda one is allows you to
+
+ align:start position:0%
+knowing what lambda one is allows you to
+ 
+
+ align:start position:0%
+knowing what lambda one is allows you to
+control the other lambdas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+she lambda one cannot be greater than
+
+ align:start position:0%
+she lambda one cannot be greater than
+ 
+
+ align:start position:0%
+she lambda one cannot be greater than
+much greater than PN also comes out at
+
+ align:start position:0%
+much greater than PN also comes out at
+ 
+
+ align:start position:0%
+much greater than PN also comes out at
+the same calculation yep thank you yeah
+
+ align:start position:0%
+the same calculation yep thank you yeah
+ 
+
+ align:start position:0%
+the same calculation yep thank you yeah
+so there's a correction so lambda one is
+
+ align:start position:0%
+so there's a correction so lambda one is
+ 
+
+ align:start position:0%
+so there's a correction so lambda one is
+so so in other words the little always
+
+ align:start position:0%
+so so in other words the little always
+ 
+
+ align:start position:0%
+so so in other words the little always
+always respect you the constant density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yep okay so the question is in I
+
+ align:start position:0%
+okay yep okay so the question is in I
+ 
+
+ align:start position:0%
+okay yep okay so the question is in I
+can value implies C for said something
+
+ align:start position:0%
+can value implies C for said something
+ 
+
+ align:start position:0%
+can value implies C for said something
+about the lower bound so I'm not saying
+
+ align:start position:0%
+about the lower bound so I'm not saying
+ 
+
+ align:start position:0%
+about the lower bound so I'm not saying
+that so as written over here what this
+
+ align:start position:0%
+that so as written over here what this
+ 
+
+ align:start position:0%
+that so as written over here what this
+is what we have proved I saw him but
+
+ align:start position:0%
+is what we have proved I saw him but
+ 
+
+ align:start position:0%
+is what we have proved I saw him but
+when you think about the pseudo
+
+ align:start position:0%
+when you think about the pseudo
+ 
+
+ align:start position:0%
+when you think about the pseudo
+randomness condition for C for it
+
+ align:start position:0%
+randomness condition for C for it
+ 
+
+ align:start position:0%
+randomness condition for C for it
+shouldn't be just that the number C for
+
+ align:start position:0%
+shouldn't be just that the number C for
+ 
+
+ align:start position:0%
+shouldn't be just that the number C for
+count is and most something should be
+
+ align:start position:0%
+count is and most something should be
+ 
+
+ align:start position:0%
+count is and most something should be
+that in close to that which would be
+
+ align:start position:0%
+that in close to that which would be
+ 
+
+ align:start position:0%
+that in close to that which would be
+implied by the c4 condition itself
+
+ align:start position:0%
+implied by the c4 condition itself
+ 
+
+ align:start position:0%
+implied by the c4 condition itself
+because we know always it is the case
+
+ align:start position:0%
+because we know always it is the case
+ 
+
+ align:start position:0%
+because we know always it is the case
+that the c-4 count is at least compare
+
+ align:start position:0%
+that the c-4 count is at least compare
+ 
+
+ align:start position:0%
+that the c-4 count is at least compare
+what it is compared to the random case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one more thing I said was that lambda
+
+ align:start position:0%
+one more thing I said was that lambda
+ 
+
+ align:start position:0%
+one more thing I said was that lambda
+one you also know that it is at most P
+
+ align:start position:0%
+one you also know that it is at most P
+ 
+
+ align:start position:0%
+one you also know that it is at most P
+and plus n right because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this finishes the proof of the Chong
+
+ align:start position:0%
+so this finishes the proof of the Chong
+ 
+
+ align:start position:0%
+so this finishes the proof of the Chong
+Graham Wilson theorem on quasi random
+
+ align:start position:0%
+Graham Wilson theorem on quasi random
+ 
+
+ align:start position:0%
+Graham Wilson theorem on quasi random
+graphs and we stated all of these
+
+ align:start position:0%
+graphs and we stated all of these
+ 
+
+ align:start position:0%
+graphs and we stated all of these
+hypotheses and they're all equivalent to
+
+ align:start position:0%
+hypotheses and they're all equivalent to
+ 
+
+ align:start position:0%
+hypotheses and they're all equivalent to
+each other and I want to emphasize again
+
+ align:start position:0%
+each other and I want to emphasize again
+ 
+
+ align:start position:0%
+each other and I want to emphasize again
+the most surprising one is that c4
+
+ align:start position:0%
+the most surprising one is that c4
+ 
+
+ align:start position:0%
+the most surprising one is that c4
+implies everything else they're fairly
+
+ align:start position:0%
+implies everything else they're fairly
+ 
+
+ align:start position:0%
+implies everything else they're fairly
+weak seeming condition seemingly weak
+
+ align:start position:0%
+weak seeming condition seemingly weak
+ 
+
+ align:start position:0%
+weak seeming condition seemingly weak
+condition this just having the correct
+
+ align:start position:0%
+condition this just having the correct
+ 
+
+ align:start position:0%
+condition this just having the correct
+number of copies of labeled C force is
+
+ align:start position:0%
+number of copies of labeled C force is
+ 
+
+ align:start position:0%
+number of copies of labeled C force is
+enough to guarantee all of these other
+
+ align:start position:0%
+enough to guarantee all of these other
+ 
+
+ align:start position:0%
+enough to guarantee all of these other
+much more complicated looking conditions
+
+ align:start position:0%
+much more complicated looking conditions
+ 
+
+ align:start position:0%
+much more complicated looking conditions
+and in particular just having the C for
+
+ align:start position:0%
+and in particular just having the C for
+ 
+
+ align:start position:0%
+and in particular just having the C for
+count correct implies that the counts of
+
+ align:start position:0%
+count correct implies that the counts of
+ 
+
+ align:start position:0%
+count correct implies that the counts of
+every other graph H is correct now one
+
+ align:start position:0%
+every other graph H is correct now one
+ 
+
+ align:start position:0%
+every other graph H is correct now one
+thing I want to stress is that the Chun
+
+ align:start position:0%
+thing I want to stress is that the Chun
+ 
+
+ align:start position:0%
+thing I want to stress is that the Chun
+Graham Wilson theorem it's really about
+
+ align:start position:0%
+Graham Wilson theorem it's really about
+ 
+
+ align:start position:0%
+Graham Wilson theorem it's really about
+dense graphs and by dense here I mean P
+
+ align:start position:0%
+dense graphs and by dense here I mean P
+ 
+
+ align:start position:0%
+dense graphs and by dense here I mean P
+constant of course the theorem as stated
+
+ align:start position:0%
+constant of course the theorem as stated
+ 
+
+ align:start position:0%
+constant of course the theorem as stated
+is true if you let P equals to zero so
+
+ align:start position:0%
+is true if you let P equals to zero so
+ 
+
+ align:start position:0%
+is true if you let P equals to zero so
+there I said P strictly between 0 and 1
+
+ align:start position:0%
+there I said P strictly between 0 and 1
+ 
+
+ align:start position:0%
+there I said P strictly between 0 and 1
+but it's also ok if you let P equal to 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you don't get such interesting theorems
+
+ align:start position:0%
+you don't get such interesting theorems
+ 
+
+ align:start position:0%
+you don't get such interesting theorems
+but but it is still true but for sparse
+
+ align:start position:0%
+but but it is still true but for sparse
+ 
+
+ align:start position:0%
+but but it is still true but for sparse
+graphs what you really want to care
+
+ align:start position:0%
+graphs what you really want to care
+ 
+
+ align:start position:0%
+graphs what you really want to care
+about is approximations at the correct
+
+ align:start position:0%
+about is approximations at the correct
+ 
+
+ align:start position:0%
+about is approximations at the correct
+order of magnitude so what I mean is
+
+ align:start position:0%
+order of magnitude so what I mean is
+ 
+
+ align:start position:0%
+order of magnitude so what I mean is
+that you can write down some sparse
+
+ align:start position:0%
+that you can write down some sparse
+ 
+
+ align:start position:0%
+that you can write down some sparse
+analogues for P going to 0 so P as a
+
+ align:start position:0%
+analogues for P going to 0 so P as a
+ 
+
+ align:start position:0%
+analogues for P going to 0 so P as a
+function of n going to 0 as n goes to
+
+ align:start position:0%
+function of n going to 0 as n goes to
+ 
+
+ align:start position:0%
+function of n going to 0 as n goes to
+infinity ok so let me just write down a
+
+ align:start position:0%
+infinity ok so let me just write down a
+ 
+
+ align:start position:0%
+infinity ok so let me just write down a
+couple of examples but I won't do all of
+
+ align:start position:0%
+couple of examples but I won't do all of
+ 
+
+ align:start position:0%
+couple of examples but I won't do all of
+them and you can imagine what they
+
+ align:start position:0%
+them and you can imagine what they
+ 
+
+ align:start position:0%
+them and you can imagine what they
+should look like so disk should say this
+
+ align:start position:0%
+should look like so disk should say this
+ 
+
+ align:start position:0%
+should look like so disk should say this
+quantity over here the discrepancy
+
+ align:start position:0%
+quantity over here the discrepancy
+ 
+
+ align:start position:0%
+quantity over here the discrepancy
+condition is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not all of P M squared because P N
+
+ align:start position:0%
+not all of P M squared because P N
+ 
+
+ align:start position:0%
+not all of P M squared because P N
+squared is the edge density overall so
+
+ align:start position:0%
+squared is the edge density overall so
+ 
+
+ align:start position:0%
+squared is the edge density overall so
+that's the quantity you should compare
+
+ align:start position:0%
+that's the quantity you should compare
+ 
+
+ align:start position:0%
+that's the quantity you should compare
+against and not N squared if you're
+
+ align:start position:0%
+against and not N squared if you're
+ 
+
+ align:start position:0%
+against and not N squared if you're
+compare N squared you know you're
+
+ align:start position:0%
+compare N squared you know you're
+ 
+
+ align:start position:0%
+compare N squared you know you're
+cheating because N squared is much
+
+ align:start position:0%
+cheating because N squared is much
+ 
+
+ align:start position:0%
+cheating because N squared is much
+bigger than the actual edge density
+
+ align:start position:0%
+bigger than the actual edge density
+ 
+
+ align:start position:0%
+bigger than the actual edge density
+likewise the number of labeled copies of
+
+ align:start position:0%
+likewise the number of labeled copies of
+ 
+
+ align:start position:0%
+likewise the number of labeled copies of
+age yes I want to put the little ol 1
+
+ align:start position:0%
+age yes I want to put the little ol 1
+ 
+
+ align:start position:0%
+age yes I want to put the little ol 1
+plus little in front right so instead of
+
+ align:start position:0%
+plus little in front right so instead of
+ 
+
+ align:start position:0%
+plus little in front right so instead of
+plus little ol end to the H at the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as you understand the difference there
+
+ align:start position:0%
+as you understand the difference there
+ 
+
+ align:start position:0%
+as you understand the difference there
+so for sparse this is the correct
+
+ align:start position:0%
+so for sparse this is the correct
+ 
+
+ align:start position:0%
+so for sparse this is the correct
+normalization that you should have when
+
+ align:start position:0%
+normalization that you should have when
+ 
+
+ align:start position:0%
+normalization that you should have when
+P is allowed to go to 0 as a function of
+
+ align:start position:0%
+P is allowed to go to 0 as a function of
+ 
+
+ align:start position:0%
+P is allowed to go to 0 as a function of
+N and you can write down all of these
+
+ align:start position:0%
+N and you can write down all of these
+ 
+
+ align:start position:0%
+N and you can write down all of these
+conditions right I'm not saying there's
+
+ align:start position:0%
+conditions right I'm not saying there's
+ 
+
+ align:start position:0%
+conditions right I'm not saying there's
+a theorem you can write down all these
+
+ align:start position:0%
+a theorem you can write down all these
+ 
+
+ align:start position:0%
+a theorem you can write down all these
+conditions and you can ask is there also
+
+ align:start position:0%
+conditions and you can ask is there also
+ 
+
+ align:start position:0%
+conditions and you can ask is there also
+some notion of equivalence I'm sorry are
+
+ align:start position:0%
+some notion of equivalence I'm sorry are
+ 
+
+ align:start position:0%
+some notion of equivalence I'm sorry are
+these corresponding conditions also
+
+ align:start position:0%
+these corresponding conditions also
+ 
+
+ align:start position:0%
+these corresponding conditions also
+equivalent to each other and the answer
+
+ align:start position:0%
+equivalent to each other and the answer
+ 
+
+ align:start position:0%
+equivalent to each other and the answer
+is emphatically no absolutely not so all
+
+ align:start position:0%
+is emphatically no absolutely not so all
+ 
+
+ align:start position:0%
+is emphatically no absolutely not so all
+of these equivalent tests fail for
+
+ align:start position:0%
+of these equivalent tests fail for
+ 
+
+ align:start position:0%
+of these equivalent tests fail for
+sparse some of them are still true in
+
+ align:start position:0%
+sparse some of them are still true in
+ 
+
+ align:start position:0%
+sparse some of them are still true in
+some of the easier ones that we did for
+
+ align:start position:0%
+some of the easier ones that we did for
+ 
+
+ align:start position:0%
+some of the easier ones that we did for
+example the two versions of discs are
+
+ align:start position:0%
+example the two versions of discs are
+ 
+
+ align:start position:0%
+example the two versions of discs are
+equivalent that's the okay and some of
+
+ align:start position:0%
+equivalent that's the okay and some of
+ 
+
+ align:start position:0%
+equivalent that's the okay and some of
+these calculations involving
+
+ align:start position:0%
+these calculations involving
+ 
+
+ align:start position:0%
+these calculations involving
+cauchy-schwarz or you know mostly still
+
+ align:start position:0%
+cauchy-schwarz or you know mostly still
+ 
+
+ align:start position:0%
+cauchy-schwarz or you know mostly still
+ok but the one that really fails is the
+
+ align:start position:0%
+ok but the one that really fails is the
+ 
+
+ align:start position:0%
+ok but the one that really fails is the
+counting lemma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let me explain why with an example
+
+ align:start position:0%
+and let me explain why with an example
+ 
+
+ align:start position:0%
+and let me explain why with an example
+so I want to give you an example of a
+
+ align:start position:0%
+so I want to give you an example of a
+ 
+
+ align:start position:0%
+so I want to give you an example of a
+graph which looks pseudo random in the
+
+ align:start position:0%
+graph which looks pseudo random in the
+ 
+
+ align:start position:0%
+graph which looks pseudo random in the
+sense of disk but has no C for let's say
+
+ align:start position:0%
+sense of disk but has no C for let's say
+ 
+
+ align:start position:0%
+sense of disk but has no C for let's say
+C 3 count also has no C for Campbell
+
+ align:start position:0%
+C 3 count also has no C for Campbell
+ 
+
+ align:start position:0%
+C 3 count also has no C for Campbell
+just Xu has no triangle as the Keene
+
+ align:start position:0%
+just Xu has no triangle as the Keene
+ 
+
+ align:start position:0%
+just Xu has no triangle as the Keene
+correct number of triangles alright so
+
+ align:start position:0%
+correct number of triangles alright so
+ 
+
+ align:start position:0%
+correct number of triangles alright so
+what's this example so let P be some
+
+ align:start position:0%
+what's this example so let P be some
+ 
+
+ align:start position:0%
+what's this example so let P be some
+number which is no off 1 over root n so
+
+ align:start position:0%
+number which is no off 1 over root n so
+ 
+
+ align:start position:0%
+number which is no off 1 over root n so
+some decaying quantity with N and let's
+
+ align:start position:0%
+some decaying quantity with N and let's
+ 
+
+ align:start position:0%
+some decaying quantity with N and let's
+consider GMP well how many triangles do
+
+ align:start position:0%
+consider GMP well how many triangles do
+ 
+
+ align:start position:0%
+consider GMP well how many triangles do
+we expect in GMP so let's think of
+
+ align:start position:0%
+we expect in GMP so let's think of
+ 
+
+ align:start position:0%
+we expect in GMP so let's think of
+Pierre just slightly below 1 over root n
+
+ align:start position:0%
+Pierre just slightly below 1 over root n
+ 
+
+ align:start position:0%
+Pierre just slightly below 1 over root n
+so the number of triangles in GMP in
+
+ align:start position:0%
+so the number of triangles in GMP in
+ 
+
+ align:start position:0%
+so the number of triangles in GMP in
+expectation so that's that's the
+
+ align:start position:0%
+expectation so that's that's the
+ 
+
+ align:start position:0%
+expectation so that's that's the
+expected number and you should expect
+
+ align:start position:0%
+expected number and you should expect
+ 
+
+ align:start position:0%
+expected number and you should expect
+the actual number to be roughly around
+
+ align:start position:0%
+the actual number to be roughly around
+ 
+
+ align:start position:0%
+the actual number to be roughly around
+that but on the other hand the number of
+
+ align:start position:0%
+that but on the other hand the number of
+ 
+
+ align:start position:0%
+that but on the other hand the number of
+edges it's also expected to be okay so
+
+ align:start position:0%
+edges it's also expected to be okay so
+ 
+
+ align:start position:0%
+edges it's also expected to be okay so
+this quantity here and you expect that
+
+ align:start position:0%
+this quantity here and you expect that
+ 
+
+ align:start position:0%
+this quantity here and you expect that
+the actual number of edges to be very
+
+ align:start position:0%
+the actual number of edges to be very
+ 
+
+ align:start position:0%
+the actual number of edges to be very
+close to it but P is chosen so that the
+
+ align:start position:0%
+close to it but P is chosen so that the
+ 
+
+ align:start position:0%
+close to it but P is chosen so that the
+number of triangles is significantly
+
+ align:start position:0%
+number of triangles is significantly
+ 
+
+ align:start position:0%
+number of triangles is significantly
+smaller than the number of edges so
+
+ align:start position:0%
+smaller than the number of edges so
+ 
+
+ align:start position:0%
+smaller than the number of edges so
+asymptotically smaller fewer copies of
+
+ align:start position:0%
+asymptotically smaller fewer copies of
+ 
+
+ align:start position:0%
+asymptotically smaller fewer copies of
+triangles than edges so what we can do
+
+ align:start position:0%
+triangles than edges so what we can do
+ 
+
+ align:start position:0%
+triangles than edges so what we can do
+now is remove
+
+ align:start position:0%
+now is remove
+ 
+
+ align:start position:0%
+now is remove
+an edge from each copy of a triangle in
+
+ align:start position:0%
+an edge from each copy of a triangle in
+ 
+
+ align:start position:0%
+an edge from each copy of a triangle in
+this GNP we removed a tiny fraction of
+
+ align:start position:0%
+this GNP we removed a tiny fraction of
+ 
+
+ align:start position:0%
+this GNP we removed a tiny fraction of
+edges because the number of triangles is
+
+ align:start position:0%
+edges because the number of triangles is
+ 
+
+ align:start position:0%
+edges because the number of triangles is
+much less than number of edges we remove
+
+ align:start position:0%
+much less than number of edges we remove
+ 
+
+ align:start position:0%
+much less than number of edges we remove
+the tiny fraction of edges and as a
+
+ align:start position:0%
+the tiny fraction of edges and as a
+ 
+
+ align:start position:0%
+the tiny fraction of edges and as a
+result we do not change the discrepancy
+
+ align:start position:0%
+result we do not change the discrepancy
+ 
+
+ align:start position:0%
+result we do not change the discrepancy
+condition up to a small there error so
+
+ align:start position:0%
+condition up to a small there error so
+ 
+
+ align:start position:0%
+condition up to a small there error so
+the discrepancy condition still holds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however the graph has normal triangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have this pseudo random graph in
+
+ align:start position:0%
+so you have this pseudo random graph in
+ 
+
+ align:start position:0%
+so you have this pseudo random graph in
+one sense namely of having discrepancy
+
+ align:start position:0%
+one sense namely of having discrepancy
+ 
+
+ align:start position:0%
+one sense namely of having discrepancy
+but fails to be pseudo random in a
+
+ align:start position:0%
+but fails to be pseudo random in a
+ 
+
+ align:start position:0%
+but fails to be pseudo random in a
+different sense namely has no triangles
+
+ align:start position:0%
+different sense namely has no triangles
+ 
+
+ align:start position:0%
+different sense namely has no triangles
+yep we're question to the condition c4
+
+ align:start position:0%
+yep we're question to the condition c4
+ 
+
+ align:start position:0%
+yep we're question to the condition c4
+and coda we still hold here basically
+
+ align:start position:0%
+and coda we still hold here basically
+ 
+
+ align:start position:0%
+and coda we still hold here basically
+downstream is okay but upstream is not
+
+ align:start position:0%
+downstream is okay but upstream is not
+ 
+
+ align:start position:0%
+downstream is okay but upstream is not
+okay so you can go from Seaforth code
+
+ align:start position:0%
+okay so you can go from Seaforth code
+ 
+
+ align:start position:0%
+okay so you can go from Seaforth code
+agree to disk but you can't go upward
+
+ align:start position:0%
+agree to disk but you can't go upward
+ 
+
+ align:start position:0%
+agree to disk but you can't go upward
+and understanding how to rectify the
+
+ align:start position:0%
+and understanding how to rectify the
+ 
+
+ align:start position:0%
+and understanding how to rectify the
+situation may perhaps adding additional
+
+ align:start position:0%
+situation may perhaps adding additional
+ 
+
+ align:start position:0%
+situation may perhaps adding additional
+hypotheses to make this true so that you
+
+ align:start position:0%
+hypotheses to make this true so that you
+ 
+
+ align:start position:0%
+hypotheses to make this true so that you
+could have counting llamas for triangles
+
+ align:start position:0%
+could have counting llamas for triangles
+ 
+
+ align:start position:0%
+could have counting llamas for triangles
+and other graphs in sparser graphs
+
+ align:start position:0%
+and other graphs in sparser graphs
+ 
+
+ align:start position:0%
+and other graphs in sparser graphs
+that's an important topic and this is
+
+ align:start position:0%
+that's an important topic and this is
+ 
+
+ align:start position:0%
+that's an important topic and this is
+something that we'll discuss at greater
+
+ align:start position:0%
+something that we'll discuss at greater
+ 
+
+ align:start position:0%
+something that we'll discuss at greater
+length in non-black not next lecture but
+
+ align:start position:0%
+length in non-black not next lecture but
+ 
+
+ align:start position:0%
+length in non-black not next lecture but
+the one after that and this is in fact
+
+ align:start position:0%
+the one after that and this is in fact
+ 
+
+ align:start position:0%
+the one after that and this is in fact
+related to the green-tailed theorem
+
+ align:start position:0%
+related to the green-tailed theorem
+ 
+
+ align:start position:0%
+related to the green-tailed theorem
+which allows you to prove similarities
+
+ align:start position:0%
+which allows you to prove similarities
+ 
+
+ align:start position:0%
+which allows you to prove similarities
+term among the primes the primes contain
+
+ align:start position:0%
+term among the primes the primes contain
+ 
+
+ align:start position:0%
+term among the primes the primes contain
+arbitrarily long arithmetic progressions
+
+ align:start position:0%
+arbitrarily long arithmetic progressions
+ 
+
+ align:start position:0%
+arbitrarily long arithmetic progressions
+because the primes are also a sparse set
+
+ align:start position:0%
+because the primes are also a sparse set
+ 
+
+ align:start position:0%
+because the primes are also a sparse set
+so as density going to zero density that
+
+ align:start position:0%
+so as density going to zero density that
+ 
+
+ align:start position:0%
+so as density going to zero density that
+came like 1 over log and according to
+
+ align:start position:0%
+came like 1 over log and according to
+ 
+
+ align:start position:0%
+came like 1 over log and according to
+prime number theorem but you want to do
+
+ align:start position:0%
+prime number theorem but you want to do
+ 
+
+ align:start position:0%
+prime number theorem but you want to do
+regularity method so you have to face
+
+ align:start position:0%
+regularity method so you have to face
+ 
+
+ align:start position:0%
+regularity method so you have to face
+this kind of issues so just okay so
+
+ align:start position:0%
+this kind of issues so just okay so
+ 
+
+ align:start position:0%
+this kind of issues so just okay so
+we'll discuss that more length in a
+
+ align:start position:0%
+we'll discuss that more length in a
+ 
+
+ align:start position:0%
+we'll discuss that more length in a
+couple of lectures but for now just a
+
+ align:start position:0%
+couple of lectures but for now just a
+ 
+
+ align:start position:0%
+couple of lectures but for now just a
+warning that everything here it's really
+
+ align:start position:0%
+warning that everything here it's really
+ 
+
+ align:start position:0%
+warning that everything here it's really
+about dense graphs the next thing I want
+
+ align:start position:0%
+about dense graphs the next thing I want
+ 
+
+ align:start position:0%
+about dense graphs the next thing I want
+to discuss is an elaboration of what
+
+ align:start position:0%
+to discuss is an elaboration of what
+ 
+
+ align:start position:0%
+to discuss is an elaboration of what
+happens to these eigenvalue conditions
+
+ align:start position:0%
+happens to these eigenvalue conditions
+ 
+
+ align:start position:0%
+happens to these eigenvalue conditions
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for dense graphs in some sense
+
+ align:start position:0%
+so for dense graphs in some sense
+ 
+
+ align:start position:0%
+so for dense graphs in some sense
+everything is very clear from this
+
+ align:start position:0%
+everything is very clear from this
+ 
+
+ align:start position:0%
+everything is very clear from this
+theorem like once you have this theorem
+
+ align:start position:0%
+theorem like once you have this theorem
+ 
+
+ align:start position:0%
+theorem like once you have this theorem
+they're all equivalent you can go back
+
+ align:start position:0%
+they're all equivalent you can go back
+ 
+
+ align:start position:0%
+they're all equivalent you can go back
+and forth and you know you lose a little
+
+ align:start position:0%
+and forth and you know you lose a little
+ 
+
+ align:start position:0%
+and forth and you know you lose a little
+bit like epsilon here and there but
+
+ align:start position:0%
+bit like epsilon here and there but
+ 
+
+ align:start position:0%
+bit like epsilon here and there but
+everything is more or less the same but
+
+ align:start position:0%
+everything is more or less the same but
+ 
+
+ align:start position:0%
+everything is more or less the same but
+if you go to sparser world then you
+
+ align:start position:0%
+if you go to sparser world then you
+ 
+
+ align:start position:0%
+if you go to sparser world then you
+really need to be much more careful we
+
+ align:start position:0%
+really need to be much more careful we
+ 
+
+ align:start position:0%
+really need to be much more careful we
+need to think about other tools and so
+
+ align:start position:0%
+need to think about other tools and so
+ 
+
+ align:start position:0%
+need to think about other tools and so
+the remainder of today I want to just
+
+ align:start position:0%
+the remainder of today I want to just
+ 
+
+ align:start position:0%
+the remainder of today I want to just
+discuss one pretty simple but powerful
+
+ align:start position:0%
+discuss one pretty simple but powerful
+ 
+
+ align:start position:0%
+discuss one pretty simple but powerful
+tool relating I can values on one hand
+
+ align:start position:0%
+tool relating I can values on one hand
+ 
+
+ align:start position:0%
+tool relating I can values on one hand
+and a discrepancy condition on the other
+
+ align:start position:0%
+and a discrepancy condition on the other
+ 
+
+ align:start position:0%
+and a discrepancy condition on the other
+hand right so you can go from eigenvalue
+
+ align:start position:0%
+hand right so you can go from eigenvalue
+ 
+
+ align:start position:0%
+hand right so you can go from eigenvalue
+to discrepancy by going down this chain
+
+ align:start position:0%
+to discrepancy by going down this chain
+ 
+
+ align:start position:0%
+to discrepancy by going down this chain
+but it's actually there's a much quicker
+
+ align:start position:0%
+but it's actually there's a much quicker
+ 
+
+ align:start position:0%
+but it's actually there's a much quicker
+route and this is known as the expander
+
+ align:start position:0%
+route and this is known as the expander
+ 
+
+ align:start position:0%
+route and this is known as the expander
+mixing them for simplicity and really
+
+ align:start position:0%
+mixing them for simplicity and really
+ 
+
+ align:start position:0%
+mixing them for simplicity and really
+will make our life much simpler we're
+
+ align:start position:0%
+will make our life much simpler we're
+ 
+
+ align:start position:0%
+will make our life much simpler we're
+only going to consider T regular graphs
+
+ align:start position:0%
+only going to consider T regular graphs
+ 
+
+ align:start position:0%
+only going to consider T regular graphs
+here T regular means every vertex s
+
+ align:start position:0%
+here T regular means every vertex s
+ 
+
+ align:start position:0%
+here T regular means every vertex s
+degree T same word but different meaning
+
+ align:start position:0%
+degree T same word but different meaning
+ 
+
+ align:start position:0%
+degree T same word but different meaning
+from epsilon regular and unfortunately
+
+ align:start position:0%
+from epsilon regular and unfortunately
+ 
+
+ align:start position:0%
+from epsilon regular and unfortunately
+that's just the way this so T regular
+
+ align:start position:0%
+that's just the way this so T regular
+ 
+
+ align:start position:0%
+that's just the way this so T regular
+and we're going to have n vertices and
+
+ align:start position:0%
+and we're going to have n vertices and
+ 
+
+ align:start position:0%
+and we're going to have n vertices and
+the adjacency matrix has eigenvalues
+
+ align:start position:0%
+the adjacency matrix has eigenvalues
+ 
+
+ align:start position:0%
+the adjacency matrix has eigenvalues
+lambda 1 lambda 2 and so on arranged in
+
+ align:start position:0%
+lambda 1 lambda 2 and so on arranged in
+ 
+
+ align:start position:0%
+lambda 1 lambda 2 and so on arranged in
+decreasing order let me write lambda as
+
+ align:start position:0%
+decreasing order let me write lambda as
+ 
+
+ align:start position:0%
+decreasing order let me write lambda as
+the maximum in absolute value of the
+
+ align:start position:0%
+the maximum in absolute value of the
+ 
+
+ align:start position:0%
+the maximum in absolute value of the
+eigenvalues except for the top one in
+
+ align:start position:0%
+eigenvalues except for the top one in
+ 
+
+ align:start position:0%
+eigenvalues except for the top one in
+particular this is either the absolute
+
+ align:start position:0%
+particular this is either the absolute
+ 
+
+ align:start position:0%
+particular this is either the absolute
+value of the second one or the last one
+
+ align:start position:0%
+value of the second one or the last one
+ 
+
+ align:start position:0%
+value of the second one or the last one
+as I mentioned earlier at the top
+
+ align:start position:0%
+as I mentioned earlier at the top
+ 
+
+ align:start position:0%
+as I mentioned earlier at the top
+eigenvalue is necessarily deep because
+
+ align:start position:0%
+eigenvalue is necessarily deep because
+ 
+
+ align:start position:0%
+eigenvalue is necessarily deep because
+you have all ones vector as an
+
+ align:start position:0%
+you have all ones vector as an
+ 
+
+ align:start position:0%
+you have all ones vector as an
+eigenvector so the expander mixing lemma
+
+ align:start position:0%
+eigenvector so the expander mixing lemma
+ 
+
+ align:start position:0%
+eigenvector so the expander mixing lemma
+says that if I look at to vertex subsets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the number of edges between them
+
+ align:start position:0%
+the number of edges between them
+ 
+
+ align:start position:0%
+the number of edges between them
+compared to what you would expect in a
+
+ align:start position:0%
+compared to what you would expect in a
+ 
+
+ align:start position:0%
+compared to what you would expect in a
+random case so just like in a disk
+
+ align:start position:0%
+random case so just like in a disk
+ 
+
+ align:start position:0%
+random case so just like in a disk
+setting but here the correct density I
+
+ align:start position:0%
+setting but here the correct density I
+ 
+
+ align:start position:0%
+setting but here the correct density I
+should put is d over N this quantity is
+
+ align:start position:0%
+should put is d over N this quantity is
+ 
+
+ align:start position:0%
+should put is d over N this quantity is
+upper bounded by lambda times the root
+
+ align:start position:0%
+upper bounded by lambda times the root
+ 
+
+ align:start position:0%
+upper bounded by lambda times the root
+of the product of x and y so in
+
+ align:start position:0%
+of the product of x and y so in
+ 
+
+ align:start position:0%
+of the product of x and y so in
+particular if this lambda so everything
+
+ align:start position:0%
+particular if this lambda so everything
+ 
+
+ align:start position:0%
+particular if this lambda so everything
+except the top eigenvalue is small then
+
+ align:start position:0%
+except the top eigenvalue is small then
+ 
+
+ align:start position:0%
+except the top eigenvalue is small then
+this discrepancy should be small and you
+
+ align:start position:0%
+this discrepancy should be small and you
+ 
+
+ align:start position:0%
+this discrepancy should be small and you
+can verify with what we did that it's
+
+ align:start position:0%
+can verify with what we did that it's
+ 
+
+ align:start position:0%
+can verify with what we did that it's
+consistent what we put what we just did
+
+ align:start position:0%
+consistent what we put what we just did
+ 
+
+ align:start position:0%
+consistent what we put what we just did
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so let's prove the expander mixing lemma
+
+ align:start position:0%
+so let's prove the expander mixing lemma
+ 
+
+ align:start position:0%
+so let's prove the expander mixing lemma
+which is pretty simple given what we've
+
+ align:start position:0%
+which is pretty simple given what we've
+ 
+
+ align:start position:0%
+which is pretty simple given what we've
+discussed so far
+
+ align:start position:0%
+discussed so far
+ 
+
+ align:start position:0%
+discussed so far
+relating so there was this spectral
+
+ align:start position:0%
+relating so there was this spectral
+ 
+
+ align:start position:0%
+relating so there was this spectral
+characterization up there of the top I
+
+ align:start position:0%
+characterization up there of the top I
+ 
+
+ align:start position:0%
+characterization up there of the top I
+can value so we can let J be B or once
+
+ align:start position:0%
+can value so we can let J be B or once
+ 
+
+ align:start position:0%
+can value so we can let J be B or once
+matrix let J be the old ones matrix and
+
+ align:start position:0%
+matrix let J be the old ones matrix and
+ 
+
+ align:start position:0%
+matrix let J be the old ones matrix and
+we know that the all one's vector is an
+
+ align:start position:0%
+we know that the all one's vector is an
+ 
+
+ align:start position:0%
+we know that the all one's vector is an
+eigenvector of the adjacency matrix of G
+
+ align:start position:0%
+eigenvector of the adjacency matrix of G
+ 
+
+ align:start position:0%
+eigenvector of the adjacency matrix of G
+with eigen value D so the eigen
+
+ align:start position:0%
+with eigen value D so the eigen
+ 
+
+ align:start position:0%
+with eigen value D so the eigen
+decomposition of J is also the ovince
+
+ align:start position:0%
+decomposition of J is also the ovince
+ 
+
+ align:start position:0%
+decomposition of J is also the ovince
+vector and it's complement so we now see
+
+ align:start position:0%
+vector and it's complement so we now see
+ 
+
+ align:start position:0%
+vector and it's complement so we now see
+that a sub G minus T over and J has the
+
+ align:start position:0%
+that a sub G minus T over and J has the
+ 
+
+ align:start position:0%
+that a sub G minus T over and J has the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can vectors as AG so you can choose
+
+ align:start position:0%
+I can vectors as AG so you can choose
+ 
+
+ align:start position:0%
+I can vectors as AG so you can choose
+the eigenvectors for that it's the same
+
+ align:start position:0%
+the eigenvectors for that it's the same
+ 
+
+ align:start position:0%
+the eigenvectors for that it's the same
+set of eigenvectors of course we
+
+ align:start position:0%
+set of eigenvectors of course we
+ 
+
+ align:start position:0%
+set of eigenvectors of course we
+consider this quantity here because this
+
+ align:start position:0%
+consider this quantity here because this
+ 
+
+ align:start position:0%
+consider this quantity here because this
+is exactly the quality that comes up in
+
+ align:start position:0%
+is exactly the quality that comes up in
+ 
+
+ align:start position:0%
+is exactly the quality that comes up in
+this expression once we hit it by
+
+ align:start position:0%
+this expression once we hit it by
+ 
+
+ align:start position:0%
+this expression once we hit it by
+characteristic vectors of subsets from
+
+ align:start position:0%
+characteristic vectors of subsets from
+ 
+
+ align:start position:0%
+characteristic vectors of subsets from
+left and right okay so so what are the
+
+ align:start position:0%
+left and right okay so so what are the
+ 
+
+ align:start position:0%
+left and right okay so so what are the
+eigenvalues okay so the eigenvalues so a
+
+ align:start position:0%
+eigenvalues okay so the eigenvalues so a
+ 
+
+ align:start position:0%
+eigenvalues okay so the eigenvalues so a
+previously had eigenvalues blend the 1
+
+ align:start position:0%
+previously had eigenvalues blend the 1
+ 
+
+ align:start position:0%
+previously had eigenvalues blend the 1
+through lambda and but now the top one
+
+ align:start position:0%
+through lambda and but now the top one
+ 
+
+ align:start position:0%
+through lambda and but now the top one
+gets chopped down to 0 so you can check
+
+ align:start position:0%
+gets chopped down to 0 so you can check
+ 
+
+ align:start position:0%
+gets chopped down to 0 so you can check
+this explicitly so you can check this
+
+ align:start position:0%
+this explicitly so you can check this
+ 
+
+ align:start position:0%
+this explicitly so you can check this
+explicitly by checking that if you take
+
+ align:start position:0%
+explicitly by checking that if you take
+ 
+
+ align:start position:0%
+explicitly by checking that if you take
+this matrix multiplied by the or ones
+
+ align:start position:0%
+this matrix multiplied by the or ones
+ 
+
+ align:start position:0%
+this matrix multiplied by the or ones
+vector you get 0 and if you have an
+
+ align:start position:0%
+vector you get 0 and if you have an
+ 
+
+ align:start position:0%
+vector you get 0 and if you have an
+eigenvector eigenvalue pair then hitting
+
+ align:start position:0%
+eigenvector eigenvalue pair then hitting
+ 
+
+ align:start position:0%
+eigenvector eigenvalue pair then hitting
+this by any of the other ones gets you
+
+ align:start position:0%
+this by any of the other ones gets you
+ 
+
+ align:start position:0%
+this by any of the other ones gets you
+the same as in a because now the
+
+ align:start position:0%
+the same as in a because now the
+ 
+
+ align:start position:0%
+the same as in a because now the
+condition or the other eigen vectors are
+
+ align:start position:0%
+condition or the other eigen vectors are
+ 
+
+ align:start position:0%
+condition or the other eigen vectors are
+orthogonal to the or once vector all
+
+ align:start position:0%
+orthogonal to the or once vector all
+ 
+
+ align:start position:0%
+orthogonal to the or once vector all
+right so now we apply the quran fisher
+
+ align:start position:0%
+right so now we apply the quran fisher
+ 
+
+ align:start position:0%
+right so now we apply the quran fisher
+criteria which tells us that the number
+
+ align:start position:0%
+criteria which tells us that the number
+ 
+
+ align:start position:0%
+criteria which tells us that the number
+in this discrepancy quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which we can write in terms of this
+
+ align:start position:0%
+which we can write in terms of this
+ 
+
+ align:start position:0%
+which we can write in terms of this
+matrix it is upper bounded by the
+
+ align:start position:0%
+matrix it is upper bounded by the
+ 
+
+ align:start position:0%
+matrix it is upper bounded by the
+product of the lengths of these two
+
+ align:start position:0%
+product of the lengths of these two
+ 
+
+ align:start position:0%
+product of the lengths of these two
+vectors x and y multiplied by the
+
+ align:start position:0%
+vectors x and y multiplied by the
+ 
+
+ align:start position:0%
+vectors x and y multiplied by the
+spectral norm not quite using the
+
+ align:start position:0%
+spectral norm not quite using the
+ 
+
+ align:start position:0%
+spectral norm not quite using the
+version up there but I'm using the
+
+ align:start position:0%
+version up there but I'm using the
+ 
+
+ align:start position:0%
+version up there but I'm using the
+spectral norm version which we discussed
+
+ align:start position:0%
+spectral norm version which we discussed
+ 
+
+ align:start position:0%
+spectral norm version which we discussed
+last time it's essentially one up there
+
+ align:start position:0%
+last time it's essentially one up there
+ 
+
+ align:start position:0%
+last time it's essentially one up there
+but you allow not just single x / x and
+
+ align:start position:0%
+but you allow not just single x / x and
+ 
+
+ align:start position:0%
+but you allow not just single x / x and
+y and that corresponds to the largest
+
+ align:start position:0%
+y and that corresponds to the largest
+ 
+
+ align:start position:0%
+y and that corresponds to the largest
+eigen value in absolute value which we
+
+ align:start position:0%
+eigen value in absolute value which we
+ 
+
+ align:start position:0%
+eigen value in absolute value which we
+see that at most lambda so it's the most
+
+ align:start position:0%
+see that at most lambda so it's the most
+ 
+
+ align:start position:0%
+see that at most lambda so it's the most
+lambda times size of x size of y okay
+
+ align:start position:0%
+lambda times size of x size of y okay
+ 
+
+ align:start position:0%
+lambda times size of x size of y okay
+nothing is the proof of the expander
+
+ align:start position:0%
+nothing is the proof of the expander
+ 
+
+ align:start position:0%
+nothing is the proof of the expander
+mixing lemma so the moral here is that
+
+ align:start position:0%
+mixing lemma so the moral here is that
+ 
+
+ align:start position:0%
+mixing lemma so the moral here is that
+just like what we saw earlier when the
+
+ align:start position:0%
+just like what we saw earlier when the
+ 
+
+ align:start position:0%
+just like what we saw earlier when the
+in the tense cadiz but for any
+
+ align:start position:0%
+in the tense cadiz but for any
+ 
+
+ align:start position:0%
+in the tense cadiz but for any
+parameters so here there's no it's a
+
+ align:start position:0%
+parameters so here there's no it's a
+ 
+
+ align:start position:0%
+parameters so here there's no it's a
+very clean statement you can even have
+
+ align:start position:0%
+very clean statement you can even have
+ 
+
+ align:start position:0%
+very clean statement you can even have
+found the degree graphs he could be
+
+ align:start position:0%
+found the degree graphs he could be
+ 
+
+ align:start position:0%
+found the degree graphs he could be
+constant if lambda is small compared to
+
+ align:start position:0%
+constant if lambda is small compared to
+ 
+
+ align:start position:0%
+constant if lambda is small compared to
+D then you have this discrepancy
+
+ align:start position:0%
+D then you have this discrepancy
+ 
+
+ align:start position:0%
+D then you have this discrepancy
+condition and the reason why this is
+
+ align:start position:0%
+condition and the reason why this is
+ 
+
+ align:start position:0%
+condition and the reason why this is
+called an expander mixing lemma is that
+
+ align:start position:0%
+called an expander mixing lemma is that
+ 
+
+ align:start position:0%
+called an expander mixing lemma is that
+there's this notion of expanders which
+
+ align:start position:0%
+there's this notion of expanders which
+ 
+
+ align:start position:0%
+there's this notion of expanders which
+is not quite the same but very
+
+ align:start position:0%
+is not quite the same but very
+ 
+
+ align:start position:0%
+is not quite the same but very
+intimately related to pseudo-random
+
+ align:start position:0%
+intimately related to pseudo-random
+ 
+
+ align:start position:0%
+intimately related to pseudo-random
+grass so one property of pseudo-random
+
+ align:start position:0%
+grass so one property of pseudo-random
+ 
+
+ align:start position:0%
+grass so one property of pseudo-random
+graphs that is quite useful in
+
+ align:start position:0%
+graphs that is quite useful in
+ 
+
+ align:start position:0%
+graphs that is quite useful in
+particular in computer science is that
+
+ align:start position:0%
+particular in computer science is that
+ 
+
+ align:start position:0%
+particular in computer science is that
+if you take a small subset of vertices
+
+ align:start position:0%
+if you take a small subset of vertices
+ 
+
+ align:start position:0%
+if you take a small subset of vertices
+it has lots of neighbors so the graph is
+
+ align:start position:0%
+it has lots of neighbors so the graph is
+ 
+
+ align:start position:0%
+it has lots of neighbors so the graph is
+now somehow in a cluster into a few
+
+ align:start position:0%
+now somehow in a cluster into a few
+ 
+
+ align:start position:0%
+now somehow in a cluster into a few
+local pieces so there's lots of
+
+ align:start position:0%
+local pieces so there's lots of
+ 
+
+ align:start position:0%
+local pieces so there's lots of
+expansion
+
+ align:start position:0%
+expansion
+ 
+
+ align:start position:0%
+expansion
+and and and that's something that you
+
+ align:start position:0%
+and and and that's something that you
+ 
+
+ align:start position:0%
+and and and that's something that you
+can guarantee using in the expand your
+
+ align:start position:0%
+can guarantee using in the expand your
+ 
+
+ align:start position:0%
+can guarantee using in the expand your
+mixing lemma that you have lots of you
+
+ align:start position:0%
+mixing lemma that you have lots of you
+ 
+
+ align:start position:0%
+mixing lemma that you have lots of you
+take a small set of vertices you can
+
+ align:start position:0%
+take a small set of vertices you can
+ 
+
+ align:start position:0%
+take a small set of vertices you can
+expand outward so graphs with that
+
+ align:start position:0%
+expand outward so graphs with that
+ 
+
+ align:start position:0%
+expand outward so graphs with that
+specific property taking small subset of
+
+ align:start position:0%
+specific property taking small subset of
+ 
+
+ align:start position:0%
+specific property taking small subset of
+vertices always gets you loss of
+
+ align:start position:0%
+vertices always gets you loss of
+ 
+
+ align:start position:0%
+vertices always gets you loss of
+neighbors are called expand their graphs
+
+ align:start position:0%
+neighbors are called expand their graphs
+ 
+
+ align:start position:0%
+neighbors are called expand their graphs
+and these graphs play important role in
+
+ align:start position:0%
+and these graphs play important role in
+ 
+
+ align:start position:0%
+and these graphs play important role in
+in particular in computer science in
+
+ align:start position:0%
+in particular in computer science in
+ 
+
+ align:start position:0%
+in particular in computer science in
+designing algorithms improving
+
+ align:start position:0%
+designing algorithms improving
+ 
+
+ align:start position:0%
+designing algorithms improving
+complexity results and so on but also
+
+ align:start position:0%
+complexity results and so on but also
+ 
+
+ align:start position:0%
+complexity results and so on but also
+play important roles in graph theory and
+
+ align:start position:0%
+play important roles in graph theory and
+ 
+
+ align:start position:0%
+play important roles in graph theory and
+combinatorics well next time we'll
+
+ align:start position:0%
+combinatorics well next time we'll
+ 
+
+ align:start position:0%
+combinatorics well next time we'll
+address a few questions which are along
+
+ align:start position:0%
+address a few questions which are along
+ 
+
+ align:start position:0%
+address a few questions which are along
+the lines of one how small can lambda B
+
+ align:start position:0%
+the lines of one how small can lambda B
+ 
+
+ align:start position:0%
+the lines of one how small can lambda B
+as a function of T right so here it's as
+
+ align:start position:0%
+as a function of T right so here it's as
+ 
+
+ align:start position:0%
+as a function of T right so here it's as
+if lambda is small compared to D then
+
+ align:start position:0%
+if lambda is small compared to D then
+ 
+
+ align:start position:0%
+if lambda is small compared to D then
+you have this discrepancy but can it be
+
+ align:start position:0%
+you have this discrepancy but can it be
+ 
+
+ align:start position:0%
+you have this discrepancy but can it be
+you know if D is let's say am Union how
+
+ align:start position:0%
+you know if D is let's say am Union how
+ 
+
+ align:start position:0%
+you know if D is let's say am Union how
+small can lambda be that's one question
+
+ align:start position:0%
+small can lambda be that's one question
+ 
+
+ align:start position:0%
+small can lambda be that's one question
+another question is is considering you
+
+ align:start position:0%
+another question is is considering you
+ 
+
+ align:start position:0%
+another question is is considering you
+know everything that we've said so far
+
+ align:start position:0%
+know everything that we've said so far
+ 
+
+ align:start position:0%
+know everything that we've said so far
+what can we say about let's say that the
+
+ align:start position:0%
+what can we say about let's say that the
+ 
+
+ align:start position:0%
+what can we say about let's say that the
+relationship between some of these
+
+ align:start position:0%
+relationship between some of these
+ 
+
+ align:start position:0%
+relationship between some of these
+conditions for sparse graphs but that
+
+ align:start position:0%
+conditions for sparse graphs but that
+ 
+
+ align:start position:0%
+conditions for sparse graphs but that
+are somewhat special for example KD
+
+ align:start position:0%
+are somewhat special for example KD
+ 
+
+ align:start position:0%
+are somewhat special for example KD
+graphs or vertex-transitive graphs and
+
+ align:start position:0%
+graphs or vertex-transitive graphs and
+ 
+
+ align:start position:0%
+graphs or vertex-transitive graphs and
+turns out some of these relations are
+
+ align:start position:0%
+turns out some of these relations are
+ 
+
+ align:start position:0%
+turns out some of these relations are
+also equivalent to each other
\ No newline at end of file
diff --git a/UesUBkX9HIQ.txt b/UesUBkX9HIQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3854cb524397322e9b0d10260e0a185d984e6cf6
--- /dev/null
+++ b/UesUBkX9HIQ.txt
@@ -0,0 +1,1979 @@
+The following content is
+provided by MIT OpenCourseWare
+
+under a Creative Commons
+license.
+
+Additional information about
+our license and MIT
+
+OpenCourseWare in general is
+available at ocw.mit.edu.
+
+At the end of last hour,
+we had just gotten to the point
+
+of having developed the
+molecular orbital energy level
+
+diagram for the BH three
+molecule, this trigonal planar
+
+entity.
+And I had not had time last
+
+hour to show you what these
+molecular orbitals look like in
+
+their calculated form.
+And so, I am going to start off
+
+today by doing that,
+and then will proceed to answer
+
+a quadrangle of questions that
+we can attack regarding diatomic
+
+molecules using molecular
+orbital theory.
+
+Remember that the BH three
+MO problem is a seven
+
+orbital problem.
+And so, we will go through and
+
+just look at these seven
+molecular orbitals in ascending
+
+energy from the lowest energy on
+up.
+
+This one is the lowest energy
+molecular orbital for BH three
+
+as calculated using a
+modern quantum chemical package.
+
+And what you can see is that
+since we are indicating the
+
+phase of the wave function by
+color, there is only one phase
+
+to be seen.
+This, of course,
+
+is a characteristic property of
+an s orbital.
+
+Remember that?
+And what we have here,
+
+at the center of the molecule,
+is the 2s orbital on boron.
+
+And in this molecular orbital
+theory, effectively what is
+
+happening is that 2s orbital on
+boron is reaching out and
+
+simultaneously overlapping with
+the three 1s orbitals on each of
+
+the hydrogens.
+And the way that we have
+
+orthogonalized it and normalized
+it amounts to a single molecular
+
+orbital that can,
+if you will,
+
+house a pair of electrons in
+this orbital that is
+
+simultaneously bonding between
+boron and the three hydrogens.
+
+You have one electron pair in
+here.
+
+Two of the six electrons in the
+valance shell of this molecule
+
+are in this lowest lying,
+most tightly held,
+
+most electronegative molecular
+orbital.
+
+Let's look now at the next one.
+
+You should be thinking in your
+mind just what was the next
+
+highest lying orbital that we
+had, and you will realize that
+
+this is an orbital formed from
+one of the boron p orbitals and
+
+a linear combination of two of
+the hydrogen wave functions.
+
+And let's see if you can
+recognize it based on what we
+
+did last time.
+Maybe I can reorient it to help
+
+in that regard.
+Here is a molecular orbital
+
+that can house a pair of
+electrons, one spin-up and one
+
+spin-down, and that is
+simultaneously bonding from that
+
+boron to this hydrogen,
+up here.
+
+And then there is a nodal
+surface, here,
+
+that is coincident with the
+nodal surfaces of the boron 2px
+
+orbital, using the same
+coordinate system that we were
+
+using last time.
+And so, the wave function
+
+changes sign as you pass through
+the boron.
+
+And then the opposite phase
+lobe of the boron 2px orbital is
+
+able to overlap with these two
+hydrogens, here.
+
+If you will remember,
+when I wrote down the
+
+normalization constants for this
+molecular orbital,
+
+we had double the coefficient
+on the hydrogen up here as
+
+compared with the two hydrogens
+down here.
+
+And they were opposite in sign.
+And that leads to a really nice
+
+overlap, as you can see here.
+This is BH bonding here,
+
+and BH bonding,
+down here.
+
+And it involves that boron 2px
+orbital.
+
+One way you can think about
+this molecular orbital theory is
+
+that this 2px orbital on the
+central atom is reaching out
+
+with its intrinsic plus-minus
+phase combination that is
+
+intrinsic to a 2px orbital
+simultaneously reaching out and
+
+bonding with all three hydrogens
+in the only way that it can,
+
+being a 2px orbital.
+And so, we created that linear
+
+combination with that idea in
+mind.
+
+And then, if we go up one more
+in energy, strike that.
+
+Not one up more in energy,
+but to the other orbital in the
+
+molecule that is at the same
+energy.
+
+What we will find is that we
+are involving,
+
+now, the 2py orbital.
+And it will reach out and
+
+interact with hydrogens in the
+only way it can,
+
+given its intrinsic nodal
+properties as a 2py orbital.
+
+Remember that a 2py orbital has
+the x,z-plane as a nodal
+
+surface.
+And there is a hydrogen up here
+
+on that x,z-plane,
+namely the one that lies on the
+
+plus x-axis.
+And because it lies on the
+
+intrinsic nodal surface of this
+2py orbital, it can contribute
+
+nothing to this molecular
+orbital.
+
+All we are seeing up here at
+the top is an arbitrarily sized
+
+sphere, just to show the
+location of that nucleus,
+
+the hydrogen nucleus that is on
+the plus x-axis.
+
+And then here,
+what you see is the 2py orbital
+
+oriented along y and overlapping
+simultaneously with a plus 1s
+
+wave function here and minus 1s
+wave function here so that you
+
+see a beautiful bonding
+molecular orbital that is at the
+
+same energy at the one we just
+looked at.
+
+And so, as you step up in
+energy, looking at the energy
+
+level diagram for BH three
+from last time,
+
+that is what you see.
+We have now six electrons in
+
+the molecule,
+two in this orbital and two
+
+each in the two orbitals we just
+looked at that provide the three
+
+BH bonds that we represent in
+the valance bond theory as
+
+electron pair bonds.
+But this is a totally different
+
+way of looking at the electronic
+structure that is very appearing
+
+because it just takes advantage
+of the atomic orbital properties
+
+that you would calculate for
+your central atom.
+
+Now, let's go up one more.
+The very next one,
+
+I will skip showing to you for
+purposes of saving time,
+
+here, but you know that the
+next orbital up is simply the
+
+2pz orbital on the boron,
+which is our lowest unoccupied
+
+molecular orbital,
+as well as being an atomic
+
+orbital in this system and
+responsible for the Lewis acid
+
+characteristics of this species.
+And one up above that,
+
+one higher in energy than the
+LUMO is the orbital that I did
+
+show you last time,
+the out-of-phase combination of
+
+the boron 2s with the three
+hydrogens all with the same
+
+sign.
+It is sort of a round nodal
+
+surface intersection each of the
+BH bonds.
+
+And then, finally,
+orbitals number six and seven
+
+are the antibonding counterparts
+to the ones that I just showed
+
+you involving boron's 2px and
+2py wave functions.
+
+Here is what these look like.
+And this one,
+
+you will see,
+involves the 2px orbital.
+
+Here is our x-axis pointing up.
+And the blue lobe of 2px,
+
+the positive lobe here,
+as you can see,
+
+is squished out and down.
+These pictures can be a little
+
+bit more complicated than what
+we are used to looking at from
+
+just sketching it out on the
+board or the qualitative
+
+pictures that you sometimes see
+in your textbook.
+
+But what we do find here that
+is the important feature is that
+
+as we go from the 1s
+contribution on this hydrogen
+
+over here to the positive lobe
+of 2px we are going through a
+
+nodal surface.
+And that is antibonding in
+
+character.
+And you can see that this
+
+deformation of this lobe of the
+p orbital, of course,
+
+looks like a high energy type
+of phenomena.
+
+And indeed it is.
+This is one of the two highest
+
+energy orbitals in the energy
+level diagram for the BH three
+
+molecule.
+And then, similarly,
+
+here is the other lobe of the
+2px orbital, the minus lobe.
+
+And, as you try to go from it
+to the adjacent hydrogens,
+
+remember, in the bonding one we
+were allowing this to overlap
+
+with the same sign on the
+hydrogens.
+
+Now we have the opposite sign
+on the hydrogens,
+
+so that we have a beautiful
+antibonding node indicated here
+
+and here between the minus phase
+lobe of 2px and the adjacent
+
+hydrogens.
+So, this antibonding orbital
+
+has lots of internuclear nodes,
+nodes that appear between
+
+nuclei and indicate that we are
+not getting overlapped and
+
+bonding, but rather we are
+getting a high frequency orbital
+
+that is likewise high in energy.
+Finally, I will show you the
+
+counterpart to this one,
+that involves 2py.
+
+It is a little easier to
+understand from inspecting it.
+
+And it also evinces the
+internuclear nodes that you
+
+would expect for an antibonding
+molecular orbital.
+
+And I am orienting it so that
+you will be able to understand
+
+it with reference to our
+coordinate system as introduced
+
+last time.
+And so, you have the boron and
+
+the hydrogen along x,
+up here.
+
+Here is our 2py.
+It is sort of bending away from
+
+these two hydrogens whose wave
+functions have opposite sign to
+
+the lobes that are directed into
+their vicinity.
+
+You can see that we have here a
+nodal surface between boron and
+
+this hydrogen wherein the
+bonding counterpart that we
+
+looked at had the same sign and
+a nice bond.
+
+And then over here,
+once again, the mirror image.
+
+So, this is one of our final
+orbitals in looking at the BH
+
+three energy level
+diagram.
+
+It is the case that if you
+start to put electrons into
+
+antibonding orbitals,
+they will cancel the bonding
+
+properties of the bonding
+counterparts.
+
+And we will explore that in
+quite a bit more detail here
+
+shortly.
+Let me leave that up there for
+
+now and tell you what quadrangle
+of problems it is that I hope to
+
+answer for you today using more
+MO theory ideas.
+
+First of these will be why He
+two is so stable?
+
+And so, today's lecture is
+predominantly devoted to
+
+diatomic molecules.
+And He two will be the
+
+first of these.
+Let's make this unstable.
+
+Let's do stable here in just a
+moment, but first let's say,
+
+next, why does O two
+have unpaired electrons?
+
+Certainly, if we draw the
+valance bond picture for O two,
+
+like that,
+it does not give us any
+
+indication that this diatomic
+molecule would have unpaired
+
+electrons.
+And so, we are going to see how
+
+MO theory can shed some light on
+this issue.
+
+And then, the final two
+questions that I will fold into
+
+one line here given the way I am
+using up space on this board is,
+
+why is N two so stable
+--
+
+-- and CO poison?
+
+MO theory can shed very clear
+light on all of these questions.
+
+And so, that is what we will
+work on for the rest of the
+
+hour.
+In MO theory,
+
+there are a couple things you
+should keep in mind when trying
+
+to grasp all the subtleties of a
+given energy level diagram with
+
+which you may be confronted in
+your textbook or on an exam or
+
+just through reading papers in
+the Journal of the American
+
+Chemical Society,
+wherever you may find these.
+
+You should keep in mind that,
+number one, interaction is
+
+strong.
+That is, when atomic orbitals
+
+interact to form molecular
+orbitals, the AO interaction is
+
+strong --
+
+-- when there is good spatial
+overlap.
+
+Overlap is a central concept in
+molecular orbital theory.
+
+The idea is that if you have
+atoms that are far apart from
+
+each other in space,
+then their wave functions have
+
+dropped off exponentially and
+are not interacting much and
+
+there is not good overlap.
+But when orbitals are close in
+
+space and if their orbitals are
+directed in space toward one
+
+another, then there may be
+overlap that leads to good
+
+bonding.
+And also I can echo this first
+
+part, AO interaction is strong
+when, and say two,
+
+AOs are close in energy.
+The interacting orbitals are
+
+close in energy.
+
+When I talk about where atomic
+orbitals are in energy,
+
+I am going to really want you
+to think about your periodic
+
+table and the properties that
+appear with periodicity and are
+
+organized and collated in the
+periodic table.
+
+We are going to be talking
+about properties like
+
+electronegativity as it relates
+to the energy.
+
+And I will get to that a little
+bit on the next board,
+
+but let's first make a small MO
+diagram here.
+
+And this will be a diagram that
+we may use both for H two
+
+or He two.
+This is the simplest of all MO
+
+diagrams and one with which you
+should be quite familiar.
+
+We have a bonding molecular
+orbital at low-end energy.
+
+And notice that if this is a 1s
+orbital over here and this is a
+
+1s orbital over here for H two
+or He two 
+
+systems, then when these come
+together and bond,
+
+here are your two nuclei,
+--
+
+-- and here is a probability
+density isosurface that I am
+
+drawing around that shows
+in-phase combination of those
+
+two 1s orbitals merging with
+each other, giving good overlap,
+
+and the interacting AOs being
+of the same energy.
+
+Because the H two and He
+two molecules have such
+
+symmetry we have a good bonding
+orbital.
+
+And then, up here,
+we must find there to be an
+
+internuclear node in that
+corresponding antibonding
+
+orbital.
+And so, it will look something
+
+like this.
+And, therefore,
+
+I am going to associate with
+this high-lying orbital an
+
+asterisk to indicate the
+antibonding character,
+
+the presence of this
+internuclear node,
+
+the change of sign as we go
+from one nucleus to the other,
+
+the absence of bonding
+character.
+
+Here we have the buildup of
+electron density in the
+
+internuclear region,
+electrons being stabilized by
+
+being held simultaneously by
+more than one nucleus that is
+
+positively charged.
+And here, the exact inverse of
+
+that, constructive interference
+and destructive interference in
+
+the H two or He two
+systems.
+
+And then we can ask,
+how many electrons do we have
+
+to put into the diagram?
+If it is the H two case,
+
+then, to figure out the bond
+order, --
+
+-- what we do is populate the
+diagram according to the same
+
+kind of Aufbau principle that
+you would for generating the
+
+energy level diagram for an
+atom, and taking into account
+
+things like Hund's rule.
+If it is H two,
+
+we have two electrons that we
+can put in, which in here with
+
+opposing spin,
+like that.
+
+That is our bonding molecular
+orbital.
+
+We have two bonding electrons.
+Zero antibonding electrons
+
+divided by two equals a bond
+order of one.
+
+We have an H-H single bond in
+the case of the H two
+
+molecule.
+But if we have He two,
+
+then in the He two system,
+we have two more electrons,
+
+and the only place they can go
+is up here in the antibonding
+
+molecular orbital.
+We have two bonding minus two
+
+antibonding over two is equal to
+zero for a bond order of zero.
+
+And so, the idea is that if two
+He atoms collide with each
+
+other, when they do so,
+their orbitals may overlap and
+
+give rise to bonding.
+But, simultaneously,
+
+you get antibonding.
+And the net bond order is zero,
+
+and so He two is not
+bound, but these atoms just
+
+bounce off each other.
+There is no stabilization.
+
+And you can certainly
+understand that if we were in
+
+the middle somewhere,
+as we would be if we had He two
+
+plus,
+missing one electron up here,
+
+then our bond order would be
+one-half.
+
+It is going to get a lot more
+complicated than this,
+
+but this you have to know
+because this is a really nice
+
+starting point for thinking
+about bonding in all kinds of
+
+scenarios where you may need to
+consider it.
+
+And so, let's look at some
+periodic properties.
+
+This will be with reference,
+again, to energy.
+
+And I am interested in how some
+of the properties of the atoms
+
+vary as we go across the
+periodic table,
+
+lithium to beryllium to boron
+to carbon to nitrogen to oxygen
+
+and over to fluorine.
+And I will stop there.
+
+We won't worry about any more
+of the noble gases today.
+
+As we go from left to right,
+one of the things that you know
+
+from your study of the periodic
+table is that electronegativity
+
+increases.
+
+This increases from left to
+right across the Periodic Table
+
+in concert with increasing Z.
+
+That is, the increasing atomic
+number.
+
+That is, the increasing number
+of positively charged protons in
+
+our nucleus, as we go across.
+Each time we are adding more
+
+protons to that nucleus.
+The nucleus is becoming more
+
+and more positively charged as
+we go across.
+
+And an important consequence of
+that has to do with the fact
+
+that s orbitals don't have a
+node at the nucleus.
+
+Whereas, p orbitals do.
+Since these elements are in the
+
+so-called p block of our
+periodic table,
+
+well, lithium in the s block,
+but we will consider the
+
+properties all the way across.
+And the energy issue up here
+
+that I am going to be concerned
+with is the energy of the atomic
+
+2s versus 2p orbitals as we go
+from left to right across the
+
+periodic table,
+systematically adding to the
+
+number of protons in our nucleus
+in a way that does not affect 2s
+
+orbitals the same way that it
+affects 2p orbitals.
+
+It turns out that by the time
+we get over to fluorine,
+
+where we have essentially our
+most electronegative element,
+
+the 2s orbital has sunk to a
+very low energy.
+
+And the 2p orbital has gone
+down in energy as well,
+
+but just not by nearly as much.
+And so, it is nearly an
+
+isotonic function as we go
+across.
+
+2p is decreasing in energy in
+response to this increased Z,
+
+but not as much as 2s is
+decreasing in energy,
+
+having to do with the fact that
+2s electrons see much more of
+
+the nucleus than 2p electrons do
+because 2s electrons don't have
+
+a node there.
+They spend a lot more time in
+
+close to the nucleus than do
+your 2p electrons.
+
+This has a really important
+influence on that set of
+
+diatomic molecule MO theory
+problems, eight orbital
+
+problems, that we call homo or
+heteronuclear diatomic molecules
+
+of these elements.
+And that has to do with the
+
+fact that in between nitrogen
+and oxygen, a fundamental change
+
+takes place in the energy level
+diagram.
+
+And that change,
+that results from the atomic
+
+structure of the elements,
+ends up with the result that
+
+the MO diagram is much easier to
+draw for oxygen,
+
+O two,
+and fluorine,
+
+F two,
+than it is for the earlier
+
+ones.
+And it is much easier to
+
+understand for O two and
+F two than it is for N
+
+two, C two, B two,
+Be two, Li two.
+
+So, let's just see what that
+means.
+
+First of all,
+when we are going to draw an
+
+energy level diagram for a
+diatomic molecule,
+
+if it is a homonuclear diatomic
+molecule, meaning the two atoms
+
+that are going to be bonded
+together are the same,
+
+that means that the atomic
+orbitals for the contributing
+
+atoms are the same.
+Here, on the left,
+
+what I am drawing is,
+let's say, an F or an O atom.
+
+We have the 2s and the 2p,
+x-y-z.
+
+That is four of the eight
+orbitals in our problem.
+
+And then, over here,
+we have the other identical F
+
+or O atom, with its 2p x-y-z and
+2s orbitals at exactly the same
+
+energy as for the counterpart,
+over here.
+
+So, this is another F or O
+atom.
+
+And then we are going to ask,
+how can these atomic orbitals
+
+combine to give molecular
+orbitals in these diatomic
+
+molecules?
+This is unlike the BH three
+
+problem because there is
+no atom at the center of gravity
+
+of our system,
+but the ideas are the same.
+
+And the ideas are very much the
+same as what we have here for H
+
+two, where also we could
+make molecular orbitals despite
+
+the fact that there was no atom
+at the center of our system.
+
+We can pretend that there is,
+and we can use that pretend
+
+atom to identify what linear
+combinations we should make.
+
+A simpler way to do it,
+at this point,
+
+would be to say that our
+molecule has the two nuclei
+
+oriented along the z-axis.
+And then you have x and y
+
+perpendicular to z.
+And so, if we take this choice
+
+of coordinate system that the
+molecule is oriented along z,
+
+the two nuclei lie one on plus
+z, one on minus z.
+
+Then we can immediately
+classify our atomic orbitals as
+
+being either sigma or pi with
+respect to the z-axis.
+
+I will say AO is sigma or pi
+with respect to z,
+
+which is the molecular axis.
+And remember what that means in
+
+terms of the nodal properties.
+If something is sigma with
+
+respect to z,
+that means if you view it down
+
+z it will look like a cylinder.
+It will look like a sphere,
+
+actually.
+It will be cylindrically
+
+symmetric about the z-axis.
+If it is sigma then,
+
+if you are viewing down z,
+you see that.
+
+That could be either an s
+orbital or it could be a pz
+
+orbital.
+They would look the same if you
+
+were viewing right down z.
+And then pi,
+
+viewing down z,
+would look like this.
+
+And that would be a px or a py
+orbital perpendicular to the
+
+z-axis.
+And this would be an s orbital
+
+or a pz orbital.
+What I can say right away is
+
+that we can separate out the
+molecular orbitals that we are
+
+going to form from these atomic
+orbitals into their sigma or pi
+
+characteristics relative to the
+z-axis.
+
+And because we are in the O or
+F atom case, very far on the
+
+right-hand side the periodic
+table, we have a large gap.
+
+This gap is large.
+
+We can make the approximation
+that this 2s orbital here,
+
+which could in principle form a
+sigma bond with this 2pz orbital
+
+over here, that would be an
+interaction looking like that,
+
+--
+-- that that does not occur.
+
+Because remember here I said
+you get strong interaction when
+
+the interacting AOs are close in
+energy.
+
+When you are talking about
+these very electronegative
+
+elements, the s manifold of
+orbitals is very well separated
+
+in energy from the p manifold.
+That leads to simplicity in the
+
+case of the diagram that we are
+about to draw.
+
+Because we say that this
+interacts with this in a sigma
+
+fashion, giving rise to bonding
+and antibonding interactions
+
+that look exactly like what we
+have drawn over there.
+
+I will draw the bonding orbital
+here.
+
+Actually, the antibonding
+orbital here and the bonding
+
+orbital here.
+And I will show the parentage
+
+of this molecular orbitals in
+this way.
+
+And you will recognize that
+this is our in-phase combination
+
+and this is our out-of-phase
+combination, analogous to the H
+
+two problem.
+This is like the H two
+
+problem built into the F two
+or the O two
+
+problem.
+And next what we find is that
+
+we can also make a sigma bond by
+interaction of pz with pz.
+
+This is going to be a nice
+strong directed bonding
+
+interaction that will look like
+this.
+
+You see we have overlap here in
+the center, a nice strong
+
+bonding interaction in the
+center with 2pz orbitals that
+
+are directed at each other.
+And this is a sigma bond
+
+because you view that down z,
+it is going to look like a
+
+round thing.
+You are not going to see any
+
+nodal surfaces.
+And then it has up here a
+
+corresponding antibonding
+orbital right there.
+
+So far I have --
+
+-- two pair-wise combinations
+that give us two sigma bonding
+
+orbitals and two sigma star
+antibonding orbitals.
+
+So, that is pretty
+straightforward.
+
+And, once again,
+I can say that we have the H
+
+two problem built into
+this energy level diagram twice,
+
+with the s interactions,
+with the pz interactions.
+
+The only thing I have left is
+to do my px and py interactions.
+
+And we can make a pair of pi
+bonds and a pair of pi
+
+anti-bonds that corresponds to
+those pi bonds.
+
+This one is pi.
+This one is pi star.
+
+And what do they look like?
+Well, they look like
+
+side-to-side bonds between pairs
+of p orbitals.
+
+This is just like what I showed
+you for the ethylene molecule.
+
+The pi bond,
+in fact, has this nice overlap
+
+on one side and up here on the
+other.
+
+There is your pi bond.
+And you have one of those that
+
+lie in the x,z-plane and one of
+those that lie in the y,z-plane.
+
+You have two of them,
+and they are at equal energy
+
+here.
+And then up here,
+
+what does the pi star look
+like?
+
+Well, the same,
+except we turn around one of
+
+the p orbitals,
+introducing a nodal surface,
+
+like that.
+And we have two of those.
+
+And here is our nodal surface.
+Now it is an internuclear
+
+between the nuclei nodal
+surface, indicating antibonding
+
+character there.
+That is the easy case because s
+
+and p are very well separated.
+What you can see,
+
+though, is that type of
+interaction of a 2s on our left
+
+atom with a pz on the right
+atom, that might start to become
+
+important as you are over here
+in this part of the diagram,
+
+where s and p are pretty close
+together in energy.
+
+And that is what happens,
+in fact.
+
+And that is what happens as
+soon as you go to the left of
+
+oxygen and to nitrogen or
+anything lighter than nitrogen.
+
+Suddenly, you cannot ignore
+interactions of s on one side
+
+with p on the other.
+
+And so, I am going to draw here
+the diagram that you would use,
+
+say, for N two.
+And, for simplicity,
+
+I am just going to draw the
+middle part.
+
+This part here in the middle is
+that which corresponds to the
+
+molecule.
+This one is what you would use
+
+for O two or F two.
+
+And let's just go ahead and
+draw that diagram for the
+
+molecule.
+This one would be this set of
+
+energy levels corresponding to,
+for example, N two.
+
+And we have increasing energy
+
+on the vertical axis.
+We are going to find that
+
+again, we have a sigma and a
+sigma star.
+
+And then, the difference comes
+right here where we find that as
+
+we go up in energy we next get
+to our pi bonds.
+
+And then, the next sigma
+orbital is slightly higher in
+
+energy than the pi system rather
+than slightly lower in energy.
+
+And then we will encounter up
+here our pi star.
+
+And then, finally,
+that highest in energy,
+
+sigma star.
+This switch,
+
+this sigma going up relative to
+that pi is really a consequence
+
+of all of the sigma orbitals
+being responsive to the value of
+
+the electronegativity of the 2s
+orbital of the atom.
+
+You can really almost consider
+the pi system independent from
+
+the sigma.
+These four sigma orbitals,
+
+sigma, sigma star,
+sigma, sigma star,
+
+I can call them one sigma,
+two, three, four,
+
+just to show you that we have,
+in ascending order,
+
+four orbitals of sigma
+symmetry.
+
+That whole manifold,
+when you can start mixing a
+
+little bit of very low energy s
+into it, sinks down relative to
+
+pi.
+In the case over here,
+
+we are basically pulling down
+the four sigma orbitals relative
+
+to pi.
+And here, because our s
+
+orbitals are higher in energy
+relative to our p orbitals,
+
+they go up a little bit and
+bumps three sigma up over pi.
+
+And what it means is that these
+orbitals are not so simple
+
+anymore.
+Any one of them is a linear
+
+combination of four atomic
+orbitals.
+
+This orbital here,
+one sigma, will not look like
+
+it looks in the H two
+problem, anymore.
+
+This one sigma will have some p
+mixed into it.
+
+And so, one way we can
+represent that through a simple
+
+drawing is like this.
+
+You see the difference between
+that sigma bonding orbital and
+
+the one up there?
+We have some extra little nodes
+
+in here that are an inherent
+characteristic of the
+
+contribution of 2pz orbitals
+into this.
+
+This is a linear combination of
+the 2s and the 2pz orbitals on
+
+the two atoms we have.
+There are four atomic orbitals
+
+that go in with different
+coefficients to these different
+
+parts of the sigma manifold.
+And then up here,
+
+the other bonding orbital,
+we can draw it this way.
+
+And this molecular orbital,
+this one here,
+
+three sigma,
+has diminished bonding
+
+character between the two nuclei
+and enhanced character on the
+
+outside, the part of the p
+orbital that is contributing to
+
+it that points away from the
+other atom.
+
+And so, while this has bonding
+character, it also has what we
+
+might think of as lone pair
+characteristics.
+
+In MO theory,
+some orbitals are not that
+
+simple.
+They might be at the same time
+
+a little bit bonding and a
+little bit lone pair in
+
+character.
+Let's look at a couple of
+
+orbitals like that,
+briefly.
+
+And here I have done this for
+the C two molecule.
+
+I have done the calculation for
+C two,
+
+so now we are over here on the
+left-hand side of that dividing
+
+line where s and p are a big
+closer together.
+
+And I am opening up this
+orbital, this one down here.
+
+It is a little more complicated
+than the way I drew it on the
+
+board, but what you should be
+able to see is --
+
+Think back, now,
+to the first orbital I showed
+
+you today, which was the lowest
+lying orbital in the BH three
+
+molecule.
+You remember,
+
+no matter which way we turned
+it, we only saw blue,
+
+which was the positive wave
+function.
+
+It looked like an s orbital,
+everywhere.
+
+It had the same sign
+everywhere, and you could not
+
+see any nodal properties.
+Well, that would be true also
+
+for this one down here in the
+case of O two or F two
+
+because it is not mixing
+in p character.
+
+Because the atomic s and p
+orbitals are so far away in
+
+energy.
+But now, when they are closer
+
+in energy, this orbital down
+here, the s over here sees the p
+
+over here and they mix in,
+and vice versa.
+
+And, if I turn this around,
+what you are going to see are
+
+these little negative lobes here
+that I am indicating that are
+
+mixing in.
+But this is hugely bonding
+
+orbital, still,
+because look at how much of the
+
+orbital is centered in the
+region between the nuclei.
+
+This is a very strongly bonding
+orbital in this system.
+
+Let's now visualize the three
+sigma, the third sigma symmetry
+
+orbital, as we ascend in energy.
+And it will look hopefully
+
+something like what I drew here.
+There it is.
+
+You see this is a sigma
+orbital, because as we look down
+
+the z-axis, it looks just round.
+But it certainly has a lot of p
+
+orbital character because as we
+go from outside the molecule
+
+through the nucleus,
+we get a change in sign.
+
+And then there is overlap in
+here, but the amount of the
+
+overlap in here is small
+compared to the amount of this
+
+lobe out here that is just
+nonbonding in character because
+
+it is pointing out into space.
+It is like a lone pair of
+
+electrons at the same time as it
+is a bonding orbital.
+
+If this molecule actually had
+enough electrons to fill up
+
+through three sigma and no
+higher, than you would recognize
+
+that this orbital that we are
+looking at would be the highest
+
+occupied molecular orbital.
+And it would be responsible for
+
+the basicity and the
+nucleophilicity of the molecule
+
+--
+-- because any Lewis acid that
+
+came in would want to come in on
+the z-axis to interact with this
+
+lone pair electron density out
+there.
+
+So, that is how our three sigma
+orbital now looks when we are on
+
+the left side of that red dotted
+line to the lighter elements.
+
+I will leave that up there for
+a moment while we consider a
+
+couple of interesting points.
+One of the things that you will
+
+often be asked to do is to write
+down the configuration.
+
+And I want to finish these two
+questions here of O two,
+
+why does it have unpaired
+electrons?
+
+In the case of O two,
+we are over on this diagram,
+
+we have 12 valance electrons.
+We can go two,
+
+four, six, eight,
+ten, and then 11 and 12,
+
+two electrons up here in the pi
+star manifold.
+
+We are completely filled up
+through pi.
+
+And then, we have a half-filled
+pi star with 12 electrons
+
+populating the O two diagram.
+
+Let's represent that this way.
+We have our one sigma with two
+
+electrons in.
+We have our second sigma,
+
+which is antibonding with two
+electrons.
+
+Then we have our third sigma
+with two electrons.
+
+And then, as we go up in
+energy, the next is our first pi
+
+orbital bonding.
+That accommodates four
+
+electrons.
+And then we have next our
+
+second pi type orbital.
+It is antibonding and has two
+
+electrons in it.
+And then all the other orbitals
+
+are empty, so I won't indicate
+them.
+
+This is the configuration for
+the O two molecule.
+
+That means, we come back over
+here, by Hund's rule of maximum
+
+multiplicity,
+we have two spin-up electrons
+
+in the O two molecule
+with all these other orbitals
+
+down here being filled.
+That configuration that I wrote
+
+down for the O two molecule over
+there is a very shorthand way of
+
+representing the MO energy level
+diagram --
+
+-- because I started here at
+the lowest energy,
+
+and I went up in energy like
+this.
+
+And what you can see is sigma
+star cancels sigma,
+
+so no bonding there.
+We have here three electron
+
+pairs in bonding orbitals,
+sigma and 2pi,
+
+but we have two electrons that
+are unpaired electrons,
+
+responsible for the
+paramagnetism of the O two
+
+molecule,
+that cancel some of the bonding
+
+down here.
+When we want to write that down
+
+in terms of our bond order
+convention, we have six bonding
+
+electrons minus two antibonding
+electrons over two,
+
+which is going to be equal to a
+bond order of two.
+
+That is our bond order for O
+two.
+
+While the bond order is what we
+expect to find based on that
+
+valance bond representation of O
+two up there,
+
+what we find out is that the
+representation of O two up there
+
+in the valance bond terminology
+would not tell us that the
+
+molecule should actually have
+two electrons that are not
+
+paired in the molecule,
+--
+
+-- that it should have
+paramagnetism due to the lack of
+
+pairing up of all the electrons,
+spin pairing in the molecule.
+
+And it has to do with this high
+symmetry of the O two molecule.
+
+And it cannot distort from high
+
+symmetry because it has just two
+atoms.
+
+It has very few degrees of
+freedom.
+
+It cannot bend or something to
+get those electrons to pair up,
+
+and so they are unpaired.
+And that is why dioxegen has
+
+unpaired electrons.
+And then, if we go to nitrogen,
+
+the order that we write these
+things down in is a little
+
+different because the energy
+level diagram is different
+
+because now s and p are closer
+together.
+
+And what we have is one sigma
+with two electrons,
+
+or two sigma star with two
+electrons.
+
+And then, next,
+we have our one pi with its
+
+four electrons.
+And then next,
+
+we have our three sigma with
+its two electrons.
+
+And that is it.
+We have two less electrons in
+
+the system than we do in 
+O two.
+
+That is N two.
+And our bond order now is
+
+three.
+That is in accord with our
+
+Lewis structure of N two,
+but it is a triple bond.
+
+And it is a triple bond in a
+molecule that is completely
+
+non-polar.
+And it is one of the strongest
+
+chemical bonds known.
+That triple bond is worth about
+
+226 kilocalories per mole.
+And it makes N two a
+
+very fascinating molecule.
+And, of course,
+
+it is the major constituent of
+our atmosphere.
+
+And it is very inert,
+due to the stability associated
+
+with having this diagram
+populated up all through the
+
+bonding orbitals,
+and then no more antibonding
+
+electrons present in the system.
+So, that is pretty interesting.
+
+And given the time,
+I think I will leave you after
+
+the following.
+I just want to show you one
+
+more picture as a prelude to
+where I will start next time.
+
+And that has to do with what
+happens when the two atoms that
+
+are bonding are different.
+Let's look at the three sigma
+
+orbital for the carbon monoxide
+molecule.
+
+It would look like it does for
+N two.
+
+It is the same number of
+electrons.
+
+But look here.
+It is very asymmetric.
+
+And that has to do with the
+fact that carbon and oxygen have
+
+very different
+electronegativity.
+
+And so, this highest occupied
+molecular orbital for carbon
+
+monoxide, again,
+an eight orbital problem,
+
+and again, a ten electron
+system, is one where we have a
+
+larger coefficient on the lone
+pair piece that is on the carbon
+
+atom of the molecule.
+And I will start off with this
+
+next time, but that is one of
+two reasons why CO is a poison.
+
+Have a nice weekend.
\ No newline at end of file
diff --git a/UiZlaJX3IRk.txt b/UiZlaJX3IRk.txt
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index 0000000000000000000000000000000000000000..8bdf1816bd7c34afb4965274909c5a5568597a89
--- /dev/null
+++ b/UiZlaJX3IRk.txt
@@ -0,0 +1,2031 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu
+
+PROFESSOR: Good morning.
+
+Oh, it's so nice to
+get a response.
+
+Thank you.
+
+I appreciate it.
+
+i have a confession to make.
+
+I stopped at my usual candy
+store this morning and they
+
+didn't have any.
+
+So I am bereft of anything
+other than crummy little
+
+Tootsie Rolls for today.
+
+But I promise I'll have a
+new supply by Thursday.
+
+We ended up the last lecture
+looking at pseudocode for
+
+k-means clustering and talking
+a little bit about the whole
+
+idea and what it's doing.
+
+So I want to start today by
+moving from the pseudocode to
+
+some real code.
+
+This was on a previous
+handout but it's
+
+also on today's handout.
+
+So let's look at it.
+
+Not so surprisingly I've chosen
+to call it k-means.
+
+And you'll notice that it's
+got some arguments.
+
+The point to be clustered,
+k, and that's
+
+an interesting question.
+
+Unlike hierarchical clustering,
+where we could run
+
+it and get what's called a
+dendrogram and stop at any
+
+level and see what we liked,
+k-means involves knowing in
+
+the very beginning how many
+clusters we want.
+
+We'll talk a little bit about
+how we could choose k.
+
+A cutoff.
+
+What the cutoff is doing, you
+may recall that in the
+
+pseudocode k-means was
+iterative and we keep
+
+re-clustering until the change
+is small enough that we feel
+
+it's stable.
+
+That is to say, the new clusters
+are not that much
+
+different from the
+old clusters.
+
+The cutoff is the definition
+of what we
+
+mean by small enough.
+
+We'll see how that gets used.
+
+The type of point
+to be clustered.
+
+The maximum number
+of iterations.
+
+There's no guarantee that
+things will converge.
+
+As we'll see, they usually
+converge very quickly in a
+
+small number of iterations.
+
+But it's prudent to have
+something like this just in
+
+case things go awry.
+
+And to print.
+
+Just my usual trick of being
+able to print some debugging
+
+information if I need it, but
+not getting buried in output
+
+if I don't.
+
+All right.
+
+Let's look at the code.
+
+And it very much follows the
+outline of the pseudocode we
+
+started with last time.
+
+We're going to start by
+choosing k initial
+
+centroids at random.
+
+So I'm just going to go and take
+all the points I have.
+
+And I'm assuming, by the way,
+I should have written this
+
+down probably, that I have
+at least k points.
+
+Otherwise it doesn't
+make much sense.
+
+If you have 10 points,
+you're not
+
+going to find 100 clusters.
+
+So I'll take k random centroids,
+and those will be
+
+my initial centroids.
+
+There are more sophisticated
+ways of choosing centroids, as
+
+discussed in the problem set,
+but most of the time people
+
+just choose them at random,
+because at least if you do it
+
+repetitively it guarantees
+against some sort of
+
+systematic error.
+
+Whoa.
+
+What happened?
+
+I see.
+
+Come back.
+
+Thank you.
+
+All right.
+
+Then I'm going to say that
+the clusters I have
+
+initially are empty.
+
+And then I'm going to create a
+bunch of singleton clusters,
+
+one for each centroid.
+
+So all of this is just
+the initialization,
+
+getting things going.
+
+I haven't had any
+iterations yet.
+
+And the biggest change so far
+I'm just setting arbitrarily
+
+to the cutoff.
+
+All right.
+
+And now I'm going to iterate
+until the change is smaller
+
+than the cutoff while biggest
+change is at least the cutoff.
+
+And just in case numIters is
+less than the maximum, I'm
+
+going to create a list
+containing k empty list.
+
+So these are the new clusters.
+
+And then I'm going to go through
+for i in range k.
+
+I'm going to append
+the empty cluster.
+
+These are going to
+be the new ones.
+
+And then for p and all the
+points I'm going to find the
+
+centroid in the existing
+clustering
+
+that's closest to p.
+
+That's what's going on here.
+
+Once I've found that, I'm going
+to add p to the correct
+
+cluster, go and do it
+for the next point.
+
+Then when I'm done, I'm going to
+compare the new clustering
+
+to the old clustering and
+get the biggest change.
+
+And then go back and
+do it again.
+
+All right?
+
+People, understand that basic
+structure and even some of the
+
+details of the code.
+
+It's not very complicated.
+
+But if you haven't seen
+it before, it can be
+
+a little bit tricky.
+
+When I'm done I'm going to just
+get some statistics here
+
+about the clusters, going to
+keep track of the number of
+
+iterations and the maximum
+diameter of a cluster, so the
+
+cluster in which things are
+least tightly grouped.
+
+And this will give me an
+indication of how good a
+
+clustering I have.
+
+OK?
+
+Does that make sense
+to everybody?
+
+Any questions about
+the k-means code?
+
+Well, before we use it, let's
+look at how we use it.
+
+I've written this function
+testOne that uses it.
+
+Some arbitrary values
+for k in the cutoff.
+
+Number of trials is kind
+of boring here.
+
+I've only said one is the
+default and I've set print
+
+steps to false.
+
+The thing I want you to notice
+here, because I'm choosing the
+
+initial clustering at random,
+I can get different results
+
+each time I run this.
+
+Because of that, I might want
+to run it many times and
+
+choose the quote, "best
+clustering." What metric am I
+
+using for best clustering?
+
+It's a minmax metric.
+
+I'm choosing the minimum of
+the maximum diameters.
+
+So I'm finding the worst cluster
+and trying to make
+
+that as good as I can make it.
+
+You could look at the
+average cluster.
+
+This is like the linkage
+distances we
+
+talked about before.
+
+That's the normal
+kind of thing.
+
+It's like when we did Monte
+Carlo simulations or random
+
+walks, flipping coins.
+
+You do a lot of trials and then
+you can either average
+
+over the trials, which wouldn't
+make sense for the
+
+clustering, or select the
+trial that has some
+
+property you like.
+
+This is the way people
+usually use k-means.
+
+Typically they may do 100 trials
+and choose the best,
+
+the one that gives them
+the best clustering.
+
+Let's look at this, and let's
+try it for a couple of
+
+examples here.
+
+Let's start it up.
+
+And we'll just run test one on
+our old mammal teeth database.
+
+We get some clustering.
+
+Now we'll run it again.
+
+We get a clustering.
+
+I don't know, is it the
+same clustering?
+
+Kind of looks like it is.
+
+No reason to suspect
+it would be.
+
+We run it again.
+
+Well you know, this is
+very unfortunate.
+
+It's supposed to give different
+answers here because
+
+it often does.
+
+I think they're the same
+answers, though.
+
+Aren't they?
+
+Yes?
+
+Anyone see a difference?
+
+No, they're the same.
+
+How unlucky can you be?
+
+Every time I ran it at my desk
+it came up the first two times
+
+with different things.
+
+But take my word for it, and
+we'll see that with other
+
+examples, it could come out
+with different answers.
+
+Let's try it with some
+printing on.
+
+We get some things here.
+
+Let's try it.
+
+What have we got out
+of this one?
+
+All right.
+
+Oh, well.
+
+Sometimes you get lucky and
+sometimes you get unlucky with
+
+randomness.
+
+All right.
+
+So, why did we start
+with k-means?
+
+Not because we needed it
+for the mammals' teeth.
+
+The hierarchical worked fine,
+but because it was too slow
+
+when we tried to look
+at something
+
+big like the counties.
+
+So now let's move on and talk
+about clustering the counties.
+
+We'll use exactly the
+k-means code.
+
+It's one of the reasons we're
+allowed to pass in the point
+
+type as an argument.
+
+But the interesting thing will
+be what we do for the counties
+
+themselves.
+
+This gets a little
+complicated.
+
+In particular, what I've added
+to the counties is this notion
+
+of a filter.
+
+The reason I've done this is,
+as we've seen before, the
+
+choice of features can make
+a big difference in what
+
+clustering you get.
+
+I didn't want to do a lot of
+typing as we do in these
+
+examples, so what I did is I
+created a bunch of filters.
+
+For example, no wealth, which
+says, all right, we're not
+
+going to look at home value.
+
+We're giving that
+a weight of 0.
+
+We're giving income a weight
+of 0, we're giving poverty
+
+level a rate of 0.
+
+But we're giving the
+population a
+
+weight of 1, et cetera.
+
+OK.
+
+What we see here is each filter
+supplies the weight, in
+
+this case either 0 or
+1, to a feature.
+
+This will allow me as we
+go forward to run some
+
+experiments with different
+features.
+
+All features, everything
+has a weight of 1.
+
+I made a mistake though.
+
+That should have been a 1.
+
+Then I have filter names, which
+are just a dictionary.
+
+And that'll make it easy for
+me to run various kinds of
+
+tests with different filters.
+
+Then I've got init, which takes
+as its arguments the
+
+things you would expect,
+plus the filter name.
+
+So it takes the original
+attributes, the normalized
+
+attributes.
+
+And you will recall that, why
+do we need to normalize
+
+attributes?
+
+If we don't, we have something
+like population, which could
+
+number in the millions, and
+we're comparing it to percent
+
+female, which we know cannot
+be more than a 100.
+
+So the small values become
+totally dominated by the big
+
+absolute values and when we run
+any clustering it ends up
+
+only looking at population or
+number of farm acres, or
+
+something that's big.
+
+Has a big dynamic range.
+
+Manhattan has no farm acres.
+
+Some county in Iowa has a lot.
+
+Maybe they're identical in
+every other respect.
+
+Unlikely, but who knows?
+
+Except I guess there's no
+baseball teams in Iowa.
+
+But at any rate, we always scale
+or we try and normalize
+
+so that we don't get
+fooled by that.
+
+Then I go through and, if I
+haven't already, this is a
+
+class variable attribute
+filter, which is
+
+initially set to none.
+
+Not an instance variable,
+but a class variable.
+
+And what we see here is, if that
+class variable is still
+
+none, this will mean it's the
+first time we've generated a
+
+point of type county, then what
+we're going to do is set
+
+up the filter to only look at
+the attributes we care about.
+
+So only the attributes which
+have a value of 1.
+
+And then I'm going to override
+distance from class point to
+
+look at the features
+we care about.
+
+OK.
+
+Does this basic structure and
+idea make sense to people?
+
+It should.
+
+I hope it does, because the
+current problem set requires
+
+you to understand it in which
+you all will be doing some
+
+experiments.
+
+So now I want to do some
+experiments with it.
+
+I'm not going to spend too
+much time, even though it
+
+would be fun, because I don't
+want to deprive you of the fun
+
+of doing your problem sets.
+
+So let's look at an example.
+
+I've got test, which is pretty
+much like testOne.
+
+Runs k-means number of times
+and chooses the best.
+
+And we can start.
+
+Well, let's start by running
+some examples ourselves.
+
+So I'm going to start
+by clustering on
+
+education level only.
+
+I'm going to get 20 clusters, 20
+chosen just so it wouldn't
+
+take too long to run, and we'll
+filter on education.
+
+And we'll see what we get.
+
+Well, I should have probably
+done more than one cluster
+
+just to make it work.
+
+But we've got it and just for
+fun I'm keeping track of what
+
+cluster Middlesex County, the
+county in which MIT shows up.
+
+So we can see that
+it's similar to a
+
+bunch of other counties.
+
+And it happens to have an
+average income of $28,665, or
+
+at least it did then.
+
+And if we look, we
+should also see--
+
+no, let me go back.
+
+I foolishly didn't uncomment
+pyLab.show.
+
+So we better go back
+and do that.
+
+Well, we're just going to nuke
+it and run it again because
+
+it's easy and I wanted
+to run it with a
+
+couple of trials anyway.
+
+So, we'll first do
+the clustering.
+
+We get cluster 0.
+
+Now we're getting
+a second one.
+
+It's going to choose whichever
+was the tightest.
+
+And we'll see that that's
+what it looks like.
+
+So we've now clustered the
+counties based on education
+
+level, no other features.
+
+And we see that it's got some
+interesting properties.
+
+There is a small number of
+counties, clusters, out here
+
+near the right side
+with high income.
+
+And, in fact, we'll see
+that we are fortunate
+
+to be in that cluster.
+
+One of the clusters that
+contains wealthy counties.
+
+And you could look at it and see
+whether you recognize any
+
+of the other counties that
+hang out with Middlesex.
+
+Things like Marin County,
+San Francisco County.
+
+Not surprisingly.
+
+Remember, we're clustering by
+education and these might be
+
+counties where you would expect
+the level of education
+
+to be comparable to the level
+of education in Middlesex.
+
+All right.
+
+Let me get rid of
+that for now.
+
+Sure.
+
+I ran it.
+
+I didn't want you to have to sit
+through it, but I ran it
+
+on a much bigger sample size.
+
+So here's what I got
+when I ran it
+
+asking for 100 clusters.
+
+And I think it was 5 trials.
+
+And you'll notice that this
+case, actually, we have a much
+
+smaller cluster containing
+Middlesex.
+
+Not surprising, because I've
+done 100 rather than 20.
+
+And it should be pretty tight
+since I chose the best--
+
+you can see we have a
+distribution here.
+
+Now, remember that the name of
+the game here is we're trying
+
+to see whether we can infer
+something interesting by
+
+clustering.
+
+Unsupervised learning.
+
+So one of the questions we
+should ask is, how different
+
+is what we're getting here
+from if we chose
+
+something at random?
+
+Now, remember we did
+not cluster on
+
+things based on income.
+
+I happened to plot income here
+just because I was curious as
+
+to how this clustering
+related to income.
+
+Suppose we had just chosen at
+random and split the counties
+
+at random into 100 different
+clusters, What would you have
+
+expected this kind of
+graph to look like?
+
+Do we have something that
+is different, obviously
+
+different, from what we might
+have gotten if we'd just done
+
+a random division into 100
+different clusters?
+
+Think about it.
+
+What would you get?
+
+AUDIENCE: A bell curve?
+
+PROFESSOR: Pardon?
+
+AUDIENCE: We'd get
+a bell curve.
+
+PROFESSOR: Well, a bell curve
+is a good guess because bell
+
+curves occur a lot in nature.
+
+And as I said, I apologize for
+the rather miserable quality
+
+of the rewards.
+
+It's a good guess but I think
+it's the wrong guess.
+
+What would you expect?
+
+Would you expect the different
+clusters--
+
+yeah, go ahead.
+
+AUDIENCE: You probably might
+expect them all to average at
+
+a certain point for a very
+sharp bell curve?
+
+PROFESSOR: A very sharp bell
+curve was one comment.
+
+Well, someone else
+want to try it?
+
+That's kind of close.
+
+I thought you were on the right
+track in the beginning.
+
+Well, take a different
+example.
+
+Let's take students.
+
+If I were to select a 100 MIT
+students at random and compute
+
+their GPA, would you it to be
+radically different from the
+
+GPA of all of MIT?
+
+The average GPA of
+all MIT students?
+
+Probably not, right?
+
+So if I take 100 counties and
+put them into a cluster, the
+
+average income of that cluster
+is probably pretty close to
+
+the average income
+in the country.
+
+So you'd actually expect it
+to be kind of flat, right?
+
+That each of the randomly chosen
+clusters would have the
+
+same income, more or less.
+
+Well, that's clearly not
+what we have here.
+
+So we can clearly infer from the
+fact that this is not flat
+
+that there is some interesting
+correlation between level of
+
+income and education.
+
+And for those of us who earn our
+living in education, we're
+
+glad to see it's positive,
+actually.
+
+Not negative.
+
+As another experiment,
+just for fun, I
+
+clustered by gender only.
+
+So this looked only
+at the female/male
+
+ratio in the counties.
+
+And here you'll see Middlesex
+is with--
+
+remember we had about 3,000
+counties to start with.
+
+So the fact that there were
+so few in the cluster on
+
+education was interesting,
+right?
+
+Here we have more.
+
+And we get a very
+different-looking picture.
+
+Which says, perhaps, that the
+female/male ratio is not
+
+unrelated to income, but it's
+a rather different relation
+
+than we get from education.
+
+This is what would be called
+a bi-modal distribution.
+
+A lot here and a lot here and
+not much in the middle.
+
+But again the dynamic range
+is much smaller.
+
+But we do have some
+counties where the
+
+income is pretty miserable.
+
+All right.
+
+We could play a lot more with
+this but I'm not going to.
+
+I do want to, before we leave
+it, because we're about to
+
+leave machine learning,
+reiterate a few of the major
+
+points that I wanted
+to make sure were
+
+the take home messages.
+
+So, we talked about supervised
+learning much less than we
+
+talked about unsupervised.
+
+Interestingly, because
+unsupervised learning is
+
+probably used more often in the
+sciences than supervised.
+
+And when we did supervised
+learning, we started with a
+
+training set that had labels.
+
+Each point had a label.
+
+And then we tried to infer the
+relationships between the
+
+features of the points and
+the associated labels.
+
+Between the features
+and the labels.
+
+We then looked at unsupervised
+learning.
+
+The issue here was, our
+training set was
+
+all unlabeled data.
+
+And what we try and infer is
+relationships among points.
+
+So, rather than trying to
+understand how the features
+
+relate to the labels, we're just
+trying to understand how
+
+the points, or actually, the
+features related to the
+
+points, relate to one another.
+
+Both of these, as I said
+earlier, are similar to what
+
+we saw when we did regression
+where we tried to
+
+fit curves to data.
+
+You need to be careful and wary
+of over-fitting just as
+
+you did with regression.
+
+In particular, if the training
+data is small, a small set of
+
+training data, you may learn
+things that are true of the
+
+training data that are not true
+of the data on which you
+
+will subsequently run the
+algorithm to test it.
+
+So you need to be
+wary of that.
+
+Another important lesson is
+that features matter.
+
+Which features matter?
+
+It matters whether they're
+normalized.
+
+And in some cases you can even
+weight them if you want to
+
+make some features more
+important than the others.
+
+Features need to be relevant to
+the kind of knowledge that
+
+you hope to acquire.
+
+For example, when I was trying
+to look at the eating habits
+
+of mammals, I chose features
+based upon teeth, not features
+
+based upon how much hair they
+had or their color of the
+
+lengths of the tails.
+
+I chose something that I had
+domain knowledge which would
+
+suggest that it was probably
+relevant to
+
+the problem at hand.
+
+Question at hand.
+
+And then we discovered it was.
+
+Just as here, I said, well,
+maybe education has something
+
+to do with income.
+
+We ran it and we discovered,
+thank goodness, that it does.
+
+OK.
+
+So I probably told you ten times
+that features matter.
+
+If not, I should have
+because they do.
+
+And it's probably the most
+important thing to get right
+
+in doing machine learning.
+
+Now, our foray into machine
+learning is part of a much
+
+larger unit.
+
+In fact, the largest unit of
+the course really, is about
+
+how to use computation to make
+sense of the kind of
+
+information one encounters
+in the world.
+
+A big part of this is finding
+useful ways to abstract from
+
+the situation you're initially
+confronted with to create a
+
+model about which
+one can reason.
+
+We saw that when we
+did curve fitting.
+
+We would abstract from
+the points to a
+
+curve to get a model.
+
+And we see that with machine
+learning, that we abstract
+
+from every detail about a county
+to say, the education
+
+level, to give us a model
+of the counties
+
+that might be useful.
+
+I now want to talk about another
+kind of way to build
+
+models that's as popular
+a way as there is.
+
+Probably the most common
+kinds of models.
+
+Those models are graph
+theoretic.
+
+There's a whole rich theory
+about graphs and graph theory
+
+that are used to understand
+these models.
+
+Suppose, for example, you had
+a list of all the airline
+
+flights between every city in
+the United States and what
+
+each flight cost.
+
+Suppose also, counterfactual
+supposition, that for all
+
+cities A, B and C, the cost of
+flying from A to C by way of B
+
+was the cost of A to B and the
+cost from B to C. We happen to
+
+know that's not true, but
+we can pretend it is.
+
+So what are some of the
+questions you might ask if I
+
+gave you all that data?
+
+And in fact, there's a company
+called ITA Software in
+
+Cambridge, recently acquired by
+Google for, I think, $700
+
+million, that is built upon
+answering these kinds of
+
+questions about these
+kinds of graphs.
+
+So you could ask, for example,
+what's the shortest number of
+
+hops between two cities?
+
+If I want to fly from here to
+Juneau, Alaska, what's the
+
+fewest number of stops?
+
+I could ask, what's the
+least expensive--
+
+different question-- flight
+from here to Juneau.
+
+I could ask what's the least
+expensive way involving no
+
+more than two stops, just in
+case I don't want to stop too
+
+many places.
+
+I could say I have ten cities.
+
+What's the least expensive
+way to visit each
+
+of them on my vacation?
+
+All of these problems are nicely
+formalized as graphs.
+
+A graph is a set of nodes.
+
+Think of those as objects.
+
+Nodes are also often called
+vertices or a
+
+vertex for one of them.
+
+Those nodes are connected
+by a set of edges,
+
+often called arcs.
+
+If the edges are
+uni-directional, the
+
+equivalent of a one-way street,
+it's called a digraph,
+
+or directed graph.
+
+Graphs are typically used in
+situations in which there are
+
+interesting relationships
+among the parts.
+
+The first documented use of this
+kind of a graph was in
+
+1735 when the Swiss
+mathematician Leonard Euler
+
+used what we now call graph
+theory to formulate and solve
+
+the Konigberg's Bridges
+problem.
+
+So this is a map of Konigsberg,
+which was then the
+
+capital of East Prussia, a part
+of what's today Germany.
+
+And it was built at the
+intersection of two rivers and
+
+contained a lot of islands.
+
+The islands were connected to
+each other and to the mainland
+
+by seven bridges.
+
+For some bizarre reason which
+history does not record and I
+
+cannot even imagine, the
+residents of this city were
+
+obsessed with the question of
+whether it was possible to
+
+take a walk through the city
+that involved crossing each
+
+bridge exactly once.
+
+Could you somehow take a walk
+and go over each bridge
+
+exactly once?
+
+I don't know why they cared.
+
+They seemed to care.
+
+They debated it, they walked
+around, they did things.
+
+It probably would be unfair for
+me to ask you to look at
+
+this map and answer
+the question.
+
+But it's kind of complicated.
+
+Euler's great insight was that
+you didn't have to actually
+
+look at the level of detail
+represented by this map to
+
+answer the question.
+
+You could vastly simplify it.
+
+And what he said is, well, let's
+represent each land mass
+
+by a point, and each
+bridge as a line.
+
+So, in fact, his map of
+Konigsberg looked like that.
+
+Considerably simpler.
+
+This is a graph.
+
+We have some vertices
+and some edges.
+
+He said, well, we can just look
+at this problem and now
+
+ask the question.
+
+Once he reformulated the problem
+this way it became a
+
+lot simpler to think about and
+he reasoned as follows.
+
+If a walk were to traverse each
+bridge exactly once, it
+
+must be the case that each node,
+except for the first and
+
+the last, in the walk must have
+an even number of edges.
+
+So if you were to go to an
+island and leave the island
+
+and traverse each bridge to the
+island unless there were
+
+an even number, you
+couldn't traverse
+
+each one exactly once.
+
+If there were only one bridge,
+once you got to the island you
+
+were stuck.
+
+If there were two bridges you
+could get there and leave.
+
+But if there were three bridges
+you could get there,
+
+leave, get there and
+you're stuck again.
+
+He then looked at it and said,
+well, none of these nodes have
+
+an even number of edges.
+
+Therefore you can't do it.
+
+End of story.
+
+Stop arguing.
+
+Kind of a nice piece of logic.
+
+And then Euler later went on to
+generalize this theorem to
+
+cover a lot of other
+situations.
+
+But what was important was not
+the fact that he solved this
+
+problem but that he thought
+about the notion of taking a
+
+map and formulating
+it as a graph.
+
+This was the first example of
+that and since then everything
+
+has worked that way.
+
+So if you take this kind of idea
+and now you extend it to
+
+digraphs, you can deal
+with one-way
+
+bridges or one-way streets.
+
+Or suppose you want to look at
+our airline problem, you can
+
+extend it to include weights.
+
+For example, the number of miles
+between two cities or
+
+the amount of toll you'd have
+to pay on some road.
+
+So, for example, once you've
+done this you can easily
+
+represent the entire US highway
+system or any roadmap
+
+by a weighted directed graph.
+
+Or, used more often, probably,
+the World Wide Web is today
+
+typically modeled as a directed
+graph where there's
+
+an edge from page A to page B,
+if there's a link on page A to
+
+page B.
+
+And then maybe if you want to
+care, ask the question how
+
+often do people go from A to B,
+a very important question,
+
+say, to somebody like Google,
+who wants to know how often
+
+people click on a link to get
+to another place so they can
+
+charge for those clicks, you
+use a weighted graph, which
+
+says how often does someone
+go from here to there.
+
+And so a company like Google
+maintains a model of what
+
+happens and uses a weighted,
+directed graph to essentially
+
+represent the Web, the clicks
+and everything else, and can
+
+do all sorts of analysis
+on traffic patterns
+
+and things like that.
+
+There are also many less
+obvious uses of graphs.
+
+Biologists use graphs to measure
+things ranging from
+
+the way proteins interact with
+each other to, more obviously,
+
+gene expression networks
+are clearly graphs.
+
+Physicists use graphs to model
+phase transitions with
+
+typically the weight of the edge
+representing the amount
+
+of energy needed to go from
+one phase to another.
+
+Those are again weighted
+directed graphs.
+
+The direction is, can you get
+from this phase to that phase?
+
+And the weight is how much
+energy does it require?
+
+Epidemiologists use graphs to
+model diseases, et cetera.
+
+We'll see an example
+of that in a bit.
+
+All right.
+
+Let's look at some code now
+to implement graphs.
+
+This is also in your handout and
+I'm going to comment this
+
+out just so we don't
+run it by accident.
+
+As you might expect, I'm
+going to use classes
+
+to implement graphs.
+
+I start with a class node
+which is at this
+
+point pretty simple.
+
+It's just got a name.
+
+Now, you might say, well, why
+did I even bother introducing
+
+a class here?
+
+Why don't I just use strings?
+
+Well, because I was kind of
+wary that sometime later I
+
+might want to associate more
+properties with nodes.
+
+So you could imagine if I'm
+using a graph to model the
+
+World Wide Web, I don't want
+more than the URL for a page.
+
+I might want to have all the
+words on the page, or who
+
+knows what else about it.
+
+So I just said, for safety,
+let's start with a simple
+
+class, but let's make it a class
+so that any code I write
+
+can be reused if at some later
+date I decide nodes are going
+
+to be more complicated
+than just strings.
+
+Good programming practice.
+
+An edge is only a little
+bit more complicated.
+
+It's got a source, a
+destination, and a weight.
+
+So you can see that I'm using
+the most general form of an
+
+edge so that I will be able use
+edges not only for graphs
+
+and digraphs, but also weighted
+directed graphs by
+
+having all the potential
+properties I might need and
+
+then some simple things
+to fetch things.
+
+The next cluster in the
+hierarchy is a digraph.
+
+So it's got an init, of course,
+I can add nodes to it.
+
+I'm not going to allow myself
+to add the same
+
+node more than once.
+
+I can add edges.
+
+And I'm going to check to make
+sure that I'm only connecting
+
+nodes that are in the graph.
+
+Then I've got children of,
+which gives me all the
+
+descendants of a node, and
+has node in string.
+
+And then interestingly enough,
+maybe surprising to some of
+
+you, I've made graph a
+sub-class of digraph.
+
+Maybe that seems a little odd.
+
+After all, when I started
+I started
+
+talking about digraphs.
+
+About graphs, and then said, and
+we can add this feature.
+
+But now I'm going the
+other way around.
+
+Why is that?
+
+Why do you think that's
+the right way
+
+to structure a hierarchy?
+
+What's the relation of
+graphs to digraphs?
+
+Digraphs are more general
+than graphs.
+
+A graph is a specialization
+of a digraph.
+
+Just like a county is a
+specialization of a point.
+
+So, typically as you design
+these class hierarchies, the
+
+more specialized something is,
+the further it has to be down.
+
+More like a subclass.
+
+Does that make sense?
+
+I can't really turn
+this on its head.
+
+I can specialize a digraph
+to get a graph.
+
+I can't specialize a graph
+to get a digraph.
+
+And that's why this hierarchy
+is organized the way it is.
+
+What else is there are
+interesting to say about this?
+
+A key question, probably the
+most important question in
+
+designing and implementation
+of graphs, is the choice of
+
+data structures to represent
+the digraph in this case.
+
+There are two possibilities
+that people typically use.
+
+They can use an adjacency
+matrix.
+
+So if you have N nodes, you have
+an N by N matrix where
+
+each entry gives, in the case
+of a digraph, a weighted
+
+digraph, the weight-connecting
+nodes on that edge.
+
+Or in the case of a graph it
+can be just true or false.
+
+So this is, can I
+get from A to B?
+
+Is that going to
+be sufficient?
+
+Suppose you have a graph
+that looks like this.
+
+And we'll call that Boston
+and this New York.
+
+And I want to model the roads.
+
+Well, I might have a road that
+looks like this and a road
+
+that looks like this from
+Boston to New York.
+
+As in, I might have more
+than one road.
+
+So I have to be careful when
+I use an adjacency matrix
+
+representation, to realize
+that each element of the
+
+matrix could itself be somewhat
+more complicated in
+
+the case that there
+are multiple edges
+
+connecting two nodes.
+
+And in fact, in many graphs we
+will see there are multiple
+
+edges connecting the
+same two nodes.
+
+It would be surprising
+if there weren't.
+
+All right.
+
+Now, the other common
+representation is
+
+an adjacency list.
+
+In an adjacency list, for every
+node I list all of the
+
+edges emanating from
+that node.
+
+Which of these is better?
+
+Well, neither.
+
+It depends upon your
+application.
+
+An adjacency matrix is often
+the best choice when the
+
+connections are dense.
+
+Everything is connected
+to everything else.
+
+But is very wasteful if the
+connections are sparse.
+
+If there are no roads connecting
+most of your cities
+
+or no airplane flights
+connecting most of your
+
+cities, then you don't want to
+have a matrix where most of
+
+the entries are empty.
+
+Just to make sure that people
+follow the difference, which
+
+am I using in my implementation
+here?
+
+Am I using an adjacency matrix
+or an adjacency list?
+
+I heard somebody say an
+adjacency list and because my
+
+candy supply is so meager they
+didn't even bother raising in
+
+their hand so I know
+who said it.
+
+But yes, it is an
+adjacency list.
+
+And we can see that by
+looking what happens
+
+when we add an edge.
+
+I'm associating it with
+the source node.
+
+So from each node, and we can
+see that when we look at the
+
+children of--
+
+here, I just return the
+edges of that node.
+
+And that's the list of all
+the places you can get
+
+to from that node.
+
+So it's very simple, but
+it's very useful.
+
+Next lecture we'll look--
+
+Yeah?
+
+Thank you.
+
+Question.
+
+I love questions.
+
+AUDIENCE: Going back to the
+digraph, what makes the graph
+
+more specialized?
+
+PROFESSOR: What makes--
+
+AUDIENCE: The graph
+more specialized?
+
+PROFESSOR: Good question.
+
+The question is, what makes the
+graph more specialized?
+
+What we'll see here when we look
+at graph, it's not a very
+
+efficient implementation, but
+every time you add an edge, I
+
+add an edge in the reverse
+direction.
+
+Because if you can get from node
+A to node B you can get
+
+from node B to node A. So I've
+removed the possibility that
+
+you have, say, one-way
+streets in the graph.
+
+And therefore it's
+a specialization.
+
+There are things I can not do
+with graphs that I can do with
+
+digraphs, but anything I can do
+with a graph I can do with
+
+the digraph.
+
+It's more general.
+
+That make sense?
+
+That's a great question and
+I'm glad you asked it.
+
+All right.
+
+Thursday we're going to look at
+a bunch of classic problems
+
+that can be solved using graphs,
+and I think that
+
+should be fun.
\ No newline at end of file
diff --git a/Usm7cWtAbRY.txt b/Usm7cWtAbRY.txt
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index 0000000000000000000000000000000000000000..e6a5ddec2e65edbe0540a06aeac234cd303248fe
--- /dev/null
+++ b/Usm7cWtAbRY.txt
@@ -0,0 +1,2108 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Welcome back.
+
+Today, we will do two problems
+involving many oscillators,
+
+or at least several oscillators,
+coupled to each other.
+
+Now, you will not be surprised,
+from past experience,
+
+that in the situation
+with several oscillators,
+
+we are going to end up with
+many equations and a lot
+
+of grindy, tough
+solving of equations.
+
+Already, with a single
+harmonic oscillator,
+
+for example, with
+damping, the equations
+
+have been pretty horrendous.
+
+Now, we considered a
+couple of oscillators
+
+with all the details, with
+damping, driven, et cetera,
+
+and it really
+becomes complicated.
+
+Now, what we are
+trying to do by doing
+
+problems is to get a feel,
+an understanding what goes on
+
+in a given situation, so one
+wants to focus on new features
+
+and try to simplify
+the mathematics as
+
+much as possible.
+
+And so in the problems
+are we doing now,
+
+I am intentionally making them
+even more ideal than before.
+
+Consider the first problem.
+
+Here is a highly
+idealized system
+
+which has 3 degrees of freedom.
+
+What we have is we have a single
+mass, 2m, two identical springs
+
+attached to two
+masses, each of mass m.
+
+This is completely idealized.
+
+We are assuming
+there's no friction,
+
+that these springs
+are ideal springs.
+
+In other words,
+they're massless,
+
+obey Hooke's laws
+with constant k.
+
+We are assuming the
+system is constrained,
+
+so it can only move
+in one direction,
+
+it can't move up and down
+or in or out from the board.
+
+So as I say, it's an
+idealized situation.
+
+And the question we want to
+answer is, for such a system,
+
+what are the normal
+mode frequencies?
+
+And you know from lectures
+given by Professor Walter Lewin
+
+that when you have coupled
+oscillators, in this case, 3,
+
+all right, one finds that there
+are very special oscillations,
+
+which we call normal mode
+oscillations, in which
+
+every part of the
+system is oscillating
+
+with the same
+frequency and phase.
+
+So first, we want to find
+out for this system, what
+
+are those three normal
+mode frequencies?
+
+And secondly, suppose
+I take this system,
+
+place these masses at some
+arbitrary positions, some
+
+maybe even moving, and
+let go, how would I
+
+predict where each mass
+would be at some later time?
+
+So those are the
+two questions I want
+
+to answer today
+for this problem.
+
+Now, in general, coupled
+oscillator problems
+
+are quite difficult.
+
+But there are
+situations in which
+
+one can use logic
+alone, well, logic
+
+and our understanding
+of coupled oscillators,
+
+to do most of the
+solution by hand-waving
+
+and not do any calculations.
+
+In this first example I'm
+doing in this problem,
+
+since the system has
+a lot of symmetry,
+
+I know from experience
+that under those conditions
+
+it might be possible to solve
+this, as I say, by logic alone
+
+and our understanding
+of coupled oscillators.
+
+So the issue is,
+can I guess what
+
+will be the motion
+in the normal modes?
+
+And the answer is, actually,
+if you stop and think
+
+for a second, at
+least the first two
+
+modes you can figure
+out rather easily.
+
+So here I'm showing
+you schematically
+
+what would be one of the
+modes of oscillation,
+
+one of the normal modes.
+
+Imagine that I first
+hold this mass fixed
+
+and I displace these
+symmetrically, one
+
+to the right, one to
+the left, and I let go.
+
+What you will find
+is, by symmetry,
+
+this spring will always be
+stretched by the same amount
+
+as this is compressed, and
+so the force on this mass
+
+will be 0.
+
+This spring will be pushing this
+mass exactly by the same amount
+
+as this one will be
+pulling it and vice versa.
+
+So there will never be any
+net force on this mass,
+
+and so they'll stay put.
+
+And these two will now behave
+as a simple harmonic oscillator
+
+consisting of a spring attached
+to a fixed wall and the mass m.
+
+So that's what this
+one will be doing,
+
+and that's what
+this will be doing.
+
+It will be out of
+phase by 180 degrees.
+
+Or what one normally
+says, it'll be in phase
+
+but the amplitude will
+be minus the other one.
+
+This, by now, you've
+had enough experience
+
+and I've done it here
+before, I can just
+
+write what will be that
+frequency of oscillation
+
+here, as we've seen many times.
+
+And, by the way, throughout
+my solving the problems here,
+
+I do not differentiate frequency
+and angular frequency, that you
+
+can see which I'm talking about
+is whether I'm using omega
+
+or F. Omega is the
+angular frequency,
+
+and there's just a fact
+of 2 pi between the two.
+
+But I'll use, interchangeably,
+I'll call this frequency.
+
+So this frequency of one of
+the normal modes is just k/m.
+
+So we found one
+normal mode frequency.
+
+Let's look for another one.
+
+We stare at this and we see,
+sure, there is another one.
+
+Another one is where I take,
+simply, these two masses
+
+and simultaneously pull
+them out, in this mass,
+
+away and let go.
+
+Effectively, these two
+will look like that.
+
+It's as if I had a mass of
+2m attached to a mass of 2m
+
+by two springs, each
+of spring constant k.
+
+And as I pull this back, this
+will oscillate like this.
+
+Everything, both this
+mass and this mass,
+
+will be oscillating with the
+same frequency, same phase,
+
+although there's
+this minus sign.
+
+I can always replace the
+180-degree phase shift
+
+by saying the
+amplitude is minus.
+
+So those are
+identical statements.
+
+So you have these two masses
+oscillating like that.
+
+OK?
+
+By the way, I've said
+that in the normal mode
+
+I want everything to move
+with the same frequency.
+
+Some of you may argue, hold on.
+
+Did I cheat on you?
+
+Here, this mass is
+not oscillating.
+
+So am I contradicting myself?
+
+And the answer is no.
+
+It's a diabolical answer.
+
+But I'll say, no,
+this is oscillating
+
+with this frequency,
+but with 0 amplitude.
+
+And you can't tell
+me that I'm wrong.
+
+It's not moving because
+the amplitude is 0,
+
+but it is oscillating
+with the same frequency.
+
+So now, what is the frequency
+of this oscillation?
+
+Again, I can do it in my head.
+
+I can imagine that the middle
+of this spring is not moving.
+
+And so this mass is a half
+a length of the spring
+
+and a mass 2 attached
+to it oscillating,
+
+and I can calculate
+the frequency
+
+of oscillation of that.
+
+Or if you prefer, I
+can do the following.
+
+I can move this mass out a
+distance dx and this one dx
+
+to the other side
+and calculate what
+
+will be the restoring force.
+
+Well, now each one has
+a spring constant k.
+
+There is two of
+them, so that's 2k.
+
+Although this mass has been
+moved by dx, this by dx,
+
+the springs have been extended
+by twice dx, so it's 2 dx.
+
+So that's the total
+restoring force
+
+by Hooke's law, which
+is equal minus 4k dx.
+
+All right?
+
+And so this will behave
+like a single mass,
+
+like this system, a single
+mass with a single spring
+
+where the spring has
+a spring constant 4k.
+
+The mass is 2m.
+
+And so the angular frequency, or
+frequency of this mode is 2k/m.
+
+So we've found two of them.
+
+Now, we know from our studies
+of coupled oscillators
+
+that for a system of
+3 degrees of freedom,
+
+so it would be three masses,
+there are three normal modes.
+
+What is the third normal mode?
+
+And I intentionally
+did not write it
+
+down here because I wanted
+you for a second to think.
+
+Well, how else can
+this system move such
+
+that every mass is moving in
+phase with the same frequency?
+
+All right?
+
+And I tell you,
+when I first saw it,
+
+it took me a long
+time to figure out,
+
+and most people don't find it.
+
+And yet the answer
+is extremely simple.
+
+This answer is there is
+one more normal mode.
+
+It is one of almost infinite
+amplitude, but 0 frequency.
+
+Just the opposite to here,
+where this was 0 amplitude, OK,
+
+and the angular frequency
+doesn't even matter.
+
+Here it has very large
+amplitude, infinite in fact,
+
+but 0 frequency.
+
+What does such motion look
+like at any instant of time?
+
+It's moving with
+the same velocity.
+
+So if I take and if I
+consider the motion where
+
+each one of these is moving
+uniformly to the right
+
+with a constant
+velocity, that is
+
+a normal mode with 0 frequency.
+
+So the last one is
+omega C is equal to 0.
+
+OK?
+
+So we have now found
+the three normal modes.
+
+OK.
+
+All right.
+
+Now that I've got a piece
+of chalk, let's continue.
+
+So we've answered the first
+part of the question, what
+
+are the normal mode
+frequencies of the system?
+
+And I found you those
+three normal modes.
+
+Now, the next question
+we want to answer
+
+is, if, at any given
+instant of time,
+
+I know the positions and the
+velocities of the three masses,
+
+can I predict what
+will happen at the end?
+
+That's equivalent
+of saying, can I
+
+write equations for the
+positions of the masses
+
+as a function of time?
+
+For that I need to define for
+myself a coordinate system.
+
+So I'll say those are
+those three masses.
+
+All the motion is
+along the x direction,
+
+so there's just one variable,
+one variable for each mass, x.
+
+So the position
+of the first mass
+
+I'll call x1, position
+of the second mass x2,
+
+and of the third is x3.
+
+And the origin of
+coordinates I will
+
+take to be through the
+center of each mass
+
+at a time when these
+are in equilibrium.
+
+In other words, the spring
+is unstretched, et cetera.
+
+OK.
+
+So I can now, using the
+information we've obtained,
+
+write down the description
+of each mass in each mode.
+
+So in mode A, I know that
+the x1 is 0 all the time.
+
+It's not moving, OK?
+
+Now, in a normal mode, that's
+what we mean by a normal mode,
+
+each mass is moving
+with the same frequency
+
+and the same phase,
+and it's oscillating.
+
+So there will be some sinusoidal
+function of the mode frequency
+
+t plus this phase times
+some arbitrary amplitude.
+
+The other one, the
+last one, will also
+
+be oscillating in
+the normal mode,
+
+so everything will be the same.
+
+It will be cosine of
+omega A t plus phi
+
+A with some other amplitude.
+
+But from our analysis
+here, we know
+
+that these two are
+not both arbitrary.
+
+Because we said that
+in the normal mode,
+
+it was the case where the
+2m mass was stationary,
+
+but these were going like this.
+
+That was the first mode.
+
+So whenever this one was going
+to the right a distance A,
+
+this one was going to
+the left a distance A.
+
+So the overall
+normalization is arbitrary.
+
+It can be anything.
+
+But these are not
+independent of the other,
+
+because we discovered
+that in that mode,
+
+this was the frequency,
+and the amplitudes were
+
+opposite to each other.
+
+So this describes the
+situation for this system
+
+if it's oscillating in
+the first normal mode.
+
+It's the most general
+description of that.
+
+Next, I will
+describe what it will
+
+do in the second normal mode.
+
+And now I can go much quicker.
+
+This time, it'll have
+the second normal mode
+
+frequency, different phase.
+
+But these have to be the same
+because all of these masses
+
+are moving in the same normal
+mode, same normal frequency.
+
+These amplitudes,
+overall, it's arbitrary.
+
+I can make it anything.
+
+It'll satisfy the equations.
+
+But I know that in the
+second normal mode,
+
+this one is moving in that
+direction and those two
+
+in the opposite direction
+with the same magnitude.
+
+So these two have to have
+the same size and magnitude,
+
+but this has to be opposite.
+
+So this describes the
+motion in the second mode.
+
+And finally, in the
+third normal mode,
+
+we said that it was 0 frequency.
+
+All right?
+
+And all that was
+happening, the three masses
+
+were moving with
+uniform velocity.
+
+So the positions
+will be some constant
+
+plus the velocity
+of that system.
+
+So this describes the
+system in the third mode,
+
+and these are the other two.
+
+Now, I know that, in general,
+each one of these masses
+
+can move in a superposition
+of the normal modes.
+
+So the most general
+expression for x1 of t
+
+has to be of the form which is
+the sum of its possible motion
+
+in each of the modes.
+
+So x1, so this is
+the mass 2m, will
+
+have possible motion in
+the first mode, which is 0.
+
+All right?
+
+So I'll write 0 plus B times
+cosine omega B t plus phi
+
+B, all right, plus
+C plus v. So that
+
+will be the most general
+description of the motion
+
+of the big mass, the 2m one.
+
+The B is arbitrary,
+this phase is arbitrary,
+
+this is arbitrary, and
+v. Those quantities
+
+will be determined by
+the initial conditions.
+
+Well, how about x2?
+
+Well, I know that if x1 is
+0, x2 is A cosine omega A t
+
+plus phi A. When the x1 is this,
+then x2 is minus B cosine omega
+
+B t plus phi B, OK,
+and plus C plus v. OK?
+
+And finally, x3 of t,
+again now just following
+
+the same pattern, this is
+minus A cosine omega A t
+
+plus phi A. This one is
+minus B cosine omega B
+
+t plus phi B plus C plus v.
+
+And I'm almost home.
+
+I have described the
+motion of each one.
+
+For each particle,
+it is oscillating
+
+in a superposition
+of its normal modes.
+
+And the amplitudes are
+arbitrary within the constraint
+
+that the ratios between
+them is determined
+
+by the constraints
+of the system.
+
+So now the question is,
+can I predict the future?
+
+Well, in order to
+predict the future,
+
+say, where will
+particle 3 be at time t?
+
+I need to know the value of
+these arbitrary constants.
+
+Omega is not an
+arbitrary constant.
+
+We found it.
+
+Omega A is here.
+
+OK?
+
+This is arbitrary, this is
+arbitrary, this, and that.
+
+So there are six
+arbitrary constants.
+
+How do I find them?
+
+They are determined by
+the initial conditions.
+
+And you know,
+fortunately, or else it
+
+would mean we've made a mistake,
+we have three conditions.
+
+At the beginning,
+someone has to tell me
+
+where each mass was, the
+location, and with what
+
+velocity is it
+moving at that time.
+
+So I can write these
+three equations at, say,
+
+with t equals 0, at t
+equals 0, and equate this
+
+to the position of x1 of t
+equals 0, wherever it is.
+
+When the t is 0, I make it
+equal to the position of x2 at t
+
+equals 0.
+
+When t is 0, this tells me has
+to be equal to where x3 is.
+
+That's three equations.
+
+I can differentiate
+each with respect
+
+to time to get the
+velocities, and likewise,
+
+get three more equations.
+
+So I'm going to end up with
+six algebraic equations.
+
+And you, as well as
+I, know that if we
+
+have six algebraic equations,
+I can solve for six unknowns.
+
+And that will give me
+those six unknowns.
+
+So once I've used the
+initial conditions,
+
+I can then find these
+arbitrary constants.
+
+They're no longer arbitrary
+for a specific situation.
+
+And I can predict the future,
+what will happen in this case.
+
+OK?
+
+So that's the way one
+would solve a problem when
+
+you are lucky
+enough that there is
+
+sufficient symmetry in
+the original situation
+
+so you can guess
+the normal modes.
+
+The next problem I'll do, I will
+do one where you cannot guess
+
+the normal modes.
+
+What do you do under
+those circumstances?
+
+And you won't be
+surprised that it's
+
+going to be mathematically much,
+much harder, but conceptually
+
+no harder.
+
+So now we'll move
+to the next problem.
+
+Here it is.
+
+But in order to be able
+to do this problem,
+
+I need more board space.
+
+So we're going to erase the
+boards and continue from there.
+
+OK.
+
+So now let's go and
+do the second problem.
+
+And it's going to be a
+problem with no symmetry,
+
+so we can't guess the
+answer like we did before.
+
+And I'll tell you
+what I decided to do.
+
+You remember
+Professor Walter Lewin
+
+in his lectures discussed
+a double pendulum.
+
+In other words,
+a situation where
+
+you had a string, a mass,
+another string, and mass.
+
+He gave you the answer,
+but he didn't prove it.
+
+He said it's hard and
+lengthy, et cetera.
+
+And I thought that would
+be a perfect example
+
+to do here from
+first principles.
+
+So let me just
+describe in detail
+
+the problem we're
+trying to solve.
+
+What we have is, again,
+an idealized situation.
+
+We have a simple pendulum
+with a string of length L,
+
+attached to it a mass m.
+
+Attached to this mass at one
+end is another string of length
+
+L to another mass m.
+
+We'll again idealize
+the situation.
+
+So the assumptions
+we are making,
+
+that this string and this string
+is massless, which, by the way,
+
+is equivalent to saying that
+it's taut and straight all
+
+the time.
+
+You can think about
+that for yourself.
+
+Next, these masses
+are point masses.
+
+And we're assuming no friction.
+
+Furthermore, as we've
+done in the past,
+
+we'll assume that
+all displacements
+
+when this is oscillating, at all
+times the angle that the string
+
+makes with the vertical is
+always such that we can ignore
+
+the difference between
+a sine theta, theta,
+
+or [INAUDIBLE] can make the
+assumption that cosine theta is
+
+0.
+
+By the way, the fact that
+we'll make this assumption
+
+is equivalent to
+saying that we'll
+
+ignore vertical motion
+of these masses.
+
+The motion is sufficiently
+small that vertically the masses
+
+are not moving.
+
+We can assume the acceleration
+vertically is 0, et cetera.
+
+OK?
+
+This is in the vertical plane.
+
+Gravity is down.
+
+OK?
+
+And what we are trying
+to derive for this,
+
+predict what are the normal
+mode frequencies of this.
+
+And once we do
+that, of course, we
+
+can use the same kind of
+technique as we did before.
+
+Once we've managed to
+find the normal modes
+
+and the frequencies,
+we can always
+
+write the most
+general expression.
+
+And then using the boundary
+conditions, initial conditions,
+
+predict what this will
+do as a function of time.
+
+OK, so let's get going.
+
+OK.
+
+Now, we are not guessing.
+
+We are not using logic.
+
+We are following the
+kind of prescription
+
+I've told you in the past.
+
+This is our description
+of the situation.
+
+And all the new words
+and ordinary language, we
+
+must now translate
+it into mathematics.
+
+We've got to
+describe this problem
+
+in terms of
+mathematical equations.
+
+So step one is we
+redraw this and define
+
+some coordinate system.
+
+So we will say that the
+angle this first string makes
+
+with respect to the
+vertical is theta 1.
+
+This angle the second
+string makes with respect
+
+to the vertical is theta 2.
+
+We will take the vertical
+through this pivot
+
+here as our origin
+of coordinate x.
+
+x equals 0 here,
+is defined here.
+
+From the point of your
+motion of the masses,
+
+it's a one-dimensional problem.
+
+The masses only move
+along the x-axis.
+
+So we'll define
+this distance as x1,
+
+and we'll define
+this distance as x2.
+
+Now we have to use the laws of
+physics, Newtonian mechanics,
+
+to derive the equations of
+motion for the two masses.
+
+So I draw a force diagram
+separately for the two masses.
+
+So the mass is there, what
+forces act on that mass?
+
+Well, I have to look at the mass
+and see what's attached to it.
+
+There is a string
+here attached to it.
+
+It's taut, so there
+will be a tension in it.
+
+So along this string,
+there will be tension T1,
+
+which will exert a force
+T1 along this string.
+
+This string is
+attached to that mass.
+
+It has a tension, so it's
+pulling on this mass.
+
+That tension I call
+T2, so there will
+
+be a force along
+that direction T2.
+
+This sits in a
+gravitational field.
+
+Gravity acts on this mass.
+
+There is a force downwards
+due to gravity, Fg.
+
+The sum of these forces,
+by Newton's laws,
+
+must equal to the mass
+times the acceleration.
+
+That acceleration, in this
+approximation that is not
+
+moving up, is
+horizontally, and it's
+
+the second derivative of x1.
+
+Similarly, for the second mass,
+again, I'll go now faster.
+
+There is this mass
+m, and this tension
+
+exerts a force here of T2
+and the gravity on it Fg.
+
+The only subtlety
+is, why did I say
+
+this force is equal
+to that force?
+
+Think about it for a second.
+
+Why should the two
+forces be equal?
+
+Why is the tension at both
+ends of the string equal?
+
+And the answer is,
+actually, a subtle one.
+
+It's equal because we made the
+assumption that the string has
+
+no mass, and there can be no net
+force on an object of 0 mass.
+
+Because if there was, that
+object would disappear,
+
+would have an
+infinite acceleration.
+
+So if you treat the
+string as a mass,
+
+there cannot be net force on it.
+
+And so the force of
+each of these masses
+
+must be pulling on this string
+with exactly the same force
+
+equal and opposite.
+
+OK?
+
+And we're using the third
+law to equate those forces.
+
+So the net result is this
+T2 is the same as that,
+
+but in opposite direction,
+and this is the mass of that.
+
+OK.
+
+So these are the force diagrams.
+
+Using now Newton's
+laws of motion,
+
+I can translate this
+into equations of motion.
+
+So let me consider
+the horizontal motion
+
+of each mass separately.
+
+First this mass, and so
+its mass times acceleration
+
+is equal to the
+horizontal force of T2.
+
+And remember that this
+angle here is theta 2.
+
+And we see that the
+force due to T2,
+
+and there's a T2 sine theta 2.
+
+And the force due to T1
+is minus T1 sine theta 1
+
+because it's in the
+opposite direction.
+
+For this, the only
+horizontal component
+
+is the force horizontal
+component of T2.
+
+And x2 double dot is equal
+to minus T2 sine theta 2.
+
+OK, that's horizontal motion.
+
+Applying Newton's laws of
+motion to the vertical motion,
+
+we said that, because cosine
+theta is 0 or approximately 0,
+
+the masses are not
+moving up and down.
+
+There's no acceleration
+of the masses.
+
+So the vertical acceleration
+of the first mass
+
+is 0 must be equal to the
+vertical component of T1, which
+
+is T1 cosine theta 1, minus
+the vertical component of this,
+
+which is minus T2
+cosine theta 2 minus mg.
+
+All right.
+
+Similarly for the second
+mass, it's 0 is equal to this.
+
+0 must equal to the
+vertical component
+
+of T1 minus the
+vertical component of T2
+
+minus the force of gravity down.
+
+And similarly for
+the second mass,
+
+we know that vertically
+the acceleration is 0.
+
+That must be equal to the
+vertical component of T2
+
+minus the gravitational
+force pulling down.
+
+Now I can make use of what we
+made the assumption-- oops,
+
+I see there is an error.
+
+If you were in this
+room, I'm sure you
+
+would have corrected me.
+
+For very small angles,
+the sine of an angle
+
+is approximately
+equal to the angle.
+
+But for small angles,
+the cosine is 1.
+
+This is an error, and
+I apologize for that.
+
+But that's the
+approximation we are making.
+
+And it is this
+approximation which
+
+is equivalent to saying that we
+can ignore the vertical motion.
+
+All right.
+
+So with the assumption
+that the cosines are all 1,
+
+I can, from these two
+equations, I clearly
+
+derive that T2 must equal to
+mg, and T1 equals twice mg.
+
+Actually, it makes sense.
+
+Imagine this is hanging
+completely vertically.
+
+Obviously, this string, the
+upper part of the string,
+
+is supporting not only
+this mass but also that.
+
+It's supporting 2m masses,
+while this string is only
+
+supporting 1.
+
+So that's consistent
+with what we see,
+
+that the top string has twice
+the tension and the lower
+
+one half the tension.
+
+Having determined T1
+and T2, we can now
+
+go back into our equation,
+replace the T1 and T2.
+
+We also can replace--
+we know what
+
+sine theta 1 and
+sine theta 2 are.
+
+We can replace those.
+
+And we end up--
+the two equations
+
+of motions are written here.
+
+All right?
+
+So here is the equation
+of motion for x1.
+
+And the second one, the
+equation for motion of x2,
+
+is written here.
+
+OK?
+
+So these are the
+equations of motion,
+
+all right, which
+we have to solve.
+
+Now, to simplify the algebra,
+let me define the quantity g/l
+
+by omega squared over 2.
+
+And you'll recognize this.
+
+This is not [INAUDIBLE].
+
+I'm using that terminology.
+
+This is the frequency
+of oscillation
+
+of a mass on a
+string of length l.
+
+All right?
+
+So here are our two differential
+equations, the two equations
+
+of motion, one for
+x1 and one for x2.
+
+When we had one mass,
+one harmonic oscillator,
+
+we had a single second-order
+differential equation.
+
+We now have two
+masses, so we have
+
+two second-order
+differential equations.
+
+These are it.
+
+They are coupled
+differential equations.
+
+You see, the derivatives of x1
+is related both to x1 and x2.
+
+The second derivative of x2 is
+related both to x1 and to x2.
+
+So these are two coupled
+differential equations.
+
+OK?
+
+This is the end of step 1.
+
+What we succeeded
+in, we've translated
+
+the physical situation
+into mathematics.
+
+These two second-order
+differential equations
+
+describe exactly that
+idealized situation we had.
+
+So if I now want to
+answer the question, what
+
+will be the motion
+of those masses,
+
+I have to go into the
+world of mathematics.
+
+I have to solve these equations.
+
+And life is not
+as easy as it was
+
+for a single second-order
+differential equation.
+
+It's more complicated.
+
+But here I will use
+my general knowledge
+
+of what happens when you
+have coupled oscillators.
+
+I know that the general
+solution of coupled oscillations
+
+is a superposition
+of normal modes.
+
+Here I have 2
+degrees of freedom,
+
+two second-order
+differential equations.
+
+There will be two normal modes.
+
+If I succeed in
+finding them, I will
+
+have found the most general
+solution to this problem,
+
+because it will be the sum
+of the two normal modes.
+
+So I will now do it by trial.
+
+In a normal mode,
+we know that x1
+
+will be oscillating
+with a single frequency
+
+omega, some phase phi,
+some amplitude A1.
+
+This will be a solution
+to these equations.
+
+If this is a solution
+to those equations,
+
+the other mass must
+also be oscillating
+
+in the same normal mode,
+meaning with the same frequency
+
+and same phase.
+
+It'll have some
+arbitrary amplitude.
+
+So I don't know what A1 is,
+and I don't know what omega is.
+
+I don't know what phi is.
+
+But I know that the
+solutions to these equations
+
+must be of this form.
+
+OK?
+
+So let me now try to find
+these various constants.
+
+Well, if this and that
+satisfies these equations--
+
+and it has to because
+that's what it's saying,
+
+these are the solutions
+of those equations--
+
+then I can take these, x1 and
+x2, plug it into this equation.
+
+In other words, calculate
+the second derivative
+
+of x1, et cetera,
+calculate second,
+
+and I'll end up
+with two equations.
+
+OK?
+
+So I won't bother to go
+in great detail here.
+
+But just to start off
+with, x1 double dot,
+
+I have to differentiate
+A1 cosine omega t twice.
+
+So I get minus omega squared A1
+times cosine omega t plus phi.
+
+If I take the next term, I get
+this, and the third term that.
+
+And in each case, if
+you notice, since it'll
+
+be multiplied by the
+same cosine function,
+
+I've just canceled in my head
+the cosine function there.
+
+All right?
+
+Just saving time.
+
+Similarly, next equation,
+I end up with this.
+
+So if my guessed functions,
+and I'm returning to this,
+
+if these two satisfy
+those equations,
+
+then here these algebraic
+equations must be satisfied.
+
+But you'll notice
+something interesting.
+
+If I take the first
+of these equations,
+
+it boils down to A1 times
+this quantity plus A2
+
+to [? then ?] this
+quantity equal to 0.
+
+And the second equation
+boils down to this.
+
+If this is true, then
+this must be true.
+
+It's A1 divided by A2
+has to be equal to that.
+
+If this is true,
+then A1 divided by A2
+
+has got to be equal to this.
+
+That means that this
+has to be equal to that,
+
+or else I have an inconsistency.
+
+So what I have found is
+that, in general, my guess
+
+is not a good one.
+
+In general, these
+equations would not
+
+satisfy my second-order
+differential equations.
+
+There is only under very
+special circumstances
+
+that they do
+satisfy it, and that
+
+is if this is equal to that.
+
+In general, they
+will not be equal.
+
+So under what conditions
+will these be equal?
+
+Well, let me force them.
+
+Let me say this is
+equal to that and see
+
+what it means for omega.
+
+I originally took omega
+to be an unknown quantity.
+
+What I am now seeing,
+that those functions
+
+would work only for
+specific values of omega.
+
+So I'm going to solve
+this equation for omega
+
+and see for what values of omega
+do I get a consistent solution.
+
+And this is a hard
+grind, unfortunately.
+
+If I take this,
+multiply it out, I
+
+get a quadratic equation
+in omega squared.
+
+If this quadratic
+equation is satisfied,
+
+then all these are
+self-consistent.
+
+All right?
+
+You know how to solve
+a quadratic equation,
+
+and this is a quadratic
+equation in omega squared.
+
+Omega square will have
+to be equal to minus
+
+this plus or minus the
+square root of this,
+
+4 times this times that,
+divided by 2a, right?
+
+This is the standard
+formula for the solution
+
+of a quadratic equation.
+
+And there's a plus or minus.
+
+If I calculate this out,
+I get that omega squared
+
+has to be equal
+to 2 plus or minus
+
+the square root of 2
+times omega 0 squared.
+
+All right?
+
+Now, omega 0 squared, earlier
+on, I defined to be g/l.
+
+So omega squared has to be this.
+
+So let's stop for
+a second and think
+
+and review what we've done.
+
+We found that our
+physical situation
+
+can be described by these two
+coupled differential equations.
+
+We looked for solutions, which
+are normal modes where both x1
+
+and x2 is oscillating with
+same frequency and phase.
+
+And we found that it was
+possible to find solution
+
+of this form to these equations
+if and only if omega squared
+
+has one of two possible values.
+
+I've rewritten them here.
+
+One is 2 plus root 2
+times g/l, and the other's
+
+2 minus root 2 g/l.
+
+With these values, these two
+equations satisfies that.
+
+So what we found is
+the two normal modes.
+
+Since this system consists
+of the coupled oscillators,
+
+in other words, two oscillators
+coupled with each other,
+
+we know there are
+two normal modes.
+
+So these are the normal mode
+frequencies in this situation.
+
+And by the way, I'm
+delighted to see
+
+that, if you remember Professor
+Walter Lewin's lectures,
+
+he actually quoted
+these numbers.
+
+So he was right.
+
+He did not make a mistake,
+as we've just seen.
+
+OK?
+
+These are the two
+normal mode frequencies.
+
+Now, how about if
+we want to predict
+
+everything, the
+amplitude, et cetera?
+
+We've got to be careful here
+with the logic we've applied.
+
+For any one of these normal
+frequencies, say this one,
+
+earlier on we found that A1 to
+A2 is given by this equation
+
+or by this equation.
+
+But for the given
+values of omega,
+
+we found these are
+now equivalent.
+
+And so if you know what
+omega is, say omega A,
+
+one of the normal
+modes, this we know.
+
+It's g/l.
+
+And this is known.
+
+So A1/A2, once we fix
+omega A, is fixed.
+
+So these are not two
+independent amplitudes.
+
+So if I go back to here when
+we said let's guess a solution,
+
+and this was an arbitrary
+number and this was an arbitrary
+
+number, now we see
+that in a normal mode
+
+the ratio between them is fixed.
+
+It depends on the
+normal mode frequency.
+
+But the [? overall ?]
+normalization
+
+is still arbitrary.
+
+I could make this 10 times
+this and 10 times that.
+
+[? It  would still ?] work.
+
+So back to here, we found one of
+the normal mode's frequencies.
+
+Using the equation
+above, it determines
+
+the value of A1 to A2.
+
+Taking the other
+normal mode frequency
+
+determines the
+ratio of those two
+
+but not the overall amplitude.
+
+Not to confuse the two, I
+will call this B1 and B2.
+
+This is the amplitude
+of the first mass,
+
+and this is of the other one.
+
+The ratio is fixed, determined
+by the value of omega B.
+
+But the overall
+amplitude is not.
+
+So now we have ended up
+in the same situation
+
+we were in our three masses,
+where, if you remember,
+
+I started by guessing
+the normal modes
+
+and guessing the
+relative amplitudes.
+
+And with that information alone
+and the initial conditions,
+
+I could predict
+what will happen.
+
+I could now repeat that here.
+
+But to save time, I think
+you can do that for yourself.
+
+For each, you can write
+now a single equation
+
+saying what a given mass will do
+as the sum of two normal modes,
+
+where you know the frequency
+of them and the amplitudes.
+
+And you have to remember
+that for the two masses,
+
+the ratio of the amplitudes
+in each normal mode
+
+have to be fixed given
+by what we've done here.
+
+And therefore, you can
+get the single equation
+
+for each mass, one for one
+mass, one for the other.
+
+Which will tell you what
+they will do in the future
+
+if you know what they're
+doing initially, for example,
+
+the initial conditions,
+that you can solve
+
+to get the final predicted
+position of each mass.
+
+So that's as much
+as I was hoping
+
+to do today on
+coupled oscillators.
+
+And we'll continue
+next time on situations
+
+with many, many more
+degrees of freedom.
+
+Thank you.
\ No newline at end of file
diff --git a/XTUe-VMvRis.txt b/XTUe-VMvRis.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3a3b4591274d57a9d410efc2ce7fcae5e7dc1384
--- /dev/null
+++ b/XTUe-VMvRis.txt
@@ -0,0 +1,587 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+hi dude what are you up to I'm picking a
+
+ align:start position:0%
+hi dude what are you up to I'm picking a
+ 
+
+ align:start position:0%
+hi dude what are you up to I'm picking a
+promoter to use in buddy I need a
+
+ align:start position:0%
+promoter to use in buddy I need a
+ 
+
+ align:start position:0%
+promoter to use in buddy I need a
+promoter that is always on that will
+
+ align:start position:0%
+promoter that is always on that will
+ 
+
+ align:start position:0%
+promoter that is always on that will
+make buddy be red so why are you poking
+
+ align:start position:0%
+make buddy be red so why are you poking
+ 
+
+ align:start position:0%
+make buddy be red so why are you poking
+at the computer screen well how else do
+
+ align:start position:0%
+at the computer screen well how else do
+ 
+
+ align:start position:0%
+at the computer screen well how else do
+I pick one I don't know which one to use
+
+ align:start position:0%
+I pick one I don't know which one to use
+ 
+
+ align:start position:0%
+I pick one I don't know which one to use
+so I figured I'd leave it to chance to
+
+ align:start position:0%
+so I figured I'd leave it to chance to
+ 
+
+ align:start position:0%
+so I figured I'd leave it to chance to
+decide well why don't you use some of
+
+ align:start position:0%
+decide well why don't you use some of
+ 
+
+ align:start position:0%
+decide well why don't you use some of
+the promoter characterization data
+
+ align:start position:0%
+the promoter characterization data
+ 
+
+ align:start position:0%
+the promoter characterization data
+available on the registry of standard
+
+ align:start position:0%
+available on the registry of standard
+ 
+
+ align:start position:0%
+available on the registry of standard
+biological parts to the side what is
+
+ align:start position:0%
+biological parts to the side what is
+ 
+
+ align:start position:0%
+biological parts to the side what is
+promoter measurement data hi dude hi
+
+ align:start position:0%
+promoter measurement data hi dude hi
+ 
+
+ align:start position:0%
+promoter measurement data hi dude hi
+Izzy sounds like you two are having an
+
+ align:start position:0%
+Izzy sounds like you two are having an
+ 
+
+ align:start position:0%
+Izzy sounds like you two are having an
+interesting conversation yeah I was just
+
+ align:start position:0%
+interesting conversation yeah I was just
+ 
+
+ align:start position:0%
+interesting conversation yeah I was just
+about to tell Dude how to use the
+
+ align:start position:0%
+about to tell Dude how to use the
+ 
+
+ align:start position:0%
+about to tell Dude how to use the
+promoter measurement data to pick the
+
+ align:start position:0%
+promoter measurement data to pick the
+ 
+
+ align:start position:0%
+promoter measurement data to pick the
+right promoter for body well before you
+
+ align:start position:0%
+right promoter for body well before you
+ 
+
+ align:start position:0%
+right promoter for body well before you
+get into those details it might be worth
+
+ align:start position:0%
+get into those details it might be worth
+ 
+
+ align:start position:0%
+get into those details it might be worth
+chatting a bit about measurement in
+
+ align:start position:0%
+chatting a bit about measurement in
+ 
+
+ align:start position:0%
+chatting a bit about measurement in
+general why synthetic biologists measure
+
+ align:start position:0%
+general why synthetic biologists measure
+ 
+
+ align:start position:0%
+general why synthetic biologists measure
+part function what measurements they
+
+ align:start position:0%
+part function what measurements they
+ 
+
+ align:start position:0%
+part function what measurements they
+make and how they do the measurements
+
+ align:start position:0%
+make and how they do the measurements
+ 
+
+ align:start position:0%
+make and how they do the measurements
+before getting into the details of the
+
+ align:start position:0%
+before getting into the details of the
+ 
+
+ align:start position:0%
+before getting into the details of the
+data itself that's true why don't we
+
+ align:start position:0%
+data itself that's true why don't we
+ 
+
+ align:start position:0%
+data itself that's true why don't we
+take a walk
+
+ align:start position:0%
+take a walk
+ 
+
+ align:start position:0%
+take a walk
+get some fresh air while we talk
+
+ align:start position:0%
+get some fresh air while we talk
+ 
+
+ align:start position:0%
+get some fresh air while we talk
+measurement is a key aspect of Science
+
+ align:start position:0%
+measurement is a key aspect of Science
+ 
+
+ align:start position:0%
+measurement is a key aspect of Science
+and Engineering it lets you quantify the
+
+ align:start position:0%
+and Engineering it lets you quantify the
+ 
+
+ align:start position:0%
+and Engineering it lets you quantify the
+function of a part or component and
+
+ align:start position:0%
+function of a part or component and
+ 
+
+ align:start position:0%
+function of a part or component and
+compare its function to that of others
+
+ align:start position:0%
+compare its function to that of others
+ 
+
+ align:start position:0%
+compare its function to that of others
+unfortunately in synthetic biology we're
+
+ align:start position:0%
+unfortunately in synthetic biology we're
+ 
+
+ align:start position:0%
+unfortunately in synthetic biology we're
+still figuring out what are the most
+
+ align:start position:0%
+still figuring out what are the most
+ 
+
+ align:start position:0%
+still figuring out what are the most
+useful measurements to make for genetic
+
+ align:start position:0%
+useful measurements to make for genetic
+ 
+
+ align:start position:0%
+useful measurements to make for genetic
+parts and devices what do you mean why
+
+ align:start position:0%
+parts and devices what do you mean why
+ 
+
+ align:start position:0%
+parts and devices what do you mean why
+don't we just measure everything for
+
+ align:start position:0%
+don't we just measure everything for
+ 
+
+ align:start position:0%
+don't we just measure everything for
+every part well that can pretty quickly
+
+ align:start position:0%
+every part well that can pretty quickly
+ 
+
+ align:start position:0%
+every part well that can pretty quickly
+lead both to a lot of waste of time in
+
+ align:start position:0%
+lead both to a lot of waste of time in
+ 
+
+ align:start position:0%
+lead both to a lot of waste of time in
+making measurements that don't matter as
+
+ align:start position:0%
+making measurements that don't matter as
+ 
+
+ align:start position:0%
+making measurements that don't matter as
+well as an overwhelming in amount of
+
+ align:start position:0%
+well as an overwhelming in amount of
+ 
+
+ align:start position:0%
+well as an overwhelming in amount of
+information ideally we'd like to be able
+
+ align:start position:0%
+information ideally we'd like to be able
+ 
+
+ align:start position:0%
+information ideally we'd like to be able
+to only measure those characteristics of
+
+ align:start position:0%
+to only measure those characteristics of
+ 
+
+ align:start position:0%
+to only measure those characteristics of
+a part that you need to know in order to
+
+ align:start position:0%
+a part that you need to know in order to
+ 
+
+ align:start position:0%
+a part that you need to know in order to
+decide whether the part will work in
+
+ align:start position:0%
+decide whether the part will work in
+ 
+
+ align:start position:0%
+decide whether the part will work in
+your system of interest for example when
+
+ align:start position:0%
+your system of interest for example when
+ 
+
+ align:start position:0%
+your system of interest for example when
+I bought a computer recently I care
+
+ align:start position:0%
+I bought a computer recently I care
+ 
+
+ align:start position:0%
+I bought a computer recently I care
+about how big the hard drive was and how
+
+ align:start position:0%
+about how big the hard drive was and how
+ 
+
+ align:start position:0%
+about how big the hard drive was and how
+much memory it had because those were
+
+ align:start position:0%
+much memory it had because those were
+ 
+
+ align:start position:0%
+much memory it had because those were
+two performance metrics that I could use
+
+ align:start position:0%
+two performance metrics that I could use
+ 
+
+ align:start position:0%
+two performance metrics that I could use
+to figure out whether the computer would
+
+ align:start position:0%
+to figure out whether the computer would
+ 
+
+ align:start position:0%
+to figure out whether the computer would
+be sufficient for my needs well in the
+
+ align:start position:0%
+be sufficient for my needs well in the
+ 
+
+ align:start position:0%
+be sufficient for my needs well in the
+case of buddy I just need to know which
+
+ align:start position:0%
+case of buddy I just need to know which
+ 
+
+ align:start position:0%
+case of buddy I just need to know which
+promoter to use that will make him red
+
+ align:start position:0%
+promoter to use that will make him red
+ 
+
+ align:start position:0%
+promoter to use that will make him red
+but how red do you want buddy to be
+
+ align:start position:0%
+but how red do you want buddy to be
+ 
+
+ align:start position:0%
+but how red do you want buddy to be
+should body be pink red or dark red to
+
+ align:start position:0%
+should body be pink red or dark red to
+ 
+
+ align:start position:0%
+should body be pink red or dark red to
+make decisions like that you might need
+
+ align:start position:0%
+make decisions like that you might need
+ 
+
+ align:start position:0%
+make decisions like that you might need
+to know a bit more about how strong the
+
+ align:start position:0%
+to know a bit more about how strong the
+ 
+
+ align:start position:0%
+to know a bit more about how strong the
+promoter is exactly another measurement
+
+ align:start position:0%
+promoter is exactly another measurement
+ 
+
+ align:start position:0%
+promoter is exactly another measurement
+you might care about is how long the
+
+ align:start position:0%
+you might care about is how long the
+ 
+
+ align:start position:0%
+you might care about is how long the
+part Works before it breaks genetic
+
+ align:start position:0%
+part Works before it breaks genetic
+ 
+
+ align:start position:0%
+part Works before it breaks genetic
+Parts can break as buddy grows and
+
+ align:start position:0%
+Parts can break as buddy grows and
+ 
+
+ align:start position:0%
+Parts can break as buddy grows and
+divides for example mutations or
+
+ align:start position:0%
+divides for example mutations or
+ 
+
+ align:start position:0%
+divides for example mutations or
+deletions can happen that interfere with
+
+ align:start position:0%
+deletions can happen that interfere with
+ 
+
+ align:start position:0%
+deletions can happen that interfere with
+part function so depending on how long
+
+ align:start position:0%
+part function so depending on how long
+ 
+
+ align:start position:0%
+part function so depending on how long
+you expect buddy to stick around you
+
+ align:start position:0%
+you expect buddy to stick around you
+ 
+
+ align:start position:0%
+you expect buddy to stick around you
+might choose promoters that are more or
+
+ align:start position:0%
+might choose promoters that are more or
+ 
+
+ align:start position:0%
+might choose promoters that are more or
+less genetically stable wao I had no
+
+ align:start position:0%
+less genetically stable wao I had no
+ 
+
+ align:start position:0%
+less genetically stable wao I had no
+idea measuring part function could be so
+
+ align:start position:0%
+idea measuring part function could be so
+ 
+
+ align:start position:0%
+idea measuring part function could be so
+complicated well I think I am going to
+
+ align:start position:0%
+complicated well I think I am going to
+ 
+
+ align:start position:0%
+complicated well I think I am going to
+find myself a strong promoter from the
+
+ align:start position:0%
+find myself a strong promoter from the
+ 
+
+ align:start position:0%
+find myself a strong promoter from the
+registry I've decided that I want buddy
+
+ align:start position:0%
+registry I've decided that I want buddy
+ 
+
+ align:start position:0%
+registry I've decided that I want buddy
+to be very dark red have
+
+ align:start position:0%
+to be very dark red have
+ 
+
+ align:start position:0%
+to be very dark red have
+fun Jin
\ No newline at end of file
diff --git a/XxvD0Yh9qCM.txt b/XxvD0Yh9qCM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ab9b1b3fc3d3ed81f6d09c370a3a8f9c2e62a455
--- /dev/null
+++ b/XxvD0Yh9qCM.txt
@@ -0,0 +1,2125 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, so we're going
+to leave off where we were
+
+last time talking
+about buffers.
+
+And I'm a big fan of buffers,
+actually, and buffers are
+
+extremely useful in my research
+because they keep the
+
+p h of things constant.
+
+So if you're going to do any
+kind of biology research or
+
+biochemistry research, you need
+to know about buffers.
+
+And as I'll mentioned later,
+also your body needs to be
+
+buffered appropriately, you
+don't want a large changes in
+
+p h in your body or things
+won't function properly.
+
+So buffering is very
+important.
+
+So let's go over buffers.
+
+So if we talk about an acid
+buffer, that's something
+
+that's buffering on the acidic
+side of the p h range.
+
+And in that, you want to have
+play on both sides.
+
+So if you have a strong acid, it
+can be neutralized, the p h
+
+stays the same.
+
+If you had a strong base, that
+would be neutralized so the p
+
+h stays the same.
+
+So what happens, you have to
+have an acid and its conjugate
+
+base in the mixture to
+have a good buffer.
+
+So what the weak acid is going
+to do is it will transfer
+
+protons or hydrogen ions to
+hydroxide ions that are
+
+supplied by the strong base to
+neutralize that strong base
+
+that was added.
+
+So you need to have an acid in
+there that's capable of giving
+
+up a proton to neutralize the
+hydroxide ion that was added.
+
+You also need to have
+a conjugate base.
+
+The conjugate base is going to
+accept protons if an acid is
+
+added, thereby neutralizing the
+effect of that added acid.
+
+So again, you need a weak acid
+and its conjugate base, you
+
+need both to have
+a good buffer.
+
+So I've been talking about weak
+acids and weak conjugate
+
+bases, so why would a strong
+acid and the salt of its
+
+conjugate base not make
+a good buffer?
+
+What do strong acids do?
+
+They dissociate almost
+completely, and that's not
+
+going to do you any good.
+
+You want to be able to shift
+that equation both directions.
+
+So a strong acid goes to
+completion is going to drive
+
+it to the right, and for a good
+buffer you want to be
+
+able to switch things around
+that if you add a strong acid,
+
+then you neutralize that, you
+add a strong base, you
+
+neutralize it.
+
+So you need the conjugate to be
+effective as a base, and a
+
+strong acid has an ineffective
+conjugate base.
+
+It's not good as a base at
+all, so that won't work.
+
+So buffers are made up of weak
+acids and their conjugate
+
+bases, or weak bases and
+their conjugate acids.
+
+They need to be in the
+weak range or there's
+
+no buffering capacity.
+
+So let's look at a base
+buffer example.
+
+The only difference here is that
+a basic buffer is going
+
+to buffer on the basic
+end of the p h range.
+
+So here's an equation.
+
+We have a base in water forming
+a conjugate of that
+
+weak base and hydroxide ions.
+
+So let's think about
+what happens if a
+
+strong acid is added.
+
+Well if a strong acid is added,
+then this base, n h 3,
+
+can accept protons from the
+incoming acid and make more n
+
+h 4 plus, thereby removing the
+strong acid from the solution
+
+and neutralizing the p h.
+
+If on the other hand a strong
+base is added, n h 4 plus or
+
+ammonium ions can donate the
+proton forming its conjugate
+
+base in water, and again, the
+p h remains about the same.
+
+So the base and its conjugate
+acid can both react,
+
+neutralizing the p h.
+
+So in the base buffer acid, a
+weak base, b, will accept
+
+protons supplied by the strong
+acid, removing a strong acid
+
+from the solution.
+
+The conjugate acid of that weak
+base, which again, would
+
+be a weak acid, can transfer
+protons to the hydroxide ions
+
+added by the strong
+base, again,
+
+neutralizing the effect there.
+
+So a buffer is a mixture of a
+weak acid base conjugate pair
+
+that will stabilize the p h
+serving as a source or a sink
+
+for the added protons.
+
+So that's how a buffer works.
+
+So, I mentioned buffering
+is very important.
+
+It's very important
+in your blood.
+
+Your blood is buffered in
+the range of p h 7 .
+
+35 to 7 .
+
+45, and you have a buffering
+pair and a conjugate acid base
+
+pair that's in your blood
+that does to work.
+
+So nature has its own buffering
+system design to
+
+keep the p h of your
+blood constant.
+
+Well what happens if the p
+h of your blood changes?
+
+So let me just tell you about
+one disease that can change
+
+the p h of your blood.
+
+This is from a vitamin B12
+dependent enzyme called
+
+methylmalonic coa mutase, and
+this enzyme is your friend.
+
+I think that most of you are
+excited about the idea of
+
+having all your fat go to
+energy, so you should be all
+
+fan of this enzyme.
+
+So it breaks down from fatty
+acids -- you get methylmalonyl
+
+coa, which is converted to
+succinyl coa and goes into the
+
+citric acid cycle.
+
+But if this step is blocked,
+if there's some kind of
+
+genetic disease associated with
+that particular enzyme,
+
+you get a condition called
+methylmalonic aciduria.
+
+So this is excreted in the body,
+it can't be converted to
+
+the succinyl coa, so it has to
+be excreted from the body, and
+
+it has an acidic p h.
+
+And so when it's excreted, it
+will actually, there's a large
+
+amount of it, and it can change
+the p h of blood.
+
+So even though you have this
+buffering system, it can
+
+overwhelm the buffering system
+and cause a change in the p h,
+
+which can lead to neurological
+disorders and sometimes death.
+
+So they can look for this in
+newborns, they can do a test,
+
+and I was -- one of the tests is
+-- it's not in every state,
+
+but it is in Massachusetts, so
+my daughter, Samantha, had
+
+this test. But they can simply
+look at the urine of a newborn
+
+and look at the p h
+and whether any of
+
+this is being excreted.
+
+And some infants that have this
+condition can excrete
+
+like a gram of this
+acid a day.
+
+So it's really large quantities
+of acid that are
+
+excreted and it goes beyond
+the buffering capacity.
+
+So, I'm going to tell you a
+little story and it sort of
+
+emphasizes some of the
+
+importance of genetic research.
+
+So before the human genome
+project, scientists were
+
+trying to find the gene to
+figure out what was wrong with
+
+these patients that had
+this condition.
+
+And here are all
+the amino acids
+
+translated from the gene.
+
+This is not a small protein,
+that's a lot of amino acids.
+
+And they found that the problem
+was right here, or one
+
+of the main problems
+is right here.
+
+There's a glycine residue, which
+glycine is the smallest
+
+amino acid and that had been
+changed to something else and
+
+that led to the disease.
+
+Now I want you to imagine if
+you were parents of a small
+
+child and you found out your
+child had this condition and
+
+then you had heard that there
+were advances, they now know
+
+what caused it, and so, they
+went to the doctor and the
+
+doctor said, yes, your child,
+the DNA is wrong, and so let's
+
+substitute a different amino
+acid for glycine here.
+
+OK.
+
+What does that do for you?
+
+Like why is that a problem?
+
+Well, they didn't know why it
+was a problem, they just knew
+
+that it had the wrong
+amino acid in there.
+
+And so, the next step was to
+try to understand what was
+
+actually going on.
+
+So what happened in this case
+was that the vitamin B12
+
+cofactor had changed its
+conformation when it bound to
+
+the protein.
+
+And instead of having this sort
+of loop structure here,
+
+it had more of a tail.
+
+So this base here had moved
+down, and so there was a
+
+different shape to the vitamin
+than had been expected.
+
+So when the first structure
+was solved of one of these
+
+enzymes, it found that here's
+kind of what the vitamin B12
+
+looked like, it had this
+extended region which no one
+
+was expecting, and so that had
+to fit into the protein.
+
+So this is the domain of the
+protein that binds the
+
+vitamin, and it had a large
+hole, and you put these
+
+together and that's
+great, it fits and
+
+you have happy enzyme.
+
+Well, how do you create a hole
+-- nature supposedly abhors a
+
+vacuum, so how do you
+have this hole?
+
+Well, what nature did was it put
+the smallest amino acids
+
+there are, glycines, right along
+here to make room for
+
+this to fit together.
+
+So, what was happening in this
+genetic case is that the
+
+switch of a glycine to an
+argenine did this to the hole.
+
+So, what people were trying to
+do is treat these patients
+
+with extra B12, you give them
+injections of it, you have a
+
+lot more B12, and you want to
+the B12 to bind and get the
+
+activity back going again.
+
+But really, no matter how much
+vitamin B12 you added to it,
+
+it wasn't really going to do
+much good, it just wasn't
+
+going to fit.
+
+So instead, there was a
+suggestion that instead of
+
+giving the whole vitamin,
+perhaps you could just give a
+
+truncated version of the
+vitamin, which was
+
+commercially available, and
+that that might bind and
+
+restore activity
+of the protein.
+
+So this is what was suggested
+once you knew what the problem
+
+actually was.
+
+So this is just an example of
+a genetic disease, and it's
+
+not that common, but as I said,
+it is tested for here in
+
+Massachusetts.
+
+And how knowing something about
+what the problem is can
+
+lead to a potential solution.
+
+But for most of you, your blood
+is doing just fine, you
+
+don't have a genetic condition
+which is pumping too much acid
+
+into your bloodstream, so that
+nature's buffering capacity is
+
+working quite well.
+
+So buffers are important.
+
+It's great to have my
+important statements
+
+emphasized up there.
+
+We've been rehearsing at home.
+
+OK.
+
+So let's do a sample
+buffer problem.
+
+All right, suppose we have an
+acid, 0.1 moles of an acid,
+
+and 0.5 moles of its conjugate
+base added in
+
+the form of a salt.
+
+And so they're put into water
+and diluted to 1.0 liter.
+
+And you're given information
+about the k a of the acid, 1 .
+
+77 times 10 to the minus
+4, and you're asked to
+
+calculate the p h.
+
+So what do you do?
+
+All right, first, it's always
+good to write the equation
+
+that you're talking about.
+
+And so you have acid in water
+forming hydronium ions and the
+
+conjugate base.
+
+So here, the acid is giving up a
+proton to the water, forming
+
+h 3 o plus and it's
+conjugate base.
+
+Now we want to think about what
+happens at equilibrium.
+
+So we know how many moles we
+have and we know what the
+
+total volume is.
+
+And in this table we should be
+using molarity, but the math
+
+here is pretty easy because we
+have 1 mole and 1 liter or 1,
+
+and 0.5 moles in 1 liter
+or 0.5 for molarity.
+
+And now at equilibrium what's
+going to happen, well, when
+
+this equilibrates some of this
+will go away and more of these
+
+are going to be formed.
+
+So we have minus x over here,
+plus x and plus x over there,
+
+and we add it all together
+you get 1 minus x plus x
+
+and 0.5 plus x.
+
+So the important thing to
+remember is in buffering
+
+problems, you have the acid
+and the conjugate.
+
+So we're used to seeing these
+tables where we only have
+
+something over here and it's
+all zero on the other side.
+
+But in a buffering problem, you
+have things on both sides
+
+from the very beginning.
+
+And that's a really important
+point, and that alone, if you
+
+can remember that, will
+get you a long way
+
+through this unit.
+
+So you remember that in a buffer
+you got to have both an
+
+acid in its conjugate base or a
+base in its conjugate acid.
+
+So here we're talking about an
+acid in water, it's an acidic
+
+buffer, and so we can use our
+k a value -- we want to know
+
+what the concentrations
+are at equilibrium to
+
+calculate our p h.
+
+So we can use our k a and we can
+set it up, so we have on
+
+the top products over reactants,
+and we we're not
+
+including water in this
+because it's dilute in
+
+solution and so it's not
+changing very much.
+
+And now we can plug in our
+values, so we have 0.5 plus x,
+
+x over 1 minus x.
+
+All right, now this is just
+written again from the last
+
+slide, we can try an
+approximation, which is it
+
+that x is small compared to
+1 molar or 0.5 molar.
+
+And so we can get rid of the
+plus x and the minus x down
+
+here and just have one x term,
+which makes it simpler to
+
+solve, but we'll have to
+go back and check that
+
+approximation in
+a few minutes.
+
+So making that approximation,
+we can calculate x as 3 .
+
+54 times 10 to the minus 4
+molar, and now we need to
+
+check that assumption.
+
+Well, you can probably guess
+it's going to be OK, because
+
+something times 10 to the minus
+4 compared to 0.5 and 1,
+
+that's probably going to
+be OK that it's small.
+
+But our assumption here is that
+it needs to be less than
+
+5%, and here it's 0.1%.
+
+So you could just take this
+value of x, divide it by the
+
+smaller of the two, 0.5 , times
+100, and calculate the
+
+percent ionization.
+
+If it's less than 5% you're OK,
+if it's more you need to
+
+use the quadratic equation
+to solve the problem.
+
+So x here is our concentration
+of hydronium ion, which is
+
+great, because then we can
+easily calculate the p h.
+
+So p h again is minus log
+of the hydronium ion
+
+concentration, and so
+the p h here is 3 .
+
+45.
+
+And again, significant figures,
+we'll be talking
+
+about this as we go through.
+
+The volume had two, it was 1 .
+
+0 liters, and so we're going
+to have two significant
+
+figures after the decimal point,
+because the volume was
+
+limiting insignificant
+figures.
+
+All right, now let's consider
+what happens if some strong
+
+acid had been added
+in the solution.
+
+So the volume is still going
+to be 1 liter, because the
+
+acid was added in before we went
+up to the 1 liter mark.
+
+So strong acids, they
+go to completion.
+
+So, if we added 0.1 moles of
+that strong acid, it will
+
+react with equal number of moles
+of the conjugate base to
+
+form the conjugate acid.
+
+So we can just do subtractions
+here.
+
+We don't have to worry about
+setting up any kind of
+
+equilibrium, we assume
+it goes completely.
+
+So for the conjugate base we had
+0.5 moles before, and it's
+
+going to be reacting then with a
+strong acid, so 0.1 of those
+
+will react, leaving us with 0.4
+moles of the conjugate,
+
+and that's in 1 liter.
+
+So now we have 0.4 molar.
+
+For the acid, we had 1 mole to
+begin with, but now we formed
+
+more as they reaction
+has taken place, and
+
+so we have 0.1 more.
+
+Now we have 1 .
+
+1 moles again in 1 liter.
+
+So now we can do the
+same thing again.
+
+So after this has happened,
+after we have added the strong
+
+acid, then a new equilibrium
+is going to be reached.
+
+And so we can plug in
+this table as well.
+
+So we have 1 .
+
+1 now over here, and 0.4
+on the other side.
+
+As equilibrium is approached,
+you lose some of the acid as
+
+it reacts with water and ionizes
+and you form more of
+
+the h 3 o plus and more
+of the conjugate.
+
+So we have 1 .
+
+1 minus x, x, and 0.4 plus x.
+
+So again, the trick here is just
+to remember that there is
+
+a reaction with a strong acid
+that has been added, and you
+
+need to figure out the new
+molarities, and then go back
+
+to your equilibrium table with
+those new molarities.
+
+So here we can set up with a
+k a again, and do the same
+
+problem that we did before.
+
+And so, we can make the
+assumption again that x is
+
+small, try it out and
+see if it works.
+
+X turns out to be 4 .
+
+87 times 10 to the minus 4
+molars -- so again, it's a
+
+small number.
+
+And so, it turns out to be 1
+. -- less than 1% of 0.4 .
+
+If it's less than 5% of the
+smaller number, you don't have
+
+to worry about the bigger
+number, and so your assumption
+
+is OK, you don't need to use
+the quadratic equation.
+
+And so, then we can calculate
+at the end that the
+
+p h is now 3 .
+
+31, again, two significant
+figures after the decimal
+
+place because of the volume.
+
+So addition of 0.1 moles of
+a strong acid changed
+
+our p h from 3 .
+
+45 to 3 .
+
+31.
+
+So we buffered pretty well.
+
+There was a change in p h, we
+added acid and the p h did go
+
+down, but not by an
+enormous amount.
+
+And so, that's because this
+turned out to be a pretty
+
+decent buffer here,
+so we didn't have
+
+a really huge effect.
+
+So, those are -- that's an
+example of a buffer problem.
+
+So, let's think for a minute
+about designing a buffer.
+
+Suppose you wanted to create a
+buffer at a particular p h,
+
+what do you need
+to think about?
+
+Well, you need to think about
+the ratio of your acid to the
+
+conjugate, and you need to think
+about the p k a of the
+
+acid, and the p h
+that's desired.
+
+So here is a generic equation
+for an acid in water, so we
+
+have our acid, h a, in water
+forming hydronium ions and our
+
+conjugate base.
+
+And now we're going to do a
+little derivation to come up
+
+with an equation that would be
+useful to you in thinking
+
+about buffers and designing
+buffers.
+
+So, we can write a generic
+term for k a.
+
+K a equals products over
+reactants, and so we have our
+
+hydronium ions are conjugate
+base over our acid.
+
+And now we can take this
+term and rearrange it.
+
+So we can pull a hydronium ion
+
+concentration over to one side.
+
+And now we're going to take the
+logs of both sides, so we
+
+get the log of hydronium ion
+concentration, the log of k a,
+
+and the log of h a concentration
+over a minus
+
+concentration, and now we're
+going to multiply everything
+
+by negative sign, so we have
+minus logs of things.
+
+And I'm just going to move this
+now up to the top of the
+
+screen, and we have
+this equation.
+
+So what is minus log of
+hydronium ion concentration?
+
+P h.
+
+What's minus log of k a?
+
+P k a.
+
+So, we have p h equals p
+k a minus the log of a
+
+concentration of your acid over
+the concentration of your
+
+conjugate base.
+
+And these are equilibrium
+concentrations for that,
+
+because remember, we derived
+it from our equilibrium
+
+expression for k a.
+
+But a lot of times when you're
+working buffer problems, you
+
+know the concentrations that you
+added of these things, not
+
+necessarily the concentrations
+of equilibrium.
+
+And if we rewrite this
+expression in terms of the
+
+initial concentrations or
+original or o concentrations,
+
+then we have p h is
+approximately equal to p k a
+
+minus log of the initial
+concentrations of your acid
+
+over your conjugate base.
+
+And this is known as a
+
+Henderson Hasselbalch equation.
+
+And people love the Henderson
+Hasselbalch equation, and it
+
+can be incredibly useful to you
+in solving these problems.
+
+But I'm going to emphasize when
+it's OK to use it and
+
+when it's not OK to use it,
+because people try to apply it
+
+to everything, and it's for
+buffer problems, and people
+
+apply it to all sorts of things
+that are not buffer
+
+problems. So I want to make sure
+that it's clear when you
+
+can use it and when
+you can't use it.
+
+And it's fine to use it and you
+should use it when it's
+
+acceptable, but not
+at other times.
+
+It's one of the few equations
+in acid base, so people get
+
+very excited by it.
+
+All right, so remember that it's
+really equal when they're
+
+at equilibrium concentrations,
+and this is just an
+
+approximation that we're saying
+that those are initial
+
+concentrations.
+
+So when is it OK to say well,
+the equilibrium concentration
+
+is more or less the same as
+the initial concentration.
+
+And that's true when x, which is
+in this particular example
+
+your hydronium ion
+concentration, is small
+
+compared to your initial
+concentration of the acid and
+
+the conjugate base that you
+added to the buffer.
+
+So, and when x is small, then
+pretty much, the equilibrium
+
+concentration equals the
+initial concentration.
+
+So there's not really very much
+change if x is a really
+
+small number.
+
+So, a lot of the time
+this is true.
+
+Remember, we're making buffers
+from weak acids and weak
+
+conjugate bases, and the
+definition of a weak acid is
+
+that it only loses a tiny
+fraction of its protons.
+
+It only ionizes slightly
+in water.
+
+And a weak base typically only
+accepts a fraction of the
+
+protons it can accept.
+
+It's a weak base, so it's
+not doing a whole lot
+
+of chemistry there.
+
+So this approximation is
+good a lot of the time.
+
+So just you know when you can
+and can not use it, we're
+
+going to give a rule and say
+it's the same rule as before.
+
+When we say when x is small
+or your hydronium ion
+
+concentration is small compared
+to the acid or the
+
+conjugate base, when it's less
+than 5%, that's what we're
+
+going to call small, so
+the same rule we've
+
+been using all along.
+
+When x is small, this
+approximation
+
+works pretty well.
+
+And you can plug in your
+concentrations right there --
+
+your initial concentrations
+not your equilibrium
+
+concentrations.
+
+All right, so let's use
+Henderson Hasselbalch and
+
+design a buffer system if
+we want a p h of 4 .
+
+6.
+
+And a good rule to remember is
+that a buffering solution is
+
+most effective when it's
+plus or minus 1 away
+
+from the p k a.
+
+So that's a good thing
+too I keep in mind
+
+for research as well.
+
+If you're really far away from
+the p k a, it's not going to
+
+be a good buffering system,
+and this is a mistake the
+
+people make in the lab
+sometimes, so you may run into
+
+that in some of your
+laboratory courses.
+
+So we want a buffer
+about p h 4 .
+
+6.
+
+So we can look at our ionization
+constants of acid,
+
+and of course, we're always
+doing everything at room
+
+temperature in this unit, and so
+we can look at what p k a's
+
+are of some weak acids, and
+acetate, acetate is an easy
+
+buffer to get your hands on,
+acetate is quite available,
+
+and it has a good p k a 4 .
+
+75.
+
+So that's great, we can use that
+in designing our buffer.
+
+So, acetic acid has the right
+p k a, and we're all set, we
+
+can prepare a buffer.
+
+But we'll need to add the acid
+and the conjugate, and we need
+
+to know how much acid and how
+much of the conjugate to add.
+
+So we can use Henderson
+Hasselbalch equation for this.
+
+We're creating a buffer, and so
+this is an equation we can
+
+use for buffers.
+
+We know what p h we want, we
+know the p k a of the thing
+
+we're going to use, and we want
+to figure out how much of
+
+the acid to use and how much
+of the conjugate to use.
+
+We need to know the ratio of one
+to the other to set up our
+
+buffer ideally.
+
+So we can plug our numbers
+in and calculate that.
+
+So, we can rearrange this if you
+want so that the unknown
+
+is on one side and we have
+to p k a and the p h
+
+on the other side.
+
+And so, we have here our p k a
+minus our p h and we get 0 .
+
+15.
+
+Now we need to inverse log and
+come up with the ratio, and
+
+the ratio that we want is 1 .
+
+4.
+
+So we want to have a ratio
+from our acid to the
+
+conjugate of 1 .
+
+4.
+
+Well how much exactly are we
+going to add them, we know the
+
+ratio now, how much are
+we going to add?
+
+Well, you could use 1 .
+
+4 molar and 1 molar, for
+example, that would have the
+
+correct ratio.
+
+But how do you know if that's
+going to be good?
+
+Well, the ratio is more
+important than the exact
+
+amounts, however, the amounts
+get to this issue of sort of
+
+the capacity of the buffer --
+how resistant it is to changes
+
+in the p h.
+
+So if you use too low
+concentrations of both, it
+
+won't be all that resistant.
+
+So if you need to have a better
+buffering capacity, the
+
+higher concentrations
+that you should use.
+
+And you can use Henderson
+Hasselbalch then to calculate
+
+what sort of the minimum amount
+you use, the minimum
+
+amount to have that
+5% rule work.
+
+So in the example I told you
+about this condition, the
+
+buffer in the blood was pretty
+good, but the acid with so
+
+much that it overwhelmed
+buffering capacity.
+
+So if there had been larger
+concentrations of the buffer,
+
+that would have certainly
+helped in that case.
+
+So the higher the concentrations
+you use, the
+
+more resistant to change.
+
+And that's the idea of
+buffering capacity.
+
+So, and if you use too low
+concentrations, then your
+
+Henderson Hasselbalch equation
+won't even be valid.
+
+So we can go back and calculate
+what is sort of the
+
+minimum concentrations we need
+to use for Henderson
+
+Hasselbalch to be valid
+to meet that 5% rule.
+
+So for a p h of 4 .
+
+6, a hydronium ion concentration
+is a 2 .
+
+5 times 10 to the minus 5.
+
+And so then if we work our
+equation backwards, we want to
+
+be less than 5%, so we have this
+over the concentration of
+
+either one of those times
+100% gives you 5%.
+
+So the concentrations need to be
+greater than 5 times 10 to
+
+the minus 4 moles or you won't
+meet this 5% rule.
+
+So at least to be greater than
+that and they need to be in
+
+the right ratio.
+
+Other than that you're somewhat
+free to decide what
+
+you're going to do with that,
+and there may be other
+
+considerations involved if
+you're working with a certain
+
+concentration of protein, you
+might not want your buffer
+
+concentration to be too high,
+it might start interfering
+
+with enzyme assay,
+for example.
+
+And often buffers are
+somewhere around 100
+
+millimolar, that's
+a pretty common
+
+concentration for buffers.
+
+All right, so this slide we're
+doing really well.
+
+So we talked about weak acids in
+water, weak bases in water,
+
+and I'm trying to convince you
+that these are the same as the
+
+salt and water problems. So
+we're going to talk much more
+
+about salt and water
+in a few minutes.
+
+And I told you about buffers,
+so we only have 2
+
+more things to go.
+
+We need to talk about strong
+acids in water, and strong
+
+bases in water, and then you'll
+have all of the 5 types
+
+of problems to do
+the problem-set.
+
+And as I mentioned last time,
+it looks deceivingly short,
+
+the number of questions on
+them, but the titration
+
+problems are long.
+
+So don't leave those to the last
+minute or there will not
+
+be a whole lot of
+sleep involved.
+
+So just a word of warning from
+the past. Everyone looks and
+
+go, "Oh, this is an easy
+problem-set, there aren't many
+
+problems." So, titration
+problems do
+
+take a lot of time.
+
+So let's talk about titration,
+so that as soon as class is
+
+over today, you can go work
+on those questions on the
+
+problem-set.
+
+All right.
+
+So acid base titrations.
+
+How many of you in high school
+titrated an acid with a base?
+
+Large fraction of you, OK.
+
+So usually what titration
+problems are meant to do, that
+
+you have something known about
+an acid or a base, base say of
+
+known concentration, and and
+acid of unknown concentration
+
+or maybe unknown molecular
+weight, and you're titrating
+
+them out, titrating them
+together to find missing
+
+information.
+
+So you can determine
+concentration, sometimes you
+
+can determine a molecular
+weight.
+
+All right, so here's what a plot
+looks like and some of
+
+the key terms involved in
+acid base titrations.
+
+So you have a p h on one side,
+and then volume of either base
+
+or acid added on
+the other side.
+
+So p h versus a volume.
+
+And the actual experiment here,
+you have a base that
+
+you're dripping, one drip at
+a time supposedly into your
+
+strong acid.
+
+And then you're looking to
+figure out when you're going
+
+to reach the either equivalence
+point or the end
+
+point, these are basically the
+same terms. It's also called
+
+the stoichiometric point, and
+often equivalence point is
+
+used as a more theoretical
+amount of volume is added,
+
+where as end point is the
+experimentally measured.
+
+So we're going to be talking a
+lot about equivalence points,
+
+because we have no lab
+associated with this course,
+
+so everything will be
+theorectical in terms of
+
+these, but they should
+be the same.
+
+So, many times you will measure
+p h with the p h meter
+
+-- this just shows
+a p h meter.
+
+And for those of you who have
+done these experiments, this
+
+should look familiar.
+
+And for those of you who
+haven't, often what you're
+
+doing when you're dripping
+something in, you're waiting
+
+for an indicator dye to change
+color as an indication that
+
+you have reached the end
+point, and often you're
+
+adding, and it's clear, clear,
+clear for what seems to be
+
+forever, and just as you get
+incredibly impatient, you
+
+start adding it faster and
+you go all the way
+
+to this dark color.
+
+And what you want is this very,
+very, very light changed
+
+color that indicates
+the end point.
+
+So you usually go too slow and
+then go too fast and then have
+
+to do the experiment
+over again.
+
+Those of you who know how to
+calculate theoretical values
+
+could sit down and do a
+calculation first and then go
+
+really fast right until you get
+around this point and add
+
+it really slowly, and be
+done with lab sooner.
+
+So, we'll talk about how you
+do the theoretical value,
+
+which could save you a lot of
+time if you ever run across
+
+these labs in any
+future class.
+
+So, here are the two curves that
+you would see for either
+
+a strong acid with a strong
+base, or strong base with a
+
+strong acid.
+
+So if you're titrating a strong
+acid with a strong
+
+base, you're going to start
+down being very acidic,
+
+because all you have is
+your strong acid.
+
+And then as you add in base,
+the p h will go up.
+
+You'll reach this point -- s
+is for the stoichiometric
+
+point, we also call this, again,
+the equivalence point,
+
+and then it'll continue to go up
+and then start to level off
+
+a bit more up here.
+
+If you're going the other
+direction, you're starting
+
+with strong base, your p h is
+going to be high, and the p h
+
+will decrease as you
+add the acid.
+
+And then you get to the
+stoichiometric or equivalence
+
+point in the middle of
+this curve here.
+
+And then as you go down farther,
+more acidic, it
+
+starts to level off.
+
+So those are what the titration
+curves look like.
+
+So let's do an example.
+
+We're going to have a strong
+base being titrated with a
+
+strong acid first. And our
+strong base is n a o h, and
+
+our strong acid is h c l.
+
+So let's calculate the p h
+at the equivalence point.
+
+Well, let's just calculate
+the p h at 5 mils --
+
+I don't know whether it's
+equivalence point, actually.
+
+5 mils of this have been added
+to the amount of base.
+
+So we have 25 mils of our strong
+base at 0.15 molar
+
+concentration, and we're adding
+5 mils of our 0.34
+
+molar acid.
+
+So what we want to do is figure
+out how many moles of
+
+base we had to start with.
+
+So how many moles of o h minus
+-- again, n a o h is a strong
+
+base, so however much n a o h
+you add, is the amount of o h
+
+minus you get, and so we just
+put in the number of liters
+
+times the concentration
+to get moles.
+
+We don't need any equilibrium
+table here.
+
+So then we want to figure out
+the amount of acid added when
+
+you're adding 5 mils of it.
+
+So again, h c l is a strong
+acid, so the amount of h c l
+
+added equals the amount of h 3 o
+plus, that's formed, goes to
+
+completion, and so we added 5
+mils, the concentration was
+
+0.34 molar, so we have 1 .
+
+7 times 10 to the
+minus 3 moles.
+
+So now, the strong acid is going
+to react with the strong
+
+base, and we want to figure out
+how much of the base is
+
+left, how much hydroxide ion is
+left after it reacts with
+
+the hydronium ions.
+
+So it'll react 1:1,
+so we had 6 .
+
+25 times 10 to the minus 3
+moles, and we added 1 .
+
+7 times 10 to the minus 3 moles
+of the acid, so we're
+
+going to have 4 .
+
+55 times 10 the minus
+3 moles left.
+
+And now we can calculate the
+molarity here, so we have the
+
+number of moles and the new
+volume, so we had 25 mils to
+
+the base to begin with.
+
+We've added 5 mils to the acid,
+so our new volume is 30,
+
+and so we have our new
+concentration.
+
+And now we can calculate p h.
+
+First we'll calculate p o h, and
+then use 14 minus to get
+
+the new p h.
+
+So if you were making your own
+little titration curve, we
+
+could have volume of acid on one
+side and p h on the other
+
+side, and you have
+a point of 13 .
+
+18.
+
+That's how much we have after
+you have 5 mils added.
+
+So we didn't, in this curve, we
+have not measured the zero
+
+point, but we know what one
+point after 5 mils of the acid
+
+has been added.
+
+So now let's go right to the
+equivalence point -- so the
+
+way I draw it should indicate
+that was not
+
+an equivalence point.
+
+So we want to figure out how
+much we need to add of the
+
+acid to reach the equivalence
+point.
+
+So the equivalence point or the
+stoichiometric point means
+
+that you add the same amount
+of moles of your titrate as
+
+you had, and so they're going
+to be equal to each other.
+
+So if you're adding acid to a
+strong base, you've added
+
+enough acid that you now have
+equal number of moles to the
+
+number of moles of base that
+you had to begin with.
+
+So we know we have 6 .
+
+25 times 10 to the
+minus 3 moles of
+
+the base were present.
+
+So at the equivalence point,
+you need to have that exact
+
+same number of moles of acid.
+
+So we know the concentration
+of the acid we have and the
+
+number of moles we need, and
+so we can calculate the
+
+volume, which is 18 .
+
+4 millimeters, or
+0.0184 liters.
+
+So what would the p h then be
+of the equivalence point?
+
+We're titrating a strong acid
+with a strong base, what
+
+should the p h be?
+
+The p h should be 7.
+
+So somewhere around here we're
+going to be at 18, so you can
+
+just try to draw a curve, and
+here we have a p h of 7 when
+
+we've gone to about 18 .
+
+4 milliliters added.
+
+So when you titrate a strong
+acid with a strong base, you
+
+form a salt that's neutral.
+
+Because the conjugates of a
+strong acid and a strong base
+
+are not basic or acidic.
+
+They're ineffective as acids or
+bases, so you're going to
+
+get a neutral salt.
+
+So if you're doing a problem
+with a strong acid and strong
+
+base, it's not a lot of
+calculations that need to be
+
+done at this point, you just
+need to recognize that your
+
+salt should be neutral.
+
+So now, we can talk about what
+happens if you add an extra
+
+milliliter of your acid, after
+you've reached that
+
+equivalence point, which is
+something that people probably
+
+have done in doing these
+titrations not meaning to,
+
+gone well beyond the
+equivalence point.
+
+So first we can find out the
+number of moles of the strong
+
+acid that we've added extra,
+so we added one mil of the
+
+strong acid, and so again,
+it goes to completion.
+
+The concentration, the acid, is
+0.34 molar times our 1 mil,
+
+so we've added 3 .
+
+4 times 10 to the minus 4 extra
+moles of our acid, and
+
+so let's calculate then what the
+molarity is that we have
+
+added that was extra.
+
+And even if you don't
+have a calculator,
+
+we've helped you out.
+
+Let's just take 10
+more seconds.
+
+I think this is a
+first, isn't it?
+
+Did I mention it's a
+good idea to start
+
+the problem-set early.
+
+So the trick here was
+about the volume.
+
+So we had 25 mils to begin
+with, then we added 18 .
+
+4 to get to the equivalence
+point, and then we're 1 mil
+
+beyond the equivalence point.
+
+And the tricks to these parts
+of the problems are to
+
+remember all the things
+that have been added
+
+to get to the volume.
+
+So the problem itself is not
+very tricky of having just an
+
+acid in water, but the one trick
+is in calculating the
+
+molarity, remembering all of the
+things that were added to
+
+get to this point.
+
+And so by the end of the
+problem-set this should be
+
+pretty familiar to you, but it's
+also something that you
+
+want to make sure that you check
+on an exam that you're
+
+not making any volume
+mistakes.
+
+So again, here are the things
+that you want to remember to
+
+add in in calculating this.
+
+And then, if you calculate
+the p h of that, you
+
+get a p h of 2 .
+
+1106, so that's down
+somewhere in here.
+
+We've added 1 more mill, and
+we're at a p h of 2 .
+
+1106, and this can be
+a check as well.
+
+If you forgot to add some of
+your volume, you might get a p
+
+h that doesn't make
+a lot of sense.
+
+So that can be a double check.
+
+Always ask yourself when you
+have a strong base and you're
+
+adding acid, before you've
+added very much, your p h
+
+should be basic.
+
+At the equivalence point of
+a strong acid, strong base
+
+titration, it'll be 7.
+
+And if you continue to add acid,
+then you should have a
+
+pretty low p h, you'll notice
+the curve drops off pretty
+
+fast. So it should be a dramatic
+change in p h by
+
+adding extra of your acid.
+
+So always check your work.
+
+OK, so let's stop there, and
+we're going to weak acid, weak
+
+base titrations next time.
\ No newline at end of file
diff --git a/aiSpEUZzP0A.txt b/aiSpEUZzP0A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..169ef454de72fe7b59ad0dd52358e41100cc2e2a
--- /dev/null
+++ b/aiSpEUZzP0A.txt
@@ -0,0 +1,699 @@
+align:start position:0%
+ 
+many of you have heard of mukes uh
+
+ align:start position:0%
+many of you have heard of mukes uh
+ 
+
+ align:start position:0%
+many of you have heard of mukes uh
+they're very famous massively open
+
+ align:start position:0%
+they're very famous massively open
+ 
+
+ align:start position:0%
+they're very famous massively open
+online courses muks are very uh open and
+
+ align:start position:0%
+online courses muks are very uh open and
+ 
+
+ align:start position:0%
+online courses muks are very uh open and
+large classes often with thousands or
+
+ align:start position:0%
+large classes often with thousands or
+ 
+
+ align:start position:0%
+large classes often with thousands or
+tens of thousands of
+
+ align:start position:0%
+tens of thousands of
+ 
+
+ align:start position:0%
+tens of thousands of
+participants and muks are essentially um
+
+ align:start position:0%
+participants and muks are essentially um
+ 
+
+ align:start position:0%
+participants and muks are essentially um
+a big movement to really Dem democratize
+
+ align:start position:0%
+a big movement to really Dem democratize
+ 
+
+ align:start position:0%
+a big movement to really Dem democratize
+education Sparks a little different so
+
+ align:start position:0%
+education Sparks a little different so
+ 
+
+ align:start position:0%
+education Sparks a little different so
+1684 842 was run as a Spock which stands
+
+ align:start position:0%
+1684 842 was run as a Spock which stands
+ 
+
+ align:start position:0%
+1684 842 was run as a Spock which stands
+for small private online course so like
+
+ align:start position:0%
+for small private online course so like
+ 
+
+ align:start position:0%
+for small private online course so like
+a moo a Spock is also offered online you
+
+ align:start position:0%
+a moo a Spock is also offered online you
+ 
+
+ align:start position:0%
+a moo a Spock is also offered online you
+can take it in person in a classroom at
+
+ align:start position:0%
+can take it in person in a classroom at
+ 
+
+ align:start position:0%
+can take it in person in a classroom at
+one of the hosting
+
+ align:start position:0%
+one of the hosting
+ 
+
+ align:start position:0%
+one of the hosting
+universities uh or you can take it
+
+ align:start position:0%
+universities uh or you can take it
+ 
+
+ align:start position:0%
+universities uh or you can take it
+entirely online it's it's really up to
+
+ align:start position:0%
+entirely online it's it's really up to
+ 
+
+ align:start position:0%
+entirely online it's it's really up to
+you it's small because we have a few
+
+ align:start position:0%
+you it's small because we have a few
+ 
+
+ align:start position:0%
+you it's small because we have a few
+dozen students instead of thousands and
+
+ align:start position:0%
+dozen students instead of thousands and
+ 
+
+ align:start position:0%
+dozen students instead of thousands and
+um it's private because in order to take
+
+ align:start position:0%
+um it's private because in order to take
+ 
+
+ align:start position:0%
+um it's private because in order to take
+the class it's by invitation
+
+ align:start position:0%
+the class it's by invitation
+ 
+
+ align:start position:0%
+the class it's by invitation
+in this particular instance we had two
+
+ align:start position:0%
+in this particular instance we had two
+ 
+
+ align:start position:0%
+in this particular instance we had two
+universities that co-sponsored this
+
+ align:start position:0%
+universities that co-sponsored this
+ 
+
+ align:start position:0%
+universities that co-sponsored this
+class one is MIT and the other one is
+
+ align:start position:0%
+class one is MIT and the other one is
+ 
+
+ align:start position:0%
+class one is MIT and the other one is
+called epfl E po technique Federal de
+
+ align:start position:0%
+called epfl E po technique Federal de
+ 
+
+ align:start position:0%
+called epfl E po technique Federal de
+Loan in Switzerland which is also quite
+
+ align:start position:0%
+Loan in Switzerland which is also quite
+ 
+
+ align:start position:0%
+Loan in Switzerland which is also quite
+active in the in the world of online
+
+ align:start position:0%
+active in the in the world of online
+ 
+
+ align:start position:0%
+active in the in the world of online
+education the way fundamentally that a
+
+ align:start position:0%
+education the way fundamentally that a
+ 
+
+ align:start position:0%
+education the way fundamentally that a
+Spock works is that you have the course
+
+ align:start position:0%
+Spock works is that you have the course
+ 
+
+ align:start position:0%
+Spock works is that you have the course
+management system at each of the hosting
+
+ align:start position:0%
+management system at each of the hosting
+ 
+
+ align:start position:0%
+management system at each of the hosting
+universities and institutions and you
+
+ align:start position:0%
+universities and institutions and you
+ 
+
+ align:start position:0%
+universities and institutions and you
+essentially post the same materials the
+
+ align:start position:0%
+essentially post the same materials the
+ 
+
+ align:start position:0%
+essentially post the same materials the
+lectures the readings the exercise is
+
+ align:start position:0%
+lectures the readings the exercise is
+ 
+
+ align:start position:0%
+lectures the readings the exercise is
+you post them in parallel at each of the
+
+ align:start position:0%
+you post them in parallel at each of the
+ 
+
+ align:start position:0%
+you post them in parallel at each of the
+hosting universities the lectures
+
+ align:start position:0%
+hosting universities the lectures
+ 
+
+ align:start position:0%
+hosting universities the lectures
+themselves however are Run online using
+
+ align:start position:0%
+themselves however are Run online using
+ 
+
+ align:start position:0%
+themselves however are Run online using
+you know an open collaboration platform
+
+ align:start position:0%
+you know an open collaboration platform
+ 
+
+ align:start position:0%
+you know an open collaboration platform
+like WebEx for example you can do it
+
+ align:start position:0%
+like WebEx for example you can do it
+ 
+
+ align:start position:0%
+like WebEx for example you can do it
+with Google Hangouts there's a lot of
+
+ align:start position:0%
+with Google Hangouts there's a lot of
+ 
+
+ align:start position:0%
+with Google Hangouts there's a lot of
+different platforms and this is
+
+ align:start position:0%
+different platforms and this is
+ 
+
+ align:start position:0%
+different platforms and this is
+important because um it is important to
+
+ align:start position:0%
+important because um it is important to
+ 
+
+ align:start position:0%
+important because um it is important to
+have live connections between the
+
+ align:start position:0%
+have live connections between the
+ 
+
+ align:start position:0%
+have live connections between the
+faculty and the students but also the
+
+ align:start position:0%
+faculty and the students but also the
+ 
+
+ align:start position:0%
+faculty and the students but also the
+students amongst themselves can discuss
+
+ align:start position:0%
+students amongst themselves can discuss
+ 
+
+ align:start position:0%
+students amongst themselves can discuss
+the trickiest part of running a Spock of
+
+ align:start position:0%
+the trickiest part of running a Spock of
+ 
+
+ align:start position:0%
+the trickiest part of running a Spock of
+course is the time zones and the time
+
+ align:start position:0%
+course is the time zones and the time
+ 
+
+ align:start position:0%
+course is the time zones and the time
+differences in this case uh the two
+
+ align:start position:0%
+differences in this case uh the two
+ 
+
+ align:start position:0%
+differences in this case uh the two
+universities were six time zones apart
+
+ align:start position:0%
+universities were six time zones apart
+ 
+
+ align:start position:0%
+universities were six time zones apart
+and so it was offered in the morning
+
+ align:start position:0%
+and so it was offered in the morning
+ 
+
+ align:start position:0%
+and so it was offered in the morning
+here at MIT and in the afternoon in
+
+ align:start position:0%
+here at MIT and in the afternoon in
+ 
+
+ align:start position:0%
+here at MIT and in the afternoon in
+Europe if you're running this as a
+
+ align:start position:0%
+Europe if you're running this as a
+ 
+
+ align:start position:0%
+Europe if you're running this as a
+global class it will be more challenging
+
+ align:start position:0%
+global class it will be more challenging
+ 
+
+ align:start position:0%
+global class it will be more challenging
+to find a time slot that works for
+
+ align:start position:0%
+to find a time slot that works for
+ 
+
+ align:start position:0%
+to find a time slot that works for
+everybody the feedback from the students
+
+ align:start position:0%
+everybody the feedback from the students
+ 
+
+ align:start position:0%
+everybody the feedback from the students
+uh has been very positive because you
+
+ align:start position:0%
+uh has been very positive because you
+ 
+
+ align:start position:0%
+uh has been very positive because you
+can think of a Spock in this particular
+
+ align:start position:0%
+can think of a Spock in this particular
+ 
+
+ align:start position:0%
+can think of a Spock in this particular
+class as a blended form of Education
+
+ align:start position:0%
+class as a blended form of Education
+ 
+
+ align:start position:0%
+class as a blended form of Education
+part of the class is live the lectures
+
+ align:start position:0%
+part of the class is live the lectures
+ 
+
+ align:start position:0%
+part of the class is live the lectures
+are given live and every lecture is
+
+ align:start position:0%
+are given live and every lecture is
+ 
+
+ align:start position:0%
+are given live and every lecture is
+recorded so even if you miss a lecture
+
+ align:start position:0%
+recorded so even if you miss a lecture
+ 
+
+ align:start position:0%
+recorded so even if you miss a lecture
+as a student you can watch it later and
+
+ align:start position:0%
+as a student you can watch it later and
+ 
+
+ align:start position:0%
+as a student you can watch it later and
+so there's a record of it uh the
+
+ align:start position:0%
+so there's a record of it uh the
+ 
+
+ align:start position:0%
+so there's a record of it uh the
+assignments are asynchronous and there
+
+ align:start position:0%
+assignments are asynchronous and there
+ 
+
+ align:start position:0%
+assignments are asynchronous and there
+are some assignments that are individual
+
+ align:start position:0%
+are some assignments that are individual
+ 
+
+ align:start position:0%
+are some assignments that are individual
+and there are team assignments as well
+
+ align:start position:0%
+and there are team assignments as well
+ 
+
+ align:start position:0%
+and there are team assignments as well
+and so it's a blended form of Education
+
+ align:start position:0%
+and so it's a blended form of Education
+ 
+
+ align:start position:0%
+and so it's a blended form of Education
+which is an important Trend in education
+
+ align:start position:0%
+which is an important Trend in education
+ 
+
+ align:start position:0%
+which is an important Trend in education
+where we take the best of the online
+
+ align:start position:0%
+where we take the best of the online
+ 
+
+ align:start position:0%
+where we take the best of the online
+experience and we try to combine it with
+
+ align:start position:0%
+experience and we try to combine it with
+ 
+
+ align:start position:0%
+experience and we try to combine it with
+best the best of the in-person
+
+ align:start position:0%
+best the best of the in-person
+ 
+
+ align:start position:0%
+best the best of the in-person
+experience teaching a Spock is uh fun
+
+ align:start position:0%
+experience teaching a Spock is uh fun
+ 
+
+ align:start position:0%
+experience teaching a Spock is uh fun
+and challenging at the same time it's
+
+ align:start position:0%
+and challenging at the same time it's
+ 
+
+ align:start position:0%
+and challenging at the same time it's
+fun because you get to converse and um
+
+ align:start position:0%
+fun because you get to converse and um
+ 
+
+ align:start position:0%
+fun because you get to converse and um
+interact with students not just in a
+
+ align:start position:0%
+interact with students not just in a
+ 
+
+ align:start position:0%
+interact with students not just in a
+physical classroom at one University but
+
+ align:start position:0%
+physical classroom at one University but
+ 
+
+ align:start position:0%
+physical classroom at one University but
+across multiple
+
+ align:start position:0%
+across multiple
+ 
+
+ align:start position:0%
+across multiple
+institutions and um and and that
+
+ align:start position:0%
+institutions and um and and that
+ 
+
+ align:start position:0%
+institutions and um and and that
+enhances the class because students will
+
+ align:start position:0%
+enhances the class because students will
+ 
+
+ align:start position:0%
+enhances the class because students will
+speak up with experiences from different
+
+ align:start position:0%
+speak up with experiences from different
+ 
+
+ align:start position:0%
+speak up with experiences from different
+cultural backgrounds uh but it's also
+
+ align:start position:0%
+cultural backgrounds uh but it's also
+ 
+
+ align:start position:0%
+cultural backgrounds uh but it's also
+challenging because you have to keep
+
+ align:start position:0%
+challenging because you have to keep
+ 
+
+ align:start position:0%
+challenging because you have to keep
+track of what's happening at uh at
+
+ align:start position:0%
+track of what's happening at uh at
+ 
+
+ align:start position:0%
+track of what's happening at uh at
+multiple places and you have a mix of
+
+ align:start position:0%
+multiple places and you have a mix of
+ 
+
+ align:start position:0%
+multiple places and you have a mix of
+students from from from different
+
+ align:start position:0%
+students from from from different
+ 
+
+ align:start position:0%
+students from from from different
+backgrounds and uh different you know
+
+ align:start position:0%
+backgrounds and uh different you know
+ 
+
+ align:start position:0%
+backgrounds and uh different you know
+institutional uh constraints as well and
+
+ align:start position:0%
+institutional uh constraints as well and
+ 
+
+ align:start position:0%
+institutional uh constraints as well and
+so it's both challenging and fun but
+
+ align:start position:0%
+so it's both challenging and fun but
+ 
+
+ align:start position:0%
+so it's both challenging and fun but
+it's a very focused experience and the
+
+ align:start position:0%
+it's a very focused experience and the
+ 
+
+ align:start position:0%
+it's a very focused experience and the
+the feedback from the students has been
+
+ align:start position:0%
+the feedback from the students has been
+ 
+
+ align:start position:0%
+the feedback from the students has been
+great
\ No newline at end of file
diff --git a/auK3PSZoidc.txt b/auK3PSZoidc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7504fb3eba469ce9ab42d4cada1e81d4532098fe
--- /dev/null
+++ b/auK3PSZoidc.txt
@@ -0,0 +1,9723 @@
+align:start position:0%
+ 
+welcome back hope you had a good long
+
+ align:start position:0%
+welcome back hope you had a good long
+ 
+
+ align:start position:0%
+welcome back hope you had a good long
+weekend
+
+ align:start position:0%
+weekend
+ 
+
+ align:start position:0%
+weekend
+so today's puzzle is I guess a classic
+
+ align:start position:0%
+so today's puzzle is I guess a classic
+ 
+
+ align:start position:0%
+so today's puzzle is I guess a classic
+puzzle it's it's Sudoku I've never
+
+ align:start position:0%
+puzzle it's it's Sudoku I've never
+ 
+
+ align:start position:0%
+puzzle it's it's Sudoku I've never
+actually successfully managed to
+
+ align:start position:0%
+actually successfully managed to
+ 
+
+ align:start position:0%
+actually successfully managed to
+complete a pseudo Koopas all by myself
+
+ align:start position:0%
+complete a pseudo Koopas all by myself
+ 
+
+ align:start position:0%
+complete a pseudo Koopas all by myself
+because I've they fall into two
+
+ align:start position:0%
+because I've they fall into two
+ 
+
+ align:start position:0%
+because I've they fall into two
+categories for me either it's easy
+
+ align:start position:0%
+categories for me either it's easy
+ 
+
+ align:start position:0%
+categories for me either it's easy
+they're easy and and I get bored and I
+
+ align:start position:0%
+they're easy and and I get bored and I
+ 
+
+ align:start position:0%
+they're easy and and I get bored and I
+stop or they're too hard and I get lazy
+
+ align:start position:0%
+stop or they're too hard and I get lazy
+ 
+
+ align:start position:0%
+stop or they're too hard and I get lazy
+and I stop but what I have done is write
+
+ align:start position:0%
+and I stop but what I have done is write
+ 
+
+ align:start position:0%
+and I stop but what I have done is write
+a computer program that essentially
+
+ align:start position:0%
+a computer program that essentially
+ 
+
+ align:start position:0%
+a computer program that essentially
+solves any pseudocode puzzle that is put
+
+ align:start position:0%
+solves any pseudocode puzzle that is put
+ 
+
+ align:start position:0%
+solves any pseudocode puzzle that is put
+in front of it in in seconds maybe if
+
+ align:start position:0%
+in front of it in in seconds maybe if
+ 
+
+ align:start position:0%
+in front of it in in seconds maybe if
+there exists puzzles for which it would
+
+ align:start position:0%
+there exists puzzles for which it would
+ 
+
+ align:start position:0%
+there exists puzzles for which it would
+take minutes but I haven't discovered
+
+ align:start position:0%
+take minutes but I haven't discovered
+ 
+
+ align:start position:0%
+take minutes but I haven't discovered
+such puzzles and what we're going to do
+
+ align:start position:0%
+such puzzles and what we're going to do
+ 
+
+ align:start position:0%
+such puzzles and what we're going to do
+today is talk about Sudoku compare and
+
+ align:start position:0%
+today is talk about Sudoku compare and
+ 
+
+ align:start position:0%
+today is talk about Sudoku compare and
+contrast the human way of solving Sudoku
+
+ align:start position:0%
+contrast the human way of solving Sudoku
+ 
+
+ align:start position:0%
+contrast the human way of solving Sudoku
+puzzles against brute force way and then
+
+ align:start position:0%
+puzzles against brute force way and then
+ 
+
+ align:start position:0%
+puzzles against brute force way and then
+try and integrate the two together you
+
+ align:start position:0%
+try and integrate the two together you
+ 
+
+ align:start position:0%
+try and integrate the two together you
+know perhaps this is the closest we're
+
+ align:start position:0%
+know perhaps this is the closest we're
+ 
+
+ align:start position:0%
+know perhaps this is the closest we're
+going to get to AI in this class where
+
+ align:start position:0%
+going to get to AI in this class where
+ 
+
+ align:start position:0%
+going to get to AI in this class where
+we're going to try and marry an
+
+ align:start position:0%
+we're going to try and marry an
+ 
+
+ align:start position:0%
+we're going to try and marry an
+exhaustive search method with some
+
+ align:start position:0%
+exhaustive search method with some
+ 
+
+ align:start position:0%
+exhaustive search method with some
+smarts and back I think when we were
+
+ align:start position:0%
+smarts and back I think when we were
+ 
+
+ align:start position:0%
+smarts and back I think when we were
+doing the N Queens puzzle one of you
+
+ align:start position:0%
+doing the N Queens puzzle one of you
+ 
+
+ align:start position:0%
+doing the N Queens puzzle one of you
+asked a question about what the number
+
+ align:start position:0%
+asked a question about what the number
+ 
+
+ align:start position:0%
+asked a question about what the number
+of possibilities were you know for an
+
+ align:start position:0%
+of possibilities were you know for an
+ 
+
+ align:start position:0%
+of possibilities were you know for an
+eight Queens puzzle was at a trace to
+
+ align:start position:0%
+eight Queens puzzle was at a trace to
+ 
+
+ align:start position:0%
+eight Queens puzzle was at a trace to
+eight and I said well no you can prune
+
+ align:start position:0%
+eight and I said well no you can prune
+ 
+
+ align:start position:0%
+eight and I said well no you can prune
+the search by figuring out that
+
+ align:start position:0%
+the search by figuring out that
+ 
+
+ align:start position:0%
+the search by figuring out that
+particular partial configurations that
+
+ align:start position:0%
+particular partial configurations that
+ 
+
+ align:start position:0%
+particular partial configurations that
+correspond to perhaps two queens being
+
+ align:start position:0%
+correspond to perhaps two queens being
+ 
+
+ align:start position:0%
+correspond to perhaps two queens being
+placed on the 8x8 board already
+
+ align:start position:0%
+placed on the 8x8 board already
+ 
+
+ align:start position:0%
+placed on the 8x8 board already
+I does not correspond to a solution
+
+ align:start position:0%
+I does not correspond to a solution
+ 
+
+ align:start position:0%
+I does not correspond to a solution
+because the two queens conflict with
+
+ align:start position:0%
+because the two queens conflict with
+ 
+
+ align:start position:0%
+because the two queens conflict with
+each other and you can then shrink this
+
+ align:start position:0%
+each other and you can then shrink this
+ 
+
+ align:start position:0%
+each other and you can then shrink this
+eight raise to 8 substantially so that's
+
+ align:start position:0%
+eight raise to 8 substantially so that's
+ 
+
+ align:start position:0%
+eight raise to 8 substantially so that's
+exactly the methodology that we're going
+
+ align:start position:0%
+exactly the methodology that we're going
+ 
+
+ align:start position:0%
+exactly the methodology that we're going
+to follow here in trying to take our
+
+ align:start position:0%
+to follow here in trying to take our
+ 
+
+ align:start position:0%
+to follow here in trying to take our
+brute force solver which will work and
+
+ align:start position:0%
+brute force solver which will work and
+ 
+
+ align:start position:0%
+brute force solver which will work and
+you know given enough time on arbitrary
+
+ align:start position:0%
+you know given enough time on arbitrary
+ 
+
+ align:start position:0%
+you know given enough time on arbitrary
+Sudoku puzzles but
+
+ align:start position:0%
+Sudoku puzzles but
+ 
+
+ align:start position:0%
+Sudoku puzzles but
+may not want to wait that long and we're
+
+ align:start position:0%
+may not want to wait that long and we're
+ 
+
+ align:start position:0%
+may not want to wait that long and we're
+gonna take this strategy of pruning the
+
+ align:start position:0%
+gonna take this strategy of pruning the
+ 
+
+ align:start position:0%
+gonna take this strategy of pruning the
+search to try and improve the solve
+
+ align:start position:0%
+search to try and improve the solve
+ 
+
+ align:start position:0%
+search to try and improve the solve
+world and one last thing before I get
+
+ align:start position:0%
+world and one last thing before I get
+ 
+
+ align:start position:0%
+world and one last thing before I get
+started on the rules of Sudoku I'm we're
+
+ align:start position:0%
+started on the rules of Sudoku I'm we're
+ 
+
+ align:start position:0%
+started on the rules of Sudoku I'm we're
+going to have to have a way of measuring
+
+ align:start position:0%
+going to have to have a way of measuring
+ 
+
+ align:start position:0%
+going to have to have a way of measuring
+performance just like we can measure a
+
+ align:start position:0%
+performance just like we can measure a
+ 
+
+ align:start position:0%
+performance just like we can measure a
+trace to 8 or 4 raise to 4 or what have
+
+ align:start position:0%
+trace to 8 or 4 raise to 4 or what have
+ 
+
+ align:start position:0%
+trace to 8 or 4 raise to 4 or what have
+you we want to have a way of measuring
+
+ align:start position:0%
+you we want to have a way of measuring
+ 
+
+ align:start position:0%
+you we want to have a way of measuring
+outside of the particular machine that's
+
+ align:start position:0%
+outside of the particular machine that's
+ 
+
+ align:start position:0%
+outside of the particular machine that's
+being used we could obviously measure
+
+ align:start position:0%
+being used we could obviously measure
+ 
+
+ align:start position:0%
+being used we could obviously measure
+real time in terms of seconds but that's
+
+ align:start position:0%
+real time in terms of seconds but that's
+ 
+
+ align:start position:0%
+real time in terms of seconds but that's
+not as precise I you want to measure
+
+ align:start position:0%
+not as precise I you want to measure
+ 
+
+ align:start position:0%
+not as precise I you want to measure
+more precisely what the number of
+
+ align:start position:0%
+more precisely what the number of
+ 
+
+ align:start position:0%
+more precisely what the number of
+combinations are and so we could
+
+ align:start position:0%
+combinations are and so we could
+ 
+
+ align:start position:0%
+combinations are and so we could
+certainly instrument our code with
+
+ align:start position:0%
+certainly instrument our code with
+ 
+
+ align:start position:0%
+certainly instrument our code with
+appropriate counters that will allow us
+
+ align:start position:0%
+appropriate counters that will allow us
+ 
+
+ align:start position:0%
+appropriate counters that will allow us
+to measure this performance and so then
+
+ align:start position:0%
+to measure this performance and so then
+ 
+
+ align:start position:0%
+to measure this performance and so then
+it won't matter if our code runs on a
+
+ align:start position:0%
+it won't matter if our code runs on a
+ 
+
+ align:start position:0%
+it won't matter if our code runs on a
+fast machine or a slow machine if we can
+
+ align:start position:0%
+fast machine or a slow machine if we can
+ 
+
+ align:start position:0%
+fast machine or a slow machine if we can
+compare it with another piece of code or
+
+ align:start position:0%
+compare it with another piece of code or
+ 
+
+ align:start position:0%
+compare it with another piece of code or
+another variant of the code and say oh
+
+ align:start position:0%
+another variant of the code and say oh
+ 
+
+ align:start position:0%
+another variant of the code and say oh
+this new variant is slower or the new
+
+ align:start position:0%
+this new variant is slower or the new
+ 
+
+ align:start position:0%
+this new variant is slower or the new
+variant is faster according to this
+
+ align:start position:0%
+variant is faster according to this
+ 
+
+ align:start position:0%
+variant is faster according to this
+metric all right so without further ado
+
+ align:start position:0%
+metric all right so without further ado
+ 
+
+ align:start position:0%
+metric all right so without further ado
+let's dive into Sudoku how many of you
+
+ align:start position:0%
+let's dive into Sudoku how many of you
+ 
+
+ align:start position:0%
+let's dive into Sudoku how many of you
+have never seen Sudoku never played
+
+ align:start position:0%
+have never seen Sudoku never played
+ 
+
+ align:start position:0%
+have never seen Sudoku never played
+Sudoku all right so that's fine it's
+
+ align:start position:0%
+Sudoku all right so that's fine it's
+ 
+
+ align:start position:0%
+Sudoku all right so that's fine it's
+only going to take me about 30 seconds
+
+ align:start position:0%
+only going to take me about 30 seconds
+ 
+
+ align:start position:0%
+only going to take me about 30 seconds
+to explain what the rules of Sudoku are
+
+ align:start position:0%
+to explain what the rules of Sudoku are
+ 
+
+ align:start position:0%
+to explain what the rules of Sudoku are
+and then we can dive into trying to at
+
+ align:start position:0%
+and then we can dive into trying to at
+ 
+
+ align:start position:0%
+and then we can dive into trying to at
+least partially solve this puzzle
+
+ align:start position:0%
+least partially solve this puzzle
+ 
+
+ align:start position:0%
+least partially solve this puzzle
+III do not want to completely solve the
+
+ align:start position:0%
+III do not want to completely solve the
+ 
+
+ align:start position:0%
+III do not want to completely solve the
+puzzle because as I said you know I'm
+
+ align:start position:0%
+puzzle because as I said you know I'm
+ 
+
+ align:start position:0%
+puzzle because as I said you know I'm
+it's either too simple or it's too hard
+
+ align:start position:0%
+it's either too simple or it's too hard
+ 
+
+ align:start position:0%
+it's either too simple or it's too hard
+and I'd rather write computer programs
+
+ align:start position:0%
+and I'd rather write computer programs
+ 
+
+ align:start position:0%
+and I'd rather write computer programs
+and so so the rules of Sudoku are simple
+
+ align:start position:0%
+and so so the rules of Sudoku are simple
+ 
+
+ align:start position:0%
+and so so the rules of Sudoku are simple
+um so this is that classic Sudoku and
+
+ align:start position:0%
+um so this is that classic Sudoku and
+ 
+
+ align:start position:0%
+um so this is that classic Sudoku and
+it's 9 by 9
+
+ align:start position:0%
+it's 9 by 9
+ 
+
+ align:start position:0%
+it's 9 by 9
+there's many variants of Sudoku in fact
+
+ align:start position:0%
+there's many variants of Sudoku in fact
+ 
+
+ align:start position:0%
+there's many variants of Sudoku in fact
+a couple of the exercises talk about two
+
+ align:start position:0%
+a couple of the exercises talk about two
+ 
+
+ align:start position:0%
+a couple of the exercises talk about two
+variants diagonal Sudoku and odd-even
+
+ align:start position:0%
+variants diagonal Sudoku and odd-even
+ 
+
+ align:start position:0%
+variants diagonal Sudoku and odd-even
+Sudoku I think there's probably odd
+
+ align:start position:0%
+Sudoku I think there's probably odd
+ 
+
+ align:start position:0%
+Sudoku I think there's probably odd
+Sudokus as well that add even more
+
+ align:start position:0%
+Sudokus as well that add even more
+ 
+
+ align:start position:0%
+Sudokus as well that add even more
+constraints to the basic constraints of
+
+ align:start position:0%
+constraints to the basic constraints of
+ 
+
+ align:start position:0%
+constraints to the basic constraints of
+Sudoku that I'm going to write up here
+
+ align:start position:0%
+Sudoku that I'm going to write up here
+ 
+
+ align:start position:0%
+Sudoku that I'm going to write up here
+and this is 9 by 9 Sudoku and the
+
+ align:start position:0%
+and this is 9 by 9 Sudoku and the
+ 
+
+ align:start position:0%
+and this is 9 by 9 Sudoku and the
+numbers are 1 through 9
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the rules are simple each row has
+
+ align:start position:0%
+and the rules are simple each row has
+ 
+
+ align:start position:0%
+and the rules are simple each row has
+all the numbers which means that no
+
+ align:start position:0%
+all the numbers which means that no
+ 
+
+ align:start position:0%
+all the numbers which means that no
+numbers could be repeated because this
+
+ align:start position:0%
+numbers could be repeated because this
+ 
+
+ align:start position:0%
+numbers could be repeated because this
+there's nine columns and nine rows so
+
+ align:start position:0%
+there's nine columns and nine rows so
+ 
+
+ align:start position:0%
+there's nine columns and nine rows so
+there's nine numbers on each row each
+
+ align:start position:0%
+there's nine numbers on each row each
+ 
+
+ align:start position:0%
+there's nine numbers on each row each
+column has all the numbers same thing so
+
+ align:start position:0%
+column has all the numbers same thing so
+ 
+
+ align:start position:0%
+column has all the numbers same thing so
+there's nine rows and nine columns and
+
+ align:start position:0%
+there's nine rows and nine columns and
+ 
+
+ align:start position:0%
+there's nine rows and nine columns and
+then each sector which is at three by
+
+ align:start position:0%
+then each sector which is at three by
+ 
+
+ align:start position:0%
+then each sector which is at three by
+three grid and so that's why I have
+
+ align:start position:0%
+three grid and so that's why I have
+ 
+
+ align:start position:0%
+three grid and so that's why I have
+these overhangs here corresponding to
+
+ align:start position:0%
+these overhangs here corresponding to
+ 
+
+ align:start position:0%
+these overhangs here corresponding to
+pointing out what the nine sectors are
+
+ align:start position:0%
+pointing out what the nine sectors are
+ 
+
+ align:start position:0%
+pointing out what the nine sectors are
+in Sudoku so this is a sector that's a
+
+ align:start position:0%
+in Sudoku so this is a sector that's a
+ 
+
+ align:start position:0%
+in Sudoku so this is a sector that's a
+sector this middle one which is
+
+ align:start position:0%
+sector this middle one which is
+ 
+
+ align:start position:0%
+sector this middle one which is
+completely blank right now is a sector
+
+ align:start position:0%
+completely blank right now is a sector
+ 
+
+ align:start position:0%
+completely blank right now is a sector
+etc so each sector has all the numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can grow the size of the puzzle it
+
+ align:start position:0%
+you can grow the size of the puzzle it
+ 
+
+ align:start position:0%
+you can grow the size of the puzzle it
+gets more difficult you could add more
+
+ align:start position:0%
+gets more difficult you could add more
+ 
+
+ align:start position:0%
+gets more difficult you could add more
+constraints as I mentioned diagonal
+
+ align:start position:0%
+constraints as I mentioned diagonal
+ 
+
+ align:start position:0%
+constraints as I mentioned diagonal
+Sudoku might say something like both of
+
+ align:start position:0%
+Sudoku might say something like both of
+ 
+
+ align:start position:0%
+Sudoku might say something like both of
+the diagonals the large diagonals the
+
+ align:start position:0%
+the diagonals the large diagonals the
+ 
+
+ align:start position:0%
+the diagonals the large diagonals the
+full-sized diagonals I have all nine
+
+ align:start position:0%
+full-sized diagonals I have all nine
+ 
+
+ align:start position:0%
+full-sized diagonals I have all nine
+numbers on them etc so that makes the
+
+ align:start position:0%
+numbers on them etc so that makes the
+ 
+
+ align:start position:0%
+numbers on them etc so that makes the
+puzzle different you may have a solution
+
+ align:start position:0%
+puzzle different you may have a solution
+ 
+
+ align:start position:0%
+puzzle different you may have a solution
+to the nine by nine original Sudoku
+
+ align:start position:0%
+to the nine by nine original Sudoku
+ 
+
+ align:start position:0%
+to the nine by nine original Sudoku
+puzzle but it may not be a solution to
+
+ align:start position:0%
+puzzle but it may not be a solution to
+ 
+
+ align:start position:0%
+puzzle but it may not be a solution to
+the diagonal a puzzle obviously the
+
+ align:start position:0%
+the diagonal a puzzle obviously the
+ 
+
+ align:start position:0%
+the diagonal a puzzle obviously the
+other way round works because the raggle
+
+ align:start position:0%
+other way round works because the raggle
+ 
+
+ align:start position:0%
+other way round works because the raggle
+puzzle only has more constraints and so
+
+ align:start position:0%
+puzzle only has more constraints and so
+ 
+
+ align:start position:0%
+puzzle only has more constraints and so
+what we do here is try and use
+
+ align:start position:0%
+what we do here is try and use
+ 
+
+ align:start position:0%
+what we do here is try and use
+implications right so we have these
+
+ align:start position:0%
+implications right so we have these
+ 
+
+ align:start position:0%
+implications right so we have these
+rules and that will first forget about
+
+ align:start position:0%
+rules and that will first forget about
+ 
+
+ align:start position:0%
+rules and that will first forget about
+computer programs and try and solve this
+
+ align:start position:0%
+computer programs and try and solve this
+ 
+
+ align:start position:0%
+computer programs and try and solve this
+by the way people do then they just have
+
+ align:start position:0%
+by the way people do then they just have
+ 
+
+ align:start position:0%
+by the way people do then they just have
+the paper and pencil and and they have a
+
+ align:start position:0%
+the paper and pencil and and they have a
+ 
+
+ align:start position:0%
+the paper and pencil and and they have a
+puzzle in front of them and they try and
+
+ align:start position:0%
+puzzle in front of them and they try and
+ 
+
+ align:start position:0%
+puzzle in front of them and they try and
+use these rules to discover empty
+
+ align:start position:0%
+use these rules to discover empty
+ 
+
+ align:start position:0%
+use these rules to discover empty
+positions and
+
+ align:start position:0%
+positions and
+ 
+
+ align:start position:0%
+positions and
+it's kind of hard to do anything with
+
+ align:start position:0%
+it's kind of hard to do anything with
+ 
+
+ align:start position:0%
+it's kind of hard to do anything with
+this sector here I'm you could use the
+
+ align:start position:0%
+this sector here I'm you could use the
+ 
+
+ align:start position:0%
+this sector here I'm you could use the
+row and column constraints obviously
+
+ align:start position:0%
+row and column constraints obviously
+ 
+
+ align:start position:0%
+row and column constraints obviously
+even for this sector because you have
+
+ align:start position:0%
+even for this sector because you have
+ 
+
+ align:start position:0%
+even for this sector because you have
+makan strains on these three based on
+
+ align:start position:0%
+makan strains on these three based on
+ 
+
+ align:start position:0%
+makan strains on these three based on
+the fact that you have nine and seven
+
+ align:start position:0%
+the fact that you have nine and seven
+ 
+
+ align:start position:0%
+the fact that you have nine and seven
+and one and six on this row etc but
+
+ align:start position:0%
+and one and six on this row etc but
+ 
+
+ align:start position:0%
+and one and six on this row etc but
+usually you go with sectors that have a
+
+ align:start position:0%
+usually you go with sectors that have a
+ 
+
+ align:start position:0%
+usually you go with sectors that have a
+few numbers in them you go with rows
+
+ align:start position:0%
+few numbers in them you go with rows
+ 
+
+ align:start position:0%
+few numbers in them you go with rows
+that have a few numbers in them and you
+
+ align:start position:0%
+that have a few numbers in them and you
+ 
+
+ align:start position:0%
+that have a few numbers in them and you
+go with columns that have a few numbers
+
+ align:start position:0%
+go with columns that have a few numbers
+ 
+
+ align:start position:0%
+go with columns that have a few numbers
+in them and then you can try and shrink
+
+ align:start position:0%
+in them and then you can try and shrink
+ 
+
+ align:start position:0%
+in them and then you can try and shrink
+the possibilities right so I just
+
+ align:start position:0%
+the possibilities right so I just
+ 
+
+ align:start position:0%
+the possibilities right so I just
+because I don't want to go overboard
+
+ align:start position:0%
+because I don't want to go overboard
+ 
+
+ align:start position:0%
+because I don't want to go overboard
+with respect to looking all over the
+
+ align:start position:0%
+with respect to looking all over the
+ 
+
+ align:start position:0%
+with respect to looking all over the
+puzzle let's focus in on on eight the
+
+ align:start position:0%
+puzzle let's focus in on on eight the
+ 
+
+ align:start position:0%
+puzzle let's focus in on on eight the
+number eight and one of you tell me if I
+
+ align:start position:0%
+number eight and one of you tell me if I
+ 
+
+ align:start position:0%
+number eight and one of you tell me if I
+can imply something based on the
+
+ align:start position:0%
+can imply something based on the
+ 
+
+ align:start position:0%
+can imply something based on the
+locations of eight on the top third of
+
+ align:start position:0%
+locations of eight on the top third of
+ 
+
+ align:start position:0%
+locations of eight on the top third of
+this puzzle right yeah go ahead top
+
+ align:start position:0%
+this puzzle right yeah go ahead top
+ 
+
+ align:start position:0%
+this puzzle right yeah go ahead top
+middle square what's your name
+
+ align:start position:0%
+middle square what's your name
+ 
+
+ align:start position:0%
+middle square what's your name
+kai so Kai says top middle square should
+
+ align:start position:0%
+kai so Kai says top middle square should
+ 
+
+ align:start position:0%
+kai so Kai says top middle square should
+be an eight right here right at the top
+
+ align:start position:0%
+be an eight right here right at the top
+ 
+
+ align:start position:0%
+be an eight right here right at the top
+okay yeah that clearly can be an eight
+
+ align:start position:0%
+okay yeah that clearly can be an eight
+ 
+
+ align:start position:0%
+okay yeah that clearly can be an eight
+because this is an eight here but good
+
+ align:start position:0%
+because this is an eight here but good
+ 
+
+ align:start position:0%
+because this is an eight here but good
+so so this this the claim as this is an
+
+ align:start position:0%
+so so this this the claim as this is an
+ 
+
+ align:start position:0%
+so so this this the claim as this is an
+eight and kai how did you figure that
+
+ align:start position:0%
+eight and kai how did you figure that
+ 
+
+ align:start position:0%
+eight and kai how did you figure that
+out it can't be here because of this
+
+ align:start position:0%
+out it can't be here because of this
+ 
+
+ align:start position:0%
+out it can't be here because of this
+eight it can be here because of this
+
+ align:start position:0%
+eight it can be here because of this
+ 
+
+ align:start position:0%
+eight it can be here because of this
+eight and you need to have an eight in
+
+ align:start position:0%
+eight and you need to have an eight in
+ 
+
+ align:start position:0%
+eight and you need to have an eight in
+here somewhere
+
+ align:start position:0%
+here somewhere
+ 
+
+ align:start position:0%
+here somewhere
+because it doesn't exist in this sector
+
+ align:start position:0%
+because it doesn't exist in this sector
+ 
+
+ align:start position:0%
+because it doesn't exist in this sector
+so that would imply that I need to put
+
+ align:start position:0%
+so that would imply that I need to put
+ 
+
+ align:start position:0%
+so that would imply that I need to put
+an eight up here okay so this is what's
+
+ align:start position:0%
+an eight up here okay so this is what's
+ 
+
+ align:start position:0%
+an eight up here okay so this is what's
+called a horizontal scan right the only
+
+ align:start position:0%
+called a horizontal scan right the only
+ 
+
+ align:start position:0%
+called a horizontal scan right the only
+thing that Qaeda here was scanned
+
+ align:start position:0%
+thing that Qaeda here was scanned
+ 
+
+ align:start position:0%
+thing that Qaeda here was scanned
+horizontally and you can imagine that so
+
+ align:start position:0%
+horizontally and you can imagine that so
+ 
+
+ align:start position:0%
+horizontally and you can imagine that so
+you do not a chi did not use in order to
+
+ align:start position:0%
+you do not a chi did not use in order to
+ 
+
+ align:start position:0%
+you do not a chi did not use in order to
+imply the eight and so this word
+
+ align:start position:0%
+imply the eight and so this word
+ 
+
+ align:start position:0%
+imply the eight and so this word
+implication imply is something that
+
+ align:start position:0%
+implication imply is something that
+ 
+
+ align:start position:0%
+implication imply is something that
+we're going to use in a more technical
+
+ align:start position:0%
+we're going to use in a more technical
+ 
+
+ align:start position:0%
+we're going to use in a more technical
+sense but as well when we write our code
+
+ align:start position:0%
+sense but as well when we write our code
+ 
+
+ align:start position:0%
+sense but as well when we write our code
+but an implication essentially says
+
+ align:start position:0%
+but an implication essentially says
+ 
+
+ align:start position:0%
+but an implication essentially says
+these rules imply the location of the
+
+ align:start position:0%
+these rules imply the location of the
+ 
+
+ align:start position:0%
+these rules imply the location of the
+eight right and a we didn't do a
+
+ align:start position:0%
+eight right and a we didn't do a
+ 
+
+ align:start position:0%
+eight right and a we didn't do a
+vertical scan we did not use the fact
+
+ align:start position:0%
+vertical scan we did not use the fact
+ 
+
+ align:start position:0%
+vertical scan we did not use the fact
+that in
+
+ align:start position:0%
+that in
+ 
+
+ align:start position:0%
+that in
+particular implication we did not use
+
+ align:start position:0%
+particular implication we did not use
+ 
+
+ align:start position:0%
+particular implication we did not use
+the fact that a column that needs to
+
+ align:start position:0%
+the fact that a column that needs to
+ 
+
+ align:start position:0%
+the fact that a column that needs to
+have all numbers on it and therefore all
+
+ align:start position:0%
+have all numbers on it and therefore all
+ 
+
+ align:start position:0%
+have all numbers on it and therefore all
+of the numbers on a column have to be
+
+ align:start position:0%
+of the numbers on a column have to be
+ 
+
+ align:start position:0%
+of the numbers on a column have to be
+unique all right take a look at take a
+
+ align:start position:0%
+unique all right take a look at take a
+ 
+
+ align:start position:0%
+unique all right take a look at take a
+look at this part here and let's look at
+
+ align:start position:0%
+look at this part here and let's look at
+ 
+
+ align:start position:0%
+look at this part here and let's look at
+let's look at one and try and use a more
+
+ align:start position:0%
+let's look at one and try and use a more
+ 
+
+ align:start position:0%
+let's look at one and try and use a more
+sophisticated form of implication
+
+ align:start position:0%
+sophisticated form of implication
+ 
+
+ align:start position:0%
+sophisticated form of implication
+corresponding to both horizontal and
+
+ align:start position:0%
+corresponding to both horizontal and
+ 
+
+ align:start position:0%
+corresponding to both horizontal and
+vertical scans to to imply the position
+
+ align:start position:0%
+vertical scans to to imply the position
+ 
+
+ align:start position:0%
+vertical scans to to imply the position
+of a one somewhere on the puzzle right
+
+ align:start position:0%
+of a one somewhere on the puzzle right
+ 
+
+ align:start position:0%
+of a one somewhere on the puzzle right
+can someone do that yeah back there okay
+
+ align:start position:0%
+can someone do that yeah back there okay
+ 
+
+ align:start position:0%
+can someone do that yeah back there okay
+so the one can't be here the one can't
+
+ align:start position:0%
+so the one can't be here the one can't
+ 
+
+ align:start position:0%
+so the one can't be here the one can't
+be here right and the one can't be here
+
+ align:start position:0%
+be here right and the one can't be here
+ 
+
+ align:start position:0%
+be here right and the one can't be here
+so it has to be over here right what's
+
+ align:start position:0%
+so it has to be over here right what's
+ 
+
+ align:start position:0%
+so it has to be over here right what's
+in it George
+
+ align:start position:0%
+in it George
+ 
+
+ align:start position:0%
+in it George
+so George says the one has to be here
+
+ align:start position:0%
+so George says the one has to be here
+ 
+
+ align:start position:0%
+so George says the one has to be here
+and he used both vertical scanning as
+
+ align:start position:0%
+and he used both vertical scanning as
+ 
+
+ align:start position:0%
+and he used both vertical scanning as
+well as horizontal scanning in order to
+
+ align:start position:0%
+well as horizontal scanning in order to
+ 
+
+ align:start position:0%
+well as horizontal scanning in order to
+imply the one so it's a little more
+
+ align:start position:0%
+imply the one so it's a little more
+ 
+
+ align:start position:0%
+imply the one so it's a little more
+sophisticated okay
+
+ align:start position:0%
+sophisticated okay
+ 
+
+ align:start position:0%
+sophisticated okay
+on top of that obviously sectors are
+
+ align:start position:0%
+on top of that obviously sectors are
+ 
+
+ align:start position:0%
+on top of that obviously sectors are
+going to give you some implications as
+
+ align:start position:0%
+going to give you some implications as
+ 
+
+ align:start position:0%
+going to give you some implications as
+well right and there's no end to this
+
+ align:start position:0%
+well right and there's no end to this
+ 
+
+ align:start position:0%
+well right and there's no end to this
+honestly there's combinations there's
+
+ align:start position:0%
+honestly there's combinations there's
+ 
+
+ align:start position:0%
+honestly there's combinations there's
+also a little bit of look ahead where
+
+ align:start position:0%
+also a little bit of look ahead where
+ 
+
+ align:start position:0%
+also a little bit of look ahead where
+the hardest puzzles are the ones where
+
+ align:start position:0%
+the hardest puzzles are the ones where
+ 
+
+ align:start position:0%
+the hardest puzzles are the ones where
+you run out of the eights and the ones
+
+ align:start position:0%
+you run out of the eights and the ones
+ 
+
+ align:start position:0%
+you run out of the eights and the ones
+in terms of the examples that we have
+
+ align:start position:0%
+in terms of the examples that we have
+ 
+
+ align:start position:0%
+in terms of the examples that we have
+here where we've just sort of implied
+
+ align:start position:0%
+here where we've just sort of implied
+ 
+
+ align:start position:0%
+here where we've just sort of implied
+without guessing
+
+ align:start position:0%
+without guessing
+ 
+
+ align:start position:0%
+without guessing
+we've implied the location of a number
+
+ align:start position:0%
+we've implied the location of a number
+ 
+
+ align:start position:0%
+we've implied the location of a number
+and then because of that our puzzle got
+
+ align:start position:0%
+and then because of that our puzzle got
+ 
+
+ align:start position:0%
+and then because of that our puzzle got
+smaller in the sense that there's fewer
+
+ align:start position:0%
+smaller in the sense that there's fewer
+ 
+
+ align:start position:0%
+smaller in the sense that there's fewer
+blank locations blank squares and then
+
+ align:start position:0%
+blank locations blank squares and then
+ 
+
+ align:start position:0%
+blank locations blank squares and then
+that helps us move forward right so the
+
+ align:start position:0%
+that helps us move forward right so the
+ 
+
+ align:start position:0%
+that helps us move forward right so the
+easy puzzles are the ones where fairly
+
+ align:start position:0%
+easy puzzles are the ones where fairly
+ 
+
+ align:start position:0%
+easy puzzles are the ones where fairly
+straightforward implications like the
+
+ align:start position:0%
+straightforward implications like the
+ 
+
+ align:start position:0%
+straightforward implications like the
+ones we did here always exist are easy
+
+ align:start position:0%
+ones we did here always exist are easy
+ 
+
+ align:start position:0%
+ones we did here always exist are easy
+to find you sometimes you have to search
+
+ align:start position:0%
+to find you sometimes you have to search
+ 
+
+ align:start position:0%
+to find you sometimes you have to search
+a little bit look at the top look at the
+
+ align:start position:0%
+a little bit look at the top look at the
+ 
+
+ align:start position:0%
+a little bit look at the top look at the
+power bottom look at the middle and and
+
+ align:start position:0%
+power bottom look at the middle and and
+ 
+
+ align:start position:0%
+power bottom look at the middle and and
+then you fill things in and because you
+
+ align:start position:0%
+then you fill things in and because you
+ 
+
+ align:start position:0%
+then you fill things in and because you
+filled things in something else now is
+
+ align:start position:0%
+filled things in something else now is
+ 
+
+ align:start position:0%
+filled things in something else now is
+in play right it becomes viable in terms
+
+ align:start position:0%
+in play right it becomes viable in terms
+ 
+
+ align:start position:0%
+in play right it becomes viable in terms
+of implication the fact that I put an
+
+ align:start position:0%
+of implication the fact that I put an
+ 
+
+ align:start position:0%
+of implication the fact that I put an
+aid in
+
+ align:start position:0%
+aid in
+ 
+
+ align:start position:0%
+aid in
+there I imply that the aid is now taken
+
+ align:start position:0%
+there I imply that the aid is now taken
+ 
+
+ align:start position:0%
+there I imply that the aid is now taken
+you know its location and so now
+
+ align:start position:0%
+you know its location and so now
+ 
+
+ align:start position:0%
+you know its location and so now
+obviously there's only four left here
+
+ align:start position:0%
+obviously there's only four left here
+ 
+
+ align:start position:0%
+obviously there's only four left here
+and the fact that it's an eight here
+
+ align:start position:0%
+and the fact that it's an eight here
+ 
+
+ align:start position:0%
+and the fact that it's an eight here
+implies that all of these can't have an
+
+ align:start position:0%
+implies that all of these can't have an
+ 
+
+ align:start position:0%
+implies that all of these can't have an
+eight in the these seven locations
+
+ align:start position:0%
+eight in the these seven locations
+ 
+
+ align:start position:0%
+eight in the these seven locations
+underneath can't have an eight in in
+
+ align:start position:0%
+underneath can't have an eight in in
+ 
+
+ align:start position:0%
+underneath can't have an eight in in
+them right because of their constraints
+
+ align:start position:0%
+them right because of their constraints
+ 
+
+ align:start position:0%
+them right because of their constraints
+so I'm this shrinking of possibilities
+
+ align:start position:0%
+so I'm this shrinking of possibilities
+ 
+
+ align:start position:0%
+so I'm this shrinking of possibilities
+it's something that a human does and you
+
+ align:start position:0%
+it's something that a human does and you
+ 
+
+ align:start position:0%
+it's something that a human does and you
+can kind of go through this process it's
+
+ align:start position:0%
+can kind of go through this process it's
+ 
+
+ align:start position:0%
+can kind of go through this process it's
+an iterative iterative process that you
+
+ align:start position:0%
+an iterative iterative process that you
+ 
+
+ align:start position:0%
+an iterative iterative process that you
+that you go through and you get stuck
+
+ align:start position:0%
+that you go through and you get stuck
+ 
+
+ align:start position:0%
+that you go through and you get stuck
+then you can't do an implication that
+
+ align:start position:0%
+then you can't do an implication that
+ 
+
+ align:start position:0%
+then you can't do an implication that
+gives you a number and some of the
+
+ align:start position:0%
+gives you a number and some of the
+ 
+
+ align:start position:0%
+gives you a number and some of the
+harder puzzles you have to you have a
+
+ align:start position:0%
+harder puzzles you have to you have a
+ 
+
+ align:start position:0%
+harder puzzles you have to you have a
+couple of choices and only one of them
+
+ align:start position:0%
+couple of choices and only one of them
+ 
+
+ align:start position:0%
+couple of choices and only one of them
+is going to be a correct one going
+
+ align:start position:0%
+is going to be a correct one going
+ 
+
+ align:start position:0%
+is going to be a correct one going
+forward but you don't know that at the
+
+ align:start position:0%
+forward but you don't know that at the
+ 
+
+ align:start position:0%
+forward but you don't know that at the
+moment at that moment so you don't have
+
+ align:start position:0%
+moment at that moment so you don't have
+ 
+
+ align:start position:0%
+moment at that moment so you don't have
+to can't guess and perhaps you put in an
+
+ align:start position:0%
+to can't guess and perhaps you put in an
+ 
+
+ align:start position:0%
+to can't guess and perhaps you put in an
+eight over here or Nate over there and
+
+ align:start position:0%
+eight over here or Nate over there and
+ 
+
+ align:start position:0%
+eight over here or Nate over there and
+then you say I'm gonna go with an eight
+
+ align:start position:0%
+then you say I'm gonna go with an eight
+ 
+
+ align:start position:0%
+then you say I'm gonna go with an eight
+over here and then you go a little bit
+
+ align:start position:0%
+over here and then you go a little bit
+ 
+
+ align:start position:0%
+over here and then you go a little bit
+further and then you realize wait a
+
+ align:start position:0%
+further and then you realize wait a
+ 
+
+ align:start position:0%
+further and then you realize wait a
+minute you know there's no way I can
+
+ align:start position:0%
+minute you know there's no way I can
+ 
+
+ align:start position:0%
+minute you know there's no way I can
+solve this puzzle because I need to put
+
+ align:start position:0%
+solve this puzzle because I need to put
+ 
+
+ align:start position:0%
+solve this puzzle because I need to put
+two sevens into the sector and then you
+
+ align:start position:0%
+two sevens into the sector and then you
+ 
+
+ align:start position:0%
+two sevens into the sector and then you
+go back and there's actually a bit of
+
+ align:start position:0%
+go back and there's actually a bit of
+ 
+
+ align:start position:0%
+go back and there's actually a bit of
+backtracking that happens at the wrong
+
+ align:start position:0%
+backtracking that happens at the wrong
+ 
+
+ align:start position:0%
+backtracking that happens at the wrong
+guess and you need to go backwards and
+
+ align:start position:0%
+guess and you need to go backwards and
+ 
+
+ align:start position:0%
+guess and you need to go backwards and
+it's very hard to do for us it's very
+
+ align:start position:0%
+it's very hard to do for us it's very
+ 
+
+ align:start position:0%
+it's very hard to do for us it's very
+hard to do for us with pencil and paper
+
+ align:start position:0%
+hard to do for us with pencil and paper
+ 
+
+ align:start position:0%
+hard to do for us with pencil and paper
+keeping things in our head or you know
+
+ align:start position:0%
+keeping things in our head or you know
+ 
+
+ align:start position:0%
+keeping things in our head or you know
+writing down notes on the side of the
+
+ align:start position:0%
+writing down notes on the side of the
+ 
+
+ align:start position:0%
+writing down notes on the side of the
+paper whereas it's very easy to do that
+
+ align:start position:0%
+paper whereas it's very easy to do that
+ 
+
+ align:start position:0%
+paper whereas it's very easy to do that
+for a computer program right and we kind
+
+ align:start position:0%
+for a computer program right and we kind
+ 
+
+ align:start position:0%
+for a computer program right and we kind
+of did that already in the in the eight
+
+ align:start position:0%
+of did that already in the in the eight
+ 
+
+ align:start position:0%
+of did that already in the in the eight
+Queens but we're gonna do that in a much
+
+ align:start position:0%
+Queens but we're gonna do that in a much
+ 
+
+ align:start position:0%
+Queens but we're gonna do that in a much
+more systematic way over here right so
+
+ align:start position:0%
+more systematic way over here right so
+ 
+
+ align:start position:0%
+more systematic way over here right so
+you kind of way these two ways of
+
+ align:start position:0%
+you kind of way these two ways of
+ 
+
+ align:start position:0%
+you kind of way these two ways of
+approaching this problem one of which is
+
+ align:start position:0%
+approaching this problem one of which is
+ 
+
+ align:start position:0%
+approaching this problem one of which is
+I'm just going to blast through the
+
+ align:start position:0%
+I'm just going to blast through the
+ 
+
+ align:start position:0%
+I'm just going to blast through the
+different combinations having a giant
+
+ align:start position:0%
+different combinations having a giant
+ 
+
+ align:start position:0%
+different combinations having a giant
+tree structure in my head where you know
+
+ align:start position:0%
+tree structure in my head where you know
+ 
+
+ align:start position:0%
+tree structure in my head where you know
+this this might imply that particular
+
+ align:start position:0%
+this this might imply that particular
+ 
+
+ align:start position:0%
+this this might imply that particular
+grid location a grid IJ equals 8
+
+ align:start position:0%
+grid location a grid IJ equals 8
+ 
+
+ align:start position:0%
+grid location a grid IJ equals 8
+this might imply that grid IJ equals 7
+
+ align:start position:0%
+this might imply that grid IJ equals 7
+ 
+
+ align:start position:0%
+this might imply that grid IJ equals 7
+and you know there's obviously a huge
+
+ align:start position:0%
+and you know there's obviously a huge
+ 
+
+ align:start position:0%
+and you know there's obviously a huge
+number of combinations corresponding to
+
+ align:start position:0%
+number of combinations corresponding to
+ 
+
+ align:start position:0%
+number of combinations corresponding to
+which of these squares that I pick and
+
+ align:start position:0%
+which of these squares that I pick and
+ 
+
+ align:start position:0%
+which of these squares that I pick and
+what value I assign to those squares and
+
+ align:start position:0%
+what value I assign to those squares and
+ 
+
+ align:start position:0%
+what value I assign to those squares and
+then once I do that there's another set
+
+ align:start position:0%
+then once I do that there's another set
+ 
+
+ align:start position:0%
+then once I do that there's another set
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+clothes on you very quickly and so if
+
+ align:start position:0%
+clothes on you very quickly and so if
+ 
+
+ align:start position:0%
+clothes on you very quickly and so if
+you just did this in a completely
+
+ align:start position:0%
+you just did this in a completely
+ 
+
+ align:start position:0%
+you just did this in a completely
+brutish way there's no way your program
+
+ align:start position:0%
+brutish way there's no way your program
+ 
+
+ align:start position:0%
+brutish way there's no way your program
+would ever end even on a simple puzzle
+
+ align:start position:0%
+would ever end even on a simple puzzle
+ 
+
+ align:start position:0%
+would ever end even on a simple puzzle
+but thanks to these rules it turns out a
+
+ align:start position:0%
+but thanks to these rules it turns out a
+ 
+
+ align:start position:0%
+but thanks to these rules it turns out a
+fairly straightforward program that's 20
+
+ align:start position:0%
+fairly straightforward program that's 20
+ 
+
+ align:start position:0%
+fairly straightforward program that's 20
+lines of code is going to solve most
+
+ align:start position:0%
+lines of code is going to solve most
+ 
+
+ align:start position:0%
+lines of code is going to solve most
+problems at least the ones that I've
+
+ align:start position:0%
+problems at least the ones that I've
+ 
+
+ align:start position:0%
+problems at least the ones that I've
+looked at in in a reasonable amount of
+
+ align:start position:0%
+looked at in in a reasonable amount of
+ 
+
+ align:start position:0%
+looked at in in a reasonable amount of
+time and and then you know it's just
+
+ align:start position:0%
+time and and then you know it's just
+ 
+
+ align:start position:0%
+time and and then you know it's just
+interesting from an algorithmic
+
+ align:start position:0%
+interesting from an algorithmic
+ 
+
+ align:start position:0%
+interesting from an algorithmic
+standpoint and a and an efficiency
+
+ align:start position:0%
+standpoint and a and an efficiency
+ 
+
+ align:start position:0%
+standpoint and a and an efficiency
+standpoint to look and see how we can
+
+ align:start position:0%
+standpoint to look and see how we can
+ 
+
+ align:start position:0%
+standpoint to look and see how we can
+take that fairly naive approach which
+
+ align:start position:0%
+take that fairly naive approach which
+ 
+
+ align:start position:0%
+take that fairly naive approach which
+does have some pruning but it's it's
+
+ align:start position:0%
+does have some pruning but it's it's
+ 
+
+ align:start position:0%
+does have some pruning but it's it's
+exhaustive and improve that all right so
+
+ align:start position:0%
+exhaustive and improve that all right so
+ 
+
+ align:start position:0%
+exhaustive and improve that all right so
+that's kind of where we're headed make
+
+ align:start position:0%
+that's kind of where we're headed make
+ 
+
+ align:start position:0%
+that's kind of where we're headed make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+any any questions about what we have so
+
+ align:start position:0%
+any any questions about what we have so
+ 
+
+ align:start position:0%
+any any questions about what we have so
+far all right so what we're going to do
+
+ align:start position:0%
+far all right so what we're going to do
+ 
+
+ align:start position:0%
+far all right so what we're going to do
+is go ahead and and and look at at code
+
+ align:start position:0%
+is go ahead and and and look at at code
+ 
+
+ align:start position:0%
+is go ahead and and and look at at code
+for Sudoku that it's of all you need to
+
+ align:start position:0%
+for Sudoku that it's of all you need to
+ 
+
+ align:start position:0%
+for Sudoku that it's of all you need to
+think about now for the next few minutes
+
+ align:start position:0%
+think about now for the next few minutes
+ 
+
+ align:start position:0%
+think about now for the next few minutes
+because we're going to move into
+
+ align:start position:0%
+because we're going to move into
+ 
+
+ align:start position:0%
+because we're going to move into
+exhaustive search mode and code things
+
+ align:start position:0%
+exhaustive search mode and code things
+ 
+
+ align:start position:0%
+exhaustive search mode and code things
+up in a computer is just those rules so
+
+ align:start position:0%
+up in a computer is just those rules so
+ 
+
+ align:start position:0%
+up in a computer is just those rules so
+you don't have to really think about
+
+ align:start position:0%
+you don't have to really think about
+ 
+
+ align:start position:0%
+you don't have to really think about
+horizontal scans and implications or
+
+ align:start position:0%
+horizontal scans and implications or
+ 
+
+ align:start position:0%
+horizontal scans and implications or
+vertical scans you know that's going to
+
+ align:start position:0%
+vertical scans you know that's going to
+ 
+
+ align:start position:0%
+vertical scans you know that's going to
+come a little bit later and we're going
+
+ align:start position:0%
+come a little bit later and we're going
+ 
+
+ align:start position:0%
+come a little bit later and we're going
+to bury that up as well but we're going
+
+ align:start position:0%
+to bury that up as well but we're going
+ 
+
+ align:start position:0%
+to bury that up as well but we're going
+to do kind of what we did for the
+
+ align:start position:0%
+to do kind of what we did for the
+ 
+
+ align:start position:0%
+to do kind of what we did for the
+n-queens problem which is set up
+
+ align:start position:0%
+n-queens problem which is set up
+ 
+
+ align:start position:0%
+n-queens problem which is set up
+recursive search that is going to
+
+ align:start position:0%
+recursive search that is going to
+ 
+
+ align:start position:0%
+recursive search that is going to
+explore all of these different
+
+ align:start position:0%
+explore all of these different
+ 
+
+ align:start position:0%
+explore all of these different
+possibilities and the equivalent of no
+
+ align:start position:0%
+possibilities and the equivalent of no
+ 
+
+ align:start position:0%
+possibilities and the equivalent of no
+conflicts for for the a queen so the N
+
+ align:start position:0%
+conflicts for for the a queen so the N
+ 
+
+ align:start position:0%
+conflicts for for the a queen so the N
+Queens problem which said there's no
+
+ align:start position:0%
+Queens problem which said there's no
+ 
+
+ align:start position:0%
+Queens problem which said there's no
+conflicts here I because none of the
+
+ align:start position:0%
+conflicts here I because none of the
+ 
+
+ align:start position:0%
+conflicts here I because none of the
+Queen's attack each other we're going to
+
+ align:start position:0%
+Queen's attack each other we're going to
+ 
+
+ align:start position:0%
+Queen's attack each other we're going to
+have something that essentially says
+
+ align:start position:0%
+have something that essentially says
+ 
+
+ align:start position:0%
+have something that essentially says
+this is valid so far none of the rules
+
+ align:start position:0%
+this is valid so far none of the rules
+ 
+
+ align:start position:0%
+this is valid so far none of the rules
+of Sudoku corresponding to these three
+
+ align:start position:0%
+of Sudoku corresponding to these three
+ 
+
+ align:start position:0%
+of Sudoku corresponding to these three
+rules that I have up on the board are
+
+ align:start position:0%
+rules that I have up on the board are
+ 
+
+ align:start position:0%
+rules that I have up on the board are
+going to be violated all right so let's
+
+ align:start position:0%
+going to be violated all right so let's
+ 
+
+ align:start position:0%
+going to be violated all right so let's
+take a look and so this structure
+
+ align:start position:0%
+take a look and so this structure
+ 
+
+ align:start position:0%
+take a look and so this structure
+hopefully given that we've done a n
+
+ align:start position:0%
+hopefully given that we've done a n
+ 
+
+ align:start position:0%
+hopefully given that we've done a n
+Queens I should be a little bit easier
+
+ align:start position:0%
+Queens I should be a little bit easier
+ 
+
+ align:start position:0%
+Queens I should be a little bit easier
+to understand so um
+
+ align:start position:0%
+to understand so um
+ 
+
+ align:start position:0%
+to understand so um
+when we did eight Queens or in Queens we
+
+ align:start position:0%
+when we did eight Queens or in Queens we
+ 
+
+ align:start position:0%
+when we did eight Queens or in Queens we
+decided to start column by column and we
+
+ align:start position:0%
+decided to start column by column and we
+ 
+
+ align:start position:0%
+decided to start column by column and we
+could have done row by row but we
+
+ align:start position:0%
+could have done row by row but we
+ 
+
+ align:start position:0%
+could have done row by row but we
+decided to start column by column and it
+
+ align:start position:0%
+decided to start column by column and it
+ 
+
+ align:start position:0%
+decided to start column by column and it
+was a fairly straightforward puzzle
+
+ align:start position:0%
+was a fairly straightforward puzzle
+ 
+
+ align:start position:0%
+was a fairly straightforward puzzle
+there's obviously no real change in an
+
+ align:start position:0%
+there's obviously no real change in an
+ 
+
+ align:start position:0%
+there's obviously no real change in an
+eight Queens puzzle I mean you're
+
+ align:start position:0%
+eight Queens puzzle I mean you're
+ 
+
+ align:start position:0%
+eight Queens puzzle I mean you're
+solving the same puzzle as I am but if I
+
+ align:start position:0%
+solving the same puzzle as I am but if I
+ 
+
+ align:start position:0%
+solving the same puzzle as I am but if I
+give you a pseudo puzzle there's more
+
+ align:start position:0%
+give you a pseudo puzzle there's more
+ 
+
+ align:start position:0%
+give you a pseudo puzzle there's more
+variety to it in the sense that
+
+ align:start position:0%
+variety to it in the sense that
+ 
+
+ align:start position:0%
+variety to it in the sense that
+depending on what I fill up the hard
+
+ align:start position:0%
+depending on what I fill up the hard
+ 
+
+ align:start position:0%
+depending on what I fill up the hard
+puzzles are the ones that are kind of
+
+ align:start position:0%
+puzzles are the ones that are kind of
+ 
+
+ align:start position:0%
+puzzles are the ones that are kind of
+intermediate in the sense of they're not
+
+ align:start position:0%
+intermediate in the sense of they're not
+ 
+
+ align:start position:0%
+intermediate in the sense of they're not
+obviously fully filled and they're not
+
+ align:start position:0%
+obviously fully filled and they're not
+ 
+
+ align:start position:0%
+obviously fully filled and they're not
+empty right if it's completely empty
+
+ align:start position:0%
+empty right if it's completely empty
+ 
+
+ align:start position:0%
+empty right if it's completely empty
+then it's it's trivial to solve a Sudoku
+
+ align:start position:0%
+then it's it's trivial to solve a Sudoku
+ 
+
+ align:start position:0%
+then it's it's trivial to solve a Sudoku
+puzzle you can take any solution to a
+
+ align:start position:0%
+puzzle you can take any solution to a
+ 
+
+ align:start position:0%
+puzzle you can take any solution to a
+Sudoku puzzle and present it as a
+
+ align:start position:0%
+Sudoku puzzle and present it as a
+ 
+
+ align:start position:0%
+Sudoku puzzle and present it as a
+solution to the empty puzzle and then if
+
+ align:start position:0%
+solution to the empty puzzle and then if
+ 
+
+ align:start position:0%
+solution to the empty puzzle and then if
+it's if it's everything is is full
+
+ align:start position:0%
+it's if it's everything is is full
+ 
+
+ align:start position:0%
+it's if it's everything is is full
+except for two things I mean it's kind
+
+ align:start position:0%
+except for two things I mean it's kind
+ 
+
+ align:start position:0%
+except for two things I mean it's kind
+of obvious what those two things are
+
+ align:start position:0%
+of obvious what those two things are
+ 
+
+ align:start position:0%
+of obvious what those two things are
+assuming that the puzzle had a valid
+
+ align:start position:0%
+assuming that the puzzle had a valid
+ 
+
+ align:start position:0%
+assuming that the puzzle had a valid
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+so really it's it's puzzles like this
+
+ align:start position:0%
+so really it's it's puzzles like this
+ 
+
+ align:start position:0%
+so really it's it's puzzles like this
+where maybe a third are full that that
+
+ align:start position:0%
+where maybe a third are full that that
+ 
+
+ align:start position:0%
+where maybe a third are full that that
+that are more difficult right and it's
+
+ align:start position:0%
+that are more difficult right and it's
+ 
+
+ align:start position:0%
+that are more difficult right and it's
+kind of a separate school a little
+
+ align:start position:0%
+kind of a separate school a little
+ 
+
+ align:start position:0%
+kind of a separate school a little
+community that designs puzzles and tries
+
+ align:start position:0%
+community that designs puzzles and tries
+ 
+
+ align:start position:0%
+community that designs puzzles and tries
+to create hard puzzles and they try and
+
+ align:start position:0%
+to create hard puzzles and they try and
+ 
+
+ align:start position:0%
+to create hard puzzles and they try and
+make the humans hard
+
+ align:start position:0%
+make the humans hard
+ 
+
+ align:start position:0%
+make the humans hard
+I'm sorry humans problem harder by
+
+ align:start position:0%
+I'm sorry humans problem harder by
+ 
+
+ align:start position:0%
+I'm sorry humans problem harder by
+making this requirement of look-ahead
+
+ align:start position:0%
+making this requirement of look-ahead
+ 
+
+ align:start position:0%
+making this requirement of look-ahead
+like I mentioned right so good so let's
+
+ align:start position:0%
+like I mentioned right so good so let's
+ 
+
+ align:start position:0%
+like I mentioned right so good so let's
+take a look at the code here um so what
+
+ align:start position:0%
+take a look at the code here um so what
+ 
+
+ align:start position:0%
+take a look at the code here um so what
+I want to do here and the first part
+
+ align:start position:0%
+I want to do here and the first part
+ 
+
+ align:start position:0%
+I want to do here and the first part
+here is it is said that as I said we
+
+ align:start position:0%
+here is it is said that as I said we
+ 
+
+ align:start position:0%
+here is it is said that as I said we
+went column by column in the case of n
+
+ align:start position:0%
+went column by column in the case of n
+ 
+
+ align:start position:0%
+went column by column in the case of n
+queens and the question is where do I
+
+ align:start position:0%
+queens and the question is where do I
+ 
+
+ align:start position:0%
+queens and the question is where do I
+start I want to do something in a fairly
+
+ align:start position:0%
+start I want to do something in a fairly
+ 
+
+ align:start position:0%
+start I want to do something in a fairly
+naive way and what I'm going to do is
+
+ align:start position:0%
+naive way and what I'm going to do is
+ 
+
+ align:start position:0%
+naive way and what I'm going to do is
+I'm going to do some sort of scan you
+
+ align:start position:0%
+I'm going to do some sort of scan you
+ 
+
+ align:start position:0%
+I'm going to do some sort of scan you
+know I'm gonna scan like that and I'm
+
+ align:start position:0%
+know I'm gonna scan like that and I'm
+ 
+
+ align:start position:0%
+know I'm gonna scan like that and I'm
+going to find as I do the scan I'm going
+
+ align:start position:0%
+going to find as I do the scan I'm going
+ 
+
+ align:start position:0%
+going to find as I do the scan I'm going
+to find the the next empty grid location
+
+ align:start position:0%
+to find the the next empty grid location
+ 
+
+ align:start position:0%
+to find the the next empty grid location
+and I'm gonna say that is going to be
+
+ align:start position:0%
+and I'm gonna say that is going to be
+ 
+
+ align:start position:0%
+and I'm gonna say that is going to be
+something that I'm going to try and fill
+
+ align:start position:0%
+something that I'm going to try and fill
+ 
+
+ align:start position:0%
+something that I'm going to try and fill
+in okay so it's not going to be I
+
+ align:start position:0%
+in okay so it's not going to be I
+ 
+
+ align:start position:0%
+in okay so it's not going to be I
+discovered this H in the in the it was
+
+ align:start position:0%
+discovered this H in the in the it was
+ 
+
+ align:start position:0%
+discovered this H in the in the it was
+if you count in terms of the empty
+
+ align:start position:0%
+if you count in terms of the empty
+ 
+
+ align:start position:0%
+if you count in terms of the empty
+locations if I went this way it was the
+
+ align:start position:0%
+locations if I went this way it was the
+ 
+
+ align:start position:0%
+locations if I went this way it was the
+fourth empty location and decided to
+
+ align:start position:0%
+fourth empty location and decided to
+ 
+
+ align:start position:0%
+fourth empty location and decided to
+fill that up but here I'm just in this
+
+ align:start position:0%
+fill that up but here I'm just in this
+ 
+
+ align:start position:0%
+fill that up but here I'm just in this
+code I'm gonna try one two three four
+
+ align:start position:0%
+code I'm gonna try one two three four
+ 
+
+ align:start position:0%
+code I'm gonna try one two three four
+five six seven eight nine here and the
+
+ align:start position:0%
+five six seven eight nine here and the
+ 
+
+ align:start position:0%
+five six seven eight nine here and the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+a part of the code here that says what
+
+ align:start position:0%
+a part of the code here that says what
+ 
+
+ align:start position:0%
+a part of the code here that says what
+is the name of this procedure it says
+
+ align:start position:0%
+is the name of this procedure it says
+ 
+
+ align:start position:0%
+is the name of this procedure it says
+fine next cell to fill you know but it
+
+ align:start position:0%
+fine next cell to fill you know but it
+ 
+
+ align:start position:0%
+fine next cell to fill you know but it
+means what it's name is find the next
+
+ align:start position:0%
+means what it's name is find the next
+ 
+
+ align:start position:0%
+means what it's name is find the next
+cell find the next weird location to
+
+ align:start position:0%
+cell find the next weird location to
+ 
+
+ align:start position:0%
+cell find the next weird location to
+fill and it simply goes for X and range
+
+ align:start position:0%
+fill and it simply goes for X and range
+ 
+
+ align:start position:0%
+fill and it simply goes for X and range
+0 through 9 for Y and range 0 through 9
+
+ align:start position:0%
+0 through 9 for Y and range 0 through 9
+ 
+
+ align:start position:0%
+0 through 9 for Y and range 0 through 9
+I'm assuming that since 0 is not a valid
+
+ align:start position:0%
+I'm assuming that since 0 is not a valid
+ 
+
+ align:start position:0%
+I'm assuming that since 0 is not a valid
+entry here I could use 0 to signify
+
+ align:start position:0%
+entry here I could use 0 to signify
+ 
+
+ align:start position:0%
+entry here I could use 0 to signify
+empty ok it's only 1 through 9 so 0 can
+
+ align:start position:0%
+empty ok it's only 1 through 9 so 0 can
+ 
+
+ align:start position:0%
+empty ok it's only 1 through 9 so 0 can
+signify empty and this just returns x
+
+ align:start position:0%
+signify empty and this just returns x
+ 
+
+ align:start position:0%
+signify empty and this just returns x
+and y corresponding to the the first
+
+ align:start position:0%
+and y corresponding to the the first
+ 
+
+ align:start position:0%
+and y corresponding to the the first
+empty location so in this case it would
+
+ align:start position:0%
+empty location so in this case it would
+ 
+
+ align:start position:0%
+empty location so in this case it would
+just return 0 0 ok and then if this were
+
+ align:start position:0%
+just return 0 0 ok and then if this were
+ 
+
+ align:start position:0%
+just return 0 0 ok and then if this were
+full then it would go obviously it
+
+ align:start position:0%
+full then it would go obviously it
+ 
+
+ align:start position:0%
+full then it would go obviously it
+exchanges and when exchanges you're
+
+ align:start position:0%
+exchanges and when exchanges you're
+ 
+
+ align:start position:0%
+exchanges and when exchanges you're
+going over to the to the right and so
+
+ align:start position:0%
+going over to the to the right and so
+ 
+
+ align:start position:0%
+going over to the to the right and so
+you would get a 1 1 0 back if this were
+
+ align:start position:0%
+you would get a 1 1 0 back if this were
+ 
+
+ align:start position:0%
+you would get a 1 1 0 back if this were
+filled the next time around I'd get this
+
+ align:start position:0%
+filled the next time around I'd get this
+ 
+
+ align:start position:0%
+filled the next time around I'd get this
+grid location etc right it doesn't
+
+ align:start position:0%
+grid location etc right it doesn't
+ 
+
+ align:start position:0%
+grid location etc right it doesn't
+matter just like I could go column by
+
+ align:start position:0%
+matter just like I could go column by
+ 
+
+ align:start position:0%
+matter just like I could go column by
+column by row by row as long as I have a
+
+ align:start position:0%
+column by row by row as long as I have a
+ 
+
+ align:start position:0%
+column by row by row as long as I have a
+deterministic way of discovering the the
+
+ align:start position:0%
+deterministic way of discovering the the
+ 
+
+ align:start position:0%
+deterministic way of discovering the the
+empty location and usually you want to
+
+ align:start position:0%
+empty location and usually you want to
+ 
+
+ align:start position:0%
+empty location and usually you want to
+have it the same way of discovering the
+
+ align:start position:0%
+have it the same way of discovering the
+ 
+
+ align:start position:0%
+have it the same way of discovering the
+empty location but even that is not a
+
+ align:start position:0%
+empty location but even that is not a
+ 
+
+ align:start position:0%
+empty location but even that is not a
+requirement as long as there's an empty
+
+ align:start position:0%
+requirement as long as there's an empty
+ 
+
+ align:start position:0%
+requirement as long as there's an empty
+location and you're fine next cell to
+
+ align:start position:0%
+location and you're fine next cell to
+ 
+
+ align:start position:0%
+location and you're fine next cell to
+fill finds that empty location and
+
+ align:start position:0%
+fill finds that empty location and
+ 
+
+ align:start position:0%
+fill finds that empty location and
+returns it to you you're good and this
+
+ align:start position:0%
+returns it to you you're good and this
+ 
+
+ align:start position:0%
+returns it to you you're good and this
+the rest of our code is going to work
+
+ align:start position:0%
+the rest of our code is going to work
+ 
+
+ align:start position:0%
+the rest of our code is going to work
+right but no reason to get more
+
+ align:start position:0%
+right but no reason to get more
+ 
+
+ align:start position:0%
+right but no reason to get more
+complicated than what I have up there
+
+ align:start position:0%
+complicated than what I have up there
+ 
+
+ align:start position:0%
+complicated than what I have up there
+all right so fine next cell to fill make
+
+ align:start position:0%
+all right so fine next cell to fill make
+ 
+
+ align:start position:0%
+all right so fine next cell to fill make
+sense right good with that all right
+
+ align:start position:0%
+sense right good with that all right
+ 
+
+ align:start position:0%
+sense right good with that all right
+and the generally with exhaustive search
+
+ align:start position:0%
+and the generally with exhaustive search
+ 
+
+ align:start position:0%
+and the generally with exhaustive search
+I think the key procedure is always I do
+
+ align:start position:0%
+I think the key procedure is always I do
+ 
+
+ align:start position:0%
+I think the key procedure is always I do
+you have a valid solution or not and you
+
+ align:start position:0%
+you have a valid solution or not and you
+ 
+
+ align:start position:0%
+you have a valid solution or not and you
+may not have a complete solution think
+
+ align:start position:0%
+may not have a complete solution think
+ 
+
+ align:start position:0%
+may not have a complete solution think
+of it as a partial configuration right
+
+ align:start position:0%
+of it as a partial configuration right
+ 
+
+ align:start position:0%
+of it as a partial configuration right
+so this is a partial configuration and
+
+ align:start position:0%
+so this is a partial configuration and
+ 
+
+ align:start position:0%
+so this is a partial configuration and
+that is valid it's not a complete
+
+ align:start position:0%
+that is valid it's not a complete
+ 
+
+ align:start position:0%
+that is valid it's not a complete
+solution to the Sudoku puzzle it's a
+
+ align:start position:0%
+solution to the Sudoku puzzle it's a
+ 
+
+ align:start position:0%
+solution to the Sudoku puzzle it's a
+partial configuration that's valid in
+
+ align:start position:0%
+partial configuration that's valid in
+ 
+
+ align:start position:0%
+partial configuration that's valid in
+the sense that it satisfies all of the
+
+ align:start position:0%
+the sense that it satisfies all of the
+ 
+
+ align:start position:0%
+the sense that it satisfies all of the
+constraints you know if I put another
+
+ align:start position:0%
+constraints you know if I put another
+ 
+
+ align:start position:0%
+constraints you know if I put another
+aid in here it would not be a valid
+
+ align:start position:0%
+aid in here it would not be a valid
+ 
+
+ align:start position:0%
+aid in here it would not be a valid
+partial configuration it would be
+
+ align:start position:0%
+partial configuration it would be
+ 
+
+ align:start position:0%
+partial configuration it would be
+partial but not bad
+
+ align:start position:0%
+partial but not bad
+ 
+
+ align:start position:0%
+partial but not bad
+right and I need to grow this I need to
+
+ align:start position:0%
+right and I need to grow this I need to
+ 
+
+ align:start position:0%
+right and I need to grow this I need to
+grow this into a solution and when I say
+
+ align:start position:0%
+grow this into a solution and when I say
+ 
+
+ align:start position:0%
+grow this into a solution and when I say
+solution I mean all the constraints have
+
+ align:start position:0%
+solution I mean all the constraints have
+ 
+
+ align:start position:0%
+solution I mean all the constraints have
+to be satisfied right a configuration
+
+ align:start position:0%
+to be satisfied right a configuration
+ 
+
+ align:start position:0%
+to be satisfied right a configuration
+could be invalid or valid a solution is
+
+ align:start position:0%
+could be invalid or valid a solution is
+ 
+
+ align:start position:0%
+could be invalid or valid a solution is
+always valid all right that's just
+
+ align:start position:0%
+always valid all right that's just
+ 
+
+ align:start position:0%
+always valid all right that's just
+terminology and so I want to be able to
+
+ align:start position:0%
+terminology and so I want to be able to
+ 
+
+ align:start position:0%
+terminology and so I want to be able to
+to look high up and be able to truncate
+
+ align:start position:0%
+to look high up and be able to truncate
+ 
+
+ align:start position:0%
+to look high up and be able to truncate
+the search and say you know what grid IJ
+
+ align:start position:0%
+the search and say you know what grid IJ
+ 
+
+ align:start position:0%
+the search and say you know what grid IJ
+equaling eight because I put an 8 in
+
+ align:start position:0%
+equaling eight because I put an 8 in
+ 
+
+ align:start position:0%
+equaling eight because I put an 8 in
+that sector which already had an 8 in it
+
+ align:start position:0%
+that sector which already had an 8 in it
+ 
+
+ align:start position:0%
+that sector which already had an 8 in it
+is is something that should not be
+
+ align:start position:0%
+is is something that should not be
+ 
+
+ align:start position:0%
+is is something that should not be
+explored and I don't have to worry about
+
+ align:start position:0%
+explored and I don't have to worry about
+ 
+
+ align:start position:0%
+explored and I don't have to worry about
+any of the branches that come here
+
+ align:start position:0%
+any of the branches that come here
+ 
+
+ align:start position:0%
+any of the branches that come here
+because immediately I've violated the
+
+ align:start position:0%
+because immediately I've violated the
+ 
+
+ align:start position:0%
+because immediately I've violated the
+constraint right so in general I can
+
+ align:start position:0%
+constraint right so in general I can
+ 
+
+ align:start position:0%
+constraint right so in general I can
+always check where their partial
+
+ align:start position:0%
+always check where their partial
+ 
+
+ align:start position:0%
+always check where their partial
+configurations violate the three
+
+ align:start position:0%
+configurations violate the three
+ 
+
+ align:start position:0%
+configurations violate the three
+constraints I have or not right and that
+
+ align:start position:0%
+constraints I have or not right and that
+ 
+
+ align:start position:0%
+constraints I have or not right and that
+is what this piece of code does and it's
+
+ align:start position:0%
+is what this piece of code does and it's
+ 
+
+ align:start position:0%
+is what this piece of code does and it's
+also straightforward it perhaps even
+
+ align:start position:0%
+also straightforward it perhaps even
+ 
+
+ align:start position:0%
+also straightforward it perhaps even
+even more straightforward than diagonal
+
+ align:start position:0%
+even more straightforward than diagonal
+ 
+
+ align:start position:0%
+even more straightforward than diagonal
+checking in the case of eight Queens but
+
+ align:start position:0%
+checking in the case of eight Queens but
+ 
+
+ align:start position:0%
+checking in the case of eight Queens but
+all this does is use the construct that
+
+ align:start position:0%
+all this does is use the construct that
+ 
+
+ align:start position:0%
+all this does is use the construct that
+says I'm going to look at essentially
+
+ align:start position:0%
+says I'm going to look at essentially
+ 
+
+ align:start position:0%
+says I'm going to look at essentially
+this is something that is list
+
+ align:start position:0%
+this is something that is list
+ 
+
+ align:start position:0%
+this is something that is list
+comprehensions in in Python the four
+
+ align:start position:0%
+comprehensions in in Python the four
+ 
+
+ align:start position:0%
+comprehensions in in Python the four
+comes after this predicate here but
+
+ align:start position:0%
+comes after this predicate here but
+ 
+
+ align:start position:0%
+comes after this predicate here but
+effectively what you're saying is for X
+
+ align:start position:0%
+effectively what you're saying is for X
+ 
+
+ align:start position:0%
+effectively what you're saying is for X
+and range nine check that grid IX is not
+
+ align:start position:0%
+and range nine check that grid IX is not
+ 
+
+ align:start position:0%
+and range nine check that grid IX is not
+equal to e okay and you're just looking
+
+ align:start position:0%
+equal to e okay and you're just looking
+ 
+
+ align:start position:0%
+equal to e okay and you're just looking
+at e so it's valid grid IJ e takes the
+
+ align:start position:0%
+at e so it's valid grid IJ e takes the
+ 
+
+ align:start position:0%
+at e so it's valid grid IJ e takes the
+grid which looks like this one let's say
+
+ align:start position:0%
+grid which looks like this one let's say
+ 
+
+ align:start position:0%
+grid which looks like this one let's say
+and so it's got zeros in all of the
+
+ align:start position:0%
+and so it's got zeros in all of the
+ 
+
+ align:start position:0%
+and so it's got zeros in all of the
+empty places and it's got a bunch of
+
+ align:start position:0%
+empty places and it's got a bunch of
+ 
+
+ align:start position:0%
+empty places and it's got a bunch of
+nonzero entries in all of the places
+
+ align:start position:0%
+nonzero entries in all of the places
+ 
+
+ align:start position:0%
+nonzero entries in all of the places
+that you see here and in addition you
+
+ align:start position:0%
+that you see here and in addition you
+ 
+
+ align:start position:0%
+that you see here and in addition you
+have perhaps zero zero and let's call it
+
+ align:start position:0%
+have perhaps zero zero and let's call it
+ 
+
+ align:start position:0%
+have perhaps zero zero and let's call it
+one right and so so this is I and this
+
+ align:start position:0%
+one right and so so this is I and this
+ 
+
+ align:start position:0%
+one right and so so this is I and this
+is J and that is e okay
+
+ align:start position:0%
+is J and that is e okay
+ 
+
+ align:start position:0%
+is J and that is e okay
+and so let me write that out here I J
+
+ align:start position:0%
+and so let me write that out here I J
+ 
+
+ align:start position:0%
+and so let me write that out here I J
+and E where I is one zero I'm sorry I is
+
+ align:start position:0%
+and E where I is one zero I'm sorry I is
+ 
+
+ align:start position:0%
+and E where I is one zero I'm sorry I is
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+J is 0 and E is 1 so that would mean
+
+ align:start position:0%
+J is 0 and E is 1 so that would mean
+ 
+
+ align:start position:0%
+J is 0 and E is 1 so that would mean
+putting a putting a 1 up here and that
+
+ align:start position:0%
+putting a putting a 1 up here and that
+ 
+
+ align:start position:0%
+putting a putting a 1 up here and that
+obviously is going to violate one of our
+
+ align:start position:0%
+obviously is going to violate one of our
+ 
+
+ align:start position:0%
+obviously is going to violate one of our
+constraints but that's fine we gonna
+
+ align:start position:0%
+constraints but that's fine we gonna
+ 
+
+ align:start position:0%
+constraints but that's fine we gonna
+check that and it's essentially doing
+
+ align:start position:0%
+check that and it's essentially doing
+ 
+
+ align:start position:0%
+check that and it's essentially doing
+incremental checking just like we did so
+
+ align:start position:0%
+incremental checking just like we did so
+ 
+
+ align:start position:0%
+incremental checking just like we did so
+it's not checking to see that that all
+
+ align:start position:0%
+it's not checking to see that that all
+ 
+
+ align:start position:0%
+it's not checking to see that that all
+of the existing grid IJ values are
+
+ align:start position:0%
+of the existing grid IJ values are
+ 
+
+ align:start position:0%
+of the existing grid IJ values are
+conflicting or not it's just saying I'm
+
+ align:start position:0%
+conflicting or not it's just saying I'm
+ 
+
+ align:start position:0%
+conflicting or not it's just saying I'm
+having I'm gonna be writing something
+
+ align:start position:0%
+having I'm gonna be writing something
+ 
+
+ align:start position:0%
+having I'm gonna be writing something
+into this grid into an empty location it
+
+ align:start position:0%
+into this grid into an empty location it
+ 
+
+ align:start position:0%
+into this grid into an empty location it
+happens to be 0 0 having the value 1 and
+
+ align:start position:0%
+happens to be 0 0 having the value 1 and
+ 
+
+ align:start position:0%
+happens to be 0 0 having the value 1 and
+I'm going to check whether the
+
+ align:start position:0%
+I'm going to check whether the
+ 
+
+ align:start position:0%
+I'm going to check whether the
+introduction of a 1 into this square is
+
+ align:start position:0%
+introduction of a 1 into this square is
+ 
+
+ align:start position:0%
+introduction of a 1 into this square is
+going to cause problems or not right
+
+ align:start position:0%
+going to cause problems or not right
+ 
+
+ align:start position:0%
+going to cause problems or not right
+that's all it's that is doing right
+
+ align:start position:0%
+that's all it's that is doing right
+ 
+
+ align:start position:0%
+that's all it's that is doing right
+incremental just like we had with with 8
+
+ align:start position:0%
+incremental just like we had with with 8
+ 
+
+ align:start position:0%
+incremental just like we had with with 8
+Queens and that check is relatively easy
+
+ align:start position:0%
+Queens and that check is relatively easy
+ 
+
+ align:start position:0%
+Queens and that check is relatively easy
+to do because I just need to go and I
+
+ align:start position:0%
+to do because I just need to go and I
+ 
+
+ align:start position:0%
+to do because I just need to go and I
+look at the row corresponding to 2 I win
+
+ align:start position:0%
+look at the row corresponding to 2 I win
+ 
+
+ align:start position:0%
+look at the row corresponding to 2 I win
+this case is the top row I look at the
+
+ align:start position:0%
+this case is the top row I look at the
+ 
+
+ align:start position:0%
+this case is the top row I look at the
+column corresponding to J which is the
+
+ align:start position:0%
+column corresponding to J which is the
+ 
+
+ align:start position:0%
+column corresponding to J which is the
+leftmost column and then I look at the
+
+ align:start position:0%
+leftmost column and then I look at the
+ 
+
+ align:start position:0%
+leftmost column and then I look at the
+sector corresponding to 0 0 which is
+
+ align:start position:0%
+sector corresponding to 0 0 which is
+ 
+
+ align:start position:0%
+sector corresponding to 0 0 which is
+this top left sector and I check to see
+
+ align:start position:0%
+this top left sector and I check to see
+ 
+
+ align:start position:0%
+this top left sector and I check to see
+for each of those three things whether
+
+ align:start position:0%
+for each of those three things whether
+ 
+
+ align:start position:0%
+for each of those three things whether
+there's a problem or not and the first
+
+ align:start position:0%
+there's a problem or not and the first
+ 
+
+ align:start position:0%
+there's a problem or not and the first
+two well actually I have a problem with
+
+ align:start position:0%
+two well actually I have a problem with
+ 
+
+ align:start position:0%
+two well actually I have a problem with
+the with the row and I would also have a
+
+ align:start position:0%
+the with the row and I would also have a
+ 
+
+ align:start position:0%
+the with the row and I would also have a
+problem with the with the sector I
+
+ align:start position:0%
+problem with the with the sector I
+ 
+
+ align:start position:0%
+problem with the with the sector I
+wouldn't have a problem with the with
+
+ align:start position:0%
+wouldn't have a problem with the with
+ 
+
+ align:start position:0%
+wouldn't have a problem with the with
+the column but in one of them is bad
+
+ align:start position:0%
+the column but in one of them is bad
+ 
+
+ align:start position:0%
+the column but in one of them is bad
+enough and so I'm gonna get a false back
+
+ align:start position:0%
+enough and so I'm gonna get a false back
+ 
+
+ align:start position:0%
+enough and so I'm gonna get a false back
+so row ok is going to be false and so I
+
+ align:start position:0%
+so row ok is going to be false and so I
+ 
+
+ align:start position:0%
+so row ok is going to be false and so I
+am going to return false out here
+
+ align:start position:0%
+am going to return false out here
+ 
+
+ align:start position:0%
+am going to return false out here
+alright that makes sense so those are
+
+ align:start position:0%
+alright that makes sense so those are
+ 
+
+ align:start position:0%
+alright that makes sense so those are
+the three things and this there's really
+
+ align:start position:0%
+the three things and this there's really
+ 
+
+ align:start position:0%
+the three things and this there's really
+not that much here beyond taking those
+
+ align:start position:0%
+not that much here beyond taking those
+ 
+
+ align:start position:0%
+not that much here beyond taking those
+constraints and and codifying them right
+
+ align:start position:0%
+constraints and and codifying them right
+ 
+
+ align:start position:0%
+constraints and and codifying them right
+any questions yeah Fadi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all is essentially a Python built-in
+
+ align:start position:0%
+all is essentially a Python built-in
+ 
+
+ align:start position:0%
+all is essentially a Python built-in
+function that is going to essentially
+
+ align:start position:0%
+function that is going to essentially
+ 
+
+ align:start position:0%
+function that is going to essentially
+say that it's going to its it's a
+
+ align:start position:0%
+say that it's going to its it's a
+ 
+
+ align:start position:0%
+say that it's going to its it's a
+conjunction that says I'm getting a
+
+ align:start position:0%
+conjunction that says I'm getting a
+ 
+
+ align:start position:0%
+conjunction that says I'm getting a
+bunch of boolean s-- that correspond to
+
+ align:start position:0%
+bunch of boolean s-- that correspond to
+ 
+
+ align:start position:0%
+bunch of boolean s-- that correspond to
+the generation of this list
+
+ align:start position:0%
+the generation of this list
+ 
+
+ align:start position:0%
+the generation of this list
+comprehension where'd he not equal to
+
+ align:start position:0%
+comprehension where'd he not equal to
+ 
+
+ align:start position:0%
+comprehension where'd he not equal to
+grid IX is it's going to give me true or
+
+ align:start position:0%
+grid IX is it's going to give me true or
+ 
+
+ align:start position:0%
+grid IX is it's going to give me true or
+false and I need all of those things to
+
+ align:start position:0%
+false and I need all of those things to
+ 
+
+ align:start position:0%
+false and I need all of those things to
+be true all right yeah even if one of
+
+ align:start position:0%
+be true all right yeah even if one of
+ 
+
+ align:start position:0%
+be true all right yeah even if one of
+them is false the end is false in order
+
+ align:start position:0%
+them is false the end is false in order
+ 
+
+ align:start position:0%
+them is false the end is false in order
+for the end to be true then all of them
+
+ align:start position:0%
+for the end to be true then all of them
+ 
+
+ align:start position:0%
+for the end to be true then all of them
+need to be true all right so it's it's
+
+ align:start position:0%
+need to be true all right so it's it's
+ 
+
+ align:start position:0%
+need to be true all right so it's it's
+just a convenient construct which is
+
+ align:start position:0%
+just a convenient construct which is
+ 
+
+ align:start position:0%
+just a convenient construct which is
+applicable in a in in sort of a perfect
+
+ align:start position:0%
+applicable in a in in sort of a perfect
+ 
+
+ align:start position:0%
+applicable in a in in sort of a perfect
+the perfect application is what you see
+
+ align:start position:0%
+the perfect application is what you see
+ 
+
+ align:start position:0%
+the perfect application is what you see
+here it's not the most sophisticated of
+
+ align:start position:0%
+here it's not the most sophisticated of
+ 
+
+ align:start position:0%
+here it's not the most sophisticated of
+applications but it works very well in
+
+ align:start position:0%
+applications but it works very well in
+ 
+
+ align:start position:0%
+applications but it works very well in
+this case now for the sector I can't
+
+ align:start position:0%
+this case now for the sector I can't
+ 
+
+ align:start position:0%
+this case now for the sector I can't
+actually do that and so it is a little
+
+ align:start position:0%
+actually do that and so it is a little
+ 
+
+ align:start position:0%
+actually do that and so it is a little
+bit more work because I kind at this
+
+ align:start position:0%
+bit more work because I kind at this
+ 
+
+ align:start position:0%
+bit more work because I kind at this
+this only works when I could put a list
+
+ align:start position:0%
+this only works when I could put a list
+ 
+
+ align:start position:0%
+this only works when I could put a list
+comprehension in here like this and
+
+ align:start position:0%
+comprehension in here like this and
+ 
+
+ align:start position:0%
+comprehension in here like this and
+generate all the boolean x' for the
+
+ align:start position:0%
+generate all the boolean x' for the
+ 
+
+ align:start position:0%
+generate all the boolean x' for the
+sector I end up having to do something a
+
+ align:start position:0%
+sector I end up having to do something a
+ 
+
+ align:start position:0%
+sector I end up having to do something a
+little bit different I mean you could do
+
+ align:start position:0%
+little bit different I mean you could do
+ 
+
+ align:start position:0%
+little bit different I mean you could do
+things more convoluted than and use all
+
+ align:start position:0%
+things more convoluted than and use all
+ 
+
+ align:start position:0%
+things more convoluted than and use all
+in here as well but it's not worth it
+
+ align:start position:0%
+in here as well but it's not worth it
+ 
+
+ align:start position:0%
+in here as well but it's not worth it
+all right okay that makes sense good so
+
+ align:start position:0%
+all right okay that makes sense good so
+ 
+
+ align:start position:0%
+all right okay that makes sense good so
+here's the the core routine that
+
+ align:start position:0%
+here's the the core routine that
+ 
+
+ align:start position:0%
+here's the the core routine that
+corresponds to the search and ignored
+
+ align:start position:0%
+corresponds to the search and ignored
+ 
+
+ align:start position:0%
+corresponds to the search and ignored
+this global variable here I'll explain
+
+ align:start position:0%
+this global variable here I'll explain
+ 
+
+ align:start position:0%
+this global variable here I'll explain
+that in a minute
+
+ align:start position:0%
+that in a minute
+ 
+
+ align:start position:0%
+that in a minute
+it's that's going to be our metric our
+
+ align:start position:0%
+it's that's going to be our metric our
+ 
+
+ align:start position:0%
+it's that's going to be our metric our
+backtracks is going to be our metric for
+
+ align:start position:0%
+backtracks is going to be our metric for
+ 
+
+ align:start position:0%
+backtracks is going to be our metric for
+computing performance and it's going to
+
+ align:start position:0%
+computing performance and it's going to
+ 
+
+ align:start position:0%
+computing performance and it's going to
+be quite interesting it's going to
+
+ align:start position:0%
+be quite interesting it's going to
+ 
+
+ align:start position:0%
+be quite interesting it's going to
+produce some interesting results for us
+
+ align:start position:0%
+produce some interesting results for us
+ 
+
+ align:start position:0%
+produce some interesting results for us
+okay and then we run this on various
+
+ align:start position:0%
+okay and then we run this on various
+ 
+
+ align:start position:0%
+okay and then we run this on various
+different examples and but but this this
+
+ align:start position:0%
+different examples and but but this this
+ 
+
+ align:start position:0%
+different examples and but but this this
+core a procedure looks a lot like the
+
+ align:start position:0%
+core a procedure looks a lot like the
+ 
+
+ align:start position:0%
+core a procedure looks a lot like the
+n-queens search in the sense that you
+
+ align:start position:0%
+n-queens search in the sense that you
+ 
+
+ align:start position:0%
+n-queens search in the sense that you
+have a for loop and a recursive call
+
+ align:start position:0%
+have a for loop and a recursive call
+ 
+
+ align:start position:0%
+have a for loop and a recursive call
+okay and in this case you
+
+ align:start position:0%
+okay and in this case you
+ 
+
+ align:start position:0%
+okay and in this case you
+the the the for loop is going to be
+
+ align:start position:0%
+the the the for loop is going to be
+ 
+
+ align:start position:0%
+the the the for loop is going to be
+something that ranges through the
+
+ align:start position:0%
+something that ranges through the
+ 
+
+ align:start position:0%
+something that ranges through the
+different values that you find the
+
+ align:start position:0%
+different values that you find the
+ 
+
+ align:start position:0%
+different values that you find the
+location that you want to to put
+
+ align:start position:0%
+location that you want to to put
+ 
+
+ align:start position:0%
+location that you want to to put
+something into which is the the next
+
+ align:start position:0%
+something into which is the the next
+ 
+
+ align:start position:0%
+something into which is the the next
+empty location in your current
+
+ align:start position:0%
+empty location in your current
+ 
+
+ align:start position:0%
+empty location in your current
+configuration and then you need to go
+
+ align:start position:0%
+configuration and then you need to go
+ 
+
+ align:start position:0%
+configuration and then you need to go
+put in one through nine in there and
+
+ align:start position:0%
+put in one through nine in there and
+ 
+
+ align:start position:0%
+put in one through nine in there and
+it's is brutish you're going to put in
+
+ align:start position:0%
+it's is brutish you're going to put in
+ 
+
+ align:start position:0%
+it's is brutish you're going to put in
+one and you're gonna check conflicts and
+
+ align:start position:0%
+one and you're gonna check conflicts and
+ 
+
+ align:start position:0%
+one and you're gonna check conflicts and
+and then you'll put in two and you're
+
+ align:start position:0%
+and then you'll put in two and you're
+ 
+
+ align:start position:0%
+and then you'll put in two and you're
+gonna check conflicts if you put in a
+
+ align:start position:0%
+gonna check conflicts if you put in a
+ 
+
+ align:start position:0%
+gonna check conflicts if you put in a
+one and you don't get a conflict then
+
+ align:start position:0%
+one and you don't get a conflict then
+ 
+
+ align:start position:0%
+one and you don't get a conflict then
+you get to recur and you now move into
+
+ align:start position:0%
+you get to recur and you now move into
+ 
+
+ align:start position:0%
+you get to recur and you now move into
+something that is a another partial
+
+ align:start position:0%
+something that is a another partial
+ 
+
+ align:start position:0%
+something that is a another partial
+configuration potentially but but but
+
+ align:start position:0%
+configuration potentially but but but
+ 
+
+ align:start position:0%
+configuration potentially but but but
+obviously has one location filled from
+
+ align:start position:0%
+obviously has one location filled from
+ 
+
+ align:start position:0%
+obviously has one location filled from
+the from the caller configuration and
+
+ align:start position:0%
+the from the caller configuration and
+ 
+
+ align:start position:0%
+the from the caller configuration and
+then you go look for the next cell so
+
+ align:start position:0%
+then you go look for the next cell so
+ 
+
+ align:start position:0%
+then you go look for the next cell so
+it's certainly possible that I'd go if
+
+ align:start position:0%
+it's certainly possible that I'd go if
+ 
+
+ align:start position:0%
+it's certainly possible that I'd go if
+when I put in a 1 here that fails but if
+
+ align:start position:0%
+when I put in a 1 here that fails but if
+ 
+
+ align:start position:0%
+when I put in a 1 here that fails but if
+I put in a 2 here I it's not gonna fail
+
+ align:start position:0%
+I put in a 2 here I it's not gonna fail
+ 
+
+ align:start position:0%
+I put in a 2 here I it's not gonna fail
+2 is not gonna fail here because if I
+
+ align:start position:0%
+2 is not gonna fail here because if I
+ 
+
+ align:start position:0%
+2 is not gonna fail here because if I
+just look at those constraints at 2 is
+
+ align:start position:0%
+just look at those constraints at 2 is
+ 
+
+ align:start position:0%
+just look at those constraints at 2 is
+okay alright so I'm gonna put in a 2
+
+ align:start position:0%
+okay alright so I'm gonna put in a 2
+ 
+
+ align:start position:0%
+okay alright so I'm gonna put in a 2
+here and then I'm going to recur and I'm
+
+ align:start position:0%
+here and then I'm going to recur and I'm
+ 
+
+ align:start position:0%
+here and then I'm going to recur and I'm
+gonna go out here and I'll try and put
+
+ align:start position:0%
+gonna go out here and I'll try and put
+ 
+
+ align:start position:0%
+gonna go out here and I'll try and put
+in a 1 here and a 1 is gonna fail
+
+ align:start position:0%
+in a 1 here and a 1 is gonna fail
+ 
+
+ align:start position:0%
+in a 1 here and a 1 is gonna fail
+because of this and that a 2 is gonna
+
+ align:start position:0%
+because of this and that a 2 is gonna
+ 
+
+ align:start position:0%
+because of this and that a 2 is gonna
+fail because of that I'm at 3 is a 3
+
+ align:start position:0%
+fail because of that I'm at 3 is a 3
+ 
+
+ align:start position:0%
+fail because of that I'm at 3 is a 3
+gonna fail no not immediately so I could
+
+ align:start position:0%
+gonna fail no not immediately so I could
+ 
+
+ align:start position:0%
+gonna fail no not immediately so I could
+put in a 3 here and then I recurred and
+
+ align:start position:0%
+put in a 3 here and then I recurred and
+ 
+
+ align:start position:0%
+put in a 3 here and then I recurred and
+go to the next one and so on and so
+
+ align:start position:0%
+go to the next one and so on and so
+ 
+
+ align:start position:0%
+go to the next one and so on and so
+forth right and for at each of these
+
+ align:start position:0%
+forth right and for at each of these
+ 
+
+ align:start position:0%
+forth right and for at each of these
+things obviously I have to do a bunch of
+
+ align:start position:0%
+things obviously I have to do a bunch of
+ 
+
+ align:start position:0%
+things obviously I have to do a bunch of
+search underneath and that you know
+
+ align:start position:0%
+search underneath and that you know
+ 
+
+ align:start position:0%
+search underneath and that you know
+thank goodness for fast computers right
+
+ align:start position:0%
+thank goodness for fast computers right
+ 
+
+ align:start position:0%
+thank goodness for fast computers right
+because that's why some in God I mean
+
+ align:start position:0%
+because that's why some in God I mean
+ 
+
+ align:start position:0%
+because that's why some in God I mean
+can you imagine the amount of paper we
+
+ align:start position:0%
+can you imagine the amount of paper we
+ 
+
+ align:start position:0%
+can you imagine the amount of paper we
+generate if you were doing this and
+
+ align:start position:0%
+generate if you were doing this and
+ 
+
+ align:start position:0%
+generate if you were doing this and
+putting two and three and I want a new
+
+ align:start position:0%
+putting two and three and I want a new
+ 
+
+ align:start position:0%
+putting two and three and I want a new
+sheet of paper for the four etc etc I
+
+ align:start position:0%
+sheet of paper for the four etc etc I
+ 
+
+ align:start position:0%
+sheet of paper for the four etc etc I
+mean we can count the number of back
+
+ align:start position:0%
+mean we can count the number of back
+ 
+
+ align:start position:0%
+mean we can count the number of back
+tracks that's how many sheets of paper
+
+ align:start position:0%
+tracks that's how many sheets of paper
+ 
+
+ align:start position:0%
+tracks that's how many sheets of paper
+you'll need okay so so what you see here
+
+ align:start position:0%
+you'll need okay so so what you see here
+ 
+
+ align:start position:0%
+you'll need okay so so what you see here
+I again ignore the back tracks I'll get
+
+ align:start position:0%
+I again ignore the back tracks I'll get
+ 
+
+ align:start position:0%
+I again ignore the back tracks I'll get
+to that in just a second it's just a way
+
+ align:start position:0%
+to that in just a second it's just a way
+ 
+
+ align:start position:0%
+to that in just a second it's just a way
+of counting the number of calls and this
+
+ align:start position:0%
+of counting the number of calls and this
+ 
+
+ align:start position:0%
+of counting the number of calls and this
+thing here essentially says you know if
+
+ align:start position:0%
+thing here essentially says you know if
+ 
+
+ align:start position:0%
+thing here essentially says you know if
+I'm going to be
+
+ align:start position:0%
+I'm going to be
+ 
+
+ align:start position:0%
+I'm going to be
+turning I'm gonna if as long as I get
+
+ align:start position:0%
+turning I'm gonna if as long as I get
+ 
+
+ align:start position:0%
+turning I'm gonna if as long as I get
+through and find a solution I want to
+
+ align:start position:0%
+through and find a solution I want to
+ 
+
+ align:start position:0%
+through and find a solution I want to
+return true right so if solve Sudoku
+
+ align:start position:0%
+return true right so if solve Sudoku
+ 
+
+ align:start position:0%
+return true right so if solve Sudoku
+grid IJ is true then I'm going to return
+
+ align:start position:0%
+grid IJ is true then I'm going to return
+ 
+
+ align:start position:0%
+grid IJ is true then I'm going to return
+true and then I'm going to pop up all
+
+ align:start position:0%
+true and then I'm going to pop up all
+ 
+
+ align:start position:0%
+true and then I'm going to pop up all
+the way into the top assuming I got I go
+
+ align:start position:0%
+the way into the top assuming I got I go
+ 
+
+ align:start position:0%
+the way into the top assuming I got I go
+all the way down to the bottom and I get
+
+ align:start position:0%
+all the way down to the bottom and I get
+ 
+
+ align:start position:0%
+all the way down to the bottom and I get
+to the point where I have a solution
+
+ align:start position:0%
+to the point where I have a solution
+ 
+
+ align:start position:0%
+to the point where I have a solution
+that returns true which is a completely
+
+ align:start position:0%
+that returns true which is a completely
+ 
+
+ align:start position:0%
+that returns true which is a completely
+full configuration that returns true
+
+ align:start position:0%
+full configuration that returns true
+ 
+
+ align:start position:0%
+full configuration that returns true
+right but if not then I need to go a try
+
+ align:start position:0%
+right but if not then I need to go a try
+ 
+
+ align:start position:0%
+right but if not then I need to go a try
+the other combinations and I'm only
+
+ align:start position:0%
+the other combinations and I'm only
+ 
+
+ align:start position:0%
+the other combinations and I'm only
+going to Bob I'm only going to make that
+
+ align:start position:0%
+going to Bob I'm only going to make that
+ 
+
+ align:start position:0%
+going to Bob I'm only going to make that
+recursive call if the if obviously IJ e
+
+ align:start position:0%
+recursive call if the if obviously IJ e
+ 
+
+ align:start position:0%
+recursive call if the if obviously IJ e
+corresponding to this is is valid and
+
+ align:start position:0%
+corresponding to this is is valid and
+ 
+
+ align:start position:0%
+corresponding to this is is valid and
+that checks the constraints and the only
+
+ align:start position:0%
+that checks the constraints and the only
+ 
+
+ align:start position:0%
+that checks the constraints and the only
+other thing I have to worry about is it
+
+ align:start position:0%
+other thing I have to worry about is it
+ 
+
+ align:start position:0%
+other thing I have to worry about is it
+is is essentially something that says
+
+ align:start position:0%
+is is essentially something that says
+ 
+
+ align:start position:0%
+is is essentially something that says
+you know reset your grid location and
+
+ align:start position:0%
+you know reset your grid location and
+ 
+
+ align:start position:0%
+you know reset your grid location and
+make sure that that you're that you're
+
+ align:start position:0%
+make sure that that you're that you're
+ 
+
+ align:start position:0%
+make sure that that you're that you're
+setting it back to zero
+
+ align:start position:0%
+setting it back to zero
+ 
+
+ align:start position:0%
+setting it back to zero
+after after you're done right and so
+
+ align:start position:0%
+after after you're done right and so
+ 
+
+ align:start position:0%
+after after you're done right and so
+I've just made a choice here grid IJ
+
+ align:start position:0%
+I've just made a choice here grid IJ
+ 
+
+ align:start position:0%
+I've just made a choice here grid IJ
+equals Z if I look at this line of code
+
+ align:start position:0%
+equals Z if I look at this line of code
+ 
+
+ align:start position:0%
+equals Z if I look at this line of code
+here this is resetting the grid IJ
+
+ align:start position:0%
+here this is resetting the grid IJ
+ 
+
+ align:start position:0%
+here this is resetting the grid IJ
+equals Z and saying it's empty because
+
+ align:start position:0%
+equals Z and saying it's empty because
+ 
+
+ align:start position:0%
+equals Z and saying it's empty because
+if I've failed in all of these and I
+
+ align:start position:0%
+if I've failed in all of these and I
+ 
+
+ align:start position:0%
+if I've failed in all of these and I
+haven't returned true in all of these
+
+ align:start position:0%
+haven't returned true in all of these
+ 
+
+ align:start position:0%
+haven't returned true in all of these
+then obviously I want to change this and
+
+ align:start position:0%
+then obviously I want to change this and
+ 
+
+ align:start position:0%
+then obviously I want to change this and
+you could argue that the next time
+
+ align:start position:0%
+you could argue that the next time
+ 
+
+ align:start position:0%
+you could argue that the next time
+around if I and J are exactly the same
+
+ align:start position:0%
+around if I and J are exactly the same
+ 
+
+ align:start position:0%
+around if I and J are exactly the same
+because I and J are set up here then I'm
+
+ align:start position:0%
+because I and J are set up here then I'm
+ 
+
+ align:start position:0%
+because I and J are set up here then I'm
+going to override the e from a 1 to a 2
+
+ align:start position:0%
+going to override the e from a 1 to a 2
+ 
+
+ align:start position:0%
+going to override the e from a 1 to a 2
+etc etc and so that is in fact correct
+
+ align:start position:0%
+etc etc and so that is in fact correct
+ 
+
+ align:start position:0%
+etc etc and so that is in fact correct
+but I do need I I do need to reset this
+
+ align:start position:0%
+but I do need I I do need to reset this
+ 
+
+ align:start position:0%
+but I do need I I do need to reset this
+outside of the loop if not inside of the
+
+ align:start position:0%
+outside of the loop if not inside of the
+ 
+
+ align:start position:0%
+outside of the loop if not inside of the
+loop so it's not like I can get away
+
+ align:start position:0%
+loop so it's not like I can get away
+ 
+
+ align:start position:0%
+loop so it's not like I can get away
+with this line of code I'm in general if
+
+ align:start position:0%
+with this line of code I'm in general if
+ 
+
+ align:start position:0%
+with this line of code I'm in general if
+you ever backtrack you have to go back
+
+ align:start position:0%
+you ever backtrack you have to go back
+ 
+
+ align:start position:0%
+you ever backtrack you have to go back
+and undo your decision and you have to
+
+ align:start position:0%
+and undo your decision and you have to
+ 
+
+ align:start position:0%
+and undo your decision and you have to
+erase the 3 and that's essentially what
+
+ align:start position:0%
+erase the 3 and that's essentially what
+ 
+
+ align:start position:0%
+erase the 3 and that's essentially what
+that grid IJ equaling 0 is doing right
+
+ align:start position:0%
+that grid IJ equaling 0 is doing right
+ 
+
+ align:start position:0%
+that grid IJ equaling 0 is doing right
+you just need to undo that decision and
+
+ align:start position:0%
+you just need to undo that decision and
+ 
+
+ align:start position:0%
+you just need to undo that decision and
+you can you can do this a few different
+
+ align:start position:0%
+you can you can do this a few different
+ 
+
+ align:start position:0%
+you can you can do this a few different
+ways but the biggest thing to remember
+
+ align:start position:0%
+ways but the biggest thing to remember
+ 
+
+ align:start position:0%
+ways but the biggest thing to remember
+when you do recursive search is to get
+
+ align:start position:0%
+when you do recursive search is to get
+ 
+
+ align:start position:0%
+when you do recursive search is to get
+your your the undoing if your decision
+
+ align:start position:0%
+your your the undoing if your decision
+ 
+
+ align:start position:0%
+your your the undoing if your decision
+which is what we call back
+
+ align:start position:0%
+which is what we call back
+ 
+
+ align:start position:0%
+which is what we call back
+to be correct and if you ever leave a
+
+ align:start position:0%
+to be correct and if you ever leave a
+ 
+
+ align:start position:0%
+to be correct and if you ever leave a
+mess then you'd have a problem that was
+
+ align:start position:0%
+mess then you'd have a problem that was
+ 
+
+ align:start position:0%
+mess then you'd have a problem that was
+that's also true in the case of the N
+
+ align:start position:0%
+that's also true in the case of the N
+ 
+
+ align:start position:0%
+that's also true in the case of the N
+Queens problem so I'm gonna go ahead and
+
+ align:start position:0%
+Queens problem so I'm gonna go ahead and
+ 
+
+ align:start position:0%
+Queens problem so I'm gonna go ahead and
+and this is just a print routine so this
+
+ align:start position:0%
+and this is just a print routine so this
+ 
+
+ align:start position:0%
+and this is just a print routine so this
+is not exactly the Sudoku that I have up
+
+ align:start position:0%
+is not exactly the Sudoku that I have up
+ 
+
+ align:start position:0%
+is not exactly the Sudoku that I have up
+up there the Sudoku puzzle that I have
+
+ align:start position:0%
+up there the Sudoku puzzle that I have
+ 
+
+ align:start position:0%
+up there the Sudoku puzzle that I have
+up there but it's kind of roughly
+
+ align:start position:0%
+up there but it's kind of roughly
+ 
+
+ align:start position:0%
+up there but it's kind of roughly
+similar in complexity and I can go ahead
+
+ align:start position:0%
+similar in complexity and I can go ahead
+ 
+
+ align:start position:0%
+similar in complexity and I can go ahead
+and run the pseudocode program and for
+
+ align:start position:0%
+and run the pseudocode program and for
+ 
+
+ align:start position:0%
+and run the pseudocode program and for
+each of those different Sudoku problems
+
+ align:start position:0%
+each of those different Sudoku problems
+ 
+
+ align:start position:0%
+each of those different Sudoku problems
+it's it's producing solve puzzles so
+
+ align:start position:0%
+it's it's producing solve puzzles so
+ 
+
+ align:start position:0%
+it's it's producing solve puzzles so
+this is a solved puzzle you can check
+
+ align:start position:0%
+this is a solved puzzle you can check
+ 
+
+ align:start position:0%
+this is a solved puzzle you can check
+this puzzle just real quick and you'll
+
+ align:start position:0%
+this puzzle just real quick and you'll
+ 
+
+ align:start position:0%
+this puzzle just real quick and you'll
+find that that all of the constraints
+
+ align:start position:0%
+find that that all of the constraints
+ 
+
+ align:start position:0%
+find that that all of the constraints
+are satisfied and then and I'm going to
+
+ align:start position:0%
+are satisfied and then and I'm going to
+ 
+
+ align:start position:0%
+are satisfied and then and I'm going to
+explain backtracks in a second so true
+
+ align:start position:0%
+explain backtracks in a second so true
+ 
+
+ align:start position:0%
+explain backtracks in a second so true
+says that there's a solution the number
+
+ align:start position:0%
+says that there's a solution the number
+ 
+
+ align:start position:0%
+says that there's a solution the number
+of backtracks was 579 for the second
+
+ align:start position:0%
+of backtracks was 579 for the second
+ 
+
+ align:start position:0%
+of backtracks was 579 for the second
+puzzle which was a little bit harder the
+
+ align:start position:0%
+puzzle which was a little bit harder the
+ 
+
+ align:start position:0%
+puzzle which was a little bit harder the
+number of backtracks was six three six
+
+ align:start position:0%
+number of backtracks was six three six
+ 
+
+ align:start position:0%
+number of backtracks was six three six
+three I'm sorry this is just scrolling
+
+ align:start position:0%
+three I'm sorry this is just scrolling
+ 
+
+ align:start position:0%
+three I'm sorry this is just scrolling
+and for the fourth one it was 335
+
+ align:start position:0%
+and for the fourth one it was 335
+ 
+
+ align:start position:0%
+and for the fourth one it was 335
+thousand and I'm sorry for the third one
+
+ align:start position:0%
+thousand and I'm sorry for the third one
+ 
+
+ align:start position:0%
+thousand and I'm sorry for the third one
+and for the fourth one was 99 49 okay
+
+ align:start position:0%
+and for the fourth one was 99 49 okay
+ 
+
+ align:start position:0%
+and for the fourth one was 99 49 okay
+these last two puzzles hard and if there
+
+ align:start position:0%
+these last two puzzles hard and if there
+ 
+
+ align:start position:0%
+these last two puzzles hard and if there
+was a finished guy called or there is a
+
+ align:start position:0%
+was a finished guy called or there is a
+ 
+
+ align:start position:0%
+was a finished guy called or there is a
+finish guy called our toe in kala who
+
+ align:start position:0%
+finish guy called our toe in kala who
+ 
+
+ align:start position:0%
+finish guy called our toe in kala who
+designs puzzles and he claimed that this
+
+ align:start position:0%
+designs puzzles and he claimed that this
+ 
+
+ align:start position:0%
+designs puzzles and he claimed that this
+hard puzzle in 2006 was the hardest
+
+ align:start position:0%
+hard puzzle in 2006 was the hardest
+ 
+
+ align:start position:0%
+hard puzzle in 2006 was the hardest
+puzzle ever design in Sudoku and then in
+
+ align:start position:0%
+puzzle ever design in Sudoku and then in
+ 
+
+ align:start position:0%
+puzzle ever design in Sudoku and then in
+2010 he came up with this more difficult
+
+ align:start position:0%
+2010 he came up with this more difficult
+ 
+
+ align:start position:0%
+2010 he came up with this more difficult
+puzzle according to him that required a
+
+ align:start position:0%
+puzzle according to him that required a
+ 
+
+ align:start position:0%
+puzzle according to him that required a
+lot of look ahead from a standpoint of
+
+ align:start position:0%
+lot of look ahead from a standpoint of
+ 
+
+ align:start position:0%
+lot of look ahead from a standpoint of
+the human being like you know we went
+
+ align:start position:0%
+the human being like you know we went
+ 
+
+ align:start position:0%
+the human being like you know we went
+back to what I said you-you-you can't
+
+ align:start position:0%
+back to what I said you-you-you can't
+ 
+
+ align:start position:0%
+back to what I said you-you-you can't
+quite do this implication you have to
+
+ align:start position:0%
+quite do this implication you have to
+ 
+
+ align:start position:0%
+quite do this implication you have to
+kind of make a guess and then you have
+
+ align:start position:0%
+kind of make a guess and then you have
+ 
+
+ align:start position:0%
+kind of make a guess and then you have
+to go further and further down and that
+
+ align:start position:0%
+to go further and further down and that
+ 
+
+ align:start position:0%
+to go further and further down and that
+I think the claim was that the hard
+
+ align:start position:0%
+I think the claim was that the hard
+ 
+
+ align:start position:0%
+I think the claim was that the hard
+puzzle required like five levels of look
+
+ align:start position:0%
+puzzle required like five levels of look
+ 
+
+ align:start position:0%
+puzzle required like five levels of look
+ahead and then the difficult puzzle
+
+ align:start position:0%
+ahead and then the difficult puzzle
+ 
+
+ align:start position:0%
+ahead and then the difficult puzzle
+required six levels of look ahead and
+
+ align:start position:0%
+required six levels of look ahead and
+ 
+
+ align:start position:0%
+required six levels of look ahead and
+obviously I given that look ahead this
+
+ align:start position:0%
+obviously I given that look ahead this
+ 
+
+ align:start position:0%
+obviously I given that look ahead this
+puzzle has to have an initial
+
+ align:start position:0%
+puzzle has to have an initial
+ 
+
+ align:start position:0%
+puzzle has to have an initial
+configuration that solvable so it's not
+
+ align:start position:0%
+configuration that solvable so it's not
+ 
+
+ align:start position:0%
+configuration that solvable so it's not
+a trivial thing to create puzzles but
+
+ align:start position:0%
+a trivial thing to create puzzles but
+ 
+
+ align:start position:0%
+a trivial thing to create puzzles but
+now people are using computer programs
+
+ align:start position:0%
+now people are using computer programs
+ 
+
+ align:start position:0%
+now people are using computer programs
+and doing things like we are doing here
+
+ align:start position:0%
+and doing things like we are doing here
+ 
+
+ align:start position:0%
+and doing things like we are doing here
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+to find difficult puzzles and
+
+ align:start position:0%
+to find difficult puzzles and
+ 
+
+ align:start position:0%
+to find difficult puzzles and
+interestingly enough the 2006 puzzle at
+
+ align:start position:0%
+interestingly enough the 2006 puzzle at
+ 
+
+ align:start position:0%
+interestingly enough the 2006 puzzle at
+least for this naive computer program it
+
+ align:start position:0%
+least for this naive computer program it
+ 
+
+ align:start position:0%
+least for this naive computer program it
+takes three hundred and thirty-five
+
+ align:start position:0%
+takes three hundred and thirty-five
+ 
+
+ align:start position:0%
+takes three hundred and thirty-five
+thousand backtracks the one that that
+
+ align:start position:0%
+thousand backtracks the one that that
+ 
+
+ align:start position:0%
+thousand backtracks the one that that
+was supposedly made more difficult into
+
+ align:start position:0%
+was supposedly made more difficult into
+ 
+
+ align:start position:0%
+was supposedly made more difficult into
+2010 which which not only takes you know
+
+ align:start position:0%
+2010 which which not only takes you know
+ 
+
+ align:start position:0%
+2010 which which not only takes you know
+about ten thousand backtracks right so
+
+ align:start position:0%
+about ten thousand backtracks right so
+ 
+
+ align:start position:0%
+about ten thousand backtracks right so
+obviously there's a difference between
+
+ align:start position:0%
+obviously there's a difference between
+ 
+
+ align:start position:0%
+obviously there's a difference between
+the way this this program behaves and
+
+ align:start position:0%
+the way this this program behaves and
+ 
+
+ align:start position:0%
+the way this this program behaves and
+how you or I would behave or that you
+
+ align:start position:0%
+how you or I would behave or that you
+ 
+
+ align:start position:0%
+how you or I would behave or that you
+would behave if you try to solve this
+
+ align:start position:0%
+would behave if you try to solve this
+ 
+
+ align:start position:0%
+would behave if you try to solve this
+puzzle okay so let me just explain
+
+ align:start position:0%
+puzzle okay so let me just explain
+ 
+
+ align:start position:0%
+puzzle okay so let me just explain
+backtracks and I'll stop to see if
+
+ align:start position:0%
+backtracks and I'll stop to see if
+ 
+
+ align:start position:0%
+backtracks and I'll stop to see if
+there's any questions about the code so
+
+ align:start position:0%
+there's any questions about the code so
+ 
+
+ align:start position:0%
+there's any questions about the code so
+when you make recursive calls and you
+
+ align:start position:0%
+when you make recursive calls and you
+ 
+
+ align:start position:0%
+when you make recursive calls and you
+want to count the number of recursive
+
+ align:start position:0%
+want to count the number of recursive
+ 
+
+ align:start position:0%
+want to count the number of recursive
+procedure calls you want to do something
+
+ align:start position:0%
+procedure calls you want to do something
+ 
+
+ align:start position:0%
+procedure calls you want to do something
+inside each of the recursive procedures
+
+ align:start position:0%
+inside each of the recursive procedures
+ 
+
+ align:start position:0%
+inside each of the recursive procedures
+and you want to sort of cumulatively or
+
+ align:start position:0%
+and you want to sort of cumulatively or
+ 
+
+ align:start position:0%
+and you want to sort of cumulatively or
+collectively keep some information one
+
+ align:start position:0%
+collectively keep some information one
+ 
+
+ align:start position:0%
+collectively keep some information one
+way of certainly doing it is to pass
+
+ align:start position:0%
+way of certainly doing it is to pass
+ 
+
+ align:start position:0%
+way of certainly doing it is to pass
+arguments and then you have to return
+
+ align:start position:0%
+arguments and then you have to return
+ 
+
+ align:start position:0%
+arguments and then you have to return
+the argument because when you pass an
+
+ align:start position:0%
+the argument because when you pass an
+ 
+
+ align:start position:0%
+the argument because when you pass an
+argument and you you you modify it it's
+
+ align:start position:0%
+argument and you you you modify it it's
+ 
+
+ align:start position:0%
+argument and you you you modify it it's
+it's not like that is going to be that
+
+ align:start position:0%
+it's not like that is going to be that
+ 
+
+ align:start position:0%
+it's not like that is going to be that
+modification if it's not if it's just an
+
+ align:start position:0%
+modification if it's not if it's just an
+ 
+
+ align:start position:0%
+modification if it's not if it's just an
+integer if it's not a mutable if it's
+
+ align:start position:0%
+integer if it's not a mutable if it's
+ 
+
+ align:start position:0%
+integer if it's not a mutable if it's
+not a mutable variable it's not going to
+
+ align:start position:0%
+not a mutable variable it's not going to
+ 
+
+ align:start position:0%
+not a mutable variable it's not going to
+be seen by the caller procedure and so
+
+ align:start position:0%
+be seen by the caller procedure and so
+ 
+
+ align:start position:0%
+be seen by the caller procedure and so
+when you do recursion and you want to do
+
+ align:start position:0%
+when you do recursion and you want to do
+ 
+
+ align:start position:0%
+when you do recursion and you want to do
+some counting the notion of global
+
+ align:start position:0%
+some counting the notion of global
+ 
+
+ align:start position:0%
+some counting the notion of global
+variables is a convenient construct to
+
+ align:start position:0%
+variables is a convenient construct to
+ 
+
+ align:start position:0%
+variables is a convenient construct to
+have okay and global variables
+
+ align:start position:0%
+have okay and global variables
+ 
+
+ align:start position:0%
+have okay and global variables
+essentially say that there's exactly one
+
+ align:start position:0%
+essentially say that there's exactly one
+ 
+
+ align:start position:0%
+essentially say that there's exactly one
+memory location associated with this
+
+ align:start position:0%
+memory location associated with this
+ 
+
+ align:start position:0%
+memory location associated with this
+variable and we're going to go ahead and
+
+ align:start position:0%
+variable and we're going to go ahead and
+ 
+
+ align:start position:0%
+variable and we're going to go ahead and
+anytime we are mutating this variable
+
+ align:start position:0%
+anytime we are mutating this variable
+ 
+
+ align:start position:0%
+anytime we are mutating this variable
+and you're modifying it you're going to
+
+ align:start position:0%
+and you're modifying it you're going to
+ 
+
+ align:start position:0%
+and you're modifying it you're going to
+see the effect of that in that memory
+
+ align:start position:0%
+see the effect of that in that memory
+ 
+
+ align:start position:0%
+see the effect of that in that memory
+location okay so so what you have here
+
+ align:start position:0%
+location okay so so what you have here
+ 
+
+ align:start position:0%
+location okay so so what you have here
+up here is I set back crack's to be zero
+
+ align:start position:0%
+up here is I set back crack's to be zero
+ 
+
+ align:start position:0%
+up here is I set back crack's to be zero
+okay and that's my global variable the
+
+ align:start position:0%
+okay and that's my global variable the
+ 
+
+ align:start position:0%
+okay and that's my global variable the
+fact that I put back crack's equals zero
+
+ align:start position:0%
+fact that I put back crack's equals zero
+ 
+
+ align:start position:0%
+fact that I put back crack's equals zero
+here doesn't make this a global variable
+
+ align:start position:0%
+here doesn't make this a global variable
+ 
+
+ align:start position:0%
+here doesn't make this a global variable
+just yet um the fact that I have global
+
+ align:start position:0%
+just yet um the fact that I have global
+ 
+
+ align:start position:0%
+just yet um the fact that I have global
+backtracks inside of solve Sudoku now
+
+ align:start position:0%
+backtracks inside of solve Sudoku now
+ 
+
+ align:start position:0%
+backtracks inside of solve Sudoku now
+says that there's a single copy of
+
+ align:start position:0%
+says that there's a single copy of
+ 
+
+ align:start position:0%
+says that there's a single copy of
+backtracks and it doesn't matter whether
+
+ align:start position:0%
+backtracks and it doesn't matter whether
+ 
+
+ align:start position:0%
+backtracks and it doesn't matter whether
+I'm you know at the top level of
+
+ align:start position:0%
+I'm you know at the top level of
+ 
+
+ align:start position:0%
+I'm you know at the top level of
+recursion or the bottom level of
+
+ align:start position:0%
+recursion or the bottom level of
+ 
+
+ align:start position:0%
+recursion or the bottom level of
+recursion
+
+ align:start position:0%
+recursion
+ 
+
+ align:start position:0%
+recursion
+it's just that memory location
+
+ align:start position:0%
+it's just that memory location
+ 
+
+ align:start position:0%
+it's just that memory location
+corresponding to the backtracks the name
+
+ align:start position:0%
+corresponding to the backtracks the name
+ 
+
+ align:start position:0%
+corresponding to the backtracks the name
+backtracks that is getting incremented
+
+ align:start position:0%
+backtracks that is getting incremented
+ 
+
+ align:start position:0%
+backtracks that is getting incremented
+and this could be you know
+
+ align:start position:0%
+and this could be you know
+ 
+
+ align:start position:0%
+and this could be you know
+ten levels deep it could be 40 levels
+
+ align:start position:0%
+ten levels deep it could be 40 levels
+ 
+
+ align:start position:0%
+ten levels deep it could be 40 levels
+deep given that I've called things you
+
+ align:start position:0%
+deep given that I've called things you
+ 
+
+ align:start position:0%
+deep given that I've called things you
+know 40 levels in but it's just the one
+
+ align:start position:0%
+know 40 levels in but it's just the one
+ 
+
+ align:start position:0%
+know 40 levels in but it's just the one
+backtracks okay so as you can see what
+
+ align:start position:0%
+backtracks okay so as you can see what
+ 
+
+ align:start position:0%
+backtracks okay so as you can see what
+backtracks does is anytime you have a
+
+ align:start position:0%
+backtracks does is anytime you have a
+ 
+
+ align:start position:0%
+backtracks does is anytime you have a
+valid location and you've gone ahead and
+
+ align:start position:0%
+valid location and you've gone ahead and
+ 
+
+ align:start position:0%
+valid location and you've gone ahead and
+and essentially you don't you failed the
+
+ align:start position:0%
+and essentially you don't you failed the
+ 
+
+ align:start position:0%
+and essentially you don't you failed the
+reason it's out here is salsa Doku did
+
+ align:start position:0%
+reason it's out here is salsa Doku did
+ 
+
+ align:start position:0%
+reason it's out here is salsa Doku did
+not return true when salsa Roku actually
+
+ align:start position:0%
+not return true when salsa Roku actually
+ 
+
+ align:start position:0%
+not return true when salsa Roku actually
+returns false is that's when you you you
+
+ align:start position:0%
+returns false is that's when you you you
+ 
+
+ align:start position:0%
+returns false is that's when you you you
+you come out and you increment
+
+ align:start position:0%
+you come out and you increment
+ 
+
+ align:start position:0%
+you come out and you increment
+backtracks okay so so it meant that you
+
+ align:start position:0%
+backtracks okay so so it meant that you
+ 
+
+ align:start position:0%
+backtracks okay so so it meant that you
+you had to do some undoing you know when
+
+ align:start position:0%
+you had to do some undoing you know when
+ 
+
+ align:start position:0%
+you had to do some undoing you know when
+you set grid IJ to be 0 that's when
+
+ align:start position:0%
+you set grid IJ to be 0 that's when
+ 
+
+ align:start position:0%
+you set grid IJ to be 0 that's when
+you're undoing your your guess right so
+
+ align:start position:0%
+you're undoing your your guess right so
+ 
+
+ align:start position:0%
+you're undoing your your guess right so
+back tracks you know makes sense from a
+
+ align:start position:0%
+back tracks you know makes sense from a
+ 
+
+ align:start position:0%
+back tracks you know makes sense from a
+standpoint of I need to backtrack and go
+
+ align:start position:0%
+standpoint of I need to backtrack and go
+ 
+
+ align:start position:0%
+standpoint of I need to backtrack and go
+in a different fork in the road okay and
+
+ align:start position:0%
+in a different fork in the road okay and
+ 
+
+ align:start position:0%
+in a different fork in the road okay and
+so that's why I have back tracks plus
+
+ align:start position:0%
+so that's why I have back tracks plus
+ 
+
+ align:start position:0%
+so that's why I have back tracks plus
+equals one right when I'm undoing you
+
+ align:start position:0%
+equals one right when I'm undoing you
+ 
+
+ align:start position:0%
+equals one right when I'm undoing you
+know my decision that I made right so
+
+ align:start position:0%
+know my decision that I made right so
+ 
+
+ align:start position:0%
+know my decision that I made right so
+this kind of gives you a sense for how
+
+ align:start position:0%
+this kind of gives you a sense for how
+ 
+
+ align:start position:0%
+this kind of gives you a sense for how
+many wrong guesses that this program did
+
+ align:start position:0%
+many wrong guesses that this program did
+ 
+
+ align:start position:0%
+many wrong guesses that this program did
+and as you can imagine then more the
+
+ align:start position:0%
+and as you can imagine then more the
+ 
+
+ align:start position:0%
+and as you can imagine then more the
+number of wrong guesses the more the
+
+ align:start position:0%
+number of wrong guesses the more the
+ 
+
+ align:start position:0%
+number of wrong guesses the more the
+computation and the longer it takes so
+
+ align:start position:0%
+computation and the longer it takes so
+ 
+
+ align:start position:0%
+computation and the longer it takes so
+it is definitely a proxy for performance
+
+ align:start position:0%
+it is definitely a proxy for performance
+ 
+
+ align:start position:0%
+it is definitely a proxy for performance
+but it's a it's a platform independent
+
+ align:start position:0%
+but it's a it's a platform independent
+ 
+
+ align:start position:0%
+but it's a it's a platform independent
+proxy that's more algorithm related as
+
+ align:start position:0%
+proxy that's more algorithm related as
+ 
+
+ align:start position:0%
+proxy that's more algorithm related as
+opposed to the speed of the computer
+
+ align:start position:0%
+opposed to the speed of the computer
+ 
+
+ align:start position:0%
+opposed to the speed of the computer
+because if this computer were twice as
+
+ align:start position:0%
+because if this computer were twice as
+ 
+
+ align:start position:0%
+because if this computer were twice as
+fast I mean I just see things running
+
+ align:start position:0%
+fast I mean I just see things running
+ 
+
+ align:start position:0%
+fast I mean I just see things running
+faster even though the algorithm isn't
+
+ align:start position:0%
+faster even though the algorithm isn't
+ 
+
+ align:start position:0%
+faster even though the algorithm isn't
+any better right that makes sense right
+
+ align:start position:0%
+any better right that makes sense right
+ 
+
+ align:start position:0%
+any better right that makes sense right
+so it's a very simple use of global but
+
+ align:start position:0%
+so it's a very simple use of global but
+ 
+
+ align:start position:0%
+so it's a very simple use of global but
+you don't want to use global variables
+
+ align:start position:0%
+you don't want to use global variables
+ 
+
+ align:start position:0%
+you don't want to use global variables
+except in certain constraint settings
+
+ align:start position:0%
+except in certain constraint settings
+ 
+
+ align:start position:0%
+except in certain constraint settings
+this is a fine use of global variables
+
+ align:start position:0%
+this is a fine use of global variables
+ 
+
+ align:start position:0%
+this is a fine use of global variables
+right cool good so any questions about
+
+ align:start position:0%
+right cool good so any questions about
+ 
+
+ align:start position:0%
+right cool good so any questions about
+this code so what I've done here is I
+
+ align:start position:0%
+this code so what I've done here is I
+ 
+
+ align:start position:0%
+this code so what I've done here is I
+just have the naive code and I happen to
+
+ align:start position:0%
+just have the naive code and I happen to
+ 
+
+ align:start position:0%
+just have the naive code and I happen to
+have different numbers of backtracks
+
+ align:start position:0%
+have different numbers of backtracks
+ 
+
+ align:start position:0%
+have different numbers of backtracks
+because I have different inputs unlike
+
+ align:start position:0%
+because I have different inputs unlike
+ 
+
+ align:start position:0%
+because I have different inputs unlike
+the n-queens problem which is kind of
+
+ align:start position:0%
+the n-queens problem which is kind of
+ 
+
+ align:start position:0%
+the n-queens problem which is kind of
+boring in some sense because once you've
+
+ align:start position:0%
+boring in some sense because once you've
+ 
+
+ align:start position:0%
+boring in some sense because once you've
+solved it there's nothing left in the
+
+ align:start position:0%
+solved it there's nothing left in the
+ 
+
+ align:start position:0%
+solved it there's nothing left in the
+case of Sudoku I could change my input
+
+ align:start position:0%
+case of Sudoku I could change my input
+ 
+
+ align:start position:0%
+case of Sudoku I could change my input
+my starting point and give you a
+
+ align:start position:0%
+my starting point and give you a
+ 
+
+ align:start position:0%
+my starting point and give you a
+different different problems right and
+
+ align:start position:0%
+different different problems right and
+ 
+
+ align:start position:0%
+different different problems right and
+so so the reason we had many different
+
+ align:start position:0%
+so so the reason we had many different
+ 
+
+ align:start position:0%
+so so the reason we had many different
+kinds of backtracks
+
+ align:start position:0%
+kinds of backtracks
+ 
+
+ align:start position:0%
+kinds of backtracks
+was was simply because numbers of
+
+ align:start position:0%
+was was simply because numbers of
+ 
+
+ align:start position:0%
+was was simply because numbers of
+backtracks was because we had four
+
+ align:start position:0%
+backtracks was because we had four
+ 
+
+ align:start position:0%
+backtracks was because we had four
+different inputs to the Sudoku puzzle
+
+ align:start position:0%
+different inputs to the Sudoku puzzle
+ 
+
+ align:start position:0%
+different inputs to the Sudoku puzzle
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so are we good here people understand
+
+ align:start position:0%
+so are we good here people understand
+ 
+
+ align:start position:0%
+so are we good here people understand
+this code you're gonna have to modify it
+
+ align:start position:0%
+this code you're gonna have to modify it
+ 
+
+ align:start position:0%
+this code you're gonna have to modify it
+right now not necessarily this code
+
+ align:start position:0%
+right now not necessarily this code
+ 
+
+ align:start position:0%
+right now not necessarily this code
+depending on the exercise you do but
+
+ align:start position:0%
+depending on the exercise you do but
+ 
+
+ align:start position:0%
+depending on the exercise you do but
+this is certainly something that
+
+ align:start position:0%
+this is certainly something that
+ 
+
+ align:start position:0%
+this is certainly something that
+hopefully you feel comfortable with
+
+ align:start position:0%
+hopefully you feel comfortable with
+ 
+
+ align:start position:0%
+hopefully you feel comfortable with
+potentially modifying all right so what
+
+ align:start position:0%
+potentially modifying all right so what
+ 
+
+ align:start position:0%
+potentially modifying all right so what
+I'm going to do now is at first I'm
+
+ align:start position:0%
+I'm going to do now is at first I'm
+ 
+
+ align:start position:0%
+I'm going to do now is at first I'm
+going to go ahead and show you some code
+
+ align:start position:0%
+going to go ahead and show you some code
+ 
+
+ align:start position:0%
+going to go ahead and show you some code
+that corresponds to something that I is
+
+ align:start position:0%
+that corresponds to something that I is
+ 
+
+ align:start position:0%
+that corresponds to something that I is
+the original code except that I'm gonna
+
+ align:start position:0%
+the original code except that I'm gonna
+ 
+
+ align:start position:0%
+the original code except that I'm gonna
+add some smarts to it all right what I'm
+
+ align:start position:0%
+add some smarts to it all right what I'm
+ 
+
+ align:start position:0%
+add some smarts to it all right what I'm
+going to do is at any given point of
+
+ align:start position:0%
+going to do is at any given point of
+ 
+
+ align:start position:0%
+going to do is at any given point of
+time I'm gonna try to do some
+
+ align:start position:0%
+time I'm gonna try to do some
+ 
+
+ align:start position:0%
+time I'm gonna try to do some
+implications without actually doing any
+
+ align:start position:0%
+implications without actually doing any
+ 
+
+ align:start position:0%
+implications without actually doing any
+guessing right so the way I'm going to
+
+ align:start position:0%
+guessing right so the way I'm going to
+ 
+
+ align:start position:0%
+guessing right so the way I'm going to
+integrate the human approach into this
+
+ align:start position:0%
+integrate the human approach into this
+ 
+
+ align:start position:0%
+integrate the human approach into this
+exhaustive search approach a top level
+
+ align:start position:0%
+exhaustive search approach a top level
+ 
+
+ align:start position:0%
+exhaustive search approach a top level
+is I'm gonna take my configuration and
+
+ align:start position:0%
+is I'm gonna take my configuration and
+ 
+
+ align:start position:0%
+is I'm gonna take my configuration and
+before I do an arbitrary guess before I
+
+ align:start position:0%
+before I do an arbitrary guess before I
+ 
+
+ align:start position:0%
+before I do an arbitrary guess before I
+call find next cell or maybe I have a
+
+ align:start position:0%
+call find next cell or maybe I have a
+ 
+
+ align:start position:0%
+call find next cell or maybe I have a
+particular location here that I'm
+
+ align:start position:0%
+particular location here that I'm
+ 
+
+ align:start position:0%
+particular location here that I'm
+eventually going to guess so I do know
+
+ align:start position:0%
+eventually going to guess so I do know
+ 
+
+ align:start position:0%
+eventually going to guess so I do know
+that but before that I'm going to try
+
+ align:start position:0%
+that but before that I'm going to try
+ 
+
+ align:start position:0%
+that but before that I'm going to try
+and see whether the current grid values
+
+ align:start position:0%
+and see whether the current grid values
+ 
+
+ align:start position:0%
+and see whether the current grid values
+imply anything or not by using the rules
+
+ align:start position:0%
+imply anything or not by using the rules
+ 
+
+ align:start position:0%
+imply anything or not by using the rules
+in exactly the same way or roughly I
+
+ align:start position:0%
+in exactly the same way or roughly I
+ 
+
+ align:start position:0%
+in exactly the same way or roughly I
+should say the same way that we did
+
+ align:start position:0%
+should say the same way that we did
+ 
+
+ align:start position:0%
+should say the same way that we did
+right when we began the lecture all
+
+ align:start position:0%
+right when we began the lecture all
+ 
+
+ align:start position:0%
+right when we began the lecture all
+right so if we're going to try and use
+
+ align:start position:0%
+right so if we're going to try and use
+ 
+
+ align:start position:0%
+right so if we're going to try and use
+some implications and maybe imply the
+
+ align:start position:0%
+some implications and maybe imply the
+ 
+
+ align:start position:0%
+some implications and maybe imply the
+eight or imply something different
+
+ align:start position:0%
+eight or imply something different
+ 
+
+ align:start position:0%
+eight or imply something different
+associated with some other location
+
+ align:start position:0%
+associated with some other location
+ 
+
+ align:start position:0%
+associated with some other location
+right so this is not a backtrack right
+
+ align:start position:0%
+right so this is not a backtrack right
+ 
+
+ align:start position:0%
+right so this is not a backtrack right
+in the sense that this is going to be I
+
+ align:start position:0%
+in the sense that this is going to be I
+ 
+
+ align:start position:0%
+in the sense that this is going to be I
+can take this to the bank assuming I
+
+ align:start position:0%
+can take this to the bank assuming I
+ 
+
+ align:start position:0%
+can take this to the bank assuming I
+haven't done any guessing up until this
+
+ align:start position:0%
+haven't done any guessing up until this
+ 
+
+ align:start position:0%
+haven't done any guessing up until this
+point and assuming that the initial
+
+ align:start position:0%
+point and assuming that the initial
+ 
+
+ align:start position:0%
+point and assuming that the initial
+configuration that was given to me
+
+ align:start position:0%
+configuration that was given to me
+ 
+
+ align:start position:0%
+configuration that was given to me
+corresponds to a valid solution right
+
+ align:start position:0%
+corresponds to a valid solution right
+ 
+
+ align:start position:0%
+corresponds to a valid solution right
+but I'm actually going to do this at
+
+ align:start position:0%
+but I'm actually going to do this at
+ 
+
+ align:start position:0%
+but I'm actually going to do this at
+different points in the search so it
+
+ align:start position:0%
+different points in the search so it
+ 
+
+ align:start position:0%
+different points in the search so it
+might be that I'm just gonna arbitrarily
+
+ align:start position:0%
+might be that I'm just gonna arbitrarily
+ 
+
+ align:start position:0%
+might be that I'm just gonna arbitrarily
+choose a two here okay and and so I go
+
+ align:start position:0%
+choose a two here okay and and so I go
+ 
+
+ align:start position:0%
+choose a two here okay and and so I go
+through and I and and and I'm gonna uh
+
+ align:start position:0%
+through and I and and and I'm gonna uh
+ 
+
+ align:start position:0%
+through and I and and and I'm gonna uh
+take this in for argument's sake and I'm
+
+ align:start position:0%
+take this in for argument's sake and I'm
+ 
+
+ align:start position:0%
+take this in for argument's sake and I'm
+gonna put up two down and then I have
+
+ align:start position:0%
+gonna put up two down and then I have
+ 
+
+ align:start position:0%
+gonna put up two down and then I have
+not the initial puzzle that was given to
+
+ align:start position:0%
+not the initial puzzle that was given to
+ 
+
+ align:start position:0%
+not the initial puzzle that was given to
+me but something that I've kind of
+
+ align:start position:0%
+me but something that I've kind of
+ 
+
+ align:start position:0%
+me but something that I've kind of
+hacked in the center of stuck a two in
+
+ align:start position:0%
+hacked in the center of stuck a two in
+ 
+
+ align:start position:0%
+hacked in the center of stuck a two in
+there and that may not correspond to the
+
+ align:start position:0%
+there and that may not correspond to the
+ 
+
+ align:start position:0%
+there and that may not correspond to the
+solution because I just sort of put the
+
+ align:start position:0%
+solution because I just sort of put the
+ 
+
+ align:start position:0%
+solution because I just sort of put the
+two down there but now given the two I'm
+
+ align:start position:0%
+two down there but now given the two I'm
+ 
+
+ align:start position:0%
+two down there but now given the two I'm
+try and do some implications okay and
+
+ align:start position:0%
+try and do some implications okay and
+ 
+
+ align:start position:0%
+try and do some implications okay and
+I'm gonna try and see whether there
+
+ align:start position:0%
+I'm gonna try and see whether there
+ 
+
+ align:start position:0%
+I'm gonna try and see whether there
+there's things that are valid or not the
+
+ align:start position:0%
+there's things that are valid or not the
+ 
+
+ align:start position:0%
+there's things that are valid or not the
+important thing is that because I put a
+
+ align:start position:0%
+important thing is that because I put a
+ 
+
+ align:start position:0%
+important thing is that because I put a
+two down in an arbitrary way without
+
+ align:start position:0%
+two down in an arbitrary way without
+ 
+
+ align:start position:0%
+two down in an arbitrary way without
+using implications the two could have
+
+ align:start position:0%
+using implications the two could have
+ 
+
+ align:start position:0%
+using implications the two could have
+been incorrect I mean that's exactly why
+
+ align:start position:0%
+been incorrect I mean that's exactly why
+ 
+
+ align:start position:0%
+been incorrect I mean that's exactly why
+we have all of these back tracks correct
+
+ align:start position:0%
+we have all of these back tracks correct
+ 
+
+ align:start position:0%
+we have all of these back tracks correct
+because I've put down incorrect guesses
+
+ align:start position:0%
+because I've put down incorrect guesses
+ 
+
+ align:start position:0%
+because I've put down incorrect guesses
+and then I've had to backtrack so once I
+
+ align:start position:0%
+and then I've had to backtrack so once I
+ 
+
+ align:start position:0%
+and then I've had to backtrack so once I
+put a two down and then I fill in a
+
+ align:start position:0%
+put a two down and then I fill in a
+ 
+
+ align:start position:0%
+put a two down and then I fill in a
+bunch of things with implications you
+
+ align:start position:0%
+bunch of things with implications you
+ 
+
+ align:start position:0%
+bunch of things with implications you
+know I may even put an ad up there I may
+
+ align:start position:0%
+know I may even put an ad up there I may
+ 
+
+ align:start position:0%
+know I may even put an ad up there I may
+put a six out here etc etc and I go deep
+
+ align:start position:0%
+put a six out here etc etc and I go deep
+ 
+
+ align:start position:0%
+put a six out here etc etc and I go deep
+in and then I realized oh you know that
+
+ align:start position:0%
+in and then I realized oh you know that
+ 
+
+ align:start position:0%
+in and then I realized oh you know that
+too was a mistake okay the two should
+
+ align:start position:0%
+too was a mistake okay the two should
+ 
+
+ align:start position:0%
+too was a mistake okay the two should
+really should have been in there okay
+
+ align:start position:0%
+really should have been in there okay
+ 
+
+ align:start position:0%
+really should have been in there okay
+now I have to clean up everything I have
+
+ align:start position:0%
+now I have to clean up everything I have
+ 
+
+ align:start position:0%
+now I have to clean up everything I have
+to clean up all of the guesses that came
+
+ align:start position:0%
+to clean up all of the guesses that came
+ 
+
+ align:start position:0%
+to clean up all of the guesses that came
+after - and all of the implications that
+
+ align:start position:0%
+after - and all of the implications that
+ 
+
+ align:start position:0%
+after - and all of the implications that
+came after - all right that's the
+
+ align:start position:0%
+came after - all right that's the
+ 
+
+ align:start position:0%
+came after - all right that's the
+biggest thing that I wanted you to take
+
+ align:start position:0%
+biggest thing that I wanted you to take
+ 
+
+ align:start position:0%
+biggest thing that I wanted you to take
+away from this integration of
+
+ align:start position:0%
+away from this integration of
+ 
+
+ align:start position:0%
+away from this integration of
+implications with the exhaustive search
+
+ align:start position:0%
+implications with the exhaustive search
+ 
+
+ align:start position:0%
+implications with the exhaustive search
+it's clean up your mess clean up your
+
+ align:start position:0%
+it's clean up your mess clean up your
+ 
+
+ align:start position:0%
+it's clean up your mess clean up your
+bad guesses your the fact that you say
+
+ align:start position:0%
+bad guesses your the fact that you say
+ 
+
+ align:start position:0%
+bad guesses your the fact that you say
+oh but the implication was was something
+
+ align:start position:0%
+oh but the implication was was something
+ 
+
+ align:start position:0%
+oh but the implication was was something
+that was deterministic it was exactly
+
+ align:start position:0%
+that was deterministic it was exactly
+ 
+
+ align:start position:0%
+that was deterministic it was exactly
+following these rules
+
+ align:start position:0%
+following these rules
+ 
+
+ align:start position:0%
+following these rules
+nananana yeah it was deterministic all
+
+ align:start position:0%
+nananana yeah it was deterministic all
+ 
+
+ align:start position:0%
+nananana yeah it was deterministic all
+of that is true but you made a wrong
+
+ align:start position:0%
+of that is true but you made a wrong
+ 
+
+ align:start position:0%
+of that is true but you made a wrong
+guess and therefore everything that you
+
+ align:start position:0%
+guess and therefore everything that you
+ 
+
+ align:start position:0%
+guess and therefore everything that you
+did from then on out is is in question
+
+ align:start position:0%
+did from then on out is is in question
+ 
+
+ align:start position:0%
+did from then on out is is in question
+and if you in fact find a contradiction
+
+ align:start position:0%
+and if you in fact find a contradiction
+ 
+
+ align:start position:0%
+and if you in fact find a contradiction
+you got to go all the way back and clean
+
+ align:start position:0%
+you got to go all the way back and clean
+ 
+
+ align:start position:0%
+you got to go all the way back and clean
+up everything and then go back and erase
+
+ align:start position:0%
+up everything and then go back and erase
+ 
+
+ align:start position:0%
+up everything and then go back and erase
+everything that you had and then go take
+
+ align:start position:0%
+everything that you had and then go take
+ 
+
+ align:start position:0%
+everything that you had and then go take
+this too and maybe turn it into a three
+
+ align:start position:0%
+this too and maybe turn it into a three
+ 
+
+ align:start position:0%
+this too and maybe turn it into a three
+or what have you
+
+ align:start position:0%
+or what have you
+ 
+
+ align:start position:0%
+or what have you
+all right so um before I show you the
+
+ align:start position:0%
+all right so um before I show you the
+ 
+
+ align:start position:0%
+all right so um before I show you the
+code that does the implications and you
+
+ align:start position:0%
+code that does the implications and you
+ 
+
+ align:start position:0%
+code that does the implications and you
+can kind of imagine that there's many
+
+ align:start position:0%
+can kind of imagine that there's many
+ 
+
+ align:start position:0%
+can kind of imagine that there's many
+ways of you could do implications we did
+
+ align:start position:0%
+ways of you could do implications we did
+ 
+
+ align:start position:0%
+ways of you could do implications we did
+that manually I want to show you this
+
+ align:start position:0%
+that manually I want to show you this
+ 
+
+ align:start position:0%
+that manually I want to show you this
+part looks exactly the same as before
+
+ align:start position:0%
+part looks exactly the same as before
+ 
+
+ align:start position:0%
+part looks exactly the same as before
+no change fine next cell - grid is
+
+ align:start position:0%
+no change fine next cell - grid is
+ 
+
+ align:start position:0%
+no change fine next cell - grid is
+exactly the same it's valid is exactly
+
+ align:start position:0%
+exactly the same it's valid is exactly
+ 
+
+ align:start position:0%
+exactly the same it's valid is exactly
+the same right um there's a large make
+
+ align:start position:0%
+the same right um there's a large make
+ 
+
+ align:start position:0%
+the same right um there's a large make
+implications procedure and an undo
+
+ align:start position:0%
+implications procedure and an undo
+ 
+
+ align:start position:0%
+implications procedure and an undo
+implications that I'll get to in a
+
+ align:start position:0%
+implications that I'll get to in a
+ 
+
+ align:start position:0%
+implications that I'll get to in a
+second but this part here looks almost
+
+ align:start position:0%
+second but this part here looks almost
+ 
+
+ align:start position:0%
+second but this part here looks almost
+exactly the same except that I've
+
+ align:start position:0%
+exactly the same except that I've
+ 
+
+ align:start position:0%
+exactly the same except that I've
+replaced grid I J equals E with make
+
+ align:start position:0%
+replaced grid I J equals E with make
+ 
+
+ align:start position:0%
+replaced grid I J equals E with make
+implications okay
+
+ align:start position:0%
+implications okay
+ 
+
+ align:start position:0%
+implications okay
+and this is something that not only is
+
+ align:start position:0%
+and this is something that not only is
+ 
+
+ align:start position:0%
+and this is something that not only is
+what is what make implications is going
+
+ align:start position:0%
+what is what make implications is going
+ 
+
+ align:start position:0%
+what is what make implications is going
+to do is it's going to set whatever I
+
+ align:start position:0%
+to do is it's going to set whatever I
+ 
+
+ align:start position:0%
+to do is it's going to set whatever I
+had up here it's going to set to up here
+
+ align:start position:0%
+had up here it's going to set to up here
+ 
+
+ align:start position:0%
+had up here it's going to set to up here
+and on top of that it's going to go use
+
+ align:start position:0%
+and on top of that it's going to go use
+ 
+
+ align:start position:0%
+and on top of that it's going to go use
+these things to go fill in a bunch of
+
+ align:start position:0%
+these things to go fill in a bunch of
+ 
+
+ align:start position:0%
+these things to go fill in a bunch of
+different values in here right so it's
+
+ align:start position:0%
+different values in here right so it's
+ 
+
+ align:start position:0%
+different values in here right so it's
+one extra step this is the integration
+
+ align:start position:0%
+one extra step this is the integration
+ 
+
+ align:start position:0%
+one extra step this is the integration
+that I talked about so the idea is that
+
+ align:start position:0%
+that I talked about so the idea is that
+ 
+
+ align:start position:0%
+that I talked about so the idea is that
+now you could do this for the original
+
+ align:start position:0%
+now you could do this for the original
+ 
+
+ align:start position:0%
+now you could do this for the original
+the original as well but the point is
+
+ align:start position:0%
+the original as well but the point is
+ 
+
+ align:start position:0%
+the original as well but the point is
+once you've made a guess you always want
+
+ align:start position:0%
+once you've made a guess you always want
+ 
+
+ align:start position:0%
+once you've made a guess you always want
+to check to see whether that guess does
+
+ align:start position:0%
+to check to see whether that guess does
+ 
+
+ align:start position:0%
+to check to see whether that guess does
+certain implications or not right I mean
+
+ align:start position:0%
+certain implications or not right I mean
+ 
+
+ align:start position:0%
+certain implications or not right I mean
+that's the whole purpose of this
+
+ align:start position:0%
+that's the whole purpose of this
+ 
+
+ align:start position:0%
+that's the whole purpose of this
+exercise even humans do this in the very
+
+ align:start position:0%
+exercise even humans do this in the very
+ 
+
+ align:start position:0%
+exercise even humans do this in the very
+difficult puzzles they make a guess and
+
+ align:start position:0%
+difficult puzzles they make a guess and
+ 
+
+ align:start position:0%
+difficult puzzles they make a guess and
+then they see whether there's some
+
+ align:start position:0%
+then they see whether there's some
+ 
+
+ align:start position:0%
+then they see whether there's some
+implication or not and and maybe there's
+
+ align:start position:0%
+implication or not and and maybe there's
+ 
+
+ align:start position:0%
+implication or not and and maybe there's
+a contradiction and they have to go back
+
+ align:start position:0%
+a contradiction and they have to go back
+ 
+
+ align:start position:0%
+a contradiction and they have to go back
+and and undo all of that damage they
+
+ align:start position:0%
+and and undo all of that damage they
+ 
+
+ align:start position:0%
+and and undo all of that damage they
+caused and change the guess okay but in
+
+ align:start position:0%
+caused and change the guess okay but in
+ 
+
+ align:start position:0%
+caused and change the guess okay but in
+general when you have a configuration
+
+ align:start position:0%
+general when you have a configuration
+ 
+
+ align:start position:0%
+general when you have a configuration
+and you add to it it's possible
+
+ align:start position:0%
+and you add to it it's possible
+ 
+
+ align:start position:0%
+and you add to it it's possible
+certainly that there will be other
+
+ align:start position:0%
+certainly that there will be other
+ 
+
+ align:start position:0%
+certainly that there will be other
+things that are employed by the the one
+
+ align:start position:0%
+things that are employed by the the one
+ 
+
+ align:start position:0%
+things that are employed by the the one
+change that you made to it all right so
+
+ align:start position:0%
+change that you made to it all right so
+ 
+
+ align:start position:0%
+change that you made to it all right so
+grid IJ equals E in the original code
+
+ align:start position:0%
+grid IJ equals E in the original code
+ 
+
+ align:start position:0%
+grid IJ equals E in the original code
+got replaced with this procedure that
+
+ align:start position:0%
+got replaced with this procedure that
+ 
+
+ align:start position:0%
+got replaced with this procedure that
+we'll talk about which I don't want to
+
+ align:start position:0%
+we'll talk about which I don't want to
+ 
+
+ align:start position:0%
+we'll talk about which I don't want to
+spend a whole lot of time on but it's
+
+ align:start position:0%
+spend a whole lot of time on but it's
+ 
+
+ align:start position:0%
+spend a whole lot of time on but it's
+it's essentially something in terms of
+
+ align:start position:0%
+it's essentially something in terms of
+ 
+
+ align:start position:0%
+it's essentially something in terms of
+details but it's essentially something
+
+ align:start position:0%
+details but it's essentially something
+ 
+
+ align:start position:0%
+details but it's essentially something
+that puts in different values in the
+
+ align:start position:0%
+that puts in different values in the
+ 
+
+ align:start position:0%
+that puts in different values in the
+different locations and grid IJ equals
+
+ align:start position:0%
+different locations and grid IJ equals
+ 
+
+ align:start position:0%
+different locations and grid IJ equals
+zero is replaced by undoing plication
+
+ align:start position:0%
+zero is replaced by undoing plication
+ 
+
+ align:start position:0%
+zero is replaced by undoing plication
+which is cleaning up all of the
+
+ align:start position:0%
+which is cleaning up all of the
+ 
+
+ align:start position:0%
+which is cleaning up all of the
+incorrect guesses and incorrect
+
+ align:start position:0%
+incorrect guesses and incorrect
+ 
+
+ align:start position:0%
+incorrect guesses and incorrect
+implications and the reason the
+
+ align:start position:0%
+implications and the reason the
+ 
+
+ align:start position:0%
+implications and the reason the
+implications are incorrect because it
+
+ align:start position:0%
+implications are incorrect because it
+ 
+
+ align:start position:0%
+implications are incorrect because it
+came from an incorrect guess okay and so
+
+ align:start position:0%
+came from an incorrect guess okay and so
+ 
+
+ align:start position:0%
+came from an incorrect guess okay and so
+so that's it undue implications is
+
+ align:start position:0%
+so that's it undue implications is
+ 
+
+ align:start position:0%
+so that's it undue implications is
+trivial it just sets all of the
+
+ align:start position:0%
+trivial it just sets all of the
+ 
+
+ align:start position:0%
+trivial it just sets all of the
+implications and I'll tell you what the
+
+ align:start position:0%
+implications and I'll tell you what the
+ 
+
+ align:start position:0%
+implications and I'll tell you what the
+data structure is in a second but think
+
+ align:start position:0%
+data structure is in a second but think
+ 
+
+ align:start position:0%
+data structure is in a second but think
+of it as as making everything zero going
+
+ align:start position:0%
+of it as as making everything zero going
+ 
+
+ align:start position:0%
+of it as as making everything zero going
+back to a clean slate right I mean clean
+
+ align:start position:0%
+back to a clean slate right I mean clean
+ 
+
+ align:start position:0%
+back to a clean slate right I mean clean
+slate in the sense that Minette
+
+ align:start position:0%
+slate in the sense that Minette
+ 
+
+ align:start position:0%
+slate in the sense that Minette
+implications and guesses are cleaned up
+
+ align:start position:0%
+implications and guesses are cleaned up
+ 
+
+ align:start position:0%
+implications and guesses are cleaned up
+all right so that's all there is over
+
+ align:start position:0%
+all right so that's all there is over
+ 
+
+ align:start position:0%
+all right so that's all there is over
+here make implications is you can do
+
+ align:start position:0%
+here make implications is you can do
+ 
+
+ align:start position:0%
+here make implications is you can do
+anything you want you can do you know
+
+ align:start position:0%
+anything you want you can do you know
+ 
+
+ align:start position:0%
+anything you want you can do you know
+vertical scans you can do horizontal
+
+ align:start position:0%
+vertical scans you can do horizontal
+ 
+
+ align:start position:0%
+vertical scans you can do horizontal
+scans you can there's if you go look at
+
+ align:start position:0%
+scans you can there's if you go look at
+ 
+
+ align:start position:0%
+scans you can there's if you go look at
+the pseudocode literature and you look
+
+ align:start position:0%
+the pseudocode literature and you look
+ 
+
+ align:start position:0%
+the pseudocode literature and you look
+in ways of playing Sudoku this books
+
+ align:start position:0%
+in ways of playing Sudoku this books
+ 
+
+ align:start position:0%
+in ways of playing Sudoku this books
+written on how you can become a better
+
+ align:start position:0%
+written on how you can become a better
+ 
+
+ align:start position:0%
+written on how you can become a better
+pseudo ku puzzle solver and there's it
+
+ align:start position:0%
+pseudo ku puzzle solver and there's it
+ 
+
+ align:start position:0%
+pseudo ku puzzle solver and there's it
+you could take that and you could code
+
+ align:start position:0%
+you could take that and you could code
+ 
+
+ align:start position:0%
+you could take that and you could code
+that in and you could replace make
+
+ align:start position:0%
+that in and you could replace make
+ 
+
+ align:start position:0%
+that in and you could replace make
+implications with those fancy techniques
+
+ align:start position:0%
+implications with those fancy techniques
+ 
+
+ align:start position:0%
+implications with those fancy techniques
+that are up there right but we've
+
+ align:start position:0%
+that are up there right but we've
+ 
+
+ align:start position:0%
+that are up there right but we've
+established I'm lazy and so I only write
+
+ align:start position:0%
+established I'm lazy and so I only write
+ 
+
+ align:start position:0%
+established I'm lazy and so I only write
+I only write a certain amount of code
+
+ align:start position:0%
+I only write a certain amount of code
+ 
+
+ align:start position:0%
+I only write a certain amount of code
+and then I get tired and so I wrote
+
+ align:start position:0%
+and then I get tired and so I wrote
+ 
+
+ align:start position:0%
+and then I get tired and so I wrote
+about 20 lines of code corresponding to
+
+ align:start position:0%
+about 20 lines of code corresponding to
+ 
+
+ align:start position:0%
+about 20 lines of code corresponding to
+a fairly straightforward implication
+
+ align:start position:0%
+a fairly straightforward implication
+ 
+
+ align:start position:0%
+a fairly straightforward implication
+just to give you a sense of of how this
+
+ align:start position:0%
+just to give you a sense of of how this
+ 
+
+ align:start position:0%
+just to give you a sense of of how this
+would work but the most important thing
+
+ align:start position:0%
+would work but the most important thing
+ 
+
+ align:start position:0%
+would work but the most important thing
+in here is not the details of making
+
+ align:start position:0%
+in here is not the details of making
+ 
+
+ align:start position:0%
+in here is not the details of making
+plication and I'll give you some sense
+
+ align:start position:0%
+plication and I'll give you some sense
+ 
+
+ align:start position:0%
+plication and I'll give you some sense
+of that before we're done but it's
+
+ align:start position:0%
+of that before we're done but it's
+ 
+
+ align:start position:0%
+of that before we're done but it's
+really this structure that is that that
+
+ align:start position:0%
+really this structure that is that that
+ 
+
+ align:start position:0%
+really this structure that is that that
+is the most important the fact that I've
+
+ align:start position:0%
+is the most important the fact that I've
+ 
+
+ align:start position:0%
+is the most important the fact that I've
+done make lubrications here and undo
+
+ align:start position:0%
+done make lubrications here and undo
+ 
+
+ align:start position:0%
+done make lubrications here and undo
+implications here it's the correctness a
+
+ align:start position:0%
+implications here it's the correctness a
+ 
+
+ align:start position:0%
+implications here it's the correctness a
+requirement that is important to
+
+ align:start position:0%
+requirement that is important to
+ 
+
+ align:start position:0%
+requirement that is important to
+exhaustive search okay so if I do this
+
+ align:start position:0%
+exhaustive search okay so if I do this
+ 
+
+ align:start position:0%
+exhaustive search okay so if I do this
+and and I do kind of the implications
+
+ align:start position:0%
+and and I do kind of the implications
+ 
+
+ align:start position:0%
+and and I do kind of the implications
+that we had right at the beginning of
+
+ align:start position:0%
+that we had right at the beginning of
+ 
+
+ align:start position:0%
+that we had right at the beginning of
+lecture and I go ahead and run it just
+
+ align:start position:0%
+lecture and I go ahead and run it just
+ 
+
+ align:start position:0%
+lecture and I go ahead and run it just
+take a look I won't write this out but
+
+ align:start position:0%
+take a look I won't write this out but
+ 
+
+ align:start position:0%
+take a look I won't write this out but
+remember what the back tracks are for
+
+ align:start position:0%
+remember what the back tracks are for
+ 
+
+ align:start position:0%
+remember what the back tracks are for
+these things roughly speaking for the
+
+ align:start position:0%
+these things roughly speaking for the
+ 
+
+ align:start position:0%
+these things roughly speaking for the
+original Sudoku I'm sorry
+
+ align:start position:0%
+original Sudoku I'm sorry
+ 
+
+ align:start position:0%
+original Sudoku I'm sorry
+I need to go to the shell and it was it
+
+ align:start position:0%
+I need to go to the shell and it was it
+ 
+
+ align:start position:0%
+I need to go to the shell and it was it
+was 335 what is it the 579 6-3 6-3
+
+ align:start position:0%
+was 335 what is it the 579 6-3 6-3
+ 
+
+ align:start position:0%
+was 335 what is it the 579 6-3 6-3
+335 thousand and nine 949 okay so if I
+
+ align:start position:0%
+335 thousand and nine 949 okay so if I
+ 
+
+ align:start position:0%
+335 thousand and nine 949 okay so if I
+go off and I I run Sudoku optimized
+
+ align:start position:0%
+go off and I I run Sudoku optimized
+ 
+
+ align:start position:0%
+go off and I I run Sudoku optimized
+which is doing these implications like I
+
+ align:start position:0%
+which is doing these implications like I
+ 
+
+ align:start position:0%
+which is doing these implications like I
+described and and I go ahead and run
+
+ align:start position:0%
+described and and I go ahead and run
+ 
+
+ align:start position:0%
+described and and I go ahead and run
+that the first one goes from 579 233
+
+ align:start position:0%
+that the first one goes from 579 233
+ 
+
+ align:start position:0%
+that the first one goes from 579 233
+backtracks okay so so that's pretty good
+
+ align:start position:0%
+backtracks okay so so that's pretty good
+ 
+
+ align:start position:0%
+backtracks okay so so that's pretty good
+it because it's done a bunch of
+
+ align:start position:0%
+it because it's done a bunch of
+ 
+
+ align:start position:0%
+it because it's done a bunch of
+implications it's still it's it's not
+
+ align:start position:0%
+implications it's still it's it's not
+ 
+
+ align:start position:0%
+implications it's still it's it's not
+super smart I mean that is a simple
+
+ align:start position:0%
+super smart I mean that is a simple
+ 
+
+ align:start position:0%
+super smart I mean that is a simple
+enough puzzle that a human being would
+
+ align:start position:0%
+enough puzzle that a human being would
+ 
+
+ align:start position:0%
+enough puzzle that a human being would
+not backtrack I mean a human being would
+
+ align:start position:0%
+not backtrack I mean a human being would
+ 
+
+ align:start position:0%
+not backtrack I mean a human being would
+not backtrack in that first puzzle right
+
+ align:start position:0%
+not backtrack in that first puzzle right
+ 
+
+ align:start position:0%
+not backtrack in that first puzzle right
+and you should you should check check
+
+ align:start position:0%
+and you should you should check check
+ 
+
+ align:start position:0%
+and you should you should check check
+that and oh this thing finished in the
+
+ align:start position:0%
+that and oh this thing finished in the
+ 
+
+ align:start position:0%
+that and oh this thing finished in the
+middle so it went to 33 only had three
+
+ align:start position:0%
+middle so it went to 33 only had three
+ 
+
+ align:start position:0%
+middle so it went to 33 only had three
+of them what do I have here instead I'll
+
+ align:start position:0%
+of them what do I have here instead I'll
+ 
+
+ align:start position:0%
+of them what do I have here instead I'll
+go opt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I see I only ran oh wow
+
+ align:start position:0%
+oh I see I only ran oh wow
+ 
+
+ align:start position:0%
+oh I see I only ran oh wow
+okay so I ran into hard and difficult so
+
+ align:start position:0%
+okay so I ran into hard and difficult so
+ 
+
+ align:start position:0%
+okay so I ran into hard and difficult so
+it really went from 6-3 6-3 to 33 it
+
+ align:start position:0%
+it really went from 6-3 6-3 to 33 it
+ 
+
+ align:start position:0%
+it really went from 6-3 6-3 to 33 it
+went from 335 thousand to 24,000 and
+
+ align:start position:0%
+went from 335 thousand to 24,000 and
+ 
+
+ align:start position:0%
+went from 335 thousand to 24,000 and
+then it went to 720 from 1949 to 726 I
+
+ align:start position:0%
+then it went to 720 from 1949 to 726 I
+ 
+
+ align:start position:0%
+then it went to 720 from 1949 to 726 I
+mean the details aren't the numbers
+
+ align:start position:0%
+mean the details aren't the numbers
+ 
+
+ align:start position:0%
+mean the details aren't the numbers
+aren't super important don't hang your
+
+ align:start position:0%
+aren't super important don't hang your
+ 
+
+ align:start position:0%
+aren't super important don't hang your
+hat on them obviously if I change the
+
+ align:start position:0%
+hat on them obviously if I change the
+ 
+
+ align:start position:0%
+hat on them obviously if I change the
+code those numbers change but you can
+
+ align:start position:0%
+code those numbers change but you can
+ 
+
+ align:start position:0%
+code those numbers change but you can
+see that there's substantial gains to be
+
+ align:start position:0%
+see that there's substantial gains to be
+ 
+
+ align:start position:0%
+see that there's substantial gains to be
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+in terms of implications not making
+
+ align:start position:0%
+in terms of implications not making
+ 
+
+ align:start position:0%
+in terms of implications not making
+these dumb guesses that clearly are
+
+ align:start position:0%
+these dumb guesses that clearly are
+ 
+
+ align:start position:0%
+these dumb guesses that clearly are
+incorrect and that you you can fill in
+
+ align:start position:0%
+incorrect and that you you can fill in
+ 
+
+ align:start position:0%
+incorrect and that you you can fill in
+if you take away some of these empty
+
+ align:start position:0%
+if you take away some of these empty
+ 
+
+ align:start position:0%
+if you take away some of these empty
+squares then the depth of the recursion
+
+ align:start position:0%
+squares then the depth of the recursion
+ 
+
+ align:start position:0%
+squares then the depth of the recursion
+that you have to go through become
+
+ align:start position:0%
+that you have to go through become
+ 
+
+ align:start position:0%
+that you have to go through become
+substantially smaller and that's why
+
+ align:start position:0%
+substantially smaller and that's why
+ 
+
+ align:start position:0%
+substantially smaller and that's why
+your your backtracking is is simpler so
+
+ align:start position:0%
+your your backtracking is is simpler so
+ 
+
+ align:start position:0%
+your your backtracking is is simpler so
+I want to leave you with a couple of
+
+ align:start position:0%
+I want to leave you with a couple of
+ 
+
+ align:start position:0%
+I want to leave you with a couple of
+things I want to give you some sense for
+
+ align:start position:0%
+things I want to give you some sense for
+ 
+
+ align:start position:0%
+things I want to give you some sense for
+what particular implication that a
+
+ align:start position:0%
+what particular implication that a
+ 
+
+ align:start position:0%
+what particular implication that a
+strategy that we used and so I'll just
+
+ align:start position:0%
+strategy that we used and so I'll just
+ 
+
+ align:start position:0%
+strategy that we used and so I'll just
+put up make implications and give you
+
+ align:start position:0%
+put up make implications and give you
+ 
+
+ align:start position:0%
+put up make implications and give you
+some sense for how this works so the
+
+ align:start position:0%
+some sense for how this works so the
+ 
+
+ align:start position:0%
+some sense for how this works so the
+basic idea is that what I'm doing here
+
+ align:start position:0%
+basic idea is that what I'm doing here
+ 
+
+ align:start position:0%
+basic idea is that what I'm doing here
+is I'm looking at a particular sector
+
+ align:start position:0%
+is I'm looking at a particular sector
+ 
+
+ align:start position:0%
+is I'm looking at a particular sector
+and and I've created a data structure
+
+ align:start position:0%
+and and I've created a data structure
+ 
+
+ align:start position:0%
+and and I've created a data structure
+that says the missing elements here if I
+
+ align:start position:0%
+that says the missing elements here if I
+ 
+
+ align:start position:0%
+that says the missing elements here if I
+put a two in here let's just say I go
+
+ align:start position:0%
+put a two in here let's just say I go
+ 
+
+ align:start position:0%
+put a two in here let's just say I go
+ahead and put a two in here the missing
+
+ align:start position:0%
+ahead and put a two in here the missing
+ 
+
+ align:start position:0%
+ahead and put a two in here the missing
+elements here are our the set is three
+
+ align:start position:0%
+elements here are our the set is three
+ 
+
+ align:start position:0%
+elements here are our the set is three
+four five six seven and nine all right
+
+ align:start position:0%
+four five six seven and nine all right
+ 
+
+ align:start position:0%
+four five six seven and nine all right
+so this could be three four five six
+
+ align:start position:0%
+so this could be three four five six
+ 
+
+ align:start position:0%
+so this could be three four five six
+seven eight nine this could be three
+
+ align:start position:0%
+seven eight nine this could be three
+ 
+
+ align:start position:0%
+seven eight nine this could be three
+four five six seven eight nine and this
+
+ align:start position:0%
+four five six seven eight nine and this
+ 
+
+ align:start position:0%
+four five six seven eight nine and this
+is quite dumb right now but each of
+
+ align:start position:0%
+is quite dumb right now but each of
+ 
+
+ align:start position:0%
+is quite dumb right now but each of
+these different squares could be three
+
+ align:start position:0%
+these different squares could be three
+ 
+
+ align:start position:0%
+these different squares could be three
+four five six seven eight nine okay
+
+ align:start position:0%
+four five six seven eight nine okay
+ 
+
+ align:start position:0%
+four five six seven eight nine okay
+possibly all right and then I say so
+
+ align:start position:0%
+possibly all right and then I say so
+ 
+
+ align:start position:0%
+possibly all right and then I say so
+that's the first part of the code and
+
+ align:start position:0%
+that's the first part of the code and
+ 
+
+ align:start position:0%
+that's the first part of the code and
+then I say I'm gonna attach essentially
+
+ align:start position:0%
+then I say I'm gonna attach essentially
+ 
+
+ align:start position:0%
+then I say I'm gonna attach essentially
+a copy of this set to each of the
+
+ align:start position:0%
+a copy of this set to each of the
+ 
+
+ align:start position:0%
+a copy of this set to each of the
+missing squares and then I'm going to go
+
+ align:start position:0%
+missing squares and then I'm going to go
+ 
+
+ align:start position:0%
+missing squares and then I'm going to go
+through and find the missing elements so
+
+ align:start position:0%
+through and find the missing elements so
+ 
+
+ align:start position:0%
+through and find the missing elements so
+so this thing here can be a nine because
+
+ align:start position:0%
+so this thing here can be a nine because
+ 
+
+ align:start position:0%
+so this thing here can be a nine because
+I see a nine here it can be a three
+
+ align:start position:0%
+I see a nine here it can be a three
+ 
+
+ align:start position:0%
+I see a nine here it can be a three
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so I can take this thing here and I'd
+
+ align:start position:0%
+so I can take this thing here and I'd
+ 
+
+ align:start position:0%
+so I can take this thing here and I'd
+take away that at the nine and then take
+
+ align:start position:0%
+take away that at the nine and then take
+ 
+
+ align:start position:0%
+take away that at the nine and then take
+away the three and and I can do the same
+
+ align:start position:0%
+away the three and and I can do the same
+ 
+
+ align:start position:0%
+away the three and and I can do the same
+thing with that obviously I can also
+
+ align:start position:0%
+thing with that obviously I can also
+ 
+
+ align:start position:0%
+thing with that obviously I can also
+take away the the eight isn't there but
+
+ align:start position:0%
+take away the the eight isn't there but
+ 
+
+ align:start position:0%
+take away the the eight isn't there but
+I could take away the seven and I could
+
+ align:start position:0%
+I could take away the seven and I could
+ 
+
+ align:start position:0%
+I could take away the seven and I could
+take away the three the six and the one
+
+ align:start position:0%
+take away the three the six and the one
+ 
+
+ align:start position:0%
+take away the three the six and the one
+so I go ahead and I take away the six
+
+ align:start position:0%
+so I go ahead and I take away the six
+ 
+
+ align:start position:0%
+so I go ahead and I take away the six
+and the three was already take taken out
+
+ align:start position:0%
+and the three was already take taken out
+ 
+
+ align:start position:0%
+and the three was already take taken out
+and I keep doing this and I try and
+
+ align:start position:0%
+and I keep doing this and I try and
+ 
+
+ align:start position:0%
+and I keep doing this and I try and
+shrink the possibilities corresponding
+
+ align:start position:0%
+shrink the possibilities corresponding
+ 
+
+ align:start position:0%
+shrink the possibilities corresponding
+to this particular square the curtain
+
+ align:start position:0%
+to this particular square the curtain
+ 
+
+ align:start position:0%
+to this particular square the curtain
+that has the set of different
+
+ align:start position:0%
+that has the set of different
+ 
+
+ align:start position:0%
+that has the set of different
+possibilities and if I ever so when can
+
+ align:start position:0%
+possibilities and if I ever so when can
+ 
+
+ align:start position:0%
+possibilities and if I ever so when can
+I make an implication what is the
+
+ align:start position:0%
+I make an implication what is the
+ 
+
+ align:start position:0%
+I make an implication what is the
+condition that is going to let me make
+
+ align:start position:0%
+condition that is going to let me make
+ 
+
+ align:start position:0%
+condition that is going to let me make
+an implication when I take this set of
+
+ align:start position:0%
+an implication when I take this set of
+ 
+
+ align:start position:0%
+an implication when I take this set of
+numbers and I start shrinking them down
+
+ align:start position:0%
+numbers and I start shrinking them down
+ 
+
+ align:start position:0%
+numbers and I start shrinking them down
+using these rules that I have over on
+
+ align:start position:0%
+using these rules that I have over on
+ 
+
+ align:start position:0%
+using these rules that I have over on
+the the right hand side there what what
+
+ align:start position:0%
+the the right hand side there what what
+ 
+
+ align:start position:0%
+the the right hand side there what what
+is an implication what does that
+
+ align:start position:0%
+is an implication what does that
+ 
+
+ align:start position:0%
+is an implication what does that
+correspond to in relation to the size in
+
+ align:start position:0%
+correspond to in relation to the size in
+ 
+
+ align:start position:0%
+correspond to in relation to the size in
+relation to the set right yeah behind
+
+ align:start position:0%
+relation to the set right yeah behind
+ 
+
+ align:start position:0%
+relation to the set right yeah behind
+you right that's exactly right
+
+ align:start position:0%
+you right that's exactly right
+ 
+
+ align:start position:0%
+you right that's exactly right
+if you have one element in this set then
+
+ align:start position:0%
+if you have one element in this set then
+ 
+
+ align:start position:0%
+if you have one element in this set then
+that's an implication if I have two
+
+ align:start position:0%
+that's an implication if I have two
+ 
+
+ align:start position:0%
+that's an implication if I have two
+elements in the set it's not implication
+
+ align:start position:0%
+elements in the set it's not implication
+ 
+
+ align:start position:0%
+elements in the set it's not implication
+because I don't quite know what you do
+
+ align:start position:0%
+because I don't quite know what you do
+ 
+
+ align:start position:0%
+because I don't quite know what you do
+there but if I had one element in the
+
+ align:start position:0%
+there but if I had one element in the
+ 
+
+ align:start position:0%
+there but if I had one element in the
+set that's an implication and that's it
+
+ align:start position:0%
+set that's an implication and that's it
+ 
+
+ align:start position:0%
+set that's an implication and that's it
+that said you know this code is not
+
+ align:start position:0%
+that said you know this code is not
+ 
+
+ align:start position:0%
+that said you know this code is not
+complicated check if the V set is a
+
+ align:start position:0%
+complicated check if the V set is a
+ 
+
+ align:start position:0%
+complicated check if the V set is a
+single turn which is a single element
+
+ align:start position:0%
+single turn which is a single element
+ 
+
+ align:start position:0%
+single turn which is a single element
+and I'm going to go ahead and append to
+
+ align:start position:0%
+and I'm going to go ahead and append to
+ 
+
+ align:start position:0%
+and I'm going to go ahead and append to
+this implication which is a very
+
+ align:start position:0%
+this implication which is a very
+ 
+
+ align:start position:0%
+this implication which is a very
+straightforward data structure that says
+
+ align:start position:0%
+straightforward data structure that says
+ 
+
+ align:start position:0%
+straightforward data structure that says
+this is the grid location I grid
+
+ align:start position:0%
+this is the grid location I grid
+ 
+
+ align:start position:0%
+this is the grid location I grid
+location J and this is the value that
+
+ align:start position:0%
+location J and this is the value that
+ 
+
+ align:start position:0%
+location J and this is the value that
+was implied by that all right so not
+
+ align:start position:0%
+was implied by that all right so not
+ 
+
+ align:start position:0%
+was implied by that all right so not
+only do I have I J E which is the which
+
+ align:start position:0%
+only do I have I J E which is the which
+ 
+
+ align:start position:0%
+only do I have I J E which is the which
+is the original guess that I have I also
+
+ align:start position:0%
+is the original guess that I have I also
+ 
+
+ align:start position:0%
+is the original guess that I have I also
+have you know kind of a bunch of other
+
+ align:start position:0%
+have you know kind of a bunch of other
+ 
+
+ align:start position:0%
+have you know kind of a bunch of other
+tuples corresponding to different
+
+ align:start position:0%
+tuples corresponding to different
+ 
+
+ align:start position:0%
+tuples corresponding to different
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+you know k ik l coordinates and the
+
+ align:start position:0%
+you know k ik l coordinates and the
+ 
+
+ align:start position:0%
+you know k ik l coordinates and the
+value call it V associated with that and
+
+ align:start position:0%
+value call it V associated with that and
+ 
+
+ align:start position:0%
+value call it V associated with that and
+these are all the different implications
+
+ align:start position:0%
+these are all the different implications
+ 
+
+ align:start position:0%
+these are all the different implications
+that I can collect together in this list
+
+ align:start position:0%
+that I can collect together in this list
+ 
+
+ align:start position:0%
+that I can collect together in this list
+and I can just add those things in to
+
+ align:start position:0%
+and I can just add those things in to
+ 
+
+ align:start position:0%
+and I can just add those things in to
+make implications and then I keep going
+
+ align:start position:0%
+make implications and then I keep going
+ 
+
+ align:start position:0%
+make implications and then I keep going
+and then if I ever realize I've made a
+
+ align:start position:0%
+and then if I ever realize I've made a
+ 
+
+ align:start position:0%
+and then if I ever realize I've made a
+bad guess I have to undo everything by
+
+ align:start position:0%
+bad guess I have to undo everything by
+ 
+
+ align:start position:0%
+bad guess I have to undo everything by
+zeroing them all out which is making
+
+ align:start position:0%
+zeroing them all out which is making
+ 
+
+ align:start position:0%
+zeroing them all out which is making
+them all empty all right so one thing
+
+ align:start position:0%
+them all empty all right so one thing
+ 
+
+ align:start position:0%
+them all empty all right so one thing
+that this code does and you can you can
+
+ align:start position:0%
+that this code does and you can you can
+ 
+
+ align:start position:0%
+that this code does and you can you can
+take a look at it and I would encourage
+
+ align:start position:0%
+take a look at it and I would encourage
+ 
+
+ align:start position:0%
+take a look at it and I would encourage
+you to do the first exercise which is
+
+ align:start position:0%
+you to do the first exercise which is
+ 
+
+ align:start position:0%
+you to do the first exercise which is
+taking these implications and making
+
+ align:start position:0%
+taking these implications and making
+ 
+
+ align:start position:0%
+taking these implications and making
+them a little more powerful by adding
+
+ align:start position:0%
+them a little more powerful by adding
+ 
+
+ align:start position:0%
+them a little more powerful by adding
+like three or four lines occurred to
+
+ align:start position:0%
+like three or four lines occurred to
+ 
+
+ align:start position:0%
+like three or four lines occurred to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+this code and exactly what you have to
+
+ align:start position:0%
+this code and exactly what you have to
+ 
+
+ align:start position:0%
+this code and exactly what you have to
+do in this exercise and I'll show you
+
+ align:start position:0%
+do in this exercise and I'll show you
+ 
+
+ align:start position:0%
+do in this exercise and I'll show you
+what the results should be in in just a
+
+ align:start position:0%
+what the results should be in in just a
+ 
+
+ align:start position:0%
+what the results should be in in just a
+minute but let me just spend 30 seconds
+
+ align:start position:0%
+minute but let me just spend 30 seconds
+ 
+
+ align:start position:0%
+minute but let me just spend 30 seconds
+explaining to you how you could do a
+
+ align:start position:0%
+explaining to you how you could do a
+ 
+
+ align:start position:0%
+explaining to you how you could do a
+little bit better than what this code
+
+ align:start position:0%
+little bit better than what this code
+ 
+
+ align:start position:0%
+little bit better than what this code
+does so what I've described to you
+
+ align:start position:0%
+does so what I've described to you
+ 
+
+ align:start position:0%
+does so what I've described to you
+really is this get this set you know
+
+ align:start position:0%
+really is this get this set you know
+ 
+
+ align:start position:0%
+really is this get this set you know
+imply get a single term etc and then you
+
+ align:start position:0%
+imply get a single term etc and then you
+ 
+
+ align:start position:0%
+imply get a single term etc and then you
+can do this obviously for each of these
+
+ align:start position:0%
+can do this obviously for each of these
+ 
+
+ align:start position:0%
+can do this obviously for each of these
+sectors and that's what this does you
+
+ align:start position:0%
+sectors and that's what this does you
+ 
+
+ align:start position:0%
+sectors and that's what this does you
+had a for loop up there that does it for
+
+ align:start position:0%
+had a for loop up there that does it for
+ 
+
+ align:start position:0%
+had a for loop up there that does it for
+each of the sectors right grab a sector
+
+ align:start position:0%
+each of the sectors right grab a sector
+ 
+
+ align:start position:0%
+each of the sectors right grab a sector
+and go ahead and do an implication for
+
+ align:start position:0%
+and go ahead and do an implication for
+ 
+
+ align:start position:0%
+and go ahead and do an implication for
+that sector now this code just runs
+
+ align:start position:0%
+that sector now this code just runs
+ 
+
+ align:start position:0%
+that sector now this code just runs
+through the sectors you know 1 2 3 4 5 6
+
+ align:start position:0%
+through the sectors you know 1 2 3 4 5 6
+ 
+
+ align:start position:0%
+through the sectors you know 1 2 3 4 5 6
+7 8 9 and then discovers the
+
+ align:start position:0%
+7 8 9 and then discovers the
+ 
+
+ align:start position:0%
+7 8 9 and then discovers the
+implications if they exist adds them to
+
+ align:start position:0%
+implications if they exist adds them to
+ 
+
+ align:start position:0%
+implications if they exist adds them to
+the apply list and then throws up his
+
+ align:start position:0%
+the apply list and then throws up his
+ 
+
+ align:start position:0%
+the apply list and then throws up his
+hands and says I'm tired I'm done I
+
+ align:start position:0%
+hands and says I'm tired I'm done I
+ 
+
+ align:start position:0%
+hands and says I'm tired I'm done I
+don't want to do any more ok what could
+
+ align:start position:0%
+don't want to do any more ok what could
+ 
+
+ align:start position:0%
+don't want to do any more ok what could
+you do that's an improvement
+
+ align:start position:0%
+you do that's an improvement
+ 
+
+ align:start position:0%
+you do that's an improvement
+given what we have described and what
+
+ align:start position:0%
+given what we have described and what
+ 
+
+ align:start position:0%
+given what we have described and what
+I've told you so far what is an
+
+ align:start position:0%
+I've told you so far what is an
+ 
+
+ align:start position:0%
+I've told you so far what is an
+incremental improvement over going over
+
+ align:start position:0%
+incremental improvement over going over
+ 
+
+ align:start position:0%
+incremental improvement over going over
+these sectors once and doing these
+
+ align:start position:0%
+these sectors once and doing these
+ 
+
+ align:start position:0%
+these sectors once and doing these
+implications and storing them and moving
+
+ align:start position:0%
+implications and storing them and moving
+ 
+
+ align:start position:0%
+implications and storing them and moving
+on what was an incremental improvement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly you don't have to stop right
+
+ align:start position:0%
+exactly you don't have to stop right
+ 
+
+ align:start position:0%
+exactly you don't have to stop right
+there's no reason to stop if you're
+
+ align:start position:0%
+there's no reason to stop if you're
+ 
+
+ align:start position:0%
+there's no reason to stop if you're
+implying right once you put something in
+
+ align:start position:0%
+implying right once you put something in
+ 
+
+ align:start position:0%
+implying right once you put something in
+here and you've gone through 1 2 3 4 5 6
+
+ align:start position:0%
+here and you've gone through 1 2 3 4 5 6
+ 
+
+ align:start position:0%
+here and you've gone through 1 2 3 4 5 6
+7 8 9 got the implications you can put
+
+ align:start position:0%
+7 8 9 got the implications you can put
+ 
+
+ align:start position:0%
+7 8 9 got the implications you can put
+them into the grid and then start over
+
+ align:start position:0%
+them into the grid and then start over
+ 
+
+ align:start position:0%
+them into the grid and then start over
+again 1 2 3 4 that's what humans do
+
+ align:start position:0%
+again 1 2 3 4 that's what humans do
+ 
+
+ align:start position:0%
+again 1 2 3 4 that's what humans do
+right when humans put something in and
+
+ align:start position:0%
+right when humans put something in and
+ 
+
+ align:start position:0%
+right when humans put something in and
+they don't stop they just keep going
+
+ align:start position:0%
+they don't stop they just keep going
+ 
+
+ align:start position:0%
+they don't stop they just keep going
+until they get to the end right now
+
+ align:start position:0%
+until they get to the end right now
+ 
+
+ align:start position:0%
+until they get to the end right now
+first all of these implications are
+
+ align:start position:0%
+first all of these implications are
+ 
+
+ align:start position:0%
+first all of these implications are
+could be incorrect if that first guess
+
+ align:start position:0%
+could be incorrect if that first guess
+ 
+
+ align:start position:0%
+could be incorrect if that first guess
+was incorrect there's no there's no
+
+ align:start position:0%
+was incorrect there's no there's no
+ 
+
+ align:start position:0%
+was incorrect there's no there's no
+change there but there's nothing that's
+
+ align:start position:0%
+change there but there's nothing that's
+ 
+
+ align:start position:0%
+change there but there's nothing that's
+stopping you from from turning this this
+
+ align:start position:0%
+stopping you from from turning this this
+ 
+
+ align:start position:0%
+stopping you from from turning this this
+little thing there's a loop here that
+
+ align:start position:0%
+little thing there's a loop here that
+ 
+
+ align:start position:0%
+little thing there's a loop here that
+simply corresponds to making a pass over
+
+ align:start position:0%
+simply corresponds to making a pass over
+ 
+
+ align:start position:0%
+simply corresponds to making a pass over
+the sector's but you can put this whole
+
+ align:start position:0%
+the sector's but you can put this whole
+ 
+
+ align:start position:0%
+the sector's but you can put this whole
+thing into a loop and and you keep going
+
+ align:start position:0%
+thing into a loop and and you keep going
+ 
+
+ align:start position:0%
+thing into a loop and and you keep going
+through the loop until you've you
+
+ align:start position:0%
+through the loop until you've you
+ 
+
+ align:start position:0%
+through the loop until you've you
+basically have no change that happens in
+
+ align:start position:0%
+basically have no change that happens in
+ 
+
+ align:start position:0%
+basically have no change that happens in
+your in your grid ok so that's four
+
+ align:start position:0%
+your in your grid ok so that's four
+ 
+
+ align:start position:0%
+your in your grid ok so that's four
+lines of code and I'm not going to show
+
+ align:start position:0%
+lines of code and I'm not going to show
+ 
+
+ align:start position:0%
+lines of code and I'm not going to show
+you what those four lines of code look
+
+ align:start position:0%
+you what those four lines of code look
+ 
+
+ align:start position:0%
+you what those four lines of code look
+like so close your eyes in case it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the solution to that code
+
+ align:start position:0%
+and this is the solution to that code
+ 
+
+ align:start position:0%
+and this is the solution to that code
+and I'm going to go ahead and run it and
+
+ align:start position:0%
+and I'm going to go ahead and run it and
+ 
+
+ align:start position:0%
+and I'm going to go ahead and run it and
+you saw what those numbers where with
+
+ align:start position:0%
+you saw what those numbers where with
+ 
+
+ align:start position:0%
+you saw what those numbers where with
+with respect to do the back tracks but
+
+ align:start position:0%
+with respect to do the back tracks but
+ 
+
+ align:start position:0%
+with respect to do the back tracks but
+if you do this extra implications the 33
+
+ align:start position:0%
+if you do this extra implications the 33
+ 
+
+ align:start position:0%
+if you do this extra implications the 33
+went down to two okay for that example
+
+ align:start position:0%
+went down to two okay for that example
+ 
+
+ align:start position:0%
+went down to two okay for that example
+so this is not optimal because I wanted
+
+ align:start position:0%
+so this is not optimal because I wanted
+ 
+
+ align:start position:0%
+so this is not optimal because I wanted
+one right so if I wanted to be a human
+
+ align:start position:0%
+one right so if I wanted to be a human
+ 
+
+ align:start position:0%
+one right so if I wanted to be a human
+being that took this easy puzzle and
+
+ align:start position:0%
+being that took this easy puzzle and
+ 
+
+ align:start position:0%
+being that took this easy puzzle and
+just sort of went all the way without
+
+ align:start position:0%
+just sort of went all the way without
+ 
+
+ align:start position:0%
+just sort of went all the way without
+making any incorrect guesses I would be
+
+ align:start position:0%
+making any incorrect guesses I would be
+ 
+
+ align:start position:0%
+making any incorrect guesses I would be
+doing implications and that would go all
+
+ align:start position:0%
+doing implications and that would go all
+ 
+
+ align:start position:0%
+doing implications and that would go all
+the way and I got close with with two
+
+ align:start position:0%
+the way and I got close with with two
+ 
+
+ align:start position:0%
+the way and I got close with with two
+and I didn't print out the intermediate
+
+ align:start position:0%
+and I didn't print out the intermediate
+ 
+
+ align:start position:0%
+and I didn't print out the intermediate
+ones but the 24,000 went down to 11,000
+
+ align:start position:0%
+ones but the 24,000 went down to 11,000
+ 
+
+ align:start position:0%
+ones but the 24,000 went down to 11,000
+and I forget what the last one was it
+
+ align:start position:0%
+and I forget what the last one was it
+ 
+
+ align:start position:0%
+and I forget what the last one was it
+went down right so with four lines of
+
+ align:start position:0%
+went down right so with four lines of
+ 
+
+ align:start position:0%
+went down right so with four lines of
+code and with the optimized code that
+
+ align:start position:0%
+code and with the optimized code that
+ 
+
+ align:start position:0%
+code and with the optimized code that
+I'll put up you should be able to get
+
+ align:start position:0%
+I'll put up you should be able to get
+ 
+
+ align:start position:0%
+I'll put up you should be able to get
+those numbers in your in your first
+
+ align:start position:0%
+those numbers in your in your first
+ 
+
+ align:start position:0%
+those numbers in your in your first
+exercise or you could solve diagonal
+
+ align:start position:0%
+exercise or you could solve diagonal
+ 
+
+ align:start position:0%
+exercise or you could solve diagonal
+Sudoku or even Sudoku or you could spend
+
+ align:start position:0%
+Sudoku or even Sudoku or you could spend
+ 
+
+ align:start position:0%
+Sudoku or even Sudoku or you could spend
+the rest of the day coding whatever you
+
+ align:start position:0%
+the rest of the day coding whatever you
+ 
+
+ align:start position:0%
+the rest of the day coding whatever you
+want whatever all right see you next
+
+ align:start position:0%
+want whatever all right see you next
+ 
+
+ align:start position:0%
+want whatever all right see you next
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/bTyxpoi2dmM.txt b/bTyxpoi2dmM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..049669cd5ad429b51231f46ed3b937fc94196c01
--- /dev/null
+++ b/bTyxpoi2dmM.txt
@@ -0,0 +1,12181 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer high quality educational
+
+ align:start position:0%
+to offer high quality educational
+ 
+
+ align:start position:0%
+to offer high quality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu So today we're going to talk
+
+ align:start position:0%
+ocw.mit.edu So today we're going to talk
+ 
+
+ align:start position:0%
+ocw.mit.edu So today we're going to talk
+about uh communication
+
+ align:start position:0%
+about uh communication
+ 
+
+ align:start position:0%
+about uh communication
+networks communication networks is a
+
+ align:start position:0%
+networks communication networks is a
+ 
+
+ align:start position:0%
+networks communication networks is a
+great application of graph Theory so
+
+ align:start position:0%
+great application of graph Theory so
+ 
+
+ align:start position:0%
+great application of graph Theory so
+what we're going to study is uh how do
+
+ align:start position:0%
+what we're going to study is uh how do
+ 
+
+ align:start position:0%
+what we're going to study is uh how do
+you route packets through networks so
+
+ align:start position:0%
+you route packets through networks so
+ 
+
+ align:start position:0%
+you route packets through networks so
+you have the internet which is a geotic
+
+ align:start position:0%
+you have the internet which is a geotic
+ 
+
+ align:start position:0%
+you have the internet which is a geotic
+network it's not organized we are
+
+ align:start position:0%
+network it's not organized we are
+ 
+
+ align:start position:0%
+network it's not organized we are
+interested in highly structured networks
+
+ align:start position:0%
+interested in highly structured networks
+ 
+
+ align:start position:0%
+interested in highly structured networks
+and you can find them for example in
+
+ align:start position:0%
+and you can find them for example in
+ 
+
+ align:start position:0%
+and you can find them for example in
+parallel computers where you want to
+
+ align:start position:0%
+parallel computers where you want to
+ 
+
+ align:start position:0%
+parallel computers where you want to
+Route um uh the data flow you can find
+
+ align:start position:0%
+Route um uh the data flow you can find
+ 
+
+ align:start position:0%
+Route um uh the data flow you can find
+them in uh certain telephone switch uh
+
+ align:start position:0%
+them in uh certain telephone switch uh
+ 
+
+ align:start position:0%
+them in uh certain telephone switch uh
+um um uh networks and so on so we're
+
+ align:start position:0%
+um um uh networks and so on so we're
+ 
+
+ align:start position:0%
+um um uh networks and so on so we're
+going to talk about few a few very
+
+ align:start position:0%
+going to talk about few a few very
+ 
+
+ align:start position:0%
+going to talk about few a few very
+special ones binary trees and then
+
+ align:start position:0%
+special ones binary trees and then
+ 
+
+ align:start position:0%
+special ones binary trees and then
+slowly we will figure out what all these
+
+ align:start position:0%
+slowly we will figure out what all these
+ 
+
+ align:start position:0%
+slowly we will figure out what all these
+performance measures really mean this
+
+ align:start position:0%
+performance measures really mean this
+ 
+
+ align:start position:0%
+performance measures really mean this
+one has to do with latency we have
+
+ align:start position:0%
+one has to do with latency we have
+ 
+
+ align:start position:0%
+one has to do with latency we have
+switches their size the number of them
+
+ align:start position:0%
+switches their size the number of them
+ 
+
+ align:start position:0%
+switches their size the number of them
+congestion and then we will slowly get
+
+ align:start position:0%
+congestion and then we will slowly get
+ 
+
+ align:start position:0%
+congestion and then we will slowly get
+down to Ben's Network which is a really
+
+ align:start position:0%
+down to Ben's Network which is a really
+ 
+
+ align:start position:0%
+down to Ben's Network which is a really
+beautiful network with beautiful uh
+
+ align:start position:0%
+beautiful network with beautiful uh
+ 
+
+ align:start position:0%
+beautiful network with beautiful uh
+parameters and we're going to prove
+
+ align:start position:0%
+parameters and we're going to prove
+ 
+
+ align:start position:0%
+parameters and we're going to prove
+those so
+
+ align:start position:0%
+those so
+ 
+
+ align:start position:0%
+those so
+um let's start off with uh the first one
+
+ align:start position:0%
+um let's start off with uh the first one
+ 
+
+ align:start position:0%
+um let's start off with uh the first one
+the complete binary tree and let me draw
+
+ align:start position:0%
+the complete binary tree and let me draw
+ 
+
+ align:start position:0%
+the complete binary tree and let me draw
+it for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you in this uh Network we will have um
+
+ align:start position:0%
+you in this uh Network we will have um
+ 
+
+ align:start position:0%
+you in this uh Network we will have um
+uh a root and let me just draw it first
+
+ align:start position:0%
+uh a root and let me just draw it first
+ 
+
+ align:start position:0%
+uh a root and let me just draw it first
+we have uh fases that uh represent here
+
+ align:start position:0%
+we have uh fases that uh represent here
+ 
+
+ align:start position:0%
+we have uh fases that uh represent here
+the switches so these C CES let me
+
+ align:start position:0%
+the switches so these C CES let me
+ 
+
+ align:start position:0%
+the switches so these C CES let me
+explain it over
+
+ align:start position:0%
+explain it over
+ 
+
+ align:start position:0%
+explain it over
+here actually represent a switch and the
+
+ align:start position:0%
+here actually represent a switch and the
+ 
+
+ align:start position:0%
+here actually represent a switch and the
+idea is that these actually
+
+ align:start position:0%
+idea is that these actually
+ 
+
+ align:start position:0%
+idea is that these actually
+direct um uh
+
+ align:start position:0%
+direct um uh
+ 
+
+ align:start position:0%
+direct um uh
+packets through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+network and these packets are fixed
+
+ align:start position:0%
+network and these packets are fixed
+ 
+
+ align:start position:0%
+network and these packets are fixed
+sized uh packets of data so like I don't
+
+ align:start position:0%
+sized uh packets of data so like I don't
+ 
+
+ align:start position:0%
+sized uh packets of data so like I don't
+know say 4,000 uh bytes or or or bits or
+
+ align:start position:0%
+know say 4,000 uh bytes or or or bits or
+ 
+
+ align:start position:0%
+know say 4,000 uh bytes or or or bits or
+whatever the network wants you to comply
+
+ align:start position:0%
+whatever the network wants you to comply
+ 
+
+ align:start position:0%
+whatever the network wants you to comply
+to so these are fixed sites pieces of
+
+ align:start position:0%
+to so these are fixed sites pieces of
+ 
+
+ align:start position:0%
+to so these are fixed sites pieces of
+data so what we want is we want to uh be
+
+ align:start position:0%
+data so what we want is we want to uh be
+ 
+
+ align:start position:0%
+data so what we want is we want to uh be
+able from every terminal and a terminal
+
+ align:start position:0%
+able from every terminal and a terminal
+ 
+
+ align:start position:0%
+able from every terminal and a terminal
+I will denote by a square from every
+
+ align:start position:0%
+I will denote by a square from every
+ 
+
+ align:start position:0%
+I will denote by a square from every
+terminal I want to be able to uh reach
+
+ align:start position:0%
+terminal I want to be able to uh reach
+ 
+
+ align:start position:0%
+terminal I want to be able to uh reach
+any other terminal so what is a terminal
+
+ align:start position:0%
+any other terminal so what is a terminal
+ 
+
+ align:start position:0%
+any other terminal so what is a terminal
+terminal is like a computer or something
+
+ align:start position:0%
+terminal is like a computer or something
+ 
+
+ align:start position:0%
+terminal is like a computer or something
+like that it's uh it's it's actually the
+
+ align:start position:0%
+like that it's uh it's it's actually the
+ 
+
+ align:start position:0%
+like that it's uh it's it's actually the
+source and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+destination of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data so what we're looking for is how
+
+ align:start position:0%
+data so what we're looking for is how
+ 
+
+ align:start position:0%
+data so what we're looking for is how
+can we route how we can find a network
+
+ align:start position:0%
+can we route how we can find a network
+ 
+
+ align:start position:0%
+can we route how we can find a network
+of switches that are connected through
+
+ align:start position:0%
+of switches that are connected through
+ 
+
+ align:start position:0%
+of switches that are connected through
+wires fibers or yeah it's the
+
+ align:start position:0%
+wires fibers or yeah it's the
+ 
+
+ align:start position:0%
+wires fibers or yeah it's the
+question top of theut
+
+ align:start position:0%
+question top of theut
+ 
+
+ align:start position:0%
+question top of theut
+off one oh sorry okay thank you um so
+
+ align:start position:0%
+off one oh sorry okay thank you um so
+ 
+
+ align:start position:0%
+off one oh sorry okay thank you um so
+what we want is we want to uh route uh
+
+ align:start position:0%
+what we want is we want to uh route uh
+ 
+
+ align:start position:0%
+what we want is we want to uh route uh
+packets that come from any terminal to
+
+ align:start position:0%
+packets that come from any terminal to
+ 
+
+ align:start position:0%
+packets that come from any terminal to
+any other terminal that is what our goal
+
+ align:start position:0%
+any other terminal that is what our goal
+ 
+
+ align:start position:0%
+any other terminal that is what our goal
+is and we want to uh make sure that that
+
+ align:start position:0%
+is and we want to uh make sure that that
+ 
+
+ align:start position:0%
+is and we want to uh make sure that that
+is efficient so the first one is this
+
+ align:start position:0%
+is efficient so the first one is this
+ 
+
+ align:start position:0%
+is efficient so the first one is this
+binary tree and let's uh
+
+ align:start position:0%
+binary tree and let's uh
+ 
+
+ align:start position:0%
+binary tree and let's uh
+um see how this may work we may have
+
+ align:start position:0%
+um see how this may work we may have
+ 
+
+ align:start position:0%
+um see how this may work we may have
+switches that actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that actually have uh inputs coming
+
+ align:start position:0%
+um that actually have uh inputs coming
+ 
+
+ align:start position:0%
+um that actually have uh inputs coming
+from a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Terminals and the switches may also
+
+ align:start position:0%
+Terminals and the switches may also
+ 
+
+ align:start position:0%
+Terminals and the switches may also
+output to terminals these are here at
+
+ align:start position:0%
+output to terminals these are here at
+ 
+
+ align:start position:0%
+output to terminals these are here at
+the bottom at this side we have a
+
+ align:start position:0%
+the bottom at this side we have a
+ 
+
+ align:start position:0%
+the bottom at this side we have a
+similar uh structure this is the root of
+
+ align:start position:0%
+similar uh structure this is the root of
+ 
+
+ align:start position:0%
+similar uh structure this is the root of
+the tree we have another switch over
+
+ align:start position:0%
+the tree we have another switch over
+ 
+
+ align:start position:0%
+the tree we have another switch over
+here we call go down we go up here and
+
+ align:start position:0%
+here we call go down we go up here and
+ 
+
+ align:start position:0%
+here we call go down we go up here and
+once more like this and again we have
+
+ align:start position:0%
+once more like this and again we have
+ 
+
+ align:start position:0%
+once more like this and again we have
+oops we have input coming in or an
+
+ align:start position:0%
+oops we have input coming in or an
+ 
+
+ align:start position:0%
+oops we have input coming in or an
+output coming
+
+ align:start position:0%
+output coming
+ 
+
+ align:start position:0%
+output coming
+out to their respective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terminals so what is happening here is
+
+ align:start position:0%
+terminals so what is happening here is
+ 
+
+ align:start position:0%
+terminals so what is happening here is
+that uh I would like to have an
+
+ align:start position:0%
+that uh I would like to have an
+ 
+
+ align:start position:0%
+that uh I would like to have an
+input say input zero wants to travel all
+
+ align:start position:0%
+input say input zero wants to travel all
+ 
+
+ align:start position:0%
+input say input zero wants to travel all
+the way over to say the output that is
+
+ align:start position:0%
+the way over to say the output that is
+ 
+
+ align:start position:0%
+the way over to say the output that is
+present over here so let me label these
+
+ align:start position:0%
+present over here so let me label these
+ 
+
+ align:start position:0%
+present over here so let me label these
+so we have the output zero input
+
+ align:start position:0%
+so we have the output zero input
+ 
+
+ align:start position:0%
+so we have the output zero input
+one output
+
+ align:start position:0%
+one output
+ 
+
+ align:start position:0%
+one output
+one input two and output
+
+ align:start position:0%
+one input two and output
+ 
+
+ align:start position:0%
+one input two and output
+two input uh three and output
+
+ align:start position:0%
+two input uh three and output
+ 
+
+ align:start position:0%
+two input uh three and output
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+so uh well I can definitely reach every
+
+ align:start position:0%
+so uh well I can definitely reach every
+ 
+
+ align:start position:0%
+so uh well I can definitely reach every
+single output from any in put so that's
+
+ align:start position:0%
+single output from any in put so that's
+ 
+
+ align:start position:0%
+single output from any in put so that's
+great so this looks like uh something
+
+ align:start position:0%
+great so this looks like uh something
+ 
+
+ align:start position:0%
+great so this looks like uh something
+that you are familiar with right it's
+
+ align:start position:0%
+that you are familiar with right it's
+ 
+
+ align:start position:0%
+that you are familiar with right it's
+like just a tree we have essentially
+
+ align:start position:0%
+like just a tree we have essentially
+ 
+
+ align:start position:0%
+like just a tree we have essentially
+it's a directed tree but but I mean it's
+
+ align:start position:0%
+it's a directed tree but but I mean it's
+ 
+
+ align:start position:0%
+it's a directed tree but but I mean it's
+a directed graph but these edges go in
+
+ align:start position:0%
+a directed graph but these edges go in
+ 
+
+ align:start position:0%
+a directed graph but these edges go in
+both directions right so I have an edge
+
+ align:start position:0%
+both directions right so I have an edge
+ 
+
+ align:start position:0%
+both directions right so I have an edge
+that goes from here to here and back
+
+ align:start position:0%
+that goes from here to here and back
+ 
+
+ align:start position:0%
+that goes from here to here and back
+from here to here so this is the kind of
+
+ align:start position:0%
+from here to here so this is the kind of
+ 
+
+ align:start position:0%
+from here to here so this is the kind of
+layout that you could try out first to
+
+ align:start position:0%
+layout that you could try out first to
+ 
+
+ align:start position:0%
+layout that you could try out first to
+see whether this type of network would
+
+ align:start position:0%
+see whether this type of network would
+ 
+
+ align:start position:0%
+see whether this type of network would
+lead to good
+
+ align:start position:0%
+lead to good
+ 
+
+ align:start position:0%
+lead to good
+performance so let's uh have a look at
+
+ align:start position:0%
+performance so let's uh have a look at
+ 
+
+ align:start position:0%
+performance so let's uh have a look at
+the different parameters and see uh how
+
+ align:start position:0%
+the different parameters and see uh how
+ 
+
+ align:start position:0%
+the different parameters and see uh how
+well this behaves so here we have a few
+
+ align:start position:0%
+well this behaves so here we have a few
+ 
+
+ align:start position:0%
+well this behaves so here we have a few
+parameters that we build that we will be
+
+ align:start position:0%
+parameters that we build that we will be
+ 
+
+ align:start position:0%
+parameters that we build that we will be
+talking
+
+ align:start position:0%
+talking
+ 
+
+ align:start position:0%
+talking
+about um so first of all let's talk
+
+ align:start position:0%
+about um so first of all let's talk
+ 
+
+ align:start position:0%
+about um so first of all let's talk
+about uh the
+
+ align:start position:0%
+about uh the
+ 
+
+ align:start position:0%
+about uh the
+latency in this particular Network so
+
+ align:start position:0%
+latency in this particular Network so
+ 
+
+ align:start position:0%
+latency in this particular Network so
+how are we going to measure
+
+ align:start position:0%
+how are we going to measure
+ 
+
+ align:start position:0%
+how are we going to measure
+this well we're going to look at this
+
+ align:start position:0%
+this well we're going to look at this
+ 
+
+ align:start position:0%
+this well we're going to look at this
+graph and we're going to measure it by
+
+ align:start position:0%
+graph and we're going to measure it by
+ 
+
+ align:start position:0%
+graph and we're going to measure it by
+the number of wires that you need to go
+
+ align:start position:0%
+the number of wires that you need to go
+ 
+
+ align:start position:0%
+the number of wires that you need to go
+through from an input to an output
+
+ align:start position:0%
+through from an input to an output
+ 
+
+ align:start position:0%
+through from an input to an output
+so let me write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down so the
+
+ align:start position:0%
+down so the
+ 
+
+ align:start position:0%
+down so the
+latency is the time that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+required uh for a packet to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+travel um to
+
+ align:start position:0%
+travel um to
+ 
+
+ align:start position:0%
+travel um to
+travel from an input to an output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how are we going to measure this
+
+ align:start position:0%
+and how are we going to measure this
+ 
+
+ align:start position:0%
+and how are we going to measure this
+well we're just going to measure this by
+
+ align:start position:0%
+well we're just going to measure this by
+ 
+
+ align:start position:0%
+well we're just going to measure this by
+the number of wires that we need to go
+
+ align:start position:0%
+the number of wires that we need to go
+ 
+
+ align:start position:0%
+the number of wires that we need to go
+through so this you have seen before we
+
+ align:start position:0%
+through so this you have seen before we
+ 
+
+ align:start position:0%
+through so this you have seen before we
+can measure this by the diameter of that
+
+ align:start position:0%
+can measure this by the diameter of that
+ 
+
+ align:start position:0%
+can measure this by the diameter of that
+particular graph so here we will Define
+
+ align:start position:0%
+particular graph so here we will Define
+ 
+
+ align:start position:0%
+particular graph so here we will Define
+it for a network so the diameter of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+network is going to be the length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the shortest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between between the input and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output that are furthest
+
+ align:start position:0%
+output that are furthest
+ 
+
+ align:start position:0%
+output that are furthest
+apart so let's have a look at the uh
+
+ align:start position:0%
+apart so let's have a look at the uh
+ 
+
+ align:start position:0%
+apart so let's have a look at the uh
+graph of
+
+ align:start position:0%
+graph of
+ 
+
+ align:start position:0%
+graph of
+above um so for
+
+ align:start position:0%
+above um so for
+ 
+
+ align:start position:0%
+above um so for
+example uh we can clearly see that for
+
+ align:start position:0%
+example uh we can clearly see that for
+ 
+
+ align:start position:0%
+example uh we can clearly see that for
+example input and output so say input
+
+ align:start position:0%
+example input and output so say input
+ 
+
+ align:start position:0%
+example input and output so say input
+zero and output one are connected by
+
+ align:start position:0%
+zero and output one are connected by
+ 
+
+ align:start position:0%
+zero and output one are connected by
+just going up uh one step over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here but just going up from here to here
+
+ align:start position:0%
+here but just going up from here to here
+ 
+
+ align:start position:0%
+here but just going up from here to here
+then this switch forwards the packet to
+
+ align:start position:0%
+then this switch forwards the packet to
+ 
+
+ align:start position:0%
+then this switch forwards the packet to
+this switch this switch reroutes it
+
+ align:start position:0%
+this switch this switch reroutes it
+ 
+
+ align:start position:0%
+this switch this switch reroutes it
+forwards it over here and then it goes
+
+ align:start position:0%
+forwards it over here and then it goes
+ 
+
+ align:start position:0%
+forwards it over here and then it goes
+back to the output output one so for
+
+ align:start position:0%
+back to the output output one so for
+ 
+
+ align:start position:0%
+back to the output output one so for
+example this particular path only has
+
+ align:start position:0%
+example this particular path only has
+ 
+
+ align:start position:0%
+example this particular path only has
+one two three four uh edges and what
+
+ align:start position:0%
+one two three four uh edges and what
+ 
+
+ align:start position:0%
+one two three four uh edges and what
+we're interested in is uh sort of the
+
+ align:start position:0%
+we're interested in is uh sort of the
+ 
+
+ align:start position:0%
+we're interested in is uh sort of the
+worst case uh time that it requires to
+
+ align:start position:0%
+worst case uh time that it requires to
+ 
+
+ align:start position:0%
+worst case uh time that it requires to
+go from an input to an output so that
+
+ align:start position:0%
+go from an input to an output so that
+ 
+
+ align:start position:0%
+go from an input to an output so that
+means that we are interested in a
+
+ align:start position:0%
+means that we are interested in a
+ 
+
+ align:start position:0%
+means that we are interested in a
+diameter and a diameter is in this case
+
+ align:start position:0%
+diameter and a diameter is in this case
+ 
+
+ align:start position:0%
+diameter and a diameter is in this case
+well the shortest path that you can find
+
+ align:start position:0%
+well the shortest path that you can find
+ 
+
+ align:start position:0%
+well the shortest path that you can find
+from an input to uh to an outputs that
+
+ align:start position:0%
+from an input to uh to an outputs that
+ 
+
+ align:start position:0%
+from an input to uh to an outputs that
+are furthest apart so what are those who
+
+ align:start position:0%
+are furthest apart so what are those who
+ 
+
+ align:start position:0%
+are furthest apart so what are those who
+are furthest apart well of course you
+
+ align:start position:0%
+are furthest apart well of course you
+ 
+
+ align:start position:0%
+are furthest apart well of course you
+would like to go through here right so
+
+ align:start position:0%
+would like to go through here right so
+ 
+
+ align:start position:0%
+would like to go through here right so
+if I connect the input zero to say
+
+ align:start position:0%
+if I connect the input zero to say
+ 
+
+ align:start position:0%
+if I connect the input zero to say
+output four I will need go I will need
+
+ align:start position:0%
+output four I will need go I will need
+ 
+
+ align:start position:0%
+output four I will need go I will need
+to go all the way up through the root
+
+ align:start position:0%
+to go all the way up through the root
+ 
+
+ align:start position:0%
+to go all the way up through the root
+down to the output and how many edges do
+
+ align:start position:0%
+down to the output and how many edges do
+ 
+
+ align:start position:0%
+down to the output and how many edges do
+we see here one two three four five six
+
+ align:start position:0%
+we see here one two three four five six
+ 
+
+ align:start position:0%
+we see here one two three four five six
+so in this example we have a
+
+ align:start position:0%
+so in this example we have a
+ 
+
+ align:start position:0%
+so in this example we have a
+diameter that is equal to six and in
+
+ align:start position:0%
+diameter that is equal to six and in
+ 
+
+ align:start position:0%
+diameter that is equal to six and in
+General if you are looking at uh at u n
+
+ align:start position:0%
+General if you are looking at uh at u n
+ 
+
+ align:start position:0%
+General if you are looking at uh at u n
+* n network so what does that mean n is
+
+ align:start position:0%
+* n network so what does that mean n is
+ 
+
+ align:start position:0%
+* n network so what does that mean n is
+the number of inputs and N is also the
+
+ align:start position:0%
+the number of inputs and N is also the
+ 
+
+ align:start position:0%
+the number of inputs and N is also the
+number of outputs so in this case we
+
+ align:start position:0%
+number of outputs so in this case we
+ 
+
+ align:start position:0%
+number of outputs so in this case we
+have a four times this is actually three
+
+ align:start position:0%
+have a four times this is actually three
+ 
+
+ align:start position:0%
+have a four times this is actually three
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+here we have a four we have four inputs
+
+ align:start position:0%
+here we have a four we have four inputs
+ 
+
+ align:start position:0%
+here we have a four we have four inputs
+and four outputs so this particular
+
+ align:start position:0%
+and four outputs so this particular
+ 
+
+ align:start position:0%
+and four outputs so this particular
+example depicted on the board is a four
+
+ align:start position:0%
+example depicted on the board is a four
+ 
+
+ align:start position:0%
+example depicted on the board is a four
+* 4 Network so if you generalize this
+
+ align:start position:0%
+* 4 Network so if you generalize this
+ 
+
+ align:start position:0%
+* 4 Network so if you generalize this
+for any size binary tree um uh say in n
+
+ align:start position:0%
+for any size binary tree um uh say in n
+ 
+
+ align:start position:0%
+for any size binary tree um uh say in n
+* n network then how many uh yeah what's
+
+ align:start position:0%
+* n network then how many uh yeah what's
+ 
+
+ align:start position:0%
+* n network then how many uh yeah what's
+the diameter of this of of of such a
+
+ align:start position:0%
+the diameter of this of of of such a
+ 
+
+ align:start position:0%
+the diameter of this of of of such a
+general Network well if we have n inputs
+
+ align:start position:0%
+general Network well if we have n inputs
+ 
+
+ align:start position:0%
+general Network well if we have n inputs
+and N outputs well we have to go all the
+
+ align:start position:0%
+and N outputs well we have to go all the
+ 
+
+ align:start position:0%
+and N outputs well we have to go all the
+way up through towards the root and all
+
+ align:start position:0%
+way up through towards the root and all
+ 
+
+ align:start position:0%
+way up through towards the root and all
+the way down so we actually count the
+
+ align:start position:0%
+the way down so we actually count the
+ 
+
+ align:start position:0%
+the way down so we actually count the
+length of a leaf to the root here twice
+
+ align:start position:0%
+length of a leaf to the root here twice
+ 
+
+ align:start position:0%
+length of a leaf to the root here twice
+so in General we have a diameter that
+
+ align:start position:0%
+so in General we have a diameter that
+ 
+
+ align:start position:0%
+so in General we have a diameter that
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+this it's uh 2
+
+ align:start position:0%
+this it's uh 2
+ 
+
+ align:start position:0%
+this it's uh 2
+* uh 1 plus the logarithm of n so in
+
+ align:start position:0%
+* uh 1 plus the logarithm of n so in
+ 
+
+ align:start position:0%
+* uh 1 plus the logarithm of n so in
+this uh lecture we will have
+
+ align:start position:0%
+this uh lecture we will have
+ 
+
+ align:start position:0%
+this uh lecture we will have
+n is going to be a power of
+
+ align:start position:0%
+n is going to be a power of
+ 
+
+ align:start position:0%
+n is going to be a power of
+two just to make calculations simple and
+
+ align:start position:0%
+two just to make calculations simple and
+ 
+
+ align:start position:0%
+two just to make calculations simple and
+uh the logarithm is always to the base
+
+ align:start position:0%
+uh the logarithm is always to the base
+ 
+
+ align:start position:0%
+uh the logarithm is always to the base
+two so this is the diameter of a general
+
+ align:start position:0%
+two so this is the diameter of a general
+ 
+
+ align:start position:0%
+two so this is the diameter of a general
+uh binary
+
+ align:start position:0%
+uh binary
+ 
+
+ align:start position:0%
+uh binary
+tree and uh well what are the other
+
+ align:start position:0%
+tree and uh well what are the other
+ 
+
+ align:start position:0%
+tree and uh well what are the other
+parameters so that does not look too bad
+
+ align:start position:0%
+parameters so that does not look too bad
+ 
+
+ align:start position:0%
+parameters so that does not look too bad
+I mean it's logarithmic in N so that
+
+ align:start position:0%
+I mean it's logarithmic in N so that
+ 
+
+ align:start position:0%
+I mean it's logarithmic in N so that
+sounds pretty good what about the switch
+
+ align:start position:0%
+sounds pretty good what about the switch
+ 
+
+ align:start position:0%
+sounds pretty good what about the switch
+sizes well how do I measure those it's
+
+ align:start position:0%
+sizes well how do I measure those it's
+ 
+
+ align:start position:0%
+sizes well how do I measure those it's
+like the number of inputs that get into
+
+ align:start position:0%
+like the number of inputs that get into
+ 
+
+ align:start position:0%
+like the number of inputs that get into
+it and the number of outputs that get
+
+ align:start position:0%
+it and the number of outputs that get
+ 
+
+ align:start position:0%
+it and the number of outputs that get
+out so in this case I will have one two
+
+ align:start position:0%
+out so in this case I will have one two
+ 
+
+ align:start position:0%
+out so in this case I will have one two
+inputs that go into this switch and
+
+ align:start position:0%
+inputs that go into this switch and
+ 
+
+ align:start position:0%
+inputs that go into this switch and
+there are two outputs coming out so this
+
+ align:start position:0%
+there are two outputs coming out so this
+ 
+
+ align:start position:0%
+there are two outputs coming out so this
+is what we call a 2 * 2 switch so this
+
+ align:start position:0%
+is what we call a 2 * 2 switch so this
+ 
+
+ align:start position:0%
+is what we call a 2 * 2 switch so this
+would be a 2 * 2 switch but if you look
+
+ align:start position:0%
+would be a 2 * 2 switch but if you look
+ 
+
+ align:start position:0%
+would be a 2 * 2 switch but if you look
+at this one for example we see one two
+
+ align:start position:0%
+at this one for example we see one two
+ 
+
+ align:start position:0%
+at this one for example we see one two
+three outgoing edges and one and and
+
+ align:start position:0%
+three outgoing edges and one and and
+ 
+
+ align:start position:0%
+three outgoing edges and one and and
+three ingoing edges so this is actually
+
+ align:start position:0%
+three ingoing edges so this is actually
+ 
+
+ align:start position:0%
+three ingoing edges so this is actually
+a three * three
+
+ align:start position:0%
+a three * three
+ 
+
+ align:start position:0%
+a three * three
+switch and uh in a general binary tree
+
+ align:start position:0%
+switch and uh in a general binary tree
+ 
+
+ align:start position:0%
+switch and uh in a general binary tree
+we will see that uh all these
+
+ align:start position:0%
+we will see that uh all these
+ 
+
+ align:start position:0%
+we will see that uh all these
+intermediate nodes over here they are
+
+ align:start position:0%
+intermediate nodes over here they are
+ 
+
+ align:start position:0%
+intermediate nodes over here they are
+all three times three switches so the
+
+ align:start position:0%
+all three times three switches so the
+ 
+
+ align:start position:0%
+all three times three switches so the
+the most the the approximately half of
+
+ align:start position:0%
+the most the the approximately half of
+ 
+
+ align:start position:0%
+the most the the approximately half of
+the the switches are actually three *
+
+ align:start position:0%
+the the switches are actually three *
+ 
+
+ align:start position:0%
+the the switches are actually three *
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+switches so that's a switch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size um now you may say well uh why
+
+ align:start position:0%
+size um now you may say well uh why
+ 
+
+ align:start position:0%
+size um now you may say well uh why
+don't I use like a larger size switch
+
+ align:start position:0%
+don't I use like a larger size switch
+ 
+
+ align:start position:0%
+don't I use like a larger size switch
+that would help me a lot right if I
+
+ align:start position:0%
+that would help me a lot right if I
+ 
+
+ align:start position:0%
+that would help me a lot right if I
+could uh uh use say a four time 4
+
+ align:start position:0%
+could uh uh use say a four time 4
+ 
+
+ align:start position:0%
+could uh uh use say a four time 4
+switch then I would be able to have more
+
+ align:start position:0%
+switch then I would be able to have more
+ 
+
+ align:start position:0%
+switch then I would be able to have more
+inputs coming in more outputs coming out
+
+ align:start position:0%
+inputs coming in more outputs coming out
+ 
+
+ align:start position:0%
+inputs coming in more outputs coming out
+and I can actually uh maybe use a tary
+
+ align:start position:0%
+and I can actually uh maybe use a tary
+ 
+
+ align:start position:0%
+and I can actually uh maybe use a tary
+tree rather than a binary tree in a
+
+ align:start position:0%
+tree rather than a binary tree in a
+ 
+
+ align:start position:0%
+tree rather than a binary tree in a
+binary tree every every node at the
+
+ align:start position:0%
+binary tree every every node at the
+ 
+
+ align:start position:0%
+binary tree every every node at the
+level has like two children right but we
+
+ align:start position:0%
+level has like two children right but we
+ 
+
+ align:start position:0%
+level has like two children right but we
+could design a tree that has at every
+
+ align:start position:0%
+could design a tree that has at every
+ 
+
+ align:start position:0%
+could design a tree that has at every
+level three children so then we can use
+
+ align:start position:0%
+level three children so then we can use
+ 
+
+ align:start position:0%
+level three children so then we can use
+four times four switches if you do that
+
+ align:start position:0%
+four times four switches if you do that
+ 
+
+ align:start position:0%
+four times four switches if you do that
+then the path from the LEF up to the
+
+ align:start position:0%
+then the path from the LEF up to the
+ 
+
+ align:start position:0%
+then the path from the LEF up to the
+root is getting shorter and the diameter
+
+ align:start position:0%
+root is getting shorter and the diameter
+ 
+
+ align:start position:0%
+root is getting shorter and the diameter
+gets smaller so if I increase sort of
+
+ align:start position:0%
+gets smaller so if I increase sort of
+ 
+
+ align:start position:0%
+gets smaller so if I increase sort of
+the switch size so rather than 3 * 3 we
+
+ align:start position:0%
+the switch size so rather than 3 * 3 we
+ 
+
+ align:start position:0%
+the switch size so rather than 3 * 3 we
+look at 4 * 4 or 5 * 5 6 * 6 and so on
+
+ align:start position:0%
+look at 4 * 4 or 5 * 5 6 * 6 and so on
+ 
+
+ align:start position:0%
+look at 4 * 4 or 5 * 5 6 * 6 and so on
+then the diameter will actually uh
+
+ align:start position:0%
+then the diameter will actually uh
+ 
+
+ align:start position:0%
+then the diameter will actually uh
+reduce so what about having a monster
+
+ align:start position:0%
+reduce so what about having a monster
+ 
+
+ align:start position:0%
+reduce so what about having a monster
+switch uh like I have just one switch
+
+ align:start position:0%
+switch uh like I have just one switch
+ 
+
+ align:start position:0%
+switch uh like I have just one switch
+and I have my input zero all the way up
+
+ align:start position:0%
+and I have my input zero all the way up
+ 
+
+ align:start position:0%
+and I have my input zero all the way up
+to input um n minus one and then I have
+
+ align:start position:0%
+to input um n minus one and then I have
+ 
+
+ align:start position:0%
+to input um n minus one and then I have
+my outputs on the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side well
+
+ align:start position:0%
+side well
+ 
+
+ align:start position:0%
+side well
+of course the switch size is n * n but
+
+ align:start position:0%
+of course the switch size is n * n but
+ 
+
+ align:start position:0%
+of course the switch size is n * n but
+the diameter is is is nothing right
+
+ align:start position:0%
+the diameter is is is nothing right
+ 
+
+ align:start position:0%
+the diameter is is is nothing right
+there's uh that you can immediately go
+
+ align:start position:0%
+there's uh that you can immediately go
+ 
+
+ align:start position:0%
+there's uh that you can immediately go
+from the diameter is reduced to one you
+
+ align:start position:0%
+from the diameter is reduced to one you
+ 
+
+ align:start position:0%
+from the diameter is reduced to one you
+can immediately go from an input to an
+
+ align:start position:0%
+can immediately go from an input to an
+ 
+
+ align:start position:0%
+can immediately go from an input to an
+output through the switch but this of
+
+ align:start position:0%
+output through the switch but this of
+ 
+
+ align:start position:0%
+output through the switch but this of
+course conceals the problem so what
+
+ align:start position:0%
+course conceals the problem so what
+ 
+
+ align:start position:0%
+course conceals the problem so what
+we're interested in is well we're
+
+ align:start position:0%
+we're interested in is well we're
+ 
+
+ align:start position:0%
+we're interested in is well we're
+actually really interested in in in in
+
+ align:start position:0%
+actually really interested in in in in
+ 
+
+ align:start position:0%
+actually really interested in in in in
+in in how to solve the problem of
+
+ align:start position:0%
+in in how to solve the problem of
+ 
+
+ align:start position:0%
+in in how to solve the problem of
+routing all these inputs to these
+
+ align:start position:0%
+routing all these inputs to these
+ 
+
+ align:start position:0%
+routing all these inputs to these
+outputs using uh smaller basic smaller
+
+ align:start position:0%
+outputs using uh smaller basic smaller
+ 
+
+ align:start position:0%
+outputs using uh smaller basic smaller
+switches of of size three times three or
+
+ align:start position:0%
+switches of of size three times three or
+ 
+
+ align:start position:0%
+switches of of size three times three or
+two time two what we really interested
+
+ align:start position:0%
+two time two what we really interested
+ 
+
+ align:start position:0%
+two time two what we really interested
+in is what is the internal structure in
+
+ align:start position:0%
+in is what is the internal structure in
+ 
+
+ align:start position:0%
+in is what is the internal structure in
+this monster switch I sort of have con
+
+ align:start position:0%
+this monster switch I sort of have con
+ 
+
+ align:start position:0%
+this monster switch I sort of have con
+concealed the problem by just saying oh
+
+ align:start position:0%
+concealed the problem by just saying oh
+ 
+
+ align:start position:0%
+concealed the problem by just saying oh
+I got a big switch but you know uh what
+
+ align:start position:0%
+I got a big switch but you know uh what
+ 
+
+ align:start position:0%
+I got a big switch but you know uh what
+we want to solve today is how do we do
+
+ align:start position:0%
+we want to solve today is how do we do
+ 
+
+ align:start position:0%
+we want to solve today is how do we do
+the routing uh in in this case within
+
+ align:start position:0%
+the routing uh in in this case within
+ 
+
+ align:start position:0%
+the routing uh in in this case within
+the monster switch so we want to use
+
+ align:start position:0%
+the monster switch so we want to use
+ 
+
+ align:start position:0%
+the monster switch so we want to use
+just small
+
+ align:start position:0%
+just small
+ 
+
+ align:start position:0%
+just small
+switch sizes and build up a network
+
+ align:start position:0%
+switch sizes and build up a network
+ 
+
+ align:start position:0%
+switch sizes and build up a network
+using these smaller ones like 3 * three
+
+ align:start position:0%
+using these smaller ones like 3 * three
+ 
+
+ align:start position:0%
+using these smaller ones like 3 * three
+switches or 2 * two
+
+ align:start position:0%
+switches or 2 * two
+ 
+
+ align:start position:0%
+switches or 2 * two
+switches um now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so um that brings us to yet another
+
+ align:start position:0%
+um so um that brings us to yet another
+ 
+
+ align:start position:0%
+um so um that brings us to yet another
+parameter because he would like to count
+
+ align:start position:0%
+parameter because he would like to count
+ 
+
+ align:start position:0%
+parameter because he would like to count
+the number of smaller switches that we
+
+ align:start position:0%
+the number of smaller switches that we
+ 
+
+ align:start position:0%
+the number of smaller switches that we
+use and that relates to the cost of the
+
+ align:start position:0%
+use and that relates to the cost of the
+ 
+
+ align:start position:0%
+use and that relates to the cost of the
+network uh the amount of Hardware that
+
+ align:start position:0%
+network uh the amount of Hardware that
+ 
+
+ align:start position:0%
+network uh the amount of Hardware that
+you need to put into it so in this
+
+ align:start position:0%
+you need to put into it so in this
+ 
+
+ align:start position:0%
+you need to put into it so in this
+example we have uh the switch
+
+ align:start position:0%
+example we have uh the switch
+ 
+
+ align:start position:0%
+example we have uh the switch
+um uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+account well it's pretty simple right
+
+ align:start position:0%
+account well it's pretty simple right
+ 
+
+ align:start position:0%
+account well it's pretty simple right
+it's uh 1 2 3 4 five six seven we have
+
+ align:start position:0%
+it's uh 1 2 3 4 five six seven we have
+ 
+
+ align:start position:0%
+it's uh 1 2 3 4 five six seven we have
+seven
+
+ align:start position:0%
+seven
+ 
+
+ align:start position:0%
+seven
+switches and in general um yeah if we
+
+ align:start position:0%
+switches and in general um yeah if we
+ 
+
+ align:start position:0%
+switches and in general um yeah if we
+have uh n
+
+ align:start position:0%
+have uh n
+ 
+
+ align:start position:0%
+have uh n
+inputs so one two three four inputs then
+
+ align:start position:0%
+inputs so one two three four inputs then
+ 
+
+ align:start position:0%
+inputs so one two three four inputs then
+the number of switches that we use in
+
+ align:start position:0%
+the number of switches that we use in
+ 
+
+ align:start position:0%
+the number of switches that we use in
+the binary tree is 2 * the number of
+
+ align:start position:0%
+the binary tree is 2 * the number of
+ 
+
+ align:start position:0%
+the binary tree is 2 * the number of
+inputs minus one um so let's write that
+
+ align:start position:0%
+inputs minus one um so let's write that
+ 
+
+ align:start position:0%
+inputs minus one um so let's write that
+down so over here we would have 2 * n
+
+ align:start position:0%
+down so over here we would have 2 * n
+ 
+
+ align:start position:0%
+down so over here we would have 2 * n
+minus one which is the number of
+
+ align:start position:0%
+minus one which is the number of
+ 
+
+ align:start position:0%
+minus one which is the number of
+switches that you actually
+
+ align:start position:0%
+switches that you actually
+ 
+
+ align:start position:0%
+switches that you actually
+use um so how can you see that actually
+
+ align:start position:0%
+use um so how can you see that actually
+ 
+
+ align:start position:0%
+use um so how can you see that actually
+uh so in general we have uh 1 + 2 + 4 +
+
+ align:start position:0%
+uh so in general we have uh 1 + 2 + 4 +
+ 
+
+ align:start position:0%
+uh so in general we have uh 1 + 2 + 4 +
+8 and so on
+
+ align:start position:0%
+8 and so on
+ 
+
+ align:start position:0%
+8 and so on
+plus n n is a power of two according to
+
+ align:start position:0%
+plus n n is a power of two according to
+ 
+
+ align:start position:0%
+plus n n is a power of two according to
+our assumptions and if you add them all
+
+ align:start position:0%
+our assumptions and if you add them all
+ 
+
+ align:start position:0%
+our assumptions and if you add them all
+up uh I think you'll well you can check
+
+ align:start position:0%
+up uh I think you'll well you can check
+ 
+
+ align:start position:0%
+up uh I think you'll well you can check
+for yourself that this is actually equal
+
+ align:start position:0%
+for yourself that this is actually equal
+ 
+
+ align:start position:0%
+for yourself that this is actually equal
+to 2 * n minus
+
+ align:start position:0%
+to 2 * n minus
+ 
+
+ align:start position:0%
+to 2 * n minus
+one okay so now we have uh the switch
+
+ align:start position:0%
+one okay so now we have uh the switch
+ 
+
+ align:start position:0%
+one okay so now we have uh the switch
+here so so far this looks pretty good
+
+ align:start position:0%
+here so so far this looks pretty good
+ 
+
+ align:start position:0%
+here so so far this looks pretty good
+actually we use small switch sizes the
+
+ align:start position:0%
+actually we use small switch sizes the
+ 
+
+ align:start position:0%
+actually we use small switch sizes the
+number of switches is linear in N
+
+ align:start position:0%
+number of switches is linear in N
+ 
+
+ align:start position:0%
+number of switches is linear in N
+diameter is logarithmic in N so that
+
+ align:start position:0%
+diameter is logarithmic in N so that
+ 
+
+ align:start position:0%
+diameter is logarithmic in N so that
+sounds good so what about congestion do
+
+ align:start position:0%
+sounds good so what about congestion do
+ 
+
+ align:start position:0%
+sounds good so what about congestion do
+you have any idea what what's what's the
+
+ align:start position:0%
+you have any idea what what's what's the
+ 
+
+ align:start position:0%
+you have any idea what what's what's the
+problem with this graph what is the big
+
+ align:start position:0%
+problem with this graph what is the big
+ 
+
+ align:start position:0%
+problem with this graph what is the big
+big problem
+
+ align:start position:0%
+big problem
+ 
+
+ align:start position:0%
+big problem
+here what can happen in a very uh yeah
+
+ align:start position:0%
+here what can happen in a very uh yeah
+ 
+
+ align:start position:0%
+here what can happen in a very uh yeah
+sort of a worst case scenario where the
+
+ align:start position:0%
+sort of a worst case scenario where the
+ 
+
+ align:start position:0%
+sort of a worst case scenario where the
+packets get routed from the inputs to
+
+ align:start position:0%
+packets get routed from the inputs to
+ 
+
+ align:start position:0%
+packets get routed from the inputs to
+the outputs if they if they need to go
+
+ align:start position:0%
+the outputs if they if they need to go
+ 
+
+ align:start position:0%
+the outputs if they if they need to go
+to certain locations then then they may
+
+ align:start position:0%
+to certain locations then then they may
+ 
+
+ align:start position:0%
+to certain locations then then they may
+all may have to travel through the rout
+
+ align:start position:0%
+all may have to travel through the rout
+ 
+
+ align:start position:0%
+all may have to travel through the rout
+so you get congestion over here we don't
+
+ align:start position:0%
+so you get congestion over here we don't
+ 
+
+ align:start position:0%
+so you get congestion over here we don't
+like that so this rout is actually then
+
+ align:start position:0%
+like that so this rout is actually then
+ 
+
+ align:start position:0%
+like that so this rout is actually then
+overloaded actually you can already see
+
+ align:start position:0%
+overloaded actually you can already see
+ 
+
+ align:start position:0%
+overloaded actually you can already see
+that if say this
+
+ align:start position:0%
+that if say this
+ 
+
+ align:start position:0%
+that if say this
+this particular switch if this switch uh
+
+ align:start position:0%
+this particular switch if this switch uh
+ 
+
+ align:start position:0%
+this particular switch if this switch uh
+fails then actually we will have two
+
+ align:start position:0%
+fails then actually we will have two
+ 
+
+ align:start position:0%
+fails then actually we will have two
+disjoint trees that cannot even
+
+ align:start position:0%
+disjoint trees that cannot even
+ 
+
+ align:start position:0%
+disjoint trees that cannot even
+communicate to one another so uh this
+
+ align:start position:0%
+communicate to one another so uh this
+ 
+
+ align:start position:0%
+communicate to one another so uh this
+brings us to uh to to the idea of
+
+ align:start position:0%
+brings us to uh to to the idea of
+ 
+
+ align:start position:0%
+brings us to uh to to the idea of
+congestion
+
+ align:start position:0%
+congestion
+ 
+
+ align:start position:0%
+congestion
+and in order to Define it better you
+
+ align:start position:0%
+and in order to Define it better you
+ 
+
+ align:start position:0%
+and in order to Define it better you
+will need a few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definitions
+
+ align:start position:0%
+definitions
+ 
+
+ align:start position:0%
+definitions
+so uh to start we will Define a
+
+ align:start position:0%
+so uh to start we will Define a
+ 
+
+ align:start position:0%
+so uh to start we will Define a
+permutation and we will use this
+
+ align:start position:0%
+permutation and we will use this
+ 
+
+ align:start position:0%
+permutation and we will use this
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh uh stipulate the requirement that we
+
+ align:start position:0%
+uh uh stipulate the requirement that we
+ 
+
+ align:start position:0%
+uh uh stipulate the requirement that we
+want on how inputs and outputs are
+
+ align:start position:0%
+want on how inputs and outputs are
+ 
+
+ align:start position:0%
+want on how inputs and outputs are
+related to one another which input needs
+
+ align:start position:0%
+related to one another which input needs
+ 
+
+ align:start position:0%
+related to one another which input needs
+to communicate to which output so
+
+ align:start position:0%
+to communicate to which output so
+ 
+
+ align:start position:0%
+to communicate to which output so
+permutation is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function function
+
+ align:start position:0%
+function function
+ 
+
+ align:start position:0%
+function function
+PI from the set 0 to n minus one one to
+
+ align:start position:0%
+PI from the set 0 to n minus one one to
+ 
+
+ align:start position:0%
+PI from the set 0 to n minus one one to
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+set and
+
+ align:start position:0%
+set and
+ 
+
+ align:start position:0%
+set and
+um it is such
+
+ align:start position:0%
+um it is such
+ 
+
+ align:start position:0%
+um it is such
+that no two
+
+ align:start position:0%
+that no two
+ 
+
+ align:start position:0%
+that no two
+numbers um no no two numbers are mapped
+
+ align:start position:0%
+numbers um no no two numbers are mapped
+ 
+
+ align:start position:0%
+numbers um no no two numbers are mapped
+to more than
+
+ align:start position:0%
+to more than
+ 
+
+ align:start position:0%
+to more than
+ones so no two numbers are mapped
+
+ align:start position:0%
+ones so no two numbers are mapped
+ 
+
+ align:start position:0%
+ones so no two numbers are mapped
+to uh the same value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we really want in to put it in
+
+ align:start position:0%
+so what we really want in to put it in
+ 
+
+ align:start position:0%
+so what we really want in to put it in
+mathematics right we want that Pi of I
+
+ align:start position:0%
+mathematics right we want that Pi of I
+ 
+
+ align:start position:0%
+mathematics right we want that Pi of I
+is only equal to Pi of J well if and
+
+ align:start position:0%
+is only equal to Pi of J well if and
+ 
+
+ align:start position:0%
+is only equal to Pi of J well if and
+only if uh I is equal to
+
+ align:start position:0%
+only if uh I is equal to
+ 
+
+ align:start position:0%
+only if uh I is equal to
+J so let's have uh an example uh to plug
+
+ align:start position:0%
+J so let's have uh an example uh to plug
+ 
+
+ align:start position:0%
+J so let's have uh an example uh to plug
+into that picture over there so a first
+
+ align:start position:0%
+into that picture over there so a first
+ 
+
+ align:start position:0%
+into that picture over there so a first
+example could be um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi of I equals say n minus one minus I
+
+ align:start position:0%
+Pi of I equals say n minus one minus I
+ 
+
+ align:start position:0%
+Pi of I equals say n minus one minus I
+this is a proper
+
+ align:start position:0%
+this is a proper
+ 
+
+ align:start position:0%
+this is a proper
+permutation no two numbers m to the same
+
+ align:start position:0%
+permutation no two numbers m to the same
+ 
+
+ align:start position:0%
+permutation no two numbers m to the same
+value another one could be the identity
+
+ align:start position:0%
+value another one could be the identity
+ 
+
+ align:start position:0%
+value another one could be the identity
+permutation like you map I to the same I
+
+ align:start position:0%
+permutation like you map I to the same I
+ 
+
+ align:start position:0%
+permutation like you map I to the same I
+so that's another example now how do we
+
+ align:start position:0%
+so that's another example now how do we
+ 
+
+ align:start position:0%
+so that's another example now how do we
+use permutations to go towards the idea
+
+ align:start position:0%
+use permutations to go towards the idea
+ 
+
+ align:start position:0%
+use permutations to go towards the idea
+of congestion so permutation can be used
+
+ align:start position:0%
+of congestion so permutation can be used
+ 
+
+ align:start position:0%
+of congestion so permutation can be used
+to formulate the permutation routing
+
+ align:start position:0%
+to formulate the permutation routing
+ 
+
+ align:start position:0%
+to formulate the permutation routing
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+and the permutation routing
+
+ align:start position:0%
+and the permutation routing
+ 
+
+ align:start position:0%
+and the permutation routing
+problem um is defined like
+
+ align:start position:0%
+problem um is defined like
+ 
+
+ align:start position:0%
+problem um is defined like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it's defined as follows but we want
+
+ align:start position:0%
+um it's defined as follows but we want
+ 
+
+ align:start position:0%
+um it's defined as follows but we want
+is that for
+
+ align:start position:0%
+is that for
+ 
+
+ align:start position:0%
+is that for
+each I we want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direct the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+packet at input
+
+ align:start position:0%
+packet at input
+ 
+
+ align:start position:0%
+packet at input
+I to
+
+ align:start position:0%
+I to
+ 
+
+ align:start position:0%
+I to
+Output Pi of I so you want to do that
+
+ align:start position:0%
+Output Pi of I so you want to do that
+ 
+
+ align:start position:0%
+Output Pi of I so you want to do that
+for all I so let's have a look at uh at
+
+ align:start position:0%
+for all I so let's have a look at uh at
+ 
+
+ align:start position:0%
+for all I so let's have a look at uh at
+at this particular example where we look
+
+ align:start position:0%
+at this particular example where we look
+ 
+
+ align:start position:0%
+at this particular example where we look
+at identity
+
+ align:start position:0%
+at identity
+ 
+
+ align:start position:0%
+at identity
+permutation so if you do that we can
+
+ align:start position:0%
+permutation so if you do that we can
+ 
+
+ align:start position:0%
+permutation so if you do that we can
+easily route this right so I want to
+
+ align:start position:0%
+easily route this right so I want to
+ 
+
+ align:start position:0%
+easily route this right so I want to
+send a packet from input zero to Output
+
+ align:start position:0%
+send a packet from input zero to Output
+ 
+
+ align:start position:0%
+send a packet from input zero to Output
+zero so I can
+
+ align:start position:0%
+zero so I can
+ 
+
+ align:start position:0%
+zero so I can
+simply go into this direction I just go
+
+ align:start position:0%
+simply go into this direction I just go
+ 
+
+ align:start position:0%
+simply go into this direction I just go
+towards this switch and gets routed back
+
+ align:start position:0%
+towards this switch and gets routed back
+ 
+
+ align:start position:0%
+towards this switch and gets routed back
+to this one I
+
+ align:start position:0%
+to this one I
+ 
+
+ align:start position:0%
+to this one I
+can go like this and this one can go
+
+ align:start position:0%
+can go like this and this one can go
+ 
+
+ align:start position:0%
+can go like this and this one can go
+like this and this one goes like that
+
+ align:start position:0%
+like this and this one goes like that
+ 
+
+ align:start position:0%
+like this and this one goes like that
+now if you look at the other permutation
+
+ align:start position:0%
+now if you look at the other permutation
+ 
+
+ align:start position:0%
+now if you look at the other permutation
+the picture looks very
+
+ align:start position:0%
+the picture looks very
+ 
+
+ align:start position:0%
+the picture looks very
+different now we want to Route input
+
+ align:start position:0%
+different now we want to Route input
+ 
+
+ align:start position:0%
+different now we want to Route input
+zero to uh output three in order to do
+
+ align:start position:0%
+zero to uh output three in order to do
+ 
+
+ align:start position:0%
+zero to uh output three in order to do
+this I will actually need to go all the
+
+ align:start position:0%
+this I will actually need to go all the
+ 
+
+ align:start position:0%
+this I will actually need to go all the
+way through here
+
+ align:start position:0%
+way through here
+ 
+
+ align:start position:0%
+way through here
+and then all the way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down to this particular
+
+ align:start position:0%
+down to this particular
+ 
+
+ align:start position:0%
+down to this particular
+output and now the picture gets into a
+
+ align:start position:0%
+output and now the picture gets into a
+ 
+
+ align:start position:0%
+output and now the picture gets into a
+big mess because uh for input one we
+
+ align:start position:0%
+big mess because uh for input one we
+ 
+
+ align:start position:0%
+big mess because uh for input one we
+have to go to Output uh three uh output
+
+ align:start position:0%
+have to go to Output uh three uh output
+ 
+
+ align:start position:0%
+have to go to Output uh three uh output
+two so for input one well we go all the
+
+ align:start position:0%
+two so for input one well we go all the
+ 
+
+ align:start position:0%
+two so for input one well we go all the
+way like this we again go through the
+
+ align:start position:0%
+way like this we again go through the
+ 
+
+ align:start position:0%
+way like this we again go through the
+root and then we go
+
+ align:start position:0%
+root and then we go
+ 
+
+ align:start position:0%
+root and then we go
+down uh to this particular output
+
+ align:start position:0%
+down uh to this particular output
+ 
+
+ align:start position:0%
+down uh to this particular output
+and as you can see for for for input two
+
+ align:start position:0%
+and as you can see for for for input two
+ 
+
+ align:start position:0%
+and as you can see for for for input two
+if well we need to connect to Output one
+
+ align:start position:0%
+if well we need to connect to Output one
+ 
+
+ align:start position:0%
+if well we need to connect to Output one
+so again we go all the way up and we go
+
+ align:start position:0%
+so again we go all the way up and we go
+ 
+
+ align:start position:0%
+so again we go all the way up and we go
+all the way down and for this one we
+
+ align:start position:0%
+all the way down and for this one we
+ 
+
+ align:start position:0%
+all the way down and for this one we
+will again go all the way up and all the
+
+ align:start position:0%
+will again go all the way up and all the
+ 
+
+ align:start position:0%
+will again go all the way up and all the
+way down to input zero so now you can
+
+ align:start position:0%
+way down to input zero so now you can
+ 
+
+ align:start position:0%
+way down to input zero so now you can
+see that this particular switch over
+
+ align:start position:0%
+see that this particular switch over
+ 
+
+ align:start position:0%
+see that this particular switch over
+here has to serve packets from all uh
+
+ align:start position:0%
+here has to serve packets from all uh
+ 
+
+ align:start position:0%
+here has to serve packets from all uh
+the inputs all the four packets have to
+
+ align:start position:0%
+the inputs all the four packets have to
+ 
+
+ align:start position:0%
+the inputs all the four packets have to
+travel through this particular note here
+
+ align:start position:0%
+travel through this particular note here
+ 
+
+ align:start position:0%
+travel through this particular note here
+so this leads us to uh the following
+
+ align:start position:0%
+so this leads us to uh the following
+ 
+
+ align:start position:0%
+so this leads us to uh the following
+definition of
+
+ align:start position:0%
+definition of
+ 
+
+ align:start position:0%
+definition of
+congestion so the
+
+ align:start position:0%
+congestion so the
+ 
+
+ align:start position:0%
+congestion so the
+congestion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh uh so oh before we continue let me
+
+ align:start position:0%
+uh uh so oh before we continue let me
+ 
+
+ align:start position:0%
+uh uh so oh before we continue let me
+first Define a path so for each I we
+
+ align:start position:0%
+first Define a path so for each I we
+ 
+
+ align:start position:0%
+first Define a path so for each I we
+direct a packet at input I to Output Pi
+
+ align:start position:0%
+direct a packet at input I to Output Pi
+ 
+
+ align:start position:0%
+direct a packet at input I to Output Pi
+of ey and the path that corresponds to
+
+ align:start position:0%
+of ey and the path that corresponds to
+ 
+
+ align:start position:0%
+of ey and the path that corresponds to
+this route is actually denoted by
+
+ align:start position:0%
+this route is actually denoted by
+ 
+
+ align:start position:0%
+this route is actually denoted by
+as as followed so the path
+
+ align:start position:0%
+as as followed so the path
+ 
+
+ align:start position:0%
+as as followed so the path
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+taken is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denoted by
+
+ align:start position:0%
+denoted by
+ 
+
+ align:start position:0%
+denoted by
+p i Pi
+
+ align:start position:0%
+p i Pi
+ 
+
+ align:start position:0%
+p i Pi
+I so now we can Define the congestion of
+
+ align:start position:0%
+I so now we can Define the congestion of
+ 
+
+ align:start position:0%
+I so now we can Define the congestion of
+a set of such paths so the con the
+
+ align:start position:0%
+a set of such paths so the con the
+ 
+
+ align:start position:0%
+a set of such paths so the con the
+congestion of the
+
+ align:start position:0%
+congestion of the
+ 
+
+ align:start position:0%
+congestion of the
+path corresponding to
+
+ align:start position:0%
+path corresponding to
+ 
+
+ align:start position:0%
+path corresponding to
+uh P0 to p pi0 and so on and we go all
+
+ align:start position:0%
+uh P0 to p pi0 and so on and we go all
+ 
+
+ align:start position:0%
+uh P0 to p pi0 and so on and we go all
+the way up to the N minus one input that
+
+ align:start position:0%
+the way up to the N minus one input that
+ 
+
+ align:start position:0%
+the way up to the N minus one input that
+needs to be mapped to Pi of n minus one
+
+ align:start position:0%
+needs to be mapped to Pi of n minus one
+ 
+
+ align:start position:0%
+needs to be mapped to Pi of n minus one
+so the congestion is now
+
+ align:start position:0%
+so the congestion is now
+ 
+
+ align:start position:0%
+so the congestion is now
+defined as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number to the largest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number of paths
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that pass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through a single
+
+ align:start position:0%
+through a single
+ 
+
+ align:start position:0%
+through a single
+switch so in our example
+
+ align:start position:0%
+switch so in our example
+ 
+
+ align:start position:0%
+switch so in our example
+we saw that in the case of the blue
+
+ align:start position:0%
+we saw that in the case of the blue
+ 
+
+ align:start position:0%
+we saw that in the case of the blue
+arrows here which for the identity
+
+ align:start position:0%
+arrows here which for the identity
+ 
+
+ align:start position:0%
+arrows here which for the identity
+permutation well uh this switch only
+
+ align:start position:0%
+permutation well uh this switch only
+ 
+
+ align:start position:0%
+permutation well uh this switch only
+needs to transmit one packet and and all
+
+ align:start position:0%
+needs to transmit one packet and and all
+ 
+
+ align:start position:0%
+needs to transmit one packet and and all
+those actually zero packets so actually
+
+ align:start position:0%
+those actually zero packets so actually
+ 
+
+ align:start position:0%
+those actually zero packets so actually
+the congestion here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to one and for this particular
+
+ align:start position:0%
+equal to one and for this particular
+ 
+
+ align:start position:0%
+equal to one and for this particular
+permutation well we had to direct all
+
+ align:start position:0%
+permutation well we had to direct all
+ 
+
+ align:start position:0%
+permutation well we had to direct all
+the packets through the root and it's
+
+ align:start position:0%
+the packets through the root and it's
+ 
+
+ align:start position:0%
+the packets through the root and it's
+the worst the most accessed switch and
+
+ align:start position:0%
+the worst the most accessed switch and
+ 
+
+ align:start position:0%
+the worst the most accessed switch and
+that switch has congestion four right
+
+ align:start position:0%
+that switch has congestion four right
+ 
+
+ align:start position:0%
+that switch has congestion four right
+so the congestion of over
+
+ align:start position:0%
+so the congestion of over
+ 
+
+ align:start position:0%
+so the congestion of over
+here is equal to
+
+ align:start position:0%
+here is equal to
+ 
+
+ align:start position:0%
+here is equal to
+four now this does not look so good
+
+ align:start position:0%
+four now this does not look so good
+ 
+
+ align:start position:0%
+four now this does not look so good
+because uh for a binary tree we always
+
+ align:start position:0%
+because uh for a binary tree we always
+ 
+
+ align:start position:0%
+because uh for a binary tree we always
+have this vulnerable root that is right
+
+ align:start position:0%
+have this vulnerable root that is right
+ 
+
+ align:start position:0%
+have this vulnerable root that is right
+here in the center
+
+ align:start position:0%
+here in the center
+ 
+
+ align:start position:0%
+here in the center
+connecting the left side to the right
+
+ align:start position:0%
+connecting the left side to the right
+ 
+
+ align:start position:0%
+connecting the left side to the right
+side so I can always find a permutation
+
+ align:start position:0%
+side so I can always find a permutation
+ 
+
+ align:start position:0%
+side so I can always find a permutation
+actually this permutation over here that
+
+ align:start position:0%
+actually this permutation over here that
+ 
+
+ align:start position:0%
+actually this permutation over here that
+leads to this worst case
+
+ align:start position:0%
+leads to this worst case
+ 
+
+ align:start position:0%
+leads to this worst case
+congestion so what we're interested in
+
+ align:start position:0%
+congestion so what we're interested in
+ 
+
+ align:start position:0%
+congestion so what we're interested in
+is the maximum congestion which is sort
+
+ align:start position:0%
+is the maximum congestion which is sort
+ 
+
+ align:start position:0%
+is the maximum congestion which is sort
+of the worst case
+
+ align:start position:0%
+of the worst case
+ 
+
+ align:start position:0%
+of the worst case
+scenario and you'll Define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it as
+
+ align:start position:0%
+it as
+ 
+
+ align:start position:0%
+it as
+follows the maximum congestion is
+
+ align:start position:0%
+follows the maximum congestion is
+ 
+
+ align:start position:0%
+follows the maximum congestion is
+actually equal to the
+
+ align:start position:0%
+actually equal to the
+ 
+
+ align:start position:0%
+actually equal to the
+maximum over all permutations Pi so this
+
+ align:start position:0%
+maximum over all permutations Pi so this
+ 
+
+ align:start position:0%
+maximum over all permutations Pi so this
+is kind of the worst case routing
+
+ align:start position:0%
+is kind of the worst case routing
+ 
+
+ align:start position:0%
+is kind of the worst case routing
+problem that I can imagine and that may
+
+ align:start position:0%
+problem that I can imagine and that may
+ 
+
+ align:start position:0%
+problem that I can imagine and that may
+occur in practice so in the worst
+
+ align:start position:0%
+occur in practice so in the worst
+ 
+
+ align:start position:0%
+occur in practice so in the worst
+case how can I solve it the best test so
+
+ align:start position:0%
+case how can I solve it the best test so
+ 
+
+ align:start position:0%
+case how can I solve it the best test so
+I want to find the
+
+ align:start position:0%
+I want to find the
+ 
+
+ align:start position:0%
+I want to find the
+minimum uh of the
+
+ align:start position:0%
+minimum uh of the
+ 
+
+ align:start position:0%
+minimum uh of the
+congestion I want to find the minimum
+
+ align:start position:0%
+congestion I want to find the minimum
+ 
+
+ align:start position:0%
+congestion I want to find the minimum
+congestion of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pass over
+
+ align:start position:0%
+pass over
+ 
+
+ align:start position:0%
+pass over
+here and uh the minimum is over these
+
+ align:start position:0%
+here and uh the minimum is over these
+ 
+
+ align:start position:0%
+here and uh the minimum is over these
+types of paths so actually this is uh
+
+ align:start position:0%
+types of paths so actually this is uh
+ 
+
+ align:start position:0%
+types of paths so actually this is uh
+our solution to this routing problem we
+
+ align:start position:0%
+our solution to this routing problem we
+ 
+
+ align:start position:0%
+our solution to this routing problem we
+want to find the best kind of solution
+
+ align:start position:0%
+want to find the best kind of solution
+ 
+
+ align:start position:0%
+want to find the best kind of solution
+for this worst case
+
+ align:start position:0%
+for this worst case
+ 
+
+ align:start position:0%
+for this worst case
+scenario
+
+ align:start position:0%
+scenario
+ 
+
+ align:start position:0%
+scenario
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh the minimum over all solutions for
+
+ align:start position:0%
+uh the minimum over all solutions for
+ 
+
+ align:start position:0%
+uh the minimum over all solutions for
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths so uh
+
+ align:start position:0%
+paths so uh
+ 
+
+ align:start position:0%
+paths so uh
+well for for this particular tree
+
+ align:start position:0%
+well for for this particular tree
+ 
+
+ align:start position:0%
+well for for this particular tree
+structure this permutation is really the
+
+ align:start position:0%
+structure this permutation is really the
+ 
+
+ align:start position:0%
+structure this permutation is really the
+worst case scenario that you can have
+
+ align:start position:0%
+worst case scenario that you can have
+ 
+
+ align:start position:0%
+worst case scenario that you can have
+because every packet needs to be routed
+
+ align:start position:0%
+because every packet needs to be routed
+ 
+
+ align:start position:0%
+because every packet needs to be routed
+through the center over here and it
+
+ align:start position:0%
+through the center over here and it
+ 
+
+ align:start position:0%
+through the center over here and it
+means that our maximum congestion for an
+
+ align:start position:0%
+means that our maximum congestion for an
+ 
+
+ align:start position:0%
+means that our maximum congestion for an
+arbitrary tree is actually equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+so now that that that looks really bad
+
+ align:start position:0%
+so now that that that looks really bad
+ 
+
+ align:start position:0%
+so now that that that looks really bad
+actually so we don't like this uh uh at
+
+ align:start position:0%
+actually so we don't like this uh uh at
+ 
+
+ align:start position:0%
+actually so we don't like this uh uh at
+all so let's find out whether we can do
+
+ align:start position:0%
+all so let's find out whether we can do
+ 
+
+ align:start position:0%
+all so let's find out whether we can do
+a little bit better and uh we're going
+
+ align:start position:0%
+a little bit better and uh we're going
+ 
+
+ align:start position:0%
+a little bit better and uh we're going
+to to look at the two-dimensional array
+
+ align:start position:0%
+to to look at the two-dimensional array
+ 
+
+ align:start position:0%
+to to look at the two-dimensional array
+and see uh what that would lead up
+
+ align:start position:0%
+and see uh what that would lead up
+ 
+
+ align:start position:0%
+and see uh what that would lead up
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+and its structure is as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follows um we essentially have inputs on
+
+ align:start position:0%
+follows um we essentially have inputs on
+ 
+
+ align:start position:0%
+follows um we essentially have inputs on
+uh the left and uh the outputs are on
+
+ align:start position:0%
+uh the left and uh the outputs are on
+ 
+
+ align:start position:0%
+uh the left and uh the outputs are on
+the bottom and they are in a grid
+
+ align:start position:0%
+the bottom and they are in a grid
+ 
+
+ align:start position:0%
+the bottom and they are in a grid
+structure so we have input zero input
+
+ align:start position:0%
+structure so we have input zero input
+ 
+
+ align:start position:0%
+structure so we have input zero input
+one input two
+
+ align:start position:0%
+one input two
+ 
+
+ align:start position:0%
+one input two
+input three they all connect to their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terminals we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switches um four of those and they are
+
+ align:start position:0%
+switches um four of those and they are
+ 
+
+ align:start position:0%
+switches um four of those and they are
+all connected in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grid and at the very bottom we will have
+
+ align:start position:0%
+grid and at the very bottom we will have
+ 
+
+ align:start position:0%
+grid and at the very bottom we will have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+outputs the output terminals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is output uh uh zero and here we
+
+ align:start position:0%
+so this is output uh uh zero and here we
+ 
+
+ align:start position:0%
+so this is output uh uh zero and here we
+will have output one output two and
+
+ align:start position:0%
+will have output one output two and
+ 
+
+ align:start position:0%
+will have output one output two and
+output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three so I notice that my circles start
+
+ align:start position:0%
+three so I notice that my circles start
+ 
+
+ align:start position:0%
+three so I notice that my circles start
+to resemble my squares
+
+ align:start position:0%
+to resemble my squares
+ 
+
+ align:start position:0%
+to resemble my squares
+but these are all the switches right
+
+ align:start position:0%
+but these are all the switches right
+ 
+
+ align:start position:0%
+but these are all the switches right
+here in the center so how does this work
+
+ align:start position:0%
+here in the center so how does this work
+ 
+
+ align:start position:0%
+here in the center so how does this work
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+um well do we have a better better
+
+ align:start position:0%
+um well do we have a better better
+ 
+
+ align:start position:0%
+um well do we have a better better
+parameter so let's look at it together
+
+ align:start position:0%
+parameter so let's look at it together
+ 
+
+ align:start position:0%
+parameter so let's look at it together
+so we need to first of all figure out
+
+ align:start position:0%
+so we need to first of all figure out
+ 
+
+ align:start position:0%
+so we need to first of all figure out
+what the diameter is so what's the
+
+ align:start position:0%
+what the diameter is so what's the
+ 
+
+ align:start position:0%
+what the diameter is so what's the
+diameter of this particular uh
+
+ align:start position:0%
+diameter of this particular uh
+ 
+
+ align:start position:0%
+diameter of this particular uh
+Network so what's the F what's the
+
+ align:start position:0%
+Network so what's the F what's the
+ 
+
+ align:start position:0%
+Network so what's the F what's the
+shortest path between the furthest uh
+
+ align:start position:0%
+shortest path between the furthest uh
+ 
+
+ align:start position:0%
+shortest path between the furthest uh
+input and
+
+ align:start position:0%
+input and
+ 
+
+ align:start position:0%
+input and
+output so well if you look at that we
+
+ align:start position:0%
+output so well if you look at that we
+ 
+
+ align:start position:0%
+output so well if you look at that we
+can see that if I go from all the way
+
+ align:start position:0%
+can see that if I go from all the way
+ 
+
+ align:start position:0%
+can see that if I go from all the way
+from here and I go all the way down to
+
+ align:start position:0%
+from here and I go all the way down to
+ 
+
+ align:start position:0%
+from here and I go all the way down to
+this corner that looks like the largest
+
+ align:start position:0%
+this corner that looks like the largest
+ 
+
+ align:start position:0%
+this corner that looks like the largest
+uh path and I need to cross all these uh
+
+ align:start position:0%
+uh path and I need to cross all these uh
+ 
+
+ align:start position:0%
+uh path and I need to cross all these uh
+wires and in general for any
+
+ align:start position:0%
+wires and in general for any
+ 
+
+ align:start position:0%
+wires and in general for any
+n we will have that the diameter is 2 *
+
+ align:start position:0%
+n we will have that the diameter is 2 *
+ 
+
+ align:start position:0%
+n we will have that the diameter is 2 *
+n now what about the switch
+
+ align:start position:0%
+n now what about the switch
+ 
+
+ align:start position:0%
+n now what about the switch
+size it looks a little bit smaller right
+
+ align:start position:0%
+size it looks a little bit smaller right
+ 
+
+ align:start position:0%
+size it looks a little bit smaller right
+because over here we had three inputs
+
+ align:start position:0%
+because over here we had three inputs
+ 
+
+ align:start position:0%
+because over here we had three inputs
+coming in and three outputs coming out
+
+ align:start position:0%
+coming in and three outputs coming out
+ 
+
+ align:start position:0%
+coming in and three outputs coming out
+but over here we see that every single
+
+ align:start position:0%
+but over here we see that every single
+ 
+
+ align:start position:0%
+but over here we see that every single
+switch has only two inputs and two
+
+ align:start position:0%
+switch has only two inputs and two
+ 
+
+ align:start position:0%
+switch has only two inputs and two
+outputs so that makes the size uh 2 *
+
+ align:start position:0%
+outputs so that makes the size uh 2 *
+ 
+
+ align:start position:0%
+outputs so that makes the size uh 2 *
+two uh now the number of switches is
+
+ align:start position:0%
+two uh now the number of switches is
+ 
+
+ align:start position:0%
+two uh now the number of switches is
+pretty bad right because we have n
+
+ align:start position:0%
+pretty bad right because we have n
+ 
+
+ align:start position:0%
+pretty bad right because we have n
+Square switches so that's that's really
+
+ align:start position:0%
+Square switches so that's that's really
+ 
+
+ align:start position:0%
+Square switches so that's that's really
+horrible that's that that's a lot we
+
+ align:start position:0%
+horrible that's that that's a lot we
+ 
+
+ align:start position:0%
+horrible that's that that's a lot we
+would like to do much better and what
+
+ align:start position:0%
+would like to do much better and what
+ 
+
+ align:start position:0%
+would like to do much better and what
+about the congestion do you have any
+
+ align:start position:0%
+about the congestion do you have any
+ 
+
+ align:start position:0%
+about the congestion do you have any
+idea what what the congestion could be
+
+ align:start position:0%
+idea what what the congestion could be
+ 
+
+ align:start position:0%
+idea what what the congestion could be
+in this particular case we will prove a
+
+ align:start position:0%
+in this particular case we will prove a
+ 
+
+ align:start position:0%
+in this particular case we will prove a
+theorem on
+
+ align:start position:0%
+theorem on
+ 
+
+ align:start position:0%
+theorem on
+that so is there a way to uh map for any
+
+ align:start position:0%
+that so is there a way to uh map for any
+ 
+
+ align:start position:0%
+that so is there a way to uh map for any
+permutation is there a way to map uh the
+
+ align:start position:0%
+permutation is there a way to map uh the
+ 
+
+ align:start position:0%
+permutation is there a way to map uh the
+inputs to Route the inputs to the
+
+ align:start position:0%
+inputs to Route the inputs to the
+ 
+
+ align:start position:0%
+inputs to Route the inputs to the
+outputs in such a way that the switches
+
+ align:start position:0%
+outputs in such a way that the switches
+ 
+
+ align:start position:0%
+outputs in such a way that the switches
+get almost not congested so in the
+
+ align:start position:0%
+get almost not congested so in the
+ 
+
+ align:start position:0%
+get almost not congested so in the
+binary tree we had a congestion of of of
+
+ align:start position:0%
+binary tree we had a congestion of of of
+ 
+
+ align:start position:0%
+binary tree we had a congestion of of of
+of n which is linear in the
+
+ align:start position:0%
+of n which is linear in the
+ 
+
+ align:start position:0%
+of n which is linear in the
+switches but uh over here we can do much
+
+ align:start position:0%
+switches but uh over here we can do much
+ 
+
+ align:start position:0%
+switches but uh over here we can do much
+better we will show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+congestion uh of
+
+ align:start position:0%
+congestion uh of
+ 
+
+ align:start position:0%
+congestion uh of
+an N
+
+ align:start position:0%
+an N
+ 
+
+ align:start position:0%
+an N
+input
+
+ align:start position:0%
+input
+ 
+
+ align:start position:0%
+input
+array is actually equal to
+
+ align:start position:0%
+array is actually equal to
+ 
+
+ align:start position:0%
+array is actually equal to
+two so that's great so so I I'll prove
+
+ align:start position:0%
+two so that's great so so I I'll prove
+ 
+
+ align:start position:0%
+two so that's great so so I I'll prove
+it in a moment but uh that looks really
+
+ align:start position:0%
+it in a moment but uh that looks really
+ 
+
+ align:start position:0%
+it in a moment but uh that looks really
+fantastic and uh so it's way better than
+
+ align:start position:0%
+fantastic and uh so it's way better than
+ 
+
+ align:start position:0%
+fantastic and uh so it's way better than
+the binary Tre now this is really not so
+
+ align:start position:0%
+the binary Tre now this is really not so
+ 
+
+ align:start position:0%
+the binary Tre now this is really not so
+good and this is also much larger but
+
+ align:start position:0%
+good and this is also much larger but
+ 
+
+ align:start position:0%
+good and this is also much larger but
+but still
+
+ align:start position:0%
+but still
+ 
+
+ align:start position:0%
+but still
+um we will start to think next after we
+
+ align:start position:0%
+um we will start to think next after we
+ 
+
+ align:start position:0%
+um we will start to think next after we
+show this particular property uh how to
+
+ align:start position:0%
+show this particular property uh how to
+ 
+
+ align:start position:0%
+show this particular property uh how to
+combine these two and see how we can
+
+ align:start position:0%
+combine these two and see how we can
+ 
+
+ align:start position:0%
+combine these two and see how we can
+come up with another Network that maybe
+
+ align:start position:0%
+come up with another Network that maybe
+ 
+
+ align:start position:0%
+come up with another Network that maybe
+combine that that's able to combine in
+
+ align:start position:0%
+combine that that's able to combine in
+ 
+
+ align:start position:0%
+combine that that's able to combine in
+some ways these two properties and maybe
+
+ align:start position:0%
+some ways these two properties and maybe
+ 
+
+ align:start position:0%
+some ways these two properties and maybe
+we can find a good solution that way
+
+ align:start position:0%
+we can find a good solution that way
+ 
+
+ align:start position:0%
+we can find a good solution that way
+turns out we will not immediately be
+
+ align:start position:0%
+turns out we will not immediately be
+ 
+
+ align:start position:0%
+turns out we will not immediately be
+able to do that and we will need to make
+
+ align:start position:0%
+able to do that and we will need to make
+ 
+
+ align:start position:0%
+able to do that and we will need to make
+another step and come to the last uh
+
+ align:start position:0%
+another step and come to the last uh
+ 
+
+ align:start position:0%
+another step and come to the last uh
+Network that really has good parameters
+
+ align:start position:0%
+Network that really has good parameters
+ 
+
+ align:start position:0%
+Network that really has good parameters
+so what about the
+
+ align:start position:0%
+so what about the
+ 
+
+ align:start position:0%
+so what about the
+theorem so if we prove
+
+ align:start position:0%
+theorem so if we prove
+ 
+
+ align:start position:0%
+theorem so if we prove
+this well how do we start you just start
+
+ align:start position:0%
+this well how do we start you just start
+ 
+
+ align:start position:0%
+this well how do we start you just start
+with any permutation if I want to prove
+
+ align:start position:0%
+with any permutation if I want to prove
+ 
+
+ align:start position:0%
+with any permutation if I want to prove
+something about the congestion it's
+
+ align:start position:0%
+something about the congestion it's
+ 
+
+ align:start position:0%
+something about the congestion it's
+defined as the maximum over all
+
+ align:start position:0%
+defined as the maximum over all
+ 
+
+ align:start position:0%
+defined as the maximum over all
+permutations well let's let's take one
+
+ align:start position:0%
+permutations well let's let's take one
+ 
+
+ align:start position:0%
+permutations well let's let's take one
+of them and see what we can prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's
+
+ align:start position:0%
+so let's
+ 
+
+ align:start position:0%
+so let's
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so let's us Define uh the path for
+
+ align:start position:0%
+uh so let's us Define uh the path for
+ 
+
+ align:start position:0%
+uh so let's us Define uh the path for
+this permutation follow so what we
+
+ align:start position:0%
+this permutation follow so what we
+ 
+
+ align:start position:0%
+this permutation follow so what we
+really want to do is we take any
+
+ align:start position:0%
+really want to do is we take any
+ 
+
+ align:start position:0%
+really want to do is we take any
+permutation and we want to find a really
+
+ align:start position:0%
+permutation and we want to find a really
+ 
+
+ align:start position:0%
+permutation and we want to find a really
+good solution for the routing if that if
+
+ align:start position:0%
+good solution for the routing if that if
+ 
+
+ align:start position:0%
+good solution for the routing if that if
+that gives us a very low congestion
+
+ align:start position:0%
+that gives us a very low congestion
+ 
+
+ align:start position:0%
+that gives us a very low congestion
+we're very
+
+ align:start position:0%
+we're very
+ 
+
+ align:start position:0%
+we're very
+happy so the way to do this is well
+
+ align:start position:0%
+happy so the way to do this is well
+ 
+
+ align:start position:0%
+happy so the way to do this is well
+maybe you have an idea already um so how
+
+ align:start position:0%
+maybe you have an idea already um so how
+ 
+
+ align:start position:0%
+maybe you have an idea already um so how
+would I route this so I want to connect
+
+ align:start position:0%
+would I route this so I want to connect
+ 
+
+ align:start position:0%
+would I route this so I want to connect
+an input uh I say one to Output two for
+
+ align:start position:0%
+an input uh I say one to Output two for
+ 
+
+ align:start position:0%
+an input uh I say one to Output two for
+example um how can I do this any
+
+ align:start position:0%
+example um how can I do this any
+ 
+
+ align:start position:0%
+example um how can I do this any
+suggestions so of course I could go any
+
+ align:start position:0%
+suggestions so of course I could go any
+ 
+
+ align:start position:0%
+suggestions so of course I could go any
+path but somehow I want to have some
+
+ align:start position:0%
+path but somehow I want to have some
+ 
+
+ align:start position:0%
+path but somehow I want to have some
+uniform structure that hopefully helps
+
+ align:start position:0%
+uniform structure that hopefully helps
+ 
+
+ align:start position:0%
+uniform structure that hopefully helps
+me to prove that the congestion in every
+
+ align:start position:0%
+me to prove that the congestion in every
+ 
+
+ align:start position:0%
+me to prove that the congestion in every
+switch is very small so how could I
+
+ align:start position:0%
+switch is very small so how could I
+ 
+
+ align:start position:0%
+switch is very small so how could I
+think about it
+
+ align:start position:0%
+think about it
+ 
+
+ align:start position:0%
+think about it
+um well um
+
+ align:start position:0%
+um well um
+ 
+
+ align:start position:0%
+um well um
+if I make sure that uh say a packet that
+
+ align:start position:0%
+if I make sure that uh say a packet that
+ 
+
+ align:start position:0%
+if I make sure that uh say a packet that
+goes from one to Output two is only
+
+ align:start position:0%
+goes from one to Output two is only
+ 
+
+ align:start position:0%
+goes from one to Output two is only
+going to be participating in the wires
+
+ align:start position:0%
+going to be participating in the wires
+ 
+
+ align:start position:0%
+going to be participating in the wires
+of the uh
+
+ align:start position:0%
+of the uh
+ 
+
+ align:start position:0%
+of the uh
+iow and the pi column then I know that
+
+ align:start position:0%
+iow and the pi column then I know that
+ 
+
+ align:start position:0%
+iow and the pi column then I know that
+uh every wire will only get uh traveled
+
+ align:start position:0%
+uh every wire will only get uh traveled
+ 
+
+ align:start position:0%
+uh every wire will only get uh traveled
+over twice it it could by by a packet it
+
+ align:start position:0%
+over twice it it could by by a packet it
+ 
+
+ align:start position:0%
+over twice it it could by by a packet it
+could either be a packet that goes into
+
+ align:start position:0%
+could either be a packet that goes into
+ 
+
+ align:start position:0%
+could either be a packet that goes into
+this direction or so so a switch will be
+
+ align:start position:0%
+this direction or so so a switch will be
+ 
+
+ align:start position:0%
+this direction or so so a switch will be
+accessed at most twice a switch can
+
+ align:start position:0%
+accessed at most twice a switch can
+ 
+
+ align:start position:0%
+accessed at most twice a switch can
+either receive a packet from this
+
+ align:start position:0%
+either receive a packet from this
+ 
+
+ align:start position:0%
+either receive a packet from this
+direction or receive a packet from uh
+
+ align:start position:0%
+direction or receive a packet from uh
+ 
+
+ align:start position:0%
+direction or receive a packet from uh
+from from the um from the upper
+
+ align:start position:0%
+from from the um from the upper
+ 
+
+ align:start position:0%
+from from the um from the upper
+part so that would be a really good idea
+
+ align:start position:0%
+part so that would be a really good idea
+ 
+
+ align:start position:0%
+part so that would be a really good idea
+so let's uh Define that
+
+ align:start position:0%
+so let's uh Define that
+ 
+
+ align:start position:0%
+so let's uh Define that
+so we say that in our solution we will
+
+ align:start position:0%
+so we say that in our solution we will
+ 
+
+ align:start position:0%
+so we say that in our solution we will
+Design such that the path from input I
+
+ align:start position:0%
+Design such that the path from input I
+ 
+
+ align:start position:0%
+Design such that the path from input I
+is actually going to be right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+word uh two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+column Pi I and then downward to the
+
+ align:start position:0%
+column Pi I and then downward to the
+ 
+
+ align:start position:0%
+column Pi I and then downward to the
+output so
+
+ align:start position:0%
+output so
+ 
+
+ align:start position:0%
+output so
+downward
+
+ align:start position:0%
+downward
+ 
+
+ align:start position:0%
+downward
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um output by I so this
+
+ align:start position:0%
+um output by I so this
+ 
+
+ align:start position:0%
+um output by I so this
+is a really uh good solution to the
+
+ align:start position:0%
+is a really uh good solution to the
+ 
+
+ align:start position:0%
+is a really uh good solution to the
+router problem because now we can uh
+
+ align:start position:0%
+router problem because now we can uh
+ 
+
+ align:start position:0%
+router problem because now we can uh
+continue our proof as follows we just
+
+ align:start position:0%
+continue our proof as follows we just
+ 
+
+ align:start position:0%
+continue our proof as follows we just
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+well um if you look at the
+
+ align:start position:0%
+well um if you look at the
+ 
+
+ align:start position:0%
+well um if you look at the
+switch in row I and a column Pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I well this one actually transmits at
+
+ align:start position:0%
+I well this one actually transmits at
+ 
+
+ align:start position:0%
+I well this one actually transmits at
+most two packets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because a packet can only come from um
+
+ align:start position:0%
+because a packet can only come from um
+ 
+
+ align:start position:0%
+because a packet can only come from um
+uh from the um left or it can go from
+
+ align:start position:0%
+uh from the um left or it can go from
+ 
+
+ align:start position:0%
+uh from the um left or it can go from
+the top so either one of the two uh at
+
+ align:start position:0%
+the top so either one of the two uh at
+ 
+
+ align:start position:0%
+the top so either one of the two uh at
+most those two packets will go through
+
+ align:start position:0%
+most those two packets will go through
+ 
+
+ align:start position:0%
+most those two packets will go through
+the switch so this shows that we have uh
+
+ align:start position:0%
+the switch so this shows that we have uh
+ 
+
+ align:start position:0%
+the switch so this shows that we have uh
+a congestion of at most two for any
+
+ align:start position:0%
+a congestion of at most two for any
+ 
+
+ align:start position:0%
+a congestion of at most two for any
+permutation and in order to prove
+
+ align:start position:0%
+permutation and in order to prove
+ 
+
+ align:start position:0%
+permutation and in order to prove
+equality because that's really what the
+
+ align:start position:0%
+equality because that's really what the
+ 
+
+ align:start position:0%
+equality because that's really what the
+theorem says we also have to show that
+
+ align:start position:0%
+theorem says we also have to show that
+ 
+
+ align:start position:0%
+theorem says we also have to show that
+there exists a permutation that achieves
+
+ align:start position:0%
+there exists a permutation that achieves
+ 
+
+ align:start position:0%
+there exists a permutation that achieves
+uh a congestion of two and that is
+
+ align:start position:0%
+uh a congestion of two and that is
+ 
+
+ align:start position:0%
+uh a congestion of two and that is
+pretty straightforward we can for
+
+ align:start position:0%
+pretty straightforward we can for
+ 
+
+ align:start position:0%
+pretty straightforward we can for
+example use a specific uh permutation
+
+ align:start position:0%
+example use a specific uh permutation
+ 
+
+ align:start position:0%
+example use a specific uh permutation
+that Maps 0 to zero and Maps n minus1 to
+
+ align:start position:0%
+that Maps 0 to zero and Maps n minus1 to
+ 
+
+ align:start position:0%
+that Maps 0 to zero and Maps n minus1 to
+n minus one well for this particular
+
+ align:start position:0%
+n minus one well for this particular
+ 
+
+ align:start position:0%
+n minus one well for this particular
+permutation when we look at uh the
+
+ align:start position:0%
+permutation when we look at uh the
+ 
+
+ align:start position:0%
+permutation when we look at uh the
+picture over here we say said that we
+
+ align:start position:0%
+picture over here we say said that we
+ 
+
+ align:start position:0%
+picture over here we say said that we
+see that input zero needs to go to
+
+ align:start position:0%
+see that input zero needs to go to
+ 
+
+ align:start position:0%
+see that input zero needs to go to
+Output zero um we also see that this uh
+
+ align:start position:0%
+Output zero um we also see that this uh
+ 
+
+ align:start position:0%
+Output zero um we also see that this uh
+lowest um input input three needs to
+
+ align:start position:0%
+lowest um input input three needs to
+ 
+
+ align:start position:0%
+lowest um input input three needs to
+travel all the way up to here but it's
+
+ align:start position:0%
+travel all the way up to here but it's
+ 
+
+ align:start position:0%
+travel all the way up to here but it's
+clear that the packet that needs to go
+
+ align:start position:0%
+clear that the packet that needs to go
+ 
+
+ align:start position:0%
+clear that the packet that needs to go
+over here needs to travel through that
+
+ align:start position:0%
+over here needs to travel through that
+ 
+
+ align:start position:0%
+over here needs to travel through that
+switch in the lower um um left bottom
+
+ align:start position:0%
+switch in the lower um um left bottom
+ 
+
+ align:start position:0%
+switch in the lower um um left bottom
+corner and uh the input three also needs
+
+ align:start position:0%
+corner and uh the input three also needs
+ 
+
+ align:start position:0%
+corner and uh the input three also needs
+to travel through that so here we
+
+ align:start position:0%
+to travel through that so here we
+ 
+
+ align:start position:0%
+to travel through that so here we
+clearly see that we have a congestion of
+
+ align:start position:0%
+clearly see that we have a congestion of
+ 
+
+ align:start position:0%
+clearly see that we have a congestion of
+two so now the proof is complete because
+
+ align:start position:0%
+two so now the proof is complete because
+ 
+
+ align:start position:0%
+two so now the proof is complete because
+we have shown uh this upper bound so for
+
+ align:start position:0%
+we have shown uh this upper bound so for
+ 
+
+ align:start position:0%
+we have shown uh this upper bound so for
+any permutation the congestion is at
+
+ align:start position:0%
+any permutation the congestion is at
+ 
+
+ align:start position:0%
+any permutation the congestion is at
+most two and we uh see that um this
+
+ align:start position:0%
+most two and we uh see that um this
+ 
+
+ align:start position:0%
+most two and we uh see that um this
+specific permutation achieves uh this
+
+ align:start position:0%
+specific permutation achieves uh this
+ 
+
+ align:start position:0%
+specific permutation achieves uh this
+congestion so this is the end of this
+
+ align:start position:0%
+congestion so this is the end of this
+ 
+
+ align:start position:0%
+congestion so this is the end of this
+proof okay so that's great so now what
+
+ align:start position:0%
+proof okay so that's great so now what
+ 
+
+ align:start position:0%
+proof okay so that's great so now what
+we like to do is we like to combine
+
+ align:start position:0%
+we like to do is we like to combine
+ 
+
+ align:start position:0%
+we like to do is we like to combine
+these two uh networks and see what we
+
+ align:start position:0%
+these two uh networks and see what we
+ 
+
+ align:start position:0%
+these two uh networks and see what we
+can learn from both so now we'll be
+
+ align:start position:0%
+can learn from both so now we'll be
+ 
+
+ align:start position:0%
+can learn from both so now we'll be
+taking out a lot of uh chalk over
+
+ align:start position:0%
+taking out a lot of uh chalk over
+ 
+
+ align:start position:0%
+taking out a lot of uh chalk over
+here so the idea is to construct a
+
+ align:start position:0%
+here so the idea is to construct a
+ 
+
+ align:start position:0%
+here so the idea is to construct a
+butterfly
+
+ align:start position:0%
+butterfly
+ 
+
+ align:start position:0%
+butterfly
+Network and uh I will draw it in such a
+
+ align:start position:0%
+Network and uh I will draw it in such a
+ 
+
+ align:start position:0%
+Network and uh I will draw it in such a
+way that you can see the recursive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure the idea is to um
+
+ align:start position:0%
+structure the idea is to um
+ 
+
+ align:start position:0%
+structure the idea is to um
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh to do the following thing so let me
+
+ align:start position:0%
+uh to do the following thing so let me
+ 
+
+ align:start position:0%
+uh to do the following thing so let me
+see how I can do this the best um so I
+
+ align:start position:0%
+see how I can do this the best um so I
+ 
+
+ align:start position:0%
+see how I can do this the best um so I
+just do the the the Top Line first and I
+
+ align:start position:0%
+just do the the the Top Line first and I
+ 
+
+ align:start position:0%
+just do the the the Top Line first and I
+have the spacing so we have input zero a
+
+ align:start position:0%
+have the spacing so we have input zero a
+ 
+
+ align:start position:0%
+have the spacing so we have input zero a
+terminal we have a switch we have a
+
+ align:start position:0%
+terminal we have a switch we have a
+ 
+
+ align:start position:0%
+terminal we have a switch we have a
+switch we have a switch and another one
+
+ align:start position:0%
+switch we have a switch and another one
+ 
+
+ align:start position:0%
+switch we have a switch and another one
+and here we have the
+
+ align:start position:0%
+and here we have the
+ 
+
+ align:start position:0%
+and here we have the
+output zero so the whole idea
+
+ align:start position:0%
+output zero so the whole idea
+ 
+
+ align:start position:0%
+output zero so the whole idea
+is that I'm going to combine every two
+
+ align:start position:0%
+is that I'm going to combine every two
+ 
+
+ align:start position:0%
+is that I'm going to combine every two
+outputs uh by using a small butterfly
+
+ align:start position:0%
+outputs uh by using a small butterfly
+ 
+
+ align:start position:0%
+outputs uh by using a small butterfly
+structure so we have
+
+ align:start position:0%
+structure so we have
+ 
+
+ align:start position:0%
+structure so we have
+two output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four actually I need a look a little bit
+
+ align:start position:0%
+four actually I need a look a little bit
+ 
+
+ align:start position:0%
+four actually I need a look a little bit
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space do it once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more I put
+
+ align:start position:0%
+more I put
+ 
+
+ align:start position:0%
+more I put
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+four five six and the last one seven
+
+ align:start position:0%
+four five six and the last one seven
+ 
+
+ align:start position:0%
+four five six and the last one seven
+okay this is going to be pretty tight on
+
+ align:start position:0%
+okay this is going to be pretty tight on
+ 
+
+ align:start position:0%
+okay this is going to be pretty tight on
+the board so what's happening is this so
+
+ align:start position:0%
+the board so what's happening is this so
+ 
+
+ align:start position:0%
+the board so what's happening is this so
+these are all connected of course to
+
+ align:start position:0%
+these are all connected of course to
+ 
+
+ align:start position:0%
+these are all connected of course to
+switches the switches output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those and uh the idea is that we create
+
+ align:start position:0%
+those and uh the idea is that we create
+ 
+
+ align:start position:0%
+those and uh the idea is that we create
+the following structure this switch can
+
+ align:start position:0%
+the following structure this switch can
+ 
+
+ align:start position:0%
+the following structure this switch can
+either forward it over here or can cross
+
+ align:start position:0%
+either forward it over here or can cross
+ 
+
+ align:start position:0%
+either forward it over here or can cross
+it over to this particular line and this
+
+ align:start position:0%
+it over to this particular line and this
+ 
+
+ align:start position:0%
+it over to this particular line and this
+switch can either forward it or cross it
+
+ align:start position:0%
+switch can either forward it or cross it
+ 
+
+ align:start position:0%
+switch can either forward it or cross it
+over to this line so this is a very
+
+ align:start position:0%
+over to this line so this is a very
+ 
+
+ align:start position:0%
+over to this line so this is a very
+small butterfly structure where we have
+
+ align:start position:0%
+small butterfly structure where we have
+ 
+
+ align:start position:0%
+small butterfly structure where we have
+two inputs and two outputs
+
+ align:start position:0%
+two inputs and two outputs
+ 
+
+ align:start position:0%
+two inputs and two outputs
+and we will repeat this process and
+
+ align:start position:0%
+and we will repeat this process and
+ 
+
+ align:start position:0%
+and we will repeat this process and
+we'll do the same on each of these other
+
+ align:start position:0%
+we'll do the same on each of these other
+ 
+
+ align:start position:0%
+we'll do the same on each of these other
+levels so we forward those or we cross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and now that we have constructed
+
+ align:start position:0%
+this and now that we have constructed
+ 
+
+ align:start position:0%
+this and now that we have constructed
+all these smaller butterfly structures
+
+ align:start position:0%
+all these smaller butterfly structures
+ 
+
+ align:start position:0%
+all these smaller butterfly structures
+we can start to combine two butterfly
+
+ align:start position:0%
+we can start to combine two butterfly
+ 
+
+ align:start position:0%
+we can start to combine two butterfly
+structures together in the bigger one so
+
+ align:start position:0%
+structures together in the bigger one so
+ 
+
+ align:start position:0%
+structures together in the bigger one so
+here we had two outputs that we combined
+
+ align:start position:0%
+here we had two outputs that we combined
+ 
+
+ align:start position:0%
+here we had two outputs that we combined
+in a butterfly structure and now we use
+
+ align:start position:0%
+in a butterfly structure and now we use
+ 
+
+ align:start position:0%
+in a butterfly structure and now we use
+two butterfly structures that we can
+
+ align:start position:0%
+two butterfly structures that we can
+ 
+
+ align:start position:0%
+two butterfly structures that we can
+that we uh that we uh put into a bigger
+
+ align:start position:0%
+that we uh that we uh put into a bigger
+ 
+
+ align:start position:0%
+that we uh that we uh put into a bigger
+version so how do we do this well we
+
+ align:start position:0%
+version so how do we do this well we
+ 
+
+ align:start position:0%
+version so how do we do this well we
+have that the upper half over here can
+
+ align:start position:0%
+have that the upper half over here can
+ 
+
+ align:start position:0%
+have that the upper half over here can
+either forward
+
+ align:start position:0%
+either forward
+ 
+
+ align:start position:0%
+either forward
+those packets or cross them over to the
+
+ align:start position:0%
+those packets or cross them over to the
+ 
+
+ align:start position:0%
+those packets or cross them over to the
+bottom part butterfly
+
+ align:start position:0%
+bottom part butterfly
+ 
+
+ align:start position:0%
+bottom part butterfly
+structure so for these we can either
+
+ align:start position:0%
+structure so for these we can either
+ 
+
+ align:start position:0%
+structure so for these we can either
+forward them straight
+
+ align:start position:0%
+forward them straight
+ 
+
+ align:start position:0%
+forward them straight
+on or we can go to the
+
+ align:start position:0%
+on or we can go to the
+ 
+
+ align:start position:0%
+on or we can go to the
+top
+
+ align:start position:0%
+top
+ 
+
+ align:start position:0%
+top
+butterfly so you see that these two
+
+ align:start position:0%
+butterfly so you see that these two
+ 
+
+ align:start position:0%
+butterfly so you see that these two
+inputs these two switches either can
+
+ align:start position:0%
+inputs these two switches either can
+ 
+
+ align:start position:0%
+inputs these two switches either can
+forward packets to this sub butterfly
+
+ align:start position:0%
+forward packets to this sub butterfly
+ 
+
+ align:start position:0%
+forward packets to this sub butterfly
+Network or to the top butterfly Network
+
+ align:start position:0%
+Network or to the top butterfly Network
+ 
+
+ align:start position:0%
+Network or to the top butterfly Network
+now we'll continue this
+
+ align:start position:0%
+now we'll continue this
+ 
+
+ align:start position:0%
+now we'll continue this
+process and for this we'll do the same
+
+ align:start position:0%
+process and for this we'll do the same
+ 
+
+ align:start position:0%
+process and for this we'll do the same
+so we can either go straight or we go
+
+ align:start position:0%
+so we can either go straight or we go
+ 
+
+ align:start position:0%
+so we can either go straight or we go
+down and over here we can go straight or
+
+ align:start position:0%
+down and over here we can go straight or
+ 
+
+ align:start position:0%
+down and over here we can go straight or
+we can go to the top butterfly
+
+ align:start position:0%
+we can go to the top butterfly
+ 
+
+ align:start position:0%
+we can go to the top butterfly
+Network well now we uh have the
+
+ align:start position:0%
+Network well now we uh have the
+ 
+
+ align:start position:0%
+Network well now we uh have the
+final part where we combine essentially
+
+ align:start position:0%
+final part where we combine essentially
+ 
+
+ align:start position:0%
+final part where we combine essentially
+these two butterfly
+
+ align:start position:0%
+these two butterfly
+ 
+
+ align:start position:0%
+these two butterfly
+networks we have two butterfly networks
+
+ align:start position:0%
+networks we have two butterfly networks
+ 
+
+ align:start position:0%
+networks we have two butterfly networks
+created here now composed again of
+
+ align:start position:0%
+created here now composed again of
+ 
+
+ align:start position:0%
+created here now composed again of
+smaller ones now these two are being
+
+ align:start position:0%
+smaller ones now these two are being
+ 
+
+ align:start position:0%
+smaller ones now these two are being
+composed to this bigger butterfly
+
+ align:start position:0%
+composed to this bigger butterfly
+ 
+
+ align:start position:0%
+composed to this bigger butterfly
+Network again we take these four uh
+
+ align:start position:0%
+Network again we take these four uh
+ 
+
+ align:start position:0%
+Network again we take these four uh
+switches they can route their packets
+
+ align:start position:0%
+switches they can route their packets
+ 
+
+ align:start position:0%
+switches they can route their packets
+forward to the top butterfly sub Network
+
+ align:start position:0%
+forward to the top butterfly sub Network
+ 
+
+ align:start position:0%
+forward to the top butterfly sub Network
+or to the bottom one so they can either
+
+ align:start position:0%
+or to the bottom one so they can either
+ 
+
+ align:start position:0%
+or to the bottom one so they can either
+go straight ahead or this one can
+
+ align:start position:0%
+go straight ahead or this one can
+ 
+
+ align:start position:0%
+go straight ahead or this one can
+connect to the first over here this one
+
+ align:start position:0%
+connect to the first over here this one
+ 
+
+ align:start position:0%
+connect to the first over here this one
+to the second to the third and this to
+
+ align:start position:0%
+to the second to the third and this to
+ 
+
+ align:start position:0%
+to the second to the third and this to
+the fourth and in the same style these
+
+ align:start position:0%
+the fourth and in the same style these
+ 
+
+ align:start position:0%
+the fourth and in the same style these
+can forward them straight
+
+ align:start position:0%
+can forward them straight
+ 
+
+ align:start position:0%
+can forward them straight
+like this and then go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up like
+
+ align:start position:0%
+up like
+ 
+
+ align:start position:0%
+up like
+this and these are all connected because
+
+ align:start position:0%
+this and these are all connected because
+ 
+
+ align:start position:0%
+this and these are all connected because
+in this example we'll just have an 8 by8
+
+ align:start position:0%
+in this example we'll just have an 8 by8
+ 
+
+ align:start position:0%
+in this example we'll just have an 8 by8
+uh network but the fly Network we have
+
+ align:start position:0%
+uh network but the fly Network we have
+ 
+
+ align:start position:0%
+uh network but the fly Network we have
+inputs uh 0 to 7
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the butterfly Network in
+
+ align:start position:0%
+okay so this is the butterfly Network in
+ 
+
+ align:start position:0%
+okay so this is the butterfly Network in
+a way what you can see here you can see
+
+ align:start position:0%
+a way what you can see here you can see
+ 
+
+ align:start position:0%
+a way what you can see here you can see
+sort of the sort of the two-dimensional
+
+ align:start position:0%
+sort of the sort of the two-dimensional
+ 
+
+ align:start position:0%
+sort of the sort of the two-dimensional
+structure like we have rows and columns
+
+ align:start position:0%
+structure like we have rows and columns
+ 
+
+ align:start position:0%
+structure like we have rows and columns
+at the same time we can also see this
+
+ align:start position:0%
+at the same time we can also see this
+ 
+
+ align:start position:0%
+at the same time we can also see this
+binary sort of tree uh feeling we get
+
+ align:start position:0%
+binary sort of tree uh feeling we get
+ 
+
+ align:start position:0%
+binary sort of tree uh feeling we get
+from it which is that a switch can
+
+ align:start position:0%
+from it which is that a switch can
+ 
+
+ align:start position:0%
+from it which is that a switch can
+forward uh sort of uh its packets to
+
+ align:start position:0%
+forward uh sort of uh its packets to
+ 
+
+ align:start position:0%
+forward uh sort of uh its packets to
+either say the top uh butterfly or the
+
+ align:start position:0%
+either say the top uh butterfly or the
+ 
+
+ align:start position:0%
+either say the top uh butterfly or the
+bottom butterfly so there's a split in
+
+ align:start position:0%
+bottom butterfly so there's a split in
+ 
+
+ align:start position:0%
+bottom butterfly so there's a split in
+two H the same for this one right this
+
+ align:start position:0%
+two H the same for this one right this
+ 
+
+ align:start position:0%
+two H the same for this one right this
+one goes either to this butterfly
+
+ align:start position:0%
+one goes either to this butterfly
+ 
+
+ align:start position:0%
+one goes either to this butterfly
+Network or it goes to this butterfly
+
+ align:start position:0%
+Network or it goes to this butterfly
+ 
+
+ align:start position:0%
+Network or it goes to this butterfly
+Network so you have this three structure
+
+ align:start position:0%
+Network so you have this three structure
+ 
+
+ align:start position:0%
+Network so you have this three structure
+sort of embedded in this two-dimensional
+
+ align:start position:0%
+sort of embedded in this two-dimensional
+ 
+
+ align:start position:0%
+sort of embedded in this two-dimensional
+structure so what are the properties of
+
+ align:start position:0%
+structure so what are the properties of
+ 
+
+ align:start position:0%
+structure so what are the properties of
+this one so let me first Define um the
+
+ align:start position:0%
+this one so let me first Define um the
+ 
+
+ align:start position:0%
+this one so let me first Define um the
+um the uh like like in more form formal
+
+ align:start position:0%
+um the uh like like in more form formal
+ 
+
+ align:start position:0%
+um the uh like like in more form formal
+mathematics
+
+ align:start position:0%
+mathematics
+ 
+
+ align:start position:0%
+mathematics
+uh how the switches uh router packets so
+
+ align:start position:0%
+uh how the switches uh router packets so
+ 
+
+ align:start position:0%
+uh how the switches uh router packets so
+how their connections
+
+ align:start position:0%
+how their connections
+ 
+
+ align:start position:0%
+how their connections
+are um so in order to do that we're
+
+ align:start position:0%
+are um so in order to do that we're
+ 
+
+ align:start position:0%
+are um so in order to do that we're
+going to uh label each uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switch and the IDE is that we're going
+
+ align:start position:0%
+switch and the IDE is that we're going
+ 
+
+ align:start position:0%
+switch and the IDE is that we're going
+to label it by its row and by its column
+
+ align:start position:0%
+to label it by its row and by its column
+ 
+
+ align:start position:0%
+to label it by its row and by its column
+so we will have
+
+ align:start position:0%
+so we will have
+ 
+
+ align:start position:0%
+so we will have
+um uh The Columns are numbered by level
+
+ align:start position:0%
+um uh The Columns are numbered by level
+ 
+
+ align:start position:0%
+um uh The Columns are numbered by level
+zero level one
+
+ align:start position:0%
+zero level one
+ 
+
+ align:start position:0%
+zero level one
+level two level
+
+ align:start position:0%
+level two level
+ 
+
+ align:start position:0%
+level two level
+three um yes and uh the rows are these
+
+ align:start position:0%
+three um yes and uh the rows are these
+ 
+
+ align:start position:0%
+three um yes and uh the rows are these
+integers but we're going to represent
+
+ align:start position:0%
+integers but we're going to represent
+ 
+
+ align:start position:0%
+integers but we're going to represent
+them by binary numbers so zero would be
+
+ align:start position:0%
+them by binary numbers so zero would be
+ 
+
+ align:start position:0%
+them by binary numbers so zero would be
+0 0 0 0 0 1 0 1 0o 0 one 1 uh oops one0
+
+ align:start position:0%
+0 0 0 0 0 1 0 1 0o 0 one 1 uh oops one0
+ 
+
+ align:start position:0%
+0 0 0 0 0 1 0 1 0o 0 one 1 uh oops one0
+0 one0 1 and then we got
+
+ align:start position:0%
+0 one0 1 and then we got
+ 
+
+ align:start position:0%
+0 one0 1 and then we got
+uh 1 1 Z and 1 11
+
+ align:start position:0%
+uh 1 1 Z and 1 11
+ 
+
+ align:start position:0%
+uh 1 1 Z and 1 11
+one so for example this particular
+
+ align:start position:0%
+one so for example this particular
+ 
+
+ align:start position:0%
+one so for example this particular
+switch would be labeled by these three
+
+ align:start position:0%
+switch would be labeled by these three
+ 
+
+ align:start position:0%
+switch would be labeled by these three
+bits 0 01 and the integer number one
+
+ align:start position:0%
+bits 0 01 and the integer number one
+ 
+
+ align:start position:0%
+bits 0 01 and the integer number one
+this one would be
+
+ align:start position:0%
+this one would be
+ 
+
+ align:start position:0%
+this one would be
+011 and its column is uh indexed by
+
+ align:start position:0%
+011 and its column is uh indexed by
+ 
+
+ align:start position:0%
+011 and its column is uh indexed by
+integer
+
+ align:start position:0%
+integer
+ 
+
+ align:start position:0%
+integer
+two okay so a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switch is uh
+
+ align:start position:0%
+switch is uh
+ 
+
+ align:start position:0%
+switch is uh
+uniquely um ident
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identified by its uh
+
+ align:start position:0%
+identified by its uh
+ 
+
+ align:start position:0%
+identified by its uh
+row and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+column uh we will have a
+
+ align:start position:0%
+column uh we will have a
+ 
+
+ align:start position:0%
+column uh we will have a
+B1 up to B logarithm of n which are the
+
+ align:start position:0%
+B1 up to B logarithm of n which are the
+ 
+
+ align:start position:0%
+B1 up to B logarithm of n which are the
+number of bits to represent the row
+
+ align:start position:0%
+number of bits to represent the row
+ 
+
+ align:start position:0%
+number of bits to represent the row
+indices and we finally have an integer L
+
+ align:start position:0%
+indices and we finally have an integer L
+ 
+
+ align:start position:0%
+indices and we finally have an integer L
+and this we will call the
+
+ align:start position:0%
+and this we will call the
+ 
+
+ align:start position:0%
+and this we will call the
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+so this particular switch either directs
+
+ align:start position:0%
+so this particular switch either directs
+ 
+
+ align:start position:0%
+so this particular switch either directs
+or or routes a packet to the switch that
+
+ align:start position:0%
+or or routes a packet to the switch that
+ 
+
+ align:start position:0%
+or or routes a packet to the switch that
+is indexed
+
+ align:start position:0%
+is indexed
+ 
+
+ align:start position:0%
+is indexed
+by um B1 up to and then we get b l + one
+
+ align:start position:0%
+by um B1 up to and then we get b l + one
+ 
+
+ align:start position:0%
+by um B1 up to and then we get b l + one
+and we take its complement so instead of
+
+ align:start position:0%
+and we take its complement so instead of
+ 
+
+ align:start position:0%
+and we take its complement so instead of
+if B+ one would be one we would have a
+
+ align:start position:0%
+if B+ one would be one we would have a
+ 
+
+ align:start position:0%
+if B+ one would be one we would have a
+zero here if it would be a zero we will
+
+ align:start position:0%
+zero here if it would be a zero we will
+ 
+
+ align:start position:0%
+zero here if it would be a zero we will
+have a one over here and
+
+ align:start position:0%
+have a one over here and
+ 
+
+ align:start position:0%
+have a one over here and
+but we repeat all the other bits and we
+
+ align:start position:0%
+but we repeat all the other bits and we
+ 
+
+ align:start position:0%
+but we repeat all the other bits and we
+get B log
+
+ align:start position:0%
+get B log
+ 
+
+ align:start position:0%
+get B log
+n and uh it routes its back to the next
+
+ align:start position:0%
+n and uh it routes its back to the next
+ 
+
+ align:start position:0%
+n and uh it routes its back to the next
+level so we will have l+
+
+ align:start position:0%
+level so we will have l+
+ 
+
+ align:start position:0%
+level so we will have l+
+one another possibility is because there
+
+ align:start position:0%
+one another possibility is because there
+ 
+
+ align:start position:0%
+one another possibility is because there
+two outgoing
+
+ align:start position:0%
+two outgoing
+ 
+
+ align:start position:0%
+two outgoing
+edges is if we have just
+
+ align:start position:0%
+edges is if we have just
+ 
+
+ align:start position:0%
+edges is if we have just
+B1 and we just copy BL + one essentially
+
+ align:start position:0%
+B1 and we just copy BL + one essentially
+ 
+
+ align:start position:0%
+B1 and we just copy BL + one essentially
+we route the packet straight forward we
+
+ align:start position:0%
+we route the packet straight forward we
+ 
+
+ align:start position:0%
+we route the packet straight forward we
+don't don't do anything
+
+ align:start position:0%
+don't don't do anything
+ 
+
+ align:start position:0%
+don't don't do anything
+special we get B log n over here and
+
+ align:start position:0%
+special we get B log n over here and
+ 
+
+ align:start position:0%
+special we get B log n over here and
+then to the next level so for
+
+ align:start position:0%
+then to the next level so for
+ 
+
+ align:start position:0%
+then to the next level so for
+example let's see where we can see how
+
+ align:start position:0%
+example let's see where we can see how
+ 
+
+ align:start position:0%
+example let's see where we can see how
+this works so for example take um this
+
+ align:start position:0%
+this works so for example take um this
+ 
+
+ align:start position:0%
+this works so for example take um this
+particular switch we have uh 0 one 0 so
+
+ align:start position:0%
+particular switch we have uh 0 one 0 so
+ 
+
+ align:start position:0%
+particular switch we have uh 0 one 0 so
+it can either go straight on to the next
+
+ align:start position:0%
+it can either go straight on to the next
+ 
+
+ align:start position:0%
+it can either go straight on to the next
+level it would go to 0 one 0 but then
+
+ align:start position:0%
+level it would go to 0 one 0 but then
+ 
+
+ align:start position:0%
+level it would go to 0 one 0 but then
+instead of level one we have level two
+
+ align:start position:0%
+instead of level one we have level two
+ 
+
+ align:start position:0%
+instead of level one we have level two
+which is the right Edge over there
+
+ align:start position:0%
+which is the right Edge over there
+ 
+
+ align:start position:0%
+which is the right Edge over there
+um the other one is if this one goes up
+
+ align:start position:0%
+um the other one is if this one goes up
+ 
+
+ align:start position:0%
+um the other one is if this one goes up
+well uh we will need to uh switch the
+
+ align:start position:0%
+well uh we will need to uh switch the
+ 
+
+ align:start position:0%
+well uh we will need to uh switch the
+first um the first um uh uh bit over
+
+ align:start position:0%
+first um the first um uh uh bit over
+ 
+
+ align:start position:0%
+first um the first um uh uh bit over
+here uh one we swap it into zero and
+
+ align:start position:0%
+here uh one we swap it into zero and
+ 
+
+ align:start position:0%
+here uh one we swap it into zero and
+then we go to the three zeros over here
+
+ align:start position:0%
+then we go to the three zeros over here
+ 
+
+ align:start position:0%
+then we go to the three zeros over here
+and we go to the next level and that
+
+ align:start position:0%
+and we go to the next level and that
+ 
+
+ align:start position:0%
+and we go to the next level and that
+would be this particular
+
+ align:start position:0%
+would be this particular
+ 
+
+ align:start position:0%
+would be this particular
+rule so what we can do here is to so so
+
+ align:start position:0%
+rule so what we can do here is to so so
+ 
+
+ align:start position:0%
+rule so what we can do here is to so so
+with when we see this we can start to uh
+
+ align:start position:0%
+with when we see this we can start to uh
+ 
+
+ align:start position:0%
+with when we see this we can start to uh
+figure out how we can direct inputs to
+
+ align:start position:0%
+figure out how we can direct inputs to
+ 
+
+ align:start position:0%
+figure out how we can direct inputs to
+outputs okay so let's uh do
+
+ align:start position:0%
+outputs okay so let's uh do
+ 
+
+ align:start position:0%
+outputs okay so let's uh do
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose I want to uh uh route a
+
+ align:start position:0%
+so suppose I want to uh uh route a
+ 
+
+ align:start position:0%
+so suppose I want to uh uh route a
+packet from a certain input one of the
+
+ align:start position:0%
+packet from a certain input one of the
+ 
+
+ align:start position:0%
+packet from a certain input one of the
+one of these all the way to one of the
+
+ align:start position:0%
+one of these all the way to one of the
+ 
+
+ align:start position:0%
+one of these all the way to one of the
+outputs uh over here
+
+ align:start position:0%
+outputs uh over here
+ 
+
+ align:start position:0%
+outputs uh over here
+so the way to do this is as follows we
+
+ align:start position:0%
+so the way to do this is as follows we
+ 
+
+ align:start position:0%
+so the way to do this is as follows we
+can just start for example I want to go
+
+ align:start position:0%
+can just start for example I want to go
+ 
+
+ align:start position:0%
+can just start for example I want to go
+from switch X1 up to X log
+
+ align:start position:0%
+from switch X1 up to X log
+ 
+
+ align:start position:0%
+from switch X1 up to X log
+n comma comma zero so I start
+
+ align:start position:0%
+n comma comma zero so I start
+ 
+
+ align:start position:0%
+n comma comma zero so I start
+completely at the left over here and I
+
+ align:start position:0%
+completely at the left over here and I
+ 
+
+ align:start position:0%
+completely at the left over here and I
+want to go somewhere of my choice to the
+
+ align:start position:0%
+want to go somewhere of my choice to the
+ 
+
+ align:start position:0%
+want to go somewhere of my choice to the
+right so I want to somehow
+
+ align:start position:0%
+right so I want to somehow
+ 
+
+ align:start position:0%
+right so I want to somehow
+move all the way to some other row
+
+ align:start position:0%
+move all the way to some other row
+ 
+
+ align:start position:0%
+move all the way to some other row
+y1 index by y by the bit pattern y1 up
+
+ align:start position:0%
+y1 index by y by the bit pattern y1 up
+ 
+
+ align:start position:0%
+y1 index by y by the bit pattern y1 up
+to Y log n but now at the very last
+
+ align:start position:0%
+to Y log n but now at the very last
+ 
+
+ align:start position:0%
+to Y log n but now at the very last
+level um which is log n well how do I do
+
+ align:start position:0%
+level um which is log n well how do I do
+ 
+
+ align:start position:0%
+level um which is log n well how do I do
+it well this switch I can use that rule
+
+ align:start position:0%
+it well this switch I can use that rule
+ 
+
+ align:start position:0%
+it well this switch I can use that rule
+up there and simply change X1 to y1 I
+
+ align:start position:0%
+up there and simply change X1 to y1 I
+ 
+
+ align:start position:0%
+up there and simply change X1 to y1 I
+can either leave X1 as it is if it's the
+
+ align:start position:0%
+can either leave X1 as it is if it's the
+ 
+
+ align:start position:0%
+can either leave X1 as it is if it's the
+same as y1 or I can swap it to its
+
+ align:start position:0%
+same as y1 or I can swap it to its
+ 
+
+ align:start position:0%
+same as y1 or I can swap it to its
+complement if that's the value of y1 so
+
+ align:start position:0%
+complement if that's the value of y1 so
+ 
+
+ align:start position:0%
+complement if that's the value of y1 so
+what I can do is I can just simply route
+
+ align:start position:0%
+what I can do is I can just simply route
+ 
+
+ align:start position:0%
+what I can do is I can just simply route
+it to uh y1 and then I leave all the
+
+ align:start position:0%
+it to uh y1 and then I leave all the
+ 
+
+ align:start position:0%
+it to uh y1 and then I leave all the
+other bits the same which are X2 X3 all
+
+ align:start position:0%
+other bits the same which are X2 X3 all
+ 
+
+ align:start position:0%
+other bits the same which are X2 X3 all
+the way up to X log
+
+ align:start position:0%
+the way up to X log
+ 
+
+ align:start position:0%
+the way up to X log
+n and uh we will have um reached the
+
+ align:start position:0%
+n and uh we will have um reached the
+ 
+
+ align:start position:0%
+n and uh we will have um reached the
+first level
+
+ align:start position:0%
+first level
+ 
+
+ align:start position:0%
+first level
+now this one can go to well now I'm
+
+ align:start position:0%
+now this one can go to well now I'm
+ 
+
+ align:start position:0%
+now this one can go to well now I'm
+going to swap the second bit into the
+
+ align:start position:0%
+going to swap the second bit into the
+ 
+
+ align:start position:0%
+going to swap the second bit into the
+bit of my choice so I leave all the
+
+ align:start position:0%
+bit of my choice so I leave all the
+ 
+
+ align:start position:0%
+bit of my choice so I leave all the
+other bits the same y1 the same X3 all
+
+ align:start position:0%
+other bits the same y1 the same X3 all
+ 
+
+ align:start position:0%
+other bits the same y1 the same X3 all
+the others the same I just swap X2 into
+
+ align:start position:0%
+the others the same I just swap X2 into
+ 
+
+ align:start position:0%
+the others the same I just swap X2 into
+Y2 so we leave all those to
+
+ align:start position:0%
+Y2 so we leave all those to
+ 
+
+ align:start position:0%
+Y2 so we leave all those to
+equal and we go to the second level and
+
+ align:start position:0%
+equal and we go to the second level and
+ 
+
+ align:start position:0%
+equal and we go to the second level and
+then we go all the
+
+ align:start position:0%
+then we go all the
+ 
+
+ align:start position:0%
+then we go all the
+way to the final level and we one by one
+
+ align:start position:0%
+way to the final level and we one by one
+ 
+
+ align:start position:0%
+way to the final level and we one by one
+Swap all these bits so let's have an
+
+ align:start position:0%
+Swap all these bits so let's have an
+ 
+
+ align:start position:0%
+Swap all these bits so let's have an
+example um suppose I want to connect uh
+
+ align:start position:0%
+example um suppose I want to connect uh
+ 
+
+ align:start position:0%
+example um suppose I want to connect uh
+say uh this
+
+ align:start position:0%
+say uh this
+ 
+
+ align:start position:0%
+say uh this
+one to uh um for example well let's say
+
+ align:start position:0%
+one to uh um for example well let's say
+ 
+
+ align:start position:0%
+one to uh um for example well let's say
+this particular output
+
+ align:start position:0%
+this particular output
+ 
+
+ align:start position:0%
+this particular output
+so uh what's
+
+ align:start position:0%
+so uh what's
+ 
+
+ align:start position:0%
+so uh what's
+the what's the binary for this one this
+
+ align:start position:0%
+the what's the binary for this one this
+ 
+
+ align:start position:0%
+the what's the binary for this one this
+is actually 1 Z
+
+ align:start position:0%
+is actually 1 Z
+ 
+
+ align:start position:0%
+is actually 1 Z
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+so um if the first bit is different
+
+ align:start position:0%
+so um if the first bit is different
+ 
+
+ align:start position:0%
+so um if the first bit is different
+I need to cross and otherwise I need to
+
+ align:start position:0%
+I need to cross and otherwise I need to
+ 
+
+ align:start position:0%
+I need to cross and otherwise I need to
+pass straight on so let's do
+
+ align:start position:0%
+pass straight on so let's do
+ 
+
+ align:start position:0%
+pass straight on so let's do
+this so over here I'm in 0 one 1 I need
+
+ align:start position:0%
+this so over here I'm in 0 one 1 I need
+ 
+
+ align:start position:0%
+this so over here I'm in 0 one 1 I need
+to go to one Z one so I need to change
+
+ align:start position:0%
+to go to one Z one so I need to change
+ 
+
+ align:start position:0%
+to go to one Z one so I need to change
+the zero into a one so I need to go
+
+ align:start position:0%
+the zero into a one so I need to go
+ 
+
+ align:start position:0%
+the zero into a one so I need to go
+down I need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross now uh if I look at the second bit
+
+ align:start position:0%
+cross now uh if I look at the second bit
+ 
+
+ align:start position:0%
+cross now uh if I look at the second bit
+um I also need to
+
+ align:start position:0%
+um I also need to
+ 
+
+ align:start position:0%
+um I also need to
+to change it into a zero so again I need
+
+ align:start position:0%
+to change it into a zero so again I need
+ 
+
+ align:start position:0%
+to change it into a zero so again I need
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+cross which is over
+
+ align:start position:0%
+cross which is over
+ 
+
+ align:start position:0%
+cross which is over
+here now the third bit is equal to
+
+ align:start position:0%
+here now the third bit is equal to
+ 
+
+ align:start position:0%
+here now the third bit is equal to
+one and it's the same so now I can go
+
+ align:start position:0%
+one and it's the same so now I can go
+ 
+
+ align:start position:0%
+one and it's the same so now I can go
+straight ahead I do not
+
+ align:start position:0%
+straight ahead I do not
+ 
+
+ align:start position:0%
+straight ahead I do not
+cross and I end up at this output so
+
+ align:start position:0%
+cross and I end up at this output so
+ 
+
+ align:start position:0%
+cross and I end up at this output so
+what do so what did I do for every bit
+
+ align:start position:0%
+what do so what did I do for every bit
+ 
+
+ align:start position:0%
+what do so what did I do for every bit
+that is different I cross and for the
+
+ align:start position:0%
+that is different I cross and for the
+ 
+
+ align:start position:0%
+that is different I cross and for the
+bits that are the same I go straight
+
+ align:start position:0%
+bits that are the same I go straight
+ 
+
+ align:start position:0%
+bits that are the same I go straight
+ahead so this is how I can route
+
+ align:start position:0%
+ahead so this is how I can route
+ 
+
+ align:start position:0%
+ahead so this is how I can route
+packets from one input to another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output okay so let's uh look at the
+
+ align:start position:0%
+output okay so let's uh look at the
+ 
+
+ align:start position:0%
+output okay so let's uh look at the
+parameters um first of all if we look at
+
+ align:start position:0%
+parameters um first of all if we look at
+ 
+
+ align:start position:0%
+parameters um first of all if we look at
+the uh uh at the at the
+
+ align:start position:0%
+the uh uh at the at the
+ 
+
+ align:start position:0%
+the uh uh at the at the
+diameter well it turns out that that's
+
+ align:start position:0%
+diameter well it turns out that that's
+ 
+
+ align:start position:0%
+diameter well it turns out that that's
+equal approximately equal to the to the
+
+ align:start position:0%
+equal approximately equal to the to the
+ 
+
+ align:start position:0%
+equal approximately equal to the to the
+number of levels which is the logarithm
+
+ align:start position:0%
+number of levels which is the logarithm
+ 
+
+ align:start position:0%
+number of levels which is the logarithm
+of N and to be precise it's actually
+
+ align:start position:0%
+of N and to be precise it's actually
+ 
+
+ align:start position:0%
+of N and to be precise it's actually
+equal to 2 plus the logarithm of n so
+
+ align:start position:0%
+equal to 2 plus the logarithm of n so
+ 
+
+ align:start position:0%
+equal to 2 plus the logarithm of n so
+that's great that's a good uh that's a
+
+ align:start position:0%
+that's great that's a good uh that's a
+ 
+
+ align:start position:0%
+that's great that's a good uh that's a
+good scaling again it's back to the
+
+ align:start position:0%
+good scaling again it's back to the
+ 
+
+ align:start position:0%
+good scaling again it's back to the
+logarithm of n so we have the best of
+
+ align:start position:0%
+logarithm of n so we have the best of
+ 
+
+ align:start position:0%
+logarithm of n so we have the best of
+these two
+
+ align:start position:0%
+these two
+ 
+
+ align:start position:0%
+these two
+parameters the switches that we see have
+
+ align:start position:0%
+parameters the switches that we see have
+ 
+
+ align:start position:0%
+parameters the switches that we see have
+two inputs and two outputs so we again
+
+ align:start position:0%
+two inputs and two outputs so we again
+ 
+
+ align:start position:0%
+two inputs and two outputs so we again
+have a two * two
+
+ align:start position:0%
+have a two * two
+ 
+
+ align:start position:0%
+have a two * two
+switch um the number of switches is the
+
+ align:start position:0%
+switch um the number of switches is the
+ 
+
+ align:start position:0%
+switch um the number of switches is the
+number of rows times the number of
+
+ align:start position:0%
+number of rows times the number of
+ 
+
+ align:start position:0%
+number of rows times the number of
+columns the number of columns is the
+
+ align:start position:0%
+columns the number of columns is the
+ 
+
+ align:start position:0%
+columns the number of columns is the
+logarithm of N and number of rows is uh
+
+ align:start position:0%
+logarithm of N and number of rows is uh
+ 
+
+ align:start position:0%
+logarithm of N and number of rows is uh
+is equal to n and to make it a little
+
+ align:start position:0%
+is equal to n and to make it a little
+ 
+
+ align:start position:0%
+is equal to n and to make it a little
+bit precise it's 1 plus the logarithm of
+
+ align:start position:0%
+bit precise it's 1 plus the logarithm of
+ 
+
+ align:start position:0%
+bit precise it's 1 plus the logarithm of
+n so that's somewhere in between those
+
+ align:start position:0%
+n so that's somewhere in between those
+ 
+
+ align:start position:0%
+n so that's somewhere in between those
+two but if you're thinking about it it's
+
+ align:start position:0%
+two but if you're thinking about it it's
+ 
+
+ align:start position:0%
+two but if you're thinking about it it's
+much better than n Square it's almost
+
+ align:start position:0%
+much better than n Square it's almost
+ 
+
+ align:start position:0%
+much better than n Square it's almost
+linear except for a logarithmic
+
+ align:start position:0%
+linear except for a logarithmic
+ 
+
+ align:start position:0%
+linear except for a logarithmic
+factor for the congestion and we're not
+
+ align:start position:0%
+factor for the congestion and we're not
+ 
+
+ align:start position:0%
+factor for the congestion and we're not
+going to talk about it here but you have
+
+ align:start position:0%
+going to talk about it here but you have
+ 
+
+ align:start position:0%
+going to talk about it here but you have
+a problem set assignment that uh will
+
+ align:start position:0%
+a problem set assignment that uh will
+ 
+
+ align:start position:0%
+a problem set assignment that uh will
+ask you to solve this is that actually
+
+ align:start position:0%
+ask you to solve this is that actually
+ 
+
+ align:start position:0%
+ask you to solve this is that actually
+the congestion is a square root of n uh
+
+ align:start position:0%
+the congestion is a square root of n uh
+ 
+
+ align:start position:0%
+the congestion is a square root of n uh
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+is equal to the square root of n / 2
+
+ align:start position:0%
+is equal to the square root of n / 2
+ 
+
+ align:start position:0%
+is equal to the square root of n / 2
+depending on whether n is an even power
+
+ align:start position:0%
+depending on whether n is an even power
+ 
+
+ align:start position:0%
+depending on whether n is an even power
+or n is an odd power now we're not going
+
+ align:start position:0%
+or n is an odd power now we're not going
+ 
+
+ align:start position:0%
+or n is an odd power now we're not going
+to prove that here because we want to
+
+ align:start position:0%
+to prove that here because we want to
+ 
+
+ align:start position:0%
+to prove that here because we want to
+step forward to this particular Network
+
+ align:start position:0%
+step forward to this particular Network
+ 
+
+ align:start position:0%
+step forward to this particular Network
+that's very
+
+ align:start position:0%
+that's very
+ 
+
+ align:start position:0%
+that's very
+exciting and uh you will prove this in
+
+ align:start position:0%
+exciting and uh you will prove this in
+ 
+
+ align:start position:0%
+exciting and uh you will prove this in
+your problem set so this one is
+
+ align:start position:0%
+your problem set so this one is
+ 
+
+ align:start position:0%
+your problem set so this one is
+somewhere in between somewhere in
+
+ align:start position:0%
+somewhere in between somewhere in
+ 
+
+ align:start position:0%
+somewhere in between somewhere in
+between these two extremes now it would
+
+ align:start position:0%
+between these two extremes now it would
+ 
+
+ align:start position:0%
+between these two extremes now it would
+be really fantastic if we can somehow
+
+ align:start position:0%
+be really fantastic if we can somehow
+ 
+
+ align:start position:0%
+be really fantastic if we can somehow
+transform this network with the trick to
+
+ align:start position:0%
+transform this network with the trick to
+ 
+
+ align:start position:0%
+transform this network with the trick to
+again have a really great congestion of
+
+ align:start position:0%
+again have a really great congestion of
+ 
+
+ align:start position:0%
+again have a really great congestion of
+just a constant like like like like two
+
+ align:start position:0%
+just a constant like like like like two
+ 
+
+ align:start position:0%
+just a constant like like like like two
+or or three or whatever or maybe even
+
+ align:start position:0%
+or or three or whatever or maybe even
+ 
+
+ align:start position:0%
+or or three or whatever or maybe even
+one so for this particular network uh in
+
+ align:start position:0%
+one so for this particular network uh in
+ 
+
+ align:start position:0%
+one so for this particular network uh in
+the 1960s Ben Babs researcher had the
+
+ align:start position:0%
+the 1960s Ben Babs researcher had the
+ 
+
+ align:start position:0%
+the 1960s Ben Babs researcher had the
+great idea to use a butterfly Network
+
+ align:start position:0%
+great idea to use a butterfly Network
+ 
+
+ align:start position:0%
+great idea to use a butterfly Network
+and attach to it again a butterfly
+
+ align:start position:0%
+and attach to it again a butterfly
+ 
+
+ align:start position:0%
+and attach to it again a butterfly
+Network backto back sort of so what was
+
+ align:start position:0%
+Network backto back sort of so what was
+ 
+
+ align:start position:0%
+Network backto back sort of so what was
+his ID his idea was to uh to do the
+
+ align:start position:0%
+his ID his idea was to uh to do the
+ 
+
+ align:start position:0%
+his ID his idea was to uh to do the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+so the butterfly
+
+ align:start position:0%
+so the butterfly
+ 
+
+ align:start position:0%
+so the butterfly
+Network as we have it right now is this
+
+ align:start position:0%
+Network as we have it right now is this
+ 
+
+ align:start position:0%
+Network as we have it right now is this
+particular part over
+
+ align:start position:0%
+particular part over
+ 
+
+ align:start position:0%
+particular part over
+here and the idea is is to uh now to
+
+ align:start position:0%
+here and the idea is is to uh now to
+ 
+
+ align:start position:0%
+here and the idea is is to uh now to
+start up mixing all those outputs that
+
+ align:start position:0%
+start up mixing all those outputs that
+ 
+
+ align:start position:0%
+start up mixing all those outputs that
+we got here together again using a
+
+ align:start position:0%
+we got here together again using a
+ 
+
+ align:start position:0%
+we got here together again using a
+similar rule so what do we do we are
+
+ align:start position:0%
+similar rule so what do we do we are
+ 
+
+ align:start position:0%
+similar rule so what do we do we are
+going going to um to essentially
+
+ align:start position:0%
+going going to um to essentially
+ 
+
+ align:start position:0%
+going going to um to essentially
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh repeat this particular structure
+
+ align:start position:0%
+um uh repeat this particular structure
+ 
+
+ align:start position:0%
+um uh repeat this particular structure
+on this
+
+ align:start position:0%
+on this
+ 
+
+ align:start position:0%
+on this
+side okay so how do we do it uh well we
+
+ align:start position:0%
+side okay so how do we do it uh well we
+ 
+
+ align:start position:0%
+side okay so how do we do it uh well we
+go either straight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forward or we start to mix them again so
+
+ align:start position:0%
+forward or we start to mix them again so
+ 
+
+ align:start position:0%
+forward or we start to mix them again so
+it's like this output this particular
+
+ align:start position:0%
+it's like this output this particular
+ 
+
+ align:start position:0%
+it's like this output this particular
+switch can either go straight the head
+
+ align:start position:0%
+switch can either go straight the head
+ 
+
+ align:start position:0%
+switch can either go straight the head
+or can cross to the lower um part over
+
+ align:start position:0%
+or can cross to the lower um part over
+ 
+
+ align:start position:0%
+or can cross to the lower um part over
+here it goes over here and this one goes
+
+ align:start position:0%
+here it goes over here and this one goes
+ 
+
+ align:start position:0%
+here it goes over here and this one goes
+over here so as you can see we have
+
+ align:start position:0%
+over here so as you can see we have
+ 
+
+ align:start position:0%
+over here so as you can see we have
+repeated this
+
+ align:start position:0%
+repeated this
+ 
+
+ align:start position:0%
+repeated this
+part is exactly the same as this
+
+ align:start position:0%
+part is exactly the same as this
+ 
+
+ align:start position:0%
+part is exactly the same as this
+structure over here and we'll we'll do
+
+ align:start position:0%
+structure over here and we'll we'll do
+ 
+
+ align:start position:0%
+structure over here and we'll we'll do
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same for the this
+
+ align:start position:0%
+same for the this
+ 
+
+ align:start position:0%
+same for the this
+part so we can either
+
+ align:start position:0%
+part so we can either
+ 
+
+ align:start position:0%
+part so we can either
+Cross or we can go straight ahead oh uh
+
+ align:start position:0%
+Cross or we can go straight ahead oh uh
+ 
+
+ align:start position:0%
+Cross or we can go straight ahead oh uh
+we also have of course that these
+
+ align:start position:0%
+we also have of course that these
+ 
+
+ align:start position:0%
+we also have of course that these
+switches can go straight ahead or can
+
+ align:start position:0%
+switches can go straight ahead or can
+ 
+
+ align:start position:0%
+switches can go straight ahead or can
+cross to the top I forgot about that so
+
+ align:start position:0%
+cross to the top I forgot about that so
+ 
+
+ align:start position:0%
+cross to the top I forgot about that so
+we have this oops as well so as you can
+
+ align:start position:0%
+we have this oops as well so as you can
+ 
+
+ align:start position:0%
+we have this oops as well so as you can
+see this particular structure repeats
+
+ align:start position:0%
+see this particular structure repeats
+ 
+
+ align:start position:0%
+see this particular structure repeats
+itself again and we slowly start to
+
+ align:start position:0%
+itself again and we slowly start to
+ 
+
+ align:start position:0%
+itself again and we slowly start to
+build up and mixing all the uh outputs
+
+ align:start position:0%
+build up and mixing all the uh outputs
+ 
+
+ align:start position:0%
+build up and mixing all the uh outputs
+again or the possibility at least to
+
+ align:start position:0%
+again or the possibility at least to
+ 
+
+ align:start position:0%
+again or the possibility at least to
+Route them to any other uh to any other
+
+ align:start position:0%
+Route them to any other uh to any other
+ 
+
+ align:start position:0%
+Route them to any other uh to any other
+U um row so how do we do this well we
+
+ align:start position:0%
+U um row so how do we do this well we
+ 
+
+ align:start position:0%
+U um row so how do we do this well we
+Contin this particular structure now
+
+ align:start position:0%
+Contin this particular structure now
+ 
+
+ align:start position:0%
+Contin this particular structure now
+over here so all these can either go
+
+ align:start position:0%
+over here so all these can either go
+ 
+
+ align:start position:0%
+over here so all these can either go
+straight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead that's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possibility or they can go
+
+ align:start position:0%
+possibility or they can go
+ 
+
+ align:start position:0%
+possibility or they can go
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down so this switch can either go
+
+ align:start position:0%
+down so this switch can either go
+ 
+
+ align:start position:0%
+down so this switch can either go
+straight ahead or can go to the lower
+
+ align:start position:0%
+straight ahead or can go to the lower
+ 
+
+ align:start position:0%
+straight ahead or can go to the lower
+half and for this we have a similar Circ
+
+ align:start position:0%
+half and for this we have a similar Circ
+ 
+
+ align:start position:0%
+half and for this we have a similar Circ
+so we can either go straight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead or such a switch can cross over to
+
+ align:start position:0%
+ahead or such a switch can cross over to
+ 
+
+ align:start position:0%
+ahead or such a switch can cross over to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+top over
+
+ align:start position:0%
+top over
+ 
+
+ align:start position:0%
+top over
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's this so this is bayis
+
+ align:start position:0%
+okay so that's this so this is bayis
+ 
+
+ align:start position:0%
+okay so that's this so this is bayis
+network and then over here of course we
+
+ align:start position:0%
+network and then over here of course we
+ 
+
+ align:start position:0%
+network and then over here of course we
+have uh the outputs
+
+ align:start position:0%
+have uh the outputs
+ 
+
+ align:start position:0%
+have uh the outputs
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero one and all the way down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seven
+
+ align:start position:0%
+seven
+ 
+
+ align:start position:0%
+seven
+okay so as you can see over here this
+
+ align:start position:0%
+okay so as you can see over here this
+ 
+
+ align:start position:0%
+okay so as you can see over here this
+structure again has a recursive nature
+
+ align:start position:0%
+structure again has a recursive nature
+ 
+
+ align:start position:0%
+structure again has a recursive nature
+to it um you can see that uh this big
+
+ align:start position:0%
+to it um you can see that uh this big
+ 
+
+ align:start position:0%
+to it um you can see that uh this big
+benis network over here consists of two
+
+ align:start position:0%
+benis network over here consists of two
+ 
+
+ align:start position:0%
+benis network over here consists of two
+smaller ones that are right here in the
+
+ align:start position:0%
+smaller ones that are right here in the
+ 
+
+ align:start position:0%
+smaller ones that are right here in the
+middle this one that goes all the way up
+
+ align:start position:0%
+middle this one that goes all the way up
+ 
+
+ align:start position:0%
+middle this one that goes all the way up
+to here so maybe I should put uh a color
+
+ align:start position:0%
+to here so maybe I should put uh a color
+ 
+
+ align:start position:0%
+to here so maybe I should put uh a color
+boundary around it let me
+
+ align:start position:0%
+boundary around it let me
+ 
+
+ align:start position:0%
+boundary around it let me
+check I want to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this right so this particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part is again a bis Network and um the
+
+ align:start position:0%
+part is again a bis Network and um the
+ 
+
+ align:start position:0%
+part is again a bis Network and um the
+top part in the same picture the top sub
+
+ align:start position:0%
+top part in the same picture the top sub
+ 
+
+ align:start position:0%
+top part in the same picture the top sub
+network is also a bis Network this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part and if you look within those we
+
+ align:start position:0%
+part and if you look within those we
+ 
+
+ align:start position:0%
+part and if you look within those we
+again see a top
+
+ align:start position:0%
+again see a top
+ 
+
+ align:start position:0%
+again see a top
+part and a bottom part and over here we
+
+ align:start position:0%
+part and a bottom part and over here we
+ 
+
+ align:start position:0%
+part and a bottom part and over here we
+see a top part and also a bottom part so
+
+ align:start position:0%
+see a top part and also a bottom part so
+ 
+
+ align:start position:0%
+see a top part and also a bottom part so
+so um you see this uh recursive nature
+
+ align:start position:0%
+so um you see this uh recursive nature
+ 
+
+ align:start position:0%
+so um you see this uh recursive nature
+again reappearing it turns out that with
+
+ align:start position:0%
+again reappearing it turns out that with
+ 
+
+ align:start position:0%
+again reappearing it turns out that with
+this trick we can completely eliminate
+
+ align:start position:0%
+this trick we can completely eliminate
+ 
+
+ align:start position:0%
+this trick we can completely eliminate
+congestion and we can get it to only one
+
+ align:start position:0%
+congestion and we can get it to only one
+ 
+
+ align:start position:0%
+congestion and we can get it to only one
+which is really surprising and that's
+
+ align:start position:0%
+which is really surprising and that's
+ 
+
+ align:start position:0%
+which is really surprising and that's
+what we're going to prove here so this
+
+ align:start position:0%
+what we're going to prove here so this
+ 
+
+ align:start position:0%
+what we're going to prove here so this
+is a great uh invention at the time it's
+
+ align:start position:0%
+is a great uh invention at the time it's
+ 
+
+ align:start position:0%
+is a great uh invention at the time it's
+really really
+
+ align:start position:0%
+really really
+ 
+
+ align:start position:0%
+really really
+beautiful um so let me put in the other
+
+ align:start position:0%
+beautiful um so let me put in the other
+ 
+
+ align:start position:0%
+beautiful um so let me put in the other
+parameters um so they stay approximately
+
+ align:start position:0%
+parameters um so they stay approximately
+ 
+
+ align:start position:0%
+parameters um so they stay approximately
+the same up to that diameter is about
+
+ align:start position:0%
+the same up to that diameter is about
+ 
+
+ align:start position:0%
+the same up to that diameter is about
+twice as large because we added another
+
+ align:start position:0%
+twice as large because we added another
+ 
+
+ align:start position:0%
+twice as large because we added another
+sort of whole butterfly structure to it
+
+ align:start position:0%
+sort of whole butterfly structure to it
+ 
+
+ align:start position:0%
+sort of whole butterfly structure to it
+the switches size and stay the same we
+
+ align:start position:0%
+the switches size and stay the same we
+ 
+
+ align:start position:0%
+the switches size and stay the same we
+again have about two times more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switches so they sort of stay about the
+
+ align:start position:0%
+switches so they sort of stay about the
+ 
+
+ align:start position:0%
+switches so they sort of stay about the
+same up to a linear uh Factor like a
+
+ align:start position:0%
+same up to a linear uh Factor like a
+ 
+
+ align:start position:0%
+same up to a linear uh Factor like a
+constant factor and uh the congestion
+
+ align:start position:0%
+constant factor and uh the congestion
+ 
+
+ align:start position:0%
+constant factor and uh the congestion
+however completely dropped down to one
+
+ align:start position:0%
+however completely dropped down to one
+ 
+
+ align:start position:0%
+however completely dropped down to one
+so that's what we're going to prove now
+
+ align:start position:0%
+so that's what we're going to prove now
+ 
+
+ align:start position:0%
+so that's what we're going to prove now
+and in order to get some
+
+ align:start position:0%
+and in order to get some
+ 
+
+ align:start position:0%
+and in order to get some
+intuition well let me first write down
+
+ align:start position:0%
+intuition well let me first write down
+ 
+
+ align:start position:0%
+intuition well let me first write down
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+um actually let me put
+
+ align:start position:0%
+um actually let me put
+ 
+
+ align:start position:0%
+um actually let me put
+this uh over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so in order to get some insight
+
+ align:start position:0%
+here so in order to get some insight
+ 
+
+ align:start position:0%
+here so in order to get some insight
+into this uh we are going to
+
+ align:start position:0%
+into this uh we are going to
+ 
+
+ align:start position:0%
+into this uh we are going to
+um well
+
+ align:start position:0%
+um well
+ 
+
+ align:start position:0%
+um well
+we we are going to use this recursive
+
+ align:start position:0%
+we we are going to use this recursive
+ 
+
+ align:start position:0%
+we we are going to use this recursive
+name nature so we're going to use
+
+ align:start position:0%
+name nature so we're going to use
+ 
+
+ align:start position:0%
+name nature so we're going to use
+induction and we're going to say
+
+ align:start position:0%
+induction and we're going to say
+ 
+
+ align:start position:0%
+induction and we're going to say
+oh I'm I can really for any permutation
+
+ align:start position:0%
+oh I'm I can really for any permutation
+ 
+
+ align:start position:0%
+oh I'm I can really for any permutation
+I can find a really good routing for say
+
+ align:start position:0%
+I can find a really good routing for say
+ 
+
+ align:start position:0%
+I can find a really good routing for say
+this red sub Network and for this blue
+
+ align:start position:0%
+this red sub Network and for this blue
+ 
+
+ align:start position:0%
+this red sub Network and for this blue
+sub Network so I know that so what I
+
+ align:start position:0%
+sub Network so I know that so what I
+ 
+
+ align:start position:0%
+sub Network so I know that so what I
+need to do is to to to if if if I have
+
+ align:start position:0%
+need to do is to to to if if if I have
+ 
+
+ align:start position:0%
+need to do is to to to if if if I have
+my bigger Banis Network like this one I
+
+ align:start position:0%
+my bigger Banis Network like this one I
+ 
+
+ align:start position:0%
+my bigger Banis Network like this one I
+would need to somehow map these
+
+ align:start position:0%
+would need to somehow map these
+ 
+
+ align:start position:0%
+would need to somehow map these
+inputs uh I need to Route them to either
+
+ align:start position:0%
+inputs uh I need to Route them to either
+ 
+
+ align:start position:0%
+inputs uh I need to Route them to either
+the top and the bottom sub Network one
+
+ align:start position:0%
+the top and the bottom sub Network one
+ 
+
+ align:start position:0%
+the top and the bottom sub Network one
+of the two in such a way that there will
+
+ align:start position:0%
+of the two in such a way that there will
+ 
+
+ align:start position:0%
+of the two in such a way that there will
+be absolutely no congestion because we
+
+ align:start position:0%
+be absolutely no congestion because we
+ 
+
+ align:start position:0%
+be absolutely no congestion because we
+want to keep this one so a switch should
+
+ align:start position:0%
+want to keep this one so a switch should
+ 
+
+ align:start position:0%
+want to keep this one so a switch should
+only see one packet coming in so that
+
+ align:start position:0%
+only see one packet coming in so that
+ 
+
+ align:start position:0%
+only see one packet coming in so that
+means for example and we'll come back to
+
+ align:start position:0%
+means for example and we'll come back to
+ 
+
+ align:start position:0%
+means for example and we'll come back to
+that that for example for this switch it
+
+ align:start position:0%
+that that for example for this switch it
+ 
+
+ align:start position:0%
+that that for example for this switch it
+should not receive a packet from both
+
+ align:start position:0%
+should not receive a packet from both
+ 
+
+ align:start position:0%
+should not receive a packet from both
+this input and from this input so the
+
+ align:start position:0%
+this input and from this input so the
+ 
+
+ align:start position:0%
+this input and from this input so the
+intuition that we are going to create is
+
+ align:start position:0%
+intuition that we are going to create is
+ 
+
+ align:start position:0%
+intuition that we are going to create is
+we're going to uh create like we we we
+
+ align:start position:0%
+we're going to uh create like we we we
+ 
+
+ align:start position:0%
+we're going to uh create like we we we
+we we going to list our constraints the
+
+ align:start position:0%
+we we going to list our constraints the
+ 
+
+ align:start position:0%
+we we going to list our constraints the
+constraints that we need to satisfy like
+
+ align:start position:0%
+constraints that we need to satisfy like
+ 
+
+ align:start position:0%
+constraints that we need to satisfy like
+the zero and the fourth input should not
+
+ align:start position:0%
+the zero and the fourth input should not
+ 
+
+ align:start position:0%
+the zero and the fourth input should not
+both be mapped to this top sub Network
+
+ align:start position:0%
+both be mapped to this top sub Network
+ 
+
+ align:start position:0%
+both be mapped to this top sub Network
+and so on so we will get into that and
+
+ align:start position:0%
+and so on so we will get into that and
+ 
+
+ align:start position:0%
+and so on so we will get into that and
+then we will uh gain a lot of intuition
+
+ align:start position:0%
+then we will uh gain a lot of intuition
+ 
+
+ align:start position:0%
+then we will uh gain a lot of intuition
+on how to solve this okay so what's the
+
+ align:start position:0%
+on how to solve this okay so what's the
+ 
+
+ align:start position:0%
+on how to solve this okay so what's the
+theorem so the theorem is that the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+congestion uh of uh uh the N
+
+ align:start position:0%
+congestion uh of uh uh the N
+ 
+
+ align:start position:0%
+congestion uh of uh uh the N
+input uh
+
+ align:start position:0%
+input uh
+ 
+
+ align:start position:0%
+input uh
+Bish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+network uh is actually equal to
+
+ align:start position:0%
+network uh is actually equal to
+ 
+
+ align:start position:0%
+network uh is actually equal to
+one uh and we will prove this for uh n
+
+ align:start position:0%
+one uh and we will prove this for uh n
+ 
+
+ align:start position:0%
+one uh and we will prove this for uh n
+equal to a power of two we have assumed
+
+ align:start position:0%
+equal to a power of two we have assumed
+ 
+
+ align:start position:0%
+equal to a power of two we have assumed
+that at the start of of of of with all
+
+ align:start position:0%
+that at the start of of of of with all
+ 
+
+ align:start position:0%
+that at the start of of of of with all
+the other networks as well and and in
+
+ align:start position:0%
+the other networks as well and and in
+ 
+
+ align:start position:0%
+the other networks as well and and in
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+we will use induction on a so that's
+
+ align:start position:0%
+we will use induction on a so that's
+ 
+
+ align:start position:0%
+we will use induction on a so that's
+uh the method that we will do because
+
+ align:start position:0%
+uh the method that we will do because
+ 
+
+ align:start position:0%
+uh the method that we will do because
+that's also the recursive structure of
+
+ align:start position:0%
+that's also the recursive structure of
+ 
+
+ align:start position:0%
+that's also the recursive structure of
+the bis Network itself so we will use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction on a
+
+ align:start position:0%
+induction on a
+ 
+
+ align:start position:0%
+induction on a
+and uh we're going to define the
+
+ align:start position:0%
+and uh we're going to define the
+ 
+
+ align:start position:0%
+and uh we're going to define the
+induction hypothesis simply as the
+
+ align:start position:0%
+induction hypothesis simply as the
+ 
+
+ align:start position:0%
+induction hypothesis simply as the
+theorem is true for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now let us do the base case we
+
+ align:start position:0%
+okay now let us do the base case we
+ 
+
+ align:start position:0%
+okay now let us do the base case we
+always start with the base case and that
+
+ align:start position:0%
+always start with the base case and that
+ 
+
+ align:start position:0%
+always start with the base case and that
+should be pretty easy because this is
+
+ align:start position:0%
+should be pretty easy because this is
+ 
+
+ align:start position:0%
+should be pretty easy because this is
+the most basic uh Bish Network so n
+
+ align:start position:0%
+the most basic uh Bish Network so n
+ 
+
+ align:start position:0%
+the most basic uh Bish Network so n
+equal 2 the^
+
+ align:start position:0%
+equal 2 the^
+ 
+
+ align:start position:0%
+equal 2 the^
+1 um we essentially have uh two inputs
+
+ align:start position:0%
+1 um we essentially have uh two inputs
+ 
+
+ align:start position:0%
+1 um we essentially have uh two inputs
+an input
+
+ align:start position:0%
+an input
+ 
+
+ align:start position:0%
+an input
+zero and an input one
+
+ align:start position:0%
+zero and an input one
+ 
+
+ align:start position:0%
+zero and an input one
+uh they are connected to these switches
+
+ align:start position:0%
+uh they are connected to these switches
+ 
+
+ align:start position:0%
+uh they are connected to these switches
+over here that can either forward
+
+ align:start position:0%
+over here that can either forward
+ 
+
+ align:start position:0%
+over here that can either forward
+them or can cross them over and then
+
+ align:start position:0%
+them or can cross them over and then
+ 
+
+ align:start position:0%
+them or can cross them over and then
+they go directly to the output uh notice
+
+ align:start position:0%
+they go directly to the output uh notice
+ 
+
+ align:start position:0%
+they go directly to the output uh notice
+that in this case you just have the most
+
+ align:start position:0%
+that in this case you just have the most
+ 
+
+ align:start position:0%
+that in this case you just have the most
+Elementary butterfly network is the
+
+ align:start position:0%
+Elementary butterfly network is the
+ 
+
+ align:start position:0%
+Elementary butterfly network is the
+same so we have output zero and output
+
+ align:start position:0%
+same so we have output zero and output
+ 
+
+ align:start position:0%
+same so we have output zero and output
+one so this corresponds in this picture
+
+ align:start position:0%
+one so this corresponds in this picture
+ 
+
+ align:start position:0%
+one so this corresponds in this picture
+to these little small things over here
+
+ align:start position:0%
+to these little small things over here
+ 
+
+ align:start position:0%
+to these little small things over here
+this one and this one and this one over
+
+ align:start position:0%
+this one and this one and this one over
+ 
+
+ align:start position:0%
+this one and this one and this one over
+here and the fourth one over here um so
+
+ align:start position:0%
+here and the fourth one over here um so
+ 
+
+ align:start position:0%
+here and the fourth one over here um so
+now let's take any permutation we want
+
+ align:start position:0%
+now let's take any permutation we want
+ 
+
+ align:start position:0%
+now let's take any permutation we want
+to show that we can route it in such a
+
+ align:start position:0%
+to show that we can route it in such a
+ 
+
+ align:start position:0%
+to show that we can route it in such a
+way that there's only a congestion of
+
+ align:start position:0%
+way that there's only a congestion of
+ 
+
+ align:start position:0%
+way that there's only a congestion of
+one so let's do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so there are essentially only two
+
+ align:start position:0%
+so so there are essentially only two
+ 
+
+ align:start position:0%
+so so there are essentially only two
+permutations either zero is mapped to
+
+ align:start position:0%
+permutations either zero is mapped to
+ 
+
+ align:start position:0%
+permutations either zero is mapped to
+zero and one is mapped to one or zero is
+
+ align:start position:0%
+zero and one is mapped to one or zero is
+ 
+
+ align:start position:0%
+zero and one is mapped to one or zero is
+mapped to one and one is mapped to
+
+ align:start position:0%
+mapped to one and one is mapped to
+ 
+
+ align:start position:0%
+mapped to one and one is mapped to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+um so in both cases we can just route
+
+ align:start position:0%
+um so in both cases we can just route
+ 
+
+ align:start position:0%
+um so in both cases we can just route
+them uh through their own
+
+ align:start position:0%
+them uh through their own
+ 
+
+ align:start position:0%
+them uh through their own
+switches so we have that either Pi of 0
+
+ align:start position:0%
+switches so we have that either Pi of 0
+ 
+
+ align:start position:0%
+switches so we have that either Pi of 0
+equals 0 and Pi of 1 equals 1 in which
+
+ align:start position:0%
+equals 0 and Pi of 1 equals 1 in which
+ 
+
+ align:start position:0%
+equals 0 and Pi of 1 equals 1 in which
+case we just direct them straight
+
+ align:start position:0%
+case we just direct them straight
+ 
+
+ align:start position:0%
+case we just direct them straight
+through and we go straight through and
+
+ align:start position:0%
+through and we go straight through and
+ 
+
+ align:start position:0%
+through and we go straight through and
+every switch which only sees a packet
+
+ align:start position:0%
+every switch which only sees a packet
+ 
+
+ align:start position:0%
+every switch which only sees a packet
+once so for this particular permutation
+
+ align:start position:0%
+once so for this particular permutation
+ 
+
+ align:start position:0%
+once so for this particular permutation
+we have a congestion of one now the
+
+ align:start position:0%
+we have a congestion of one now the
+ 
+
+ align:start position:0%
+we have a congestion of one now the
+other permutation that we can have is if
+
+ align:start position:0%
+other permutation that we can have is if
+ 
+
+ align:start position:0%
+other permutation that we can have is if
+zero is mapped to one and if one is
+
+ align:start position:0%
+zero is mapped to one and if one is
+ 
+
+ align:start position:0%
+zero is mapped to one and if one is
+mapped to zero well in that
+
+ align:start position:0%
+mapped to zero well in that
+ 
+
+ align:start position:0%
+mapped to zero well in that
+case we just route this cross over to
+
+ align:start position:0%
+case we just route this cross over to
+ 
+
+ align:start position:0%
+case we just route this cross over to
+the bottom row and here we go from this
+
+ align:start position:0%
+the bottom row and here we go from this
+ 
+
+ align:start position:0%
+the bottom row and here we go from this
+switch to the to the top row again every
+
+ align:start position:0%
+switch to the to the top row again every
+ 
+
+ align:start position:0%
+switch to the to the top row again every
+switch only sees a packet once so in
+
+ align:start position:0%
+switch only sees a packet once so in
+ 
+
+ align:start position:0%
+switch only sees a packet once so in
+this case in the base case we are done
+
+ align:start position:0%
+this case in the base case we are done
+ 
+
+ align:start position:0%
+this case in the base case we are done
+we are happy we have shown that the
+
+ align:start position:0%
+we are happy we have shown that the
+ 
+
+ align:start position:0%
+we are happy we have shown that the
+congestion is equal to one so now we get
+
+ align:start position:0%
+congestion is equal to one so now we get
+ 
+
+ align:start position:0%
+congestion is equal to one so now we get
+to uh the harder part because for the
+
+ align:start position:0%
+to uh the harder part because for the
+ 
+
+ align:start position:0%
+to uh the harder part because for the
+inductive
+
+ align:start position:0%
+inductive
+ 
+
+ align:start position:0%
+inductive
+step we are going to assume of
+
+ align:start position:0%
+step we are going to assume of
+ 
+
+ align:start position:0%
+step we are going to assume of
+course uh that it holds true for a
+
+ align:start position:0%
+course uh that it holds true for a
+ 
+
+ align:start position:0%
+course uh that it holds true for a
+smaller uh bis Network so we
+
+ align:start position:0%
+smaller uh bis Network so we
+ 
+
+ align:start position:0%
+smaller uh bis Network so we
+assume that uh p a is true
+
+ align:start position:0%
+assume that uh p a is true
+ 
+
+ align:start position:0%
+assume that uh p a is true
+and uh well let's try to gain some
+
+ align:start position:0%
+and uh well let's try to gain some
+ 
+
+ align:start position:0%
+and uh well let's try to gain some
+inside
+
+ align:start position:0%
+inside
+ 
+
+ align:start position:0%
+inside
+here so we know that within each from
+
+ align:start position:0%
+here so we know that within each from
+ 
+
+ align:start position:0%
+here so we know that within each from
+our induction hypothesis within each
+
+ align:start position:0%
+our induction hypothesis within each
+ 
+
+ align:start position:0%
+our induction hypothesis within each
+subn Network we can achieve a we can
+
+ align:start position:0%
+subn Network we can achieve a we can
+ 
+
+ align:start position:0%
+subn Network we can achieve a we can
+solve any routing problem with
+
+ align:start position:0%
+solve any routing problem with
+ 
+
+ align:start position:0%
+solve any routing problem with
+congestion one and for this sub Network
+
+ align:start position:0%
+congestion one and for this sub Network
+ 
+
+ align:start position:0%
+congestion one and for this sub Network
+the same that's our induction
+
+ align:start position:0%
+the same that's our induction
+ 
+
+ align:start position:0%
+the same that's our induction
+hypothesis so how do we go ahead we need
+
+ align:start position:0%
+hypothesis so how do we go ahead we need
+ 
+
+ align:start position:0%
+hypothesis so how do we go ahead we need
+to uh somehow map these inputs according
+
+ align:start position:0%
+to uh somehow map these inputs according
+ 
+
+ align:start position:0%
+to uh somehow map these inputs according
+to the permutation of our choice so that
+
+ align:start position:0%
+to the permutation of our choice so that
+ 
+
+ align:start position:0%
+to the permutation of our choice so that
+could be for example input zero goes to
+
+ align:start position:0%
+could be for example input zero goes to
+ 
+
+ align:start position:0%
+could be for example input zero goes to
+Output five or input one goes to Output
+
+ align:start position:0%
+Output five or input one goes to Output
+ 
+
+ align:start position:0%
+Output five or input one goes to Output
+two Etc so somehow we need to choose
+
+ align:start position:0%
+two Etc so somehow we need to choose
+ 
+
+ align:start position:0%
+two Etc so somehow we need to choose
+where we are going to map this
+
+ align:start position:0%
+where we are going to map this
+ 
+
+ align:start position:0%
+where we are going to map this
+particular input too so the packet that
+
+ align:start position:0%
+particular input too so the packet that
+ 
+
+ align:start position:0%
+particular input too so the packet that
+goes packet zero that comes from this
+
+ align:start position:0%
+goes packet zero that comes from this
+ 
+
+ align:start position:0%
+goes packet zero that comes from this
+input should either go to the red
+
+ align:start position:0%
+input should either go to the red
+ 
+
+ align:start position:0%
+input should either go to the red
+Network or it should go to the blue
+
+ align:start position:0%
+Network or it should go to the blue
+ 
+
+ align:start position:0%
+Network or it should go to the blue
+Network and for each of these inputs we
+
+ align:start position:0%
+Network and for each of these inputs we
+ 
+
+ align:start position:0%
+Network and for each of these inputs we
+can make such a choice but we have to be
+
+ align:start position:0%
+can make such a choice but we have to be
+ 
+
+ align:start position:0%
+can make such a choice but we have to be
+very smart about it because we need to
+
+ align:start position:0%
+very smart about it because we need to
+ 
+
+ align:start position:0%
+very smart about it because we need to
+avoid any
+
+ align:start position:0%
+avoid any
+ 
+
+ align:start position:0%
+avoid any
+congestion so the intuition is is that
+
+ align:start position:0%
+congestion so the intuition is is that
+ 
+
+ align:start position:0%
+congestion so the intuition is is that
+we're going to uh set up a constrained
+
+ align:start position:0%
+we're going to uh set up a constrained
+ 
+
+ align:start position:0%
+we're going to uh set up a constrained
+uh gra uh uh graph a graph that that
+
+ align:start position:0%
+uh gra uh uh graph a graph that that
+ 
+
+ align:start position:0%
+uh gra uh uh graph a graph that that
+that uh represents all the constraints
+
+ align:start position:0%
+that uh represents all the constraints
+ 
+
+ align:start position:0%
+that uh represents all the constraints
+that we need to satisfy in order to
+
+ align:start position:0%
+that we need to satisfy in order to
+ 
+
+ align:start position:0%
+that we need to satisfy in order to
+achieve congestion of
+
+ align:start position:0%
+achieve congestion of
+ 
+
+ align:start position:0%
+achieve congestion of
+one so let's do an example so that we
+
+ align:start position:0%
+one so let's do an example so that we
+ 
+
+ align:start position:0%
+one so let's do an example so that we
+can figure out what's going on actually
+
+ align:start position:0%
+can figure out what's going on actually
+ 
+
+ align:start position:0%
+can figure out what's going on actually
+let me put that over
+
+ align:start position:0%
+let me put that over
+ 
+
+ align:start position:0%
+let me put that over
+here so the so just take an example
+
+ align:start position:0%
+here so the so just take an example
+ 
+
+ align:start position:0%
+here so the so just take an example
+permutation and we'll go through this
+
+ align:start position:0%
+permutation and we'll go through this
+ 
+
+ align:start position:0%
+permutation and we'll go through this
+example and then see how uh the proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works so let's as an example have Pi of
+
+ align:start position:0%
+works so let's as an example have Pi of
+ 
+
+ align:start position:0%
+works so let's as an example have Pi of
+zero maps to
+
+ align:start position:0%
+zero maps to
+ 
+
+ align:start position:0%
+zero maps to
+one Pi of 1 maps to
+
+ align:start position:0%
+one Pi of 1 maps to
+ 
+
+ align:start position:0%
+one Pi of 1 maps to
+five Pi of two goes to
+
+ align:start position:0%
+five Pi of two goes to
+ 
+
+ align:start position:0%
+five Pi of two goes to
+four input three goes to seven um
+
+ align:start position:0%
+four input three goes to seven um
+ 
+
+ align:start position:0%
+four input three goes to seven um
+four maps to
+
+ align:start position:0%
+four maps to
+ 
+
+ align:start position:0%
+four maps to
+three 5 to
+
+ align:start position:0%
+three 5 to
+ 
+
+ align:start position:0%
+three 5 to
+six 6
+
+ align:start position:0%
+six 6
+ 
+
+ align:start position:0%
+six 6
+to0 and 7 to2 so it's just an arbitrary
+
+ align:start position:0%
+to0 and 7 to2 so it's just an arbitrary
+ 
+
+ align:start position:0%
+to0 and 7 to2 so it's just an arbitrary
+permutation and
+
+ align:start position:0%
+permutation and
+ 
+
+ align:start position:0%
+permutation and
+um okay so what do we see we want to
+
+ align:start position:0%
+um okay so what do we see we want to
+ 
+
+ align:start position:0%
+um okay so what do we see we want to
+make sure that for example this switch
+
+ align:start position:0%
+make sure that for example this switch
+ 
+
+ align:start position:0%
+make sure that for example this switch
+is only seeing one packet so it cannot
+
+ align:start position:0%
+is only seeing one packet so it cannot
+ 
+
+ align:start position:0%
+is only seeing one packet so it cannot
+see a
+
+ align:start position:0%
+see a
+ 
+
+ align:start position:0%
+see a
+packet both coming from input zero as
+
+ align:start position:0%
+packet both coming from input zero as
+ 
+
+ align:start position:0%
+packet both coming from input zero as
+well as from input four I cannot see
+
+ align:start position:0%
+well as from input four I cannot see
+ 
+
+ align:start position:0%
+well as from input four I cannot see
+that I do not want that to happen
+
+ align:start position:0%
+that I do not want that to happen
+ 
+
+ align:start position:0%
+that I do not want that to happen
+similarly for this one I do not want to
+
+ align:start position:0%
+similarly for this one I do not want to
+ 
+
+ align:start position:0%
+similarly for this one I do not want to
+see a packet coming from one or one from
+
+ align:start position:0%
+see a packet coming from one or one from
+ 
+
+ align:start position:0%
+see a packet coming from one or one from
+five so let me Define a constrainted
+
+ align:start position:0%
+five so let me Define a constrainted
+ 
+
+ align:start position:0%
+five so let me Define a constrainted
+graph that sort of represents
+
+ align:start position:0%
+graph that sort of represents
+ 
+
+ align:start position:0%
+graph that sort of represents
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so the constraint graph that we are
+
+ align:start position:0%
+so the constraint graph that we are
+ 
+
+ align:start position:0%
+so the constraint graph that we are
+interested
+
+ align:start position:0%
+interested
+ 
+
+ align:start position:0%
+interested
+in is defined as
+
+ align:start position:0%
+in is defined as
+ 
+
+ align:start position:0%
+in is defined as
+follows uh
+
+ align:start position:0%
+follows uh
+ 
+
+ align:start position:0%
+follows uh
+um if two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+packets
+
+ align:start position:0%
+packets
+ 
+
+ align:start position:0%
+packets
+uh if two packets must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pass through different
+
+ align:start position:0%
+pass through different
+ 
+
+ align:start position:0%
+pass through different
+networks uh sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+networks so in our case the red in the
+
+ align:start position:0%
+networks so in our case the red in the
+ 
+
+ align:start position:0%
+networks so in our case the red in the
+blue sub Network
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we'll actually um have an edge
+
+ align:start position:0%
+then we'll actually um have an edge
+ 
+
+ align:start position:0%
+then we'll actually um have an edge
+between those two
+
+ align:start position:0%
+between those two
+ 
+
+ align:start position:0%
+between those two
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+then there is an
+
+ align:start position:0%
+then there is an
+ 
+
+ align:start position:0%
+then there is an
+edge uh between them so for this example
+
+ align:start position:0%
+edge uh between them so for this example
+ 
+
+ align:start position:0%
+edge uh between them so for this example
+we're going to set up this constraint
+
+ align:start position:0%
+we're going to set up this constraint
+ 
+
+ align:start position:0%
+we're going to set up this constraint
+graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so I was just talking about this
+
+ align:start position:0%
+um so I was just talking about this
+ 
+
+ align:start position:0%
+um so I was just talking about this
+particular switch it cannot see one
+
+ align:start position:0%
+particular switch it cannot see one
+ 
+
+ align:start position:0%
+particular switch it cannot see one
+coming from four and a packet from zero
+
+ align:start position:0%
+coming from four and a packet from zero
+ 
+
+ align:start position:0%
+coming from four and a packet from zero
+so what we do what we have we have an
+
+ align:start position:0%
+so what we do what we have we have an
+ 
+
+ align:start position:0%
+so what we do what we have we have an
+edge between zero and four in the same
+
+ align:start position:0%
+edge between zero and four in the same
+ 
+
+ align:start position:0%
+edge between zero and four in the same
+way we have an edge from uh one to five
+
+ align:start position:0%
+way we have an edge from uh one to five
+ 
+
+ align:start position:0%
+way we have an edge from uh one to five
+why because a packet that that comes
+
+ align:start position:0%
+why because a packet that that comes
+ 
+
+ align:start position:0%
+why because a packet that that comes
+from input one and a packet that comes
+
+ align:start position:0%
+from input one and a packet that comes
+ 
+
+ align:start position:0%
+from input one and a packet that comes
+from from output F from input five
+
+ align:start position:0%
+from from output F from input five
+ 
+
+ align:start position:0%
+from from output F from input five
+cannot both be routed through this
+
+ align:start position:0%
+cannot both be routed through this
+ 
+
+ align:start position:0%
+cannot both be routed through this
+switch because then the switch would see
+
+ align:start position:0%
+switch because then the switch would see
+ 
+
+ align:start position:0%
+switch because then the switch would see
+two packets and then the congestion
+
+ align:start position:0%
+two packets and then the congestion
+ 
+
+ align:start position:0%
+two packets and then the congestion
+would not be one but two right so one
+
+ align:start position:0%
+would not be one but two right so one
+ 
+
+ align:start position:0%
+would not be one but two right so one
+and five also have an edge in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between and in the same way we have two
+
+ align:start position:0%
+between and in the same way we have two
+ 
+
+ align:start position:0%
+between and in the same way we have two
+and six and seven and three so two and
+
+ align:start position:0%
+and six and seven and three so two and
+ 
+
+ align:start position:0%
+and six and seven and three so two and
+six
+
+ align:start position:0%
+six
+ 
+
+ align:start position:0%
+six
+are these is this this constraint like
+
+ align:start position:0%
+are these is this this constraint like
+ 
+
+ align:start position:0%
+are these is this this constraint like
+two and six over here and three and
+
+ align:start position:0%
+two and six over here and three and
+ 
+
+ align:start position:0%
+two and six over here and three and
+seven is the other constraint so if I
+
+ align:start position:0%
+seven is the other constraint so if I
+ 
+
+ align:start position:0%
+seven is the other constraint so if I
+have those constraints in
+
+ align:start position:0%
+have those constraints in
+ 
+
+ align:start position:0%
+have those constraints in
+place well then I know that um the
+
+ align:start position:0%
+place well then I know that um the
+ 
+
+ align:start position:0%
+place well then I know that um the
+routing that goes from Level zero to
+
+ align:start position:0%
+routing that goes from Level zero to
+ 
+
+ align:start position:0%
+routing that goes from Level zero to
+level one will not violate my congestion
+
+ align:start position:0%
+level one will not violate my congestion
+ 
+
+ align:start position:0%
+level one will not violate my congestion
+of one so that's great then I hope to be
+
+ align:start position:0%
+of one so that's great then I hope to be
+ 
+
+ align:start position:0%
+of one so that's great then I hope to be
+able to use the induction hypothesis and
+
+ align:start position:0%
+able to use the induction hypothesis and
+ 
+
+ align:start position:0%
+able to use the induction hypothesis and
+I get a proper routing within the red
+
+ align:start position:0%
+I get a proper routing within the red
+ 
+
+ align:start position:0%
+I get a proper routing within the red
+sub Network and one within the blue
+
+ align:start position:0%
+sub Network and one within the blue
+ 
+
+ align:start position:0%
+sub Network and one within the blue
+Network and then I need to map all these
+
+ align:start position:0%
+Network and then I need to map all these
+ 
+
+ align:start position:0%
+Network and then I need to map all these
+to these outputs so I also have
+
+ align:start position:0%
+to these outputs so I also have
+ 
+
+ align:start position:0%
+to these outputs so I also have
+constraints on these outputs because uh
+
+ align:start position:0%
+constraints on these outputs because uh
+ 
+
+ align:start position:0%
+constraints on these outputs because uh
+well for example take this particular
+
+ align:start position:0%
+well for example take this particular
+ 
+
+ align:start position:0%
+well for example take this particular
+switch it should not see a packet coming
+
+ align:start position:0%
+switch it should not see a packet coming
+ 
+
+ align:start position:0%
+switch it should not see a packet coming
+from this particular one and one from
+
+ align:start position:0%
+from this particular one and one from
+ 
+
+ align:start position:0%
+from this particular one and one from
+this one so how do I code that
+
+ align:start position:0%
+this one so how do I code that
+ 
+
+ align:start position:0%
+this one so how do I code that
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um okay so let me first write out what
+
+ align:start position:0%
+um okay so let me first write out what
+ 
+
+ align:start position:0%
+um okay so let me first write out what
+we did here and then we'll do the same
+
+ align:start position:0%
+we did here and then we'll do the same
+ 
+
+ align:start position:0%
+we did here and then we'll do the same
+for the last level over there
+
+ align:start position:0%
+for the last level over there
+ 
+
+ align:start position:0%
+for the last level over there
+so um oh no that's not really
+
+ align:start position:0%
+so um oh no that's not really
+ 
+
+ align:start position:0%
+so um oh no that's not really
+necessary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay yeah so so at the output side
+
+ align:start position:0%
+um okay yeah so so at the output side
+ 
+
+ align:start position:0%
+um okay yeah so so at the output side
+over here we have similar constraints as
+
+ align:start position:0%
+over here we have similar constraints as
+ 
+
+ align:start position:0%
+over here we have similar constraints as
+we did over here and in this particular
+
+ align:start position:0%
+we did over here and in this particular
+ 
+
+ align:start position:0%
+we did over here and in this particular
+example just as an
+
+ align:start position:0%
+example just as an
+ 
+
+ align:start position:0%
+example just as an
+example um suppose we look at the packet
+
+ align:start position:0%
+example um suppose we look at the packet
+ 
+
+ align:start position:0%
+example um suppose we look at the packet
+that is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+destined for output
+
+ align:start position:0%
+destined for output
+ 
+
+ align:start position:0%
+destined for output
+zero well what is this packet well I
+
+ align:start position:0%
+zero well what is this packet well I
+ 
+
+ align:start position:0%
+zero well what is this packet well I
+know that Pi of 6 is equal to zero
+
+ align:start position:0%
+know that Pi of 6 is equal to zero
+ 
+
+ align:start position:0%
+know that Pi of 6 is equal to zero
+according to my example so packet six is
+
+ align:start position:0%
+according to my example so packet six is
+ 
+
+ align:start position:0%
+according to my example so packet six is
+destined for this particular output zero
+
+ align:start position:0%
+destined for this particular output zero
+ 
+
+ align:start position:0%
+destined for this particular output zero
+over here and comes goes through this
+
+ align:start position:0%
+over here and comes goes through this
+ 
+
+ align:start position:0%
+over here and comes goes through this
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+switch so this packet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+packet for output
+
+ align:start position:0%
+packet for output
+ 
+
+ align:start position:0%
+packet for output
+four which is if you look at the mapping
+
+ align:start position:0%
+four which is if you look at the mapping
+ 
+
+ align:start position:0%
+four which is if you look at the mapping
+Pi of two is equal to four so that's
+
+ align:start position:0%
+Pi of two is equal to four so that's
+ 
+
+ align:start position:0%
+Pi of two is equal to four so that's
+packet number
+
+ align:start position:0%
+packet number
+ 
+
+ align:start position:0%
+packet number
+two well both of these packets cannot
+
+ align:start position:0%
+two well both of these packets cannot
+ 
+
+ align:start position:0%
+two well both of these packets cannot
+pass through the same sub
+
+ align:start position:0%
+pass through the same sub
+ 
+
+ align:start position:0%
+pass through the same sub
+Network cannot pass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+same sub Network so why is this so let's
+
+ align:start position:0%
+same sub Network so why is this so let's
+ 
+
+ align:start position:0%
+same sub Network so why is this so let's
+look at this particular example so
+
+ align:start position:0%
+look at this particular example so
+ 
+
+ align:start position:0%
+look at this particular example so
+output zero um well comes from uh packet
+
+ align:start position:0%
+output zero um well comes from uh packet
+ 
+
+ align:start position:0%
+output zero um well comes from uh packet
+six somewhere over there now suppose
+
+ align:start position:0%
+six somewhere over there now suppose
+ 
+
+ align:start position:0%
+six somewhere over there now suppose
+packet six was routed through the red
+
+ align:start position:0%
+packet six was routed through the red
+ 
+
+ align:start position:0%
+packet six was routed through the red
+Network
+
+ align:start position:0%
+Network
+ 
+
+ align:start position:0%
+Network
+and at the same moment also output four
+
+ align:start position:0%
+and at the same moment also output four
+ 
+
+ align:start position:0%
+and at the same moment also output four
+the packet that is destined for output
+
+ align:start position:0%
+the packet that is destined for output
+ 
+
+ align:start position:0%
+the packet that is destined for output
+four which is Packet number two suppose
+
+ align:start position:0%
+four which is Packet number two suppose
+ 
+
+ align:start position:0%
+four which is Packet number two suppose
+packet two was also going through the
+
+ align:start position:0%
+packet two was also going through the
+ 
+
+ align:start position:0%
+packet two was also going through the
+red
+
+ align:start position:0%
+red
+ 
+
+ align:start position:0%
+red
+Network
+
+ align:start position:0%
+Network
+ 
+
+ align:start position:0%
+Network
+well then I notice that both of these
+
+ align:start position:0%
+well then I notice that both of these
+ 
+
+ align:start position:0%
+well then I notice that both of these
+packets must arrive at this particular
+
+ align:start position:0%
+packets must arrive at this particular
+ 
+
+ align:start position:0%
+packets must arrive at this particular
+switch in order for one to be routed to
+
+ align:start position:0%
+switch in order for one to be routed to
+ 
+
+ align:start position:0%
+switch in order for one to be routed to
+Output zero and the other one to be
+
+ align:start position:0%
+Output zero and the other one to be
+ 
+
+ align:start position:0%
+Output zero and the other one to be
+routed to Output
+
+ align:start position:0%
+routed to Output
+ 
+
+ align:start position:0%
+routed to Output
+four so in order to avoid congestion in
+
+ align:start position:0%
+four so in order to avoid congestion in
+ 
+
+ align:start position:0%
+four so in order to avoid congestion in
+this particular switch over here we need
+
+ align:start position:0%
+this particular switch over here we need
+ 
+
+ align:start position:0%
+this particular switch over here we need
+to have a constraint the constraint says
+
+ align:start position:0%
+to have a constraint the constraint says
+ 
+
+ align:start position:0%
+to have a constraint the constraint says
+that the packet for two uh for packets
+
+ align:start position:0%
+that the packet for two uh for packets
+ 
+
+ align:start position:0%
+that the packet for two uh for packets
+two and six uh that those two cannot go
+
+ align:start position:0%
+two and six uh that those two cannot go
+ 
+
+ align:start position:0%
+two and six uh that those two cannot go
+through the same sub Network so we
+
+ align:start position:0%
+through the same sub Network so we
+ 
+
+ align:start position:0%
+through the same sub Network so we
+essentially have another Edge over here
+
+ align:start position:0%
+essentially have another Edge over here
+ 
+
+ align:start position:0%
+essentially have another Edge over here
+we already had the constr but uh but
+
+ align:start position:0%
+we already had the constr but uh but
+ 
+
+ align:start position:0%
+we already had the constr but uh but
+it's it's it's just the same Edge so
+
+ align:start position:0%
+it's it's it's just the same Edge so
+ 
+
+ align:start position:0%
+it's it's it's just the same Edge so
+let's look at the other
+
+ align:start position:0%
+let's look at the other
+ 
+
+ align:start position:0%
+let's look at the other
+um constraints that we have well for
+
+ align:start position:0%
+um constraints that we have well for
+ 
+
+ align:start position:0%
+um constraints that we have well for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+um uh well let's uh look at a different
+
+ align:start position:0%
+um uh well let's uh look at a different
+ 
+
+ align:start position:0%
+um uh well let's uh look at a different
+example so for example um if I look at
+
+ align:start position:0%
+example so for example um if I look at
+ 
+
+ align:start position:0%
+example so for example um if I look at
+uh this switch well it can if if if if a
+
+ align:start position:0%
+uh this switch well it can if if if if a
+ 
+
+ align:start position:0%
+uh this switch well it can if if if if a
+packet goes through here that needs to
+
+ align:start position:0%
+packet goes through here that needs to
+ 
+
+ align:start position:0%
+packet goes through here that needs to
+end up at one and a packet that goes to
+
+ align:start position:0%
+end up at one and a packet that goes to
+ 
+
+ align:start position:0%
+end up at one and a packet that goes to
+five if those two packets are routed
+
+ align:start position:0%
+five if those two packets are routed
+ 
+
+ align:start position:0%
+five if those two packets are routed
+through the same red sub Network they
+
+ align:start position:0%
+through the same red sub Network they
+ 
+
+ align:start position:0%
+through the same red sub Network they
+have to end up here in order to go to
+
+ align:start position:0%
+have to end up here in order to go to
+ 
+
+ align:start position:0%
+have to end up here in order to go to
+both here and to there so have
+
+ align:start position:0%
+both here and to there so have
+ 
+
+ align:start position:0%
+both here and to there so have
+congestion of two so what are those
+
+ align:start position:0%
+congestion of two so what are those
+ 
+
+ align:start position:0%
+congestion of two so what are those
+packets well what does Pi map to two one
+
+ align:start position:0%
+packets well what does Pi map to two one
+ 
+
+ align:start position:0%
+packets well what does Pi map to two one
+and five let's so let's look over here
+
+ align:start position:0%
+and five let's so let's look over here
+ 
+
+ align:start position:0%
+and five let's so let's look over here
+we see that Pi uh uh zero is equal to 1
+
+ align:start position:0%
+we see that Pi uh uh zero is equal to 1
+ 
+
+ align:start position:0%
+we see that Pi uh uh zero is equal to 1
+and Pi uh 1 is equal to 5 so packet zero
+
+ align:start position:0%
+and Pi uh 1 is equal to 5 so packet zero
+ 
+
+ align:start position:0%
+and Pi uh 1 is equal to 5 so packet zero
+and one are actually mapped to Output uh
+
+ align:start position:0%
+and one are actually mapped to Output uh
+ 
+
+ align:start position:0%
+and one are actually mapped to Output uh
+one and five and they should not go both
+
+ align:start position:0%
+one and five and they should not go both
+ 
+
+ align:start position:0%
+one and five and they should not go both
+through the same sub
+
+ align:start position:0%
+through the same sub
+ 
+
+ align:start position:0%
+through the same sub
+Network okay so we have another Edge
+
+ align:start position:0%
+Network okay so we have another Edge
+ 
+
+ align:start position:0%
+Network okay so we have another Edge
+over here and now we can continue this
+
+ align:start position:0%
+over here and now we can continue this
+ 
+
+ align:start position:0%
+over here and now we can continue this
+and we have five and seven so just have
+
+ align:start position:0%
+and we have five and seven so just have
+ 
+
+ align:start position:0%
+and we have five and seven so just have
+a look over there say five and seven
+
+ align:start position:0%
+a look over there say five and seven
+ 
+
+ align:start position:0%
+a look over there say five and seven
+they map to the outputs two and six
+
+ align:start position:0%
+they map to the outputs two and six
+ 
+
+ align:start position:0%
+they map to the outputs two and six
+again we have two and six if they are
+
+ align:start position:0%
+again we have two and six if they are
+ 
+
+ align:start position:0%
+again we have two and six if they are
+both mapped to the same network this one
+
+ align:start position:0%
+both mapped to the same network this one
+ 
+
+ align:start position:0%
+both mapped to the same network this one
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+example uh then I will have a
+
+ align:start position:0%
+example uh then I will have a
+ 
+
+ align:start position:0%
+example uh then I will have a
+problem um Okay so
+
+ align:start position:0%
+problem um Okay so
+ 
+
+ align:start position:0%
+problem um Okay so
+the other Edge is over
+
+ align:start position:0%
+the other Edge is over
+ 
+
+ align:start position:0%
+the other Edge is over
+here okay so what did we do here we
+
+ align:start position:0%
+here okay so what did we do here we
+ 
+
+ align:start position:0%
+here okay so what did we do here we
+started to write out the constraints on
+
+ align:start position:0%
+started to write out the constraints on
+ 
+
+ align:start position:0%
+started to write out the constraints on
+this side and we wrote out the
+
+ align:start position:0%
+this side and we wrote out the
+ 
+
+ align:start position:0%
+this side and we wrote out the
+constraints on this side um uh so I only
+
+ align:start position:0%
+constraints on this side um uh so I only
+ 
+
+ align:start position:0%
+constraints on this side um uh so I only
+looked at the red sub Network that's
+
+ align:start position:0%
+looked at the red sub Network that's
+ 
+
+ align:start position:0%
+looked at the red sub Network that's
+what I realized now I could also have
+
+ align:start position:0%
+what I realized now I could also have
+ 
+
+ align:start position:0%
+what I realized now I could also have
+looked at the blue Network so let's do
+
+ align:start position:0%
+looked at the blue Network so let's do
+ 
+
+ align:start position:0%
+looked at the blue Network so let's do
+that also just to make the picture
+
+ align:start position:0%
+that also just to make the picture
+ 
+
+ align:start position:0%
+that also just to make the picture
+complete so for example let's look at uh
+
+ align:start position:0%
+complete so for example let's look at uh
+ 
+
+ align:start position:0%
+complete so for example let's look at uh
+this particular example the packet six
+
+ align:start position:0%
+this particular example the packet six
+ 
+
+ align:start position:0%
+this particular example the packet six
+and two should not both be routed
+
+ align:start position:0%
+and two should not both be routed
+ 
+
+ align:start position:0%
+and two should not both be routed
+through the blue Network because then
+
+ align:start position:0%
+through the blue Network because then
+ 
+
+ align:start position:0%
+through the blue Network because then
+they would both have to go through this
+
+ align:start position:0%
+they would both have to go through this
+ 
+
+ align:start position:0%
+they would both have to go through this
+switch one going up to Output zero and
+
+ align:start position:0%
+switch one going up to Output zero and
+ 
+
+ align:start position:0%
+switch one going up to Output zero and
+one going to the left to the right to
+
+ align:start position:0%
+one going to the left to the right to
+ 
+
+ align:start position:0%
+one going to the left to the right to
+Output
+
+ align:start position:0%
+Output
+ 
+
+ align:start position:0%
+Output
+four so to in order to avoid congestion
+
+ align:start position:0%
+four so to in order to avoid congestion
+ 
+
+ align:start position:0%
+four so to in order to avoid congestion
+at all at all costs we have this
+
+ align:start position:0%
+at all at all costs we have this
+ 
+
+ align:start position:0%
+at all at all costs we have this
+constraint graph so now we come to the
+
+ align:start position:0%
+constraint graph so now we come to the
+ 
+
+ align:start position:0%
+constraint graph so now we come to the
+key inside and the key inside is to use
+
+ align:start position:0%
+key inside and the key inside is to use
+ 
+
+ align:start position:0%
+key inside and the key inside is to use
+a two coloring of this of this graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the key
+
+ align:start position:0%
+so the key
+ 
+
+ align:start position:0%
+so the key
+inside is a two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coloring of the constrainted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph which will lead to a uh best
+
+ align:start position:0%
+graph which will lead to a uh best
+ 
+
+ align:start position:0%
+graph which will lead to a uh best
+solution for the routing
+
+ align:start position:0%
+solution for the routing
+ 
+
+ align:start position:0%
+solution for the routing
+problem okay so let's uh do this so we
+
+ align:start position:0%
+problem okay so let's uh do this so we
+ 
+
+ align:start position:0%
+problem okay so let's uh do this so we
+will color this one blue as you can see
+
+ align:start position:0%
+will color this one blue as you can see
+ 
+
+ align:start position:0%
+will color this one blue as you can see
+this is an even
+
+ align:start position:0%
+this is an even
+ 
+
+ align:start position:0%
+this is an even
+cycle uh blue
+
+ align:start position:0%
+cycle uh blue
+ 
+
+ align:start position:0%
+cycle uh blue
+red blue
+
+ align:start position:0%
+red blue
+ 
+
+ align:start position:0%
+red blue
+red um blue and red we'll make this one
+
+ align:start position:0%
+red um blue and red we'll make this one
+ 
+
+ align:start position:0%
+red um blue and red we'll make this one
+blue and this one
+
+ align:start position:0%
+blue and this one
+ 
+
+ align:start position:0%
+blue and this one
+red well it turns out that we can now
+
+ align:start position:0%
+red well it turns out that we can now
+ 
+
+ align:start position:0%
+red well it turns out that we can now
+start our routing process um so for
+
+ align:start position:0%
+start our routing process um so for
+ 
+
+ align:start position:0%
+start our routing process um so for
+example um actually I will draw a new
+
+ align:start position:0%
+example um actually I will draw a new
+ 
+
+ align:start position:0%
+example um actually I will draw a new
+graph to make that really clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so I have my blue and my red chalk
+
+ align:start position:0%
+um so I have my blue and my red chalk
+ 
+
+ align:start position:0%
+um so I have my blue and my red chalk
+over here to demonstrate what I mean
+
+ align:start position:0%
+over here to demonstrate what I mean
+ 
+
+ align:start position:0%
+over here to demonstrate what I mean
+um so what I do I do I have zero 1 2 3 4
+
+ align:start position:0%
+um so what I do I do I have zero 1 2 3 4
+ 
+
+ align:start position:0%
+um so what I do I do I have zero 1 2 3 4
+five six and
+
+ align:start position:0%
+five six and
+ 
+
+ align:start position:0%
+five six and
+seven I have the switches that
+
+ align:start position:0%
+seven I have the switches that
+ 
+
+ align:start position:0%
+seven I have the switches that
+correspond to those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um well if it's colored uh uh red uh so
+
+ align:start position:0%
+um well if it's colored uh uh red uh so
+ 
+
+ align:start position:0%
+um well if it's colored uh uh red uh so
+zero over here is colored red I will
+
+ align:start position:0%
+zero over here is colored red I will
+ 
+
+ align:start position:0%
+zero over here is colored red I will
+direct it to the red sub Network so
+
+ align:start position:0%
+direct it to the red sub Network so
+ 
+
+ align:start position:0%
+direct it to the red sub Network so
+where is this red sub
+
+ align:start position:0%
+where is this red sub
+ 
+
+ align:start position:0%
+where is this red sub
+Network it's really
+
+ align:start position:0%
+Network it's really
+ 
+
+ align:start position:0%
+Network it's really
+contained over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and the blue
+
+ align:start position:0%
+here and the blue
+ 
+
+ align:start position:0%
+here and the blue
+one so this is the red
+
+ align:start position:0%
+one so this is the red
+ 
+
+ align:start position:0%
+one so this is the red
+one and the blue one is right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and over here we have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outputs ranging from 0 one two all the
+
+ align:start position:0%
+outputs ranging from 0 one two all the
+ 
+
+ align:start position:0%
+outputs ranging from 0 one two all the
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+27 okay so input zero is colored red we
+
+ align:start position:0%
+27 okay so input zero is colored red we
+ 
+
+ align:start position:0%
+27 okay so input zero is colored red we
+go straight ahead we want to go to the
+
+ align:start position:0%
+go straight ahead we want to go to the
+ 
+
+ align:start position:0%
+go straight ahead we want to go to the
+red Network input one is colored blue it
+
+ align:start position:0%
+red Network input one is colored blue it
+ 
+
+ align:start position:0%
+red Network input one is colored blue it
+goes therefore
+
+ align:start position:0%
+goes therefore
+ 
+
+ align:start position:0%
+goes therefore
+to the blue Network so this is the only
+
+ align:start position:0%
+to the blue Network so this is the only
+ 
+
+ align:start position:0%
+to the blue Network so this is the only
+way how to do it input two is calleded
+
+ align:start position:0%
+way how to do it input two is calleded
+ 
+
+ align:start position:0%
+way how to do it input two is calleded
+red go straight ahead input three is
+
+ align:start position:0%
+red go straight ahead input three is
+ 
+
+ align:start position:0%
+red go straight ahead input three is
+also colored red go straight ahead input
+
+ align:start position:0%
+also colored red go straight ahead input
+ 
+
+ align:start position:0%
+also colored red go straight ahead input
+five oh input
+
+ align:start position:0%
+five oh input
+ 
+
+ align:start position:0%
+five oh input
+four is color blue goes to the blue
+
+ align:start position:0%
+four is color blue goes to the blue
+ 
+
+ align:start position:0%
+four is color blue goes to the blue
+Network input five goes up to the red
+
+ align:start position:0%
+Network input five goes up to the red
+ 
+
+ align:start position:0%
+Network input five goes up to the red
+Network and input six goes straight
+
+ align:start position:0%
+Network and input six goes straight
+ 
+
+ align:start position:0%
+Network and input six goes straight
+ahead to the blue network is called it
+
+ align:start position:0%
+ahead to the blue network is called it
+ 
+
+ align:start position:0%
+ahead to the blue network is called it
+blue input seven is also color
+
+ align:start position:0%
+blue input seven is also color
+ 
+
+ align:start position:0%
+blue input seven is also color
+blue okay let's look at the outputs so
+
+ align:start position:0%
+blue okay let's look at the outputs so
+ 
+
+ align:start position:0%
+blue okay let's look at the outputs so
+for example um well let's have a look at
+
+ align:start position:0%
+for example um well let's have a look at
+ 
+
+ align:start position:0%
+for example um well let's have a look at
+uh output
+
+ align:start position:0%
+uh output
+ 
+
+ align:start position:0%
+uh output
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+um so output
+
+ align:start position:0%
+um so output
+ 
+
+ align:start position:0%
+um so output
+zero um which packet is mapped to Output
+
+ align:start position:0%
+zero um which packet is mapped to Output
+ 
+
+ align:start position:0%
+zero um which packet is mapped to Output
+zero it's a packet number uh
+
+ align:start position:0%
+zero it's a packet number uh
+ 
+
+ align:start position:0%
+zero it's a packet number uh
+six so six was mapped Into the Blue
+
+ align:start position:0%
+six so six was mapped Into the Blue
+ 
+
+ align:start position:0%
+six so six was mapped Into the Blue
+Network and then it needs to be mapped
+
+ align:start position:0%
+Network and then it needs to be mapped
+ 
+
+ align:start position:0%
+Network and then it needs to be mapped
+to uh output zero so it's only one Edge
+
+ align:start position:0%
+to uh output zero so it's only one Edge
+ 
+
+ align:start position:0%
+to uh output zero so it's only one Edge
+that goes from the blue Network to
+
+ align:start position:0%
+that goes from the blue Network to
+ 
+
+ align:start position:0%
+that goes from the blue Network to
+Output zero which is uh this particular
+
+ align:start position:0%
+Output zero which is uh this particular
+ 
+
+ align:start position:0%
+Output zero which is uh this particular
+one and then somehow this one needs to
+
+ align:start position:0%
+one and then somehow this one needs to
+ 
+
+ align:start position:0%
+one and then somehow this one needs to
+be mapped to this one over here now we
+
+ align:start position:0%
+be mapped to this one over here now we
+ 
+
+ align:start position:0%
+be mapped to this one over here now we
+can continue like this um output one
+
+ align:start position:0%
+can continue like this um output one
+ 
+
+ align:start position:0%
+can continue like this um output one
+should receive a packet from let's look
+
+ align:start position:0%
+should receive a packet from let's look
+ 
+
+ align:start position:0%
+should receive a packet from let's look
+at the permutation from five so uh no
+
+ align:start position:0%
+at the permutation from five so uh no
+ 
+
+ align:start position:0%
+at the permutation from five so uh no
+sorry output one uh Pi of0 is equal to
+
+ align:start position:0%
+sorry output one uh Pi of0 is equal to
+ 
+
+ align:start position:0%
+sorry output one uh Pi of0 is equal to
+one one so packet zero needs to go to
+
+ align:start position:0%
+one one so packet zero needs to go to
+ 
+
+ align:start position:0%
+one one so packet zero needs to go to
+this particular output now P packet zero
+
+ align:start position:0%
+this particular output now P packet zero
+ 
+
+ align:start position:0%
+this particular output now P packet zero
+is in the red Network so it's only one
+
+ align:start position:0%
+is in the red Network so it's only one
+ 
+
+ align:start position:0%
+is in the red Network so it's only one
+Edge that goes from the red Network to
+
+ align:start position:0%
+Edge that goes from the red Network to
+ 
+
+ align:start position:0%
+Edge that goes from the red Network to
+this output so we need to have
+
+ align:start position:0%
+this output so we need to have
+ 
+
+ align:start position:0%
+this output so we need to have
+connection over here now we can continue
+
+ align:start position:0%
+connection over here now we can continue
+ 
+
+ align:start position:0%
+connection over here now we can continue
+this and Note and and demonstrate and
+
+ align:start position:0%
+this and Note and and demonstrate and
+ 
+
+ align:start position:0%
+this and Note and and demonstrate and
+you can test it for yourself too that
+
+ align:start position:0%
+you can test it for yourself too that
+ 
+
+ align:start position:0%
+you can test it for yourself too that
+output four needs to receive a packet
+
+ align:start position:0%
+output four needs to receive a packet
+ 
+
+ align:start position:0%
+output four needs to receive a packet
+from the red Network actually it should
+
+ align:start position:0%
+from the red Network actually it should
+ 
+
+ align:start position:0%
+from the red Network actually it should
+be this particular one which happens to
+
+ align:start position:0%
+be this particular one which happens to
+ 
+
+ align:start position:0%
+be this particular one which happens to
+be packet number
+
+ align:start position:0%
+be packet number
+ 
+
+ align:start position:0%
+be packet number
+two and then we have this one uh
+
+ align:start position:0%
+two and then we have this one uh
+ 
+
+ align:start position:0%
+two and then we have this one uh
+right so let me just finish it we have
+
+ align:start position:0%
+right so let me just finish it we have
+ 
+
+ align:start position:0%
+right so let me just finish it we have
+this and we have uh these
+
+ align:start position:0%
+this and we have uh these
+ 
+
+ align:start position:0%
+this and we have uh these
+two and we
+
+ align:start position:0%
+two and we
+ 
+
+ align:start position:0%
+two and we
+have this
+
+ align:start position:0%
+have this
+ 
+
+ align:start position:0%
+have this
+one we have this one and we have this
+
+ align:start position:0%
+one we have this one and we have this
+ 
+
+ align:start position:0%
+one we have this one and we have this
+one this one goes Straight
+
+ align:start position:0%
+one this one goes Straight
+ 
+
+ align:start position:0%
+one this one goes Straight
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Ahead uh this one goes all the way up
+
+ align:start position:0%
+Ahead uh this one goes all the way up
+ 
+
+ align:start position:0%
+Ahead uh this one goes all the way up
+and this one goes all the way up so what
+
+ align:start position:0%
+and this one goes all the way up so what
+ 
+
+ align:start position:0%
+and this one goes all the way up so what
+do we see we see that packets over
+
+ align:start position:0%
+do we see we see that packets over
+ 
+
+ align:start position:0%
+do we see we see that packets over
+here that these switch switches only see
+
+ align:start position:0%
+here that these switch switches only see
+ 
+
+ align:start position:0%
+here that these switch switches only see
+a packet once and these ones as well
+
+ align:start position:0%
+a packet once and these ones as well
+ 
+
+ align:start position:0%
+a packet once and these ones as well
+this one also and these ones also
+
+ align:start position:0%
+this one also and these ones also
+ 
+
+ align:start position:0%
+this one also and these ones also
+so um we have directed the packets
+
+ align:start position:0%
+so um we have directed the packets
+ 
+
+ align:start position:0%
+so um we have directed the packets
+routed the packets to the red and the
+
+ align:start position:0%
+routed the packets to the red and the
+ 
+
+ align:start position:0%
+routed the packets to the red and the
+blue sub networks in such a way that the
+
+ align:start position:0%
+blue sub networks in such a way that the
+ 
+
+ align:start position:0%
+blue sub networks in such a way that the
+congestion at the uh at at the last
+
+ align:start position:0%
+congestion at the uh at at the last
+ 
+
+ align:start position:0%
+congestion at the uh at at the last
+level and at the first level is still
+
+ align:start position:0%
+level and at the first level is still
+ 
+
+ align:start position:0%
+level and at the first level is still
+equal to one now we use our induction
+
+ align:start position:0%
+equal to one now we use our induction
+ 
+
+ align:start position:0%
+equal to one now we use our induction
+hypothesis and we conclude that we can
+
+ align:start position:0%
+hypothesis and we conclude that we can
+ 
+
+ align:start position:0%
+hypothesis and we conclude that we can
+map uh the route that we can have a
+
+ align:start position:0%
+map uh the route that we can have a
+ 
+
+ align:start position:0%
+map uh the route that we can have a
+routing from packets from here to here
+
+ align:start position:0%
+routing from packets from here to here
+ 
+
+ align:start position:0%
+routing from packets from here to here
+such that the congestion within the sub
+
+ align:start position:0%
+such that the congestion within the sub
+ 
+
+ align:start position:0%
+such that the congestion within the sub
+networks is only one so within the blue
+
+ align:start position:0%
+networks is only one so within the blue
+ 
+
+ align:start position:0%
+networks is only one so within the blue
+as well as in the
+
+ align:start position:0%
+as well as in the
+ 
+
+ align:start position:0%
+as well as in the
+red so this is the insight into how this
+
+ align:start position:0%
+red so this is the insight into how this
+ 
+
+ align:start position:0%
+red so this is the insight into how this
+works and and I notice I'm running out
+
+ align:start position:0%
+works and and I notice I'm running out
+ 
+
+ align:start position:0%
+works and and I notice I'm running out
+of time so the formal proof we will have
+
+ align:start position:0%
+of time so the formal proof we will have
+ 
+
+ align:start position:0%
+of time so the formal proof we will have
+to postpone till
+
+ align:start position:0%
+to postpone till
+ 
+
+ align:start position:0%
+to postpone till
+recitation but uh that's actually really
+
+ align:start position:0%
+recitation but uh that's actually really
+ 
+
+ align:start position:0%
+recitation but uh that's actually really
+a very simple thing to do that right now
+
+ align:start position:0%
+a very simple thing to do that right now
+ 
+
+ align:start position:0%
+a very simple thing to do that right now
+to just keep this key inside and then uh
+
+ align:start position:0%
+to just keep this key inside and then uh
+ 
+
+ align:start position:0%
+to just keep this key inside and then uh
+you can easily uh prove the
+
+ align:start position:0%
+you can easily uh prove the
+ 
+
+ align:start position:0%
+you can easily uh prove the
+theorem so but this is the real the real
+
+ align:start position:0%
+theorem so but this is the real the real
+ 
+
+ align:start position:0%
+theorem so but this is the real the real
+insight thank you
\ No newline at end of file
diff --git a/blBcCjIY7Sg.txt b/blBcCjIY7Sg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9921eccadb69e3e97d988d54c73272f9d0f9bc5a
--- /dev/null
+++ b/blBcCjIY7Sg.txt
@@ -0,0 +1,487 @@
+Good morning.  Good morning.  Today I'm going to talk about,   
+
+this is lecture 14, and I'm going to talk about protein localization.   
+
+Now, some of you may remember that earlier in the semester I was  
+
+walking around with this sling.  And so to help me from writing on  
+
+the board, even though it is this arm, I have made a PowerPoint  
+
+presentation of most of the things that I would have written  
+
+on the board.  And for your ease and comfort,   
+
+this PowerPoint presentation will be posted online so you won't have to  
+
+write down everything in my slides.  So just sort of sit back.  And I  
+
+will write a few things on the board,  so you can write those down.   
+
+OK.  So now you guys have heard about central dogma from Professor  
+
+Eric Lander and you've heard about gene regulation last Friday.   
+
+Here is something that you're familiar with,   
+
+this image here depicting central dogma.   
+
+DNA replicates to DNA.  This is replication.  Replication.   
+
+DNA is translated, excuse me,  transcribed to RNA.   
+
+Transcription.  And RNA is translated to protein.   
+
+Central dogma.  Where does this occur?  Where does replication  
+
+occur in a cell?  Nucleus.  Good.   
+
+Where does transcription occur in a cell?  Nucleus.   
+
+I heard nucleus.  That is correct.  And where does  
+
+translation occur?  Cytoplasm.  Ah, and yet we know  
+
+that these processes require proteins to do them.   
+
+OK.  You've just described where these processes occur in a  
+
+eukaryotic cell.  Let's say you're a bacterium.   
+
+In bacteria, where does replication,  transcription and translation occur?   
+
+Where?  Cytoplasm.  OK.  So now we've made bacteria look very  
+
+simple.  But they're not that simple.  And so let's take a look here.   
+
+Here's a bacterial cell.  I've drawn what could be E.   
+
+coli.  I has an outer membrane,  an inner membrane, and the space in  
+
+between is the perisplasm.  Now, here is its circular  
+
+chromosome.  I've transcribed some gene to an RNA and a ribosomal pop  
+
+on and make a protein which his in the cytoplasm.   
+
+Yet some proteins are localized to the inner membrane,   
+
+others are localized to the periplasm, and some are localized to  
+
+the outer membrane,  and others are actually exported  
+
+completely outside the cell.  Even more complicated is a  
+
+eukaryotic protein,  because not only does it have a  
+
+plasma membrane where proteins are localized.  It has a bunch  
+
+of organelles.  There's the nucleus and there's  
+
+mitochondria and there's endoplasmic reticulum and Golgi apparatus.   
+
+And it, too, translates RNA by ribosomes in the cytoplasm.   
+
+So how do these proteins get back to the nucleus or go into the  
+
+mitochondria or get into the organelles?  So what we're going to  
+
+do in the next few slides is we're going to follow the process,   
+
+because they're so similar in bacteria and eukaryotic cells,   
+
+of how proteins get to the membrane and how they get outside the cell.   
+
+And then I'll go back and talk about how proteins get into some of the  
+
+organelles.  So let me show you what some of the proteins are.   
+
+So an example of a cytoplasmic protein in bacteria is beta  
+
+galactosidase.  You've heard about it.   
+
+It breaks down lactose.  It's in the cytoplasm.  And example  
+
+of a membrane protein is a lactose receptor.   
+
+The lacY permease that's on the surface of the cell brings lactose  
+
+in.  An example of a fully secreted protein is a toxin.   
+
+For instance, bacillus anthracis makes anthrax toxin.   
+
+It's completely exported from the cell.  In a eukaryotic cell there's  
+
+a bunch of cytoplasmic proteins.  There are all of the glycolytic  
+
+enzymes.  And,  for instance, biosynthetic amino  
+
+acid enzymes like histidine synthesis enzymes, those  
+
+are cytoplasmic.  For a membrane protein there are  
+
+receptors, like the receptor for insulin, a hormone,   
+
+a peptide hormone, or growth factor receptors, every receptor that's  
+
+membrane-bound.  And a fully secreted protein.   
+
+Some cells like pancreatic cells secrete insulin.   
+
+Some cells like some of your immune cells secrete antibodies.   
+
+OK.  So it was not clear how these cytoplasmically made proteins,   
+
+proteins that were made in the cytoplasm got to this location.   
+
+And the person who worked on this was George Palade.   
+
+And this was in the fifties.  And he studied pancreatic cells  
+
+because they're master secretors.  And he was able to perfect his  
+
+microscopic technique.  And you can see here this is a  
+
+pancreatic cell.  This is endoplasmic reticulum  
+
+studded with ribosomes.  These are mitochondria.   
+
+This is the nucleus.  Here is another picture that he took.   
+
+And here is the rough endoplasmic reticulum studded with ribosomes.   
+
+Here's Golgi apparatus.  And then there are like little vesicles.   
+
+So he did this experiment where he decided he would pulse label  
+
+proteins as they were being synthesized in a pancreas,   
+
+directly in a pancreas.  So what he did was he injected  
+
+radioactive amino acids directly into the pancreas of hamsters.   
+
+ I guess I could draw a little  
+
+hamster here.  And he directly injected radioactive isotopes.   
+
+And what he's doing is these radioactive amino acids will be  
+
+incorporated into proteins as they're being translated,   
+
+and he can follow the population of freshly translated proteins through  
+
+the cell.  So he injects hamsters with the radioactive amino acids.   
+
+And then at various time points he adds, he also injects glutaraldehyde.   
+
+So first the label,  then glutaraldehyde.  And what this  
+
+does is it fixes the cells in its tracks.  Whatever the cell is doing  
+
+it just stops.  And he removes the pancreas and he  
+
+looks at the cells.  This is fixes the cells.   
+
+So, Tom, I don't know what's going on here.  Can we not use this,   
+
+Tom?  All right.  It's just doing it on its own.  It has some time thing?   
+
+Oh.  All right.  So what he found was at the early time points,   
+
+now, what I did, I did this, OK?  He didn't see yellow.  What I did  
+
+was I added yellow to his original slide to show you at the earliest  
+
+time point he found the label associated with the endoplasmic  
+
+reticulum.  At the next time point he found the  
+
+label associated with the Golgi apparatus.  And then at even later  
+
+time points he found the label in secretory vesicles.   
+
+So this is my representation of what he found.   
+
+So here's a cell,  nucleus, mitochondria.   
+
+The early time points the label was in the ER followed by the Golgi.   
+
+I didn't do that.  Yeah, take it out.   
+
+Followed by vesicles.  It's not working.  OK.   
+
+Sorry for that.  I'm sorry.  So he won a Nobel Prize for this  
+
+work because it is the pathway that still holds true today.   
+
+Now, he won the Nobel Prize in '74.  And at about that time, maybe '71,   
+
+another scientist names Cesar Milstein was working on immunology.   
+
+And what he did was he fused a cancer cell with a cell that  
+
+constantly secreted antibodies,  so he ended up having an  
+
+immortalized antibody producing cell.  And he was doing some research and  
+
+he did in vitro analysis.  And he found that antibodies that  
+
+were produced in vitro were longer than the ones that were actually  
+
+coming out of the cell.  So he proposed that there was an  
+
+N-terminal end.  He looked and saw that the  
+
+N-terminus was different,  and he proposed that it would  
+
+possibly be cleaved upon export.  OK?  And so this is, he won a Nobel  
+
+Prize, not for this work but for his work in immunology.   
+
+And this was also correct.  And so this is from his lecture,   
+
+Nobel lecture.  It says in vitro synthesis of immunoglobulin light  
+
+chains, that's what he was doing,  to our delight we ran into the  
+
+unexpected observation of the existence of a biosynthetic  
+
+precursor of light chain.  Further experiments led us to  
+
+propose the extra N-terminal sequence was a signal for vectorial  
+
+transport across the membrane during protein synthesis.   
+
+This was the first evidence that indicated the signal for secretion  
+
+was an N-terminal segment rapidly cleaved upon protein synthesis.   
+
+OK.  So now there was a student of Palade.  He was a post-doctoral  
+
+student.  His name was Guther Blobel.   
+
+And he saw this experiment in 1971.  And he thought how do we know it's  
+
+not an artifact of in vitro science?  Well, how do you know that the  
+
+ribosomes are not just hoping on earlier in the message?   
+
+Maybe that's why it's a longer protein.  And he didn't buy it.   
+
+So he wanted to further pursue this.  And he did it in the  
+
+Palade manner.  So what he did was he took a test  
+
+tube and he added message for exported protein,   
+
+ribosomes and charged tRNAs.  And when I say charged tRNAs I mean  
+
+tRNAs that have amino acids attached to them.  And so if you add those  
+
+three things to a test tube you find a protein is made.  So then  
+
+he added microsomes.  What are microsomes?   
+
+OK.  We're going to pause this.    
+
+Now, I told you what Palade found out.  He found out that proteins  
+
+were first seen in the rough ER in the lumen.  This is the lumen right  
+
+here.  This is where he first observed radioactivity.   
+
+Now, if you take endoplasmic reticulum and you share it,   
+
+it forms little tiny vesicles,  little vesicles with ribosomes on  
+
+the outside.  And they're called microsomes for  
+
+small things.  Microsomes.  And they're essentially little  
+
+rough endoplasmic reticulum vesicles.  So when Blobel added to the same  
+
+test tube that had the RNA,  the ribosomes, the tRNA.   
+
+When he added microsomes he found that the protein was still in the  
+
+supernatant.  There was no protein found in the lumen of the microsomes.   
+
+So he figured,  OK, it needs something.   
+
+Let me go extract something from the cytoplasm.   
+
+And he extracted lots of fractions.  And he added these cytoplasmic  
+
+fractions.  And he found that one faction actually was able to cause  
+
+the peptide to enter the microsome.  And if he added this fraction late  
+
+in the reaction,  the protein would never get into the  
+
+lumen of the microsome.  But if he added the fraction late,   
+
+I mean, excuse me, early, if he added the faction early they would  
+
+get in.  So let me just summarize.  So message ribosomes, tRNA, you  
+
+find protein in the supernatant.  Message ribosomes, tRNAs, plus  
+
+microsomes, protein in the supernatant, not in the microsomes.   
+
+You add a fraction that works sometimes, but if it's added late  
+
+the protein is in the supernatant.  But if you add that fraction early  
+
+the protein is in the lumen of the microsomes.  So he interpreted this  
+
+result as that there was an amino acid sequence at the beginning of an  
+
+exported protein.  And that's recognized by a complex  
+
+that was in the fraction.  This complex is required to get the  
+
+protein to the lumen of the ER.  And to get to the lumen of the ER  
+
+the protein has to be just beginning to be translated.   
+
+Now, since not all proteins have the same N-terminus,   
+
+Blobel predicated, like Milstein,  whatever the sequence was it would  
+
+later be cleaved.  And he won a Nobel Prize for this  
+
+in 1999.  And it wasn't just for this, because he went on and he  
+
+actually figured out the entire pathway.   
+
+In the next few slides I'm going to show you what he discerned.   
+
+One thing I want to just point out,  though, the experiment he did was  
+
+heterologous.  So the extract came from wheat germ,   
+
+the microsomes came from dog,  and yet it still worked.  And it was  
+
+right because this pathway is universal.  And let me show you how  
+
+universal.  It's used in bacteria and it's used in eukaryotic cells.   
+
+So here's a bacterium,  it's translating a message.   
+
+Here's the signal starting to be translated, it's an exported protein.   
+
+The same thing,  in the cytoplasm a signal sequence  
+
+is being newly made.  And here's a close look of the  
+
+signal sequence.  It's about 20 amino acids long.   
+
+It has a couple of positive charges at its extreme N-terminus.   
+
+In the middle there's about seven to twelve hydrophobic amino acids  
+
+variable.  And this called a signal sequence.  OK,   
+
+so let's take a look at what happens.  OK.  Now we're in the cytoplasm of  
+
+a eukaryotic cell.  Here is a signal sequence emerging  
+
+from a ribosome here.  What recognizes it is SRP.   
+
+That's what he named his complex for signal recognition particle.   
+
+So SRP binds to the signal sequence.  And, if you recall, it takes it to  
+
+the ER to be translated.  Here's a picture of the ER.   
+
+And there's a docking protein or SRP receptor.  So the SRP binds to  
+
+the docking protein,  it brings with it the signal  
+
+sequence which is attached to the ribosome, which is attached to the  
+
+message.  Adjacent to the docking protein is a translocon which is a  
+
+channel composed of proteins.  The ribosome pops onto the  
+
+translocon.  The SRP floats away.  And notice that the signal sequence  
+
+is in the membrane,  excuse me, starts to enter through  
+
+the membrane and translation resumes.   
+
+The signal sequence is cleaved by a signal peptidase within the ER,   
+
+it cleaves off the signal and translation continues.   
+
+And if it's a fully secreted protein it's fully internalized  
+
+within the lumen of the ER and the ribosome pops up.   
+
+If it's a membrane protein the signal is cleaved again,   
+
+translation resumes, and then it gets imbedded in the membrane.   
+
+And so I'm going to shut this off,  otherwise it's going to keep going  
+
+on its own here.  So if it's a membrane protein what  
+
+does it have?  It has a transmembrane stretch.   
+
+You've seen this maybe before in problem sets.  So it's a  
+
+transmembrane stretch.    
+
+Or transmembrane domain.  It's about 20, 22 amino acids long.   
+
+It can be 30 maybe.  So we'll say 20 to 25 amino acids of  
+
+hydrophobic residues.    
+
+It is a stop transfer sequence.  Stop transfer for going across an  
+
+ER membrane.  It anchors it in the membrane.   
+
+ It forms alpha helix.   
+
+ If this part is the lumen of the ER  
+
+right in here then this is the cytoplasm.   
+
+ OK.  So that's how membranes and  
+
+proteins look of this kind.  Now, as you can see here,   
+
+it's in the membrane.  It's imbedded in the membrane.   
+
+And I've drawn a different membrane protein over here because this  
+
+protein is going to work its way to the far side of the endoplasmic  
+
+reticulum.  OK?  As the fully secreted protein will  
+
+also work its way.  In the endoplasmic reticulum sugars  
+
+get put on these proteins.  So when they get to the far side  
+
+they bleb off into little transport vesicles.   
+
+OK?  So here's the cytoplasmic protein completely within the lumen  
+
+of the vesicle.  Here's the membrane protein  
+
+imbedded in the membrane of the vesicle.  And if you remember Palade  
+
+sequence, the next stop is the Golgi.  So the head over to the Golgi,   
+
+they bind, they fuse, and what was imbedded in the membrane is still  
+
+imbedded in the membrane.  And the fully secreted protein is  
+
+within the lumen of the Golgi.  Here the sugars are modified.  I  
+
+put little bows on them.  And they work there way over to the  
+
+far side of the Golgi where they bleb off again into  
+
+secretory vesicles.
\ No newline at end of file
diff --git a/cEoteBfcBE0.txt b/cEoteBfcBE0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ed62eefd4a617640ba9e2cdcaea63ae550a3a179
--- /dev/null
+++ b/cEoteBfcBE0.txt
@@ -0,0 +1,3763 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+we're now on story board 12 session 13
+
+ align:start position:0%
+we're now on story board 12 session 13
+ 
+
+ align:start position:0%
+we're now on story board 12 session 13
+let's take a look first at panel a I
+
+ align:start position:0%
+let's take a look first at panel a I
+ 
+
+ align:start position:0%
+let's take a look first at panel a I
+mentioned earlier that respiration is
+
+ align:start position:0%
+mentioned earlier that respiration is
+ 
+
+ align:start position:0%
+mentioned earlier that respiration is
+the oxidative metabolism of all
+
+ align:start position:0%
+the oxidative metabolism of all
+ 
+
+ align:start position:0%
+the oxidative metabolism of all
+metabolic fuels carbohydrates as well as
+
+ align:start position:0%
+metabolic fuels carbohydrates as well as
+ 
+
+ align:start position:0%
+metabolic fuels carbohydrates as well as
+lipids if we were starting with a
+
+ align:start position:0%
+lipids if we were starting with a
+ 
+
+ align:start position:0%
+lipids if we were starting with a
+carbohydrate than respiration starts
+
+ align:start position:0%
+carbohydrate than respiration starts
+ 
+
+ align:start position:0%
+carbohydrate than respiration starts
+with the pyruvate dehydrogenase reaction
+
+ align:start position:0%
+with the pyruvate dehydrogenase reaction
+ 
+
+ align:start position:0%
+with the pyruvate dehydrogenase reaction
+and then proceeds into the TCA cycle and
+
+ align:start position:0%
+and then proceeds into the TCA cycle and
+ 
+
+ align:start position:0%
+and then proceeds into the TCA cycle and
+then into electron transport and
+
+ align:start position:0%
+then into electron transport and
+ 
+
+ align:start position:0%
+then into electron transport and
+oxidative phosphorylation
+
+ align:start position:0%
+oxidative phosphorylation
+ 
+
+ align:start position:0%
+oxidative phosphorylation
+if the acetyl co a comes from fatty acid
+
+ align:start position:0%
+if the acetyl co a comes from fatty acid
+ 
+
+ align:start position:0%
+if the acetyl co a comes from fatty acid
+oxidation which we'll cover later that
+
+ align:start position:0%
+oxidation which we'll cover later that
+ 
+
+ align:start position:0%
+oxidation which we'll cover later that
+we do not have to do the pyruvate
+
+ align:start position:0%
+we do not have to do the pyruvate
+ 
+
+ align:start position:0%
+we do not have to do the pyruvate
+dehydrogenase step three molecules of
+
+ align:start position:0%
+dehydrogenase step three molecules of
+ 
+
+ align:start position:0%
+dehydrogenase step three molecules of
+NADH and one molecule of fadh2 are
+
+ align:start position:0%
+NADH and one molecule of fadh2 are
+ 
+
+ align:start position:0%
+NADH and one molecule of fadh2 are
+produced as the carriers of electrons
+
+ align:start position:0%
+produced as the carriers of electrons
+ 
+
+ align:start position:0%
+produced as the carriers of electrons
+from the intermediates in the TCA cycle
+
+ align:start position:0%
+from the intermediates in the TCA cycle
+ 
+
+ align:start position:0%
+from the intermediates in the TCA cycle
+from each input molecule of acetyl
+
+ align:start position:0%
+from each input molecule of acetyl
+ 
+
+ align:start position:0%
+from each input molecule of acetyl
+coenzyme a as I mentioned a number of
+
+ align:start position:0%
+coenzyme a as I mentioned a number of
+ 
+
+ align:start position:0%
+coenzyme a as I mentioned a number of
+times we look at nadh and fadh2 is
+
+ align:start position:0%
+times we look at nadh and fadh2 is
+ 
+
+ align:start position:0%
+times we look at nadh and fadh2 is
+relatively mobile electron carriers
+
+ align:start position:0%
+relatively mobile electron carriers
+ 
+
+ align:start position:0%
+relatively mobile electron carriers
+they're going to be picking up electrons
+
+ align:start position:0%
+they're going to be picking up electrons
+ 
+
+ align:start position:0%
+they're going to be picking up electrons
+from intermediates and biochemical
+
+ align:start position:0%
+from intermediates and biochemical
+ 
+
+ align:start position:0%
+from intermediates and biochemical
+pathways and then they bring those
+
+ align:start position:0%
+pathways and then they bring those
+ 
+
+ align:start position:0%
+pathways and then they bring those
+electrons into the mitochondrial inner
+
+ align:start position:0%
+electrons into the mitochondrial inner
+ 
+
+ align:start position:0%
+electrons into the mitochondrial inner
+membrane where the reducing equivalents
+
+ align:start position:0%
+membrane where the reducing equivalents
+ 
+
+ align:start position:0%
+membrane where the reducing equivalents
+are passed along to the electron
+
+ align:start position:0%
+are passed along to the electron
+ 
+
+ align:start position:0%
+are passed along to the electron
+transport chain ultimately the electrons
+
+ align:start position:0%
+transport chain ultimately the electrons
+ 
+
+ align:start position:0%
+transport chain ultimately the electrons
+will end up being deposited into oxygen
+
+ align:start position:0%
+will end up being deposited into oxygen
+ 
+
+ align:start position:0%
+will end up being deposited into oxygen
+to make water let's turn to panel B
+
+ align:start position:0%
+to make water let's turn to panel B
+ 
+
+ align:start position:0%
+to make water let's turn to panel B
+where I'm going to start laying out the
+
+ align:start position:0%
+where I'm going to start laying out the
+ 
+
+ align:start position:0%
+where I'm going to start laying out the
+big picture in this small cartoon we see
+
+ align:start position:0%
+big picture in this small cartoon we see
+ 
+
+ align:start position:0%
+big picture in this small cartoon we see
+fuel being oxidized to carbon dioxide
+
+ align:start position:0%
+fuel being oxidized to carbon dioxide
+ 
+
+ align:start position:0%
+fuel being oxidized to carbon dioxide
+the electrons are passed to either nad
+
+ align:start position:0%
+the electrons are passed to either nad
+ 
+
+ align:start position:0%
+the electrons are passed to either nad
+plus or fa d to form the reduced
+
+ align:start position:0%
+plus or fa d to form the reduced
+ 
+
+ align:start position:0%
+plus or fa d to form the reduced
+cofactor the reduced cofactors find
+
+ align:start position:0%
+cofactor the reduced cofactors find
+ 
+
+ align:start position:0%
+cofactor the reduced cofactors find
+their way to the mitochondrial inner
+
+ align:start position:0%
+their way to the mitochondrial inner
+ 
+
+ align:start position:0%
+their way to the mitochondrial inner
+membrane and the electrons are reducing
+
+ align:start position:0%
+membrane and the electrons are reducing
+ 
+
+ align:start position:0%
+membrane and the electrons are reducing
+equivalents are passed to oxygen to make
+
+ align:start position:0%
+equivalents are passed to oxygen to make
+ 
+
+ align:start position:0%
+equivalents are passed to oxygen to make
+water this process is highly exergonic
+
+ align:start position:0%
+water this process is highly exergonic
+ 
+
+ align:start position:0%
+water this process is highly exergonic
+and we'll do a model calculation in a
+
+ align:start position:0%
+and we'll do a model calculation in a
+ 
+
+ align:start position:0%
+and we'll do a model calculation in a
+minute to show just how energy-yielding
+
+ align:start position:0%
+minute to show just how energy-yielding
+ 
+
+ align:start position:0%
+minute to show just how energy-yielding
+it is resulting in the liberation of a
+
+ align:start position:0%
+it is resulting in the liberation of a
+ 
+
+ align:start position:0%
+it is resulting in the liberation of a
+lot of free energy that energy is
+
+ align:start position:0%
+lot of free energy that energy is
+ 
+
+ align:start position:0%
+lot of free energy that energy is
+captured by the movement of protons
+
+ align:start position:0%
+captured by the movement of protons
+ 
+
+ align:start position:0%
+captured by the movement of protons
+from one side of the mitochondrial inner
+
+ align:start position:0%
+from one side of the mitochondrial inner
+ 
+
+ align:start position:0%
+from one side of the mitochondrial inner
+membrane to the other side of the
+
+ align:start position:0%
+membrane to the other side of the
+ 
+
+ align:start position:0%
+membrane to the other side of the
+membrane in this process you're taking a
+
+ align:start position:0%
+membrane in this process you're taking a
+ 
+
+ align:start position:0%
+membrane in this process you're taking a
+low concentration of protons and
+
+ align:start position:0%
+low concentration of protons and
+ 
+
+ align:start position:0%
+low concentration of protons and
+creating a relatively high concentration
+
+ align:start position:0%
+creating a relatively high concentration
+ 
+
+ align:start position:0%
+creating a relatively high concentration
+of protons that's an uphill process
+
+ align:start position:0%
+of protons that's an uphill process
+ 
+
+ align:start position:0%
+of protons that's an uphill process
+that's going to require an energy input
+
+ align:start position:0%
+that's going to require an energy input
+ 
+
+ align:start position:0%
+that's going to require an energy input
+and the energy from nutrient oxidation
+
+ align:start position:0%
+and the energy from nutrient oxidation
+ 
+
+ align:start position:0%
+and the energy from nutrient oxidation
+is what powers this generation of an ion
+
+ align:start position:0%
+is what powers this generation of an ion
+ 
+
+ align:start position:0%
+is what powers this generation of an ion
+gradient concentrating the protons in a
+
+ align:start position:0%
+gradient concentrating the protons in a
+ 
+
+ align:start position:0%
+gradient concentrating the protons in a
+small defined space is kind of like
+
+ align:start position:0%
+small defined space is kind of like
+ 
+
+ align:start position:0%
+small defined space is kind of like
+charging a battery it took energy to
+
+ align:start position:0%
+charging a battery it took energy to
+ 
+
+ align:start position:0%
+charging a battery it took energy to
+create that high concentration of
+
+ align:start position:0%
+create that high concentration of
+ 
+
+ align:start position:0%
+create that high concentration of
+protons we'll see that nature invented a
+
+ align:start position:0%
+protons we'll see that nature invented a
+ 
+
+ align:start position:0%
+protons we'll see that nature invented a
+way to channel the protons back through
+
+ align:start position:0%
+way to channel the protons back through
+ 
+
+ align:start position:0%
+way to channel the protons back through
+a device and a way to capture the energy
+
+ align:start position:0%
+a device and a way to capture the energy
+ 
+
+ align:start position:0%
+a device and a way to capture the energy
+released when the gradient is dissipated
+
+ align:start position:0%
+released when the gradient is dissipated
+ 
+
+ align:start position:0%
+released when the gradient is dissipated
+that energy can be captured in various
+
+ align:start position:0%
+that energy can be captured in various
+ 
+
+ align:start position:0%
+that energy can be captured in various
+ways enabling us to be able to do useful
+
+ align:start position:0%
+ways enabling us to be able to do useful
+ 
+
+ align:start position:0%
+ways enabling us to be able to do useful
+things with it for example the energy
+
+ align:start position:0%
+things with it for example the energy
+ 
+
+ align:start position:0%
+things with it for example the energy
+could be used to accomplish the
+
+ align:start position:0%
+could be used to accomplish the
+ 
+
+ align:start position:0%
+could be used to accomplish the
+otherwise energy requiring process of
+
+ align:start position:0%
+otherwise energy requiring process of
+ 
+
+ align:start position:0%
+otherwise energy requiring process of
+putting a phosphate onto ADP to make ATP
+
+ align:start position:0%
+putting a phosphate onto ADP to make ATP
+ 
+
+ align:start position:0%
+putting a phosphate onto ADP to make ATP
+and that way the energy is captured in a
+
+ align:start position:0%
+and that way the energy is captured in a
+ 
+
+ align:start position:0%
+and that way the energy is captured in a
+chemical bond alternatively let's think
+
+ align:start position:0%
+chemical bond alternatively let's think
+ 
+
+ align:start position:0%
+chemical bond alternatively let's think
+of a situation in which you may need to
+
+ align:start position:0%
+of a situation in which you may need to
+ 
+
+ align:start position:0%
+of a situation in which you may need to
+generate heat you could allow the proton
+
+ align:start position:0%
+generate heat you could allow the proton
+ 
+
+ align:start position:0%
+generate heat you could allow the proton
+simply to flow back across the membrane
+
+ align:start position:0%
+simply to flow back across the membrane
+ 
+
+ align:start position:0%
+simply to flow back across the membrane
+through a channel the energy of the
+
+ align:start position:0%
+through a channel the energy of the
+ 
+
+ align:start position:0%
+through a channel the energy of the
+proton gradient would then be released
+
+ align:start position:0%
+proton gradient would then be released
+ 
+
+ align:start position:0%
+proton gradient would then be released
+as heat thirdly we can perhaps allow the
+
+ align:start position:0%
+as heat thirdly we can perhaps allow the
+ 
+
+ align:start position:0%
+as heat thirdly we can perhaps allow the
+protons to flow back through a device
+
+ align:start position:0%
+protons to flow back through a device
+ 
+
+ align:start position:0%
+protons to flow back through a device
+that creates rotary movement and that's
+
+ align:start position:0%
+that creates rotary movement and that's
+ 
+
+ align:start position:0%
+that creates rotary movement and that's
+how for example a flagellar motor can
+
+ align:start position:0%
+how for example a flagellar motor can
+ 
+
+ align:start position:0%
+how for example a flagellar motor can
+spin to move a bacterium from one place
+
+ align:start position:0%
+spin to move a bacterium from one place
+ 
+
+ align:start position:0%
+spin to move a bacterium from one place
+to another let's now turn to panel C
+
+ align:start position:0%
+to another let's now turn to panel C
+ 
+
+ align:start position:0%
+to another let's now turn to panel C
+we've seen earlier that oxidation can
+
+ align:start position:0%
+we've seen earlier that oxidation can
+ 
+
+ align:start position:0%
+we've seen earlier that oxidation can
+result in the production of nadh or
+
+ align:start position:0%
+result in the production of nadh or
+ 
+
+ align:start position:0%
+result in the production of nadh or
+fadh2 to begin let's consider NADH in
+
+ align:start position:0%
+fadh2 to begin let's consider NADH in
+ 
+
+ align:start position:0%
+fadh2 to begin let's consider NADH in
+this panel you can see the NADH oxidized
+
+ align:start position:0%
+this panel you can see the NADH oxidized
+ 
+
+ align:start position:0%
+this panel you can see the NADH oxidized
+where the electrons flow and it doesn't
+
+ align:start position:0%
+where the electrons flow and it doesn't
+ 
+
+ align:start position:0%
+where the electrons flow and it doesn't
+matter what the path of the flow is all
+
+ align:start position:0%
+matter what the path of the flow is all
+ 
+
+ align:start position:0%
+matter what the path of the flow is all
+the way to oxygen thermodynamics gives
+
+ align:start position:0%
+the way to oxygen thermodynamics gives
+ 
+
+ align:start position:0%
+the way to oxygen thermodynamics gives
+us the tools to calculate how much
+
+ align:start position:0%
+us the tools to calculate how much
+ 
+
+ align:start position:0%
+us the tools to calculate how much
+energy you would get in this process
+
+ align:start position:0%
+energy you would get in this process
+ 
+
+ align:start position:0%
+energy you would get in this process
+Joanne taught you a lot about
+
+ align:start position:0%
+Joanne taught you a lot about
+ 
+
+ align:start position:0%
+Joanne taught you a lot about
+thermodynamics and biological systems
+
+ align:start position:0%
+thermodynamics and biological systems
+ 
+
+ align:start position:0%
+thermodynamics and biological systems
+and this is just a repeat of what she
+
+ align:start position:0%
+and this is just a repeat of what she
+ 
+
+ align:start position:0%
+and this is just a repeat of what she
+said but what I'm going to do is put
+
+ align:start position:0%
+said but what I'm going to do is put
+ 
+
+ align:start position:0%
+said but what I'm going to do is put
+what she said into a concrete practical
+
+ align:start position:0%
+what she said into a concrete practical
+ 
+
+ align:start position:0%
+what she said into a concrete practical
+example I've drawn out at the bottom of
+
+ align:start position:0%
+example I've drawn out at the bottom of
+ 
+
+ align:start position:0%
+example I've drawn out at the bottom of
+panels see the overall reaction showing
+
+ align:start position:0%
+panels see the overall reaction showing
+ 
+
+ align:start position:0%
+panels see the overall reaction showing
+electrons going from NADH to oxygen in
+
+ align:start position:0%
+electrons going from NADH to oxygen in
+ 
+
+ align:start position:0%
+electrons going from NADH to oxygen in
+the four
+
+ align:start position:0%
+the four
+ 
+
+ align:start position:0%
+the four
+word direction now of course we could
+
+ align:start position:0%
+word direction now of course we could
+ 
+
+ align:start position:0%
+word direction now of course we could
+also think about the back reaction where
+
+ align:start position:0%
+also think about the back reaction where
+ 
+
+ align:start position:0%
+also think about the back reaction where
+electrons would flow from water in to
+
+ align:start position:0%
+electrons would flow from water in to
+ 
+
+ align:start position:0%
+electrons would flow from water in to
+NAD+ to form NADH at this point this is
+
+ align:start position:0%
+NAD+ to form NADH at this point this is
+ 
+
+ align:start position:0%
+NAD+ to form NADH at this point this is
+just an equation on a piece of paper and
+
+ align:start position:0%
+just an equation on a piece of paper and
+ 
+
+ align:start position:0%
+just an equation on a piece of paper and
+we don't know in which direction the
+
+ align:start position:0%
+we don't know in which direction the
+ 
+
+ align:start position:0%
+we don't know in which direction the
+reaction is overall favorable that is is
+
+ align:start position:0%
+reaction is overall favorable that is is
+ 
+
+ align:start position:0%
+reaction is overall favorable that is is
+it favorable in the forward direction as
+
+ align:start position:0%
+it favorable in the forward direction as
+ 
+
+ align:start position:0%
+it favorable in the forward direction as
+drawn left to right or in the reverse
+
+ align:start position:0%
+drawn left to right or in the reverse
+ 
+
+ align:start position:0%
+drawn left to right or in the reverse
+direction right to left the reaction
+
+ align:start position:0%
+direction right to left the reaction
+ 
+
+ align:start position:0%
+direction right to left the reaction
+from left to right is the direction we
+
+ align:start position:0%
+from left to right is the direction we
+ 
+
+ align:start position:0%
+from left to right is the direction we
+usually think about in the context of
+
+ align:start position:0%
+usually think about in the context of
+ 
+
+ align:start position:0%
+usually think about in the context of
+nutrient oxidation interestingly the
+
+ align:start position:0%
+nutrient oxidation interestingly the
+ 
+
+ align:start position:0%
+nutrient oxidation interestingly the
+reaction from right to left is
+
+ align:start position:0%
+reaction from right to left is
+ 
+
+ align:start position:0%
+reaction from right to left is
+photosynthesis so both directions are
+
+ align:start position:0%
+photosynthesis so both directions are
+ 
+
+ align:start position:0%
+photosynthesis so both directions are
+biologically used but we'll see that one
+
+ align:start position:0%
+biologically used but we'll see that one
+ 
+
+ align:start position:0%
+biologically used but we'll see that one
+of the directions will require
+
+ align:start position:0%
+of the directions will require
+ 
+
+ align:start position:0%
+of the directions will require
+substantial energy input in order to
+
+ align:start position:0%
+substantial energy input in order to
+ 
+
+ align:start position:0%
+substantial energy input in order to
+make it biologically useful probably you
+
+ align:start position:0%
+make it biologically useful probably you
+ 
+
+ align:start position:0%
+make it biologically useful probably you
+can appreciate that photosynthesis is
+
+ align:start position:0%
+can appreciate that photosynthesis is
+ 
+
+ align:start position:0%
+can appreciate that photosynthesis is
+the energy requiring process because we
+
+ align:start position:0%
+the energy requiring process because we
+ 
+
+ align:start position:0%
+the energy requiring process because we
+all know that sunlight is needed to make
+
+ align:start position:0%
+all know that sunlight is needed to make
+ 
+
+ align:start position:0%
+all know that sunlight is needed to make
+the process thermodynamically and
+
+ align:start position:0%
+the process thermodynamically and
+ 
+
+ align:start position:0%
+the process thermodynamically and
+kinetically favorable we don't cover
+
+ align:start position:0%
+kinetically favorable we don't cover
+ 
+
+ align:start position:0%
+kinetically favorable we don't cover
+photosynthesis in 507 so let me say a
+
+ align:start position:0%
+photosynthesis in 507 so let me say a
+ 
+
+ align:start position:0%
+photosynthesis in 507 so let me say a
+few words about it in photosynthesis
+
+ align:start position:0%
+few words about it in photosynthesis
+ 
+
+ align:start position:0%
+few words about it in photosynthesis
+nature takes electrons from water and
+
+ align:start position:0%
+nature takes electrons from water and
+ 
+
+ align:start position:0%
+nature takes electrons from water and
+uses them to reduce nadp+ to nadph note
+
+ align:start position:0%
+uses them to reduce nadp+ to nadph note
+ 
+
+ align:start position:0%
+uses them to reduce nadp+ to nadph note
+that I said in adp plus and not any d
+
+ align:start position:0%
+that I said in adp plus and not any d
+ 
+
+ align:start position:0%
+that I said in adp plus and not any d
+plus but for the purposes here they are
+
+ align:start position:0%
+plus but for the purposes here they are
+ 
+
+ align:start position:0%
+plus but for the purposes here they are
+equivalent in the case of photosynthesis
+
+ align:start position:0%
+equivalent in the case of photosynthesis
+ 
+
+ align:start position:0%
+equivalent in the case of photosynthesis
+we know intuitively that the overall
+
+ align:start position:0%
+we know intuitively that the overall
+ 
+
+ align:start position:0%
+we know intuitively that the overall
+process is power bud light so in going
+
+ align:start position:0%
+process is power bud light so in going
+ 
+
+ align:start position:0%
+process is power bud light so in going
+from right to left the process
+
+ align:start position:0%
+from right to left the process
+ 
+
+ align:start position:0%
+from right to left the process
+intuitively once again should require
+
+ align:start position:0%
+intuitively once again should require
+ 
+
+ align:start position:0%
+intuitively once again should require
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+by contrast nutrient oxidation where we
+
+ align:start position:0%
+by contrast nutrient oxidation where we
+ 
+
+ align:start position:0%
+by contrast nutrient oxidation where we
+go from left to right in this equation
+
+ align:start position:0%
+go from left to right in this equation
+ 
+
+ align:start position:0%
+go from left to right in this equation
+should be a process that generates
+
+ align:start position:0%
+should be a process that generates
+ 
+
+ align:start position:0%
+should be a process that generates
+energy but intuition aside let's do the
+
+ align:start position:0%
+energy but intuition aside let's do the
+ 
+
+ align:start position:0%
+energy but intuition aside let's do the
+calculation so the question is in which
+
+ align:start position:0%
+calculation so the question is in which
+ 
+
+ align:start position:0%
+calculation so the question is in which
+direction is the equation at the bottom
+
+ align:start position:0%
+direction is the equation at the bottom
+ 
+
+ align:start position:0%
+direction is the equation at the bottom
+of paneled seat thermodynamically
+
+ align:start position:0%
+of paneled seat thermodynamically
+ 
+
+ align:start position:0%
+of paneled seat thermodynamically
+favorable left to right or right to left
+
+ align:start position:0%
+favorable left to right or right to left
+ 
+
+ align:start position:0%
+favorable left to right or right to left
+let's take a look now at panel D you'll
+
+ align:start position:0%
+let's take a look now at panel D you'll
+ 
+
+ align:start position:0%
+let's take a look now at panel D you'll
+see here that I have split the master
+
+ align:start position:0%
+see here that I have split the master
+ 
+
+ align:start position:0%
+see here that I have split the master
+equation into two half reactions
+
+ align:start position:0%
+equation into two half reactions
+ 
+
+ align:start position:0%
+equation into two half reactions
+I always write out the half reaction in
+
+ align:start position:0%
+I always write out the half reaction in
+ 
+
+ align:start position:0%
+I always write out the half reaction in
+the direction of reduction for example
+
+ align:start position:0%
+the direction of reduction for example
+ 
+
+ align:start position:0%
+the direction of reduction for example
+look at the second half reaction it
+
+ align:start position:0%
+look at the second half reaction it
+ 
+
+ align:start position:0%
+look at the second half reaction it
+shows that half a mole of oxygen plus
+
+ align:start position:0%
+shows that half a mole of oxygen plus
+ 
+
+ align:start position:0%
+shows that half a mole of oxygen plus
+two protons plus two electrons go to
+
+ align:start position:0%
+two protons plus two electrons go to
+ 
+
+ align:start position:0%
+two protons plus two electrons go to
+water again I've written out these
+
+ align:start position:0%
+water again I've written out these
+ 
+
+ align:start position:0%
+water again I've written out these
+reactions in the direction of reduction
+
+ align:start position:0%
+reactions in the direction of reduction
+ 
+
+ align:start position:0%
+reactions in the direction of reduction
+it's just the way I do it
+
+ align:start position:0%
+it's just the way I do it
+ 
+
+ align:start position:0%
+it's just the way I do it
+next I go to the redox chart that is a
+
+ align:start position:0%
+next I go to the redox chart that is a
+ 
+
+ align:start position:0%
+next I go to the redox chart that is a
+table of redox potentials of
+
+ align:start position:0%
+table of redox potentials of
+ 
+
+ align:start position:0%
+table of redox potentials of
+electrochemical reactions and I figure
+
+ align:start position:0%
+electrochemical reactions and I figure
+ 
+
+ align:start position:0%
+electrochemical reactions and I figure
+out what the standard energies are for
+
+ align:start position:0%
+out what the standard energies are for
+ 
+
+ align:start position:0%
+out what the standard energies are for
+each of these half reactions as you can
+
+ align:start position:0%
+each of these half reactions as you can
+ 
+
+ align:start position:0%
+each of these half reactions as you can
+see it's 0.32 volts and plus point eight
+
+ align:start position:0%
+see it's 0.32 volts and plus point eight
+ 
+
+ align:start position:0%
+see it's 0.32 volts and plus point eight
+two volts respectively for the two half
+
+ align:start position:0%
+two volts respectively for the two half
+ 
+
+ align:start position:0%
+two volts respectively for the two half
+reactions next I use variant of the
+
+ align:start position:0%
+reactions next I use variant of the
+ 
+
+ align:start position:0%
+reactions next I use variant of the
+Nernst equation to calculate the free
+
+ align:start position:0%
+Nernst equation to calculate the free
+ 
+
+ align:start position:0%
+Nernst equation to calculate the free
+energy and ultimately the directionality
+
+ align:start position:0%
+energy and ultimately the directionality
+ 
+
+ align:start position:0%
+energy and ultimately the directionality
+of the reaction the equation I use is
+
+ align:start position:0%
+of the reaction the equation I use is
+ 
+
+ align:start position:0%
+of the reaction the equation I use is
+Delta G naught prime equals n times
+
+ align:start position:0%
+Delta G naught prime equals n times
+ 
+
+ align:start position:0%
+Delta G naught prime equals n times
+Faraday's constant times the difference
+
+ align:start position:0%
+Faraday's constant times the difference
+ 
+
+ align:start position:0%
+Faraday's constant times the difference
+in the reduction potentials of the two
+
+ align:start position:0%
+in the reduction potentials of the two
+ 
+
+ align:start position:0%
+in the reduction potentials of the two
+half-reactions
+
+ align:start position:0%
+half-reactions
+ 
+
+ align:start position:0%
+half-reactions
+to find Delta e naught Prime we look at
+
+ align:start position:0%
+to find Delta e naught Prime we look at
+ 
+
+ align:start position:0%
+to find Delta e naught Prime we look at
+the reaction that I've written out the
+
+ align:start position:0%
+the reaction that I've written out the
+ 
+
+ align:start position:0%
+the reaction that I've written out the
+overall reaction and we look to see
+
+ align:start position:0%
+overall reaction and we look to see
+ 
+
+ align:start position:0%
+overall reaction and we look to see
+which is the electron acceptor and which
+
+ align:start position:0%
+which is the electron acceptor and which
+ 
+
+ align:start position:0%
+which is the electron acceptor and which
+is the electron donor the way the
+
+ align:start position:0%
+is the electron donor the way the
+ 
+
+ align:start position:0%
+is the electron donor the way the
+reaction was written then we subtract
+
+ align:start position:0%
+reaction was written then we subtract
+ 
+
+ align:start position:0%
+reaction was written then we subtract
+the reduction potential of the electron
+
+ align:start position:0%
+the reduction potential of the electron
+ 
+
+ align:start position:0%
+the reduction potential of the electron
+receptor from that of the electron donor
+
+ align:start position:0%
+receptor from that of the electron donor
+ 
+
+ align:start position:0%
+receptor from that of the electron donor
+the way the equation is written left to
+
+ align:start position:0%
+the way the equation is written left to
+ 
+
+ align:start position:0%
+the way the equation is written left to
+right oxygen is the electron acceptor
+
+ align:start position:0%
+right oxygen is the electron acceptor
+ 
+
+ align:start position:0%
+right oxygen is the electron acceptor
+its reduction potential is plus 0.8 2
+
+ align:start position:0%
+its reduction potential is plus 0.8 2
+ 
+
+ align:start position:0%
+its reduction potential is plus 0.8 2
+volts so Delta e naught prime is plus
+
+ align:start position:0%
+volts so Delta e naught prime is plus
+ 
+
+ align:start position:0%
+volts so Delta e naught prime is plus
+0.8 to minus a minus 0.32 or a total of
+
+ align:start position:0%
+0.8 to minus a minus 0.32 or a total of
+ 
+
+ align:start position:0%
+0.8 to minus a minus 0.32 or a total of
+plus 1 point 1 4 volts in the Nernst
+
+ align:start position:0%
+plus 1 point 1 4 volts in the Nernst
+ 
+
+ align:start position:0%
+plus 1 point 1 4 volts in the Nernst
+equation the number of electron
+
+ align:start position:0%
+equation the number of electron
+ 
+
+ align:start position:0%
+equation the number of electron
+transferred in this case is 2 in
+
+ align:start position:0%
+transferred in this case is 2 in
+ 
+
+ align:start position:0%
+transferred in this case is 2 in
+Faraday's constant is 96.4 kilojoules
+
+ align:start position:0%
+Faraday's constant is 96.4 kilojoules
+ 
+
+ align:start position:0%
+Faraday's constant is 96.4 kilojoules
+per mole times volts if you do the math
+
+ align:start position:0%
+per mole times volts if you do the math
+ 
+
+ align:start position:0%
+per mole times volts if you do the math
+or as we say at MIT plug and chug what
+
+ align:start position:0%
+or as we say at MIT plug and chug what
+ 
+
+ align:start position:0%
+or as we say at MIT plug and chug what
+you find out is that the free energy
+
+ align:start position:0%
+you find out is that the free energy
+ 
+
+ align:start position:0%
+you find out is that the free energy
+change of the reaction that's written
+
+ align:start position:0%
+change of the reaction that's written
+ 
+
+ align:start position:0%
+change of the reaction that's written
+the NADH oxidation reaction is minus 220
+
+ align:start position:0%
+the NADH oxidation reaction is minus 220
+ 
+
+ align:start position:0%
+the NADH oxidation reaction is minus 220
+kilojoules per mole this number is
+
+ align:start position:0%
+kilojoules per mole this number is
+ 
+
+ align:start position:0%
+kilojoules per mole this number is
+negative and that means the reaction is
+
+ align:start position:0%
+negative and that means the reaction is
+ 
+
+ align:start position:0%
+negative and that means the reaction is
+favorable as drawn that is the reaction
+
+ align:start position:0%
+favorable as drawn that is the reaction
+ 
+
+ align:start position:0%
+favorable as drawn that is the reaction
+goes from left to right the 220
+
+ align:start position:0%
+goes from left to right the 220
+ 
+
+ align:start position:0%
+goes from left to right the 220
+kilojoules is the amount of energy
+
+ align:start position:0%
+kilojoules is the amount of energy
+ 
+
+ align:start position:0%
+kilojoules is the amount of energy
+that's available for the three purposes
+
+ align:start position:0%
+that's available for the three purposes
+ 
+
+ align:start position:0%
+that's available for the three purposes
+of the pathway that is ATP synthesis
+
+ align:start position:0%
+of the pathway that is ATP synthesis
+ 
+
+ align:start position:0%
+of the pathway that is ATP synthesis
+heat generation or movement if we were
+
+ align:start position:0%
+heat generation or movement if we were
+ 
+
+ align:start position:0%
+heat generation or movement if we were
+going to make ATP we would divide 220 by
+
+ align:start position:0%
+going to make ATP we would divide 220 by
+ 
+
+ align:start position:0%
+going to make ATP we would divide 220 by
+32 because we get about 30
+
+ align:start position:0%
+32 because we get about 30
+ 
+
+ align:start position:0%
+32 because we get about 30
+kilojoules of energy by hydrolysis of
+
+ align:start position:0%
+kilojoules of energy by hydrolysis of
+ 
+
+ align:start position:0%
+kilojoules of energy by hydrolysis of
+ATP and we can calculate that we're
+
+ align:start position:0%
+ATP and we can calculate that we're
+ 
+
+ align:start position:0%
+ATP and we can calculate that we're
+going to get something in the order of
+
+ align:start position:0%
+going to get something in the order of
+ 
+
+ align:start position:0%
+going to get something in the order of
+about three atps for every NADH that
+
+ align:start position:0%
+about three atps for every NADH that
+ 
+
+ align:start position:0%
+about three atps for every NADH that
+gives up two electrons to the electron
+
+ align:start position:0%
+gives up two electrons to the electron
+ 
+
+ align:start position:0%
+gives up two electrons to the electron
+transport chain we could easily do the
+
+ align:start position:0%
+transport chain we could easily do the
+ 
+
+ align:start position:0%
+transport chain we could easily do the
+same oxidation reaction and study fadh2
+
+ align:start position:0%
+same oxidation reaction and study fadh2
+ 
+
+ align:start position:0%
+same oxidation reaction and study fadh2
+but in this case we would calculate that
+
+ align:start position:0%
+but in this case we would calculate that
+ 
+
+ align:start position:0%
+but in this case we would calculate that
+we would get actually less energy
+
+ align:start position:0%
+we would get actually less energy
+ 
+
+ align:start position:0%
+we would get actually less energy
+because the oxidation potential of
+
+ align:start position:0%
+because the oxidation potential of
+ 
+
+ align:start position:0%
+because the oxidation potential of
+Flavin's as compared to nad is different
+
+ align:start position:0%
+Flavin's as compared to nad is different
+ 
+
+ align:start position:0%
+Flavin's as compared to nad is different
+in that case that is fadh2 oxidation
+
+ align:start position:0%
+in that case that is fadh2 oxidation
+ 
+
+ align:start position:0%
+in that case that is fadh2 oxidation
+will get only about two atps per fadh2
+
+ align:start position:0%
+will get only about two atps per fadh2
+ 
+
+ align:start position:0%
+will get only about two atps per fadh2
+oxidize so the fadh2 produced in the
+
+ align:start position:0%
+oxidize so the fadh2 produced in the
+ 
+
+ align:start position:0%
+oxidize so the fadh2 produced in the
+succinate dehydrogenase step of the TCA
+
+ align:start position:0%
+succinate dehydrogenase step of the TCA
+ 
+
+ align:start position:0%
+succinate dehydrogenase step of the TCA
+cycle is less energy yielding man
+
+ align:start position:0%
+cycle is less energy yielding man
+ 
+
+ align:start position:0%
+cycle is less energy yielding man
+for example the oxidation of malate to
+
+ align:start position:0%
+for example the oxidation of malate to
+ 
+
+ align:start position:0%
+for example the oxidation of malate to
+oxaloacetate that occurs later in the
+
+ align:start position:0%
+oxaloacetate that occurs later in the
+ 
+
+ align:start position:0%
+oxaloacetate that occurs later in the
+pathway let's turn now to storyboard
+
+ align:start position:0%
+pathway let's turn now to storyboard
+ 
+
+ align:start position:0%
+pathway let's turn now to storyboard
+thirteen we now have an idea of the
+
+ align:start position:0%
+thirteen we now have an idea of the
+ 
+
+ align:start position:0%
+thirteen we now have an idea of the
+rough amount of energy that's going to
+
+ align:start position:0%
+rough amount of energy that's going to
+ 
+
+ align:start position:0%
+rough amount of energy that's going to
+be generated by nutrient oxidation next
+
+ align:start position:0%
+be generated by nutrient oxidation next
+ 
+
+ align:start position:0%
+be generated by nutrient oxidation next
+we're going to look a little bit more in
+
+ align:start position:0%
+we're going to look a little bit more in
+ 
+
+ align:start position:0%
+we're going to look a little bit more in
+detail at the mechanism by which the
+
+ align:start position:0%
+detail at the mechanism by which the
+ 
+
+ align:start position:0%
+detail at the mechanism by which the
+electrons are transported from the
+
+ align:start position:0%
+electrons are transported from the
+ 
+
+ align:start position:0%
+electrons are transported from the
+reduced substances that constitute our
+
+ align:start position:0%
+reduced substances that constitute our
+ 
+
+ align:start position:0%
+reduced substances that constitute our
+electron donors nadh and fadh2 to
+
+ align:start position:0%
+electron donors nadh and fadh2 to
+ 
+
+ align:start position:0%
+electron donors nadh and fadh2 to
+molecular oxygen or whatever the
+
+ align:start position:0%
+molecular oxygen or whatever the
+ 
+
+ align:start position:0%
+molecular oxygen or whatever the
+terminal electron acceptor is in the
+
+ align:start position:0%
+terminal electron acceptor is in the
+ 
+
+ align:start position:0%
+terminal electron acceptor is in the
+biological system under study as we've
+
+ align:start position:0%
+biological system under study as we've
+ 
+
+ align:start position:0%
+biological system under study as we've
+seen the electron transfer process that
+
+ align:start position:0%
+seen the electron transfer process that
+ 
+
+ align:start position:0%
+seen the electron transfer process that
+we've been studying liberate energy and
+
+ align:start position:0%
+we've been studying liberate energy and
+ 
+
+ align:start position:0%
+we've been studying liberate energy and
+that energy is going to be used to power
+
+ align:start position:0%
+that energy is going to be used to power
+ 
+
+ align:start position:0%
+that energy is going to be used to power
+pumps that will transport protons from
+
+ align:start position:0%
+pumps that will transport protons from
+ 
+
+ align:start position:0%
+pumps that will transport protons from
+the matrix of the mitochondrion out into
+
+ align:start position:0%
+the matrix of the mitochondrion out into
+ 
+
+ align:start position:0%
+the matrix of the mitochondrion out into
+the intermembrane space between the
+
+ align:start position:0%
+the intermembrane space between the
+ 
+
+ align:start position:0%
+the intermembrane space between the
+mitochondrial inner and outer membranes
+
+ align:start position:0%
+mitochondrial inner and outer membranes
+ 
+
+ align:start position:0%
+mitochondrial inner and outer membranes
+in the case of electron transport with
+
+ align:start position:0%
+in the case of electron transport with
+ 
+
+ align:start position:0%
+in the case of electron transport with
+the goal of ATP synthesis the protons
+
+ align:start position:0%
+the goal of ATP synthesis the protons
+ 
+
+ align:start position:0%
+the goal of ATP synthesis the protons
+that are generated in the intermembrane
+
+ align:start position:0%
+that are generated in the intermembrane
+ 
+
+ align:start position:0%
+that are generated in the intermembrane
+space will be allowed to flow back
+
+ align:start position:0%
+space will be allowed to flow back
+ 
+
+ align:start position:0%
+space will be allowed to flow back
+through a device that mechanically
+
+ align:start position:0%
+through a device that mechanically
+ 
+
+ align:start position:0%
+through a device that mechanically
+couples motion that is the spinning of a
+
+ align:start position:0%
+couples motion that is the spinning of a
+ 
+
+ align:start position:0%
+couples motion that is the spinning of a
+shaft to drive conformational changes in
+
+ align:start position:0%
+shaft to drive conformational changes in
+ 
+
+ align:start position:0%
+shaft to drive conformational changes in
+enzymes that will allow the otherwise
+
+ align:start position:0%
+enzymes that will allow the otherwise
+ 
+
+ align:start position:0%
+enzymes that will allow the otherwise
+endergonic synthesis of ATP from ADP and
+
+ align:start position:0%
+endergonic synthesis of ATP from ADP and
+ 
+
+ align:start position:0%
+endergonic synthesis of ATP from ADP and
+inorganic phosphate that machine is
+
+ align:start position:0%
+inorganic phosphate that machine is
+ 
+
+ align:start position:0%
+inorganic phosphate that machine is
+called the ATP synthase let's look at
+
+ align:start position:0%
+called the ATP synthase let's look at
+ 
+
+ align:start position:0%
+called the ATP synthase let's look at
+panel a this panel shows the details of
+
+ align:start position:0%
+panel a this panel shows the details of
+ 
+
+ align:start position:0%
+panel a this panel shows the details of
+the electron transport system it looks a
+
+ align:start position:0%
+the electron transport system it looks a
+ 
+
+ align:start position:0%
+the electron transport system it looks a
+little bit complicated but let's not
+
+ align:start position:0%
+little bit complicated but let's not
+ 
+
+ align:start position:0%
+little bit complicated but let's not
+lose sight of the fact
+
+ align:start position:0%
+lose sight of the fact
+ 
+
+ align:start position:0%
+lose sight of the fact
+what it's all about is powering pumps
+
+ align:start position:0%
+what it's all about is powering pumps
+ 
+
+ align:start position:0%
+what it's all about is powering pumps
+pumps that pump protons in the lower
+
+ align:start position:0%
+pumps that pump protons in the lower
+ 
+
+ align:start position:0%
+pumps that pump protons in the lower
+left of the panel we see the TCA cycle
+
+ align:start position:0%
+left of the panel we see the TCA cycle
+ 
+
+ align:start position:0%
+left of the panel we see the TCA cycle
+generating nadh and fadh2 the nadh
+
+ align:start position:0%
+generating nadh and fadh2 the nadh
+ 
+
+ align:start position:0%
+generating nadh and fadh2 the nadh
+approaches complex one of the
+
+ align:start position:0%
+approaches complex one of the
+ 
+
+ align:start position:0%
+approaches complex one of the
+mitochondrial inner membrane complex one
+
+ align:start position:0%
+mitochondrial inner membrane complex one
+ 
+
+ align:start position:0%
+mitochondrial inner membrane complex one
+is an NADH dehydrogenase enzyme the
+
+ align:start position:0%
+is an NADH dehydrogenase enzyme the
+ 
+
+ align:start position:0%
+is an NADH dehydrogenase enzyme the
+enzyme has a flavin that accepts the
+
+ align:start position:0%
+enzyme has a flavin that accepts the
+ 
+
+ align:start position:0%
+enzyme has a flavin that accepts the
+electrons from NADH passes them along to
+
+ align:start position:0%
+electrons from NADH passes them along to
+ 
+
+ align:start position:0%
+electrons from NADH passes them along to
+iron sulfur centers and then to a
+
+ align:start position:0%
+iron sulfur centers and then to a
+ 
+
+ align:start position:0%
+iron sulfur centers and then to a
+variety of cytochromes and moves the
+
+ align:start position:0%
+variety of cytochromes and moves the
+ 
+
+ align:start position:0%
+variety of cytochromes and moves the
+electrons up to the point where they're
+
+ align:start position:0%
+electrons up to the point where they're
+ 
+
+ align:start position:0%
+electrons up to the point where they're
+going to be transferred to coenzyme q in
+
+ align:start position:0%
+going to be transferred to coenzyme q in
+ 
+
+ align:start position:0%
+going to be transferred to coenzyme q in
+its oxidized form coenzyme q binds to
+
+ align:start position:0%
+its oxidized form coenzyme q binds to
+ 
+
+ align:start position:0%
+its oxidized form coenzyme q binds to
+complex one the oxidized form of
+
+ align:start position:0%
+complex one the oxidized form of
+ 
+
+ align:start position:0%
+complex one the oxidized form of
+coenzyme q will be reduced first to a
+
+ align:start position:0%
+coenzyme q will be reduced first to a
+ 
+
+ align:start position:0%
+coenzyme q will be reduced first to a
+semi CRO known and then to a
+
+ align:start position:0%
+semi CRO known and then to a
+ 
+
+ align:start position:0%
+semi CRO known and then to a
+hydroquinone which are located as shown
+
+ align:start position:0%
+hydroquinone which are located as shown
+ 
+
+ align:start position:0%
+hydroquinone which are located as shown
+inside the mitochondrial inner membrane
+
+ align:start position:0%
+inside the mitochondrial inner membrane
+ 
+
+ align:start position:0%
+inside the mitochondrial inner membrane
+we usually draw them as being
+
+ align:start position:0%
+we usually draw them as being
+ 
+
+ align:start position:0%
+we usually draw them as being
+free-floating within the membrane but
+
+ align:start position:0%
+free-floating within the membrane but
+ 
+
+ align:start position:0%
+free-floating within the membrane but
+that's probably inaccurate these
+
+ align:start position:0%
+that's probably inaccurate these
+ 
+
+ align:start position:0%
+that's probably inaccurate these
+cofactors are probably bound to physical
+
+ align:start position:0%
+cofactors are probably bound to physical
+ 
+
+ align:start position:0%
+cofactors are probably bound to physical
+entities inside the mitochondrial inner
+
+ align:start position:0%
+entities inside the mitochondrial inner
+ 
+
+ align:start position:0%
+entities inside the mitochondrial inner
+membrane the picture also shows fadh2
+
+ align:start position:0%
+membrane the picture also shows fadh2
+ 
+
+ align:start position:0%
+membrane the picture also shows fadh2
+from the TCA cycle interacting with
+
+ align:start position:0%
+from the TCA cycle interacting with
+ 
+
+ align:start position:0%
+from the TCA cycle interacting with
+complex 2 which is a flavin containing
+
+ align:start position:0%
+complex 2 which is a flavin containing
+ 
+
+ align:start position:0%
+complex 2 which is a flavin containing
+enzyme and it will also transfer its
+
+ align:start position:0%
+enzyme and it will also transfer its
+ 
+
+ align:start position:0%
+enzyme and it will also transfer its
+electrons to the oxidized form of
+
+ align:start position:0%
+electrons to the oxidized form of
+ 
+
+ align:start position:0%
+electrons to the oxidized form of
+coenzyme q ultimately to create the
+
+ align:start position:0%
+coenzyme q ultimately to create the
+ 
+
+ align:start position:0%
+coenzyme q ultimately to create the
+reduced coenzyme q h 2 which is the
+
+ align:start position:0%
+reduced coenzyme q h 2 which is the
+ 
+
+ align:start position:0%
+reduced coenzyme q h 2 which is the
+hydroquinone just as a point of
+
+ align:start position:0%
+hydroquinone just as a point of
+ 
+
+ align:start position:0%
+hydroquinone just as a point of
+reference to the TCA cycle complex 2 is
+
+ align:start position:0%
+reference to the TCA cycle complex 2 is
+ 
+
+ align:start position:0%
+reference to the TCA cycle complex 2 is
+also known as succinate dehydrogenase we
+
+ align:start position:0%
+also known as succinate dehydrogenase we
+ 
+
+ align:start position:0%
+also known as succinate dehydrogenase we
+haven't done fatty acid oxidation yet
+
+ align:start position:0%
+haven't done fatty acid oxidation yet
+ 
+
+ align:start position:0%
+haven't done fatty acid oxidation yet
+but there's a step in fatty acid
+
+ align:start position:0%
+but there's a step in fatty acid
+ 
+
+ align:start position:0%
+but there's a step in fatty acid
+oxidation in which an alkane is
+
+ align:start position:0%
+oxidation in which an alkane is
+ 
+
+ align:start position:0%
+oxidation in which an alkane is
+converted to an alkene the electrons
+
+ align:start position:0%
+converted to an alkene the electrons
+ 
+
+ align:start position:0%
+converted to an alkene the electrons
+from that oxidation reaction go through
+
+ align:start position:0%
+from that oxidation reaction go through
+ 
+
+ align:start position:0%
+from that oxidation reaction go through
+a flavin protein called ETF pre for
+
+ align:start position:0%
+a flavin protein called ETF pre for
+ 
+
+ align:start position:0%
+a flavin protein called ETF pre for
+electron transferring flavor protein and
+
+ align:start position:0%
+electron transferring flavor protein and
+ 
+
+ align:start position:0%
+electron transferring flavor protein and
+once again those electrons flow into
+
+ align:start position:0%
+once again those electrons flow into
+ 
+
+ align:start position:0%
+once again those electrons flow into
+coenzyme q to form the reduced form of
+
+ align:start position:0%
+coenzyme q to form the reduced form of
+ 
+
+ align:start position:0%
+coenzyme q to form the reduced form of
+coenzyme q remember when we talked about
+
+ align:start position:0%
+coenzyme q remember when we talked about
+ 
+
+ align:start position:0%
+coenzyme q remember when we talked about
+the glycerol 3-phosphate shuttle i
+
+ align:start position:0%
+the glycerol 3-phosphate shuttle i
+ 
+
+ align:start position:0%
+the glycerol 3-phosphate shuttle i
+mentioned that there's a mitochondrial
+
+ align:start position:0%
+mentioned that there's a mitochondrial
+ 
+
+ align:start position:0%
+mentioned that there's a mitochondrial
+membrane associated glycerol 3-phosphate
+
+ align:start position:0%
+membrane associated glycerol 3-phosphate
+ 
+
+ align:start position:0%
+membrane associated glycerol 3-phosphate
+dehydrogenase you can see that enzyme at
+
+ align:start position:0%
+dehydrogenase you can see that enzyme at
+ 
+
+ align:start position:0%
+dehydrogenase you can see that enzyme at
+the top part of the inner membrane as
+
+ align:start position:0%
+the top part of the inner membrane as
+ 
+
+ align:start position:0%
+the top part of the inner membrane as
+i've drawn it and once again flavin in
+
+ align:start position:0%
+i've drawn it and once again flavin in
+ 
+
+ align:start position:0%
+i've drawn it and once again flavin in
+that enzyme will carry the electrons
+
+ align:start position:0%
+that enzyme will carry the electrons
+ 
+
+ align:start position:0%
+that enzyme will carry the electrons
+into coenzyme q generating
+
+ align:start position:0%
+into coenzyme q generating
+ 
+
+ align:start position:0%
+into coenzyme q generating
+reduced form of the cofactor qh2 the
+
+ align:start position:0%
+reduced form of the cofactor qh2 the
+ 
+
+ align:start position:0%
+reduced form of the cofactor qh2 the
+left part of this picture pretty neatly
+
+ align:start position:0%
+left part of this picture pretty neatly
+ 
+
+ align:start position:0%
+left part of this picture pretty neatly
+shows how nutrient oxidation can channel
+
+ align:start position:0%
+shows how nutrient oxidation can channel
+ 
+
+ align:start position:0%
+shows how nutrient oxidation can channel
+the electrons into a common mobile
+
+ align:start position:0%
+the electrons into a common mobile
+ 
+
+ align:start position:0%
+the electrons into a common mobile
+electron carrier coenzyme q lots of
+
+ align:start position:0%
+electron carrier coenzyme q lots of
+ 
+
+ align:start position:0%
+electron carrier coenzyme q lots of
+different fuels give up their electrons
+
+ align:start position:0%
+different fuels give up their electrons
+ 
+
+ align:start position:0%
+different fuels give up their electrons
+to a common electron carrier the
+
+ align:start position:0%
+to a common electron carrier the
+ 
+
+ align:start position:0%
+to a common electron carrier the
+hydroquinone q h2 will then go and
+
+ align:start position:0%
+hydroquinone q h2 will then go and
+ 
+
+ align:start position:0%
+hydroquinone q h2 will then go and
+interact with complex three of the
+
+ align:start position:0%
+interact with complex three of the
+ 
+
+ align:start position:0%
+interact with complex three of the
+electron transport chain in complex
+
+ align:start position:0%
+electron transport chain in complex
+ 
+
+ align:start position:0%
+electron transport chain in complex
+three electrons will be transported
+
+ align:start position:0%
+three electrons will be transported
+ 
+
+ align:start position:0%
+three electrons will be transported
+through a number of different electron
+
+ align:start position:0%
+through a number of different electron
+ 
+
+ align:start position:0%
+through a number of different electron
+relay stations and ultimately be picked
+
+ align:start position:0%
+relay stations and ultimately be picked
+ 
+
+ align:start position:0%
+relay stations and ultimately be picked
+up by cytochrome c which is in initially
+
+ align:start position:0%
+up by cytochrome c which is in initially
+ 
+
+ align:start position:0%
+up by cytochrome c which is in initially
+in its +3 oxidation state cytochrome c
+
+ align:start position:0%
+in its +3 oxidation state cytochrome c
+ 
+
+ align:start position:0%
+in its +3 oxidation state cytochrome c
+is reduced by the single electron coming
+
+ align:start position:0%
+is reduced by the single electron coming
+ 
+
+ align:start position:0%
+is reduced by the single electron coming
+through complex 3 in this process its
+
+ align:start position:0%
+through complex 3 in this process its
+ 
+
+ align:start position:0%
+through complex 3 in this process its
+iron is reduced to its +2 state this
+
+ align:start position:0%
+iron is reduced to its +2 state this
+ 
+
+ align:start position:0%
+iron is reduced to its +2 state this
+electron on cytochrome c then migrates
+
+ align:start position:0%
+electron on cytochrome c then migrates
+ 
+
+ align:start position:0%
+electron on cytochrome c then migrates
+across the outer surface of the inner
+
+ align:start position:0%
+across the outer surface of the inner
+ 
+
+ align:start position:0%
+across the outer surface of the inner
+membrane of the mitochondrion to
+
+ align:start position:0%
+membrane of the mitochondrion to
+ 
+
+ align:start position:0%
+membrane of the mitochondrion to
+interact with complex 4 when it
+
+ align:start position:0%
+interact with complex 4 when it
+ 
+
+ align:start position:0%
+interact with complex 4 when it
+interacts with complex for the reduced
+
+ align:start position:0%
+interacts with complex for the reduced
+ 
+
+ align:start position:0%
+interacts with complex for the reduced
+form of cytochrome c gives up its
+
+ align:start position:0%
+form of cytochrome c gives up its
+ 
+
+ align:start position:0%
+form of cytochrome c gives up its
+electron to a copper residue on the
+
+ align:start position:0%
+electron to a copper residue on the
+ 
+
+ align:start position:0%
+electron to a copper residue on the
+copper a subunit of complex 4 in the
+
+ align:start position:0%
+copper a subunit of complex 4 in the
+ 
+
+ align:start position:0%
+copper a subunit of complex 4 in the
+figure this complex is called Cu a the
+
+ align:start position:0%
+figure this complex is called Cu a the
+ 
+
+ align:start position:0%
+figure this complex is called Cu a the
+more common name for a complex four is
+
+ align:start position:0%
+more common name for a complex four is
+ 
+
+ align:start position:0%
+more common name for a complex four is
+cytochrome C oxidase so cytochrome C
+
+ align:start position:0%
+cytochrome C oxidase so cytochrome C
+ 
+
+ align:start position:0%
+cytochrome C oxidase so cytochrome C
+oxidase oxidizes the iron back to its
+
+ align:start position:0%
+oxidase oxidizes the iron back to its
+ 
+
+ align:start position:0%
+oxidase oxidizes the iron back to its
+iron 3 oxidation state then cytochrome C
+
+ align:start position:0%
+iron 3 oxidation state then cytochrome C
+ 
+
+ align:start position:0%
+iron 3 oxidation state then cytochrome C
+migrates back to complex 3 where it's
+
+ align:start position:0%
+migrates back to complex 3 where it's
+ 
+
+ align:start position:0%
+migrates back to complex 3 where it's
+able to pick up another electron we can
+
+ align:start position:0%
+able to pick up another electron we can
+ 
+
+ align:start position:0%
+able to pick up another electron we can
+think of cytochrome C as a mobile
+
+ align:start position:0%
+think of cytochrome C as a mobile
+ 
+
+ align:start position:0%
+think of cytochrome C as a mobile
+electron carrier that shuttles an
+
+ align:start position:0%
+electron carrier that shuttles an
+ 
+
+ align:start position:0%
+electron carrier that shuttles an
+electron along the inner surface of the
+
+ align:start position:0%
+electron along the inner surface of the
+ 
+
+ align:start position:0%
+electron along the inner surface of the
+mitochondrial inner membrane looking
+
+ align:start position:0%
+mitochondrial inner membrane looking
+ 
+
+ align:start position:0%
+mitochondrial inner membrane looking
+back at complex 4 or cytochrome C
+
+ align:start position:0%
+back at complex 4 or cytochrome C
+ 
+
+ align:start position:0%
+back at complex 4 or cytochrome C
+oxidase the electrons are passed from
+
+ align:start position:0%
+oxidase the electrons are passed from
+ 
+
+ align:start position:0%
+oxidase the electrons are passed from
+cytochrome a to a series of other
+
+ align:start position:0%
+cytochrome a to a series of other
+ 
+
+ align:start position:0%
+cytochrome a to a series of other
+electron carriers and ultimately they
+
+ align:start position:0%
+electron carriers and ultimately they
+ 
+
+ align:start position:0%
+electron carriers and ultimately they
+flow into molecular oxygen molecular
+
+ align:start position:0%
+flow into molecular oxygen molecular
+ 
+
+ align:start position:0%
+flow into molecular oxygen molecular
+oxygen is anchored on one side to heme
+
+ align:start position:0%
+oxygen is anchored on one side to heme
+ 
+
+ align:start position:0%
+oxygen is anchored on one side to heme
+a3 and on the other side to copper B
+
+ align:start position:0%
+a3 and on the other side to copper B
+ 
+
+ align:start position:0%
+a3 and on the other side to copper B
+oxygen undergoes a 4 electron reduction
+
+ align:start position:0%
+oxygen undergoes a 4 electron reduction
+ 
+
+ align:start position:0%
+oxygen undergoes a 4 electron reduction
+and picks up 4 protons along the way to
+
+ align:start position:0%
+and picks up 4 protons along the way to
+ 
+
+ align:start position:0%
+and picks up 4 protons along the way to
+form 2 molecules of water if the
+
+ align:start position:0%
+form 2 molecules of water if the
+ 
+
+ align:start position:0%
+form 2 molecules of water if the
+electron started with NADH and ends up
+
+ align:start position:0%
+electron started with NADH and ends up
+ 
+
+ align:start position:0%
+electron started with NADH and ends up
+in oxygen to form water
+
+ align:start position:0%
+in oxygen to form water
+ 
+
+ align:start position:0%
+in oxygen to form water
+you get 220 kilojoules of energy and as
+
+ align:start position:0%
+you get 220 kilojoules of energy and as
+ 
+
+ align:start position:0%
+you get 220 kilojoules of energy and as
+I said you get somewhat less if your
+
+ align:start position:0%
+I said you get somewhat less if your
+ 
+
+ align:start position:0%
+I said you get somewhat less if your
+electron started out as a reduced flavin
+
+ align:start position:0%
+electron started out as a reduced flavin
+ 
+
+ align:start position:0%
+electron started out as a reduced flavin
+now let's look at panel B I want to say
+
+ align:start position:0%
+now let's look at panel B I want to say
+ 
+
+ align:start position:0%
+now let's look at panel B I want to say
+a few words at the outset about proton
+
+ align:start position:0%
+a few words at the outset about proton
+ 
+
+ align:start position:0%
+a few words at the outset about proton
+pumps keeping in mind that the reason
+
+ align:start position:0%
+pumps keeping in mind that the reason
+ 
+
+ align:start position:0%
+pumps keeping in mind that the reason
+electrons were moved through the
+
+ align:start position:0%
+electrons were moved through the
+ 
+
+ align:start position:0%
+electrons were moved through the
+electron transport chain was to power
+
+ align:start position:0%
+electron transport chain was to power
+ 
+
+ align:start position:0%
+electron transport chain was to power
+these pumps in the lower-left part of
+
+ align:start position:0%
+these pumps in the lower-left part of
+ 
+
+ align:start position:0%
+these pumps in the lower-left part of
+the figure we can see complex one the
+
+ align:start position:0%
+the figure we can see complex one the
+ 
+
+ align:start position:0%
+the figure we can see complex one the
+transit of electrons through complex one
+
+ align:start position:0%
+transit of electrons through complex one
+ 
+
+ align:start position:0%
+transit of electrons through complex one
+from nadh results in the transport of
+
+ align:start position:0%
+from nadh results in the transport of
+ 
+
+ align:start position:0%
+from nadh results in the transport of
+four protons from the mitochondrial
+
+ align:start position:0%
+four protons from the mitochondrial
+ 
+
+ align:start position:0%
+four protons from the mitochondrial
+matrix into the intermembrane space that
+
+ align:start position:0%
+matrix into the intermembrane space that
+ 
+
+ align:start position:0%
+matrix into the intermembrane space that
+is two electrons from NADH are
+
+ align:start position:0%
+is two electrons from NADH are
+ 
+
+ align:start position:0%
+is two electrons from NADH are
+transported and coincident with that
+
+ align:start position:0%
+transported and coincident with that
+ 
+
+ align:start position:0%
+transported and coincident with that
+four protons are pumped into the
+
+ align:start position:0%
+four protons are pumped into the
+ 
+
+ align:start position:0%
+four protons are pumped into the
+intermembrane space later we'll see that
+
+ align:start position:0%
+intermembrane space later we'll see that
+ 
+
+ align:start position:0%
+intermembrane space later we'll see that
+complex 3 is location of something
+
+ align:start position:0%
+complex 3 is location of something
+ 
+
+ align:start position:0%
+complex 3 is location of something
+called the Q cycle I'm going to cover
+
+ align:start position:0%
+called the Q cycle I'm going to cover
+ 
+
+ align:start position:0%
+called the Q cycle I'm going to cover
+the proton pumping properties of the q
+
+ align:start position:0%
+the proton pumping properties of the q
+ 
+
+ align:start position:0%
+the proton pumping properties of the q
+sy q cycle in some detail in the next
+
+ align:start position:0%
+sy q cycle in some detail in the next
+ 
+
+ align:start position:0%
+sy q cycle in some detail in the next
+storyboard the passage of those two
+
+ align:start position:0%
+storyboard the passage of those two
+ 
+
+ align:start position:0%
+storyboard the passage of those two
+electrons through complex three results
+
+ align:start position:0%
+electrons through complex three results
+ 
+
+ align:start position:0%
+electrons through complex three results
+in the transport of an additional four
+
+ align:start position:0%
+in the transport of an additional four
+ 
+
+ align:start position:0%
+in the transport of an additional four
+protons into the intermembrane space
+
+ align:start position:0%
+protons into the intermembrane space
+ 
+
+ align:start position:0%
+protons into the intermembrane space
+lastly the transit of electrons through
+
+ align:start position:0%
+lastly the transit of electrons through
+ 
+
+ align:start position:0%
+lastly the transit of electrons through
+complex for the cytochrome C oxidase
+
+ align:start position:0%
+complex for the cytochrome C oxidase
+ 
+
+ align:start position:0%
+complex for the cytochrome C oxidase
+results in the transport of another two
+
+ align:start position:0%
+results in the transport of another two
+ 
+
+ align:start position:0%
+results in the transport of another two
+protons into the intermembrane space now
+
+ align:start position:0%
+protons into the intermembrane space now
+ 
+
+ align:start position:0%
+protons into the intermembrane space now
+let's look at panel C adding things up
+
+ align:start position:0%
+let's look at panel C adding things up
+ 
+
+ align:start position:0%
+let's look at panel C adding things up
+if we start with two electrons coming
+
+ align:start position:0%
+if we start with two electrons coming
+ 
+
+ align:start position:0%
+if we start with two electrons coming
+from NADH we transport about 10 protons
+
+ align:start position:0%
+from NADH we transport about 10 protons
+ 
+
+ align:start position:0%
+from NADH we transport about 10 protons
+into the intermembrane space that's
+
+ align:start position:0%
+into the intermembrane space that's
+ 
+
+ align:start position:0%
+into the intermembrane space that's
+enough to make about three molecules of
+
+ align:start position:0%
+enough to make about three molecules of
+ 
+
+ align:start position:0%
+enough to make about three molecules of
+ATP if our electrons start with fadh2
+
+ align:start position:0%
+ATP if our electrons start with fadh2
+ 
+
+ align:start position:0%
+ATP if our electrons start with fadh2
+reduced flavin we only transport about
+
+ align:start position:0%
+reduced flavin we only transport about
+ 
+
+ align:start position:0%
+reduced flavin we only transport about
+six protons that's enough to make two
+
+ align:start position:0%
+six protons that's enough to make two
+ 
+
+ align:start position:0%
+six protons that's enough to make two
+ATP's if you remember making ATP is only
+
+ align:start position:0%
+ATP's if you remember making ATP is only
+ 
+
+ align:start position:0%
+ATP's if you remember making ATP is only
+one of the things that we can do with
+
+ align:start position:0%
+one of the things that we can do with
+ 
+
+ align:start position:0%
+one of the things that we can do with
+the power of the proton gradient I
+
+ align:start position:0%
+the power of the proton gradient I
+ 
+
+ align:start position:0%
+the power of the proton gradient I
+mentioned earlier that we can also use
+
+ align:start position:0%
+mentioned earlier that we can also use
+ 
+
+ align:start position:0%
+mentioned earlier that we can also use
+it to generate heat and motion let me
+
+ align:start position:0%
+it to generate heat and motion let me
+ 
+
+ align:start position:0%
+it to generate heat and motion let me
+talk for a minute about why one would
+
+ align:start position:0%
+talk for a minute about why one would
+ 
+
+ align:start position:0%
+talk for a minute about why one would
+want to generate heat newborn babies are
+
+ align:start position:0%
+want to generate heat newborn babies are
+ 
+
+ align:start position:0%
+want to generate heat newborn babies are
+like small balls they have a high
+
+ align:start position:0%
+like small balls they have a high
+ 
+
+ align:start position:0%
+like small balls they have a high
+surface to volume ratio their high
+
+ align:start position:0%
+surface to volume ratio their high
+ 
+
+ align:start position:0%
+surface to volume ratio their high
+surface to volume ratio makes heat loss
+
+ align:start position:0%
+surface to volume ratio makes heat loss
+ 
+
+ align:start position:0%
+surface to volume ratio makes heat loss
+a very significant reality and in fact a
+
+ align:start position:0%
+a very significant reality and in fact a
+ 
+
+ align:start position:0%
+a very significant reality and in fact a
+problem for the newborn they have
+
+ align:start position:0%
+problem for the newborn they have
+ 
+
+ align:start position:0%
+problem for the newborn they have
+therefore specialised mitochondria in
+
+ align:start position:0%
+therefore specialised mitochondria in
+ 
+
+ align:start position:0%
+therefore specialised mitochondria in
+their neck in an area called brown fat
+
+ align:start position:0%
+their neck in an area called brown fat
+ 
+
+ align:start position:0%
+their neck in an area called brown fat
+the fat is brown because
+
+ align:start position:0%
+the fat is brown because
+ 
+
+ align:start position:0%
+the fat is brown because
+loaded with highly colored mitochondria
+
+ align:start position:0%
+loaded with highly colored mitochondria
+ 
+
+ align:start position:0%
+loaded with highly colored mitochondria
+these mitochondria have a protein that
+
+ align:start position:0%
+these mitochondria have a protein that
+ 
+
+ align:start position:0%
+these mitochondria have a protein that
+enables the protons pumped into the
+
+ align:start position:0%
+enables the protons pumped into the
+ 
+
+ align:start position:0%
+enables the protons pumped into the
+intermembrane space to flow back freely
+
+ align:start position:0%
+intermembrane space to flow back freely
+ 
+
+ align:start position:0%
+intermembrane space to flow back freely
+into the mitochondrial matrix with the
+
+ align:start position:0%
+into the mitochondrial matrix with the
+ 
+
+ align:start position:0%
+into the mitochondrial matrix with the
+generation of heat that is they don't
+
+ align:start position:0%
+generation of heat that is they don't
+ 
+
+ align:start position:0%
+generation of heat that is they don't
+make ATP in the brown fat they make heat
+
+ align:start position:0%
+make ATP in the brown fat they make heat
+ 
+
+ align:start position:0%
+make ATP in the brown fat they make heat
+this helps promote thermal regulation in
+
+ align:start position:0%
+this helps promote thermal regulation in
+ 
+
+ align:start position:0%
+this helps promote thermal regulation in
+the baby this is also the mechanism by
+
+ align:start position:0%
+the baby this is also the mechanism by
+ 
+
+ align:start position:0%
+the baby this is also the mechanism by
+which hibernating animals such as a bear
+
+ align:start position:0%
+which hibernating animals such as a bear
+ 
+
+ align:start position:0%
+which hibernating animals such as a bear
+can maintain body temperature during the
+
+ align:start position:0%
+can maintain body temperature during the
+ 
+
+ align:start position:0%
+can maintain body temperature during the
+winter when the bear is hibernating this
+
+ align:start position:0%
+winter when the bear is hibernating this
+ 
+
+ align:start position:0%
+winter when the bear is hibernating this
+process overall is called uncoupling of
+
+ align:start position:0%
+process overall is called uncoupling of
+ 
+
+ align:start position:0%
+process overall is called uncoupling of
+electron transport from the process that
+
+ align:start position:0%
+electron transport from the process that
+ 
+
+ align:start position:0%
+electron transport from the process that
+we're going to be looking at next
+
+ align:start position:0%
+we're going to be looking at next
+ 
+
+ align:start position:0%
+we're going to be looking at next
+oxidative phosphorylation oxidative
+
+ align:start position:0%
+oxidative phosphorylation oxidative
+ 
+
+ align:start position:0%
+oxidative phosphorylation oxidative
+phosphorylation is the process by which
+
+ align:start position:0%
+phosphorylation is the process by which
+ 
+
+ align:start position:0%
+phosphorylation is the process by which
+we're going to be making ATP uncoupling
+
+ align:start position:0%
+we're going to be making ATP uncoupling
+ 
+
+ align:start position:0%
+we're going to be making ATP uncoupling
+is also a process used by some flowers
+
+ align:start position:0%
+is also a process used by some flowers
+ 
+
+ align:start position:0%
+is also a process used by some flowers
+that have to come up through frozen
+
+ align:start position:0%
+that have to come up through frozen
+ 
+
+ align:start position:0%
+that have to come up through frozen
+ground in the springtime for example the
+
+ align:start position:0%
+ground in the springtime for example the
+ 
+
+ align:start position:0%
+ground in the springtime for example the
+skunk cabbage and the crocus are very
+
+ align:start position:0%
+skunk cabbage and the crocus are very
+ 
+
+ align:start position:0%
+skunk cabbage and the crocus are very
+good at uncoupling electron transport
+
+ align:start position:0%
+good at uncoupling electron transport
+ 
+
+ align:start position:0%
+good at uncoupling electron transport
+from oxidative phosphorylation
+
+ align:start position:0%
+from oxidative phosphorylation
+ 
+
+ align:start position:0%
+from oxidative phosphorylation
+they let the protons in the proton
+
+ align:start position:0%
+they let the protons in the proton
+ 
+
+ align:start position:0%
+they let the protons in the proton
+gradient flow back across the
+
+ align:start position:0%
+gradient flow back across the
+ 
+
+ align:start position:0%
+gradient flow back across the
+mitochondrial inner membrane and by
+
+ align:start position:0%
+mitochondrial inner membrane and by
+ 
+
+ align:start position:0%
+mitochondrial inner membrane and by
+doing so these plants are able to
+
+ align:start position:0%
+doing so these plants are able to
+ 
+
+ align:start position:0%
+doing so these plants are able to
+generate heat that will allow them to
+
+ align:start position:0%
+generate heat that will allow them to
+ 
+
+ align:start position:0%
+generate heat that will allow them to
+grow at sub-freezing temperatures in
+
+ align:start position:0%
+grow at sub-freezing temperatures in
+ 
+
+ align:start position:0%
+grow at sub-freezing temperatures in
+other words the plant itself becomes a
+
+ align:start position:0%
+other words the plant itself becomes a
+ 
+
+ align:start position:0%
+other words the plant itself becomes a
+little heater at this point let me give
+
+ align:start position:0%
+little heater at this point let me give
+ 
+
+ align:start position:0%
+little heater at this point let me give
+you a little bit of a preview of how we
+
+ align:start position:0%
+you a little bit of a preview of how we
+ 
+
+ align:start position:0%
+you a little bit of a preview of how we
+use this proton gradient in order to
+
+ align:start position:0%
+use this proton gradient in order to
+ 
+
+ align:start position:0%
+use this proton gradient in order to
+synthesize ATP as we've seen it took
+
+ align:start position:0%
+synthesize ATP as we've seen it took
+ 
+
+ align:start position:0%
+synthesize ATP as we've seen it took
+energy in order to create a gradient in
+
+ align:start position:0%
+energy in order to create a gradient in
+ 
+
+ align:start position:0%
+energy in order to create a gradient in
+which there are protons in the
+
+ align:start position:0%
+which there are protons in the
+ 
+
+ align:start position:0%
+which there are protons in the
+intermembrane space and protons are
+
+ align:start position:0%
+intermembrane space and protons are
+ 
+
+ align:start position:0%
+intermembrane space and protons are
+chemical entities so we've created a
+
+ align:start position:0%
+chemical entities so we've created a
+ 
+
+ align:start position:0%
+chemical entities so we've created a
+chemical gradient but also we're putting
+
+ align:start position:0%
+chemical gradient but also we're putting
+ 
+
+ align:start position:0%
+chemical gradient but also we're putting
+a very high positive charge density in
+
+ align:start position:0%
+a very high positive charge density in
+ 
+
+ align:start position:0%
+a very high positive charge density in
+the small enclosed inter membrane space
+
+ align:start position:0%
+the small enclosed inter membrane space
+ 
+
+ align:start position:0%
+the small enclosed inter membrane space
+so we've also created an electrochemical
+
+ align:start position:0%
+so we've also created an electrochemical
+ 
+
+ align:start position:0%
+so we've also created an electrochemical
+gradient it is the release of those
+
+ align:start position:0%
+gradient it is the release of those
+ 
+
+ align:start position:0%
+gradient it is the release of those
+gradients that empowers many of our
+
+ align:start position:0%
+gradients that empowers many of our
+ 
+
+ align:start position:0%
+gradients that empowers many of our
+vital processes for a final comment
+
+ align:start position:0%
+vital processes for a final comment
+ 
+
+ align:start position:0%
+vital processes for a final comment
+please see panel D Peter Mitchell
+
+ align:start position:0%
+please see panel D Peter Mitchell
+ 
+
+ align:start position:0%
+please see panel D Peter Mitchell
+figured out how the energy in that
+
+ align:start position:0%
+figured out how the energy in that
+ 
+
+ align:start position:0%
+figured out how the energy in that
+electrochemical gradient could be
+
+ align:start position:0%
+electrochemical gradient could be
+ 
+
+ align:start position:0%
+electrochemical gradient could be
+released and converted into the energy
+
+ align:start position:0%
+released and converted into the energy
+ 
+
+ align:start position:0%
+released and converted into the energy
+it takes to make chemical bonds
+
+ align:start position:0%
+it takes to make chemical bonds
+ 
+
+ align:start position:0%
+it takes to make chemical bonds
+Mitchell's conclusions serve as the
+
+ align:start position:0%
+Mitchell's conclusions serve as the
+ 
+
+ align:start position:0%
+Mitchell's conclusions serve as the
+basis of what is called the chemiosmotic
+
+ align:start position:0%
+basis of what is called the chemiosmotic
+ 
+
+ align:start position:0%
+basis of what is called the chemiosmotic
+coupling hypothesis and we'd be looking
+
+ align:start position:0%
+coupling hypothesis and we'd be looking
+ 
+
+ align:start position:0%
+coupling hypothesis and we'd be looking
+at that in some detail later
\ No newline at end of file
diff --git a/e3Bsb1mELcc.txt b/e3Bsb1mELcc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a30953fd3f0516f14fcbabab429a11c671984272
--- /dev/null
+++ b/e3Bsb1mELcc.txt
@@ -0,0 +1,2761 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+mitopencourseware@ocw.mit.edu.
+
+PROFESSOR: Economics--
+
+oligopoly.
+
+Which is basically trying
+to move towards the most
+
+realistic modeling of
+markets that we can.
+
+We've talked about two extreme
+versions of modeling markets.
+
+One is perfect competition,
+which is the extreme case of
+
+perfect entry and exit.
+
+Free entry and exit.
+
+Perfect consumer information.
+
+An idealized market.
+
+We know that doesn't really
+exist in practice anywhere.
+
+The second extreme was monopoly,
+which we do see in
+
+practice in some places.
+
+In particular, when there's
+natural monopolies.
+
+We do see that.
+
+But that's still doesn't
+describe most markets.
+
+Most markets are better
+described as oligopolies.
+
+These are markets where there's
+more than one market
+
+player, yet where each firm is
+large enough to actually
+
+affect the price.
+
+So an oligopoly market is where
+there'll be a small
+
+number of firms in the market
+with substantial barriers to
+
+entry from additional firms.
+An oligopoly market where
+
+there's a small number of firms
+with enough barriers to
+
+entry that additional
+firms don't enter.
+
+So the classic example
+of an oligopoly
+
+industry is the auto industry.
+
+Here's a market with a small
+number of dominant players.
+
+There's been some entry and exit
+over time, obviously, but
+
+it moves pretty slowly.
+
+By and large it's a market
+where there's
+
+very limited entry.
+
+And the question is, how do
+firms behave in this market?
+
+Obviously it's not like perfect
+competition where they
+
+can lazily take a price out of
+the market and just produce
+
+based on that price.
+
+But it's also not the same as
+monopoly where they can just
+
+get to set the price and
+not worry about what
+
+other people do.
+
+They're in this in-between
+situation where they have
+
+price setting power.
+
+They have some market power but
+in a context where they
+
+have to worry about
+competitors.
+
+And so in this context there are
+two different ways firms
+
+can behave. It's important
+to lay out to start.
+
+There's two different ways for
+firms to behave. They can
+
+behave cooperatively or
+non-cooperatively.
+
+If they behave cooperatively
+we say
+
+that they form a cartel.
+
+So our cartel is what happens
+when oligopolistic firms, when
+
+firms in an oligopolistic market
+behave cooperatively to
+
+determine the outcome.
+
+We call that a cartel.
+
+The classic example, of course,
+here being OPEC.
+
+The Organization of Petroleum
+Exporting Countries, which is
+
+a cartel that drives
+the price of oil.
+
+Those countries cooperate in how
+much oil they produce to
+
+move the price up or
+down according to
+
+what the group desires.
+
+And what cartels do is
+essentially turn oligopolies
+
+into monopolies.
+
+So what cartelization does, what
+a cooperative equilibrium
+
+does is essentially say, let's
+all get together and behave as
+
+if we're one big monopoly
+by cooperating.
+
+And therefore, if you cooperate
+you can get all the
+
+wonderful things monopolies get:
+huge market power, huge
+
+markets et cetera.
+
+But as we'll talk about next
+time, it turns out to be
+
+pretty hard to get a cooperative
+oligopoly.
+
+There's lots of reasons why
+it might fall apart.
+
+And that's why in most
+oligopolistic markets firms
+
+behave non cooperatively.
+
+In most oligopolistic markets
+firms are behaving
+
+non-cooperatively.
+
+They're competing with each
+other, not cooperating.
+
+And that's what we're going to
+spend today analyzing is the
+
+case of non-cooperative
+oligopolies.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Depends
+on the context.
+
+In the US, and I'll talk about
+this, in the US there's
+
+anti-trust legislation which
+can make it illegal in many
+
+contexts to cooperate.
+
+Obviously OPEC is not subject
+to some world legislation.
+
+But even in the US there can be
+implicit cartelization and
+
+implicit cooperation, and
+we'll talk about that.
+
+It's a good question.
+
+So technically you're right.
+
+Technically it is illegal in
+the US in most contexts to
+
+form a cooperative,
+to form a cartel.
+
+Whether in practice those laws
+can be enforced is an
+
+interesting, legitimate
+question.
+
+So today we want to focus on
+the case of non-cooperative
+
+oligopolies.
+
+And to do so we're going
+to turn to a new tool.
+
+And one of the fundamental tools
+of economics in the last
+
+30 years which is game theory.
+
+So today we're going to talk
+about game theory.
+
+Game theory is a tool of
+economics that was not really
+
+used early in economics but
+has come to dominate
+
+theoretical economics over
+the past 30 or 40 years.
+
+And basically the way that game
+theory works is to think,
+
+literally, of oligopolistic
+firms as engaging in a game.
+
+So when you play, don't want to
+say play Monopoly, that's
+
+confusing terms. When
+you play Sorry!
+
+or whatever with someone, or
+play some online game with
+
+someone, you're competing
+to win.
+
+You're behaving
+non-cooperatively.
+
+You're competing to win.
+
+So basically what the insights
+of game theory are that all
+
+the tools we used strategically
+to make
+
+decisions in playing games can
+actually be used in modeling
+
+how firms compete
+non-cooperatively in
+
+oligopolistic market.
+
+The key insight is that each
+firm will develop a strategy.
+
+Just as when you're playing
+chess you have some strategy
+
+going in, firms develop
+a strategy.
+
+And that based on that strategy
+they will determine
+
+their behavior.
+
+And what is going to determine
+that behavior is going to be
+
+how firms' strategies combine to
+determine a market outcome.
+
+When firms come in with
+different strategies, or when
+
+a bunch of firms with strategies
+come in to compete
+
+with each other, what determines
+the market outcome.
+
+And what that's going to depend
+on is something we call
+
+an equilibrium concept.
+
+Which is how do we measure--
+
+essentially the equilibrium
+concept is in game theory
+
+terms, think about how
+do we determine
+
+when the game's over?
+
+How do we determine when
+we've decided on the
+
+outcome of the market.
+
+What's the equilibrium
+concept?
+
+So when you're reading the rules
+of a new game the first
+
+thing you look for is how
+do you decide who wins.
+
+That's kind of like what the
+equilibrium concept is.
+
+It's what determines whether
+the game has ended.
+
+What determines whether you've
+reached equilibrium.
+
+Where you've reached a point
+where the market is stable and
+
+therefore the game has ended.
+
+Not ended in the sense the firm
+shut down, but ended in
+
+the sense that you know what
+everybody's doing.
+
+So it's not quite like
+winning or losing.
+
+It's more just like what
+determines when you're at the
+
+point where that market
+is at equilibrium.
+
+Now the most famous concept is
+due to John Nash, who many of
+
+you heard of from the movie and
+book A Beautiful Mind, and
+
+that's called the Nash
+Equilibrium.
+
+A Nash equilibrium is the point
+at which no firm wants
+
+to change its strategy
+given what the
+
+other firms are doing.
+
+I'm going to say that again.
+
+A Nash equilibrium is the point
+where no firm wants to
+
+change its strategy given what
+the other firms are doing.
+
+It's a little bit bizarre,
+but we'll work it out.
+
+In other words, more formally,
+the idea is that holding
+
+constant, given the strategies
+all your competitors use
+
+there's nothing that I can do
+to raise my profits further.
+
+Given the strategies all my
+competitors are playing,
+
+there's no strategy I can choose
+that will make me more
+
+profitable than the
+one I'm choosing.
+
+And likewise for every player
+in the market that will turn
+
+out to be true.
+
+So have players sitting
+around a game board,
+
+going around the circle.
+
+Each player says, given what I
+know each of the rest you are
+
+doing, I'm doing the
+best thing I can.
+
+And they go around the circle
+and everybody says, OK, I'm at
+
+that point.
+
+You've reached a stable
+Nash equilibrium.
+
+This was named, of course,
+for John Nash.
+
+You all know the story
+of John Nash.
+
+He was a famous, actually
+mathematician.
+
+We use his tools in economics,
+but he was a mathematician.
+
+Developed these incredible
+theories, and then developed
+
+schizophrenia, went crazy.
+
+But not before he developed
+some of the most important
+
+concepts in both mathematics
+and economics.
+
+The most important is the
+Nash equilibrium.
+
+Now the best illustration we use
+of the Nash equilibrium is
+
+an example that we refer to
+as the prisoner's dilemma.
+
+And many of you will be familiar
+with this from more
+
+popular reading you've
+done in economics.
+
+But let me just go through it
+because it's important to
+
+understand it.
+
+The prisoner's dilemma.
+
+The prisoner's dilemma the title
+comes from the old way
+
+they used to make
+police movies.
+
+Where the idea is you catch
+two guys at a crime.
+
+You can't put them away unless
+one of them fesses up.
+
+So what you do is you put them
+each a separate room.
+
+And you say to the one,
+your buddy's cracked.
+
+He's going to he's going to
+sell you down the river.
+
+You better, I'm using all my
+'50s analogies, he's going to
+
+put you away for good.
+
+But if you admit that he's
+guilty and he did the crime,
+
+we'll let you off with
+a light sentence.
+
+Then they go to the other room
+and say the same thing to the
+
+other guy hoping they'll both
+rat on each other and they'll
+
+both get a sentence.
+
+So basically the idea is, let's
+say that you walk into
+
+each room and you say to each
+person, look, we have enough
+
+evidence right here, and you
+show them, to send you each to
+
+prison for a year.
+
+We would have enough evidence
+to send you each to
+
+prison for a year.
+
+But we aren't sure about
+this other thing.
+
+If you'll admit that your friend
+did this other thing,
+
+then he'll go for five years
+and you'll go free.
+
+And then we go to the friend
+and say the same thing.
+
+If you'll admit that your friend
+did the other thing
+
+he'll go five years and
+you'll go free.
+
+But if they both admit then they
+both go for two years.
+
+So if they both admit, they
+both go for two years.
+
+Now the way to write this
+down, what we do here to
+
+explain this, is we write down
+what we call a payoff matrix.
+
+So write down a payoff matrix.
+
+So the idea is we have
+prisoner A here
+
+and prisoner B here.
+
+And they each have an option.
+
+They could remain silent
+or they can talk.
+
+Silent or talk.
+
+Now if they both remain silent,
+if they both say I
+
+would never rat out my friend,
+I'm happy to go to jail for a
+
+year rather than rat out my
+friend, then they each get one
+
+year in jail.
+
+a equals 1, b equals 1.
+
+However if prisoner A rats out
+his buddy and prisoner B
+
+chooses not to rat out his
+buddy, then A gets--
+
+so I'm sorry, if prisoner
+A talks and
+
+prisoner B remains silent.
+
+Prisoner A talks, prisoner B
+remains silent, then A gets
+
+zero but B get five
+years in prison.
+
+On the other hand, if prisoner
+B rats out his friend, but a
+
+prisoner A is true and doesn't
+say anything, then prisoner A
+
+is going to get stuck with five
+years and prisoner B is
+
+going to get nothing.
+
+And if they both rat each
+other out then they
+
+both get two years.
+
+So people understand
+the payoff.
+
+Are there questions about
+the set-up here?
+
+This is complicated so
+got to make sure you
+
+understand the set-up.
+
+Now, could someone tell me, if
+A and B could truthfully
+
+cooperate, what would be the
+optimal cooperative strategy?
+
+Yeah.
+
+AUDIENCE: You both
+go for a year.
+
+PROFESSOR: Right, you'd
+both be silent.
+
+So the optimal cooperative
+strategy is clear, which is to
+
+both be silent.
+
+So if the cop said, you know
+what, we'll let you guys get
+
+together and discuss what
+you want to do first--
+
+which the cops would never be
+stupid enough to do-- but if
+
+they did and the guys can trust
+each other, then that's
+
+the optimal cooperative
+strategy.
+
+What we call optimal in the
+language of game theory, we
+
+call that the dominant
+strategy.
+
+A dominant strategy is the best
+thing to do no matter
+
+what the other guy does is
+the dominant strategy.
+
+So the dominant cooperative
+equilibrium strategy is to
+
+both stay quiet.
+
+But what's the dominant,
+non-cooperative strategy?
+
+What is the dominant
+non-cooperative strategy?
+
+So the ways with dominant
+strategy, we run through.
+
+Take prisoner A, ask
+the following.
+
+The dominant strategy is, is
+there a strategy that makes
+
+him better off regardless
+of what B does.
+
+Is there a strategy that makes
+A better off regardless of
+
+what B does.
+
+Let's go through.
+
+If A remains silent, if B
+remains silent he gets a year.
+
+If B talks he gets five years.
+
+Now compare that to prisoner
+A strategy of talking.
+
+Well if he talks he's better off
+than if he doesn't talk,
+
+if B's remaining silent.
+
+If he talks he's better
+off than if he
+
+doesn't talk if B talks.
+
+That is regardless of what B
+does, he's better off talking.
+
+Regardless of what B chooses to
+do, his dominant strategy
+
+is to talk.
+
+Because if B is silent, he's
+better off if he talks.
+
+If B talks he's better
+off if he talks.
+
+So matter what B chooses to do,
+A is better off talking.
+
+What about B?
+
+Well B, by the same logic,
+is always better
+
+off talking as well.
+
+No matter what A chooses
+to do, B is
+
+better off if he talks.
+
+So where do we end up?
+
+What ends up as the
+Nash equilibrium?
+
+The Nash equilibrium is that
+both prisoners talk.
+
+The dominant strategy for both
+prisoners is to talk.
+
+And they both end up worse off
+than they could have if they
+
+could have cooperated.
+
+So the dominant non-cooperative
+strategy is to
+
+both talk, even though if they
+could get together they'd be
+
+better both not talking.
+
+And this is basically how
+game theory works.
+
+Game theory math gets
+incredibly hard.
+
+And if you're interested,
+14.12 is one of our most
+
+popular undergraduate courses,
+game theory.
+
+It's a great course where you
+take this and go run with it
+
+for a whole semester.
+
+It gets very complicated
+mathematically.
+
+But the basic idea in game
+theory is pretty
+
+straightforward, which is just
+ask, are there dominant
+
+strategies that can be played
+by each player.
+
+If each player has a dominant
+strategy and those dominant
+
+strategies lead to a Nash
+equilibrium then you're done.
+
+Here we're in a Nash
+equilibrium.
+
+Why are we in a Nash
+Equilibrium?
+
+Because given that A has talked,
+B's strategy, which is
+
+talking is the optimal
+thing to do.
+
+Given that B has talked, A's
+strategy which is talking is
+
+the optimal thing to do.
+
+So given what the other person's
+doing, each person is
+
+doing the right thing.
+
+So you're in Nash equilibrium.
+
+Given that B has chosen
+to talk, A is talking.
+
+That's the profit maximizing
+thing to do.
+
+Given that A is talking,
+B is talking.
+
+That's the profit maximizing
+thing to do.
+
+So given the strategy the other
+player's chosen that's
+
+an equilibrium.
+
+Yeah.
+
+AUDIENCE: If they both talk and
+got 10 years would that be
+
+the Nash equilibrium.
+
+PROFESSOR: No if they both
+talk, the 10 years only
+
+happens if one talks and
+the other one doesn't.
+
+AUDIENCE: No, I mean
+like, [INAUDIBLE].
+
+PROFESSOR: Oh, if they
+both got 10 years?
+
+So let's ask that.
+
+Let's change this.
+
+Now let's just rework it.
+
+So now what's A's choice?
+
+Well A if he talks
+and B's silent,
+
+then he's better talking.
+
+But if he talks and B talks,
+he's worse talking.
+
+So then what he does depends
+on what B does.
+
+What B does is going to
+depend on what A does.
+
+And we can't obviously see the
+Nash equilibrium here.
+
+Because there's no dominant
+strategy.
+
+What you do depends on what
+the other person does.
+
+So there's no dominant
+strategy.
+
+Dominant strategies only occur
+if there's something that you
+
+should do no matter what
+the other person does.
+
+So in this case were these are
+both 2, there is a dominant
+
+strategy, It's to talk.
+
+If those are both 10 there's no
+longer a dominant strategy
+
+so we can't quickly get
+the Nash equilibrium.
+
+It's a good question.
+
+Now this is not just a cute
+example that you can use for
+
+prisoners, but actually
+explains firm
+
+behavior in many contexts.
+
+So the best example I like to
+think of of this is to think
+
+about advertising.
+
+So imagine if Coke and Pepsi,
+and imagine a world where
+
+Pepsi was as popular as Coke.
+
+That should never happen.
+
+Coke's way better.
+
+But imagine that
+was that world.
+
+So imagine a world where if
+there's no advertising then
+
+basically Pepsi and Coke would
+split the market 50-50.
+
+Imagine that set up.
+
+So if Pepsi and Coke could agree
+not to advertise they'd
+
+split the market 50-50.
+
+However, it's going to turn out
+that while that may be the
+
+dominant cooperative outcome,
+that's not the dominant
+
+non-cooperative outcome because
+each firm is better
+
+off advertising if the other
+one doesn't, or regardless.
+
+So for example, imagine the
+following payoffs matrix.
+
+I'm just making this up.
+
+But here you have Pepsi and
+here you have Coke.
+
+And imagine the payoff matrix.
+
+And the payoff matrix is if they
+don't advertise, so Pepsi
+
+can choose not to advertise,
+or it can advertise.
+
+So if they both don't advertise
+Pepsi gets 8 and
+
+Coke gets 8.
+
+I don't know what 8 is.
+
+8 is billion dollars.
+
+I'm just making up numbers
+here, doesn't matter.
+
+So $8 billion each.
+
+If they both do advertise then
+they still end up splitting
+
+the market.
+
+Because basically they're just
+as good as each other.
+
+So they both spend all the money
+advertising and just
+
+back up where they would have
+started, except they've wasted
+
+all this money in advertising.
+
+So if they both advertise they
+each earn $3 billion instead
+
+of $8 billion.
+
+That is, they each
+split the market.
+
+They end up back where they
+would have started but they
+
+pissed away a bunch of money
+advertising along the way.
+
+However if Coke advertised
+and Pepsi doesn't.
+
+Then almost everybody sees Coke,
+Coke, Coke everywhere
+
+and is like, Pepsi?
+
+Never heard of that.
+
+Coke makes $13 billion and
+Pepsi loses $2 billion.
+
+And likewise if Coke doesn't
+advertise but Pepsi does,
+
+people are like, I've
+never heard of Coke.
+
+I'm going to drink Pepsi.
+
+So Pepsi makes $13 billion and
+Coke makes minus $2 billion.
+
+Once again I just made numbers
+here so it would work, but
+
+these aren't real
+world examples.
+
+So once again we can see there
+is a dominant cooperative
+
+strategy, which is
+they both should
+
+agree let's not advertise.
+
+But if they can cooperate, then
+in fact what's the Nash
+
+equilibrium?
+
+Let's work it through.
+
+And there's no shortcuts here.
+
+You've just got to work
+this through.
+
+Let's look for Pepsi.
+
+Well Pepsi says if Coke doesn't
+advertise I'm better
+
+off advertising.
+
+If Coke does advertise, I'm
+better off advertising.
+
+So my dominant strategy
+is to advertise.
+
+Coke says, well gee, if Pepsi
+doesn't advertise I'm better
+
+off advertising.
+
+I make $13 billion instead
+of $8 billion.
+
+If Pepsi does advertise I make
+$3 billion instead of negative
+
+$2 billion.
+
+So I'm better off
+advertising too.
+
+So my dominant strategy
+is to advertise.
+
+So for both firms the dominant
+non-cooperative
+
+strategy is to advertise.
+
+So they both advertise and you
+end up in this equilibrium.
+
+It's an example of how a
+non-cooperative equilibrium
+
+can lead to what we call
+a race to the bottom.
+
+You can think of it as
+a race to the bottom.
+
+In other words, if they could
+cooperate they could just be
+
+better off.
+
+But because they can't trust the
+other, there's this race
+
+to the bottom where they
+both end up worse off.
+
+This is pretty striking.
+
+I thought they brought this out
+well in A Beautiful Mind,
+
+both the movie and the book,
+which is that all we've
+
+learned about economics
+so far is that
+
+competition is good, right?
+
+Competition is beneficial.
+
+Well here's a case, where in
+fact, at least in the firm's
+
+perspective, competition
+is bad.
+
+If they could just get together
+and cooperate they
+
+could make more money.
+
+Now, in fact, this example
+is not so far-fetched.
+
+I don't know when it
+started but it
+
+was during your lifetimes.
+
+When you were young, hard
+liquors, scotch, bourbon,
+
+whisky, et cetera, did not
+advertise on television.
+
+You never saw a Johnny Walker
+ad or anything on television
+
+until, I don't know when
+it changed maybe five
+
+or six years ago.
+
+Maybe 10 years ago,
+I don't know.
+
+But certainly in
+your lifetimes.
+
+That was not by government
+regulation.
+
+Many people thought there
+was a government
+
+regulation, they couldn't.
+
+That was not.
+
+That was a cooperative
+equilibrium where the makers
+
+of hard liquors got together and
+agreed not to advertise on
+
+TV. And they said it was in
+the "public interest" yada
+
+yada yada, but that wasn't.
+
+It was just they recognized the
+benefits of cooperating
+
+and not wasting money
+advertising on TV and
+
+competing with each other.
+
+Well that broke down some
+number of years ago.
+
+And now you see whiskey ads
+and scotch ads and other
+
+things on television.
+
+And they've moved to this
+non-cooperative equilibrium
+
+where they're all losing money
+by having this advertising.
+
+So that's in advertising.
+
+For me, once again, this is a
+hard thing, what intuition
+
+works for you.
+
+For me the intuition works best
+maybe from my scars from
+
+my dating life is thinking
+about personal decisions.
+
+So imagine that there's some
+girl named Allison.
+
+And Allison has a potential
+problem with her boyfriend.
+
+They've had a fight and now
+she's deciding whether or not
+
+to make up or break up.
+
+Now we can think of this just
+like Coke and Pepsi.
+
+Allison is going to be thinking,
+well gee, if he
+
+wants to make up with me and I
+want to make up with him then
+
+we're both better off.
+
+But if I want to make up with
+him and he doesn't want to
+
+make up with me, that makes me
+look like a total idiot.
+
+Whereas if I break up with him
+preemptively, yes it would be
+
+sad if he wanted to stay with
+me, but at least if he wanted
+
+to break up with me
+I look better.
+
+So she preemptively breaks
+up with him.
+
+John, her boyfriend, thinking
+the same thing, behaves in
+
+exactly the same way.
+
+So it could be that even though
+they both would be
+
+better off if they just said,
+look the honest truth is,
+
+we're both wrong, let's make
+up and we'll both be happy.
+
+Because they're so afraid of
+being the one being dumped,
+
+they end up breaking up.
+
+Now we all know of examples
+like this from life, where
+
+people stupidly if they could
+have just cooperated had a
+
+better outcome because they're
+so afraid of being left with
+
+the short end of the stick,
+because they don't cooperate
+
+you end up with the worst
+outcome for both.
+
+That's an example of
+a non-cooperative
+
+equilibrium in real life.
+
+Now in real life there is one
+aspect of oligopolistic
+
+non-cooperative equilibria
+that allow them to be
+
+enforced, however.
+
+That allow you to overcome
+the prisoner's dilemma.
+
+There's one thing that allows
+you to overcome the prisoner's
+
+dilemma and that's
+repeated games.
+
+Repeated games can
+help you overcome
+
+the prisoner's dilemma.
+
+Now let's take the Coke and
+Pepsi example and let's
+
+imagine that they're making
+the advertising
+
+decision every period.
+
+Every period they
+have to make an
+
+independent advertising decision.
+
+They can advertise or not
+advertise every period.
+
+And imagine Coke says to Pepsi,
+I've got the following
+
+deal for you.
+
+I commit to not advertise as
+long as you don't, but the
+
+minute you advertise I'm going
+to advertise forever.
+
+So as long as you don't
+advertise I won't.
+
+But if you ever run an ad, the
+bet's off and I'm never going
+
+to cooperate with you.
+
+I'm going to advertise
+forever.
+
+Let's think about Pepsi's choice
+in period one if Coke
+
+presents them with this deal.
+
+Let's think about Pepsi's choice
+if Coke presents them
+
+with this deal.
+
+Well one thing is they could
+say, ha ha, great Coke, good
+
+job trusting me.
+
+I'm going to screw you in
+advertising period one.
+
+So Pepsi could say, great,
+Coke's laid down arms in
+
+period one.
+
+I'm going to go and advertise.
+
+I'll make $13 billion in period
+one because Coke's
+
+wimped out.
+
+And then I'll make $3 billion
+forever after, because forever
+
+after we're both going
+to advertise.
+
+But at least I' beat them
+up that first period.
+
+However, if Pepsi says, wait
+a second, if Coke's really
+
+right, honest, then I can get
+an equilibrium where we make
+
+$8 billion forever.
+
+And certainly $8 billion forever
+a better deal than $13
+
+billion one year and
+$3 billion forever.
+
+So in fact if Coke's willing
+to live up to that promise
+
+then that is a good deal.
+
+And actually we can turn this
+non-cooperative equilibrium
+
+into a cooperative equilibrium
+through the enforcement of a
+
+repeated game.
+
+Through the fact that this game
+gets played over and over
+
+and over again you can enforce
+a cooperative equilibrium.
+
+We can come back to
+relationships again.
+
+If you're in a committed
+relationship and you know that
+
+if I say it's your fault over
+and over again, eventually
+
+person's going to leave. Then
+people say gee, I'm willing to
+
+take some of the blame and not
+always say it's your fault and
+
+we have a fight.
+
+Because I know that if I always
+say it's your fault
+
+ultimately that will break the
+relationship up and that makes
+
+me worse off then admitting it
+was my fault some of the time.
+
+It's the same logic.
+
+Yeah.
+
+AUDIENCE: Is the point of the
+game to make more than the
+
+other guy or to make as
+much as possible?
+
+PROFESSOR: Make as
+much as possible.
+
+That's a good point.
+
+I presume that the point is to
+make as much as possible.
+
+I'm ruling out cut off your
+nose to spite your face
+
+equilibria.
+
+So in other words, I'm assuming
+the goals is to
+
+maximize profits not relevant
+mark position.
+
+That's a good point.
+
+I should have made that
+assumption clear.
+
+It's the assumption we're always
+making whatever we
+
+confirm behavior is assuming
+it's profit maximization.
+
+So repeated games can enforce
+a cooperative equilibria,
+
+essentially.
+
+Even in a non-cooperative
+set up.
+
+But it turns out this
+only works if the
+
+game goes on forever.
+
+This only works if the game
+is going to go on forever.
+
+So, for example, imagine that
+Pepsi knows that in 10 years
+
+the US government is going to
+ban the advertisement of
+
+sugared sodas.
+
+The US government is going to
+finally say, look, people are
+
+too obese, no more advertising
+sugary sodas.
+
+Pepsi knows this.
+
+In 10 years that's
+going to happen.
+
+Well Pepsi's thinking,
+gee, that means in
+
+year 10 I should advertise.
+
+In that last year I should
+advertise because Coke can't
+
+punish me the next year because
+no one can advertise
+
+the next year.
+
+So I know starting after 10
+years we're both in this
+
+equilibrium because
+the government's
+
+going to enforce it.
+
+So in ninth year, right
+beforehand, right before that
+
+government ban I should
+advertise and Coke can't get
+
+me the next period because
+they don't have the
+
+tool to punish me.
+
+Well Coke, of course,
+knows Pepsi is going
+
+to behave that way.
+
+So Coke says, wait a second,
+if Pepsi's going to behave
+
+that way then I better advertise
+in the ninth period
+
+too or I'm going to get hit
+with a minus $2 billion.
+
+So I'm going to advertise
+in the ninth period too.
+
+Well Pepsi says, look, if Coke's
+going to advertise in
+
+the ninth period for sure, I may
+as well advertise in the
+
+eight period because Coke's
+going to advertise in the
+
+ninth period for sure.
+
+And by the same logic you can
+work it back that they'll both
+
+advertise right away and
+you'll end up with a
+
+non-cooperative equilibrium.
+
+That is a repeated game that
+does not enforce the
+
+cooperative equilibrium.
+
+Because by working that logic
+backwards if it ends in some
+
+realistic time frame, then you
+better off just breaking it
+
+now rather waiting for
+that period where
+
+you're the one who loses.
+
+Yeah.
+
+AUDIENCE: [INAUDIBLE]
+
+what if Pepsi [INAUDIBLE]?
+
+PROFESSOR: Exactly.
+
+If they don't then you could
+imagine that if Pepsi knows
+
+this and Coke doesn't, then
+Pepsi's optimal strategy will
+
+be to cooperate to the next to
+last period then go ahead and
+
+screw Coke and then
+Coke will lose.
+
+But presuming symmetric
+information, repeated games
+
+cannot enforce these equilibria
+if they end.
+
+So this is just an incredibly
+quick introduction to the fun
+
+that is game theory.
+
+We're going to go on now and do
+more rigorous versions of
+
+these models.
+
+But this is just to get you
+excited about the tools you
+
+can do with game theory
+with fun examples.
+
+Game theory is about taking
+these fun examples and
+
+thinking a lot harder
+about a lot.
+
+What if there's asymmetric
+information?
+
+What if the game ends long
+enough in the future that
+
+you're willing to be patient?
+
+How far off in the future does
+the game have to end to still
+
+enforce the cooperate
+equilibrium?
+
+What if there are
+three players?
+
+What if players move in
+different orders?
+
+What if one player goes first,
+the second player responds to
+
+that, is it different than if
+they go simultaneously?
+
+These are all really interesting
+issues that are
+
+very relevant to the real world
+firm behavior that you
+
+learn about game theory.
+
+So this is just to whet your
+appetite for that.
+
+Having done that we're going to
+now turn, leave aside these
+
+more interesting dynamic issues
+and focus on a specific
+
+example of a non-cooperative
+oligopoly.
+
+Because, once again, this is
+all fun intuitively, but we
+
+want you to be able to work
+through a problem.
+
+And the way to work that through
+is we're going to have
+
+to move to a specific,
+simplified example.
+
+And the example we're
+going to focus on is
+
+called the Cournot model.
+
+The Cournot model of
+non-cooperative oligopoly.
+
+The way we're going to do this
+here, is we're going to return
+
+to the example we had with
+the prisoner's dilemma.
+
+But instead of just facing two
+choices, talk or not talk,
+
+we're going to talk about firms
+facing a whole continuum
+
+of choices.
+
+Firms choosing how much they
+produce in a non-cooperative
+
+equilibria situation.
+
+So, for example, let's
+take the example
+
+they use in the book.
+
+Let's imagine there's two
+airlines that fly between New
+
+York and Chicago, American
+and United.
+
+And let's imagine for simplicity
+those are the only
+
+two airlines.
+
+Because of the hub and spoke
+system we talked about last
+
+time, let's say all the gates in
+Chicago that are available
+
+to come from New York are
+taken by two airlines--
+
+United and American.
+
+Those are your only two options
+
+flying New York to Chicago.
+
+And the question we want to ask
+is, get in that world, how
+
+do United and American decide
+how many flights to run and
+
+what price to charge?
+
+If they're monopolies
+we'd know.
+
+If it was a perfect competition
+we'd know, but how
+
+do they decide this
+all oligopolistic.
+
+The way we figure this out is
+by looking for the Nash
+
+equilibrium in this case, which
+we also call Cournot
+
+equilibrium.
+
+Which is basically the quantity
+is chosen by each
+
+firm such that holding
+all other
+
+firms' quantities constant.
+
+So each firm chooses quantity
+such that holding all other
+
+firm's quantities constant they
+are maximizing profits.
+
+So I choose a quantity such
+that holding all the other
+
+firm's quantities constant
+I'm choosing a
+
+profit-maximizing quantity.
+
+And if each firm can choose a
+quantity that makes the market
+
+function where this is met,
+then you're in Cournot
+
+equilibrium.
+
+You're in Cournot equilibrium
+when each firm has
+
+decided, I'm happy.
+
+It's the same as the
+Nash concept.
+
+I'm happy with what I'm
+producing given what everybody
+
+else is producing.
+
+If everybody feels that way
+then you're in a Nash
+
+equilibrium or a Cournot
+equilibrium.
+
+So to see this, this is not
+immediately intuitive.
+
+Let me just talk you through
+the steps of how
+
+you'd solve for this.
+
+How do you actually solve for
+a Cournot equilibrium?
+
+So basically what are the
+steps to solving?
+
+Step one for solving a Cournot
+equilibrium is to create each
+
+firm's residual demand.
+
+So compute residual demand.
+
+We talked about residual
+demand curves earlier.
+
+Which is, that's the demand for
+my firm given the quantity
+
+absorbed by other firms
+in the market.
+
+In this case it's quantities
+absorbed by the one other firm
+
+in the market, but in
+general you do this
+
+with multiple players.
+
+So first you calculate
+residual demand.
+
+Then having computed your
+residual demand you develop a
+
+marginal revenue function.
+
+You calculate your marginal
+revenue which will be a
+
+function of other firm's
+quantities.
+
+So your residual demand will
+lead you to calculate a
+
+marginal revenue function.
+
+It's a function of other
+firms' quantities.
+
+You then do the same, do one and
+two for all firms. So for
+
+each firm you end up with a
+marginal revenue function and
+
+a function of all the
+firm's quantities.
+
+Step four is you have
+n equations and n
+
+unknowns and you solve.
+
+So you develop a series of
+equation where each firm's
+
+marginal revenue function is a
+function of each other firms
+
+quantities.
+
+You get one equation like
+that for each firm.
+
+That leaves you n equations
+and n unknowns you solve.
+
+If you can solve it then
+you reach equilibrium.
+
+If you don't have a solution
+then there is no stable Nash
+
+equilibrium.
+
+But if you can solve that there
+is a Cournot equilibrium
+
+and you solve for it.
+
+So what we're going to do here
+is I'm going to illustrate
+
+this to you graphically today
+and we'll work through some
+
+more of the math of
+it next time.
+
+So we'll start by doing
+this graphically.
+
+So let's start by considering
+the case of American Airlines.
+
+Let's start with figure 16-1.
+
+Start by considering the case
+of American Airlines.
+
+And let's say that the demand
+curve in this market in our
+
+example we're going to do,
+let's say that the demand
+
+curve is of the form p
+equals 339 minus q.
+
+So there's 339,000 flights that
+are demanded each month.
+
+Each month there are 339,000
+flights demanded
+
+in the whole market.
+
+So 339,000 people want to
+go from New York to
+
+Chicago every month.
+
+And let's also assume the
+marginal cost is $147.
+
+I don't know where Perloff came
+up with these numbers,
+
+but let's just go with them.
+
+The specific numbers
+don't matter.
+
+Now what would American Airlines
+do if it was a
+
+monopolist?
+
+If American Airlines was a
+monopolist, it would set
+
+marginal revenues which are 339
+minus 2q by the same math
+
+we did before.
+
+You just multiply it through
+by q and then differentiate
+
+and you get 339 minus 2q
+equal to the marginal
+
+cost which is 147.
+
+So if it was a monopolist it
+would choose a quantity of 96
+
+and it would choose
+a price of $243.
+
+A prices of $243 which
+we would just get
+
+out the demand curve.
+
+If the quantity is 96,
+the price is $243.
+
+And that's what we see here.
+
+The marginal revenue curve
+intersects the marginal cost
+
+curve at a quantity of 96,000.
+
+You then go up to the demand
+curve to read off the price.
+
+Remember for a monopolist you've
+got to still respect
+
+the demand curve.
+
+You get the demand curve
+to read off the
+
+price, that's $243.
+
+That's what American would do if
+they were monopolist. So if
+
+they were the only folks flying
+New York to Chicago,
+
+they fly 96,000 people a month
+at a price of $243,000.
+
+However, now let's say American
+recognizes that
+
+United is in the market.
+
+And let's say American
+recognizes that United is
+
+going to deliver some amount
+of flights q sub u.
+
+They know American is going
+to do some amount of
+
+flights q sub u.
+
+They don't quite know yet what
+it is, but they know there's
+
+going to be some amount
+of flights q sub u.
+
+So the residual demand for
+American is q sub a equals
+
+total demand minus q sub u.
+
+That's their residual demand.
+
+So, for example, let's say that
+American just guesses
+
+that United will fly
+64,000 passengers.
+
+Let's say Americans says, look,
+I just know, I've got
+
+some corporate spy who's told me
+that United will fly 64,000
+
+passengers.
+
+So what you want to do is then
+you just re-solve the problem
+
+but using residual demand.
+
+So then you say, well if United
+is going to fly 64,000
+
+passengers then my residual
+demand is that price equals
+
+339 minus the quantity I sell,
+q sub a, minus q sub u, which
+
+I think is 64,000,
+which is 64.
+
+So my new residual demand is
+p equals 275 minus q sub a.
+
+That's my new residual demand.
+
+Because I thought United is
+going to sell 64,000.
+
+So instead of my demand
+being 339 minus q, now
+
+275 minus q sub a.
+
+That's what's left.
+
+So if I use this as my new
+demand function and re-solve,
+
+if this is my demand function,
+my marginal revenues are then
+
+275 minus 2 qa.
+
+My marginal cost is the
+same which is 147.
+
+So instead of my equation being
+339 minus 2q equals 147.
+
+Now it's 275 minus
+2qa equals 147.
+
+If I do that I'm going to get
+a qa star of 64,000 flights.
+
+I'm going to say, well look, if
+I was a monopolist I would
+
+have deliver 96,000 flights.
+
+But given that United is
+delivering 64,000, that's it's
+
+going to be optimal for me
+to also deliver 64,000.
+
+At 64,000 flights what's
+my price going to be?
+
+Well my price is 275 minus qa.
+
+So my price is going
+be to be $211.
+
+If I think United is delivering
+64,000 flights then
+
+I'm going to deliver 64,000
+flights at a price of $211.
+
+So that's basically how American
+would function.
+
+Now what's strange about this
+is American doesn't know how
+
+many flights United is
+going to deliver.
+
+There isn't such a thing.
+
+In fact, it's not like there's
+not some rule which says we're
+
+going to go 64,000.
+
+United is trying to figure
+this out too.
+
+So, in fact, simultaneously to
+American making this decision,
+
+United is making the
+same decision.
+
+And they're going through
+the exact same math.
+
+They're saying, well gee, given
+how much American flies,
+
+how much should we fly?
+
+They're going through
+the same math.
+
+And in fact if we assume that
+both firms have to face the
+
+same marginal cost and the same
+demand curve, then in
+
+fact they're solving a
+symmetric problem.
+
+They are also creating a
+residual demand function, but
+
+instead of being qa equals d
+minus qu, now United is making
+
+qu equals d minus qa.
+
+They're making a parallel
+residual demand function and
+
+they are solving as well.
+
+And both firms, therefore, are
+ending up with choices of
+
+quantities that depend on the
+other firm's quantity.
+
+And in particular what they're
+developing is what we call a
+
+best response curve.
+
+So figure 16-2, I skipped
+over figure 16-2.
+
+This just illustrates what
+happens when American thinks
+
+United is committing 64,000.
+
+Let's go through that
+in one second.
+
+Get through it mathematically.
+
+This is an example where
+American knows United is doing
+
+64,000 flights.
+
+So they say, well look, my
+residual demand is essentially
+
+this new line d super r.
+
+And that's what I choose
+on that new line.
+
+So that creates a new marginal
+revenue curve, mr super r.
+
+That new marginal revenue curve
+intersects marginal cost
+
+at 64,000 and that's why I
+fly only 64,000 flights
+
+at a price of $211.
+
+So you see here is one example
+of how given an amount United
+
+is flying, how American chooses
+how much to fly.
+
+Questions about that graphic
+that ties the math I did here?
+
+What figure 16-3 does is say,
+look, we can actually do this
+
+for a whole host of possible
+production levels
+
+by the other firm.
+
+And we can develop what we call
+best response curves.
+
+Best response curves are, given
+what the other firm
+
+does, what should I do.
+
+So, for example, American's best
+response curve is given
+
+that-- so on the x-axis we have
+how many thousands of
+
+flights American's passengers
+are flying per quarter.
+
+On the y-axis how many thousands
+of flights United
+
+passengers are flying
+per quarter.
+
+So, for example, if American
+decides to fly zero flights
+
+then United should fly
+96 flights, right?
+
+Then United is a monopolist.
+So that's the point on the
+
+y-axis, to 96,0 point
+on the curve.
+
+With a 0 on the x-axis,
+96 on the y-axis.
+
+If American decides to fly 0.
+
+United should fly 96.
+
+That's the monopoly case
+we just solved.
+
+If American decides to fly
+64, United should fly 64.
+
+That's the case we just
+solved as well.
+
+Likewise, American's best
+response curve is
+
+this steeper line.
+
+But it's the same thing.
+
+If United flies 0, American
+should fly 96 then at 0 on the
+
+y-axis, 96 on the x-axis.
+
+So if United flies 0 American
+should fly 96.
+
+If United flies 64, American
+should fly 64.
+
+So you can actually, literally
+trace out these curves asking
+
+at every single point, given
+what the other guy's doing,
+
+what should I do.
+
+So we solved for two points
+on this curve.
+
+We solved for the other guy
+producing zero point, which is
+
+you produce 96.
+
+We solved for the other guy
+producing 64 point which is
+
+you produce 64.
+
+That same math can be used
+to solve for every
+
+point on this curve.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+192 point.
+
+PROFESSOR: The 192
+point is it's the
+
+question is the following.
+
+At what point would American
+produce zero.
+
+How much when United have to
+produce for American to
+
+produce zero.
+
+Well they'd only produce
+zero if United
+
+was producing 192,000.
+
+Only at that point would they
+actually say, forget it, we're
+
+just going to produce zero.
+
+That's what the 192
+point means.
+
+Only if they knew United was
+producing all that much would
+
+they just drop out
+of the market.
+
+So that's the 192
+intersection.
+
+A backwards way to
+read the curves.
+
+But the bottom line, is
+essentially we can write these
+
+best response curves.
+
+They're basically the quantity
+I'm going to produce given the
+
+quantity the other
+firm produces.
+
+And the key thing is
+that these are
+
+symmetric in this example.
+
+Since the costs are the same
+and they both face the same
+
+market demand then these
+curves are symmetric.
+
+What that means is that these
+curves are having figured out
+
+one you can automatically
+draw the other.
+
+A trick for solving these
+problems is that if you have a
+
+symmetric Cournot equilibrium
+you don't need to calculate
+
+the math to find each firm's
+best response curve.
+
+Once you calculate one you know
+the other firm's just a
+
+complement of it.
+
+So having calculated American's
+best response curve
+
+we could have automatically
+drawn the United best response
+
+curve as a complement of that.
+
+The other key point is by
+drawing this diagram we can
+
+see the Cournot equilibrium.
+
+Remember Cournot equilibrium.
+
+Cournot equilibrium is where
+I'm happy with my quantity
+
+given what the other
+firm's doing.
+
+Given what the other firm's
+doing I can't
+
+make any more money.
+
+Once again, I don't care about
+market share, I just care
+
+about money.
+
+So given what the other
+firm's doing I can't
+
+make any more money.
+
+Well that happens
+at 64,000 each.
+
+Because when American is
+producing 64,000, United is
+
+happy to produce 64,000.
+
+That's their profit
+maximizing choice.
+
+If United is producing
+64,000 American's
+
+happy to produce 64,000.
+
+That's their profit
+maximizing choice.
+
+So that point of each producing
+64,000 we are in a
+
+Nash or Cournot equilibrium.
+
+Both firms are happy given what
+the other firm is doing.
+
+Both firms are profit maximizing
+given what the
+
+other firm is doing.
+
+Now basically, for example,
+another way to look at this is
+
+that you're only in equilibrium
+if you're on both
+
+firms' reaction curves.
+
+So, for example, American
+might say, look the
+
+equilibrium I like is
+where I do 96,000
+
+flights and you none.
+
+So the equilibrium I like is on
+the x-axis the point 96, 0,
+
+where I do 96,000 flights
+and you United do none.
+
+United says, however, no that's
+not optimal for me.
+
+Because if you're doing
+that, then you're
+
+charging a price of $243.
+
+So there's money to
+be made for me.
+
+I can come in and start stealing
+some of your flights.
+
+So that's not an equilibrium
+from my perspective.
+
+Might be an equilibrium
+from your perspective.
+
+You're delighted you're a
+monopolist. But not from my
+
+perspective.
+
+At that price I'll
+come in and start
+
+stealing some your business.
+
+And I'm going to start stealing
+
+some of your business.
+
+As I steal your business you are
+going to have to move up
+
+your best response curve because
+your residual demand
+
+is shrinking.
+
+And you'll only reach
+equilibrium when you're both
+
+happy with the outcome.
+
+If only one firm is happy with
+the outcome the other firm can
+
+always change its behavior,
+raise its price up or down or
+
+its quantity up or down to
+change the market share and
+
+change the outcome.
+
+So equilibrium will only be when
+you're at both firms best
+
+response curves.
+
+You'll only be at both firm's
+best response curves where
+
+they intersect.
+
+Let's stop there I'm going
+to come back next time.
+
+Jessica we should have the
+same handout next time.
+
+Let's make sure this figure
+is in the handout
+
+next time as well.
+
+And we'll come back and talk
+about this last figure and
+
+we'll do the math behind
+it as well.
\ No newline at end of file
diff --git a/eGSXsaJ-BlY.txt b/eGSXsaJ-BlY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a6ac49c1ab583c715a670a5ebadc531ebd14e770
--- /dev/null
+++ b/eGSXsaJ-BlY.txt
@@ -0,0 +1,2949 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: We're going to
+cover hashing next time.
+
+Now we're Going to
+focus on pset three
+
+because I heard
+pset three is hard
+
+so we're going to look at the
+code and try to understand it.
+
+AUDIENCE: This course is hard.
+
+PROFESSOR: I've tried
+to make it easy.
+
+I really tried.
+
+How many people
+recognize the code?
+
+Does this look familiar?
+
+One, two, three.
+
+Everyone else got
+stuck on question one?
+
+I'm not going to give you
+the answers to the psets.
+
+We are going to--
+
+AUDIENCE: [LAUGHING]
+
+PROFESSOR: Sorry.
+
+We're going to look at
+the code and understand
+
+what it does because once
+you understand what it does
+
+you can understand
+how to modify it.
+
+All right, before I do
+that, any questions?
+
+And I might not answer
+them right away,
+
+but I will keep them in mind
+while I go through the code.
+
+Are there any
+specific pin-points.
+
+AUDIENCE: The types.
+
+PROFESSOR: Yep.
+
+Covered in five minutes.
+
+Oh well.
+
+The first thing that
+I want to talk about
+
+is sweep line algorithms.
+
+We're asking you to implement
+the sweep line algorithm
+
+and we're giving you one
+that is horribly inefficient.
+
+Suppose you have some line
+segments that look like this.
+
+Sorry, drawing isn't.
+
+They look like this.
+
+And suppose you want to find
+the intersections between them.
+
+Now let's figure out
+what the algorithm
+
+that we gave you does.
+
+Did people look at
+the trace for that?
+
+Not the good trace, the trace
+that's output by the algorithm
+
+that we gave you.
+
+Does anyone understand
+what that does.
+
+AUDIENCE: I kind of get it.
+
+PROFESSOR: OK.
+
+AUDIENCE: I think what it does
+is it just hits through all
+
+the horizontal lines and it goes
+through all the vertical ones.
+
+First it goes through
+all the horizontal lines
+
+and what does it do with them?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: They get bolded
+in the visualizer which
+
+means they're added
+to the range index.
+
+So one, add all the
+horizontal lines.
+
+And two-- oh you said it goes
+through all the vertical lines
+
+after that.
+
+Any idea what it does?
+
+AUDIENCE: It looks
+for intersections.
+
+PROFESSOR: When he looks
+at a vertical line segment
+
+you'll see some blue
+square and you'll
+
+see some segments
+that are green.
+
+This is a query
+to the range index
+
+and the green segments
+are the answers
+
+and the blue square is
+the range that's queried.
+
+First add all the segments
+to the range index
+
+and then do a query.
+
+In principle sweep
+line algorithms
+
+have some geometric inputs.
+
+For example, a bunch of lines.
+
+And conceptually they
+have this vertical line
+
+that they sweep across the plane
+all the way from minus infinity
+
+to plus infinity.
+
+Now if you try to sweep
+a line continuously
+
+from minus infinity to
+plus infinity in code
+
+it might take forever.
+
+We don't really do it that way.
+
+The way we do it
+in code is you know
+
+when something interesting
+is going to happen
+
+and you only simulate what
+happens to the sweep line
+
+at that point.
+
+In this case the sweep line
+starts at minus infinity
+
+and then all the
+horizontal segments
+
+are added to our range index.
+
+And then as the sweep line
+goes across the plane, when
+
+it hits a vertical
+segment a query happens.
+
+The only times when
+the sweep line stops
+
+is first, at the beginning to
+add all the horizontal line
+
+segments, and then every time
+it hits a vertical line segment.
+
+We know this ahead
+of time so we can
+
+compute a list of
+all these coordinates
+
+of interesting things.
+
+And then we can sort them
+and then go through them
+
+and simulate the behavior
+of the sweep line that way.
+
+If you look at the code
+listing at events from there,
+
+this is the gist of it.
+
+This is what it does.
+
+It compiles a list of events.
+
+The first key in each
+event is the x, is that x?
+
+Yeah. x like this, y like this.
+
+The first case, the
+x-coordinate of an event
+
+and by sorting
+that list of events
+
+it will then process
+them in order.
+
+Events from there is responsible
+for looking at all the wires
+
+and compiling events.
+
+How does an event for a
+horizontal layer look like?
+
+Can anyone tell me?
+
+Sorry, for a horizontal wire.
+
+AUDIENCE: It will run
+across [INAUDIBLE].
+
+PROFESSOR: First off it
+looks like a list, right?
+
+It's a regular python list.
+
+And I will try to call it vector
+so that we don't confuse it
+
+with a big list
+of all the events.
+
+You said the first thing
+is the leftmost point.
+
+Right?
+
+If this segment, for
+example, starts at minus 100,
+
+this one starts at minus 95,
+this one starts at minus 90,
+
+and this one starts at minus
+50, by the way not to scale,
+
+then the leftmost
+point is minus 100.
+
+Right?
+
+This is the first
+element in the vector.
+
+And that's computed
+on line four where
+
+it goes through
+all the segments,
+
+looks at all the X-coordinates
+and chooses the minimum.
+
+What's the next
+thing in the vector?
+
+We don't have to understand why.
+
+We'll go through why in a bit.
+
+I'm just interested in what?
+
+AUDIENCE: Zero.
+
+PROFESSOR: Zero.
+
+Excellent.
+
+PROFESSOR: After that
+there is a wire ID.
+
+Each wire gets a unique ID,
+that's a number between zero
+
+and the number of wires.
+
+Say this is one, two, three.
+
+This is going to be one.
+
+And then I have the string add.
+
+And then I have the
+actual wire object.
+
+What does the vector look
+like for a query event?
+
+Sorry, what does it look
+like for a vertical wire?
+
+I'm giving away
+some of the answer.
+
+Bad, bad, bad.
+
+All right, vertical wire,
+look at the code and.
+
+AUDIENCE: It keeps
+the left [INAUDIBLE].
+
+PROFESSOR: Of the wire.
+
+OK.
+
+And?
+
+AUDIENCE: It keeps the
+x-coordinate [INAUDIBLE].
+
+PROFESSOR: A vertical wire will
+have the same X-coordinates
+
+for all the points
+on the wire, right?
+
+I don't really worry about
+which coordinate it is.
+
+This wire is at minus 50.
+
+The first element here
+is going to be minus 50.
+
+What's next?
+
+AUDIENCE: A 1.
+
+PROFESSOR: A 1.
+
+OK.
+
+And suppose this is wire ID 4.
+
+I'm going to have 4.
+
+AUDIENCE: Query.
+
+PROFESSOR: Query.
+
+AUDIENCE: And the wire.
+
+PROFESSOR: And the wire.
+
+All right, what happens with
+these in the init method, which
+
+is not shown in
+the code listing,
+
+is after the list is put
+together sort is called on it.
+
+These are all compared
+and then reordered
+
+to be sorted according to
+some ordering relationship.
+
+Does anyone know what
+the ordering relationship
+
+is for Python lists?
+
+Yeah.
+
+AUDIENCE: It starts from
+the first, from zero,
+
+and the next it goes to
+sort the same with as X 1.
+
+PROFESSOR: OK.
+
+Say if I have 1,
+2, 3 and 1, 3, 2.
+
+Sorry, and 2, 1, 2.
+
+He's going to look
+at the first element
+
+and if they are different
+than the one with the smaller
+
+element is smaller.
+
+1, 2, 3 as a vector,
+sorry, as a list,
+
+is smaller than
+2, 1, 2 as a list.
+
+If this guy becomes
+one then they're equal.
+
+Then it has to go
+to the next element,
+
+compare them and see if
+they're different we have
+
+an answer, if not
+we have to keep
+
+going all the way until
+the end of the list.
+
+This is called
+lexicographic comparison
+
+and this is the same ordering
+that you have for the words
+
+in a dictionary.
+
+Right, if you think
+of each letter
+
+as an element in a list
+and the word is the list
+
+then this is how you look
+up words in a dictionary.
+
+The reason events
+look like this is
+
+so that sort would output
+them in the right order
+
+for the next state.
+
+So, yes.
+
+AUDIENCE: Does that mean
+all the horizontal wires,
+
+does that mean that they start
+at same place even though that
+
+they don't?
+
+PROFESSOR: Yup.
+
+all the horizontal
+wires will be sorted.
+
+All these add events will be
+sorted before the query events.
+
+Yup, very good observation.
+
+This is what I'm
+trying to achieve.
+
+That's why I have this
+special value here.
+
+I go through some extra
+effort to compute it.
+
+I had to write an
+extra line of code
+
+so this is the
+motivation for it.
+
+The first key in the
+vector is the X element
+
+on the sweep line.
+
+I could've also had the
+very large negative value
+
+that something that would
+behave like minus infinity here
+
+and that would
+work just as well.
+
+By computing the left edge I
+don't have to deal with that.
+
+I don't have to worry of
+whether my negative infinity is
+
+small enough, because if
+it's not I will fail the test
+
+and that's bad.
+
+This is the x-coordinate at
+which the sweep line stops
+
+and something happens.
+
+So if all the events are
+different the x-coordinates
+
+then I have my
+ordering, I'm done.
+
+Now what if I have two
+events at the same time?
+
+For example, what if I
+have two vertical wires?
+
+The x-coordinates are
+going to be the same
+
+so I need to use something
+else to break the ties, right?
+
+The first thing that I
+use to break the ties
+
+is all add events
+have a zero here
+
+and all the query
+events have a one.
+
+And the point of
+that is if I have
+
+two events at the
+same x-coordinate,
+
+if I have a query
+and an add, I want
+
+the add to happen
+before the query.
+
+If this is the
+same this is going
+
+to be different for
+ad versus query.
+
+Does that make sense?
+
+This is how we order
+events relatively
+
+to each other on the same line.
+
+Now suppose I have
+these two wires,
+
+they're both vertical so they're
+both going to be queries.
+
+They're both at the same index.
+
+I need something else, and
+that other thing that I have
+
+is the wire ID which is
+guaranteed to be unique.
+
+I know for sure the
+comparison will stop here.
+
+And the comparison
+had better stop here
+
+because if the comparison
+gets all the way to here,
+
+wires aren't comparable so
+the code is going to crash.
+
+It stops here because the IDs
+are unique, everyone is happy.
+
+All right, do the events
+make more sense now?
+
+To complete the
+picture if you look
+
+at compute crossings,
+lines nine and ten.
+
+Line nine goes through
+the vector-- sorry,
+
+goes through the list of
+events that have been sorted
+
+and processes them
+in order so sort
+
+had better do the right job.
+
+And then it extracts the
+x-coordinate, that's here,
+
+it extracts the event
+type, that's here,
+
+and then it extracts
+the wire from here.
+
+These guys really are just
+there to help with the sorting,
+
+they're never read afterwards.
+
+AUDIENCE: Where are the
+events actually sort?
+
+I thought they just
+put into order.
+
+PROFESSOR: The events are
+sorted in an init method that's
+
+not here.
+
+It's in the piece of
+code but it's not here.
+
+And that may be a hint that
+you don't want to change it.
+
+As in you don't need to.
+
+All right, events
+look like this.
+
+Any questions about events?
+
+Everything make sense?
+
+Presumably when you write
+your own sweep line algorithm
+
+you're going to come up
+with your own events which
+
+are going to be different.
+
+You're going to change
+these methods to add
+
+your own events to the list.
+
+And then it's going
+to be sorted for you
+
+and then you're going to change
+compute crossings to process
+
+your events in the way that
+they should be processed.
+
+Let's look at the range index.
+
+What do we store
+in a range index?
+
+AUDIENCE: The horizontal wires.
+
+PROFESSOR: Horizontal wires.
+
+Very good.
+
+What's the point of storing
+horizontal wires in an index?
+
+AUDIENCE: That's when
+you want to query,
+
+the area has a line through it.
+
+PROFESSOR: For the
+algorithm that we gave you
+
+how does a query look like?
+
+Suppose I have this wire here
+and I'm doing a query for it.
+
+AUDIENCE: Just ask to
+list horizontal wires that
+
+are between that Y.
+
+PROFESSOR: Between this guy's
+top and this guy's bottom.
+
+Right?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: A query
+would look like this.
+
+Basically all the
+horizontal wires
+
+that have their y-coordinates
+between this guy and this guy.
+
+Now if I have a wire that's
+way up here or way down here
+
+I know for sure that it's not
+going to intersect this wire.
+
+Right?
+
+I don't care about it.
+
+The range index helps
+me eliminate some wires.
+
+Now, will the range index
+eliminate all the wires
+
+that don't intersect
+with this wire?
+
+No, OK.
+
+Why not?
+
+AUDIENCE: Well in
+this code it doesn't.
+
+PROFESSOR: OK, in
+this code it doesn't.
+
+We're only talking
+about this code,
+
+I'm not talking about
+the solution code
+
+that you guys have to implement.
+
+AUDIENCE: It doesn't
+because it never
+
+removes the horizontal wires.
+
+PROFESSOR: OK.
+
+What's an example of a
+query that would give me
+
+some wires that don't
+intersect my wire?
+
+AUDIENCE: Like if they're
+in between the y-axis,
+
+they're, yeah but
+they're not actually.
+
+PROFESSOR: OK.
+
+So you mean.
+
+AUDIENCE: Yeah.
+
+AUDIENCE: Negative infinity
+and infinity on the x-axis
+
+would give you a bunch of
+wires and not many of them
+
+will intersect with
+the vertical wires.
+
+AUDIENCE: If the end were a
+vertical wire, [INAUDIBLE].
+
+PROFESSOR: OK.
+
+I understood this because
+it matches what I drew.
+
+I didn't understand the
+minus infinity plus infinity.
+
+AUDIENCE: Well if you think
+about the x-axis on the bottom,
+
+if you go from all the way
+on the left to all the way
+
+on the right you're going to get
+a whole bunch of wires that are
+
+short that--
+
+PROFESSOR: Are you
+talking about one wire
+
+that's like that, or many?
+
+AUDIENCE: If you're grabbing
+from your range index.
+
+PROFESSOR: The range index
+has horizontal wires in it.
+
+AUDIENCE: Right.
+
+AUDIENCE: Are you assuming
+that they're all short?
+
+AUDIENCE: Yes.
+
+But it's not necessarily true.
+
+Some of them will be short.
+
+PROFESSOR: You're saying a lot
+of short horizontal lines--
+
+you mean like this, right?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: OK.
+
+That's what you mean.
+
+AUDIENCE: You have
+one intersection and--
+
+PROFESSOR: A ton of
+non-intersections.
+
+AUDIENCE: Exactly.
+
+PROFESSOR: OK, cool.
+
+Thank you.
+
+Doing a range query
+on this can give me
+
+a lot of false positives.
+
+That's why after
+I get them I have
+
+to make sure that
+they intersect and I
+
+can't just blindly output them.
+
+These are bad false positives,
+these are bad false positive.
+
+Now let's look at how
+the range index works.
+
+Can anyone remind me of
+what the range index does?
+
+It's a data structure, right?
+
+And it has some operations.
+
+What are the operations for it?
+
+AUDIENCE: It returns
+everything between two values.
+
+PROFESSOR: You have a list
+operation where you give it
+
+two values and it will return
+everything inside the index,
+
+in the interval between
+those two values.
+
+What else can I do?
+
+AUDIENCE: It can also
+tell you how many.
+
+It returns those keys
+and how many there are.
+
+PROFESSOR: I have
+the count and you
+
+said that I have some
+things in the index.
+
+Right?
+
+How do I get them in there?
+
+These are queries,
+I need updates.
+
+AUDIENCE: Add and remove.
+
+PROFESSOR: For the code
+that they gave you,
+
+what is the running time for
+each of these operations?
+
+AUDIENCE: It would be
+constant had to be removed.
+
+PROFESSOR: OK.
+
+Add calls the pend.
+
+Right?
+
+So that is constant.
+
+I will agree there.
+
+AUDIENCE: To remove it you
+had to shift everything.
+
+PROFESSOR: Yep.
+
+Let's start with an example.
+
+Say I have these keys
+in my range index.
+
+5, 8, 11, 13.
+
+Suppose they're magically
+inserted in this order.
+
+If I want to remove two,
+since this is an array
+
+I have to shift
+everything to the left.
+
+AUDIENCE: Yes.
+
+PROFESSOR: So that's.
+
+AUDIENCE: Order and time.
+
+PROFESSOR: OK.
+
+How about list and counts?
+
+What's the running
+time for counts?
+
+How does count work?
+
+AUDIENCE: It's not just
+through all of the keys.
+
+PROFESSOR: Count goes
+through everything and--
+
+AUDIENCE: It has to
+be order [INAUDIBLE].
+
+PROFESSOR: Cool.
+
+Count goes through all
+the keys, evaluates
+
+the predicate that checks
+whether they're in the range
+
+and then it adds up one to
+the sum for the right place.
+
+How about list?
+
+AUDIENCE: Also [INAUDIBLE].
+
+PROFESSOR: OK, that's
+a list comprehension.
+
+The code is a bit tricky,
+but it pretty much
+
+does the same thing.
+
+It goes through the list
+and it puts all the keys
+
+that are in the
+interval in the list.
+
+Now let's look at
+another version
+
+on the next page of our range
+index that is slightly better.
+
+What's the rapid
+variance for this?
+
+How is it different
+from the first one?
+
+AUDIENCE: Sorted already.
+
+PROFESSOR: Sorted already.
+
+Very good.
+
+The keys look exactly like this.
+
+Right?
+
+What is the running time for--
+let's start with add or remove,
+
+what's the running time
+for add and remove?
+
+AUDIENCE: N, order of N.
+
+PROFESSOR: Why is it order of N?
+
+AUDIENCE: No, oder log N.
+
+PROFESSOR: Why is
+it order log N.
+
+AUDIENCE: Because if it's sorted
+you can look in the middle
+
+and do a binary search.
+
+PROFESSOR: I can do a
+binary search in order
+
+to find out where
+I insert something.
+
+Right?
+
+But what if I want to
+insert zero in this?
+
+AUDIENCE: Is it
+log N plus order N?
+
+Does that make sense?
+
+Because you have to shift
+all of the [INAUDIBLE].
+
+PROFESSOR: Yeah.
+
+So worst case if I have
+to insert zero here,
+
+I have to shift everything to
+the right to make room for it.
+
+Right?
+
+So your first instinct was good.
+
+Order N. And questions?
+
+No more?
+
+Cool.
+
+How about remove?
+
+AUDIENCE: Order N.
+
+PROFESSOR: Order N.
+Why is it order N?
+
+AUDIENCE: You have to shift
+left everything to the right.
+
+PROFESSOR: Is this what
+you were going to say too?
+
+Same reason as before,
+if I want to remove 2
+
+I still have to move
+everything to the left.
+
+I can find the key that I
+want to remove very fast
+
+but then shifting
+things is still
+
+order N. OK how about count?
+
+How does count work?
+
+AUDIENCE: It's the
+same thing, isn't it?
+
+AUDIENCE: Binary
+search so it's log n.
+
+PROFESSOR: Binary
+search, so it's log n.
+
+If I look at the
+count there it's--
+
+AUDIENCE: It's
+not though, that's
+
+telling you how
+many keys between.
+
+AUDIENCE: So it's a
+simple subtraction
+
+to find the number
+of keys between.
+
+PROFESSOR: Count calls
+binary search twice
+
+and then it does a
+arithmetic operation, yes.
+
+AUDIENCE: It would be log n
+because with the count where
+
+the range is that's log n
+because you have to actually
+
+sift through it, but
+binary search you have two
+
+other operations and then
+you just do a surprise.
+
+PROFESSOR: Yep, thank you.
+
+Very good.
+
+This is log n because of
+good old binary search.
+
+How about lists?
+
+I think you were
+thinking ahead of lists.
+
+How about lists?
+
+AUDIENCE: You have to list every
+single thing that you read.
+
+AUDIENCE: You've got the
+values you might potentially
+
+have to [INAUDIBLE].
+
+AUDIENCE: Is it log n plus
+the length of the list.
+
+PROFESSOR: Yeah.
+
+I was going to do a
+nice long analysis
+
+and there's the answer.
+
+Log n plus, suppose you return
+i values from the list, i.
+
+Why does this matter?
+
+If I have a range query from
+minus infinity to plus infinity
+
+I have to create a new
+list, copy all these keys in
+
+and return them.
+
+That's order n.
+
+I can't just say it's log n.
+
+On the other hand, if the
+answers to my list queries
+
+are small, if
+they're one element,
+
+then it's going to take log
+n time to do a binary search
+
+and then order one to
+produce the list if I
+
+have a constant size list.
+
+If I just say order n
+I'm selling myself short.
+
+It's a lot better if I
+want to have short queries.
+
+What would be the best possible
+running time for lists?
+
+If I had a magic algorithm that
+works as fast as possible would
+
+I be able to run
+in order one time?
+
+AUDIENCE: No.
+
+PROFESSOR: Super fast
+magic algorithm order one.
+
+No, why not?
+
+AUDIENCE: Because you still have
+to find l and h in your array.
+
+PROFESSOR: Suppose I
+have some other data
+
+structure, a super
+magical data structure.
+
+AUDIENCE: You can do
+searches in order one time,
+
+is what you're saying.
+
+AUDIENCE: You still have
+to have the contents of it
+
+for what you're listing.
+
+It would have to be order i.
+
+PROFESSOR: Even if I
+have a super magical data
+
+structure where I can do
+everything that I want inside
+
+in order one time then
+when I produce the output
+
+I still have to
+write the output.
+
+This thing is
+going to be omega i
+
+and I can't possibly do
+any better than that.
+
+No matter what
+running time you have
+
+for list it has
+to include this i.
+
+Unless you're running time
+is order i, in which case
+
+i is smaller or equal to n.
+
+Does this look right to you?
+
+There is a small
+bug in this code.
+
+What if I do count of 4, 11.
+
+Binary search returns,
+if there's a key
+
+there it will give me
+the position of that key.
+
+And if there's no
+key it will tell me
+
+where I should insert the
+key if the key doesn't
+
+exist in theory.
+
+So if this is my array then the
+positions are 0, 1, 2, 3, 4, 5.
+
+Count of 4, 11 would do a
+binary search of 11 and see 4
+
+and then it will do a binary
+search for 4 and return 2.
+
+Right?
+
+Because if I want
+to insert 4 I would
+
+have to put it here and then
+shift everything to the right.
+
+And 4 minus 2 is 2
+therefore it's broken.
+
+AUDIENCE: Off by one block.
+
+PROFESSOR: Off by
+one block, right?
+
+Well the interesting thing about
+it is that I had this code,
+
+we actually shipped this
+code between Saturday morning
+
+and Sunday evening and
+it passed all the tests.
+
+As we go to the next
+section keep in mind
+
+that this is broken
+but it would still
+
+pass the test for our problem
+and we'll see why in a bit.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Count of 4, 11.
+
+AUDIENCE: So
+confined to them then
+
+it says that when
+you're down 5, right?
+
+Four.
+
+PROFESSOR: Four.
+
+Binary search, if
+it finds the key
+
+it returns the
+position of they key.
+
+AUDIENCE: [INAUDIBLE]
+4 divided by x, and 4,
+
+4 would it have had two?
+
+PROFESSOR: Yeah, because it
+tells me where to insert it.
+
+AUDIENCE: OK, then it is.
+
+[INAUDIBLE]
+
+PROFESSOR: Well it
+says 4 minus 2, right?
+
+The last line is high
+index minus low index?
+
+AUDIENCE: Oh, well that's
+wrong. [INAUDIBLE].
+
+AUDIENCE: So are you saying that
+it tells you where to insert it
+
+instead of actually
+inserting it.
+
+PROFESSOR: Yeah.
+
+Binary search doesn't
+insert the element.
+
+It just tells me this
+is where you put it.
+
+And then if you look at add,
+add inserts it right there.
+
+That's why binary
+search is done that way
+
+so that that would work.
+
+AUDIENCE: Can I ask
+a style question?
+
+PROFESSOR: Sure.
+
+AUDIENCE: The underscore
+before binary search,
+
+is that like saying private?
+
+PROFESSOR: Yep.
+
+AUDIENCE: OK.
+
+AUDIENCE: Wait, what
+does private mean?
+
+PROFESSOR: Private
+means that it's not
+
+part of the public
+interface of the class.
+
+If we're in a team and
+we're working on something,
+
+if I mark a method as private
+that means if you use my class,
+
+you're not supposed to call
+it because I might change
+
+it's name, I might
+delete it completely,
+
+I can do anything I want to it.
+
+But if the method is public, so
+add, remove, list, and count,
+
+those are the API or the
+public interface of the class.
+
+I guarantee that as long as the
+blit range index class exists
+
+it's going to have an
+add to remove a list
+
+and the conduct will behave
+in exactly in that way.
+
+Once you have a class
+with public methods
+
+you're not supposed
+to change them
+
+because other people
+might depend on them
+
+and that would make
+other people unhappy.
+
+We said that this range
+index holds wires.
+
+Right?
+
+So if you have these wires here
+they're not really numbers.
+
+I know how to compare
+numbers, I don't
+
+know how to compare wires.
+
+That's not something that's
+readily comparable, right?
+
+We have to bridge the gap
+between numbers or things
+
+that are comparable and wires.
+
+The way we do that is
+the key wire pair class.
+
+If you look at key
+wire pair class
+
+it has-- I will
+write it as KWP here.
+
+So it has a key and the wire.
+
+Right?
+
+That's why it's a key wire pair.
+
+And if you look at the
+comparison methods,
+
+lines 11 through 26,
+but if you look at 11
+
+through 13 pretty much
+everything else is the same.
+
+Then comparisons are
+done in a certain way.
+
+So the first
+criterion is the key.
+
+If you have two key wire pairs
+that have different keys,
+
+then the one with
+the bigger key wins.
+
+Now if they have
+the same key then
+
+this field called wire
+IDs is used to break ties.
+
+So first key and then wire ID.
+
+What's the wire ID set to?
+
+And where?
+
+Where would you set a
+field in a nice class?
+
+AUDIENCE: The constructor.
+
+PROFESSOR: In the
+constructor, very good.
+
+Where is it set?
+
+Line number?
+
+AUDIENCE: 10.
+
+PROFESSOR: Line 10.
+
+So the wire ID uses the same
+object IDs that we had earlier.
+
+So each wire has a unique
+ID that's between zero
+
+and the number of wires.
+
+This works when I insert
+my wires into the index.
+
+What's the key for
+wires, by the way?
+
+Where are wires inserted into
+the index in the algorithm
+
+that we have and what's the key?
+
+The algorithm that we gave you.
+
+Yes.
+
+AUDIENCE: The y-coordinates.
+
+PROFESSOR: The?
+
+Which one, I couldn't hear you.
+
+AUDIENCE: The y-coordinate.
+
+PROFESSOR: The y-coordinate.
+
+Can you tell me which line?
+
+The intuition is very good.
+
+You want the wires to be
+keyed by the y-coordinate
+
+so that when you a range query
+between this guy and this guy
+
+you get these wires.
+
+That's the intuition.
+
+Now what's the code?
+
+AUDIENCE: Line 13.
+
+PROFESSOR: Line?
+
+I didn't hear you well.
+
+Line?
+
+AUDIENCE: 13.
+
+PROFESSOR: 13.
+
+Wires are added to the
+index when an event of type
+
+add is processed.
+
+Right?
+
+Line 12 says if
+event type is add
+
+so that's probably what we want.
+
+And line 13 adds it to the index
+and builds the key wire repair
+
+with the key, the
+y-coordinate of the wire.
+
+Now let's look back
+at the keys and see
+
+that we have two special
+key wire repair classes.
+
+Key wire pair l and
+key wire pair h.
+
+These don't want the wire.
+
+Why would I make a wire key
+pair that doesn't want the wire?
+
+Why is that useful?
+
+AUDIENCE: You have the minimum
+and maximum wire at ease.
+
+PROFESSOR: Very
+good observation.
+
+The wire ID for the
+low key pair looks
+
+like minus infinity and the
+one for the high key pair
+
+look like plus
+infinity as long as I
+
+don't have more than
+a billion wires.
+
+What do these things not have?
+
+They don't have a wire.
+
+So if you look at key
+wire pair l and h,
+
+if you look at the initializers
+on lines two and eight,
+
+they only take a key
+they don't take a wire.
+
+This is useful in
+which situation?
+
+Where do I want to create
+an index key that's
+
+not associated
+with the real wire?
+
+AUDIENCE: When you want
+to make the list when
+
+you want to do a query.
+
+PROFESSOR: When I do a query.
+
+Very good.
+
+If I'm querying, if I have
+this vertical wire, which
+
+starts from minus
+80 to plus 80 then I
+
+would like to make a low key
+that corresponds to minus 80
+
+and a high key that
+corresponds to plus 80,
+
+but I don't have any wire with
+a horizontal coordinate of 80.
+
+Right?
+
+A hackish solution
+would be to make
+
+fake wires with
+those coordinates
+
+but if I make fake wires God
+knows where my system is going
+
+to break elsewhere.
+
+Instead the clean solution is
+to have these key wire pairs
+
+so that when I insert
+wires I have a wire
+
+and when I don't the
+wire is set to none.
+
+And the wire IDs are
+these special values,
+
+minus infinity
+and plus infinity.
+
+What's cool about setting the
+wire IDs to minus infinity
+
+and plus infinity?
+
+AUDIENCE: It's so that
+if you have a y of 80
+
+this y is at negative
+infinity so it's
+
+going to take that y also
+because its y value is
+
+[INAUDIBLE].
+
+PROFESSOR: All right.
+
+Cool.
+
+If I have a real
+key wire pair and it
+
+has a wire whose
+coordinate is 80
+
+this is going to be bigger
+than a key wire pair
+
+l with coordinate
+80 and it's going
+
+to be smaller than a key wire
+pair h with coordinate 80.
+
+If you do a query
+using this and this
+
+it's going to grab all the
+wires with coordinate 80.
+
+Does this makes sense?
+
+So what's cool about
+this in terms of coding?
+
+Do I have equal keys
+in my range index?
+
+Do I have to handle
+multiple equal keys?
+
+AUDIENCE: No because,
+actually in this case yes.
+
+PROFESSOR: Do I?
+
+AUDIENCE: Because if you
+have all the horizontal wires
+
+then it's possible
+that you have two
+
+horizontal wires at the same--
+
+PROFESSOR: If I have
+two horizontal wires,
+
+say this guy here
+and this other guy
+
+here, this guy here, what's
+the key value pair for it?
+
+Key wire pair?
+
+Let's say the coordinate is
+minus 95 and the wire ID is 2.
+
+The key wire pair is
+they key is minus 95
+
+and the wire ID is 2, right?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: And then
+for this other wire,
+
+suppose the wire ID is
+10, the coordinate is
+
+going to be minus 95 then the
+wire ID is going to be 10.
+
+So how are they
+going to compare?
+
+AUDIENCE: Then that one
+is less than that one.
+
+PROFESSOR: Yup.
+
+So even though I have two wires
+with the same y-coordinates
+
+of the key as far as the
+algorithm is concerned
+
+is the same, in
+the implementation
+
+the keys are artificially
+different because I introduce
+
+an artificial ordering on
+the wires using that wire ID.
+
+In Which case would I have the
+same key inserted in my index
+
+twice?
+
+Yes?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK.
+
+If these two wires overlap,
+say this guy ends here
+
+and this guy ends here, and if
+I put their keys into the index
+
+they're still different.
+
+AUDIENCE: Only if they're
+the same wire ID would
+
+they have the same--
+
+PROFESSOR: OK, and when do two
+wires have the same wire ID?
+
+AUDIENCE: If one of them
+was negative infinity.
+
+PROFESSOR: Let's assume
+that the infinities
+
+were in the right way.
+
+Yes?
+
+No?
+
+Wire IDs are unique.
+
+Every wire has it's own wire ID.
+
+Wires will never have
+the same wire ID.
+
+So the only case
+in which you have
+
+two equal keys in the index
+is if you insert the same wire
+
+twice.
+
+Would you ever want to do that?
+
+Probably not.
+
+You're going to the same wire
+twice from the range query
+
+and that's not useful.
+
+When implementing a data
+structure for the range index
+
+we don't have to
+deal with equal keys
+
+and that is nice because
+that's less thinking.
+
+Now when we do a query,
+will the keys in the query
+
+be in the range index?
+
+AUDIENCE: Not necessarily.
+
+PROFESSOR: How
+would I do a query
+
+if I want to do a query
+from minus 80 to plus 80?
+
+AUDIENCE: You grab all
+the horizontal wires whose
+
+y-coordinates are--
+
+PROFESSOR: You're thinking
+in the range index.
+
+I'm thinking as the
+client of the range index.
+
+So you have this
+range index class,
+
+how would you issue a
+query to the range index?
+
+AUDIENCE: The list on this page.
+
+PROFESSOR: OK.
+
+I would call the list method.
+
+And-- oh crap, I
+thought I was going
+
+to avoid doing that today.
+
+l and h are keys, right?
+
+How do I construct my keys?
+
+AUDIENCE: Use key wire pair.
+
+PROFESSOR: Key wire
+pair left of 80--
+
+sorry low, and key
+wire pair high of 80.
+
+So then I'm going
+to get to these--
+
+I don't have wires for
+this 80 coordinate.
+
+Sorry, minus 80 to
+80 because that's
+
+what the query looks like.
+
+I don't have wires
+for these coordinates
+
+so I'm going to use
+these special values
+
+and this one is smaller than
+all the wires with coordinate
+
+minus 80 and this one
+is bigger than all
+
+the wires with coordinate 80.
+
+Will these keys ever
+be in the index?
+
+Nope, we're only using
+them for updates.
+
+If you put this in
+the index then when
+
+you're getting it back and you
+try to get the wire associated
+
+with it you're
+going to get none,
+
+your code is going to crash.
+
+If I have a query will
+the keys in the query ever
+
+being the index?
+
+AUDIENCE: No.
+
+PROFESSOR: No.
+
+That means fewer border
+cases to consider
+
+when implementing query.
+
+All the keys in the
+range index are different
+
+and they keys in the query will
+never be in the range index.
+
+AUDIENCE: When
+you do the count l
+
+and h aren't in your range
+index you have to count that.
+
+PROFESSOR: Yeah.
+
+In this case that's why the
+code didn't fail any test.
+
+Because I'm not using numbers
+I'm actually using this.
+
+So for the number
+analogy this is
+
+equivalent to when I'm
+doing a count of 4,11 that
+
+would get rewritten as count of
+3, 99 and 11.01 and this works.
+
+This is what these
+two values are doing.
+
+Except if you try
+to do 0.99 and 0.01
+
+that's brittle because you
+might actually have those keys.
+
+All right, does this make sense?
+
+Any questions on this part?
+
+Nope?
+
+Yes?
+
+Yes.
+
+AUDIENCE: Is this thing
+in a count off situation
+
+where you have a
+gap in the wires
+
+but you still have a
+[INAUDIBLE] associated with it
+
+as it's going through it.
+
+PROFESSOR: Sorry,
+say that again.
+
+AUDIENCE: So with that
+example right there.
+
+PROFESSOR: Yeah.
+
+PROFESSOR: Are you
+worried about the fact
+
+that I'll have two equal keys or
+are you worried about the fact
+
+that these wires are crossing?
+
+AUDIENCE: No that
+they're not overlapping.
+
+You have a wire and you
+have a wire coming down
+
+and you have another wire.
+
+PROFESSOR: OK.
+
+This is not going
+to account for that.
+
+You have to write the
+better sweep line algorithm.
+
+AUDIENCE: OK.
+
+PROFESSOR: What
+I'm talking about
+
+now will make your
+range index faster.
+
+Or it makes your range
+index simpler to implement.
+
+AUDIENCE: OK.
+
+PROFESSOR: This is magic
+behind the scenes that
+
+makes your code smaller.
+
+You still have to implement
+the sweep line algorithm that
+
+makes sure that when
+you a range query
+
+it will either return less false
+positives or ideally no false
+
+positives.
+
+And then the code
+will be faster.
+
+But then when you
+do that, you'll
+
+see that it's still slow
+because the range index
+
+that we have here isn't optimal.
+
+Why isn't the range index
+here optimal, by the way?
+
+What can I improve about it?
+
+AUDIENCE: Add and remove.
+
+PROFESSOR: Add and remove.
+
+OK.
+
+We're using the comparison
+model because it's
+
+convenient to use
+the comparison model.
+
+You have complex objects to
+implement those six methods
+
+that you see in key
+wire pair and bam.
+
+You can do comparisons, you
+can use any data structure
+
+or algorithm that assume
+a comparison model.
+
+What's the penalty of
+the comparison model?
+
+What's the problem with it?
+
+Yes.
+
+AUDIENCE: It will be
+slower, or it will never
+
+be faster than the [INAUDIBLE].
+
+PROFESSOR: Yup.
+
+If I want to do a
+sort that is n log n.
+
+And if I want to do a
+search that is theta what?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Now what are the best
+bounds that they have for these
+
+if we can go outside
+the comparison model?
+
+Just to see if you guys are
+paying attention in lecture.
+
+So best running
+time for sort if we
+
+don't have to use
+the comparison model.
+
+AUDIENCE: n.
+
+PROFESSOR: n.
+
+OK.
+
+Best running time
+for search if we
+
+don't to use the
+comparison model.
+
+AUDIENCE: It's order
+one with [INAUDIBLE].
+
+PROFESSOR: Order
+one, with hashing.
+
+Can you do any better than that?
+
+AUDIENCE: You can
+code it as zero.
+
+[LAUGHING]
+
+PROFESSOR: Sort has
+to output an array
+
+of elements so it can
+be faster than order n.
+
+Search has to output yes
+or no so it has to output
+
+something so it has
+to be order one.
+
+So this is as fast
+as it gets, we're
+
+definitely not going
+to go faster than that.
+
+We have this extra
+log n factor that we
+
+pay if we use the comparison
+model if we don't collect
+
+more information about our keys.
+
+But in return we
+have the convenience
+
+that all we have
+to do is establish
+
+an ordering relationship.
+
+Does it make sense?
+
+Cool.
+
+Let's try to talk about
+the list pseudocode, which
+
+you might have seen
+on the pset before.
+
+And that's on the
+last page here.
+
+I can't give you a
+proof of why it works,
+
+but we can work together
+to figure out how it works
+
+and get an intuitive
+understanding.
+
+Let's get the keys
+here and let's
+
+assume we're using a regular BSD
+for implementing a range index.
+
+I'm going to put
+my keys in a BSD.
+
+8, 3, 2, 5.
+
+OK.
+
+List those two things.
+
+LCA and no list.
+
+Right.
+
+What's LCA?
+
+Suppose I want to list all
+the keys between one and six.
+
+First I'm going to call
+LCA and get some answer
+
+and then I'm going
+to call node list.
+
+What's the answer for LCA?
+
+OK.
+
+AUDIENCE: Node at three.
+
+Key value three.
+
+PROFESSOR: What is this?
+
+What's LCA?
+
+It's OK to give out an answer
+to a dumb question on the pset.
+
+So LCA is lowest
+common ancestor.
+
+Very good.
+
+It's the lowest common
+ancestor of what?
+
+AUDIENCE: Subtree of values that
+should be returned nodeless.
+
+PROFESSOR: So usually you
+have two nodes in a tree
+
+and you want to return the LCA.
+
+If I want to find out the
+LCA of 2 and 5, that is 3.
+
+If I want to find out the
+LCA of 2 and 13, that's 8.
+
+Now if the keys are not in the
+tree what does the LCA give me?
+
+AUDIENCE: It's
+where they would be.
+
+PROFESSOR: It's where they
+would be if they were inserted.
+
+Right.
+
+So 1 would be inserted here
+and 6 would be inserted here.
+
+And then their LCA is indeed 3.
+
+What does that tell me?
+
+Why is that useful?
+
+AUDIENCE: You can cut off a
+bunch of the rest of the tree
+
+so you don't have
+to look at that.
+
+PROFESSOR: A bunch of,
+or the rest of the tree?
+
+AUDIENCE: The rest of the tree.
+
+PROFESSOR: The rest of the tree.
+
+So if 1 is here and
+6 is here, then I
+
+know that all the keys--
+sorry, so 3 is to the left of 8
+
+so all the keys
+to the right of 8
+
+are going to be bigger
+than 6, for example.
+
+Right.
+
+Because 6 is here
+and it's under 8.
+
+I can throw this away.
+
+Now if this would be to
+the left of something else,
+
+because 1 is here I
+know that all the keys
+
+to the left side of that
+thing would be smaller than 1.
+
+This subtree has to have all
+the keys between 1 and 6.
+
+Yes.
+
+AUDIENCE: You don't
+have to move 8, right?
+
+Where would you move 8?
+
+PROFESSOR: Yup.
+
+So we only look at the
+subtree rooted at LCA.
+
+LCA is passed as an
+argument to node list,
+
+and node list seems to
+do sort of an-- this
+
+is a pre-ordered traversal.
+
+You look at the key, you
+look at the left node,
+
+at the left subtree, you
+look at the right subtree.
+
+Except there is some magic
+there and in some cases
+
+it doesn't go and look.
+
+Let's see what would a good case
+where it doesn't go and look
+
+like.
+
+Let's get the same tree.
+
+Suppose I want to do a
+list between 4 and 11--
+
+sorry between 4 and 10.
+
+We'll the LCA of 4 and 10?
+
+AUDIENCE: Eight.
+
+PROFESSOR: OK, so node list
+would have to start here.
+
+Suppose I'm here and I go to 3.
+
+I know 3 is smaller than 4.
+
+Do I want to go left?
+
+Everything to the left
+of 3 is smaller than 4.
+
+This entire subtree
+can be pruned.
+
+Now suppose I'm on the right
+side and I'm at the 11.
+
+11 is bigger than 10,
+do I want to go right?
+
+So if 11 is bigger
+than 10 I never
+
+want to go right
+because everything
+
+to the right of that is bigger.
+
+OK so this is how pruning works.
+
+Now if I'm at 3, can I stop?
+
+I can't stop and exit completely
+because on the right side of 3
+
+I might have keys that
+are bigger than three
+
+and that are in my interval.
+
+And in this example that
+seems to be the case.
+
+Let's look very quickly
+at the intuitive way
+
+of analyzing the
+running time for this.
+
+Suppose I have my LCA
+up here and suppose
+
+I go on a path from LCA
+to L and then-- let's
+
+not worry about the right,
+about h. h is somewhere here,
+
+the case is going
+to be symmetric.
+
+When I go down the path, after I
+go here would I ever want to go
+
+left?
+
+If this node is before
+a right turn then
+
+I know that l is going to
+be bigger than that node.
+
+Right?
+
+So I'm never going
+to take a left turn.
+
+This subtree be pruned,
+this subtree will be pruned,
+
+this subtree will be pruned.
+
+Now if I go right
+here, what happens?
+
+AUDIENCE: It's node--
+
+PROFESSOR: All
+the nodes here are
+
+going to be between l and LCA.
+
+LCA is smaller or equal to
+h so all these nodes here
+
+are guaranteed to be nodes
+that come out in my list.
+
+All right, why am I doing this?
+
+I was saying before
+that I absolutely
+
+have to have an
+order i because I
+
+have to produce the output list.
+
+If we look at the
+lines three and four,
+
+line four outputs a key right?
+
+Line four is definitely
+order i and line three
+
+is an if condition
+so we know for sure
+
+that line four is
+only going to execute
+
+four keys that are
+between l and h.
+
+This algorithm is going to
+visit some nodes in the tree.
+
+For example, if I have a list of
+4 and 10 it's going to visit 8,
+
+it's going to
+visit 3, 5, and 11.
+
+And for some of the
+nodes that are visited
+
+it's going to output them.
+
+Right this guy gets output
+and this guy gets output.
+
+The nodes that are
+outputs are order i.
+
+Those are already
+covered in the i term.
+
+And in order to get the running
+time what I need to know
+
+is, how many nodes do
+I visit that are not
+
+part of the output.
+
+Because if I end up visiting
+the entire tree then
+
+that's order n plus i.
+
+So order n.
+
+But if I only end up visiting a
+few nodes outside of the output
+
+then that might be a lot better.
+
+And here I'm trying to
+argue that I will only
+
+visit a few notes
+the outside the path.
+
+In fact, for every
+node I'm going
+
+to visit at most of the node
+and the node at its left.
+
+And then everything to the right
+of the path is between l and h,
+
+so everything to the right
+is going to be output.
+
+Everything here is in
+order i and everything here
+
+is visited in that output.
+
+And potentially everything
+on the path as well.
+
+So what's the height of a
+path in a binary search tree?
+
+Regular binary search tree?
+
+OK, and worst case.
+
+So worst case the
+height is order n.
+
+But we usually call it height
+because on average, at least,
+
+it's log n.
+
+It's somewhere
+between n and log n.
+
+What is the running time for
+lists in a binary search tree?
+
+If you buy this argument here.
+
+What is the running time?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: You could say n plus
+i and you're perfectly correct.
+
+But we can make it a bit better.
+
+What's the height of this path?
+
+AUDIENCE: h.
+
+PROFESSOR: H. What's
+the running time?
+
+AUDIENCE: h plus i.
+
+PROFESSOR: OK.
+
+Cool.
+
+Does this make sense at all?
+
+Is this too complicated?
+
+AUDIENCE: That's the
+running time for what?
+
+PROFESSOR: This is the
+running time for lists.
+
+All right so, questions?
+
+Is this too far out?
+
+Did I lose you guys completely?
+
+Makes perfect sense.
+
+I like that.
+
+AUDIENCE: It's oder
+n plus i because it
+
+could have up to any
+nodes on it, right?
+
+PROFESSOR: Yup.
+
+AUDIENCE: And then it's
+order i because you
+
+have to add that
+[INAUDIBLE] of nodes anyway.
+
+It's order h.
+
+PROFESSOR: I'm saying that it's
+a binary search tree of height
+
+h and if h is better
+than n then I'm
+
+going to do much better
+than n and that's
+
+why I'm putting that h there.
+
+AUDIENCE: OK, that makes sense.
+
+I think it's just a ltitle
+confusing at that part,
+
+but the [INAUDIBLE] makes
+sense because of course
+
+that's a smaller
+node you're not going
+
+to look at the
+left portion you're
+
+going to look at the
+right because it's bigger
+
+than your smaller
+[INAUDIBLE], right?
+
+So if you go to the
+right, that means that--
+
+PROFESSOR: Here I know that
+l is on the left, right?
+
+So l is smaller than this key.
+
+Everything to the right of
+this key is between l and LCA.
+
+LCA is smaller or equal to h.
+
+Everything here is
+between l and h,
+
+so all the nodes here
+are going to be output.
+
+All the nodes here count as i.
+
+AUDIENCE: OK.
+
+PROFESSOR: Now when I turn left
+here, this is smaller than l.
+
+This is smaller than l
+because l is on the right.
+
+This thing is
+going to be pruned.
+
+So I will visit the parent,
+this node, and that's it.
+
+I'm not going to look down.
+
+And this is how the
+nodes look like.
+
+Everything that's to
+the left of the path
+
+is not visited, everything
+that's to the right it open.
+
+Any more questions?
+
+I hope you get it
+right on pset then.
+
+Thanks guys.
\ No newline at end of file
diff --git a/f866lUTRXE4.txt b/f866lUTRXE4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..05a769a5ac45a8b20a56f3c6f8199bdb0d92a730
--- /dev/null
+++ b/f866lUTRXE4.txt
@@ -0,0 +1,427 @@
+align:start position:0%
+ 
+given a set of symbols and their
+
+ align:start position:0%
+given a set of symbols and their
+ 
+
+ align:start position:0%
+given a set of symbols and their
+probabilities Huffman's algorithm tells
+
+ align:start position:0%
+probabilities Huffman's algorithm tells
+ 
+
+ align:start position:0%
+probabilities Huffman's algorithm tells
+us how to construct an optimal variable
+
+ align:start position:0%
+us how to construct an optimal variable
+ 
+
+ align:start position:0%
+us how to construct an optimal variable
+length encoding by optimal we mean that
+
+ align:start position:0%
+length encoding by optimal we mean that
+ 
+
+ align:start position:0%
+length encoding by optimal we mean that
+assuming we're encoding each symbol one
+
+ align:start position:0%
+assuming we're encoding each symbol one
+ 
+
+ align:start position:0%
+assuming we're encoding each symbol one
+at a time no other variable length code
+
+ align:start position:0%
+at a time no other variable length code
+ 
+
+ align:start position:0%
+at a time no other variable length code
+will have a shorter expected length the
+
+ align:start position:0%
+will have a shorter expected length the
+ 
+
+ align:start position:0%
+will have a shorter expected length the
+algorithm builds the binary tree for the
+
+ align:start position:0%
+algorithm builds the binary tree for the
+ 
+
+ align:start position:0%
+algorithm builds the binary tree for the
+encoding from the bottom up start by
+
+ align:start position:0%
+encoding from the bottom up start by
+ 
+
+ align:start position:0%
+encoding from the bottom up start by
+choosing the two symbols with the
+
+ align:start position:0%
+choosing the two symbols with the
+ 
+
+ align:start position:0%
+choosing the two symbols with the
+smallest probability which means they
+
+ align:start position:0%
+smallest probability which means they
+ 
+
+ align:start position:0%
+smallest probability which means they
+have the highest information content and
+
+ align:start position:0%
+have the highest information content and
+ 
+
+ align:start position:0%
+have the highest information content and
+should have the longest encoding if
+
+ align:start position:0%
+should have the longest encoding if
+ 
+
+ align:start position:0%
+should have the longest encoding if
+anywhere along the way two symbols have
+
+ align:start position:0%
+anywhere along the way two symbols have
+ 
+
+ align:start position:0%
+anywhere along the way two symbols have
+the same probability simply choose one
+
+ align:start position:0%
+the same probability simply choose one
+ 
+
+ align:start position:0%
+the same probability simply choose one
+arbitrarily in our running example the
+
+ align:start position:0%
+arbitrarily in our running example the
+ 
+
+ align:start position:0%
+arbitrarily in our running example the
+two symbols with the lowest probability
+
+ align:start position:0%
+two symbols with the lowest probability
+ 
+
+ align:start position:0%
+two symbols with the lowest probability
+are C and D combine the symbols as a
+
+ align:start position:0%
+are C and D combine the symbols as a
+ 
+
+ align:start position:0%
+are C and D combine the symbols as a
+binary sub tree with one branch labeled
+
+ align:start position:0%
+binary sub tree with one branch labeled
+ 
+
+ align:start position:0%
+binary sub tree with one branch labeled
+zero and the other one it doesn't matter
+
+ align:start position:0%
+zero and the other one it doesn't matter
+ 
+
+ align:start position:0%
+zero and the other one it doesn't matter
+which labels go with which branch remove
+
+ align:start position:0%
+which labels go with which branch remove
+ 
+
+ align:start position:0%
+which labels go with which branch remove
+C and D from our list of symbols and
+
+ align:start position:0%
+C and D from our list of symbols and
+ 
+
+ align:start position:0%
+C and D from our list of symbols and
+replace them with a newly constructed
+
+ align:start position:0%
+replace them with a newly constructed
+ 
+
+ align:start position:0%
+replace them with a newly constructed
+sub tree whose root has the Associated
+
+ align:start position:0%
+sub tree whose root has the Associated
+ 
+
+ align:start position:0%
+sub tree whose root has the Associated
+probability 1/6 the sum of the
+
+ align:start position:0%
+probability 1/6 the sum of the
+ 
+
+ align:start position:0%
+probability 1/6 the sum of the
+probability of its two branches now
+
+ align:start position:0%
+probability of its two branches now
+ 
+
+ align:start position:0%
+probability of its two branches now
+continue at each step choosing the two
+
+ align:start position:0%
+continue at each step choosing the two
+ 
+
+ align:start position:0%
+continue at each step choosing the two
+symbols and/or sub trees with the lowest
+
+ align:start position:0%
+symbols and/or sub trees with the lowest
+ 
+
+ align:start position:0%
+symbols and/or sub trees with the lowest
+probabilities combining the choices into
+
+ align:start position:0%
+probabilities combining the choices into
+ 
+
+ align:start position:0%
+probabilities combining the choices into
+a new sub tree at this point in our
+
+ align:start position:0%
+a new sub tree at this point in our
+ 
+
+ align:start position:0%
+a new sub tree at this point in our
+example the symbol a has the probability
+
+ align:start position:0%
+example the symbol a has the probability
+ 
+
+ align:start position:0%
+example the symbol a has the probability
+1/3 the symbol B the probability 1/2 and
+
+ align:start position:0%
+1/3 the symbol B the probability 1/2 and
+ 
+
+ align:start position:0%
+1/3 the symbol B the probability 1/2 and
+the CD sub tree probability 1/6 so we'll
+
+ align:start position:0%
+the CD sub tree probability 1/6 so we'll
+ 
+
+ align:start position:0%
+the CD sub tree probability 1/6 so we'll
+combine a with the CD sub tree on the
+
+ align:start position:0%
+combine a with the CD sub tree on the
+ 
+
+ align:start position:0%
+combine a with the CD sub tree on the
+final step we only have two choices left
+
+ align:start position:0%
+final step we only have two choices left
+ 
+
+ align:start position:0%
+final step we only have two choices left
+B and the ACD subtree which we combine
+
+ align:start position:0%
+B and the ACD subtree which we combine
+ 
+
+ align:start position:0%
+B and the ACD subtree which we combine
+in a new sub tree whose root then
+
+ align:start position:0%
+in a new sub tree whose root then
+ 
+
+ align:start position:0%
+in a new sub tree whose root then
+becomes the root of the tree
+
+ align:start position:0%
+becomes the root of the tree
+ 
+
+ align:start position:0%
+becomes the root of the tree
+representing the optimal variable length
+
+ align:start position:0%
+representing the optimal variable length
+ 
+
+ align:start position:0%
+representing the optimal variable length
+code happily this is the code we've been
+
+ align:start position:0%
+code happily this is the code we've been
+ 
+
+ align:start position:0%
+code happily this is the code we've been
+using all along as mentioned above we
+
+ align:start position:0%
+using all along as mentioned above we
+ 
+
+ align:start position:0%
+using all along as mentioned above we
+can produce a number of different
+
+ align:start position:0%
+can produce a number of different
+ 
+
+ align:start position:0%
+can produce a number of different
+variable length codes by swapping the 0
+
+ align:start position:0%
+variable length codes by swapping the 0
+ 
+
+ align:start position:0%
+variable length codes by swapping the 0
+and 1 labels on any of the sub tree
+
+ align:start position:0%
+and 1 labels on any of the sub tree
+ 
+
+ align:start position:0%
+and 1 labels on any of the sub tree
+branches but all those encoding x' would
+
+ align:start position:0%
+branches but all those encoding x' would
+ 
+
+ align:start position:0%
+branches but all those encoding x' would
+have the same expected length which is
+
+ align:start position:0%
+have the same expected length which is
+ 
+
+ align:start position:0%
+have the same expected length which is
+determined by the distance of each
+
+ align:start position:0%
+determined by the distance of each
+ 
+
+ align:start position:0%
+determined by the distance of each
+symbol from the root of the tree not the
+
+ align:start position:0%
+symbol from the root of the tree not the
+ 
+
+ align:start position:0%
+symbol from the root of the tree not the
+labels along the path from root to leaf
+
+ align:start position:0%
+labels along the path from root to leaf
+ 
+
+ align:start position:0%
+labels along the path from root to leaf
+so all these different encodings are
+
+ align:start position:0%
+so all these different encodings are
+ 
+
+ align:start position:0%
+so all these different encodings are
+equivalent in terms of their efficiency
+
+ align:start position:0%
+equivalent in terms of their efficiency
+ 
+
+ align:start position:0%
+equivalent in terms of their efficiency
+now try your hand at Huffman's algorithm
+
+ align:start position:0%
+now try your hand at Huffman's algorithm
+ 
+
+ align:start position:0%
+now try your hand at Huffman's algorithm
+to construct optimal variable length
+
+ align:start position:0%
+to construct optimal variable length
+ 
+
+ align:start position:0%
+to construct optimal variable length
+encoding x'
\ No newline at end of file
diff --git a/fAeShezAGLE.txt b/fAeShezAGLE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2329418976e42ade44725cabd99b6f91bfcf6690
--- /dev/null
+++ b/fAeShezAGLE.txt
@@ -0,0 +1,11767 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer high quality educational
+
+ align:start position:0%
+to offer high quality educational
+ 
+
+ align:start position:0%
+to offer high quality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu today we're going to start
+
+ align:start position:0%
+ocw.mit.edu today we're going to start
+ 
+
+ align:start position:0%
+ocw.mit.edu today we're going to start
+with a simple problem that many of you
+
+ align:start position:0%
+with a simple problem that many of you
+ 
+
+ align:start position:0%
+with a simple problem that many of you
+may have already encountered for example
+
+ align:start position:0%
+may have already encountered for example
+ 
+
+ align:start position:0%
+may have already encountered for example
+when you got a student loan or or if
+
+ align:start position:0%
+when you got a student loan or or if
+ 
+
+ align:start position:0%
+when you got a student loan or or if
+your family took a loan out on your
+
+ align:start position:0%
+your family took a loan out on your
+ 
+
+ align:start position:0%
+your family took a loan out on your
+house you know a home mortgage loan and
+
+ align:start position:0%
+house you know a home mortgage loan and
+ 
+
+ align:start position:0%
+house you know a home mortgage loan and
+it's the problem of pricing an annuity
+
+ align:start position:0%
+it's the problem of pricing an annuity
+ 
+
+ align:start position:0%
+it's the problem of pricing an annuity
+an annuity is a financial instrument
+
+ align:start position:0%
+an annuity is a financial instrument
+ 
+
+ align:start position:0%
+an annuity is a financial instrument
+that pays a fixed amount of money every
+
+ align:start position:0%
+that pays a fixed amount of money every
+ 
+
+ align:start position:0%
+that pays a fixed amount of money every
+year for some number of years and it has
+
+ align:start position:0%
+year for some number of years and it has
+ 
+
+ align:start position:0%
+year for some number of years and it has
+a value associated with it for example
+
+ align:start position:0%
+a value associated with it for example
+ 
+
+ align:start position:0%
+a value associated with it for example
+with the student loan the value is the
+
+ align:start position:0%
+with the student loan the value is the
+ 
+
+ align:start position:0%
+with the student loan the value is the
+amount of money they gave you to pay MIT
+
+ align:start position:0%
+amount of money they gave you to pay MIT
+ 
+
+ align:start position:0%
+amount of money they gave you to pay MIT
+then later in life every year or every
+
+ align:start position:0%
+then later in life every year or every
+ 
+
+ align:start position:0%
+then later in life every year or every
+month you're going to send them a check
+
+ align:start position:0%
+month you're going to send them a check
+ 
+
+ align:start position:0%
+month you're going to send them a check
+all right and you want to sort of equate
+
+ align:start position:0%
+all right and you want to sort of equate
+ 
+
+ align:start position:0%
+all right and you want to sort of equate
+those two things to find out you know
+
+ align:start position:0%
+those two things to find out you know
+ 
+
+ align:start position:0%
+those two things to find out you know
+are you getting enough money for the
+
+ align:start position:0%
+are you getting enough money for the
+ 
+
+ align:start position:0%
+are you getting enough money for the
+money you're going to pay back monthly
+
+ align:start position:0%
+money you're going to pay back monthly
+ 
+
+ align:start position:0%
+money you're going to pay back monthly
+sometime in the future so let's define
+
+ align:start position:0%
+sometime in the future so let's define
+ 
+
+ align:start position:0%
+sometime in the future so let's define
+this and there's a lot of variations on
+
+ align:start position:0%
+this and there's a lot of variations on
+ 
+
+ align:start position:0%
+this and there's a lot of variations on
+annuities but we'll start with one
+
+ align:start position:0%
+annuities but we'll start with one
+ 
+
+ align:start position:0%
+annuities but we'll start with one
+that's called an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Nye
+
+ align:start position:0%
+Nye
+ 
+
+ align:start position:0%
+Nye
+M
+
+ align:start position:0%
+M
+ 
+
+ align:start position:0%
+M
+payment annuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it works by
+
+ align:start position:0%
+and it works by
+ 
+
+ align:start position:0%
+and it works by
+paying
+
+ align:start position:0%
+paying
+ 
+
+ align:start position:0%
+paying
+M at the start of each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year and it lasts for n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+years now usually n is finite but not
+
+ align:start position:0%
+years now usually n is finite but not
+ 
+
+ align:start position:0%
+years now usually n is finite but not
+always and in a few minutes we'll talk
+
+ align:start position:0%
+always and in a few minutes we'll talk
+ 
+
+ align:start position:0%
+always and in a few minutes we'll talk
+about the case when it's
+
+ align:start position:0%
+about the case when it's
+ 
+
+ align:start position:0%
+about the case when it's
+infinite uh but this includes you know
+
+ align:start position:0%
+infinite uh but this includes you know
+ 
+
+ align:start position:0%
+infinite uh but this includes you know
+home mortgages where you pay every month
+
+ align:start position:0%
+home mortgages where you pay every month
+ 
+
+ align:start position:0%
+home mortgages where you pay every month
+for 30 years meab bucks the lottery they
+
+ align:start position:0%
+for 30 years meab bucks the lottery they
+ 
+
+ align:start position:0%
+for 30 years meab bucks the lottery they
+don't actually give you the million
+
+ align:start position:0%
+don't actually give you the million
+ 
+
+ align:start position:0%
+don't actually give you the million
+dollars they give you $50,000 per year
+
+ align:start position:0%
+dollars they give you $50,000 per year
+ 
+
+ align:start position:0%
+dollars they give you $50,000 per year
+for 20 years and call it a million bucks
+
+ align:start position:0%
+for 20 years and call it a million bucks
+ 
+
+ align:start position:0%
+for 20 years and call it a million bucks
+retirement plans you know you pay in
+
+ align:start position:0%
+retirement plans you know you pay in
+ 
+
+ align:start position:0%
+retirement plans you know you pay in
+every year and then you get some big
+
+ align:start position:0%
+every year and then you get some big
+ 
+
+ align:start position:0%
+every year and then you get some big
+lump suum later life insurance benefits
+
+ align:start position:0%
+lump suum later life insurance benefits
+ 
+
+ align:start position:0%
+lump suum later life insurance benefits
+you know and so forth now if you go to
+
+ align:start position:0%
+you know and so forth now if you go to
+ 
+
+ align:start position:0%
+you know and so forth now if you go to
+Wall Street this is a big deal a lot of
+
+ align:start position:0%
+Wall Street this is a big deal a lot of
+ 
+
+ align:start position:0%
+Wall Street this is a big deal a lot of
+the stuff that happens on Wall Street
+
+ align:start position:0%
+the stuff that happens on Wall Street
+ 
+
+ align:start position:0%
+the stuff that happens on Wall Street
+involves annuities in one form or
+
+ align:start position:0%
+involves annuities in one form or
+ 
+
+ align:start position:0%
+involves annuities in one form or
+another packaging them all up uh and in
+
+ align:start position:0%
+another packaging them all up uh and in
+ 
+
+ align:start position:0%
+another packaging them all up uh and in
+fact we we'll look at later when we do
+
+ align:start position:0%
+fact we we'll look at later when we do
+ 
+
+ align:start position:0%
+fact we we'll look at later when we do
+probability it was how these things were
+
+ align:start position:0%
+probability it was how these things were
+ 
+
+ align:start position:0%
+probability it was how these things were
+packaged and sold that led to the S
+
+ align:start position:0%
+packaged and sold that led to the S
+ 
+
+ align:start position:0%
+packaged and sold that led to the S
+subprime mortgage disaster and we'll see
+
+ align:start position:0%
+subprime mortgage disaster and we'll see
+ 
+
+ align:start position:0%
+subprime mortgage disaster and we'll see
+how some confusion over Independence
+
+ align:start position:0%
+how some confusion over Independence
+ 
+
+ align:start position:0%
+how some confusion over Independence
+when you look at random variables led to
+
+ align:start position:0%
+when you look at random variables led to
+ 
+
+ align:start position:0%
+when you look at random variables led to
+the global recession a real disaster of
+
+ align:start position:0%
+the global recession a real disaster of
+ 
+
+ align:start position:0%
+the global recession a real disaster of
+course some people who understood how
+
+ align:start position:0%
+course some people who understood how
+ 
+
+ align:start position:0%
+course some people who understood how
+all that worked made hundreds of
+
+ align:start position:0%
+all that worked made hundreds of
+ 
+
+ align:start position:0%
+all that worked made hundreds of
+billions of dollars at the same time so
+
+ align:start position:0%
+billions of dollars at the same time so
+ 
+
+ align:start position:0%
+billions of dollars at the same time so
+it was sort of a money went from one
+
+ align:start position:0%
+it was sort of a money went from one
+ 
+
+ align:start position:0%
+it was sort of a money went from one
+place to another so it's pretty
+
+ align:start position:0%
+place to another so it's pretty
+ 
+
+ align:start position:0%
+place to another so it's pretty
+important to understand how much this is
+
+ align:start position:0%
+important to understand how much this is
+ 
+
+ align:start position:0%
+important to understand how much this is
+worth what is this instrument a piece of
+
+ align:start position:0%
+worth what is this instrument a piece of
+ 
+
+ align:start position:0%
+worth what is this instrument a piece of
+paper that says it'll pay you MLL at the
+
+ align:start position:0%
+paper that says it'll pay you MLL at the
+ 
+
+ align:start position:0%
+paper that says it'll pay you MLL at the
+beginning of each year for n years what
+
+ align:start position:0%
+beginning of each year for n years what
+ 
+
+ align:start position:0%
+beginning of each year for n years what
+is that worth today for example say I
+
+ align:start position:0%
+is that worth today for example say I
+ 
+
+ align:start position:0%
+is that worth today for example say I
+gave you a choice the mega buuck Choice
+
+ align:start position:0%
+gave you a choice the mega buuck Choice
+ 
+
+ align:start position:0%
+gave you a choice the mega buuck Choice
+50,000 a year for 20 years or a million
+
+ align:start position:0%
+50,000 a year for 20 years or a million
+ 
+
+ align:start position:0%
+50,000 a year for 20 years or a million
+dollars today how many people would
+
+ align:start position:0%
+dollars today how many people would
+ 
+
+ align:start position:0%
+dollars today how many people would
+prefer the 50,000 a year for 20
+
+ align:start position:0%
+prefer the 50,000 a year for 20
+ 
+
+ align:start position:0%
+prefer the 50,000 a year for 20
+years few of you how many would prefer
+
+ align:start position:0%
+years few of you how many would prefer
+ 
+
+ align:start position:0%
+years few of you how many would prefer
+the million bucks right up front
+
+ align:start position:0%
+the million bucks right up front
+ 
+
+ align:start position:0%
+the million bucks right up front
+ah yeah much better okay always better
+
+ align:start position:0%
+ah yeah much better okay always better
+ 
+
+ align:start position:0%
+ah yeah much better okay always better
+to have the cash in hand because there's
+
+ align:start position:0%
+to have the cash in hand because there's
+ 
+
+ align:start position:0%
+to have the cash in hand because there's
+things like inflation pretty low now um
+
+ align:start position:0%
+things like inflation pretty low now um
+ 
+
+ align:start position:0%
+things like inflation pretty low now um
+interest you know you can put the money
+
+ align:start position:0%
+interest you know you can put the money
+ 
+
+ align:start position:0%
+interest you know you can put the money
+in the bank or invest it and make some
+
+ align:start position:0%
+in the bank or invest it and make some
+ 
+
+ align:start position:0%
+in the bank or invest it and make some
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+hopefully um so the million dollars
+
+ align:start position:0%
+hopefully um so the million dollars
+ 
+
+ align:start position:0%
+hopefully um so the million dollars
+today is a lot better which is why the
+
+ align:start position:0%
+today is a lot better which is why the
+ 
+
+ align:start position:0%
+today is a lot better which is why the
+state pays you 20 50 Grand a year for 20
+
+ align:start position:0%
+state pays you 20 50 Grand a year for 20
+ 
+
+ align:start position:0%
+state pays you 20 50 Grand a year for 20
+years it's better for them and they call
+
+ align:start position:0%
+years it's better for them and they call
+ 
+
+ align:start position:0%
+years it's better for them and they call
+it a million bucks so that was pretty
+
+ align:start position:0%
+it a million bucks so that was pretty
+ 
+
+ align:start position:0%
+it a million bucks so that was pretty
+clear but what if I gave you this
+
+ align:start position:0%
+clear but what if I gave you this
+ 
+
+ align:start position:0%
+clear but what if I gave you this
+option 700 Grand today
+
+ align:start position:0%
+option 700 Grand today
+ 
+
+ align:start position:0%
+option 700 Grand today
+or 50 Grand a year for 20 years how many
+
+ align:start position:0%
+or 50 Grand a year for 20 years how many
+ 
+
+ align:start position:0%
+or 50 Grand a year for 20 years how many
+people want the cash up front 700 Grand
+
+ align:start position:0%
+people want the cash up front 700 Grand
+ 
+
+ align:start position:0%
+people want the cash up front 700 Grand
+only a few how many people want 20 grand
+
+ align:start position:0%
+only a few how many people want 20 grand
+ 
+
+ align:start position:0%
+only a few how many people want 20 grand
+50 Grand a year for 20
+
+ align:start position:0%
+50 Grand a year for 20
+ 
+
+ align:start position:0%
+50 Grand a year for 20
+years all right we're almost that's
+
+ align:start position:0%
+years all right we're almost that's
+ 
+
+ align:start position:0%
+years all right we're almost that's
+pretty close to halfway how about 500
+
+ align:start position:0%
+pretty close to halfway how about 500
+ 
+
+ align:start position:0%
+pretty close to halfway how about 500
+Grand today versus 50 Grand a year for
+
+ align:start position:0%
+Grand today versus 50 Grand a year for
+ 
+
+ align:start position:0%
+Grand today versus 50 Grand a year for
+20 years how many want five half a
+
+ align:start position:0%
+20 years how many want five half a
+ 
+
+ align:start position:0%
+20 years how many want five half a
+million
+
+ align:start position:0%
+million
+ 
+
+ align:start position:0%
+million
+today a lot of people like the cash you
+
+ align:start position:0%
+today a lot of people like the cash you
+ 
+
+ align:start position:0%
+today a lot of people like the cash you
+know it's this kind of a time you have
+
+ align:start position:0%
+know it's this kind of a time you have
+ 
+
+ align:start position:0%
+know it's this kind of a time you have
+the recession it's a disaster on Wall
+
+ align:start position:0%
+the recession it's a disaster on Wall
+ 
+
+ align:start position:0%
+the recession it's a disaster on Wall
+Street you know on Wall Street they like
+
+ align:start position:0%
+Street you know on Wall Street they like
+ 
+
+ align:start position:0%
+Street you know on Wall Street they like
+the cash how many want instead of a half
+
+ align:start position:0%
+the cash how many want instead of a half
+ 
+
+ align:start position:0%
+the cash how many want instead of a half
+a million upfront 50 Grand a year for 20
+
+ align:start position:0%
+a million upfront 50 Grand a year for 20
+ 
+
+ align:start position:0%
+a million upfront 50 Grand a year for 20
+years right now we're about halfway all
+
+ align:start position:0%
+years right now we're about halfway all
+ 
+
+ align:start position:0%
+years right now we're about halfway all
+right well that's that's pretty good so
+
+ align:start position:0%
+right well that's that's pretty good so
+ 
+
+ align:start position:0%
+right well that's that's pretty good so
+we're going to find out what you should
+
+ align:start position:0%
+we're going to find out what you should
+ 
+
+ align:start position:0%
+we're going to find out what you should
+pay or at least one way of of estimating
+
+ align:start position:0%
+pay or at least one way of of estimating
+ 
+
+ align:start position:0%
+pay or at least one way of of estimating
+that now to do that we got to figure out
+
+ align:start position:0%
+that now to do that we got to figure out
+ 
+
+ align:start position:0%
+that now to do that we got to figure out
+what $1 today is worth in a
+
+ align:start position:0%
+what $1 today is worth in a
+ 
+
+ align:start position:0%
+what $1 today is worth in a
+year okay and to do that we make an
+
+ align:start position:0%
+year okay and to do that we make an
+ 
+
+ align:start position:0%
+year okay and to do that we make an
+assumption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the assumption is that there's a
+
+ align:start position:0%
+and the assumption is that there's a
+ 
+
+ align:start position:0%
+and the assumption is that there's a
+fixed we'll call it an interest
+
+ align:start position:0%
+fixed we'll call it an interest
+ 
+
+ align:start position:0%
+fixed we'll call it an interest
+rate it's sort of the the devaluation of
+
+ align:start position:0%
+rate it's sort of the the devaluation of
+ 
+
+ align:start position:0%
+rate it's sort of the the devaluation of
+the money per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year we're going to call it P later
+
+ align:start position:0%
+year we're going to call it P later
+ 
+
+ align:start position:0%
+year we're going to call it P later
+we'll plug in values for p but you could
+
+ align:start position:0%
+we'll plug in values for p but you could
+ 
+
+ align:start position:0%
+we'll plug in values for p but you could
+think of it is like 6% 1% you know it's
+
+ align:start position:0%
+think of it is like 6% 1% you know it's
+ 
+
+ align:start position:0%
+think of it is like 6% 1% you know it's
+the money if you put money in a bank
+
+ align:start position:0%
+the money if you put money in a bank
+ 
+
+ align:start position:0%
+the money if you put money in a bank
+they'll give you some percent back every
+
+ align:start position:0%
+they'll give you some percent back every
+ 
+
+ align:start position:0%
+they'll give you some percent back every
+year and of course the fact that
+
+ align:start position:0%
+year and of course the fact that
+ 
+
+ align:start position:0%
+year and of course the fact that
+different people have different ideas of
+
+ align:start position:0%
+different people have different ideas of
+ 
+
+ align:start position:0%
+different people have different ideas of
+what this would be allows people to make
+
+ align:start position:0%
+what this would be allows people to make
+ 
+
+ align:start position:0%
+what this would be allows people to make
+money on Wall Street as we'll see a
+
+ align:start position:0%
+money on Wall Street as we'll see a
+ 
+
+ align:start position:0%
+money on Wall Street as we'll see a
+slight difference in in P can make big
+
+ align:start position:0%
+slight difference in in P can make big
+ 
+
+ align:start position:0%
+slight difference in in P can make big
+differences in what the annuity is worth
+
+ align:start position:0%
+differences in what the annuity is worth
+ 
+
+ align:start position:0%
+differences in what the annuity is worth
+so for
+
+ align:start position:0%
+so for
+ 
+
+ align:start position:0%
+so for
+example $1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today is going to equal 1 plus
+
+ align:start position:0%
+today is going to equal 1 plus
+ 
+
+ align:start position:0%
+today is going to equal 1 plus
+p in one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year similarly $1 today how much is that
+
+ align:start position:0%
+year similarly $1 today how much is that
+ 
+
+ align:start position:0%
+year similarly $1 today how much is that
+going to be worth in two years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say that P stays fixed the same over all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time 1+ p^
+
+ align:start position:0%
+time 1+ p^
+ 
+
+ align:start position:0%
+time 1+ p^
+s because every year you multiply what
+
+ align:start position:0%
+s because every year you multiply what
+ 
+
+ align:start position:0%
+s because every year you multiply what
+you got by one plus P because that's the
+
+ align:start position:0%
+you got by one plus P because that's the
+ 
+
+ align:start position:0%
+you got by one plus P because that's the
+interest you're getting right we'll
+
+ align:start position:0%
+interest you're getting right we'll
+ 
+
+ align:start position:0%
+interest you're getting right we'll
+think of it in terms of interest in
+
+ align:start position:0%
+think of it in terms of interest in
+ 
+
+ align:start position:0%
+think of it in terms of interest in
+three years $1 today is worth 1+ P
+
+ align:start position:0%
+three years $1 today is worth 1+ P
+ 
+
+ align:start position:0%
+three years $1 today is worth 1+ P
+cubed in 3 years and so
+
+ align:start position:0%
+cubed in 3 years and so
+ 
+
+ align:start position:0%
+cubed in 3 years and so
+forth all right now what we really care
+
+ align:start position:0%
+forth all right now what we really care
+ 
+
+ align:start position:0%
+forth all right now what we really care
+about is what's a dollar or M dollar
+
+ align:start position:0%
+about is what's a dollar or M dollar
+ 
+
+ align:start position:0%
+about is what's a dollar or M dollar
+worth today if you're getting it next
+
+ align:start position:0%
+worth today if you're getting it next
+ 
+
+ align:start position:0%
+worth today if you're getting it next
+year so we need to sort of flip this and
+
+ align:start position:0%
+year so we need to sort of flip this and
+ 
+
+ align:start position:0%
+year so we need to sort of flip this and
+back the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so what is
+
+ align:start position:0%
+way so what is
+ 
+
+ align:start position:0%
+way so what is
+$1 in a year worth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today in terms of
+
+ align:start position:0%
+today in terms of
+ 
+
+ align:start position:0%
+today in terms of
+P so if I'm be paid a dollar in a year
+
+ align:start position:0%
+P so if I'm be paid a dollar in a year
+ 
+
+ align:start position:0%
+P so if I'm be paid a dollar in a year
+what would be the equivalent amount to
+
+ align:start position:0%
+what would be the equivalent amount to
+ 
+
+ align:start position:0%
+what would be the equivalent amount to
+be paid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today one over 1 plus
+
+ align:start position:0%
+today one over 1 plus
+ 
+
+ align:start position:0%
+today one over 1 plus
+P because What's Happening Here is as
+
+ align:start position:0%
+P because What's Happening Here is as
+ 
+
+ align:start position:0%
+P because What's Happening Here is as
+you go forward in a year you just
+
+ align:start position:0%
+you go forward in a year you just
+ 
+
+ align:start position:0%
+you go forward in a year you just
+multiply by 1 plus P so one over 1 plus
+
+ align:start position:0%
+multiply by 1 plus P so one over 1 plus
+ 
+
+ align:start position:0%
+multiply by 1 plus P so one over 1 plus
+P turns into
+
+ align:start position:0%
+P turns into
+ 
+
+ align:start position:0%
+P turns into
+$1 in a year being paid in a
+
+ align:start position:0%
+$1 in a year being paid in a
+ 
+
+ align:start position:0%
+$1 in a year being paid in a
+year all right what is one in a year in
+
+ align:start position:0%
+year all right what is one in a year in
+ 
+
+ align:start position:0%
+year all right what is one in a year in
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+years worth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today 1 over 1 + P
+
+ align:start position:0%
+today 1 over 1 + P
+ 
+
+ align:start position:0%
+today 1 over 1 + P
+Squared all right so a dollar in two
+
+ align:start position:0%
+Squared all right so a dollar in two
+ 
+
+ align:start position:0%
+Squared all right so a dollar in two
+years is worth this much
+
+ align:start position:0%
+years is worth this much
+ 
+
+ align:start position:0%
+years is worth this much
+today all right well now we can use this
+
+ align:start position:0%
+today all right well now we can use this
+ 
+
+ align:start position:0%
+today all right well now we can use this
+to go figure out the current value of
+
+ align:start position:0%
+to go figure out the current value of
+ 
+
+ align:start position:0%
+to go figure out the current value of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+annuity we just figure out what every
+
+ align:start position:0%
+annuity we just figure out what every
+ 
+
+ align:start position:0%
+annuity we just figure out what every
+payment is worth today and then add it
+
+ align:start position:0%
+payment is worth today and then add it
+ 
+
+ align:start position:0%
+payment is worth today and then add it
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+so we'll put the payments over here and
+
+ align:start position:0%
+so we'll put the payments over here and
+ 
+
+ align:start position:0%
+so we'll put the payments over here and
+we'll compute the current value of every
+
+ align:start position:0%
+we'll compute the current value of every
+ 
+
+ align:start position:0%
+we'll compute the current value of every
+payment on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side so with the annuity the way we've
+
+ align:start position:0%
+side so with the annuity the way we've
+ 
+
+ align:start position:0%
+side so with the annuity the way we've
+set it up is it pays MLL at the start of
+
+ align:start position:0%
+set it up is it pays MLL at the start of
+ 
+
+ align:start position:0%
+set it up is it pays MLL at the start of
+every year so the first payment is
+
+ align:start position:0%
+every year so the first payment is
+ 
+
+ align:start position:0%
+every year so the first payment is
+now so the first of the end payments is
+
+ align:start position:0%
+now so the first of the end payments is
+ 
+
+ align:start position:0%
+now so the first of the end payments is
+now and since it's being paid now that's
+
+ align:start position:0%
+now and since it's being paid now that's
+ 
+
+ align:start position:0%
+now and since it's being paid now that's
+worth M there's no uh devaluation
+
+ align:start position:0%
+worth M there's no uh devaluation
+ 
+
+ align:start position:0%
+worth M there's no uh devaluation
+the next payment is
+
+ align:start position:0%
+the next payment is
+ 
+
+ align:start position:0%
+the next payment is
+m in one
+
+ align:start position:0%
+m in one
+ 
+
+ align:start position:0%
+m in one
+year and so that's going to be
+
+ align:start position:0%
+year and so that's going to be
+ 
+
+ align:start position:0%
+year and so that's going to be
+worth M over 1 plus P
+
+ align:start position:0%
+worth M over 1 plus P
+ 
+
+ align:start position:0%
+worth M over 1 plus P
+today and the next payment is m in 2
+
+ align:start position:0%
+today and the next payment is m in 2
+ 
+
+ align:start position:0%
+today and the next payment is m in 2
+years that's worth M over 1+
+
+ align:start position:0%
+years that's worth M over 1+
+ 
+
+ align:start position:0%
+years that's worth M over 1+
+p^2 and we keep on going until the last
+
+ align:start position:0%
+p^2 and we keep on going until the last
+ 
+
+ align:start position:0%
+p^2 and we keep on going until the last
+payment it's the nth payment so it's MLL
+
+ align:start position:0%
+payment it's the nth payment so it's MLL
+ 
+
+ align:start position:0%
+payment it's the nth payment so it's MLL
+in N minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+years and so that's going to be worth
+
+ align:start position:0%
+years and so that's going to be worth
+ 
+
+ align:start position:0%
+years and so that's going to be worth
+M over 1 + P to the N minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all right so we can compute the
+
+ align:start position:0%
+one all right so we can compute the
+ 
+
+ align:start position:0%
+one all right so we can compute the
+current value of all those payments then
+
+ align:start position:0%
+current value of all those payments then
+ 
+
+ align:start position:0%
+current value of all those payments then
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+annuity is computed the value is
+
+ align:start position:0%
+annuity is computed the value is
+ 
+
+ align:start position:0%
+annuity is computed the value is
+computed just by adding these up of all
+
+ align:start position:0%
+computed just by adding these up of all
+ 
+
+ align:start position:0%
+computed just by adding these up of all
+the current values so the total current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value is the
+
+ align:start position:0%
+value is the
+ 
+
+ align:start position:0%
+value is the
+sum i = 0 to
+
+ align:start position:0%
+sum i = 0 to
+ 
+
+ align:start position:0%
+sum i = 0 to
+n-1 of M over 1 + P to the
+
+ align:start position:0%
+n-1 of M over 1 + P to the
+ 
+
+ align:start position:0%
+n-1 of M over 1 + P to the
+I and that is the total current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value that's what you should pay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today for the
+
+ align:start position:0%
+today for the
+ 
+
+ align:start position:0%
+today for the
+annuity any questions
+
+ align:start position:0%
+annuity any questions
+ 
+
+ align:start position:0%
+annuity any questions
+what we did
+
+ align:start position:0%
+what we did
+ 
+
+ align:start position:0%
+what we did
+here all
+
+ align:start position:0%
+here all
+ 
+
+ align:start position:0%
+here all
+right well of course what we'd like is a
+
+ align:start position:0%
+right well of course what we'd like is a
+ 
+
+ align:start position:0%
+right well of course what we'd like is a
+closed form expression here something
+
+ align:start position:0%
+closed form expression here something
+ 
+
+ align:start position:0%
+closed form expression here something
+that's simple so we could actually get a
+
+ align:start position:0%
+that's simple so we could actually get a
+ 
+
+ align:start position:0%
+that's simple so we could actually get a
+feel without having to add up all those
+
+ align:start position:0%
+feel without having to add up all those
+ 
+
+ align:start position:0%
+feel without having to add up all those
+terms uh and that's not hard to get in
+
+ align:start position:0%
+terms uh and that's not hard to get in
+ 
+
+ align:start position:0%
+terms uh and that's not hard to get in
+fact let's put this sum in a form that
+
+ align:start position:0%
+fact let's put this sum in a form that
+ 
+
+ align:start position:0%
+fact let's put this sum in a form that
+might be more
+
+ align:start position:0%
+might be more
+ 
+
+ align:start position:0%
+might be more
+familiar this equals we'll pull the M
+
+ align:start position:0%
+familiar this equals we'll pull the M
+ 
+
+ align:start position:0%
+familiar this equals we'll pull the M
+out in front and let's use x to be one
+
+ align:start position:0%
+out in front and let's use x to be one
+ 
+
+ align:start position:0%
+out in front and let's use x to be one
+over 1 plus P to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I and so
+
+ align:start position:0%
+I and so
+ 
+
+ align:start position:0%
+I and so
+x equal 1 over 1+
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P all right and I wrote it this way
+
+ align:start position:0%
+P all right and I wrote it this way
+ 
+
+ align:start position:0%
+P all right and I wrote it this way
+because this might be familiar so
+
+ align:start position:0%
+because this might be familiar so
+ 
+
+ align:start position:0%
+because this might be familiar so
+everybody remember that from I think it
+
+ align:start position:0%
+everybody remember that from I think it
+ 
+
+ align:start position:0%
+everybody remember that from I think it
+was the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recitation anybody remember the formula
+
+ align:start position:0%
+recitation anybody remember the formula
+ 
+
+ align:start position:0%
+recitation anybody remember the formula
+what this evaluates
+
+ align:start position:0%
+what this evaluates
+ 
+
+ align:start position:0%
+what this evaluates
+to the sum of x to the I where I goes
+
+ align:start position:0%
+to the sum of x to the I where I goes
+ 
+
+ align:start position:0%
+to the sum of x to the I where I goes
+from 0 to n
+
+ align:start position:0%
+from 0 to n
+ 
+
+ align:start position:0%
+from 0 to n
+minus1 remember that we 1 - x to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n 1 - x all right in the second
+
+ align:start position:0%
+n 1 - x all right in the second
+ 
+
+ align:start position:0%
+n 1 - x all right in the second
+recitation I think we proved that this
+
+ align:start position:0%
+recitation I think we proved that this
+ 
+
+ align:start position:0%
+recitation I think we proved that this
+equals that what was the proof Technique
+
+ align:start position:0%
+equals that what was the proof Technique
+ 
+
+ align:start position:0%
+equals that what was the proof Technique
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+used induction okay all right
+
+ align:start position:0%
+used induction okay all right
+ 
+
+ align:start position:0%
+used induction okay all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um all right so in
+
+ align:start position:0%
+um all right so in
+ 
+
+ align:start position:0%
+um all right so in
+fact there's a theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here for all n bigger than equal to one
+
+ align:start position:0%
+here for all n bigger than equal to one
+ 
+
+ align:start position:0%
+here for all n bigger than equal to one
+and X not equal to
+
+ align:start position:0%
+and X not equal to
+ 
+
+ align:start position:0%
+and X not equal to
+one we proved I the sum IAL 0 to n
+
+ align:start position:0%
+one we proved I the sum IAL 0 to n
+ 
+
+ align:start position:0%
+one we proved I the sum IAL 0 to n
+minus1 x to the I = 1 - x the N over 1 -
+
+ align:start position:0%
+minus1 x to the I = 1 - x the N over 1 -
+ 
+
+ align:start position:0%
+minus1 x to the I = 1 - x the N over 1 -
+x okay and so this is a nice closed form
+
+ align:start position:0%
+x okay and so this is a nice closed form
+ 
+
+ align:start position:0%
+x okay and so this is a nice closed form
+no SU anymore just just that which is
+
+ align:start position:0%
+no SU anymore just just that which is
+ 
+
+ align:start position:0%
+no SU anymore just just that which is
+nice now induction proved it was the
+
+ align:start position:0%
+nice now induction proved it was the
+ 
+
+ align:start position:0%
+nice now induction proved it was the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+answer once you once you knew knew it
+
+ align:start position:0%
+answer once you once you knew knew it
+ 
+
+ align:start position:0%
+answer once you once you knew knew it
+you know we gave it to you using
+
+ align:start position:0%
+you know we gave it to you using
+ 
+
+ align:start position:0%
+you know we gave it to you using
+induction to prove that theorem wasn't
+
+ align:start position:0%
+induction to prove that theorem wasn't
+ 
+
+ align:start position:0%
+induction to prove that theorem wasn't
+hard what we're going to look at doing
+
+ align:start position:0%
+hard what we're going to look at doing
+ 
+
+ align:start position:0%
+hard what we're going to look at doing
+this week and next week is figuring out
+
+ align:start position:0%
+this week and next week is figuring out
+ 
+
+ align:start position:0%
+this week and next week is figuring out
+how to figure out this was the answer in
+
+ align:start position:0%
+how to figure out this was the answer in
+ 
+
+ align:start position:0%
+how to figure out this was the answer in
+the first place methods for doing that
+
+ align:start position:0%
+the first place methods for doing that
+ 
+
+ align:start position:0%
+the first place methods for doing that
+to evaluate the
+
+ align:start position:0%
+to evaluate the
+ 
+
+ align:start position:0%
+to evaluate the
+sum and there's a lot of ways that you
+
+ align:start position:0%
+sum and there's a lot of ways that you
+ 
+
+ align:start position:0%
+sum and there's a lot of ways that you
+can do uh that particular sum probably
+
+ align:start position:0%
+can do uh that particular sum probably
+ 
+
+ align:start position:0%
+can do uh that particular sum probably
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+easiest is known as the perturbation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method and this sometimes works with
+
+ align:start position:0%
+method and this sometimes works with
+ 
+
+ align:start position:0%
+method and this sometimes works with
+certainly with sums like that it often
+
+ align:start position:0%
+certainly with sums like that it often
+ 
+
+ align:start position:0%
+certainly with sums like that it often
+works the idea is as follows we're
+
+ align:start position:0%
+works the idea is as follows we're
+ 
+
+ align:start position:0%
+works the idea is as follows we're
+trying to compute the sum s which is 1 +
+
+ align:start position:0%
+trying to compute the sum s which is 1 +
+ 
+
+ align:start position:0%
+trying to compute the sum s which is 1 +
+x +
+
+ align:start position:0%
+x +
+ 
+
+ align:start position:0%
+x +
+x^2 plus X the n
+
+ align:start position:0%
+x^2 plus X the n
+ 
+
+ align:start position:0%
+x^2 plus X the n
+minus1 and what we're going to do is
+
+ align:start position:0%
+minus1 and what we're going to do is
+ 
+
+ align:start position:0%
+minus1 and what we're going to do is
+perturb it a little
+
+ align:start position:0%
+perturb it a little
+ 
+
+ align:start position:0%
+perturb it a little
+bit and then subtract to get big
+
+ align:start position:0%
+bit and then subtract to get big
+ 
+
+ align:start position:0%
+bit and then subtract to get big
+cancellation in this case it's pretty
+
+ align:start position:0%
+cancellation in this case it's pretty
+ 
+
+ align:start position:0%
+cancellation in this case it's pretty
+simple we multiply the sum by X to get x
+
+ align:start position:0%
+simple we multiply the sum by X to get x
+ 
+
+ align:start position:0%
+simple we multiply the sum by X to get x
++ x^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
++ all right I've defined s to be that x
+
+ align:start position:0%
++ all right I've defined s to be that x
+ 
+
+ align:start position:0%
++ all right I've defined s to be that x
+x s well I get X Plus X2 and so forth up
+
+ align:start position:0%
+x s well I get X Plus X2 and so forth up
+ 
+
+ align:start position:0%
+x s well I get X Plus X2 and so forth up
+to x to the
+
+ align:start position:0%
+to x to the
+ 
+
+ align:start position:0%
+to x to the
+n and now I can subtract one from the
+
+ align:start position:0%
+n and now I can subtract one from the
+ 
+
+ align:start position:0%
+n and now I can subtract one from the
+other and almost everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cancels so I get one - x * s
+
+ align:start position:0%
+cancels so I get one - x * s
+ 
+
+ align:start position:0%
+cancels so I get one - x * s
+equals 1 these cancel cancel
+
+ align:start position:0%
+equals 1 these cancel cancel
+ 
+
+ align:start position:0%
+equals 1 these cancel cancel
+cancel - x
+
+ align:start position:0%
+cancel - x
+ 
+
+ align:start position:0%
+cancel - x
+n and
+
+ align:start position:0%
+n and
+ 
+
+ align:start position:0%
+n and
+therefore s = 1 - x n over 1 -
+
+ align:start position:0%
+therefore s = 1 - x n over 1 -
+ 
+
+ align:start position:0%
+therefore s = 1 - x n over 1 -
+x all right so that's sort of a
+
+ align:start position:0%
+x all right so that's sort of a
+ 
+
+ align:start position:0%
+x all right so that's sort of a
+a vague method um this gets used all the
+
+ align:start position:0%
+a vague method um this gets used all the
+ 
+
+ align:start position:0%
+a vague method um this gets used all the
+time in Applied Mathematics and they
+
+ align:start position:0%
+time in Applied Mathematics and they
+ 
+
+ align:start position:0%
+time in Applied Mathematics and they
+call it the perturbation method take
+
+ align:start position:0%
+call it the perturbation method take
+ 
+
+ align:start position:0%
+call it the perturbation method take
+your sum you know wiggle it around a
+
+ align:start position:0%
+your sum you know wiggle it around a
+ 
+
+ align:start position:0%
+your sum you know wiggle it around a
+little bit get something that looks
+
+ align:start position:0%
+little bit get something that looks
+ 
+
+ align:start position:0%
+little bit get something that looks
+close subtract it everything cancels
+
+ align:start position:0%
+close subtract it everything cancels
+ 
+
+ align:start position:0%
+close subtract it everything cancels
+life is nice and all of a sudden you
+
+ align:start position:0%
+life is nice and all of a sudden you
+ 
+
+ align:start position:0%
+life is nice and all of a sudden you
+figured out the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer okay so getting back to our
+
+ align:start position:0%
+answer okay so getting back to our
+ 
+
+ align:start position:0%
+answer okay so getting back to our
+annuity
+
+ align:start position:0%
+annuity
+ 
+
+ align:start position:0%
+annuity
+problem we can plug that formula
+
+ align:start position:0%
+problem we can plug that formula
+ 
+
+ align:start position:0%
+problem we can plug that formula
+back in here so the value of the
+
+ align:start position:0%
+back in here so the value of the
+ 
+
+ align:start position:0%
+back in here so the value of the
+annuity is M times 1 - x n over 1 - x
+
+ align:start position:0%
+annuity is M times 1 - x n over 1 - x
+ 
+
+ align:start position:0%
+annuity is M times 1 - x n over 1 - x
+we'll plug in x
+
+ align:start position:0%
+we'll plug in x
+ 
+
+ align:start position:0%
+we'll plug in x
+= 1 over 1 +
+
+ align:start position:0%
+= 1 over 1 +
+ 
+
+ align:start position:0%
+= 1 over 1 +
+p and we get m 1 - 1 over 1 +
+
+ align:start position:0%
+p and we get m 1 - 1 over 1 +
+ 
+
+ align:start position:0%
+p and we get m 1 - 1 over 1 +
+P to the N over 1 - 1 over 1 + p
+
+ align:start position:0%
+P to the N over 1 - 1 over 1 + p
+ 
+
+ align:start position:0%
+P to the N over 1 - 1 over 1 + p
+just plugging in and now to simplify
+
+ align:start position:0%
+just plugging in and now to simplify
+ 
+
+ align:start position:0%
+just plugging in and now to simplify
+this I'll multiply the top and bottom by
+
+ align:start position:0%
+this I'll multiply the top and bottom by
+ 
+
+ align:start position:0%
+this I'll multiply the top and bottom by
+1 plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p and I'll get 1 plus P minus one on the
+
+ align:start position:0%
+p and I'll get 1 plus P minus one on the
+ 
+
+ align:start position:0%
+p and I'll get 1 plus P minus one on the
+bottom just gives me a p on the bottom
+
+ align:start position:0%
+bottom just gives me a p on the bottom
+ 
+
+ align:start position:0%
+bottom just gives me a p on the bottom
+have a 1 plus p on the top
+
+ align:start position:0%
+have a 1 plus p on the top
+ 
+
+ align:start position:0%
+have a 1 plus p on the top
+minus 1 over 1 +
+
+ align:start position:0%
+minus 1 over 1 +
+ 
+
+ align:start position:0%
+minus 1 over 1 +
+P to the N minus one all over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P all right so now we have a formula
+
+ align:start position:0%
+P all right so now we have a formula
+ 
+
+ align:start position:0%
+P all right so now we have a formula
+closed form expression formula for the
+
+ align:start position:0%
+closed form expression formula for the
+ 
+
+ align:start position:0%
+closed form expression formula for the
+value of the annuity all you got to plug
+
+ align:start position:0%
+value of the annuity all you got to plug
+ 
+
+ align:start position:0%
+value of the annuity all you got to plug
+in is M the payment every year and the
+
+ align:start position:0%
+in is M the payment every year and the
+ 
+
+ align:start position:0%
+in is M the payment every year and the
+number of years and then P the interest
+
+ align:start position:0%
+number of years and then P the interest
+ 
+
+ align:start position:0%
+number of years and then P the interest
+rate and so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example if we made M be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$50,000 as in the lottery we made n be
+
+ align:start position:0%
+$50,000 as in the lottery we made n be
+ 
+
+ align:start position:0%
+$50,000 as in the lottery we made n be
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+years and say we took 6% interest which
+
+ align:start position:0%
+years and say we took 6% interest which
+ 
+
+ align:start position:0%
+years and say we took 6% interest which
+is actually very good these
+
+ align:start position:0%
+is actually very good these
+ 
+
+ align:start position:0%
+is actually very good these
+days and I plug those in here the value
+
+ align:start position:0%
+days and I plug those in here the value
+ 
+
+ align:start position:0%
+days and I plug those in here the value
+is going to be
+
+ align:start position:0%
+is going to be
+ 
+
+ align:start position:0%
+is going to be
+$67,900
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so those of you that preferred
+
+ align:start position:0%
+all right so those of you that preferred
+ 
+
+ align:start position:0%
+all right so those of you that preferred
+700 Grand if you assume 6% interest
+
+ align:start position:0%
+700 Grand if you assume 6% interest
+ 
+
+ align:start position:0%
+700 Grand if you assume 6% interest
+you're right those of you preferred 500
+
+ align:start position:0%
+you're right those of you preferred 500
+ 
+
+ align:start position:0%
+you're right those of you preferred 500
+Grand no you're better off waiting and
+
+ align:start position:0%
+Grand no you're better off waiting and
+ 
+
+ align:start position:0%
+Grand no you're better off waiting and
+getting your 50 Grand a year now of
+
+ align:start position:0%
+getting your 50 Grand a year now of
+ 
+
+ align:start position:0%
+getting your 50 Grand a year now of
+course if the interest rate is lower
+
+ align:start position:0%
+course if the interest rate is lower
+ 
+
+ align:start position:0%
+course if the interest rate is lower
+well that changes things all right that
+
+ align:start position:0%
+well that changes things all right that
+ 
+
+ align:start position:0%
+well that changes things all right that
+shifts it even more the annuity is worth
+
+ align:start position:0%
+shifts it even more the annuity is worth
+ 
+
+ align:start position:0%
+shifts it even more the annuity is worth
+even more if the interest rate is lower
+
+ align:start position:0%
+even more if the interest rate is lower
+ 
+
+ align:start position:0%
+even more if the interest rate is lower
+right if p is
+
+ align:start position:0%
+right if p is
+ 
+
+ align:start position:0%
+right if p is
+smaller in fact say p was
+
+ align:start position:0%
+smaller in fact say p was
+ 
+
+ align:start position:0%
+smaller in fact say p was
+zero say the interest rate is zero so a
+
+ align:start position:0%
+zero say the interest rate is zero so a
+ 
+
+ align:start position:0%
+zero say the interest rate is zero so a
+dollar today equals a dollar tomorrow
+
+ align:start position:0%
+dollar today equals a dollar tomorrow
+ 
+
+ align:start position:0%
+dollar today equals a dollar tomorrow
+then what is the lottery
+
+ align:start position:0%
+then what is the lottery
+ 
+
+ align:start position:0%
+then what is the lottery
+worth a million dollars all right and
+
+ align:start position:0%
+worth a million dollars all right and
+ 
+
+ align:start position:0%
+worth a million dollars all right and
+the bigger P gets the less your payment
+
+ align:start position:0%
+the bigger P gets the less your payment
+ 
+
+ align:start position:0%
+the bigger P gets the less your payment
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worth all right any questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what if you were paid
+
+ align:start position:0%
+okay what if you were paid
+ 
+
+ align:start position:0%
+okay what if you were paid
+$50,000 a year
+
+ align:start position:0%
+$50,000 a year
+ 
+
+ align:start position:0%
+$50,000 a year
+forever you live forever or it goes to
+
+ align:start position:0%
+forever you live forever or it goes to
+ 
+
+ align:start position:0%
+forever you live forever or it goes to
+your estate and your airs $50,000 a year
+
+ align:start position:0%
+your estate and your airs $50,000 a year
+ 
+
+ align:start position:0%
+your estate and your airs $50,000 a year
+forever or a million dollars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today how many people want the millionar
+
+ align:start position:0%
+today how many people want the millionar
+ 
+
+ align:start position:0%
+today how many people want the millionar
+today how many want 50 Grand a year
+
+ align:start position:0%
+today how many want 50 Grand a year
+ 
+
+ align:start position:0%
+today how many want 50 Grand a year
+forever
+
+ align:start position:0%
+forever
+ 
+
+ align:start position:0%
+forever
+sounds good you know 50 that's an
+
+ align:start position:0%
+sounds good you know 50 that's an
+ 
+
+ align:start position:0%
+sounds good you know 50 that's an
+infinite amount of money sort
+
+ align:start position:0%
+infinite amount of money sort
+ 
+
+ align:start position:0%
+infinite amount of money sort
+of it's not as good as it sounds let's
+
+ align:start position:0%
+of it's not as good as it sounds let's
+ 
+
+ align:start position:0%
+of it's not as good as it sounds let's
+let's see why uh so this is a case where
+
+ align:start position:0%
+let's see why uh so this is a case where
+ 
+
+ align:start position:0%
+let's see why uh so this is a case where
+n equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity and so I'll claim that if n
+
+ align:start position:0%
+infinity and so I'll claim that if n
+ 
+
+ align:start position:0%
+infinity and so I'll claim that if n
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+infinity then the value of this
+
+ align:start position:0%
+infinity then the value of this
+ 
+
+ align:start position:0%
+infinity then the value of this
+annuity is just m * 1 + p over p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see why that's the
+
+ align:start position:0%
+let's see why that's the
+ 
+
+ align:start position:0%
+let's see why that's the
+case you know it sounds hard to evaluate
+
+ align:start position:0%
+case you know it sounds hard to evaluate
+ 
+
+ align:start position:0%
+case you know it sounds hard to evaluate
+because it's an infinite number of
+
+ align:start position:0%
+because it's an infinite number of
+ 
+
+ align:start position:0%
+because it's an infinite number of
+payments but what happens here when n
+
+ align:start position:0%
+payments but what happens here when n
+ 
+
+ align:start position:0%
+payments but what happens here when n
+goes to
+
+ align:start position:0%
+goes to
+ 
+
+ align:start position:0%
+goes to
+Infinity what happens to this
+
+ align:start position:0%
+Infinity what happens to this
+ 
+
+ align:start position:0%
+Infinity what happens to this
+thing that goes to zero as n goes to
+
+ align:start position:0%
+thing that goes to zero as n goes to
+ 
+
+ align:start position:0%
+thing that goes to zero as n goes to
+Infinity as long as p is bigger than
+
+ align:start position:0%
+Infinity as long as p is bigger than
+ 
+
+ align:start position:0%
+Infinity as long as p is bigger than
+zero so we're going to assume 6%
+
+ align:start position:0%
+zero so we're going to assume 6%
+ 
+
+ align:start position:0%
+zero so we're going to assume 6%
+interest so that goes away so the
+
+ align:start position:0%
+interest so that goes away so the
+ 
+
+ align:start position:0%
+interest so that goes away so the
+annuity is worth just that M * 1 plus p
+
+ align:start position:0%
+annuity is worth just that M * 1 plus p
+ 
+
+ align:start position:0%
+annuity is worth just that M * 1 plus p
+over p
+
+ align:start position:0%
+over p
+ 
+
+ align:start position:0%
+over p
+because the LI the limit as n goes to
+
+ align:start position:0%
+because the LI the limit as n goes to
+ 
+
+ align:start position:0%
+because the LI the limit as n goes to
+Infinity of 1 over 1 + P to the N minus
+
+ align:start position:0%
+Infinity of 1 over 1 + P to the N minus
+ 
+
+ align:start position:0%
+Infinity of 1 over 1 + P to the N minus
+one that's going to
+
+ align:start position:0%
+one that's going to
+ 
+
+ align:start position:0%
+one that's going to
+zero so the
+
+ align:start position:0%
+zero so the
+ 
+
+ align:start position:0%
+zero so the
+value for m is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$50,000 and at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+6% V is only $883,000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so you're better off taking a
+
+ align:start position:0%
+all right so you're better off taking a
+ 
+
+ align:start position:0%
+all right so you're better off taking a
+million dollars today than $50,000 a
+
+ align:start position:0%
+million dollars today than $50,000 a
+ 
+
+ align:start position:0%
+million dollars today than $50,000 a
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+forever now if you think about it you
+
+ align:start position:0%
+forever now if you think about it you
+ 
+
+ align:start position:0%
+forever now if you think about it you
+think about it as an interest rate why
+
+ align:start position:0%
+think about it as an interest rate why
+ 
+
+ align:start position:0%
+think about it as an interest rate why
+should it be obvious that you're better
+
+ align:start position:0%
+should it be obvious that you're better
+ 
+
+ align:start position:0%
+should it be obvious that you're better
+off with a million dollars today than 50
+
+ align:start position:0%
+off with a million dollars today than 50
+ 
+
+ align:start position:0%
+off with a million dollars today than 50
+Grand a year
+
+ align:start position:0%
+Grand a year
+ 
+
+ align:start position:0%
+Grand a year
+forever think about what you could do
+
+ align:start position:0%
+forever think about what you could do
+ 
+
+ align:start position:0%
+forever think about what you could do
+with that million dollars if you had it
+
+ align:start position:0%
+with that million dollars if you had it
+ 
+
+ align:start position:0%
+with that million dollars if you had it
+today at 6%
+
+ align:start position:0%
+today at 6%
+ 
+
+ align:start position:0%
+today at 6%
+interest what would you do with it to to
+
+ align:start position:0%
+interest what would you do with it to to
+ 
+
+ align:start position:0%
+interest what would you do with it to to
+make more money than 50 Grand a year
+
+ align:start position:0%
+make more money than 50 Grand a year
+ 
+
+ align:start position:0%
+make more money than 50 Grand a year
+forever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah in this model if the interest
+
+ align:start position:0%
+yeah yeah in this model if the interest
+ 
+
+ align:start position:0%
+yeah yeah in this model if the interest
+rate is 6% you can put in the bank make
+
+ align:start position:0%
+rate is 6% you can put in the bank make
+ 
+
+ align:start position:0%
+rate is 6% you can put in the bank make
+6% every year that's 60 Grand a year
+
+ align:start position:0%
+6% every year that's 60 Grand a year
+ 
+
+ align:start position:0%
+6% every year that's 60 Grand a year
+forever better than 50 Grand a year
+
+ align:start position:0%
+forever better than 50 Grand a year
+ 
+
+ align:start position:0%
+forever better than 50 Grand a year
+forever all right so maybe it's you know
+
+ align:start position:0%
+forever all right so maybe it's you know
+ 
+
+ align:start position:0%
+forever all right so maybe it's you know
+even without doing the math you can tell
+
+ align:start position:0%
+even without doing the math you can tell
+ 
+
+ align:start position:0%
+even without doing the math you can tell
+which way it's going to go but this
+
+ align:start position:0%
+which way it's going to go but this
+ 
+
+ align:start position:0%
+which way it's going to go but this
+tells you exactly what it's
+
+ align:start position:0%
+tells you exactly what it's
+ 
+
+ align:start position:0%
+tells you exactly what it's
+worth all right any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah how much worth to you right now
+
+ align:start position:0%
+yeah how much worth to you right now
+ 
+
+ align:start position:0%
+yeah how much worth to you right now
+yeah so um it might be like if you have
+
+ align:start position:0%
+yeah so um it might be like if you have
+ 
+
+ align:start position:0%
+yeah so um it might be like if you have
+$1 in the future
+
+ align:start position:0%
+$1 in the future
+ 
+
+ align:start position:0%
+$1 in the future
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right lat
+
+ align:start position:0%
+right lat
+ 
+
+ align:start position:0%
+right lat
+it's ah so if you move yourself forward
+
+ align:start position:0%
+it's ah so if you move yourself forward
+ 
+
+ align:start position:0%
+it's ah so if you move yourself forward
+in time $1 in a year in a year will be
+
+ align:start position:0%
+in time $1 in a year in a year will be
+ 
+
+ align:start position:0%
+in time $1 in a year in a year will be
+worth $1 to you
+
+ align:start position:0%
+worth $1 to you
+ 
+
+ align:start position:0%
+worth $1 to you
+but today it's worth less than a dollar
+
+ align:start position:0%
+but today it's worth less than a dollar
+ 
+
+ align:start position:0%
+but today it's worth less than a dollar
+to you because you could take the dollar
+
+ align:start position:0%
+to you because you could take the dollar
+ 
+
+ align:start position:0%
+to you because you could take the dollar
+today and invest it in the bank and it's
+
+ align:start position:0%
+today and invest it in the bank and it's
+ 
+
+ align:start position:0%
+today and invest it in the bank and it's
+worth more in a year because the money
+
+ align:start position:0%
+worth more in a year because the money
+ 
+
+ align:start position:0%
+worth more in a year because the money
+grows in value is a way to think of it
+
+ align:start position:0%
+grows in value is a way to think of it
+ 
+
+ align:start position:0%
+grows in value is a way to think of it
+because you can earn interest on it
+
+ align:start position:0%
+because you can earn interest on it
+ 
+
+ align:start position:0%
+because you can earn interest on it
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+that yeah if depend yeah if you just
+
+ align:start position:0%
+that yeah if depend yeah if you just
+ 
+
+ align:start position:0%
+that yeah if depend yeah if you just
+spend it well then you at least you had
+
+ align:start position:0%
+spend it well then you at least you had
+ 
+
+ align:start position:0%
+spend it well then you at least you had
+the use of what you spend it on for the
+
+ align:start position:0%
+the use of what you spend it on for the
+ 
+
+ align:start position:0%
+the use of what you spend it on for the
+year so there's some other kind of value
+
+ align:start position:0%
+year so there's some other kind of value
+ 
+
+ align:start position:0%
+year so there's some other kind of value
+right maybe you bought a house or you
+
+ align:start position:0%
+right maybe you bought a house or you
+ 
+
+ align:start position:0%
+right maybe you bought a house or you
+know something that maybe something that
+
+ align:start position:0%
+know something that maybe something that
+ 
+
+ align:start position:0%
+know something that maybe something that
+even appreciated in value
+
+ align:start position:0%
+even appreciated in value
+ 
+
+ align:start position:0%
+even appreciated in value
+okay but yeah these things get get you
+
+ align:start position:0%
+okay but yeah these things get get you
+ 
+
+ align:start position:0%
+okay but yeah these things get get you
+know sort of squishy and that is where a
+
+ align:start position:0%
+know sort of squishy and that is where a
+ 
+
+ align:start position:0%
+know sort of squishy and that is where a
+lot of people make make money on Wall
+
+ align:start position:0%
+lot of people make make money on Wall
+ 
+
+ align:start position:0%
+lot of people make make money on Wall
+Street is because different companies
+
+ align:start position:0%
+Street is because different companies
+ 
+
+ align:start position:0%
+Street is because different companies
+have different needs for money they have
+
+ align:start position:0%
+have different needs for money they have
+ 
+
+ align:start position:0%
+have different needs for money they have
+different views of what the interest
+
+ align:start position:0%
+different views of what the interest
+ 
+
+ align:start position:0%
+different views of what the interest
+rates are going to be and you can play
+
+ align:start position:0%
+rates are going to be and you can play
+ 
+
+ align:start position:0%
+rates are going to be and you can play
+in the middle all right make make a lot
+
+ align:start position:0%
+in the middle all right make make a lot
+ 
+
+ align:start position:0%
+in the middle all right make make a lot
+of money that
+
+ align:start position:0%
+of money that
+ 
+
+ align:start position:0%
+of money that
+way okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so more generally there's a
+
+ align:start position:0%
+all right so more generally there's a
+ 
+
+ align:start position:0%
+all right so more generally there's a
+corollary to the
+
+ align:start position:0%
+corollary to the
+ 
+
+ align:start position:0%
+corollary to the
+theorem and that is that if the absolute
+
+ align:start position:0%
+theorem and that is that if the absolute
+ 
+
+ align:start position:0%
+theorem and that is that if the absolute
+value of x is less than one then the
+
+ align:start position:0%
+value of x is less than one then the
+ 
+
+ align:start position:0%
+value of x is less than one then the
+sum IAL 0 To infinity x to the I is just
+
+ align:start position:0%
+sum IAL 0 To infinity x to the I is just
+ 
+
+ align:start position:0%
+sum IAL 0 To infinity x to the I is just
+1 over 1 -
+
+ align:start position:0%
+1 over 1 -
+ 
+
+ align:start position:0%
+1 over 1 -
+x all right and we didn't prove this
+
+ align:start position:0%
+x all right and we didn't prove this
+ 
+
+ align:start position:0%
+x all right and we didn't prove this
+back in the second recitation because
+
+ align:start position:0%
+back in the second recitation because
+ 
+
+ align:start position:0%
+back in the second recitation because
+there's no n to induct on here but the
+
+ align:start position:0%
+there's no n to induct on here but the
+ 
+
+ align:start position:0%
+there's no n to induct on here but the
+proof is simple from the
+
+ align:start position:0%
+proof is simple from the
+ 
+
+ align:start position:0%
+proof is simple from the
+theorem and it's simply because if x is
+
+ align:start position:0%
+theorem and it's simply because if x is
+ 
+
+ align:start position:0%
+theorem and it's simply because if x is
+less than one an absolute value as n
+
+ align:start position:0%
+less than one an absolute value as n
+ 
+
+ align:start position:0%
+less than one an absolute value as n
+goes to Infinity that goes to zero and
+
+ align:start position:0%
+goes to Infinity that goes to zero and
+ 
+
+ align:start position:0%
+goes to Infinity that goes to zero and
+so you're just left with one over one -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x okay so for example
+
+ align:start position:0%
+x okay so for example
+ 
+
+ align:start position:0%
+x okay so for example
+uh what's this sum this one you all know
+
+ align:start position:0%
+uh what's this sum this one you all know
+ 
+
+ align:start position:0%
+uh what's this sum this one you all know
+I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure out to Infinity what's that sum
+
+ align:start position:0%
+sure out to Infinity what's that sum
+ 
+
+ align:start position:0%
+sure out to Infinity what's that sum
+to to two yeah it's 1 over 1 minus a
+
+ align:start position:0%
+to to two yeah it's 1 over 1 minus a
+ 
+
+ align:start position:0%
+to to two yeah it's 1 over 1 minus a
+half which is
+
+ align:start position:0%
+half which is
+ 
+
+ align:start position:0%
+half which is
+two what about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum out to Infinity what does that sum
+
+ align:start position:0%
+sum out to Infinity what does that sum
+ 
+
+ align:start position:0%
+sum out to Infinity what does that sum
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah three Hales 1 over 1 - A3 is
+
+ align:start position:0%
+yeah three Hales 1 over 1 - A3 is
+ 
+
+ align:start position:0%
+yeah three Hales 1 over 1 - A3 is
+three all right so easy
+
+ align:start position:0%
+three all right so easy
+ 
+
+ align:start position:0%
+three all right so easy
+cories uh these are all examples of
+
+ align:start position:0%
+cories uh these are all examples of
+ 
+
+ align:start position:0%
+cories uh these are all examples of
+geometric series that's what a
+
+ align:start position:0%
+geometric series that's what a
+ 
+
+ align:start position:0%
+geometric series that's what a
+definition of a geometric series is
+
+ align:start position:0%
+definition of a geometric series is
+ 
+
+ align:start position:0%
+definition of a geometric series is
+something is going down by a fixed each
+
+ align:start position:0%
+something is going down by a fixed each
+ 
+
+ align:start position:0%
+something is going down by a fixed each
+term goes down by the same fixed amount
+
+ align:start position:0%
+term goes down by the same fixed amount
+ 
+
+ align:start position:0%
+term goes down by the same fixed amount
+every time and geometric series
+
+ align:start position:0%
+every time and geometric series
+ 
+
+ align:start position:0%
+every time and geometric series
+generally sum to something that is very
+
+ align:start position:0%
+generally sum to something that is very
+ 
+
+ align:start position:0%
+generally sum to something that is very
+close to the largest term in this case
+
+ align:start position:0%
+close to the largest term in this case
+ 
+
+ align:start position:0%
+close to the largest term in this case
+it's one
+
+ align:start position:0%
+it's one
+ 
+
+ align:start position:0%
+it's one
+very common because of that formula it's
+
+ align:start position:0%
+very common because of that formula it's
+ 
+
+ align:start position:0%
+very common because of that formula it's
+one over one minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X any questions about this or geometric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series all
+
+ align:start position:0%
+series all
+ 
+
+ align:start position:0%
+series all
+right well those are straight geometric
+
+ align:start position:0%
+right well those are straight geometric
+ 
+
+ align:start position:0%
+right well those are straight geometric
+sums sometimes you run into things that
+
+ align:start position:0%
+sums sometimes you run into things that
+ 
+
+ align:start position:0%
+sums sometimes you run into things that
+are a little bit more complicated for
+
+ align:start position:0%
+are a little bit more complicated for
+ 
+
+ align:start position:0%
+are a little bit more complicated for
+example say I have this kind of a sum I
+
+ align:start position:0%
+example say I have this kind of a sum I
+ 
+
+ align:start position:0%
+example say I have this kind of a sum I
+= 1 to
+
+ align:start position:0%
+= 1 to
+ 
+
+ align:start position:0%
+= 1 to
+n i * x to the
+
+ align:start position:0%
+n i * x to the
+ 
+
+ align:start position:0%
+n i * x to the
+I other are adding up x +
+
+ align:start position:0%
+I other are adding up x +
+ 
+
+ align:start position:0%
+I other are adding up x +
+2x^2 + 3x
+
+ align:start position:0%
+2x^2 + 3x
+ 
+
+ align:start position:0%
+2x^2 + 3x
+cubed and so forth up to n x to the
+
+ align:start position:0%
+cubed and so forth up to n x to the
+ 
+
+ align:start position:0%
+cubed and so forth up to n x to the
+N you know that's a little more
+
+ align:start position:0%
+N you know that's a little more
+ 
+
+ align:start position:0%
+N you know that's a little more
+complicated the terms are
+
+ align:start position:0%
+complicated the terms are
+ 
+
+ align:start position:0%
+complicated the terms are
+getting you know decreasing by a factor
+
+ align:start position:0%
+getting you know decreasing by a factor
+ 
+
+ align:start position:0%
+getting you know decreasing by a factor
+of X increasing by one in terms of the
+
+ align:start position:0%
+of X increasing by one in terms of the
+ 
+
+ align:start position:0%
+of X increasing by one in terms of the
+coefficient every time little trickier
+
+ align:start position:0%
+coefficient every time little trickier
+ 
+
+ align:start position:0%
+coefficient every time little trickier
+so say we wanted to get a closed form
+
+ align:start position:0%
+so say we wanted to get a closed form
+ 
+
+ align:start position:0%
+so say we wanted to get a closed form
+expression for that there's several ways
+
+ align:start position:0%
+expression for that there's several ways
+ 
+
+ align:start position:0%
+expression for that there's several ways
+we can do it the first would be to try
+
+ align:start position:0%
+we can do it the first would be to try
+ 
+
+ align:start position:0%
+we can do it the first would be to try
+to use perturbation the perturbation
+
+ align:start position:0%
+to use perturbation the perturbation
+ 
+
+ align:start position:0%
+to use perturbation the perturbation
+method so let's try
+
+ align:start position:0%
+method so let's try
+ 
+
+ align:start position:0%
+method so let's try
+that so we write s = x + 2x^2 + 3x
+
+ align:start position:0%
+that so we write s = x + 2x^2 + 3x
+ 
+
+ align:start position:0%
+that so we write s = x + 2x^2 + 3x
+cubed plus n x the
+
+ align:start position:0%
+cubed plus n x the
+ 
+
+ align:start position:0%
+cubed plus n x the
+n and let's try the same perturbation
+
+ align:start position:0%
+n and let's try the same perturbation
+ 
+
+ align:start position:0%
+n and let's try the same perturbation
+multiply by
+
+ align:start position:0%
+multiply by
+ 
+
+ align:start position:0%
+multiply by
+X I get x2 + 2 x
+
+ align:start position:0%
+X I get x2 + 2 x
+ 
+
+ align:start position:0%
+X I get x2 + 2 x
+cubed + n -1 x n + n x the n +
+
+ align:start position:0%
+cubed + n -1 x n + n x the n +
+ 
+
+ align:start position:0%
+cubed + n -1 x n + n x the n +
+one and then I subtract to try to get
+
+ align:start position:0%
+one and then I subtract to try to get
+ 
+
+ align:start position:0%
+one and then I subtract to try to get
+all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cancellation so and I do that I get 1 -
+
+ align:start position:0%
+cancellation so and I do that I get 1 -
+ 
+
+ align:start position:0%
+cancellation so and I do that I get 1 -
+x *
+
+ align:start position:0%
+x *
+ 
+
+ align:start position:0%
+x *
+S I didn't quite cancel
+
+ align:start position:0%
+S I didn't quite cancel
+ 
+
+ align:start position:0%
+S I didn't quite cancel
+everything x +
+
+ align:start position:0%
+everything x +
+ 
+
+ align:start position:0%
+everything x +
+X2 + x
+
+ align:start position:0%
+X2 + x
+ 
+
+ align:start position:0%
+X2 + x
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+cubed plus x to the N plus n or minus n
+
+ align:start position:0%
+cubed plus x to the N plus n or minus n
+ 
+
+ align:start position:0%
+cubed plus x to the N plus n or minus n
+x to the n + one ah it didn't quite
+
+ align:start position:0%
+x to the n + one ah it didn't quite
+ 
+
+ align:start position:0%
+x to the n + one ah it didn't quite
+work anybody see a way though I can fix
+
+ align:start position:0%
+work anybody see a way though I can fix
+ 
+
+ align:start position:0%
+work anybody see a way though I can fix
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up what about this piece that's still a
+
+ align:start position:0%
+up what about this piece that's still a
+ 
+
+ align:start position:0%
+up what about this piece that's still a
+mess here can I simplify
+
+ align:start position:0%
+mess here can I simplify
+ 
+
+ align:start position:0%
+mess here can I simplify
+that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah there's a simpler way yeah that's a
+
+ align:start position:0%
+yeah there's a simpler way yeah that's a
+ 
+
+ align:start position:0%
+yeah there's a simpler way yeah that's a
+geometric series that's a geometric
+
+ align:start position:0%
+geometric series that's a geometric
+ 
+
+ align:start position:0%
+geometric series that's a geometric
+series we just got the formula for it so
+
+ align:start position:0%
+series we just got the formula for it so
+ 
+
+ align:start position:0%
+series we just got the formula for it so
+that's easy this
+
+ align:start position:0%
+that's easy this
+ 
+
+ align:start position:0%
+that's easy this
+equals 1 - x the N over 1 - x minus the
+
+ align:start position:0%
+equals 1 - x the N over 1 - x minus the
+ 
+
+ align:start position:0%
+equals 1 - x the N over 1 - x minus the
+one because I'm missing the one here so
+
+ align:start position:0%
+one because I'm missing the one here so
+ 
+
+ align:start position:0%
+one because I'm missing the one here so
+we can rewrite this whole thing over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here oops yikes got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attacked what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+yes it would that's right I got to add
+
+ align:start position:0%
+yes it would that's right I got to add
+ 
+
+ align:start position:0%
+yes it would that's right I got to add
+one to there
+
+ align:start position:0%
+one to there
+ 
+
+ align:start position:0%
+one to there
+there okay so that's good so that says
+
+ align:start position:0%
+there okay so that's good so that says
+ 
+
+ align:start position:0%
+there okay so that's good so that says
+that 1 - x * s = 1 - x n + 1 over 1 - x
+
+ align:start position:0%
+that 1 - x * s = 1 - x n + 1 over 1 - x
+ 
+
+ align:start position:0%
+that 1 - x * s = 1 - x n + 1 over 1 - x
+-1 and then I got to remember to
+
+ align:start position:0%
+-1 and then I got to remember to
+ 
+
+ align:start position:0%
+-1 and then I got to remember to
+subtract that term too minus n actually
+
+ align:start position:0%
+subtract that term too minus n actually
+ 
+
+ align:start position:0%
+subtract that term too minus n actually
+n +
+
+ align:start position:0%
+n +
+ 
+
+ align:start position:0%
+n +
+one that means now I just divide through
+
+ align:start position:0%
+one that means now I just divide through
+ 
+
+ align:start position:0%
+one that means now I just divide through
+and I simplify divide through by 1 - x
+
+ align:start position:0%
+and I simplify divide through by 1 - x
+ 
+
+ align:start position:0%
+and I simplify divide through by 1 - x
+and simplify and I get the following
+
+ align:start position:0%
+and simplify and I get the following
+ 
+
+ align:start position:0%
+and simplify and I get the following
+formula I won't go through all the
+
+ align:start position:0%
+formula I won't go through all the
+ 
+
+ align:start position:0%
+formula I won't go through all the
+details but it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard let's see if I got that right yeah
+
+ align:start position:0%
+hard let's see if I got that right yeah
+ 
+
+ align:start position:0%
+hard let's see if I got that right yeah
+that looks right okay so that is the
+
+ align:start position:0%
+that looks right okay so that is the
+ 
+
+ align:start position:0%
+that looks right okay so that is the
+closed form expression for that sum
+
+ align:start position:0%
+closed form expression for that sum
+ 
+
+ align:start position:0%
+closed form expression for that sum
+which we can get from the perturbation
+
+ align:start position:0%
+which we can get from the perturbation
+ 
+
+ align:start position:0%
+which we can get from the perturbation
+method and the fact that we'd already
+
+ align:start position:0%
+method and the fact that we'd already
+ 
+
+ align:start position:0%
+method and the fact that we'd already
+done the geometric
+
+ align:start position:0%
+done the geometric
+ 
+
+ align:start position:0%
+done the geometric
+series all right there's another way to
+
+ align:start position:0%
+series all right there's another way to
+ 
+
+ align:start position:0%
+series all right there's another way to
+compute these kinds of
+
+ align:start position:0%
+compute these kinds of
+ 
+
+ align:start position:0%
+compute these kinds of
+sums which I want to show you because
+
+ align:start position:0%
+sums which I want to show you because
+ 
+
+ align:start position:0%
+sums which I want to show you because
+can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful so we're going to do the same sum
+
+ align:start position:0%
+useful so we're going to do the same sum
+ 
+
+ align:start position:0%
+useful so we're going to do the same sum
+and and derive the formula a different
+
+ align:start position:0%
+and and derive the formula a different
+ 
+
+ align:start position:0%
+and and derive the formula a different
+way this method is called the derivative
+
+ align:start position:0%
+way this method is called the derivative
+ 
+
+ align:start position:0%
+way this method is called the derivative
+method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the idea is to start with the
+
+ align:start position:0%
+and the idea is to start with the
+ 
+
+ align:start position:0%
+and the idea is to start with the
+geometric series which it's close to and
+
+ align:start position:0%
+geometric series which it's close to and
+ 
+
+ align:start position:0%
+geometric series which it's close to and
+then take a
+
+ align:start position:0%
+then take a
+ 
+
+ align:start position:0%
+then take a
+derivative so for X not equal to one we
+
+ align:start position:0%
+derivative so for X not equal to one we
+ 
+
+ align:start position:0%
+derivative so for X not equal to one we
+already know from the theorem that I = 0
+
+ align:start position:0%
+already know from the theorem that I = 0
+ 
+
+ align:start position:0%
+already know from the theorem that I = 0
+to n x the I = 1 - x n + 1 over 1 - x
+
+ align:start position:0%
+to n x the I = 1 - x n + 1 over 1 - x
+ 
+
+ align:start position:0%
+to n x the I = 1 - x n + 1 over 1 - x
+that was the theorem we already know
+
+ align:start position:0%
+that was the theorem we already know
+ 
+
+ align:start position:0%
+that was the theorem we already know
+that now I can take the d derivative of
+
+ align:start position:0%
+that now I can take the d derivative of
+ 
+
+ align:start position:0%
+that now I can take the d derivative of
+both sides and let's see what we get by
+
+ align:start position:0%
+both sides and let's see what we get by
+ 
+
+ align:start position:0%
+both sides and let's see what we get by
+taking the
+
+ align:start position:0%
+taking the
+ 
+
+ align:start position:0%
+taking the
+derivative well
+
+ align:start position:0%
+derivative well
+ 
+
+ align:start position:0%
+derivative well
+here I get the sum the derivative of x
+
+ align:start position:0%
+here I get the sum the derivative of x
+ 
+
+ align:start position:0%
+here I get the sum the derivative of x
+to the I is just I * X the
+
+ align:start position:0%
+to the I is just I * X the
+ 
+
+ align:start position:0%
+to the I is just I * X the
+ius1 the derivative over here is a
+
+ align:start position:0%
+ius1 the derivative over here is a
+ 
+
+ align:start position:0%
+ius1 the derivative over here is a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+Messier I got to have I take 1 - x times
+
+ align:start position:0%
+Messier I got to have I take 1 - x times
+ 
+
+ align:start position:0%
+Messier I got to have I take 1 - x times
+the derivative of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that derivative of this is now minus n
+
+ align:start position:0%
+that derivative of this is now minus n
+ 
+
+ align:start position:0%
+that derivative of this is now minus n
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+1 x to the
+
+ align:start position:0%
+1 x to the
+ 
+
+ align:start position:0%
+1 x to the
+N then I take this times the derivative
+
+ align:start position:0%
+N then I take this times the derivative
+ 
+
+ align:start position:0%
+N then I take this times the derivative
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+that is now Min -
+
+ align:start position:0%
+that is now Min -
+ 
+
+ align:start position:0%
+that is now Min -
+-1 1 - x n +
+
+ align:start position:0%
+-1 1 - x n +
+ 
+
+ align:start position:0%
+-1 1 - x n +
+1 and then I divide
+
+ align:start position:0%
+1 and then I divide
+ 
+
+ align:start position:0%
+1 and then I divide
+by that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared now when we compute all that out
+
+ align:start position:0%
+squared now when we compute all that out
+ 
+
+ align:start position:0%
+squared now when we compute all that out
+we get
+
+ align:start position:0%
+we get
+ 
+
+ align:start position:0%
+we get
+this 1 minus n + 1 x the
+
+ align:start position:0%
+this 1 minus n + 1 x the
+ 
+
+ align:start position:0%
+this 1 minus n + 1 x the
+n + n x n +
+
+ align:start position:0%
+n + n x n +
+ 
+
+ align:start position:0%
+n + n x n +
+1 over 1 -
+
+ align:start position:0%
+1 over 1 -
+ 
+
+ align:start position:0%
+1 over 1 -
+x^2 right I won't drag you through the
+
+ align:start position:0%
+x^2 right I won't drag you through the
+ 
+
+ align:start position:0%
+x^2 right I won't drag you through the
+algebra but it's not hard to go from
+
+ align:start position:0%
+algebra but it's not hard to go from
+ 
+
+ align:start position:0%
+algebra but it's not hard to go from
+there to there this is pretty close to
+
+ align:start position:0%
+there to there this is pretty close to
+ 
+
+ align:start position:0%
+there to there this is pretty close to
+what we
+
+ align:start position:0%
+what we
+ 
+
+ align:start position:0%
+what we
+wanted we're trying to figure
+
+ align:start position:0%
+wanted we're trying to figure
+ 
+
+ align:start position:0%
+wanted we're trying to figure
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+this and we almost got
+
+ align:start position:0%
+this and we almost got
+ 
+
+ align:start position:0%
+this and we almost got
+there what do I do to finish it up
+
+ align:start position:0%
+there what do I do to finish it up
+ 
+
+ align:start position:0%
+there what do I do to finish it up
+multiply by X good so if I take this and
+
+ align:start position:0%
+multiply by X good so if I take this and
+ 
+
+ align:start position:0%
+multiply by X good so if I take this and
+multiply by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x i = 0 to n IX to the I
+
+ align:start position:0%
+x i = 0 to n IX to the I
+ 
+
+ align:start position:0%
+x i = 0 to n IX to the I
+equals x - n + 1 x n + 1 + n x n + 2 all
+
+ align:start position:0%
+equals x - n + 1 x n + 1 + n x n + 2 all
+ 
+
+ align:start position:0%
+equals x - n + 1 x n + 1 + n x n + 2 all
+over 1 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x^2 okay we which should be the same
+
+ align:start position:0%
+x^2 okay we which should be the same
+ 
+
+ align:start position:0%
+x^2 okay we which should be the same
+yeah the same form that we had up there
+
+ align:start position:0%
+yeah the same form that we had up there
+ 
+
+ align:start position:0%
+yeah the same form that we had up there
+all right so that's called the
+
+ align:start position:0%
+all right so that's called the
+ 
+
+ align:start position:0%
+all right so that's called the
+derivative method you can start
+
+ align:start position:0%
+derivative method you can start
+ 
+
+ align:start position:0%
+derivative method you can start
+manipulating you treat these things as
+
+ align:start position:0%
+manipulating you treat these things as
+ 
+
+ align:start position:0%
+manipulating you treat these things as
+polinomial these sums and you start
+
+ align:start position:0%
+polinomial these sums and you start
+ 
+
+ align:start position:0%
+polinomial these sums and you start
+manipulating manipulating them like you
+
+ align:start position:0%
+manipulating manipulating them like you
+ 
+
+ align:start position:0%
+manipulating manipulating them like you
+would polinomial in fact there's a whole
+
+ align:start position:0%
+would polinomial in fact there's a whole
+ 
+
+ align:start position:0%
+would polinomial in fact there's a whole
+branch of mathematics called generating
+
+ align:start position:0%
+branch of mathematics called generating
+ 
+
+ align:start position:0%
+branch of mathematics called generating
+functions that we won't have time to do
+
+ align:start position:0%
+functions that we won't have time to do
+ 
+
+ align:start position:0%
+functions that we won't have time to do
+in this class uh that's in chapter 12 of
+
+ align:start position:0%
+in this class uh that's in chapter 12 of
+ 
+
+ align:start position:0%
+in this class uh that's in chapter 12 of
+the text but you do things like that to
+
+ align:start position:0%
+the text but you do things like that to
+ 
+
+ align:start position:0%
+the text but you do things like that to
+get sums
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions about what we did there
+
+ align:start position:0%
+any questions about what we did there
+ 
+
+ align:start position:0%
+any questions about what we did there
+you can also do a version where you take
+
+ align:start position:0%
+you can also do a version where you take
+ 
+
+ align:start position:0%
+you can also do a version where you take
+integrals of this if you want and then
+
+ align:start position:0%
+integrals of this if you want and then
+ 
+
+ align:start position:0%
+integrals of this if you want and then
+you get the eyes in the denominator
+
+ align:start position:0%
+you get the eyes in the denominator
+ 
+
+ align:start position:0%
+you get the eyes in the denominator
+instead of as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coefficients for homework I think we've
+
+ align:start position:0%
+coefficients for homework I think we've
+ 
+
+ align:start position:0%
+coefficients for homework I think we've
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+you the sum of I 2 x to the
+
+ align:start position:0%
+you the sum of I 2 x to the
+ 
+
+ align:start position:0%
+you the sum of I 2 x to the
+I how do you think you're going to do
+
+ align:start position:0%
+I how do you think you're going to do
+ 
+
+ align:start position:0%
+I how do you think you're going to do
+that any thoughts about how you're going
+
+ align:start position:0%
+that any thoughts about how you're going
+ 
+
+ align:start position:0%
+that any thoughts about how you're going
+to solve that
+
+ align:start position:0%
+to solve that
+ 
+
+ align:start position:0%
+to solve that
+get the sum closed form for the sum of
+
+ align:start position:0%
+get the sum closed form for the sum of
+ 
+
+ align:start position:0%
+get the sum closed form for the sum of
+i^2 x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i yeah do it twice take this which now
+
+ align:start position:0%
+i yeah do it twice take this which now
+ 
+
+ align:start position:0%
+i yeah do it twice take this which now
+you know take the derivative
+
+ align:start position:0%
+you know take the derivative
+ 
+
+ align:start position:0%
+you know take the derivative
+again right won't be too too
+
+ align:start position:0%
+again right won't be too too
+ 
+
+ align:start position:0%
+again right won't be too too
+hard all right
+
+ align:start position:0%
+hard all right
+ 
+
+ align:start position:0%
+hard all right
+um You can also take the version of this
+
+ align:start position:0%
+um You can also take the version of this
+ 
+
+ align:start position:0%
+um You can also take the version of this
+where n goes to
+
+ align:start position:0%
+where n goes to
+ 
+
+ align:start position:0%
+where n goes to
+Infinity let's do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the absolute value of x is less than
+
+ align:start position:0%
+if the absolute value of x is less than
+ 
+
+ align:start position:0%
+if the absolute value of x is less than
+one the sum I equals one to
+
+ align:start position:0%
+one the sum I equals one to
+ 
+
+ align:start position:0%
+one the sum I equals one to
+Infinity of IX to the i what does that
+
+ align:start position:0%
+Infinity of IX to the i what does that
+ 
+
+ align:start position:0%
+Infinity of IX to the i what does that
+equal this one you can see it easier up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here what happens when n goes to
+
+ align:start position:0%
+here what happens when n goes to
+ 
+
+ align:start position:0%
+here what happens when n goes to
+Infinity what does this
+
+ align:start position:0%
+Infinity what does this
+ 
+
+ align:start position:0%
+Infinity what does this
+do X is less than one in absolute value
+
+ align:start position:0%
+do X is less than one in absolute value
+ 
+
+ align:start position:0%
+do X is less than one in absolute value
+what happens to this as n goes to
+
+ align:start position:0%
+what happens to this as n goes to
+ 
+
+ align:start position:0%
+what happens to this as n goes to
+Infinity this
+
+ align:start position:0%
+Infinity this
+ 
+
+ align:start position:0%
+Infinity this
+term what goes to
+
+ align:start position:0%
+term what goes to
+ 
+
+ align:start position:0%
+term what goes to
+zero right this gets big but this gets
+
+ align:start position:0%
+zero right this gets big but this gets
+ 
+
+ align:start position:0%
+zero right this gets big but this gets
+smaller faster what happens to this term
+
+ align:start position:0%
+smaller faster what happens to this term
+ 
+
+ align:start position:0%
+smaller faster what happens to this term
+as n goes to
+
+ align:start position:0%
+as n goes to
+ 
+
+ align:start position:0%
+as n goes to
+Infinity same thing zero alls I'm left
+
+ align:start position:0%
+Infinity same thing zero alls I'm left
+ 
+
+ align:start position:0%
+Infinity same thing zero alls I'm left
+with is X over 1 - x^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now this formula is useful if
+
+ align:start position:0%
+all right now this formula is useful if
+ 
+
+ align:start position:0%
+all right now this formula is useful if
+you're trying to say a value get the
+
+ align:start position:0%
+you're trying to say a value get the
+ 
+
+ align:start position:0%
+you're trying to say a value get the
+value of a company and the company is
+
+ align:start position:0%
+value of a company and the company is
+ 
+
+ align:start position:0%
+value of a company and the company is
+growing every year the company grows its
+
+ align:start position:0%
+growing every year the company grows its
+ 
+
+ align:start position:0%
+growing every year the company grows its
+bottom line by m dollars so the first
+
+ align:start position:0%
+bottom line by m dollars so the first
+ 
+
+ align:start position:0%
+bottom line by m dollars so the first
+year the company generates MLL the next
+
+ align:start position:0%
+year the company generates MLL the next
+ 
+
+ align:start position:0%
+year the company generates MLL the next
+year it generates two2 MLL in profit the
+
+ align:start position:0%
+year it generates two2 MLL in profit the
+ 
+
+ align:start position:0%
+year it generates two2 MLL in profit the
+next year is three MLL so you got an
+
+ align:start position:0%
+next year is three MLL so you got an
+ 
+
+ align:start position:0%
+next year is three MLL so you got an
+entity that every year is growing by a
+
+ align:start position:0%
+entity that every year is growing by a
+ 
+
+ align:start position:0%
+entity that every year is growing by a
+fixed amount it's not doubling every
+
+ align:start position:0%
+fixed amount it's not doubling every
+ 
+
+ align:start position:0%
+fixed amount it's not doubling every
+year but every year adds in MLL more of
+
+ align:start position:0%
+year but every year adds in MLL more of
+ 
+
+ align:start position:0%
+year but every year adds in MLL more of
+profit what would you pay to buy that
+
+ align:start position:0%
+profit what would you pay to buy that
+ 
+
+ align:start position:0%
+profit what would you pay to buy that
+company what is that worth all right so
+
+ align:start position:0%
+company what is that worth all right so
+ 
+
+ align:start position:0%
+company what is that worth all right so
+you can think of s as again an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+annuity here the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+annuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pays I
+
+ align:start position:0%
+pays I
+ 
+
+ align:start position:0%
+pays I
+am in this case at the
+
+ align:start position:0%
+am in this case at the
+ 
+
+ align:start position:0%
+am in this case at the
+end not the beginning say of year
+
+ align:start position:0%
+end not the beginning say of year
+ 
+
+ align:start position:0%
+end not the beginning say of year
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forever this company is or this annuity
+
+ align:start position:0%
+forever this company is or this annuity
+ 
+
+ align:start position:0%
+forever this company is or this annuity
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+worth well we just plug into the
+
+ align:start position:0%
+worth well we just plug into the
+ 
+
+ align:start position:0%
+worth well we just plug into the
+formula instead of $1 each year it's m
+
+ align:start position:0%
+formula instead of $1 each year it's m
+ 
+
+ align:start position:0%
+formula instead of $1 each year it's m
+so there's an M out front X is 1 over 1
+
+ align:start position:0%
+so there's an M out front X is 1 over 1
+ 
+
+ align:start position:0%
+so there's an M out front X is 1 over 1
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p and then we have oneus 1 over 1 + p^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 and if we multiply the top and bottom
+
+ align:start position:0%
+2 and if we multiply the top and bottom
+ 
+
+ align:start position:0%
+2 and if we multiply the top and bottom
+by 1 + p^
+
+ align:start position:0%
+by 1 + p^
+ 
+
+ align:start position:0%
+by 1 + p^
+2 we
+
+ align:start position:0%
+2 we
+ 
+
+ align:start position:0%
+2 we
+get m 1 + p over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p^2 all right so it's possible a very
+
+ align:start position:0%
+p^2 all right so it's possible a very
+ 
+
+ align:start position:0%
+p^2 all right so it's possible a very
+simple formula to figure out how much
+
+ align:start position:0%
+simple formula to figure out how much
+ 
+
+ align:start position:0%
+simple formula to figure out how much
+you should spend to buy this company
+
+ align:start position:0%
+you should spend to buy this company
+ 
+
+ align:start position:0%
+you should spend to buy this company
+what its value is today so for example
+
+ align:start position:0%
+what its value is today so for example
+ 
+
+ align:start position:0%
+what its value is today so for example
+say the company was adding $50,000 a
+
+ align:start position:0%
+say the company was adding $50,000 a
+ 
+
+ align:start position:0%
+say the company was adding $50,000 a
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+profit the interest rate was
+
+ align:start position:0%
+profit the interest rate was
+ 
+
+ align:start position:0%
+profit the interest rate was
+6% the value of this company is $14
+
+ align:start position:0%
+6% the value of this company is $14
+ 
+
+ align:start position:0%
+6% the value of this company is $14
+million $ 14.7
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+million just plugging into that
+
+ align:start position:0%
+million just plugging into that
+ 
+
+ align:start position:0%
+million just plugging into that
+formula all right so people that do that
+
+ align:start position:0%
+formula all right so people that do that
+ 
+
+ align:start position:0%
+formula all right so people that do that
+buy companies and stuff they use
+
+ align:start position:0%
+buy companies and stuff they use
+ 
+
+ align:start position:0%
+buy companies and stuff they use
+formulas like this to figure out what
+
+ align:start position:0%
+formulas like this to figure out what
+ 
+
+ align:start position:0%
+formulas like this to figure out what
+it's worth of course you got to make
+
+ align:start position:0%
+it's worth of course you got to make
+ 
+
+ align:start position:0%
+it's worth of course you got to make
+sure it's really going to keep paying
+
+ align:start position:0%
+sure it's really going to keep paying
+ 
+
+ align:start position:0%
+sure it's really going to keep paying
+you know the $50,000 more every year and
+
+ align:start position:0%
+you know the $50,000 more every year and
+ 
+
+ align:start position:0%
+you know the $50,000 more every year and
+that this is the right interest rate to
+
+ align:start position:0%
+that this is the right interest rate to
+ 
+
+ align:start position:0%
+that this is the right interest rate to
+be thinking
+
+ align:start position:0%
+be thinking
+ 
+
+ align:start position:0%
+be thinking
+about you know and the guys on Wall
+
+ align:start position:0%
+about you know and the guys on Wall
+ 
+
+ align:start position:0%
+about you know and the guys on Wall
+Street the bankers on Wall Street
+
+ align:start position:0%
+Street the bankers on Wall Street
+ 
+
+ align:start position:0%
+Street the bankers on Wall Street
+they'll have their estimations for what
+
+ align:start position:0%
+they'll have their estimations for what
+ 
+
+ align:start position:0%
+they'll have their estimations for what
+these things you know are the value of P
+
+ align:start position:0%
+these things you know are the value of P
+ 
+
+ align:start position:0%
+these things you know are the value of P
+they would put into these
+
+ align:start position:0%
+they would put into these
+ 
+
+ align:start position:0%
+they would put into these
+formulas any questions about
+
+ align:start position:0%
+formulas any questions about
+ 
+
+ align:start position:0%
+formulas any questions about
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay good all right so this one is
+
+ align:start position:0%
+yeah okay good all right so this one is
+ 
+
+ align:start position:0%
+yeah okay good all right so this one is
+okay okay I plugged x = 1 1 + P like we
+
+ align:start position:0%
+okay okay I plugged x = 1 1 + P like we
+ 
+
+ align:start position:0%
+okay okay I plugged x = 1 1 + P like we
+did before remember for the annuity
+
+ align:start position:0%
+did before remember for the annuity
+ 
+
+ align:start position:0%
+did before remember for the annuity
+because every year you're degrading it
+
+ align:start position:0%
+because every year you're degrading it
+ 
+
+ align:start position:0%
+because every year you're degrading it
+devaluing it by one over 1 plus P so
+
+ align:start position:0%
+devaluing it by one over 1 plus P so
+ 
+
+ align:start position:0%
+devaluing it by one over 1 plus P so
+that's the X
+
+ align:start position:0%
+that's the X
+ 
+
+ align:start position:0%
+that's the X
+term and it's paying uh in the E year it
+
+ align:start position:0%
+term and it's paying uh in the E year it
+ 
+
+ align:start position:0%
+term and it's paying uh in the E year it
+it's paying IM
+
+ align:start position:0%
+it's paying IM
+ 
+
+ align:start position:0%
+it's paying IM
+doll all right so the first year it pays
+
+ align:start position:0%
+doll all right so the first year it pays
+ 
+
+ align:start position:0%
+doll all right so the first year it pays
+M the next year 2m the next year 3M
+
+ align:start position:0%
+M the next year 2m the next year 3M
+ 
+
+ align:start position:0%
+M the next year 2m the next year 3M
+the next year
+
+ align:start position:0%
+the next year
+ 
+
+ align:start position:0%
+the next year
+4M but every year you're knocking it
+
+ align:start position:0%
+4M but every year you're knocking it
+ 
+
+ align:start position:0%
+4M but every year you're knocking it
+down by 1 plus 1 over P to the number of
+
+ align:start position:0%
+down by 1 plus 1 over P to the number of
+ 
+
+ align:start position:0%
+down by 1 plus 1 over P to the number of
+years so what you what you get the sum
+
+ align:start position:0%
+years so what you what you get the sum
+ 
+
+ align:start position:0%
+years so what you what you get the sum
+you've really got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is I equal 1 to Infinity I am
+
+ align:start position:0%
+here is I equal 1 to Infinity I am
+ 
+
+ align:start position:0%
+here is I equal 1 to Infinity I am
+dollars are paid but those dollars are
+
+ align:start position:0%
+dollars are paid but those dollars are
+ 
+
+ align:start position:0%
+dollars are paid but those dollars are
+worth one over 1 plus P to the I today
+
+ align:start position:0%
+worth one over 1 plus P to the I today
+ 
+
+ align:start position:0%
+worth one over 1 plus P to the I today
+the current value that's a good question
+
+ align:start position:0%
+the current value that's a good question
+ 
+
+ align:start position:0%
+the current value that's a good question
+I should have should have said that
+
+ align:start position:0%
+I should have should have said that
+ 
+
+ align:start position:0%
+I should have should have said that
+that's a great question all right so
+
+ align:start position:0%
+that's a great question all right so
+ 
+
+ align:start position:0%
+that's a great question all right so
+that's how we connect this up because
+
+ align:start position:0%
+that's how we connect this up because
+ 
+
+ align:start position:0%
+that's how we connect this up because
+you're getting paid this much in I years
+
+ align:start position:0%
+you're getting paid this much in I years
+ 
+
+ align:start position:0%
+you're getting paid this much in I years
+and that's worth that much degradation
+
+ align:start position:0%
+and that's worth that much degradation
+ 
+
+ align:start position:0%
+and that's worth that much degradation
+or that much devaluation today and now
+
+ align:start position:0%
+or that much devaluation today and now
+ 
+
+ align:start position:0%
+or that much devaluation today and now
+we add up the total current
+
+ align:start position:0%
+we add up the total current
+ 
+
+ align:start position:0%
+we add up the total current
+value all right so even a company that
+
+ align:start position:0%
+value all right so even a company that
+ 
+
+ align:start position:0%
+value all right so even a company that
+is paying you more and more every year
+
+ align:start position:0%
+is paying you more and more every year
+ 
+
+ align:start position:0%
+is paying you more and more every year
+still has a finite
+
+ align:start position:0%
+still has a finite
+ 
+
+ align:start position:0%
+still has a finite
+value because the extra you know the
+
+ align:start position:0%
+value because the extra you know the
+ 
+
+ align:start position:0%
+value because the extra you know the
+payments are increasing but only
+
+ align:start position:0%
+payments are increasing but only
+ 
+
+ align:start position:0%
+payments are increasing but only
+linearly the value today is decreasing
+
+ align:start position:0%
+linearly the value today is decreasing
+ 
+
+ align:start position:0%
+linearly the value today is decreasing
+geometrically and the geometric decrease
+
+ align:start position:0%
+geometrically and the geometric decrease
+ 
+
+ align:start position:0%
+geometrically and the geometric decrease
+wipes out the value of the company in
+
+ align:start position:0%
+wipes out the value of the company in
+ 
+
+ align:start position:0%
+wipes out the value of the company in
+the future yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which where should I uh what did I do oh
+
+ align:start position:0%
+which where should I uh what did I do oh
+ 
+
+ align:start position:0%
+which where should I uh what did I do oh
+wait wait wait I screwed up here
+
+ align:start position:0%
+wait wait wait I screwed up here
+ 
+
+ align:start position:0%
+wait wait wait I screwed up here
+too is that what you're asking
+
+ align:start position:0%
+too is that what you're asking
+ 
+
+ align:start position:0%
+too is that what you're asking
+about yeah that's what I should have
+
+ align:start position:0%
+about yeah that's what I should have
+ 
+
+ align:start position:0%
+about yeah that's what I should have
+done right because I got 1 - x is 1 - 1
+
+ align:start position:0%
+done right because I got 1 - x is 1 - 1
+ 
+
+ align:start position:0%
+done right because I got 1 - x is 1 - 1
+over 1+ P that gets squared and now when
+
+ align:start position:0%
+over 1+ P that gets squared and now when
+ 
+
+ align:start position:0%
+over 1+ P that gets squared and now when
+I multiply 1 + p^ 2 it's multiplying
+
+ align:start position:0%
+I multiply 1 + p^ 2 it's multiplying
+ 
+
+ align:start position:0%
+I multiply 1 + p^ 2 it's multiplying
+this by 1 plus p P it's 1 + P minus 1 is
+
+ align:start position:0%
+this by 1 plus p P it's 1 + P minus 1 is
+ 
+
+ align:start position:0%
+this by 1 plus p P it's 1 + P minus 1 is
+p so I have p^2 all right so this part's
+
+ align:start position:0%
+p so I have p^2 all right so this part's
+ 
+
+ align:start position:0%
+p so I have p^2 all right so this part's
+okay that part I wrote wrong that's good
+
+ align:start position:0%
+okay that part I wrote wrong that's good
+ 
+
+ align:start position:0%
+okay that part I wrote wrong that's good
+any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions all
+
+ align:start position:0%
+questions all
+ 
+
+ align:start position:0%
+questions all
+right uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's do a simple example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum a half plus 24s + 38 +
+
+ align:start position:0%
+sum a half plus 24s + 38 +
+ 
+
+ align:start position:0%
+sum a half plus 24s + 38 +
+416 forever what's that sum equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plug that in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula uh
+
+ align:start position:0%
+formula uh
+ 
+
+ align:start position:0%
+formula uh
+y that's right
+
+ align:start position:0%
+y that's right
+ 
+
+ align:start position:0%
+y that's right
+good these
+
+ align:start position:0%
+good these
+ 
+
+ align:start position:0%
+good these
+details yeah otherwise that sum would be
+
+ align:start position:0%
+details yeah otherwise that sum would be
+ 
+
+ align:start position:0%
+details yeah otherwise that sum would be
+what if I didn't put the negative here
+
+ align:start position:0%
+what if I didn't put the negative here
+ 
+
+ align:start position:0%
+what if I didn't put the negative here
+it would be Infinity that's not so
+
+ align:start position:0%
+it would be Infinity that's not so
+ 
+
+ align:start position:0%
+it would be Infinity that's not so
+interesting the negative makes it more
+
+ align:start position:0%
+interesting the negative makes it more
+ 
+
+ align:start position:0%
+interesting the negative makes it more
+interesting so I got one over two to the
+
+ align:start position:0%
+interesting so I got one over two to the
+ 
+
+ align:start position:0%
+interesting so I got one over two to the
+ion there what's it worth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I can plug it in the formula what's
+
+ align:start position:0%
+then I can plug it in the formula what's
+ 
+
+ align:start position:0%
+then I can plug it in the formula what's
+x 12 so I get 12 over 1 - 12
+
+ align:start position:0%
+x 12 so I get 12 over 1 - 12
+ 
+
+ align:start position:0%
+x 12 so I get 12 over 1 - 12
+squared is 12 over a quarter and that's
+
+ align:start position:0%
+squared is 12 over a quarter and that's
+ 
+
+ align:start position:0%
+squared is 12 over a quarter and that's
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+okay all
+
+ align:start position:0%
+okay all
+ 
+
+ align:start position:0%
+okay all
+right any questions on that formula
+
+ align:start position:0%
+right any questions on that formula
+ 
+
+ align:start position:0%
+right any questions on that formula
+okay it's amazing how useful these
+
+ align:start position:0%
+okay it's amazing how useful these
+ 
+
+ align:start position:0%
+okay it's amazing how useful these
+things get to be later
+
+ align:start position:0%
+things get to be later
+ 
+
+ align:start position:0%
+things get to be later
+um all right so that's sort of the
+
+ align:start position:0%
+um all right so that's sort of the
+ 
+
+ align:start position:0%
+um all right so that's sort of the
+geometric kinds of
+
+ align:start position:0%
+geometric kinds of
+ 
+
+ align:start position:0%
+geometric kinds of
+things next I want to talk about more
+
+ align:start position:0%
+things next I want to talk about more
+ 
+
+ align:start position:0%
+things next I want to talk about more
+the arithmetic kinds of sums and what
+
+ align:start position:0%
+the arithmetic kinds of sums and what
+ 
+
+ align:start position:0%
+the arithmetic kinds of sums and what
+you do
+
+ align:start position:0%
+you do
+ 
+
+ align:start position:0%
+you do
+there in fact we've already seen one
+
+ align:start position:0%
+there in fact we've already seen one
+ 
+
+ align:start position:0%
+there in fact we've already seen one
+that we've
+
+ align:start position:0%
+that we've
+ 
+
+ align:start position:0%
+that we've
+done if I sum I equals 1 to n of I I
+
+ align:start position:0%
+done if I sum I equals 1 to n of I I
+ 
+
+ align:start position:0%
+done if I sum I equals 1 to n of I I
+think we've already done this one that's
+
+ align:start position:0%
+think we've already done this one that's
+ 
+
+ align:start position:0%
+think we've already done this one that's
+just n * n + 1 / 2 probably most of you
+
+ align:start position:0%
+just n * n + 1 / 2 probably most of you
+ 
+
+ align:start position:0%
+just n * n + 1 / 2 probably most of you
+even learned that formula back in middle
+
+ align:start position:0%
+even learned that formula back in middle
+ 
+
+ align:start position:0%
+even learned that formula back in middle
+school I'm guessing maybe
+
+ align:start position:0%
+school I'm guessing maybe
+ 
+
+ align:start position:0%
+school I'm guessing maybe
+before how many people know the answer
+
+ align:start position:0%
+before how many people know the answer
+ 
+
+ align:start position:0%
+before how many people know the answer
+for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum the sum of the squares the first n
+
+ align:start position:0%
+sum the sum of the squares the first n
+ 
+
+ align:start position:0%
+sum the sum of the squares the first n
+squares all right somebody knows what's
+
+ align:start position:0%
+squares all right somebody knows what's
+ 
+
+ align:start position:0%
+squares all right somebody knows what's
+what is it n * n +
+
+ align:start position:0%
+what is it n * n +
+ 
+
+ align:start position:0%
+what is it n * n +
+1 * 2 n + 1 all over 6 all right very
+
+ align:start position:0%
+1 * 2 n + 1 all over 6 all right very
+ 
+
+ align:start position:0%
+1 * 2 n + 1 all over 6 all right very
+good good that is correct all right most
+
+ align:start position:0%
+good good that is correct all right most
+ 
+
+ align:start position:0%
+good good that is correct all right most
+people don't remember that one it's a
+
+ align:start position:0%
+people don't remember that one it's a
+ 
+
+ align:start position:0%
+people don't remember that one it's a
+little harder to
+
+ align:start position:0%
+little harder to
+ 
+
+ align:start position:0%
+little harder to
+derive um how would you prove
+
+ align:start position:0%
+derive um how would you prove
+ 
+
+ align:start position:0%
+derive um how would you prove
+this by induction unfortunately
+
+ align:start position:0%
+this by induction unfortunately
+ 
+
+ align:start position:0%
+this by induction unfortunately
+induction doesn't tell you how to
+
+ align:start position:0%
+induction doesn't tell you how to
+ 
+
+ align:start position:0%
+induction doesn't tell you how to
+remember what the formula was and
+
+ align:start position:0%
+remember what the formula was and
+ 
+
+ align:start position:0%
+remember what the formula was and
+there's a couple of ways you can go
+
+ align:start position:0%
+there's a couple of ways you can go
+ 
+
+ align:start position:0%
+there's a couple of ways you can go
+about that one is you could remember or
+
+ align:start position:0%
+about that one is you could remember or
+ 
+
+ align:start position:0%
+about that one is you could remember or
+guess that the answer is a polinomial in
+
+ align:start position:0%
+guess that the answer is a polinomial in
+ 
+
+ align:start position:0%
+guess that the answer is a polinomial in
+n in fact because you're summing squares
+
+ align:start position:0%
+n in fact because you're summing squares
+ 
+
+ align:start position:0%
+n in fact because you're summing squares
+you might guess that it's a cubic
+
+ align:start position:0%
+you might guess that it's a cubic
+ 
+
+ align:start position:0%
+you might guess that it's a cubic
+polinomial inet and if you remember just
+
+ align:start position:0%
+polinomial inet and if you remember just
+ 
+
+ align:start position:0%
+polinomial inet and if you remember just
+that or guess just that then you could
+
+ align:start position:0%
+that or guess just that then you could
+ 
+
+ align:start position:0%
+that or guess just that then you could
+actually plug in values and get the
+
+ align:start position:0%
+actually plug in values and get the
+ 
+
+ align:start position:0%
+actually plug in values and get the
+answer and this is you know a common
+
+ align:start position:0%
+answer and this is you know a common
+ 
+
+ align:start position:0%
+answer and this is you know a common
+method of solving these sums is you sort
+
+ align:start position:0%
+method of solving these sums is you sort
+ 
+
+ align:start position:0%
+method of solving these sums is you sort
+of guess the form of the solution in
+
+ align:start position:0%
+of guess the form of the solution in
+ 
+
+ align:start position:0%
+of guess the form of the solution in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+case you might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess that for all n the sum I = 1 to n
+
+ align:start position:0%
+guess that for all n the sum I = 1 to n
+ 
+
+ align:start position:0%
+guess that for all n the sum I = 1 to n
+of i^2
+
+ align:start position:0%
+of i^2
+ 
+
+ align:start position:0%
+of i^2
+equals a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubic and then what you would do is plug
+
+ align:start position:0%
+cubic and then what you would do is plug
+ 
+
+ align:start position:0%
+cubic and then what you would do is plug
+in the value
+
+ align:start position:0%
+in the value
+ 
+
+ align:start position:0%
+in the value
+Nal 1 Nal 2 maybe even we'll make it n
+
+ align:start position:0%
+Nal 1 Nal 2 maybe even we'll make it n
+ 
+
+ align:start position:0%
+Nal 1 Nal 2 maybe even we'll make it n
+equals Zer make it simple and start
+
+ align:start position:0%
+equals Zer make it simple and start
+ 
+
+ align:start position:0%
+equals Zer make it simple and start
+getting some constraints on the
+
+ align:start position:0%
+getting some constraints on the
+ 
+
+ align:start position:0%
+getting some constraints on the
+coefficients so you would plug
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in N equal 0
+
+ align:start position:0%
+in N equal 0
+ 
+
+ align:start position:0%
+in N equal 0
+the sum is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero the polinomial evaluates to
+
+ align:start position:0%
+zero the polinomial evaluates to
+ 
+
+ align:start position:0%
+zero the polinomial evaluates to
+D that tells you what D's got to be
+
+ align:start position:0%
+D that tells you what D's got to be
+ 
+
+ align:start position:0%
+D that tells you what D's got to be
+right away n equals 1 the sum is one and
+
+ align:start position:0%
+right away n equals 1 the sum is one and
+ 
+
+ align:start position:0%
+right away n equals 1 the sum is one and
+when you plug into the polinomial you
+
+ align:start position:0%
+when you plug into the polinomial you
+ 
+
+ align:start position:0%
+when you plug into the polinomial you
+get a plus b plus C plus
+
+ align:start position:0%
+get a plus b plus C plus
+ 
+
+ align:start position:0%
+get a plus b plus C plus
+d n equal
+
+ align:start position:0%
+d n equal
+ 
+
+ align:start position:0%
+d n equal
+2 well that's 1 + 4 is
+
+ align:start position:0%
+2 well that's 1 + 4 is
+ 
+
+ align:start position:0%
+2 well that's 1 + 4 is
+5 2 cubed is 8 so you have8 8 a + 4 b +
+
+ align:start position:0%
+5 2 cubed is 8 so you have8 8 a + 4 b +
+ 
+
+ align:start position:0%
+5 2 cubed is 8 so you have8 8 a + 4 b +
+2 C + D and you'll need one more since
+
+ align:start position:0%
+2 C + D and you'll need one more since
+ 
+
+ align:start position:0%
+2 C + D and you'll need one more since
+you got four
+
+ align:start position:0%
+you got four
+ 
+
+ align:start position:0%
+you got four
+variables let's see 1 + 4 + 9 is
+
+ align:start position:0%
+variables let's see 1 + 4 + 9 is
+ 
+
+ align:start position:0%
+variables let's see 1 + 4 + 9 is
+14 uh I've now got 3 cubed is 27 a plus
+
+ align:start position:0%
+14 uh I've now got 3 cubed is 27 a plus
+ 
+
+ align:start position:0%
+14 uh I've now got 3 cubed is 27 a plus
+uh 9 b + 3 C +
+
+ align:start position:0%
+uh 9 b + 3 C +
+ 
+
+ align:start position:0%
+uh 9 b + 3 C +
+D so now I got four equations and four
+
+ align:start position:0%
+D so now I got four equations and four
+ 
+
+ align:start position:0%
+D so now I got four equations and four
+variables and with any luck I can solve
+
+ align:start position:0%
+variables and with any luck I can solve
+ 
+
+ align:start position:0%
+variables and with any luck I can solve
+that system of equations and get the
+
+ align:start position:0%
+that system of equations and get the
+ 
+
+ align:start position:0%
+that system of equations and get the
+answer and in fact you can when you
+
+ align:start position:0%
+answer and in fact you can when you
+ 
+
+ align:start position:0%
+answer and in fact you can when you
+solve this system you get AAL
+
+ align:start position:0%
+solve this system you get AAL
+ 
+
+ align:start position:0%
+solve this system you get AAL
+1/3 B = 12 c = 1 16 and D equal 0 and
+
+ align:start position:0%
+1/3 B = 12 c = 1 16 and D equal 0 and
+ 
+
+ align:start position:0%
+1/3 B = 12 c = 1 16 and D equal 0 and
+that's exactly what you get in that
+
+ align:start position:0%
+that's exactly what you get in that
+ 
+
+ align:start position:0%
+that's exactly what you get in that
+formula so that's a way to reproduce the
+
+ align:start position:0%
+formula so that's a way to reproduce the
+ 
+
+ align:start position:0%
+formula so that's a way to reproduce the
+formula if you forgot
+
+ align:start position:0%
+formula if you forgot
+ 
+
+ align:start position:0%
+formula if you forgot
+it uh now this method really to be sure
+
+ align:start position:0%
+it uh now this method really to be sure
+ 
+
+ align:start position:0%
+it uh now this method really to be sure
+you got the right answer you got to go
+
+ align:start position:0%
+you got the right answer you got to go
+ 
+
+ align:start position:0%
+you got the right answer you got to go
+prove it by induction because I didn't D
+
+ align:start position:0%
+prove it by induction because I didn't D
+ 
+
+ align:start position:0%
+prove it by induction because I didn't D
+I didn't I derived the answer if it was
+
+ align:start position:0%
+I didn't I derived the answer if it was
+ 
+
+ align:start position:0%
+I didn't I derived the answer if it was
+a polinomial I would have gotten it
+
+ align:start position:0%
+a polinomial I would have gotten it
+ 
+
+ align:start position:0%
+a polinomial I would have gotten it
+right but I might be wrong in my guess
+
+ align:start position:0%
+right but I might be wrong in my guess
+ 
+
+ align:start position:0%
+right but I might be wrong in my guess
+and to make sure your guess is right you
+
+ align:start position:0%
+and to make sure your guess is right you
+ 
+
+ align:start position:0%
+and to make sure your guess is right you
+got to go back and use induction to
+
+ align:start position:0%
+got to go back and use induction to
+ 
+
+ align:start position:0%
+got to go back and use induction to
+prove it for this approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well it turns out that anytime
+
+ align:start position:0%
+yeah well it turns out that anytime
+ 
+
+ align:start position:0%
+yeah well it turns out that anytime
+you're summing Powers the answer is a
+
+ align:start position:0%
+you're summing Powers the answer is a
+ 
+
+ align:start position:0%
+you're summing Powers the answer is a
+polinomial to one higher
+
+ align:start position:0%
+polinomial to one higher
+ 
+
+ align:start position:0%
+polinomial to one higher
+degree so if you just remembered that
+
+ align:start position:0%
+degree so if you just remembered that
+ 
+
+ align:start position:0%
+degree so if you just remembered that
+fact or you guessed that fact another
+
+ align:start position:0%
+fact or you guessed that fact another
+ 
+
+ align:start position:0%
+fact or you guessed that fact another
+way to sort of Imagine That might be
+
+ align:start position:0%
+way to sort of Imagine That might be
+ 
+
+ align:start position:0%
+way to sort of Imagine That might be
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+is that you know I'm getting n of them
+
+ align:start position:0%
+is that you know I'm getting n of them
+ 
+
+ align:start position:0%
+is that you know I'm getting n of them
+so I might be multiplying and the top
+
+ align:start position:0%
+so I might be multiplying and the top
+ 
+
+ align:start position:0%
+so I might be multiplying and the top
+one is n^ s so I'm going to have n of
+
+ align:start position:0%
+one is n^ s so I'm going to have n of
+ 
+
+ align:start position:0%
+one is n^ s so I'm going to have n of
+them about n s may be something like n
+
+ align:start position:0%
+them about n s may be something like n
+ 
+
+ align:start position:0%
+them about n s may be something like n
+cubed um that's another way you know you
+
+ align:start position:0%
+cubed um that's another way you know you
+ 
+
+ align:start position:0%
+cubed um that's another way you know you
+could think of it to Guess
+
+ align:start position:0%
+could think of it to Guess
+ 
+
+ align:start position:0%
+could think of it to Guess
+that any other
+
+ align:start position:0%
+that any other
+ 
+
+ align:start position:0%
+that any other
+questions on
+
+ align:start position:0%
+questions on
+ 
+
+ align:start position:0%
+questions on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay all right so far all these sums had
+
+ align:start position:0%
+okay all right so far all these sums had
+ 
+
+ align:start position:0%
+okay all right so far all these sums had
+nice Clos forms and a lot of them do
+
+ align:start position:0%
+nice Clos forms and a lot of them do
+ 
+
+ align:start position:0%
+nice Clos forms and a lot of them do
+that you'll encounter later on but not
+
+ align:start position:0%
+that you'll encounter later on but not
+ 
+
+ align:start position:0%
+that you'll encounter later on but not
+all and sometimes you get sums that
+
+ align:start position:0%
+all and sometimes you get sums that
+ 
+
+ align:start position:0%
+all and sometimes you get sums that
+don't have a nice closed form at least
+
+ align:start position:0%
+don't have a nice closed form at least
+ 
+
+ align:start position:0%
+don't have a nice closed form at least
+nobody's ever figured out one and
+
+ align:start position:0%
+nobody's ever figured out one and
+ 
+
+ align:start position:0%
+nobody's ever figured out one and
+probably doesn't always exist for
+
+ align:start position:0%
+probably doesn't always exist for
+ 
+
+ align:start position:0%
+probably doesn't always exist for
+example what if I want to sum the first
+
+ align:start position:0%
+example what if I want to sum the first
+ 
+
+ align:start position:0%
+example what if I want to sum the first
+n square roots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integers let's write that down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so say I want a closed form for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy you know nobody knows an answer for
+
+ align:start position:0%
+guy you know nobody knows an answer for
+ 
+
+ align:start position:0%
+guy you know nobody knows an answer for
+that but there are ways of getting very
+
+ align:start position:0%
+that but there are ways of getting very
+ 
+
+ align:start position:0%
+that but there are ways of getting very
+good close bounds on it that are closed
+
+ align:start position:0%
+good close bounds on it that are closed
+ 
+
+ align:start position:0%
+good close bounds on it that are closed
+for and these are very important we're
+
+ align:start position:0%
+for and these are very important we're
+ 
+
+ align:start position:0%
+for and these are very important we're
+going to use this the rest of today and
+
+ align:start position:0%
+going to use this the rest of today and
+ 
+
+ align:start position:0%
+going to use this the rest of today and
+the rest of next time
+
+ align:start position:0%
+the rest of next time
+ 
+
+ align:start position:0%
+the rest of next time
+uh and they're based on replacing the
+
+ align:start position:0%
+uh and they're based on replacing the
+ 
+
+ align:start position:0%
+uh and they're based on replacing the
+sum with an integral and the integral is
+
+ align:start position:0%
+sum with an integral and the integral is
+ 
+
+ align:start position:0%
+sum with an integral and the integral is
+very close to the right answer and then
+
+ align:start position:0%
+very close to the right answer and then
+ 
+
+ align:start position:0%
+very close to the right answer and then
+we can see what the error terms are so
+
+ align:start position:0%
+we can see what the error terms are so
+ 
+
+ align:start position:0%
+we can see what the error terms are so
+let's first look at the case when we've
+
+ align:start position:0%
+let's first look at the case when we've
+ 
+
+ align:start position:0%
+let's first look at the case when we've
+got a sum where the terms are increasing
+
+ align:start position:0%
+got a sum where the terms are increasing
+ 
+
+ align:start position:0%
+got a sum where the terms are increasing
+as I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grows all right and these we'll call
+
+ align:start position:0%
+grows all right and these we'll call
+ 
+
+ align:start position:0%
+grows all right and these we'll call
+these integration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounds and a general sum will look like
+
+ align:start position:0%
+bounds and a general sum will look like
+ 
+
+ align:start position:0%
+bounds and a general sum will look like
+this I 1 to n of f of
+
+ align:start position:0%
+this I 1 to n of f of
+ 
+
+ align:start position:0%
+this I 1 to n of f of
+I and the first case is when f is a
+
+ align:start position:0%
+I and the first case is when f is a
+ 
+
+ align:start position:0%
+I and the first case is when f is a
+positive increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function increasing in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I right ration bounds and so we're
+
+ align:start position:0%
+I right ration bounds and so we're
+ 
+
+ align:start position:0%
+I right ration bounds and so we're
+increasing function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let me draw a picture
+
+ align:start position:0%
+all right so let me draw a picture
+ 
+
+ align:start position:0%
+all right so let me draw a picture
+that'll
+
+ align:start position:0%
+that'll
+ 
+
+ align:start position:0%
+that'll
+hopefully make the bounds we're going to
+
+ align:start position:0%
+hopefully make the bounds we're going to
+ 
+
+ align:start position:0%
+hopefully make the bounds we're going to
+get pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easy so let's
+
+ align:start position:0%
+easy so let's
+ 
+
+ align:start position:0%
+easy so let's
+draw the sum here as follows I got 0 1 2
+
+ align:start position:0%
+draw the sum here as follows I got 0 1 2
+ 
+
+ align:start position:0%
+draw the sum here as follows I got 0 1 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N - 2 N
+
+ align:start position:0%
+N - 2 N
+ 
+
+ align:start position:0%
+N - 2 N
+-1
+
+ align:start position:0%
+-1
+ 
+
+ align:start position:0%
+-1
+n and draw the values of f here here's F
+
+ align:start position:0%
+n and draw the values of f here here's F
+ 
+
+ align:start position:0%
+n and draw the values of f here here's F
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+one F of two it's
+
+ align:start position:0%
+one F of two it's
+ 
+
+ align:start position:0%
+one F of two it's
+increasing F of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three F of n minus one and F of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n then I'll draw
+
+ align:start position:0%
+n then I'll draw
+ 
+
+ align:start position:0%
+n then I'll draw
+the rect angles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so this has
+
+ align:start position:0%
+here so this has
+ 
+
+ align:start position:0%
+here so this has
+area of f of one this has area F of two
+
+ align:start position:0%
+area of f of one this has area F of two
+ 
+
+ align:start position:0%
+area of f of one this has area F of two
+this has area F of
+
+ align:start position:0%
+this has area F of
+ 
+
+ align:start position:0%
+this has area F of
+three and we keep on
+
+ align:start position:0%
+three and we keep on
+ 
+
+ align:start position:0%
+three and we keep on
+going see this will be F of n minus two
+
+ align:start position:0%
+going see this will be F of n minus two
+ 
+
+ align:start position:0%
+going see this will be F of n minus two
+on this one I'll just do F of n minus
+
+ align:start position:0%
+on this one I'll just do F of n minus
+ 
+
+ align:start position:0%
+on this one I'll just do F of n minus
+one draw this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so it's unit width its height is f
+
+ align:start position:0%
+here so it's unit width its height is f
+ 
+
+ align:start position:0%
+here so it's unit width its height is f
+of n minus one so so it's area is f of n
+
+ align:start position:0%
+of n minus one so so it's area is f of n
+ 
+
+ align:start position:0%
+of n minus one so so it's area is f of n
+minus one and
+
+ align:start position:0%
+minus one and
+ 
+
+ align:start position:0%
+minus one and
+then F of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n all right and let me also so the the
+
+ align:start position:0%
+n all right and let me also so the the
+ 
+
+ align:start position:0%
+n all right and let me also so the the
+sum of f ofi is the areas in the
+
+ align:start position:0%
+sum of f ofi is the areas in the
+ 
+
+ align:start position:0%
+sum of f ofi is the areas in the
+rectangles that's what the sum is and I
+
+ align:start position:0%
+rectangles that's what the sum is and I
+ 
+
+ align:start position:0%
+rectangles that's what the sum is and I
+want to get bounds on this sum using the
+
+ align:start position:0%
+want to get bounds on this sum using the
+ 
+
+ align:start position:0%
+want to get bounds on this sum using the
+integral because integrals are easier to
+
+ align:start position:0%
+integral because integrals are easier to
+ 
+
+ align:start position:0%
+integral because integrals are easier to
+compute so let's draw the
+
+ align:start position:0%
+compute so let's draw the
+ 
+
+ align:start position:0%
+compute so let's draw the
+function F ofx from 1 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n all right so this is f ofx as a
+
+ align:start position:0%
+n all right so this is f ofx as a
+ 
+
+ align:start position:0%
+n all right so this is f ofx as a
+function now I
+
+ align:start position:0%
+function now I
+ 
+
+ align:start position:0%
+function now I
+claim that the
+
+ align:start position:0%
+claim that the
+ 
+
+ align:start position:0%
+claim that the
+sum I = 1 to n of f of
+
+ align:start position:0%
+sum I = 1 to n of f of
+ 
+
+ align:start position:0%
+sum I = 1 to n of f of
+I is at least F of 1 plus the integral
+
+ align:start position:0%
+I is at least F of 1 plus the integral
+ 
+
+ align:start position:0%
+I is at least F of 1 plus the integral
+from 1 to n
+
+ align:start position:0%
+from 1 to n
+ 
+
+ align:start position:0%
+from 1 to n
+F ofx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX now the integral from 1 to n of f
+
+ align:start position:0%
+DX now the integral from 1 to n of f
+ 
+
+ align:start position:0%
+DX now the integral from 1 to n of f
+ofx is this stuff the stuff under the
+
+ align:start position:0%
+ofx is this stuff the stuff under the
+ 
+
+ align:start position:0%
+ofx is this stuff the stuff under the
+curve all right comes down here starts
+
+ align:start position:0%
+curve all right comes down here starts
+ 
+
+ align:start position:0%
+curve all right comes down here starts
+at one and it's a stuff under the
+
+ align:start position:0%
+at one and it's a stuff under the
+ 
+
+ align:start position:0%
+at one and it's a stuff under the
+curve and what I'm saying here is that
+
+ align:start position:0%
+curve and what I'm saying here is that
+ 
+
+ align:start position:0%
+curve and what I'm saying here is that
+if you take that stuff under the curve
+
+ align:start position:0%
+if you take that stuff under the curve
+ 
+
+ align:start position:0%
+if you take that stuff under the curve
+and add F of one which is this piece
+
+ align:start position:0%
+and add F of one which is this piece
+ 
+
+ align:start position:0%
+and add F of one which is this piece
+that's a lower bound on our sum the
+
+ align:start position:0%
+that's a lower bound on our sum the
+ 
+
+ align:start position:0%
+that's a lower bound on our sum the
+sum's bigger than
+
+ align:start position:0%
+sum's bigger than
+ 
+
+ align:start position:0%
+sum's bigger than
+that all right so what I'm saying is the
+
+ align:start position:0%
+that all right so what I'm saying is the
+ 
+
+ align:start position:0%
+that all right so what I'm saying is the
+area in the
+
+ align:start position:0%
+area in the
+ 
+
+ align:start position:0%
+area in the
+rectangles is at least as big as the
+
+ align:start position:0%
+rectangles is at least as big as the
+ 
+
+ align:start position:0%
+rectangles is at least as big as the
+area in the first rectangle plus the
+
+ align:start position:0%
+area in the first rectangle plus the
+ 
+
+ align:start position:0%
+area in the first rectangle plus the
+area under the
+
+ align:start position:0%
+area under the
+ 
+
+ align:start position:0%
+area under the
+curve does everybody see why that
+
+ align:start position:0%
+curve does everybody see why that
+ 
+
+ align:start position:0%
+curve does everybody see why that
+is all right I'm saying the sum is the
+
+ align:start position:0%
+is all right I'm saying the sum is the
+ 
+
+ align:start position:0%
+is all right I'm saying the sum is the
+area in the
+
+ align:start position:0%
+area in the
+ 
+
+ align:start position:0%
+area in the
+rectangles all right that's pretty clear
+
+ align:start position:0%
+rectangles all right that's pretty clear
+ 
+
+ align:start position:0%
+rectangles all right that's pretty clear
+and that is at least as big as the first
+
+ align:start position:0%
+and that is at least as big as the first
+ 
+
+ align:start position:0%
+and that is at least as big as the first
+rectangle F of one plus the stuff under
+
+ align:start position:0%
+rectangle F of one plus the stuff under
+ 
+
+ align:start position:0%
+rectangle F of one plus the stuff under
+the curve which is the integral and I've
+
+ align:start position:0%
+the curve which is the integral and I've
+ 
+
+ align:start position:0%
+the curve which is the integral and I've
+left I've chopped off these guys that's
+
+ align:start position:0%
+left I've chopped off these guys that's
+ 
+
+ align:start position:0%
+left I've chopped off these guys that's
+extra
+
+ align:start position:0%
+extra
+ 
+
+ align:start position:0%
+extra
+okay is that all right it's a lower
+
+ align:start position:0%
+okay is that all right it's a lower
+ 
+
+ align:start position:0%
+okay is that all right it's a lower
+bound any questions on the lower bound
+
+ align:start position:0%
+bound any questions on the lower bound
+ 
+
+ align:start position:0%
+bound any questions on the lower bound
+this is a picture proof right which we
+
+ align:start position:0%
+this is a picture proof right which we
+ 
+
+ align:start position:0%
+this is a picture proof right which we
+always tell you not to do but we're
+
+ align:start position:0%
+always tell you not to do but we're
+ 
+
+ align:start position:0%
+always tell you not to do but we're
+going to do one here
+
+ align:start position:0%
+going to do one here
+ 
+
+ align:start position:0%
+going to do one here
+uh and of course it totally hides what H
+
+ align:start position:0%
+uh and of course it totally hides what H
+ 
+
+ align:start position:0%
+uh and of course it totally hides what H
+you know why did I need f is increasing
+
+ align:start position:0%
+you know why did I need f is increasing
+ 
+
+ align:start position:0%
+you know why did I need f is increasing
+but we'll see that in a minute the proof
+
+ align:start position:0%
+but we'll see that in a minute the proof
+ 
+
+ align:start position:0%
+but we'll see that in a minute the proof
+would not work unless it is increasing
+
+ align:start position:0%
+would not work unless it is increasing
+ 
+
+ align:start position:0%
+would not work unless it is increasing
+here all
+
+ align:start position:0%
+here all
+ 
+
+ align:start position:0%
+here all
+right any questions because now I'm
+
+ align:start position:0%
+right any questions because now I'm
+ 
+
+ align:start position:0%
+right any questions because now I'm
+going to do the other bound the other
+
+ align:start position:0%
+going to do the other bound the other
+ 
+
+ align:start position:0%
+going to do the other bound the other
+side right I also claim this will be a
+
+ align:start position:0%
+side right I also claim this will be a
+ 
+
+ align:start position:0%
+side right I also claim this will be a
+little trickier to see that the
+
+ align:start position:0%
+little trickier to see that the
+ 
+
+ align:start position:0%
+little trickier to see that the
+sum is at most F of n plus the integral
+
+ align:start position:0%
+sum is at most F of n plus the integral
+ 
+
+ align:start position:0%
+sum is at most F of n plus the integral
+from 1 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n all right so this is the lower bound
+
+ align:start position:0%
+n all right so this is the lower bound
+ 
+
+ align:start position:0%
+n all right so this is the lower bound
+add in F of one the upper bound just add
+
+ align:start position:0%
+add in F of one the upper bound just add
+ 
+
+ align:start position:0%
+add in F of one the upper bound just add
+an F of n so let's see why that's
+
+ align:start position:0%
+an F of n so let's see why that's
+ 
+
+ align:start position:0%
+an F of n so let's see why that's
+true now to see that this is I'm not
+
+ align:start position:0%
+true now to see that this is I'm not
+ 
+
+ align:start position:0%
+true now to see that this is I'm not
+going to be able to draw
+
+ align:start position:0%
+going to be able to draw
+ 
+
+ align:start position:0%
+going to be able to draw
+it I want you to imagine taking this
+
+ align:start position:0%
+it I want you to imagine taking this
+ 
+
+ align:start position:0%
+it I want you to imagine taking this
+this curve and the area under it down to
+
+ align:start position:0%
+this curve and the area under it down to
+ 
+
+ align:start position:0%
+this curve and the area under it down to
+here and sliding it left one
+
+ align:start position:0%
+here and sliding it left one
+ 
+
+ align:start position:0%
+here and sliding it left one
+unit all right sliding it
+
+ align:start position:0%
+unit all right sliding it
+ 
+
+ align:start position:0%
+unit all right sliding it
+left to here sliding it left one unit
+
+ align:start position:0%
+left to here sliding it left one unit
+ 
+
+ align:start position:0%
+left to here sliding it left one unit
+over to here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when I slide it left one unit did
+
+ align:start position:0%
+now when I slide it left one unit did
+ 
+
+ align:start position:0%
+now when I slide it left one unit did
+the area under it
+
+ align:start position:0%
+the area under it
+ 
+
+ align:start position:0%
+the area under it
+change no it's the same area under it
+
+ align:start position:0%
+change no it's the same area under it
+ 
+
+ align:start position:0%
+change no it's the same area under it
+just where it sits on the picture is now
+
+ align:start position:0%
+just where it sits on the picture is now
+ 
+
+ align:start position:0%
+just where it sits on the picture is now
+out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here all right it's this area under this
+
+ align:start position:0%
+here all right it's this area under this
+ 
+
+ align:start position:0%
+here all right it's this area under this
+guy but it's the same thing it's the
+
+ align:start position:0%
+guy but it's the same thing it's the
+ 
+
+ align:start position:0%
+guy but it's the same thing it's the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+integral and you can see that it's more
+
+ align:start position:0%
+integral and you can see that it's more
+ 
+
+ align:start position:0%
+integral and you can see that it's more
+than what's in these rectangles because
+
+ align:start position:0%
+than what's in these rectangles because
+ 
+
+ align:start position:0%
+than what's in these rectangles because
+I got all this
+
+ align:start position:0%
+I got all this
+ 
+
+ align:start position:0%
+I got all this
+stuff and of course I didn't even
+
+ align:start position:0%
+stuff and of course I didn't even
+ 
+
+ align:start position:0%
+stuff and of course I didn't even
+include this so now I add the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+FN so if I take the area under the curve
+
+ align:start position:0%
+FN so if I take the area under the curve
+ 
+
+ align:start position:0%
+FN so if I take the area under the curve
+which is the integral shifted left one
+
+ align:start position:0%
+which is the integral shifted left one
+ 
+
+ align:start position:0%
+which is the integral shifted left one
+so it only goes up to here now and then
+
+ align:start position:0%
+so it only goes up to here now and then
+ 
+
+ align:start position:0%
+so it only goes up to here now and then
+add in this
+
+ align:start position:0%
+add in this
+ 
+
+ align:start position:0%
+add in this
+rectangle that dominates the area in the
+
+ align:start position:0%
+rectangle that dominates the area in the
+ 
+
+ align:start position:0%
+rectangle that dominates the area in the
+rectangles bigger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than all right you you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I could do a lot of equations on
+
+ align:start position:0%
+that I could do a lot of equations on
+ 
+
+ align:start position:0%
+that I could do a lot of equations on
+the board but for sure that would be
+
+ align:start position:0%
+the board but for sure that would be
+ 
+
+ align:start position:0%
+the board but for sure that would be
+hopeless to follow uh any questions
+
+ align:start position:0%
+hopeless to follow uh any questions
+ 
+
+ align:start position:0%
+hopeless to follow uh any questions
+about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah is there is a lot of hand waving or
+
+ align:start position:0%
+yeah is there is a lot of hand waving or
+ 
+
+ align:start position:0%
+yeah is there is a lot of hand waving or
+am I just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always yeah there's a little hand waving
+
+ align:start position:0%
+always yeah there's a little hand waving
+ 
+
+ align:start position:0%
+always yeah there's a little hand waving
+going on uh but I do believe it it's
+
+ align:start position:0%
+going on uh but I do believe it it's
+ 
+
+ align:start position:0%
+going on uh but I do believe it it's
+true we can with equations you can make
+
+ align:start position:0%
+true we can with equations you can make
+ 
+
+ align:start position:0%
+true we can with equations you can make
+it precise so let's look at it again do
+
+ align:start position:0%
+it precise so let's look at it again do
+ 
+
+ align:start position:0%
+it precise so let's look at it again do
+the this one more
+
+ align:start position:0%
+the this one more
+ 
+
+ align:start position:0%
+the this one more
+time yeah I'm waving hands a little bit
+
+ align:start position:0%
+time yeah I'm waving hands a little bit
+ 
+
+ align:start position:0%
+time yeah I'm waving hands a little bit
+but but it also hopefully the intuition
+
+ align:start position:0%
+but but it also hopefully the intuition
+ 
+
+ align:start position:0%
+but but it also hopefully the intuition
+comes across
+
+ align:start position:0%
+comes across
+ 
+
+ align:start position:0%
+comes across
+because when I shift left by one this
+
+ align:start position:0%
+because when I shift left by one this
+ 
+
+ align:start position:0%
+because when I shift left by one this
+point becomes this point that point
+
+ align:start position:0%
+point becomes this point that point
+ 
+
+ align:start position:0%
+point becomes this point that point
+becomes that point and I'm catching the
+
+ align:start position:0%
+becomes that point and I'm catching the
+ 
+
+ align:start position:0%
+becomes that point and I'm catching the
+sort of the cusp of these rectangles and
+
+ align:start position:0%
+sort of the cusp of these rectangles and
+ 
+
+ align:start position:0%
+sort of the cusp of these rectangles and
+now I take this curve
+
+ align:start position:0%
+now I take this curve
+ 
+
+ align:start position:0%
+now I take this curve
+here Shifting the whole curve left one
+
+ align:start position:0%
+here Shifting the whole curve left one
+ 
+
+ align:start position:0%
+here Shifting the whole curve left one
+unit
+
+ align:start position:0%
+unit
+ 
+
+ align:start position:0%
+unit
+and the area doesn't
+
+ align:start position:0%
+and the area doesn't
+ 
+
+ align:start position:0%
+and the area doesn't
+change it would be equivalent of taking
+
+ align:start position:0%
+change it would be equivalent of taking
+ 
+
+ align:start position:0%
+change it would be equivalent of taking
+the integral from 0 to n minus one you
+
+ align:start position:0%
+the integral from 0 to n minus one you
+ 
+
+ align:start position:0%
+the integral from 0 to n minus one you
+know is what I'm doing of f ofx + one
+
+ align:start position:0%
+know is what I'm doing of f ofx + one
+ 
+
+ align:start position:0%
+know is what I'm doing of f ofx + one
+right there another way to look at it
+
+ align:start position:0%
+right there another way to look at it
+ 
+
+ align:start position:0%
+right there another way to look at it
+mathematically maybe probably the formal
+
+ align:start position:0%
+mathematically maybe probably the formal
+ 
+
+ align:start position:0%
+mathematically maybe probably the formal
+way to do it but the idea is that this
+
+ align:start position:0%
+way to do it but the idea is that this
+ 
+
+ align:start position:0%
+way to do it but the idea is that this
+now contains all these first n minus one
+
+ align:start position:0%
+now contains all these first n minus one
+ 
+
+ align:start position:0%
+now contains all these first n minus one
+rectangles are contained underneath it
+
+ align:start position:0%
+rectangles are contained underneath it
+ 
+
+ align:start position:0%
+rectangles are contained underneath it
+and then I just add this
+
+ align:start position:0%
+and then I just add this
+ 
+
+ align:start position:0%
+and then I just add this
+in and I'm ready to I'm good to go I've
+
+ align:start position:0%
+in and I'm ready to I'm good to go I've
+ 
+
+ align:start position:0%
+in and I'm ready to I'm good to go I've
+contained all the rectangles now for the
+
+ align:start position:0%
+contained all the rectangles now for the
+ 
+
+ align:start position:0%
+contained all the rectangles now for the
+upper
+
+ align:start position:0%
+upper
+ 
+
+ align:start position:0%
+upper
+bound all right mathematically what this
+
+ align:start position:0%
+bound all right mathematically what this
+ 
+
+ align:start position:0%
+bound all right mathematically what this
+is this curve is 0 to n minus one FX +
+
+ align:start position:0%
+is this curve is 0 to n minus one FX +
+ 
+
+ align:start position:0%
+is this curve is 0 to n minus one FX +
+one which is the same thing as what that
+
+ align:start position:0%
+one which is the same thing as what that
+ 
+
+ align:start position:0%
+one which is the same thing as what that
+is okay any any
+
+ align:start position:0%
+is okay any any
+ 
+
+ align:start position:0%
+is okay any any
+questions for
+
+ align:start position:0%
+questions for
+ 
+
+ align:start position:0%
+questions for
+that all right but now I have good
+
+ align:start position:0%
+that all right but now I have good
+ 
+
+ align:start position:0%
+that all right but now I have good
+bounds on the
+
+ align:start position:0%
+bounds on the
+ 
+
+ align:start position:0%
+bounds on the
+sum right we know that the sum is at
+
+ align:start position:0%
+sum right we know that the sum is at
+ 
+
+ align:start position:0%
+sum right we know that the sum is at
+least this and at most
+
+ align:start position:0%
+least this and at most
+ 
+
+ align:start position:0%
+least this and at most
+that and those two bounds only differ by
+
+ align:start position:0%
+that and those two bounds only differ by
+ 
+
+ align:start position:0%
+that and those two bounds only differ by
+a single
+
+ align:start position:0%
+a single
+ 
+
+ align:start position:0%
+a single
+term in the sum so they're very close
+
+ align:start position:0%
+term in the sum so they're very close
+ 
+
+ align:start position:0%
+term in the sum so they're very close
+right and these actually are good
+
+ align:start position:0%
+right and these actually are good
+ 
+
+ align:start position:0%
+right and these actually are good
+formulas to write down for your crib
+
+ align:start position:0%
+formulas to write down for your crib
+ 
+
+ align:start position:0%
+formulas to write down for your crib
+sheet that is worth
+
+ align:start position:0%
+sheet that is worth
+ 
+
+ align:start position:0%
+sheet that is worth
+doing on the
+
+ align:start position:0%
+doing on the
+ 
+
+ align:start position:0%
+doing on the
+test and we'll use them more today and
+
+ align:start position:0%
+test and we'll use them more today and
+ 
+
+ align:start position:0%
+test and we'll use them more today and
+we'll also use them on Thursday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we can actually get close
+
+ align:start position:0%
+okay so now we can actually get close
+ 
+
+ align:start position:0%
+okay so now we can actually get close
+bounds on the sum of the square
+
+ align:start position:0%
+bounds on the sum of the square
+ 
+
+ align:start position:0%
+bounds on the sum of the square
+roots all right so let's see how this
+
+ align:start position:0%
+roots all right so let's see how this
+ 
+
+ align:start position:0%
+roots all right so let's see how this
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+for f of I equal the root of I which is
+
+ align:start position:0%
+for f of I equal the root of I which is
+ 
+
+ align:start position:0%
+for f of I equal the root of I which is
+increasing so I compute the integral
+
+ align:start position:0%
+increasing so I compute the integral
+ 
+
+ align:start position:0%
+increasing so I compute the integral
+from one to n of square root of x
+
+ align:start position:0%
+from one to n of square root of x
+ 
+
+ align:start position:0%
+from one to n of square root of x
+DX and that's just X the 3es over three
+
+ align:start position:0%
+DX and that's just X the 3es over three
+ 
+
+ align:start position:0%
+DX and that's just X the 3es over three
+halves evaluated at n and
+
+ align:start position:0%
+halves evaluated at n and
+ 
+
+ align:start position:0%
+halves evaluated at n and
+one and that just equals 23
+
+ align:start position:0%
+one and that just equals 23
+ 
+
+ align:start position:0%
+one and that just equals 23
+thir and the 3us
+
+ align:start position:0%
+thir and the 3us
+ 
+
+ align:start position:0%
+thir and the 3us
+one and now I can compute the bounds on
+
+ align:start position:0%
+one and now I can compute the bounds on
+ 
+
+ align:start position:0%
+one and now I can compute the bounds on
+the sum of the first n square
+
+ align:start position:0%
+the sum of the first n square
+ 
+
+ align:start position:0%
+the sum of the first n square
+roots all right so I know that square
+
+ align:start position:0%
+roots all right so I know that square
+ 
+
+ align:start position:0%
+roots all right so I know that square
+root I = 1 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n well the upper bound is
+
+ align:start position:0%
+n well the upper bound is
+ 
+
+ align:start position:0%
+n well the upper bound is
+FN plus the integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the lower bound is f of
+
+ align:start position:0%
+and the lower bound is f of
+ 
+
+ align:start position:0%
+and the lower bound is f of
+one plus the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral what is f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n that's the square root of
+
+ align:start position:0%
+n that's the square root of
+ 
+
+ align:start position:0%
+n that's the square root of
+n what is f of
+
+ align:start position:0%
+n what is f of
+ 
+
+ align:start position:0%
+n what is f of
+one square root of one which is
+
+ align:start position:0%
+one square root of one which is
+ 
+
+ align:start position:0%
+one square root of one which is
+one all right so I'll plug that in here
+
+ align:start position:0%
+one all right so I'll plug that in here
+ 
+
+ align:start position:0%
+one all right so I'll plug that in here
+I get 2/3
+
+ align:start position:0%
+I get 2/3
+ 
+
+ align:start position:0%
+I get 2/3
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+3 + 1 - 2/3 is plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A3 and here I get
+
+ align:start position:0%
+A3 and here I get
+ 
+
+ align:start position:0%
+A3 and here I get
+2/3 n the
+
+ align:start position:0%
+2/3 n the
+ 
+
+ align:start position:0%
+2/3 n the
+3es plus the < TK of n minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2/3 all right so now I have pretty good
+
+ align:start position:0%
+2/3 all right so now I have pretty good
+ 
+
+ align:start position:0%
+2/3 all right so now I have pretty good
+bounds on the sum of the first n square
+
+ align:start position:0%
+bounds on the sum of the first n square
+ 
+
+ align:start position:0%
+bounds on the sum of the first n square
+roots using this
+
+ align:start position:0%
+roots using this
+ 
+
+ align:start position:0%
+roots using this
+method so for example take n equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+100 this number evaluates to
+
+ align:start position:0%
+100 this number evaluates to
+ 
+
+ align:start position:0%
+100 this number evaluates to
+667 this number evaluates to
+
+ align:start position:0%
+667 this number evaluates to
+ 
+
+ align:start position:0%
+667 this number evaluates to
+676 and the difference is N9 which is
+
+ align:start position:0%
+676 and the difference is N9 which is
+ 
+
+ align:start position:0%
+676 and the difference is N9 which is
+the square root of 100 minus
+
+ align:start position:0%
+the square root of 100 minus
+ 
+
+ align:start position:0%
+the square root of 100 minus
+one this is square root of n this is one
+
+ align:start position:0%
+one this is square root of n this is one
+ 
+
+ align:start position:0%
+one this is square root of n this is one
+so the Gap here isun of n minus one and
+
+ align:start position:0%
+so the Gap here isun of n minus one and
+ 
+
+ align:start position:0%
+so the Gap here isun of n minus one and
+Nal 100 Ro of 100 - 1 is 9 so I
+
+ align:start position:0%
+Nal 100 Ro of 100 - 1 is 9 so I
+ 
+
+ align:start position:0%
+Nal 100 Ro of 100 - 1 is 9 so I
+shouldn't be surprised my Gap here is
+
+ align:start position:0%
+shouldn't be surprised my Gap here is
+ 
+
+ align:start position:0%
+shouldn't be surprised my Gap here is
+nine so I didn't get exactly the right
+
+ align:start position:0%
+nine so I didn't get exactly the right
+ 
+
+ align:start position:0%
+nine so I didn't get exactly the right
+answer but I'm pretty close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here now as n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grows what happens to the gap between
+
+ align:start position:0%
+grows what happens to the gap between
+ 
+
+ align:start position:0%
+grows what happens to the gap between
+the upper bound and the lower
+
+ align:start position:0%
+the upper bound and the lower
+ 
+
+ align:start position:0%
+the upper bound and the lower
+bound what does it do it gets bigger so
+
+ align:start position:0%
+bound what does it do it gets bigger so
+ 
+
+ align:start position:0%
+bound what does it do it gets bigger so
+my Gap gets bigger that's not so nice
+
+ align:start position:0%
+my Gap gets bigger that's not so nice
+ 
+
+ align:start position:0%
+my Gap gets bigger that's not so nice
+doesn't always stay nine forever
+
+ align:start position:0%
+doesn't always stay nine forever
+ 
+
+ align:start position:0%
+doesn't always stay nine forever
+but somehow though this is still pretty
+
+ align:start position:0%
+but somehow though this is still pretty
+ 
+
+ align:start position:0%
+but somehow though this is still pretty
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+because the Gap grows but the Gap only
+
+ align:start position:0%
+because the Gap grows but the Gap only
+ 
+
+ align:start position:0%
+because the Gap grows but the Gap only
+grows as square root of
+
+ align:start position:0%
+grows as square root of
+ 
+
+ align:start position:0%
+grows as square root of
+n where the answer the bounds are
+
+ align:start position:0%
+n where the answer the bounds are
+ 
+
+ align:start position:0%
+n where the answer the bounds are
+growing as end of the three
+
+ align:start position:0%
+growing as end of the three
+ 
+
+ align:start position:0%
+growing as end of the three
+halves in other words my
+
+ align:start position:0%
+halves in other words my
+ 
+
+ align:start position:0%
+halves in other words my
+error is somewhere around here and that
+
+ align:start position:0%
+error is somewhere around here and that
+ 
+
+ align:start position:0%
+error is somewhere around here and that
+gets smaller compared to my answer which
+
+ align:start position:0%
+gets smaller compared to my answer which
+ 
+
+ align:start position:0%
+gets smaller compared to my answer which
+is somewhere around
+
+ align:start position:0%
+is somewhere around
+ 
+
+ align:start position:0%
+is somewhere around
+there all right and 's a special
+
+ align:start position:0%
+there all right and 's a special
+ 
+
+ align:start position:0%
+there all right and 's a special
+notation that people
+
+ align:start position:0%
+notation that people
+ 
+
+ align:start position:0%
+notation that people
+use fact
+
+ align:start position:0%
+use fact
+ 
+
+ align:start position:0%
+use fact
+let's let's write that down and then do
+
+ align:start position:0%
+let's let's write that down and then do
+ 
+
+ align:start position:0%
+let's let's write that down and then do
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation another way of writing this is
+
+ align:start position:0%
+notation another way of writing this is
+ 
+
+ align:start position:0%
+notation another way of writing this is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+sum I = 1 to n ofun of I
+
+ align:start position:0%
+sum I = 1 to n ofun of I
+ 
+
+ align:start position:0%
+sum I = 1 to n ofun of I
+the leading term here is 2/3 and the
+
+ align:start position:0%
+the leading term here is 2/3 and the
+ 
+
+ align:start position:0%
+the leading term here is 2/3 and the
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hales and then there's some error term
+
+ align:start position:0%
+Hales and then there's some error term
+ 
+
+ align:start position:0%
+Hales and then there's some error term
+Delta term here call that Delta
+
+ align:start position:0%
+Delta term here call that Delta
+ 
+
+ align:start position:0%
+Delta term here call that Delta
+n and we know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the error term is at least a
+
+ align:start position:0%
+that the error term is at least a
+ 
+
+ align:start position:0%
+that the error term is at least a
+third and at most Ro of n minus
+
+ align:start position:0%
+third and at most Ro of n minus
+ 
+
+ align:start position:0%
+third and at most Ro of n minus
+2/3 all
+
+ align:start position:0%
+2/3 all
+ 
+
+ align:start position:0%
+2/3 all
+right so this Delta term is bounded by
+
+ align:start position:0%
+right so this Delta term is bounded by
+ 
+
+ align:start position:0%
+right so this Delta term is bounded by
+square root of n that's getting bigger
+
+ align:start position:0%
+square root of n that's getting bigger
+ 
+
+ align:start position:0%
+square root of n that's getting bigger
+as n gets big but this value compared to
+
+ align:start position:0%
+as n gets big but this value compared to
+ 
+
+ align:start position:0%
+as n gets big but this value compared to
+your answer is getting
+
+ align:start position:0%
+your answer is getting
+ 
+
+ align:start position:0%
+your answer is getting
+small that's nice and so the way that
+
+ align:start position:0%
+small that's nice and so the way that
+ 
+
+ align:start position:0%
+small that's nice and so the way that
+gets
+
+ align:start position:0%
+gets
+ 
+
+ align:start position:0%
+gets
+represented is as follows we would say
+
+ align:start position:0%
+represented is as follows we would say
+ 
+
+ align:start position:0%
+represented is as follows we would say
+it's using the Tilda
+
+ align:start position:0%
+it's using the Tilda
+ 
+
+ align:start position:0%
+it's using the Tilda
+notation we write
+
+ align:start position:0%
+notation we write
+ 
+
+ align:start position:0%
+notation we write
+Tilda 2/3 time n the 3es and now we've
+
+ align:start position:0%
+Tilda 2/3 time n the 3es and now we've
+ 
+
+ align:start position:0%
+Tilda 2/3 time n the 3es and now we've
+gotten rid of the Delta because this
+
+ align:start position:0%
+gotten rid of the Delta because this
+ 
+
+ align:start position:0%
+gotten rid of the Delta because this
+Tilda is telling us that everything else
+
+ align:start position:0%
+Tilda is telling us that everything else
+ 
+
+ align:start position:0%
+Tilda is telling us that everything else
+out here gets small compared to this as
+
+ align:start position:0%
+out here gets small compared to this as
+ 
+
+ align:start position:0%
+out here gets small compared to this as
+n gets big and the formal definition let
+
+ align:start position:0%
+n gets big and the formal definition let
+ 
+
+ align:start position:0%
+n gets big and the formal definition let
+write out the formal definition for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it now a lot of times you you'll see
+
+ align:start position:0%
+it now a lot of times you you'll see
+ 
+
+ align:start position:0%
+it now a lot of times you you'll see
+people use this symbol to mean about
+
+ align:start position:0%
+people use this symbol to mean about
+ 
+
+ align:start position:0%
+people use this symbol to mean about
+that's informal when I'm using it here
+
+ align:start position:0%
+that's informal when I'm using it here
+ 
+
+ align:start position:0%
+that's informal when I'm using it here
+it's a very formal meaning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mathematically a function G ofx is till
+
+ align:start position:0%
+mathematically a function G ofx is till
+ 
+
+ align:start position:0%
+mathematically a function G ofx is till
+a function h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx means that the
+
+ align:start position:0%
+ofx means that the
+ 
+
+ align:start position:0%
+ofx means that the
+limit as X goes to
+
+ align:start position:0%
+limit as X goes to
+ 
+
+ align:start position:0%
+limit as X goes to
+Infinity of
+
+ align:start position:0%
+Infinity of
+ 
+
+ align:start position:0%
+Infinity of
+G over
+
+ align:start position:0%
+G over
+ 
+
+ align:start position:0%
+G over
+H is one
+
+ align:start position:0%
+H is one
+ 
+
+ align:start position:0%
+H is one
+in other words that as X goes to
+
+ align:start position:0%
+in other words that as X goes to
+ 
+
+ align:start position:0%
+in other words that as X goes to
+Infinity as X gets big the ratio of
+
+ align:start position:0%
+Infinity as X gets big the ratio of
+ 
+
+ align:start position:0%
+Infinity as X gets big the ratio of
+these guys becomes
+
+ align:start position:0%
+these guys becomes
+ 
+
+ align:start position:0%
+these guys becomes
+one all right and let's see if that's
+
+ align:start position:0%
+one all right and let's see if that's
+ 
+
+ align:start position:0%
+one all right and let's see if that's
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+here all right
+
+ align:start position:0%
+here all right
+ 
+
+ align:start position:0%
+here all right
+well square root of I equals this so I
+
+ align:start position:0%
+well square root of I equals this so I
+ 
+
+ align:start position:0%
+well square root of I equals this so I
+need to show the limit of this over that
+
+ align:start position:0%
+need to show the limit of this over that
+ 
+
+ align:start position:0%
+need to show the limit of this over that
+is one so let's check
+
+ align:start position:0%
+is one so let's check
+ 
+
+ align:start position:0%
+is one so let's check
+that limit as n goes to
+
+ align:start position:0%
+that limit as n goes to
+ 
+
+ align:start position:0%
+that limit as n goes to
+Infinity of 2/3 n 3
+
+ align:start position:0%
+Infinity of 2/3 n 3
+ 
+
+ align:start position:0%
+Infinity of 2/3 n 3
+plus that Delta term over 2/3 n the
+
+ align:start position:0%
+plus that Delta term over 2/3 n the
+ 
+
+ align:start position:0%
+plus that Delta term over 2/3 n the
+3es well that
+
+ align:start position:0%
+3es well that
+ 
+
+ align:start position:0%
+3es well that
+equals divide out by 2/3 and the three
+
+ align:start position:0%
+equals divide out by 2/3 and the three
+ 
+
+ align:start position:0%
+equals divide out by 2/3 and the three
+Hales I get a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one uh did I should I have subtracted no
+
+ align:start position:0%
+one uh did I should I have subtracted no
+ 
+
+ align:start position:0%
+one uh did I should I have subtracted no
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+1+ Delta n/ 2/3 n the 3
+
+ align:start position:0%
+1+ Delta n/ 2/3 n the 3
+ 
+
+ align:start position:0%
+1+ Delta n/ 2/3 n the 3
+I can pull the one out front that's 1
+
+ align:start position:0%
+I can pull the one out front that's 1
+ 
+
+ align:start position:0%
+I can pull the one out front that's 1
+plus the
+
+ align:start position:0%
+plus the
+ 
+
+ align:start position:0%
+plus the
+limit and this is now Delta n is at most
+
+ align:start position:0%
+limit and this is now Delta n is at most
+ 
+
+ align:start position:0%
+limit and this is now Delta n is at most
+sare root of n so I getun of n over 2/3
+
+ align:start position:0%
+sare root of n so I getun of n over 2/3
+ 
+
+ align:start position:0%
+sare root of n so I getun of n over 2/3
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+3es square root of n Over N the 3 halves
+
+ align:start position:0%
+3es square root of n Over N the 3 halves
+ 
+
+ align:start position:0%
+3es square root of n Over N the 3 halves
+that goes to
+
+ align:start position:0%
+that goes to
+ 
+
+ align:start position:0%
+that goes to
+zero so this equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all right so this limit is one and
+
+ align:start position:0%
+one all right so this limit is one and
+ 
+
+ align:start position:0%
+one all right so this limit is one and
+so therefore I can say that the sum of
+
+ align:start position:0%
+so therefore I can say that the sum of
+ 
+
+ align:start position:0%
+so therefore I can say that the sum of
+the first n square roots is till the 2/3
+
+ align:start position:0%
+the first n square roots is till the 2/3
+ 
+
+ align:start position:0%
+the first n square roots is till the 2/3
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+3es any
+
+ align:start position:0%
+3es any
+ 
+
+ align:start position:0%
+3es any
+questions about this we're going to do a
+
+ align:start position:0%
+questions about this we're going to do a
+ 
+
+ align:start position:0%
+questions about this we're going to do a
+lot of this kind of notation next time
+
+ align:start position:0%
+lot of this kind of notation next time
+ 
+
+ align:start position:0%
+lot of this kind of notation next time
+yeah and got 23 n^ 3
+
+ align:start position:0%
+yeah and got 23 n^ 3
+ 
+
+ align:start position:0%
+yeah and got 23 n^ 3
+-1 why did the
+
+ align:start position:0%
+-1 why did the
+ 
+
+ align:start position:0%
+-1 why did the
+minus1 not become part of the actual
+
+ align:start position:0%
+minus1 not become part of the actual
+ 
+
+ align:start position:0%
+minus1 not become part of the actual
+solution become part of the
+
+ align:start position:0%
+solution become part of the
+ 
+
+ align:start position:0%
+solution become part of the
+Delta okay so you bought it up to here
+
+ align:start position:0%
+Delta okay so you bought it up to here
+ 
+
+ align:start position:0%
+Delta okay so you bought it up to here
+right okay so so then I plug that in to
+
+ align:start position:0%
+right okay so so then I plug that in to
+ 
+
+ align:start position:0%
+right okay so so then I plug that in to
+the integral it appears on both sides
+
+ align:start position:0%
+the integral it appears on both sides
+ 
+
+ align:start position:0%
+the integral it appears on both sides
+here and here I add the F1 here I add
+
+ align:start position:0%
+here and here I add the F1 here I add
+ 
+
+ align:start position:0%
+here and here I add the F1 here I add
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+FN and now I have the lower bound here
+
+ align:start position:0%
+FN and now I have the lower bound here
+ 
+
+ align:start position:0%
+FN and now I have the lower bound here
+and the upper bound here are you good
+
+ align:start position:0%
+and the upper bound here are you good
+ 
+
+ align:start position:0%
+and the upper bound here are you good
+with those all right now some judgment
+
+ align:start position:0%
+with those all right now some judgment
+ 
+
+ align:start position:0%
+with those all right now some judgment
+takes place and what I'm really trying
+
+ align:start position:0%
+takes place and what I'm really trying
+ 
+
+ align:start position:0%
+takes place and what I'm really trying
+to do here is figure out what are the
+
+ align:start position:0%
+to do here is figure out what are the
+ 
+
+ align:start position:0%
+to do here is figure out what are the
+important terms in these bounds as n
+
+ align:start position:0%
+important terms in these bounds as n
+ 
+
+ align:start position:0%
+important terms in these bounds as n
+gets big how big is this growing as n
+
+ align:start position:0%
+gets big how big is this growing as n
+ 
+
+ align:start position:0%
+gets big how big is this growing as n
+gets big well as n gets big the Third is
+
+ align:start position:0%
+gets big well as n gets big the Third is
+ 
+
+ align:start position:0%
+gets big well as n gets big the Third is
+not doing
+
+ align:start position:0%
+not doing
+ 
+
+ align:start position:0%
+not doing
+much as n gets big the square root of n
+
+ align:start position:0%
+much as n gets big the square root of n
+ 
+
+ align:start position:0%
+much as n gets big the square root of n
+grows but it's nothing like what's
+
+ align:start position:0%
+grows but it's nothing like what's
+ 
+
+ align:start position:0%
+grows but it's nothing like what's
+happening here if you had to describe to
+
+ align:start position:0%
+happening here if you had to describe to
+ 
+
+ align:start position:0%
+happening here if you had to describe to
+somebody what's going on in this bound
+
+ align:start position:0%
+somebody what's going on in this bound
+ 
+
+ align:start position:0%
+somebody what's going on in this bound
+would you start here or here no you'd
+
+ align:start position:0%
+would you start here or here no you'd
+ 
+
+ align:start position:0%
+would you start here or here no you'd
+start here this is the action and
+
+ align:start position:0%
+start here this is the action and
+ 
+
+ align:start position:0%
+start here this is the action and
+there's a little bit the rest is just in
+
+ align:start position:0%
+there's a little bit the rest is just in
+ 
+
+ align:start position:0%
+there's a little bit the rest is just in
+the slop in the air and so now I've used
+
+ align:start position:0%
+the slop in the air and so now I've used
+ 
+
+ align:start position:0%
+the slop in the air and so now I've used
+judgment to say the Delta is somewhere
+
+ align:start position:0%
+judgment to say the Delta is somewhere
+ 
+
+ align:start position:0%
+judgment to say the Delta is somewhere
+in this stuff here all right what's
+
+ align:start position:0%
+in this stuff here all right what's
+ 
+
+ align:start position:0%
+in this stuff here all right what's
+really happening the nice thing is they
+
+ align:start position:0%
+really happening the nice thing is they
+ 
+
+ align:start position:0%
+really happening the nice thing is they
+match the lower bound and the upper
+
+ align:start position:0%
+match the lower bound and the upper
+ 
+
+ align:start position:0%
+match the lower bound and the upper
+bound match on that term so what I do is
+
+ align:start position:0%
+bound match on that term so what I do is
+ 
+
+ align:start position:0%
+bound match on that term so what I do is
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+write it equals this term plus something
+
+ align:start position:0%
+write it equals this term plus something
+ 
+
+ align:start position:0%
+write it equals this term plus something
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+smaller and in particular it's between a
+
+ align:start position:0%
+smaller and in particular it's between a
+ 
+
+ align:start position:0%
+smaller and in particular it's between a
+third and squ of n minus
+
+ align:start position:0%
+third and squ of n minus
+ 
+
+ align:start position:0%
+third and squ of n minus
+2/3 all right so what I'm trying to
+
+ align:start position:0%
+2/3 all right so what I'm trying to
+ 
+
+ align:start position:0%
+2/3 all right so what I'm trying to
+capture here is just the guts of what's
+
+ align:start position:0%
+capture here is just the guts of what's
+ 
+
+ align:start position:0%
+capture here is just the guts of what's
+happening to this function as as n grows
+
+ align:start position:0%
+happening to this function as as n grows
+ 
+
+ align:start position:0%
+happening to this function as as n grows
+and the guts of it is this it's not
+
+ align:start position:0%
+and the guts of it is this it's not
+ 
+
+ align:start position:0%
+and the guts of it is this it's not
+exactly equal 2/3 * n the three Hales
+
+ align:start position:0%
+exactly equal 2/3 * n the three Hales
+ 
+
+ align:start position:0%
+exactly equal 2/3 * n the three Hales
+but it's close and in fact if I take the
+
+ align:start position:0%
+but it's close and in fact if I take the
+ 
+
+ align:start position:0%
+but it's close and in fact if I take the
+limit of this over that that limit goes
+
+ align:start position:0%
+limit of this over that that limit goes
+ 
+
+ align:start position:0%
+limit of this over that that limit goes
+to one it's a way of saying they're
+
+ align:start position:0%
+to one it's a way of saying they're
+ 
+
+ align:start position:0%
+to one it's a way of saying they're
+approximately the same or that's called
+
+ align:start position:0%
+approximately the same or that's called
+ 
+
+ align:start position:0%
+approximately the same or that's called
+ASM totically the same and we'll talk a
+
+ align:start position:0%
+ASM totically the same and we'll talk a
+ 
+
+ align:start position:0%
+ASM totically the same and we'll talk a
+lot more about ASM totic notation next
+
+ align:start position:0%
+lot more about ASM totic notation next
+ 
+
+ align:start position:0%
+lot more about ASM totic notation next
+time we'll give you five more symbols
+
+ align:start position:0%
+time we'll give you five more symbols
+ 
+
+ align:start position:0%
+time we'll give you five more symbols
+besides Tilda uh that people
+
+ align:start position:0%
+besides Tilda uh that people
+ 
+
+ align:start position:0%
+besides Tilda uh that people
+use but all right any questions about
+
+ align:start position:0%
+use but all right any questions about
+ 
+
+ align:start position:0%
+use but all right any questions about
+maybe start with the bounds any question
+
+ align:start position:0%
+maybe start with the bounds any question
+ 
+
+ align:start position:0%
+maybe start with the bounds any question
+on the bounds that we got that's the
+
+ align:start position:0%
+on the bounds that we got that's the
+ 
+
+ align:start position:0%
+on the bounds that we got that's the
+integration method first getting the
+
+ align:start position:0%
+integration method first getting the
+ 
+
+ align:start position:0%
+integration method first getting the
+bounds you take the
+
+ align:start position:0%
+bounds you take the
+ 
+
+ align:start position:0%
+bounds you take the
+integral you add F of one for the lower
+
+ align:start position:0%
+integral you add F of one for the lower
+ 
+
+ align:start position:0%
+integral you add F of one for the lower
+bound you add F of n for the upper bound
+
+ align:start position:0%
+bound you add F of n for the upper bound
+ 
+
+ align:start position:0%
+bound you add F of n for the upper bound
+and it's in between somewhere in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there questions
+
+ align:start position:0%
+there questions
+ 
+
+ align:start position:0%
+there questions
+there all right then we plugged it in
+
+ align:start position:0%
+there all right then we plugged it in
+ 
+
+ align:start position:0%
+there all right then we plugged it in
+and now we we look at this Tia notation
+
+ align:start position:0%
+and now we we look at this Tia notation
+ 
+
+ align:start position:0%
+and now we we look at this Tia notation
+that says well first we write it like
+
+ align:start position:0%
+that says well first we write it like
+ 
+
+ align:start position:0%
+that says well first we write it like
+this the sum is this Value Plus an error
+
+ align:start position:0%
+this the sum is this Value Plus an error
+ 
+
+ align:start position:0%
+this the sum is this Value Plus an error
+term and lo and behold that error term
+
+ align:start position:0%
+term and lo and behold that error term
+ 
+
+ align:start position:0%
+term and lo and behold that error term
+is small if I I can if I take the limit
+
+ align:start position:0%
+is small if I I can if I take the limit
+ 
+
+ align:start position:0%
+is small if I I can if I take the limit
+of the whole thing divided by the the
+
+ align:start position:0%
+of the whole thing divided by the the
+ 
+
+ align:start position:0%
+of the whole thing divided by the the
+big term I get one which means this
+
+ align:start position:0%
+big term I get one which means this
+ 
+
+ align:start position:0%
+big term I get one which means this
+thing is really not important so I write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this questions on
+
+ align:start position:0%
+this questions on
+ 
+
+ align:start position:0%
+this questions on
+that all
+
+ align:start position:0%
+that all
+ 
+
+ align:start position:0%
+that all
+right all right there's one more case to
+
+ align:start position:0%
+right all right there's one more case to
+ 
+
+ align:start position:0%
+right all right there's one more case to
+consider and now we're going to go back
+
+ align:start position:0%
+consider and now we're going to go back
+ 
+
+ align:start position:0%
+consider and now we're going to go back
+to the integration bounds and that is
+
+ align:start position:0%
+to the integration bounds and that is
+ 
+
+ align:start position:0%
+to the integration bounds and that is
+when f is a a decreasing function and
+
+ align:start position:0%
+when f is a a decreasing function and
+ 
+
+ align:start position:0%
+when f is a a decreasing function and
+we're going to do the analysis for that
+
+ align:start position:0%
+we're going to do the analysis for that
+ 
+
+ align:start position:0%
+we're going to do the analysis for that
+and then we'll be all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done so we're going to look at
+
+ align:start position:0%
+done so we're going to look at
+ 
+
+ align:start position:0%
+done so we're going to look at
+integration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounds when f is decreasing and positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+still all right the example here might
+
+ align:start position:0%
+still all right the example here might
+ 
+
+ align:start position:0%
+still all right the example here might
+be for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example uh the sum I = 1 to n 1 over the
+
+ align:start position:0%
+example uh the sum I = 1 to n 1 over the
+ 
+
+ align:start position:0%
+example uh the sum I = 1 to n 1 over the
+otk of
+
+ align:start position:0%
+otk of
+ 
+
+ align:start position:0%
+otk of
+I say you had to get some idea of how
+
+ align:start position:0%
+I say you had to get some idea of how
+ 
+
+ align:start position:0%
+I say you had to get some idea of how
+fast that function is growing as a
+
+ align:start position:0%
+fast that function is growing as a
+ 
+
+ align:start position:0%
+fast that function is growing as a
+function of n I'm summing the first
+
+ align:start position:0%
+function of n I'm summing the first
+ 
+
+ align:start position:0%
+function of n I'm summing the first
+n inverses of square
+
+ align:start position:0%
+n inverses of square
+ 
+
+ align:start position:0%
+n inverses of square
+roots what is what is that roughly going
+
+ align:start position:0%
+roots what is what is that roughly going
+ 
+
+ align:start position:0%
+roots what is what is that roughly going
+to be how fast does that grow as a
+
+ align:start position:0%
+to be how fast does that grow as a
+ 
+
+ align:start position:0%
+to be how fast does that grow as a
+function of
+
+ align:start position:0%
+function of
+ 
+
+ align:start position:0%
+function of
+n all right so let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and of course one/ square of I
+
+ align:start position:0%
+that and of course one/ square of I
+ 
+
+ align:start position:0%
+that and of course one/ square of I
+decreases as I gets
+
+ align:start position:0%
+decreases as I gets
+ 
+
+ align:start position:0%
+decreases as I gets
+bigger so let's do the general picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again see what happens so we have
+
+ align:start position:0%
+again see what happens so we have
+ 
+
+ align:start position:0%
+again see what happens so we have
+zero 1 2
+
+ align:start position:0%
+zero 1 2
+ 
+
+ align:start position:0%
+zero 1 2
+3 nus 2 N minus one n
+
+ align:start position:0%
+3 nus 2 N minus one n
+ 
+
+ align:start position:0%
+3 nus 2 N minus one n
+and now F of n is the small
+
+ align:start position:0%
+and now F of n is the small
+ 
+
+ align:start position:0%
+and now F of n is the small
+term and F of n minus
+
+ align:start position:0%
+term and F of n minus
+ 
+
+ align:start position:0%
+term and F of n minus
+one F of three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here F of
+
+ align:start position:0%
+here F of
+ 
+
+ align:start position:0%
+here F of
+one now I'm going to draw the rectangle
+
+ align:start position:0%
+one now I'm going to draw the rectangle
+ 
+
+ align:start position:0%
+one now I'm going to draw the rectangle
+this has area F of
+
+ align:start position:0%
+this has area F of
+ 
+
+ align:start position:0%
+this has area F of
+one this one has area F of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two this one one has area F of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three and then this one has area F of n
+
+ align:start position:0%
+three and then this one has area F of n
+ 
+
+ align:start position:0%
+three and then this one has area F of n
+minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and then lastly area F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofn so the sum is the area in the
+
+ align:start position:0%
+ofn so the sum is the area in the
+ 
+
+ align:start position:0%
+ofn so the sum is the area in the
+rectangles just like before except now
+
+ align:start position:0%
+rectangles just like before except now
+ 
+
+ align:start position:0%
+rectangles just like before except now
+the rectangles are getting
+
+ align:start position:0%
+the rectangles are getting
+ 
+
+ align:start position:0%
+the rectangles are getting
+smaller let's draw the
+
+ align:start position:0%
+smaller let's draw the
+ 
+
+ align:start position:0%
+smaller let's draw the
+integral like we did before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the integral is the area under this
+
+ align:start position:0%
+the integral is the area under this
+ 
+
+ align:start position:0%
+the integral is the area under this
+curve F ofx here just like
+
+ align:start position:0%
+curve F ofx here just like
+ 
+
+ align:start position:0%
+curve F ofx here just like
+before so this is f
+
+ align:start position:0%
+before so this is f
+ 
+
+ align:start position:0%
+before so this is f
+ofx only it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreasing now let's take the area under
+
+ align:start position:0%
+decreasing now let's take the area under
+ 
+
+ align:start position:0%
+decreasing now let's take the area under
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve and add F of one to
+
+ align:start position:0%
+curve and add F of one to
+ 
+
+ align:start position:0%
+curve and add F of one to
+it if I take the area under this curve
+
+ align:start position:0%
+it if I take the area under this curve
+ 
+
+ align:start position:0%
+it if I take the area under this curve
+all the way down to here
+
+ align:start position:0%
+all the way down to here
+ 
+
+ align:start position:0%
+all the way down to here
+here and then add F of one what do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get upper bound on my
+
+ align:start position:0%
+get upper bound on my
+ 
+
+ align:start position:0%
+get upper bound on my
+sum okay so the sum IAL 1 to n f of I is
+
+ align:start position:0%
+sum okay so the sum IAL 1 to n f of I is
+ 
+
+ align:start position:0%
+sum okay so the sum IAL 1 to n f of I is
+upper bounded
+
+ align:start position:0%
+upper bounded
+ 
+
+ align:start position:0%
+upper bounded
+by that guy which is f of
+
+ align:start position:0%
+by that guy which is f of
+ 
+
+ align:start position:0%
+by that guy which is f of
+one plus my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral which is the area under the
+
+ align:start position:0%
+integral which is the area under the
+ 
+
+ align:start position:0%
+integral which is the area under the
+curve the integral is the area under
+
+ align:start position:0%
+curve the integral is the area under
+ 
+
+ align:start position:0%
+curve the integral is the area under
+that curve starting here and that in
+
+ align:start position:0%
+that curve starting here and that in
+ 
+
+ align:start position:0%
+that curve starting here and that in
+contains all these
+
+ align:start position:0%
+contains all these
+ 
+
+ align:start position:0%
+contains all these
+rectangles and then I just add in F of
+
+ align:start position:0%
+rectangles and then I just add in F of
+ 
+
+ align:start position:0%
+rectangles and then I just add in F of
+one to get an upper
+
+ align:start position:0%
+one to get an upper
+ 
+
+ align:start position:0%
+one to get an upper
+bound all right now for the lower bound
+
+ align:start position:0%
+bound all right now for the lower bound
+ 
+
+ align:start position:0%
+bound all right now for the lower bound
+think about Shifting the whole curve
+
+ align:start position:0%
+think about Shifting the whole curve
+ 
+
+ align:start position:0%
+think about Shifting the whole curve
+left by one that goes to there this goes
+
+ align:start position:0%
+left by one that goes to there this goes
+ 
+
+ align:start position:0%
+left by one that goes to there this goes
+to here that goes to here that goes to
+
+ align:start position:0%
+to here that goes to here that goes to
+ 
+
+ align:start position:0%
+to here that goes to here that goes to
+there and that goes to there
+
+ align:start position:0%
+there and that goes to there
+ 
+
+ align:start position:0%
+there and that goes to there
+the area under the curve did not change
+
+ align:start position:0%
+the area under the curve did not change
+ 
+
+ align:start position:0%
+the area under the curve did not change
+when I shifted it left by
+
+ align:start position:0%
+when I shifted it left by
+ 
+
+ align:start position:0%
+when I shifted it left by
+one this is now my area under the
+
+ align:start position:0%
+one this is now my area under the
+ 
+
+ align:start position:0%
+one this is now my area under the
+curve stops
+
+ align:start position:0%
+curve stops
+ 
+
+ align:start position:0%
+curve stops
+here what do I get when I take that area
+
+ align:start position:0%
+here what do I get when I take that area
+ 
+
+ align:start position:0%
+here what do I get when I take that area
+and add in this last box F of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n a lower bound right because it's
+
+ align:start position:0%
+n a lower bound right because it's
+ 
+
+ align:start position:0%
+n a lower bound right because it's
+contained in all the rectangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what's really
+
+ align:start position:0%
+now what's really
+ 
+
+ align:start position:0%
+now what's really
+weird about these
+
+ align:start position:0%
+weird about these
+ 
+
+ align:start position:0%
+weird about these
+formulas do they look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+familiar yeah yeah I switched them yeah
+
+ align:start position:0%
+familiar yeah yeah I switched them yeah
+ 
+
+ align:start position:0%
+familiar yeah yeah I switched them yeah
+they're the same formulas we had over
+
+ align:start position:0%
+they're the same formulas we had over
+ 
+
+ align:start position:0%
+they're the same formulas we had over
+here except we switch the direction on
+
+ align:start position:0%
+here except we switch the direction on
+ 
+
+ align:start position:0%
+here except we switch the direction on
+the less than and greater than
+
+ align:start position:0%
+the less than and greater than
+ 
+
+ align:start position:0%
+the less than and greater than
+signs or I swapped F of one and F of n
+
+ align:start position:0%
+signs or I swapped F of one and F of n
+ 
+
+ align:start position:0%
+signs or I swapped F of one and F of n
+however you want to think about it the
+
+ align:start position:0%
+however you want to think about it the
+ 
+
+ align:start position:0%
+however you want to think about it the
+lower bound here in that case became the
+
+ align:start position:0%
+lower bound here in that case became the
+ 
+
+ align:start position:0%
+lower bound here in that case became the
+upper Bound in this
+
+ align:start position:0%
+upper Bound in this
+ 
+
+ align:start position:0%
+upper Bound in this
+case I mean is that possible that the
+
+ align:start position:0%
+case I mean is that possible that the
+ 
+
+ align:start position:0%
+case I mean is that possible that the
+lower bound became the upper
+
+ align:start position:0%
+lower bound became the upper
+ 
+
+ align:start position:0%
+lower bound became the upper
+bound yeah that's yeah because what
+
+ align:start position:0%
+bound yeah that's yeah because what
+ 
+
+ align:start position:0%
+bound yeah that's yeah because what
+really happened here which is the big
+
+ align:start position:0%
+really happened here which is the big
+ 
+
+ align:start position:0%
+really happened here which is the big
+term in this case FN or F1 F1 is the big
+
+ align:start position:0%
+term in this case FN or F1 F1 is the big
+ 
+
+ align:start position:0%
+term in this case FN or F1 F1 is the big
+term because it's decreasing so it's
+
+ align:start position:0%
+term because it's decreasing so it's
+ 
+
+ align:start position:0%
+term because it's decreasing so it's
+totally symmetric all right the proof
+
+ align:start position:0%
+totally symmetric all right the proof
+ 
+
+ align:start position:0%
+totally symmetric all right the proof
+was very similar so the nice thing is
+
+ align:start position:0%
+was very similar so the nice thing is
+ 
+
+ align:start position:0%
+was very similar so the nice thing is
+you only got to remember the bounds are
+
+ align:start position:0%
+you only got to remember the bounds are
+ 
+
+ align:start position:0%
+you only got to remember the bounds are
+now simple for any sum as long as
+
+ align:start position:0%
+now simple for any sum as long as
+ 
+
+ align:start position:0%
+now simple for any sum as long as
+increasing or decreasing it's the same
+
+ align:start position:0%
+increasing or decreasing it's the same
+ 
+
+ align:start position:0%
+increasing or decreasing it's the same
+as the integral the lower bound is the
+
+ align:start position:0%
+as the integral the lower bound is the
+ 
+
+ align:start position:0%
+as the integral the lower bound is the
+smaller of the first and last term and
+
+ align:start position:0%
+smaller of the first and last term and
+ 
+
+ align:start position:0%
+smaller of the first and last term and
+the upper bounds are larger of the first
+
+ align:start position:0%
+the upper bounds are larger of the first
+ 
+
+ align:start position:0%
+the upper bounds are larger of the first
+and last term very easy to remember
+
+ align:start position:0%
+and last term very easy to remember
+ 
+
+ align:start position:0%
+and last term very easy to remember
+probably don't even need the crib sheet
+
+ align:start position:0%
+probably don't even need the crib sheet
+ 
+
+ align:start position:0%
+probably don't even need the crib sheet
+for it although to be
+
+ align:start position:0%
+for it although to be
+ 
+
+ align:start position:0%
+for it although to be
+safe want to write that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down so now it's easy to compute good
+
+ align:start position:0%
+down so now it's easy to compute good
+ 
+
+ align:start position:0%
+down so now it's easy to compute good
+bounds on the sum of the inverse square
+
+ align:start position:0%
+bounds on the sum of the inverse square
+ 
+
+ align:start position:0%
+bounds on the sum of the inverse square
+roots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions there before I
+
+ align:start position:0%
+any questions there before I
+ 
+
+ align:start position:0%
+any questions there before I
+go do it okay so let's take the case
+
+ align:start position:0%
+go do it okay so let's take the case
+ 
+
+ align:start position:0%
+go do it okay so let's take the case
+where we're summing 1 over < TK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I so we compute the
+
+ align:start position:0%
+I so we compute the
+ 
+
+ align:start position:0%
+I so we compute the
+integral of 1 overun of X
+
+ align:start position:0%
+integral of 1 overun of X
+ 
+
+ align:start position:0%
+integral of 1 overun of X
+DX that equals theun of X over a half
+
+ align:start position:0%
+DX that equals theun of X over a half
+ 
+
+ align:start position:0%
+DX that equals theun of X over a half
+evaluated at n and
+
+ align:start position:0%
+evaluated at n and
+ 
+
+ align:start position:0%
+evaluated at n and
+1 that equals 2 < TK
+
+ align:start position:0%
+1 that equals 2 < TK
+ 
+
+ align:start position:0%
+1 that equals 2 < TK
+nus1 or 2un of
+
+ align:start position:0%
+nus1 or 2un of
+ 
+
+ align:start position:0%
+nus1 or 2un of
+nus
+
+ align:start position:0%
+nus
+ 
+
+ align:start position:0%
+nus
+2 and now we can bound the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum the upper bound is f of one plus the
+
+ align:start position:0%
+sum the upper bound is f of one plus the
+ 
+
+ align:start position:0%
+sum the upper bound is f of one plus the
+integral the lower bound
+
+ align:start position:0%
+integral the lower bound
+ 
+
+ align:start position:0%
+integral the lower bound
+is f of n plus the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral what is f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one one one over theun of one is one
+
+ align:start position:0%
+one one one over theun of one is one
+ 
+
+ align:start position:0%
+one one one over theun of one is one
+what is f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n one over the root of n
+
+ align:start position:0%
+n one over the root of n
+ 
+
+ align:start position:0%
+n one over the root of n
+small all right so these bounds are
+
+ align:start position:0%
+small all right so these bounds are
+ 
+
+ align:start position:0%
+small all right so these bounds are
+pretty close here right in fact this
+
+ align:start position:0%
+pretty close here right in fact this
+ 
+
+ align:start position:0%
+pretty close here right in fact this
+gets really tiny as then gets big so I'm
+
+ align:start position:0%
+gets really tiny as then gets big so I'm
+ 
+
+ align:start position:0%
+gets really tiny as then gets big so I'm
+just going to replace this with 2un n 2
+
+ align:start position:0%
+just going to replace this with 2un n 2
+ 
+
+ align:start position:0%
+just going to replace this with 2un n 2
+and make it a strict lower bound and
+
+ align:start position:0%
+and make it a strict lower bound and
+ 
+
+ align:start position:0%
+and make it a strict lower bound and
+this cancel there I get 2un nus
+
+ align:start position:0%
+this cancel there I get 2un nus
+ 
+
+ align:start position:0%
+this cancel there I get 2un nus
+1 wow these bounds are great they're
+
+ align:start position:0%
+1 wow these bounds are great they're
+ 
+
+ align:start position:0%
+1 wow these bounds are great they're
+within one for all
+
+ align:start position:0%
+within one for all
+ 
+
+ align:start position:0%
+within one for all
+in that's really
+
+ align:start position:0%
+in that's really
+ 
+
+ align:start position:0%
+in that's really
+good okay so we can rewrite this in
+
+ align:start position:0%
+good okay so we can rewrite this in
+ 
+
+ align:start position:0%
+good okay so we can rewrite this in
+terms of the what really matters what
+
+ align:start position:0%
+terms of the what really matters what
+ 
+
+ align:start position:0%
+terms of the what really matters what
+what really matters in these
+
+ align:start position:0%
+what really matters in these
+ 
+
+ align:start position:0%
+what really matters in these
+bounds what's the how fast is this
+
+ align:start position:0%
+bounds what's the how fast is this
+ 
+
+ align:start position:0%
+bounds what's the how fast is this
+function growing two 2un n that's what
+
+ align:start position:0%
+function growing two 2un n that's what
+ 
+
+ align:start position:0%
+function growing two 2un n that's what
+really matters so let's write that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down all right so this says that the sum
+
+ align:start position:0%
+down all right so this says that the sum
+ 
+
+ align:start position:0%
+down all right so this says that the sum
+I = 1 to n of 1 over < TK
+
+ align:start position:0%
+I = 1 to n of 1 over < TK
+ 
+
+ align:start position:0%
+I = 1 to n of 1 over < TK
+I equals 2 < TK of n have a minus Delta
+
+ align:start position:0%
+I equals 2 < TK of n have a minus Delta
+ 
+
+ align:start position:0%
+I equals 2 < TK of n have a minus Delta
+n where Delta is
+
+ align:start position:0%
+n where Delta is
+ 
+
+ align:start position:0%
+n where Delta is
+between one and two
+
+ align:start position:0%
+between one and two
+ 
+
+ align:start position:0%
+between one and two
+and so if I use the Tia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation what would I write down here
+
+ align:start position:0%
+notation what would I write down here
+ 
+
+ align:start position:0%
+notation what would I write down here
+for the Tilda pass the
+
+ align:start position:0%
+for the Tilda pass the
+ 
+
+ align:start position:0%
+for the Tilda pass the
+Tilda I don't want to mess I don't want
+
+ align:start position:0%
+Tilda I don't want to mess I don't want
+ 
+
+ align:start position:0%
+Tilda I don't want to mess I don't want
+to keep all the Delta Stuff n gets big
+
+ align:start position:0%
+to keep all the Delta Stuff n gets big
+ 
+
+ align:start position:0%
+to keep all the Delta Stuff n gets big
+2ot n 2un
+
+ align:start position:0%
+2ot n 2un
+ 
+
+ align:start position:0%
+2ot n 2un
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+because this term over that goes to zero
+
+ align:start position:0%
+because this term over that goes to zero
+ 
+
+ align:start position:0%
+because this term over that goes to zero
+as then gets large so let's just check
+
+ align:start position:0%
+as then gets large so let's just check
+ 
+
+ align:start position:0%
+as then gets large so let's just check
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we take the limit as n goes to
+
+ align:start position:0%
+so we take the limit as n goes to
+ 
+
+ align:start position:0%
+so we take the limit as n goes to
+Infinity of 2un n minus Delta
+
+ align:start position:0%
+Infinity of 2un n minus Delta
+ 
+
+ align:start position:0%
+Infinity of 2un n minus Delta
+n Over 2un N just checking the
+
+ align:start position:0%
+n Over 2un N just checking the
+ 
+
+ align:start position:0%
+n Over 2un N just checking the
+definition now that's what the
+
+ align:start position:0%
+definition now that's what the
+ 
+
+ align:start position:0%
+definition now that's what the
+definition would
+
+ align:start position:0%
+definition would
+ 
+
+ align:start position:0%
+definition would
+be equals
+
+ align:start position:0%
+be equals
+ 
+
+ align:start position:0%
+be equals
+1 minus the
+
+ align:start position:0%
+1 minus the
+ 
+
+ align:start position:0%
+1 minus the
+limit as n goes to Infinity of 2 over
+
+ align:start position:0%
+limit as n goes to Infinity of 2 over
+ 
+
+ align:start position:0%
+limit as n goes to Infinity of 2 over
+2un n this is zero so it equals one
+
+ align:start position:0%
+2un n this is zero so it equals one
+ 
+
+ align:start position:0%
+2un n this is zero so it equals one
+and so now you know that the sum of the
+
+ align:start position:0%
+and so now you know that the sum of the
+ 
+
+ align:start position:0%
+and so now you know that the sum of the
+first n inverse square roots grows as
+
+ align:start position:0%
+first n inverse square roots grows as
+ 
+
+ align:start position:0%
+first n inverse square roots grows as
+2un n which is the integral yeah dropped
+
+ align:start position:0%
+2un n which is the integral yeah dropped
+ 
+
+ align:start position:0%
+2un n which is the integral yeah dropped
+off the lower bound that F of n was 1ot
+
+ align:start position:0%
+off the lower bound that F of n was 1ot
+ 
+
+ align:start position:0%
+off the lower bound that F of n was 1ot
+n yeah I dropped it off because it was
+
+ align:start position:0%
+n yeah I dropped it off because it was
+ 
+
+ align:start position:0%
+n yeah I dropped it off because it was
+so tiny and going to zero and just made
+
+ align:start position:0%
+so tiny and going to zero and just made
+ 
+
+ align:start position:0%
+so tiny and going to zero and just made
+a strict less than in fact yeah so I
+
+ align:start position:0%
+a strict less than in fact yeah so I
+ 
+
+ align:start position:0%
+a strict less than in fact yeah so I
+don't hurt myself by dropping it off in
+
+ align:start position:0%
+don't hurt myself by dropping it off in
+ 
+
+ align:start position:0%
+don't hurt myself by dropping it off in
+fact the lower bound was a little bit I
+
+ align:start position:0%
+fact the lower bound was a little bit I
+ 
+
+ align:start position:0%
+fact the lower bound was a little bit I
+made a little weaker lower bound so this
+
+ align:start position:0%
+made a little weaker lower bound so this
+ 
+
+ align:start position:0%
+made a little weaker lower bound so this
+is still true I just it wasn't as tight
+
+ align:start position:0%
+is still true I just it wasn't as tight
+ 
+
+ align:start position:0%
+is still true I just it wasn't as tight
+as it used to be so I could keep I could
+
+ align:start position:0%
+as it used to be so I could keep I could
+ 
+
+ align:start position:0%
+as it used to be so I could keep I could
+keep it
+
+ align:start position:0%
+keep it
+ 
+
+ align:start position:0%
+keep it
+around yeah it doesn't hurt to keep it
+
+ align:start position:0%
+around yeah it doesn't hurt to keep it
+ 
+
+ align:start position:0%
+around yeah it doesn't hurt to keep it
+around then it's a less than or equal
+
+ align:start position:0%
+around then it's a less than or equal
+ 
+
+ align:start position:0%
+around then it's a less than or equal
+there um and now this would
+
+ align:start position:0%
+there um and now this would
+ 
+
+ align:start position:0%
+there um and now this would
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh something like that so I could keep
+
+ align:start position:0%
+uh something like that so I could keep
+ 
+
+ align:start position:0%
+uh something like that so I could keep
+it around but I'm going to get rid of it
+
+ align:start position:0%
+it around but I'm going to get rid of it
+ 
+
+ align:start position:0%
+it around but I'm going to get rid of it
+anyway because I'm going to go to the
+
+ align:start position:0%
+anyway because I'm going to go to the
+ 
+
+ align:start position:0%
+anyway because I'm going to go to the
+Tilted
+
+ align:start position:0%
+Tilted
+ 
+
+ align:start position:0%
+Tilted
+notation and this as then gets big this
+
+ align:start position:0%
+notation and this as then gets big this
+ 
+
+ align:start position:0%
+notation and this as then gets big this
+is really tiny so in this case the
+
+ align:start position:0%
+is really tiny so in this case the
+ 
+
+ align:start position:0%
+is really tiny so in this case the
+bounds are great they're you can nail it
+
+ align:start position:0%
+bounds are great they're you can nail it
+ 
+
+ align:start position:0%
+bounds are great they're you can nail it
+pretty much right on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah one there the number is bigger than
+
+ align:start position:0%
+yeah one there the number is bigger than
+ 
+
+ align:start position:0%
+yeah one there the number is bigger than
+would be so we need take it out it
+
+ align:start position:0%
+would be so we need take it out it
+ 
+
+ align:start position:0%
+would be so we need take it out it
+becomes smaller so how could you go
+
+ align:start position:0%
+becomes smaller so how could you go
+ 
+
+ align:start position:0%
+becomes smaller so how could you go
+to well you're saying you don't like the
+
+ align:start position:0%
+to well you're saying you don't like the
+ 
+
+ align:start position:0%
+to well you're saying you don't like the
+fact that dropped it here yes like when
+
+ align:start position:0%
+fact that dropped it here yes like when
+ 
+
+ align:start position:0%
+fact that dropped it here yes like when
+you drop it why do you go to instead of
+
+ align:start position:0%
+you drop it why do you go to instead of
+ 
+
+ align:start position:0%
+you drop it why do you go to instead of
+oh because I've got I've got a bigger
+
+ align:start position:0%
+oh because I've got I've got a bigger
+ 
+
+ align:start position:0%
+oh because I've got I've got a bigger
+bigger bound that I made less when I
+
+ align:start position:0%
+bigger bound that I made less when I
+ 
+
+ align:start position:0%
+bigger bound that I made less when I
+dropped it I took something away so I
+
+ align:start position:0%
+dropped it I took something away so I
+ 
+
+ align:start position:0%
+dropped it I took something away so I
+know I could never equal this because I
+
+ align:start position:0%
+know I could never equal this because I
+ 
+
+ align:start position:0%
+know I could never equal this because I
+know it's bigger than
+
+ align:start position:0%
+know it's bigger than
+ 
+
+ align:start position:0%
+know it's bigger than
+this I know that the real answer has to
+
+ align:start position:0%
+this I know that the real answer has to
+ 
+
+ align:start position:0%
+this I know that the real answer has to
+be at least this big and so it has to be
+
+ align:start position:0%
+be at least this big and so it has to be
+ 
+
+ align:start position:0%
+be at least this big and so it has to be
+bigger than something smaller that's why
+
+ align:start position:0%
+bigger than something smaller that's why
+ 
+
+ align:start position:0%
+bigger than something smaller that's why
+I did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay any other
+
+ align:start position:0%
+it okay any other
+ 
+
+ align:start position:0%
+it okay any other
+questions all right we'll get more
+
+ align:start position:0%
+questions all right we'll get more
+ 
+
+ align:start position:0%
+questions all right we'll get more
+practice tomorrow and next time with
+
+ align:start position:0%
+practice tomorrow and next time with
+ 
+
+ align:start position:0%
+practice tomorrow and next time with
+this stuff
\ No newline at end of file
diff --git a/feEXMWBQGZk.txt b/feEXMWBQGZk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7567dda5e0a78d2eafb4d75f368094df44a3762e
--- /dev/null
+++ b/feEXMWBQGZk.txt
@@ -0,0 +1,1779 @@
+align:start position:0%
+ 
+in this video let us look at a basic yet
+
+ align:start position:0%
+in this video let us look at a basic yet
+ 
+
+ align:start position:0%
+in this video let us look at a basic yet
+important Concept in probability known
+
+ align:start position:0%
+important Concept in probability known
+ 
+
+ align:start position:0%
+important Concept in probability known
+as linearity of expectations and use it
+
+ align:start position:0%
+as linearity of expectations and use it
+ 
+
+ align:start position:0%
+as linearity of expectations and use it
+to deduce some interesting consequences
+
+ align:start position:0%
+to deduce some interesting consequences
+ 
+
+ align:start position:0%
+to deduce some interesting consequences
+in combinatorics via the probabilistic
+
+ align:start position:0%
+in combinatorics via the probabilistic
+ 
+
+ align:start position:0%
+in combinatorics via the probabilistic
+method linearity of expectations set
+
+ align:start position:0%
+method linearity of expectations set
+ 
+
+ align:start position:0%
+method linearity of expectations set
+that if you're given random variables X1
+
+ align:start position:0%
+that if you're given random variables X1
+ 
+
+ align:start position:0%
+that if you're given random variables X1
+through XM and constants C1 through
+
+ align:start position:0%
+through XM and constants C1 through
+ 
+
+ align:start position:0%
+through XM and constants C1 through
+CM then when we took it when we take a
+
+ align:start position:0%
+CM then when we took it when we take a
+ 
+
+ align:start position:0%
+CM then when we took it when we take a
+linear combination of these random
+
+ align:start position:0%
+linear combination of these random
+ 
+
+ align:start position:0%
+linear combination of these random
+variables as such so C1 * X1 so imagine
+
+ align:start position:0%
+variables as such so C1 * X1 so imagine
+ 
+
+ align:start position:0%
+variables as such so C1 * X1 so imagine
+these are real valued random variables
+
+ align:start position:0%
+these are real valued random variables
+ 
+
+ align:start position:0%
+these are real valued random variables
+and these are real constants for
+
+ align:start position:0%
+and these are real constants for
+ 
+
+ align:start position:0%
+and these are real constants for
+instance then the sum of these uh C1 *
+
+ align:start position:0%
+instance then the sum of these uh C1 *
+ 
+
+ align:start position:0%
+instance then the sum of these uh C1 *
+X1 plus C2 * X2 and so on Plus CN * XM
+
+ align:start position:0%
+X1 plus C2 * X2 and so on Plus CN * XM
+ 
+
+ align:start position:0%
+X1 plus C2 * X2 and so on Plus CN * XM
+so this sum has
+
+ align:start position:0%
+so this sum has
+ 
+
+ align:start position:0%
+so this sum has
+expectation the following which can be
+
+ align:start position:0%
+expectation the following which can be
+ 
+
+ align:start position:0%
+expectation the following which can be
+computed by Distributing this
+
+ align:start position:0%
+computed by Distributing this
+ 
+
+ align:start position:0%
+computed by Distributing this
+expectation symbol across to the
+
+ align:start position:0%
+expectation symbol across to the
+ 
+
+ align:start position:0%
+expectation symbol across to the
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+variables so this is a basic and
+
+ align:start position:0%
+variables so this is a basic and
+ 
+
+ align:start position:0%
+variables so this is a basic and
+important property and it's worth noting
+
+ align:start position:0%
+important property and it's worth noting
+ 
+
+ align:start position:0%
+important property and it's worth noting
+that a similar statement written for
+
+ align:start position:0%
+that a similar statement written for
+ 
+
+ align:start position:0%
+that a similar statement written for
+products is often not true so it is not
+
+ align:start position:0%
+products is often not true so it is not
+ 
+
+ align:start position:0%
+products is often not true so it is not
+usually the case that the expectation of
+
+ align:start position:0%
+usually the case that the expectation of
+ 
+
+ align:start position:0%
+usually the case that the expectation of
+a product of two random
+
+ align:start position:0%
+a product of two random
+ 
+
+ align:start position:0%
+a product of two random
+variables is the product of their
+
+ align:start position:0%
+variables is the product of their
+ 
+
+ align:start position:0%
+variables is the product of their
+expectations unless you're in some
+
+ align:start position:0%
+expectations unless you're in some
+ 
+
+ align:start position:0%
+expectations unless you're in some
+special circumstances such as when X and
+
+ align:start position:0%
+special circumstances such as when X and
+ 
+
+ align:start position:0%
+special circumstances such as when X and
+Y are independent or
+
+ align:start position:0%
+Y are independent or
+ 
+
+ align:start position:0%
+Y are independent or
+uncorrelated okay anyway let us focus on
+
+ align:start position:0%
+uncorrelated okay anyway let us focus on
+ 
+
+ align:start position:0%
+uncorrelated okay anyway let us focus on
+the linearity of expectations and see
+
+ align:start position:0%
+the linearity of expectations and see
+ 
+
+ align:start position:0%
+the linearity of expectations and see
+some ways to use this in combinatorial
+
+ align:start position:0%
+some ways to use this in combinatorial
+ 
+
+ align:start position:0%
+some ways to use this in combinatorial
+applications and the first example is
+
+ align:start position:0%
+applications and the first example is
+ 
+
+ align:start position:0%
+applications and the first example is
+the following question which will be
+
+ align:start position:0%
+the following question which will be
+ 
+
+ align:start position:0%
+the following question which will be
+able to give a very quick and clean
+
+ align:start position:0%
+able to give a very quick and clean
+ 
+
+ align:start position:0%
+able to give a very quick and clean
+answer the question is what is the
+
+ align:start position:0%
+answer the question is what is the
+ 
+
+ align:start position:0%
+answer the question is what is the
+average number of fixed points of a
+
+ align:start position:0%
+average number of fixed points of a
+ 
+
+ align:start position:0%
+average number of fixed points of a
+permutation of 1 through n
+
+ align:start position:0%
+permutation of 1 through n
+ 
+
+ align:start position:0%
+permutation of 1 through n
+chosen uniformly at random as a reminder
+
+ align:start position:0%
+chosen uniformly at random as a reminder
+ 
+
+ align:start position:0%
+chosen uniformly at random as a reminder
+if we
+
+ align:start position:0%
+if we
+ 
+
+ align:start position:0%
+if we
+have numbers 1 2 3 4 here n equals to 4
+
+ align:start position:0%
+have numbers 1 2 3 4 here n equals to 4
+ 
+
+ align:start position:0%
+have numbers 1 2 3 4 here n equals to 4
+then a permutation can be thought as
+
+ align:start position:0%
+then a permutation can be thought as
+ 
+
+ align:start position:0%
+then a permutation can be thought as
+some way to map these numbers the sets
+
+ align:start position:0%
+some way to map these numbers the sets
+ 
+
+ align:start position:0%
+some way to map these numbers the sets
+back to themselves in one to one
+
+ align:start position:0%
+back to themselves in one to one
+ 
+
+ align:start position:0%
+back to themselves in one to one
+correspondence and a fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point is some number
+
+ align:start position:0%
+point is some number
+ 
+
+ align:start position:0%
+point is some number
+that gets mapped back back to themselves
+
+ align:start position:0%
+that gets mapped back back to themselves
+ 
+
+ align:start position:0%
+that gets mapped back back to themselves
+so in this permutation there are exactly
+
+ align:start position:0%
+so in this permutation there are exactly
+ 
+
+ align:start position:0%
+so in this permutation there are exactly
+two fixed
+
+ align:start position:0%
+two fixed
+ 
+
+ align:start position:0%
+two fixed
+points okay
+
+ align:start position:0%
+points okay
+ 
+
+ align:start position:0%
+points okay
+great let's answer this question using
+
+ align:start position:0%
+great let's answer this question using
+ 
+
+ align:start position:0%
+great let's answer this question using
+linearity of
+
+ align:start position:0%
+linearity of
+ 
+
+ align:start position:0%
+linearity of
+expectations
+
+ align:start position:0%
+expectations
+ 
+
+ align:start position:0%
+expectations
+well one way to think about the problem
+
+ align:start position:0%
+well one way to think about the problem
+ 
+
+ align:start position:0%
+well one way to think about the problem
+is that well there are n factorial
+
+ align:start position:0%
+is that well there are n factorial
+ 
+
+ align:start position:0%
+is that well there are n factorial
+permutations and maybe we want to try to
+
+ align:start position:0%
+permutations and maybe we want to try to
+ 
+
+ align:start position:0%
+permutations and maybe we want to try to
+go about counting how many of them have
+
+ align:start position:0%
+go about counting how many of them have
+ 
+
+ align:start position:0%
+go about counting how many of them have
+zero fixed points how many of them have
+
+ align:start position:0%
+zero fixed points how many of them have
+ 
+
+ align:start position:0%
+zero fixed points how many of them have
+one fixed points how many have two fixed
+
+ align:start position:0%
+one fixed points how many have two fixed
+ 
+
+ align:start position:0%
+one fixed points how many have two fixed
+points but that method can get pretty
+
+ align:start position:0%
+points but that method can get pretty
+ 
+
+ align:start position:0%
+points but that method can get pretty
+cumbersome and pretty difficult quite
+
+ align:start position:0%
+cumbersome and pretty difficult quite
+ 
+
+ align:start position:0%
+cumbersome and pretty difficult quite
+quickly however if we look at this
+
+ align:start position:0%
+quickly however if we look at this
+ 
+
+ align:start position:0%
+quickly however if we look at this
+problem through the lens of linearity of
+
+ align:start position:0%
+problem through the lens of linearity of
+ 
+
+ align:start position:0%
+problem through the lens of linearity of
+expectations there turns out to be a
+
+ align:start position:0%
+expectations there turns out to be a
+ 
+
+ align:start position:0%
+expectations there turns out to be a
+very quick
+
+ align:start position:0%
+very quick
+ 
+
+ align:start position:0%
+very quick
+solution and the method is to let
+
+ align:start position:0%
+solution and the method is to let
+ 
+
+ align:start position:0%
+solution and the method is to let
+introduce some random variables let X I
+
+ align:start position:0%
+introduce some random variables let X I
+ 
+
+ align:start position:0%
+introduce some random variables let X I
+be a random variable that equals to one
+
+ align:start position:0%
+be a random variable that equals to one
+ 
+
+ align:start position:0%
+be a random variable that equals to one
+if I is a fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Point meaning that in this permutation I
+
+ align:start position:0%
+Point meaning that in this permutation I
+ 
+
+ align:start position:0%
+Point meaning that in this permutation I
+gets mapped to itself and zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otherwise so X of I is the indicator
+
+ align:start position:0%
+otherwise so X of I is the indicator
+ 
+
+ align:start position:0%
+otherwise so X of I is the indicator
+random variable for the element I being
+
+ align:start position:0%
+random variable for the element I being
+ 
+
+ align:start position:0%
+random variable for the element I being
+a fixed point of this random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+permutation what's the expectation of XI
+
+ align:start position:0%
+permutation what's the expectation of XI
+ 
+
+ align:start position:0%
+permutation what's the expectation of XI
+well this is the
+
+ align:start position:0%
+well this is the
+ 
+
+ align:start position:0%
+well this is the
+probability that I is a fixed point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well this being a uniform permutation
+
+ align:start position:0%
+well this being a uniform permutation
+ 
+
+ align:start position:0%
+well this being a uniform permutation
+chosen uniformly at random I is sent to
+
+ align:start position:0%
+chosen uniformly at random I is sent to
+ 
+
+ align:start position:0%
+chosen uniformly at random I is sent to
+each of the elements 1 through n with
+
+ align:start position:0%
+each of the elements 1 through n with
+ 
+
+ align:start position:0%
+each of the elements 1 through n with
+equal probabilities so in particular it
+
+ align:start position:0%
+equal probabilities so in particular it
+ 
+
+ align:start position:0%
+equal probabilities so in particular it
+is sent back to itself with probability
+
+ align:start position:0%
+is sent back to itself with probability
+ 
+
+ align:start position:0%
+is sent back to itself with probability
+1 /
+
+ align:start position:0%
+1 /
+ 
+
+ align:start position:0%
+1 /
+n and then the number of fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points equals to the sum of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X XIs so X1 plus X2 so on to xn and now
+
+ align:start position:0%
+X XIs so X1 plus X2 so on to xn and now
+ 
+
+ align:start position:0%
+X XIs so X1 plus X2 so on to xn and now
+we can take expectation of both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sides and apply linearity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectations and see that while each
+
+ align:start position:0%
+expectations and see that while each
+ 
+
+ align:start position:0%
+expectations and see that while each
+individual term is 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n and there are n such terms so the
+
+ align:start position:0%
+n and there are n such terms so the
+ 
+
+ align:start position:0%
+n and there are n such terms so the
+answer is one and that is the answer to
+
+ align:start position:0%
+answer is one and that is the answer to
+ 
+
+ align:start position:0%
+answer is one and that is the answer to
+this question so the average number of
+
+ align:start position:0%
+this question so the average number of
+ 
+
+ align:start position:0%
+this question so the average number of
+fixed points of a permutation chosen
+
+ align:start position:0%
+fixed points of a permutation chosen
+ 
+
+ align:start position:0%
+fixed points of a permutation chosen
+uniformly at random is exactly one and
+
+ align:start position:0%
+uniformly at random is exactly one and
+ 
+
+ align:start position:0%
+uniformly at random is exactly one and
+you see that there's a very quick
+
+ align:start position:0%
+you see that there's a very quick
+ 
+
+ align:start position:0%
+you see that there's a very quick
+calculation once you get a hang of the
+
+ align:start position:0%
+calculation once you get a hang of the
+ 
+
+ align:start position:0%
+calculation once you get a hang of the
+idea of of linearity of
+
+ align:start position:0%
+idea of of linearity of
+ 
+
+ align:start position:0%
+idea of of linearity of
+expectations let us look at a slightly
+
+ align:start position:0%
+expectations let us look at a slightly
+ 
+
+ align:start position:0%
+expectations let us look at a slightly
+more interesting
+
+ align:start position:0%
+more interesting
+ 
+
+ align:start position:0%
+more interesting
+example and for this example we'll
+
+ align:start position:0%
+example and for this example we'll
+ 
+
+ align:start position:0%
+example and for this example we'll
+consider the concept of a tournament
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so a tournament is a concept in
+
+ align:start position:0%
+okay so a tournament is a concept in
+ 
+
+ align:start position:0%
+okay so a tournament is a concept in
+graph Theory referring
+
+ align:start position:0%
+graph Theory referring
+ 
+
+ align:start position:0%
+graph Theory referring
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+following there are nend vertices think
+
+ align:start position:0%
+following there are nend vertices think
+ 
+
+ align:start position:0%
+following there are nend vertices think
+of nend players in some tournament and
+
+ align:start position:0%
+of nend players in some tournament and
+ 
+
+ align:start position:0%
+of nend players in some tournament and
+between every pair of vertices we have
+
+ align:start position:0%
+between every pair of vertices we have
+ 
+
+ align:start position:0%
+between every pair of vertices we have
+some directed Edge pointing in one of
+
+ align:start position:0%
+some directed Edge pointing in one of
+ 
+
+ align:start position:0%
+some directed Edge pointing in one of
+these two directions so every pair of
+
+ align:start position:0%
+these two directions so every pair of
+ 
+
+ align:start position:0%
+these two directions so every pair of
+vertices there's some Edge pointing to
+
+ align:start position:0%
+vertices there's some Edge pointing to
+ 
+
+ align:start position:0%
+vertices there's some Edge pointing to
+one of the two directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's an example of a
+
+ align:start position:0%
+okay so that's an example of a
+ 
+
+ align:start position:0%
+okay so that's an example of a
+tournament I'll need to introduce
+
+ align:start position:0%
+tournament I'll need to introduce
+ 
+
+ align:start position:0%
+tournament I'll need to introduce
+another concept which is that of a
+
+ align:start position:0%
+another concept which is that of a
+ 
+
+ align:start position:0%
+another concept which is that of a
+Hamilton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path so a Hamilton path is a directed
+
+ align:start position:0%
+path so a Hamilton path is a directed
+ 
+
+ align:start position:0%
+path so a Hamilton path is a directed
+path meaning we travel along the
+
+ align:start position:0%
+path meaning we travel along the
+ 
+
+ align:start position:0%
+path meaning we travel along the
+directions of these ver these edges
+
+ align:start position:0%
+directions of these ver these edges
+ 
+
+ align:start position:0%
+directions of these ver these edges
+according to their directions so
+
+ align:start position:0%
+according to their directions so
+ 
+
+ align:start position:0%
+according to their directions so
+directed path that passes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through each
+
+ align:start position:0%
+through each
+ 
+
+ align:start position:0%
+through each
+vertex so every vertex of the graph
+
+ align:start position:0%
+vertex so every vertex of the graph
+ 
+
+ align:start position:0%
+vertex so every vertex of the graph
+exactly once no more no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+less so let's see if we can find any
+
+ align:start position:0%
+less so let's see if we can find any
+ 
+
+ align:start position:0%
+less so let's see if we can find any
+hilon paths in
+
+ align:start position:0%
+hilon paths in
+ 
+
+ align:start position:0%
+hilon paths in
+this in this examp example well I see
+
+ align:start position:0%
+this in this examp example well I see
+ 
+
+ align:start position:0%
+this in this examp example well I see
+one so if we start with the middle
+
+ align:start position:0%
+one so if we start with the middle
+ 
+
+ align:start position:0%
+one so if we start with the middle
+vertex and go along this one this Edge
+
+ align:start position:0%
+vertex and go along this one this Edge
+ 
+
+ align:start position:0%
+vertex and go along this one this Edge
+then this Edge and then this Edge okay
+
+ align:start position:0%
+then this Edge and then this Edge okay
+ 
+
+ align:start position:0%
+then this Edge and then this Edge okay
+so that's a hemoton path that goes
+
+ align:start position:0%
+so that's a hemoton path that goes
+ 
+
+ align:start position:0%
+so that's a hemoton path that goes
+through all four
+
+ align:start position:0%
+through all four
+ 
+
+ align:start position:0%
+through all four
+vertices each vertex passing through it
+
+ align:start position:0%
+vertices each vertex passing through it
+ 
+
+ align:start position:0%
+vertices each vertex passing through it
+exactly once and it always traverses
+
+ align:start position:0%
+exactly once and it always traverses
+ 
+
+ align:start position:0%
+exactly once and it always traverses
+along the direction of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges okay let us prove the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem for every n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tournament on N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n factorial * 2 to the minus
+
+ align:start position:0%
+n factorial * 2 to the minus
+ 
+
+ align:start position:0%
+n factorial * 2 to the minus
+n +
+
+ align:start position:0%
+n +
+ 
+
+ align:start position:0%
+n +
+one hoton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths okay so in other words for every n
+
+ align:start position:0%
+paths okay so in other words for every n
+ 
+
+ align:start position:0%
+paths okay so in other words for every n
+there is some way to orient the edges of
+
+ align:start position:0%
+there is some way to orient the edges of
+ 
+
+ align:start position:0%
+there is some way to orient the edges of
+the complete graph on N vertices so that
+
+ align:start position:0%
+the complete graph on N vertices so that
+ 
+
+ align:start position:0%
+the complete graph on N vertices so that
+it has lots and lots of Hamilton paths
+
+ align:start position:0%
+it has lots and lots of Hamilton paths
+ 
+
+ align:start position:0%
+it has lots and lots of Hamilton paths
+specifically at least this many okay so
+
+ align:start position:0%
+specifically at least this many okay so
+ 
+
+ align:start position:0%
+specifically at least this many okay so
+that's a theorem that we're aiming to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prove we will not prove this theorem by
+
+ align:start position:0%
+prove we will not prove this theorem by
+ 
+
+ align:start position:0%
+prove we will not prove this theorem by
+explicitly constructing such a
+
+ align:start position:0%
+explicitly constructing such a
+ 
+
+ align:start position:0%
+explicitly constructing such a
+tournament instead we'll invoke the
+
+ align:start position:0%
+tournament instead we'll invoke the
+ 
+
+ align:start position:0%
+tournament instead we'll invoke the
+probabilistic method and show that a
+
+ align:start position:0%
+probabilistic method and show that a
+ 
+
+ align:start position:0%
+probabilistic method and show that a
+random tournament has in expectation
+
+ align:start position:0%
+random tournament has in expectation
+ 
+
+ align:start position:0%
+random tournament has in expectation
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+property so here's the
+
+ align:start position:0%
+property so here's the
+ 
+
+ align:start position:0%
+property so here's the
+proof let's consider a random tournament
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices chosen uniformly at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+random one way to do this is to take a
+
+ align:start position:0%
+random one way to do this is to take a
+ 
+
+ align:start position:0%
+random one way to do this is to take a
+complete graph on n verticy and for
+
+ align:start position:0%
+complete graph on n verticy and for
+ 
+
+ align:start position:0%
+complete graph on n verticy and for
+every Edge flip a Fair coin and use that
+
+ align:start position:0%
+every Edge flip a Fair coin and use that
+ 
+
+ align:start position:0%
+every Edge flip a Fair coin and use that
+coin to decide which way the edge
+
+ align:start position:0%
+coin to decide which way the edge
+ 
+
+ align:start position:0%
+coin to decide which way the edge
+orients of the two different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions now let's think about the
+
+ align:start position:0%
+directions now let's think about the
+ 
+
+ align:start position:0%
+directions now let's think about the
+number of Hamilton paths right so
+
+ align:start position:0%
+number of Hamilton paths right so
+ 
+
+ align:start position:0%
+number of Hamilton paths right so
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+path of the so each um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so each of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the N factorial permutations of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices
+
+ align:start position:0%
+vertices
+ 
+
+ align:start position:0%
+vertices
+forms a directed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path okay so first consider a
+
+ align:start position:0%
+path okay so first consider a
+ 
+
+ align:start position:0%
+path okay so first consider a
+permutation of vertices so for example 2
+
+ align:start position:0%
+permutation of vertices so for example 2
+ 
+
+ align:start position:0%
+permutation of vertices so for example 2
+1 3 3 4 and think about what is the
+
+ align:start position:0%
+1 3 3 4 and think about what is the
+ 
+
+ align:start position:0%
+1 3 3 4 and think about what is the
+probability that the edges that go in
+
+ align:start position:0%
+probability that the edges that go in
+ 
+
+ align:start position:0%
+probability that the edges that go in
+the direction of these uh of this
+
+ align:start position:0%
+the direction of these uh of this
+ 
+
+ align:start position:0%
+the direction of these uh of this
+permutation that the edges are all
+
+ align:start position:0%
+permutation that the edges are all
+ 
+
+ align:start position:0%
+permutation that the edges are all
+oriented according to the
+
+ align:start position:0%
+oriented according to the
+ 
+
+ align:start position:0%
+oriented according to the
+permutation well we have to Flip n minus
+
+ align:start position:0%
+permutation well we have to Flip n minus
+ 
+
+ align:start position:0%
+permutation well we have to Flip n minus
+one coins and all of them have to come
+
+ align:start position:0%
+one coins and all of them have to come
+ 
+
+ align:start position:0%
+one coins and all of them have to come
+up in such a way so that the edges are
+
+ align:start position:0%
+up in such a way so that the edges are
+ 
+
+ align:start position:0%
+up in such a way so that the edges are
+pointing in the direction of this
+
+ align:start position:0%
+pointing in the direction of this
+ 
+
+ align:start position:0%
+pointing in the direction of this
+permutation in order of this permutation
+
+ align:start position:0%
+permutation in order of this permutation
+ 
+
+ align:start position:0%
+permutation in order of this permutation
+so the probability
+
+ align:start position:0%
+so the probability
+ 
+
+ align:start position:0%
+so the probability
+that this is a directed path for a for
+
+ align:start position:0%
+that this is a directed path for a for
+ 
+
+ align:start position:0%
+that this is a directed path for a for
+each of these permutations is precisely
+
+ align:start position:0%
+each of these permutations is precisely
+ 
+
+ align:start position:0%
+each of these permutations is precisely
+2 to the
+
+ align:start position:0%
+2 to the
+ 
+
+ align:start position:0%
+2 to the
+minus parenthesis n minus
+
+ align:start position:0%
+minus parenthesis n minus
+ 
+
+ align:start position:0%
+minus parenthesis n minus
+one okay and now we invoke the linearity
+
+ align:start position:0%
+one okay and now we invoke the linearity
+ 
+
+ align:start position:0%
+one okay and now we invoke the linearity
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+expectations to claim that the expected
+
+ align:start position:0%
+expectations to claim that the expected
+ 
+
+ align:start position:0%
+expectations to claim that the expected
+number of Hamilton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths must then be well each of the N
+
+ align:start position:0%
+paths must then be well each of the N
+ 
+
+ align:start position:0%
+paths must then be well each of the N
+factorial permutations has probability
+
+ align:start position:0%
+factorial permutations has probability
+ 
+
+ align:start position:0%
+factorial permutations has probability
+of 2
+
+ align:start position:0%
+of 2
+ 
+
+ align:start position:0%
+of 2
+Theus n minus one of
+
+ align:start position:0%
+Theus n minus one of
+ 
+
+ align:start position:0%
+Theus n minus one of
+being a directed path right so this is a
+
+ align:start position:0%
+being a directed path right so this is a
+ 
+
+ align:start position:0%
+being a directed path right so this is a
+calculation that is analogous to the
+
+ align:start position:0%
+calculation that is analogous to the
+ 
+
+ align:start position:0%
+calculation that is analogous to the
+calculation that we did in the earlier
+
+ align:start position:0%
+calculation that we did in the earlier
+ 
+
+ align:start position:0%
+calculation that we did in the earlier
+part of this
+
+ align:start position:0%
+part of this
+ 
+
+ align:start position:0%
+part of this
+video this is what happens in
+
+ align:start position:0%
+video this is what happens in
+ 
+
+ align:start position:0%
+video this is what happens in
+expectation on average and
+
+ align:start position:0%
+expectation on average and
+ 
+
+ align:start position:0%
+expectation on average and
+thus there must be some instance where
+
+ align:start position:0%
+thus there must be some instance where
+ 
+
+ align:start position:0%
+thus there must be some instance where
+we can beat this average or at least be
+
+ align:start position:0%
+we can beat this average or at least be
+ 
+
+ align:start position:0%
+we can beat this average or at least be
+at least as large as this average so
+
+ align:start position:0%
+at least as large as this average so
+ 
+
+ align:start position:0%
+at least as large as this average so
+thus
+
+ align:start position:0%
+thus
+ 
+
+ align:start position:0%
+thus
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+exists a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tournament
+
+ align:start position:0%
+tournament
+ 
+
+ align:start position:0%
+tournament
+with at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+least this
+
+ align:start position:0%
+least this
+ 
+
+ align:start position:0%
+least this
+many Hamilton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths okay and that concludes the proof
+
+ align:start position:0%
+paths okay and that concludes the proof
+ 
+
+ align:start position:0%
+paths okay and that concludes the proof
+of this theorem that we laid out earlier
+
+ align:start position:0%
+of this theorem that we laid out earlier
+ 
+
+ align:start position:0%
+of this theorem that we laid out earlier
+so this is an example of applying
+
+ align:start position:0%
+so this is an example of applying
+ 
+
+ align:start position:0%
+so this is an example of applying
+linearity expectations as a step in the
+
+ align:start position:0%
+linearity expectations as a step in the
+ 
+
+ align:start position:0%
+linearity expectations as a step in the
+probabilistic method to prove this nice
+
+ align:start position:0%
+probabilistic method to prove this nice
+ 
+
+ align:start position:0%
+probabilistic method to prove this nice
+and simple result that there exist
+
+ align:start position:0%
+and simple result that there exist
+ 
+
+ align:start position:0%
+and simple result that there exist
+tournaments with lots of Hamilton paths
\ No newline at end of file
diff --git a/gEX7MjWwocE.txt b/gEX7MjWwocE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb42afe29281313818f19486505edb7559f0110f
--- /dev/null
+++ b/gEX7MjWwocE.txt
@@ -0,0 +1,491 @@
+align:start position:0%
+ 
+the little princess asteroid b612 is
+
+ align:start position:0%
+the little princess asteroid b612 is
+ 
+
+ align:start position:0%
+the little princess asteroid b612 is
+being orbited by a small body it has a
+
+ align:start position:0%
+being orbited by a small body it has a
+ 
+
+ align:start position:0%
+being orbited by a small body it has a
+mass m and it goes around this asteroid
+
+ align:start position:0%
+mass m and it goes around this asteroid
+ 
+
+ align:start position:0%
+mass m and it goes around this asteroid
+b612 that has a mass M one you know we
+
+ align:start position:0%
+b612 that has a mass M one you know we
+ 
+
+ align:start position:0%
+b612 that has a mass M one you know we
+should add a coordinate system we always
+
+ align:start position:0%
+should add a coordinate system we always
+ 
+
+ align:start position:0%
+should add a coordinate system we always
+know that our head goes radially outward
+
+ align:start position:0%
+know that our head goes radially outward
+ 
+
+ align:start position:0%
+know that our head goes radially outward
+and we know from the universal law of
+
+ align:start position:0%
+and we know from the universal law of
+ 
+
+ align:start position:0%
+and we know from the universal law of
+gravitation that we have mutual
+
+ align:start position:0%
+gravitation that we have mutual
+ 
+
+ align:start position:0%
+gravitation that we have mutual
+attraction between these bodies and
+
+ align:start position:0%
+attraction between these bodies and
+ 
+
+ align:start position:0%
+attraction between these bodies and
+actually that's going to point inward
+
+ align:start position:0%
+actually that's going to point inward
+ 
+
+ align:start position:0%
+actually that's going to point inward
+and because we're having orbital motion
+
+ align:start position:0%
+and because we're having orbital motion
+ 
+
+ align:start position:0%
+and because we're having orbital motion
+here so circular motion the acceleration
+
+ align:start position:0%
+here so circular motion the acceleration
+ 
+
+ align:start position:0%
+here so circular motion the acceleration
+the radial component of the acceleration
+
+ align:start position:0%
+the radial component of the acceleration
+ 
+
+ align:start position:0%
+the radial component of the acceleration
+will also point inward we need to
+
+ align:start position:0%
+will also point inward we need to
+ 
+
+ align:start position:0%
+will also point inward we need to
+consider all of that for our F equals MA
+
+ align:start position:0%
+consider all of that for our F equals MA
+ 
+
+ align:start position:0%
+consider all of that for our F equals MA
+analysis that we are going to do now
+
+ align:start position:0%
+analysis that we are going to do now
+ 
+
+ align:start position:0%
+analysis that we are going to do now
+because the little prince'
+
+ align:start position:0%
+because the little prince'
+ 
+
+ align:start position:0%
+because the little prince'
+wants to know how far this little body
+
+ align:start position:0%
+wants to know how far this little body
+ 
+
+ align:start position:0%
+wants to know how far this little body
+is away from his asteroid okay so we
+
+ align:start position:0%
+is away from his asteroid okay so we
+ 
+
+ align:start position:0%
+is away from his asteroid okay so we
+have the gravitational universal law
+
+ align:start position:0%
+have the gravitational universal law
+ 
+
+ align:start position:0%
+have the gravitational universal law
+here minus G m1 over the distance
+
+ align:start position:0%
+here minus G m1 over the distance
+ 
+
+ align:start position:0%
+here minus G m1 over the distance
+squared so the distance here between the
+
+ align:start position:0%
+squared so the distance here between the
+ 
+
+ align:start position:0%
+squared so the distance here between the
+two planets R which is what we want to
+
+ align:start position:0%
+two planets R which is what we want to
+ 
+
+ align:start position:0%
+two planets R which is what we want to
+calculate and then we have over here for
+
+ align:start position:0%
+calculate and then we have over here for
+ 
+
+ align:start position:0%
+calculate and then we have over here for
+circular motion the description of M
+
+ align:start position:0%
+circular motion the description of M
+ 
+
+ align:start position:0%
+circular motion the description of M
+Omega squared now the little prince'
+
+ align:start position:0%
+Omega squared now the little prince'
+ 
+
+ align:start position:0%
+Omega squared now the little prince'
+can't measure omega but the little
+
+ align:start position:0%
+can't measure omega but the little
+ 
+
+ align:start position:0%
+can't measure omega but the little
+prince has a little time clock so what
+
+ align:start position:0%
+prince has a little time clock so what
+ 
+
+ align:start position:0%
+prince has a little time clock so what
+he can measure is the period from here
+
+ align:start position:0%
+he can measure is the period from here
+ 
+
+ align:start position:0%
+he can measure is the period from here
+until he sees the body again and that is
+
+ align:start position:0%
+until he sees the body again and that is
+ 
+
+ align:start position:0%
+until he sees the body again and that is
+2 PI over Omega so we can add that in
+
+ align:start position:0%
+2 PI over Omega so we can add that in
+ 
+
+ align:start position:0%
+2 PI over Omega so we can add that in
+here M R 4 PI squared over T squared and
+
+ align:start position:0%
+here M R 4 PI squared over T squared and
+ 
+
+ align:start position:0%
+here M R 4 PI squared over T squared and
+well there this M here will cancel out
+
+ align:start position:0%
+well there this M here will cancel out
+ 
+
+ align:start position:0%
+well there this M here will cancel out
+and now we have to solve this for R what
+
+ align:start position:0%
+and now we have to solve this for R what
+ 
+
+ align:start position:0%
+and now we have to solve this for R what
+we're going to see oh and of course we
+
+ align:start position:0%
+we're going to see oh and of course we
+ 
+
+ align:start position:0%
+we're going to see oh and of course we
+have a minus sign here because in
+
+ align:start position:0%
+have a minus sign here because in
+ 
+
+ align:start position:0%
+have a minus sign here because in
+life of the planer of the little prince
+
+ align:start position:0%
+life of the planer of the little prince
+ 
+
+ align:start position:0%
+life of the planer of the little prince
+of course gravitational obv the
+
+ align:start position:0%
+of course gravitational obv the
+ 
+
+ align:start position:0%
+of course gravitational obv the
+acceleration is not going outwards it's
+
+ align:start position:0%
+acceleration is not going outwards it's
+ 
+
+ align:start position:0%
+acceleration is not going outwards it's
+going inward so we better give this a -
+
+ align:start position:0%
+going inward so we better give this a -
+ 
+
+ align:start position:0%
+going inward so we better give this a -
+here and here as well and we will
+
+ align:start position:0%
+here and here as well and we will
+ 
+
+ align:start position:0%
+here and here as well and we will
+actually see that that then cancels out
+
+ align:start position:0%
+actually see that that then cancels out
+ 
+
+ align:start position:0%
+actually see that that then cancels out
+against this one and we're going to
+
+ align:start position:0%
+against this one and we're going to
+ 
+
+ align:start position:0%
+against this one and we're going to
+solve this for R so we get R cubed
+
+ align:start position:0%
+solve this for R so we get R cubed
+ 
+
+ align:start position:0%
+solve this for R so we get R cubed
+actually and then we have G 1 over 4 pi
+
+ align:start position:0%
+actually and then we have G 1 over 4 pi
+ 
+
+ align:start position:0%
+actually and then we have G 1 over 4 pi
+squared and here we have a t squared and
+
+ align:start position:0%
+squared and here we have a t squared and
+ 
+
+ align:start position:0%
+squared and here we have a t squared and
+you can also just write that as G 1 4 pi
+
+ align:start position:0%
+you can also just write that as G 1 4 pi
+ 
+
+ align:start position:0%
+you can also just write that as G 1 4 pi
+squared T squared and then we have third
+
+ align:start position:0%
+squared T squared and then we have third
+ 
+
+ align:start position:0%
+squared T squared and then we have third
+root so you might have seen this
+
+ align:start position:0%
+root so you might have seen this
+ 
+
+ align:start position:0%
+root so you might have seen this
+equation here this actually Kepler's law
+
+ align:start position:0%
+equation here this actually Kepler's law
+ 
+
+ align:start position:0%
+equation here this actually Kepler's law
+it describes the motion of the planets
+
+ align:start position:0%
+it describes the motion of the planets
+ 
+
+ align:start position:0%
+it describes the motion of the planets
+around the Sun well it really only does
+
+ align:start position:0%
+around the Sun well it really only does
+ 
+
+ align:start position:0%
+around the Sun well it really only does
+it if the motions are fairly circular
+
+ align:start position:0%
+it if the motions are fairly circular
+ 
+
+ align:start position:0%
+it if the motions are fairly circular
+for elliptical orbits it is not such a
+
+ align:start position:0%
+for elliptical orbits it is not such a
+ 
+
+ align:start position:0%
+for elliptical orbits it is not such a
+good approximation
+
+ align:start position:0%
+good approximation
+ 
+
+ align:start position:0%
+good approximation
+although kepler derived it like that
+
+ align:start position:0%
+although kepler derived it like that
+ 
+
+ align:start position:0%
+although kepler derived it like that
+quite quite a while ago and that was
+
+ align:start position:0%
+quite quite a while ago and that was
+ 
+
+ align:start position:0%
+quite quite a while ago and that was
+really an astonishing result so here we
+
+ align:start position:0%
+really an astonishing result so here we
+ 
+
+ align:start position:0%
+really an astonishing result so here we
+have this again that the cube of the
+
+ align:start position:0%
+have this again that the cube of the
+ 
+
+ align:start position:0%
+have this again that the cube of the
+distance between two objects is
+
+ align:start position:0%
+distance between two objects is
+ 
+
+ align:start position:0%
+distance between two objects is
+proportional to the square of the the
+
+ align:start position:0%
+proportional to the square of the the
+ 
+
+ align:start position:0%
+proportional to the square of the the
+period of the orbiting time
\ No newline at end of file
diff --git a/hL2GwqBRJJA.txt b/hL2GwqBRJJA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..48d82bfa8761a52db112b07670119131848510de
--- /dev/null
+++ b/hL2GwqBRJJA.txt
@@ -0,0 +1,2755 @@
+align:start position:0%
+ 
+Before I um pass it over to our next
+
+ align:start position:0%
+Before I um pass it over to our next
+ 
+
+ align:start position:0%
+Before I um pass it over to our next
+moderator for the amazing panel on
+
+ align:start position:0%
+moderator for the amazing panel on
+ 
+
+ align:start position:0%
+moderator for the amazing panel on
+policy, I just want to do a a brief
+
+ align:start position:0%
+policy, I just want to do a a brief
+ 
+
+ align:start position:0%
+policy, I just want to do a a brief
+moment summarizing um our first two
+
+ align:start position:0%
+moment summarizing um our first two
+ 
+
+ align:start position:0%
+moment summarizing um our first two
+sessions. Um, and I know we started with
+
+ align:start position:0%
+sessions. Um, and I know we started with
+ 
+
+ align:start position:0%
+sessions. Um, and I know we started with
+the enormity of the global challenge in
+
+ align:start position:0%
+the enormity of the global challenge in
+ 
+
+ align:start position:0%
+the enormity of the global challenge in
+front of us at from multiple
+
+ align:start position:0%
+front of us at from multiple
+ 
+
+ align:start position:0%
+front of us at from multiple
+perspectives and I thought that was a
+
+ align:start position:0%
+perspectives and I thought that was a
+ 
+
+ align:start position:0%
+perspectives and I thought that was a
+fantastic conversation and then we turn
+
+ align:start position:0%
+fantastic conversation and then we turn
+ 
+
+ align:start position:0%
+fantastic conversation and then we turn
+to people and it's easy um to skip the
+
+ align:start position:0%
+to people and it's easy um to skip the
+ 
+
+ align:start position:0%
+to people and it's easy um to skip the
+people part and uh and to not have the
+
+ align:start position:0%
+people part and uh and to not have the
+ 
+
+ align:start position:0%
+people part and uh and to not have the
+harder conversations about all the
+
+ align:start position:0%
+harder conversations about all the
+ 
+
+ align:start position:0%
+harder conversations about all the
+different stakeholders and viewpoints
+
+ align:start position:0%
+different stakeholders and viewpoints
+ 
+
+ align:start position:0%
+different stakeholders and viewpoints
+and challenges. Um, so I'm I'm glad we
+
+ align:start position:0%
+and challenges. Um, so I'm I'm glad we
+ 
+
+ align:start position:0%
+and challenges. Um, so I'm I'm glad we
+did it. And I also um felt uh the
+
+ align:start position:0%
+did it. And I also um felt uh the
+ 
+
+ align:start position:0%
+did it. And I also um felt uh the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I don't know, I irony isn't quite the
+
+ align:start position:0%
+I don't know, I irony isn't quite the
+ 
+
+ align:start position:0%
+I don't know, I irony isn't quite the
+right word. I'm going to misuse it, but
+
+ align:start position:0%
+right word. I'm going to misuse it, but
+ 
+
+ align:start position:0%
+right word. I'm going to misuse it, but
+I felt the um the kind of human level of
+
+ align:start position:0%
+I felt the um the kind of human level of
+ 
+
+ align:start position:0%
+I felt the um the kind of human level of
+what it is to be in a conversation about
+
+ align:start position:0%
+what it is to be in a conversation about
+ 
+
+ align:start position:0%
+what it is to be in a conversation about
+people. Um our emotions and our beliefs.
+
+ align:start position:0%
+people. Um our emotions and our beliefs.
+ 
+
+ align:start position:0%
+people. Um our emotions and our beliefs.
+um aligning them to take action is
+
+ align:start position:0%
+um aligning them to take action is
+ 
+
+ align:start position:0%
+um aligning them to take action is
+probably the largest challenge larger
+
+ align:start position:0%
+probably the largest challenge larger
+ 
+
+ align:start position:0%
+probably the largest challenge larger
+than that first panel.
+
+ align:start position:0%
+than that first panel.
+ 
+
+ align:start position:0%
+than that first panel.
+Um and to do that requires a degree of
+
+ align:start position:0%
+Um and to do that requires a degree of
+ 
+
+ align:start position:0%
+Um and to do that requires a degree of
+vulnerability and human connection. I
+
+ align:start position:0%
+vulnerability and human connection. I
+ 
+
+ align:start position:0%
+vulnerability and human connection. I
+think it was mentioned by some of the
+
+ align:start position:0%
+think it was mentioned by some of the
+ 
+
+ align:start position:0%
+think it was mentioned by some of the
+speakers that um you know
+
+ align:start position:0%
+speakers that um you know
+ 
+
+ align:start position:0%
+speakers that um you know
+heat likes to say ch change happens at
+
+ align:start position:0%
+heat likes to say ch change happens at
+ 
+
+ align:start position:0%
+heat likes to say ch change happens at
+the speed of trust. Um it is
+
+ align:start position:0%
+the speed of trust. Um it is
+ 
+
+ align:start position:0%
+the speed of trust. Um it is
+relationshipbased. And so, um, during
+
+ align:start position:0%
+relationshipbased. And so, um, during
+ 
+
+ align:start position:0%
+relationshipbased. And so, um, during
+the lunch break, uh, after that
+
+ align:start position:0%
+the lunch break, uh, after that
+ 
+
+ align:start position:0%
+the lunch break, uh, after that
+conversation about, um, utilities and
+
+ align:start position:0%
+conversation about, um, utilities and
+ 
+
+ align:start position:0%
+conversation about, um, utilities and
+the question about trust, I was, um,
+
+ align:start position:0%
+the question about trust, I was, um,
+ 
+
+ align:start position:0%
+the question about trust, I was, um,
+chatting with, um, a leader in a gas
+
+ align:start position:0%
+chatting with, um, a leader in a gas
+ 
+
+ align:start position:0%
+chatting with, um, a leader in a gas
+utility. Um, and we ended up, and I'm
+
+ align:start position:0%
+utility. Um, and we ended up, and I'm
+ 
+
+ align:start position:0%
+utility. Um, and we ended up, and I'm
+going to totally make this incredibly
+
+ align:start position:0%
+going to totally make this incredibly
+ 
+
+ align:start position:0%
+going to totally make this incredibly
+uncomfortable and call her up. Come on,
+
+ align:start position:0%
+uncomfortable and call her up. Come on,
+ 
+
+ align:start position:0%
+uncomfortable and call her up. Come on,
+Nikki.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> So, here's what we were talking about.
+
+ align:start position:0%
+>> So, here's what we were talking about.
+ 
+
+ align:start position:0%
+>> So, here's what we were talking about.
+We're going to just demonstrate um a
+
+ align:start position:0%
+We're going to just demonstrate um a
+ 
+
+ align:start position:0%
+We're going to just demonstrate um a
+little bit of vulnerability and trust.
+
+ align:start position:0%
+little bit of vulnerability and trust.
+ 
+
+ align:start position:0%
+little bit of vulnerability and trust.
+We ended up in a very um personal
+
+ align:start position:0%
+We ended up in a very um personal
+ 
+
+ align:start position:0%
+We ended up in a very um personal
+conversation about how to deal with
+
+ align:start position:0%
+conversation about how to deal with
+ 
+
+ align:start position:0%
+conversation about how to deal with
+waking up in the middle of the night
+
+ align:start position:0%
+waking up in the middle of the night
+ 
+
+ align:start position:0%
+waking up in the middle of the night
+with work issues
+
+ align:start position:0%
+with work issues
+ 
+
+ align:start position:0%
+with work issues
+and challenges and and you know was was
+
+ align:start position:0%
+and challenges and and you know was was
+ 
+
+ align:start position:0%
+and challenges and and you know was was
+was diet, coffee, um uh acupuncture, um
+
+ align:start position:0%
+was diet, coffee, um uh acupuncture, um
+ 
+
+ align:start position:0%
+was diet, coffee, um uh acupuncture, um
+other methods the way to cope with the
+
+ align:start position:0%
+other methods the way to cope with the
+ 
+
+ align:start position:0%
+other methods the way to cope with the
+burden and the exhaustion of trying to
+
+ align:start position:0%
+burden and the exhaustion of trying to
+ 
+
+ align:start position:0%
+burden and the exhaustion of trying to
+lead in this space.
+
+ align:start position:0%
+lead in this space.
+ 
+
+ align:start position:0%
+lead in this space.
+>> I'm just going to hand you the mic.
+
+ align:start position:0%
+>> I'm just going to hand you the mic.
+ 
+
+ align:start position:0%
+>> I'm just going to hand you the mic.
+Well, I'm sure it's a foreign issue to
+
+ align:start position:0%
+Well, I'm sure it's a foreign issue to
+ 
+
+ align:start position:0%
+Well, I'm sure it's a foreign issue to
+everybody in the room. No one ever has
+
+ align:start position:0%
+everybody in the room. No one ever has
+ 
+
+ align:start position:0%
+everybody in the room. No one ever has
+woken up in the middle of the night. Um,
+
+ align:start position:0%
+woken up in the middle of the night. Um,
+ 
+
+ align:start position:0%
+woken up in the middle of the night. Um,
+but I think where we we came out is just
+
+ align:start position:0%
+but I think where we we came out is just
+ 
+
+ align:start position:0%
+but I think where we we came out is just
+uh the enormity of it all on your
+
+ align:start position:0%
+uh the enormity of it all on your
+ 
+
+ align:start position:0%
+uh the enormity of it all on your
+shoulders and kind of goes back to what
+
+ align:start position:0%
+shoulders and kind of goes back to what
+ 
+
+ align:start position:0%
+shoulders and kind of goes back to what
+some of the panels were saying about how
+
+ align:start position:0%
+some of the panels were saying about how
+ 
+
+ align:start position:0%
+some of the panels were saying about how
+do you break that down and helpffectuate
+
+ align:start position:0%
+do you break that down and helpffectuate
+ 
+
+ align:start position:0%
+do you break that down and helpffectuate
+change where you can. Um, and then kind
+
+ align:start position:0%
+change where you can. Um, and then kind
+ 
+
+ align:start position:0%
+change where you can. Um, and then kind
+of detach really because you know you if
+
+ align:start position:0%
+of detach really because you know you if
+ 
+
+ align:start position:0%
+of detach really because you know you if
+you're working on something that you
+
+ align:start position:0%
+you're working on something that you
+ 
+
+ align:start position:0%
+you're working on something that you
+love, even if you're exhausted, it feels
+
+ align:start position:0%
+love, even if you're exhausted, it feels
+ 
+
+ align:start position:0%
+love, even if you're exhausted, it feels
+a little less weighty than if you're
+
+ align:start position:0%
+a little less weighty than if you're
+ 
+
+ align:start position:0%
+a little less weighty than if you're
+just putting the paces in, but you know,
+
+ align:start position:0%
+just putting the paces in, but you know,
+ 
+
+ align:start position:0%
+just putting the paces in, but you know,
+you don't really care. Because I'm I get
+
+ align:start position:0%
+you don't really care. Because I'm I get
+ 
+
+ align:start position:0%
+you don't really care. Because I'm I get
+asked sometimes um sometimes by people I
+
+ align:start position:0%
+asked sometimes um sometimes by people I
+ 
+
+ align:start position:0%
+asked sometimes um sometimes by people I
+love, why do you care so much? It's just
+
+ align:start position:0%
+love, why do you care so much? It's just
+ 
+
+ align:start position:0%
+love, why do you care so much? It's just
+a job. Or and I said, well, geez, if I
+
+ align:start position:0%
+a job. Or and I said, well, geez, if I
+ 
+
+ align:start position:0%
+a job. Or and I said, well, geez, if I
+went to work and I treated it as just a
+
+ align:start position:0%
+went to work and I treated it as just a
+ 
+
+ align:start position:0%
+went to work and I treated it as just a
+job, I would be really bored. Probably
+
+ align:start position:0%
+job, I would be really bored. Probably
+ 
+
+ align:start position:0%
+job, I would be really bored. Probably
+wouldn't perform as well. And and I know
+
+ align:start position:0%
+wouldn't perform as well. And and I know
+ 
+
+ align:start position:0%
+wouldn't perform as well. And and I know
+I you know not everybody's wired that
+
+ align:start position:0%
+I you know not everybody's wired that
+ 
+
+ align:start position:0%
+I you know not everybody's wired that
+way, right? And then you think, do I
+
+ align:start position:0%
+way, right? And then you think, do I
+ 
+
+ align:start position:0%
+way, right? And then you think, do I
+have this all wrong? Because then you
+
+ align:start position:0%
+have this all wrong? Because then you
+ 
+
+ align:start position:0%
+have this all wrong? Because then you
+could detach a little easier. And so I
+
+ align:start position:0%
+could detach a little easier. And so I
+ 
+
+ align:start position:0%
+could detach a little easier. And so I
+know and it's not just me. I mean, I
+
+ align:start position:0%
+know and it's not just me. I mean, I
+ 
+
+ align:start position:0%
+know and it's not just me. I mean, I
+stand here on behalf of my team, but um
+
+ align:start position:0%
+stand here on behalf of my team, but um
+ 
+
+ align:start position:0%
+stand here on behalf of my team, but um
+a lot of us are dealing with that. And
+
+ align:start position:0%
+a lot of us are dealing with that. And
+ 
+
+ align:start position:0%
+a lot of us are dealing with that. And
+and I think it's just thinking about the
+
+ align:start position:0%
+and I think it's just thinking about the
+ 
+
+ align:start position:0%
+and I think it's just thinking about the
+global picture and the to use the word
+
+ align:start position:0%
+global picture and the to use the word
+ 
+
+ align:start position:0%
+global picture and the to use the word
+enormity of it all, but what locally can
+
+ align:start position:0%
+enormity of it all, but what locally can
+ 
+
+ align:start position:0%
+enormity of it all, but what locally can
+you control and what can you do and
+
+ align:start position:0%
+you control and what can you do and
+ 
+
+ align:start position:0%
+you control and what can you do and
+trying to do the now I sound like a
+
+ align:start position:0%
+trying to do the now I sound like a
+ 
+
+ align:start position:0%
+trying to do the now I sound like a
+Frozen movie, but the next right thing I
+
+ align:start position:0%
+Frozen movie, but the next right thing I
+ 
+
+ align:start position:0%
+Frozen movie, but the next right thing I
+think was the song. You can tell how old
+
+ align:start position:0%
+think was the song. You can tell how old
+ 
+
+ align:start position:0%
+think was the song. You can tell how old
+my kids are. Yeah,
+
+ align:start position:0%
+my kids are. Yeah,
+ 
+
+ align:start position:0%
+my kids are. Yeah,
+>> I was going to say that.
+
+ align:start position:0%
+>> I was going to say that.
+ 
+
+ align:start position:0%
+>> I was going to say that.
+>> Thank you so much, Nikki, for for
+
+ align:start position:0%
+>> Thank you so much, Nikki, for for
+ 
+
+ align:start position:0%
+>> Thank you so much, Nikki, for for
+volunteering to do that. Um, and I just
+
+ align:start position:0%
+volunteering to do that. Um, and I just
+ 
+
+ align:start position:0%
+volunteering to do that. Um, and I just
+I wanted to do that to bring like that
+
+ align:start position:0%
+I wanted to do that to bring like that
+ 
+
+ align:start position:0%
+I wanted to do that to bring like that
+level of the people conversation in in
+
+ align:start position:0%
+level of the people conversation in in
+ 
+
+ align:start position:0%
+level of the people conversation in in
+response to some of the conversation we
+
+ align:start position:0%
+response to some of the conversation we
+ 
+
+ align:start position:0%
+response to some of the conversation we
+had before is just it's actually just
+
+ align:start position:0%
+had before is just it's actually just
+ 
+
+ align:start position:0%
+had before is just it's actually just
+human. And as you get to know other
+
+ align:start position:0%
+human. And as you get to know other
+ 
+
+ align:start position:0%
+human. And as you get to know other
+humans, no matter where they are in the
+
+ align:start position:0%
+humans, no matter where they are in the
+ 
+
+ align:start position:0%
+humans, no matter where they are in the
+system, you will find over and over
+
+ align:start position:0%
+system, you will find over and over
+ 
+
+ align:start position:0%
+system, you will find over and over
+again that they are just humans and that
+
+ align:start position:0%
+again that they are just humans and that
+ 
+
+ align:start position:0%
+again that they are just humans and that
+it is the systems that we must evolve
+
+ align:start position:0%
+it is the systems that we must evolve
+ 
+
+ align:start position:0%
+it is the systems that we must evolve
+and change to meet the moment. So with
+
+ align:start position:0%
+and change to meet the moment. So with
+ 
+
+ align:start position:0%
+and change to meet the moment. So with
+that note,
+
+ align:start position:0%
+that note,
+ 
+
+ align:start position:0%
+that note,
+turning it over to Andrew Eiff who is
+
+ align:start position:0%
+turning it over to Andrew Eiff who is
+ 
+
+ align:start position:0%
+turning it over to Andrew Eiff who is
+going to be our next moderator. And I'm
+
+ align:start position:0%
+going to be our next moderator. And I'm
+ 
+
+ align:start position:0%
+going to be our next moderator. And I'm
+so excited for this panel.
+
+ align:start position:0%
+so excited for this panel.
+ 
+
+ align:start position:0%
+so excited for this panel.
+>> I'm excited too. I hope you all are too.
+
+ align:start position:0%
+>> I'm excited too. I hope you all are too.
+ 
+
+ align:start position:0%
+>> I'm excited too. I hope you all are too.
+I think that's a great segue. We spent
+
+ align:start position:0%
+I think that's a great segue. We spent
+ 
+
+ align:start position:0%
+I think that's a great segue. We spent
+the morning, excuse me, talking about
+
+ align:start position:0%
+the morning, excuse me, talking about
+ 
+
+ align:start position:0%
+the morning, excuse me, talking about
+the sort of high level and talking about
+
+ align:start position:0%
+the sort of high level and talking about
+ 
+
+ align:start position:0%
+the sort of high level and talking about
+people and I think policy can seem like
+
+ align:start position:0%
+people and I think policy can seem like
+ 
+
+ align:start position:0%
+people and I think policy can seem like
+a sort of depersonified kind of a thing.
+
+ align:start position:0%
+a sort of depersonified kind of a thing.
+ 
+
+ align:start position:0%
+a sort of depersonified kind of a thing.
+It's just out there in the system, in
+
+ align:start position:0%
+It's just out there in the system, in
+ 
+
+ align:start position:0%
+It's just out there in the system, in
+the atmosphere, in the water. But I
+
+ align:start position:0%
+the atmosphere, in the water. But I
+ 
+
+ align:start position:0%
+the atmosphere, in the water. But I
+think we're going to hear in this panel
+
+ align:start position:0%
+think we're going to hear in this panel
+ 
+
+ align:start position:0%
+think we're going to hear in this panel
+about people making that policy and what
+
+ align:start position:0%
+about people making that policy and what
+ 
+
+ align:start position:0%
+about people making that policy and what
+is driving them, what are the
+
+ align:start position:0%
+is driving them, what are the
+ 
+
+ align:start position:0%
+is driving them, what are the
+opportunities, what are the challenges
+
+ align:start position:0%
+opportunities, what are the challenges
+ 
+
+ align:start position:0%
+opportunities, what are the challenges
+that they see. Uh we're going to begin
+
+ align:start position:0%
+that they see. Uh we're going to begin
+ 
+
+ align:start position:0%
+that they see. Uh we're going to begin
+with a video from Laurig Shakudian. She
+
+ align:start position:0%
+with a video from Laurig Shakudian. She
+ 
+
+ align:start position:0%
+with a video from Laurig Shakudian. She
+represents district 20 in in the
+
+ align:start position:0%
+represents district 20 in in the
+ 
+
+ align:start position:0%
+represents district 20 in in the
+Maryland assembly and serves on the
+
+ align:start position:0%
+Maryland assembly and serves on the
+ 
+
+ align:start position:0%
+Maryland assembly and serves on the
+economic matters committee. As you will
+
+ align:start position:0%
+economic matters committee. As you will
+ 
+
+ align:start position:0%
+economic matters committee. As you will
+hear, Laurig is a passionate and
+
+ align:start position:0%
+hear, Laurig is a passionate and
+ 
+
+ align:start position:0%
+hear, Laurig is a passionate and
+thoughtful advocate and also runs
+
+ align:start position:0%
+thoughtful advocate and also runs
+ 
+
+ align:start position:0%
+thoughtful advocate and also runs
+ultramarathons, which may help explain
+
+ align:start position:0%
+ultramarathons, which may help explain
+ 
+
+ align:start position:0%
+ultramarathons, which may help explain
+her stamina in pushing for geothermal
+
+ align:start position:0%
+her stamina in pushing for geothermal
+ 
+
+ align:start position:0%
+her stamina in pushing for geothermal
+networks.
+
+ align:start position:0%
+networks.
+ 
+
+ align:start position:0%
+networks.
+>> Delegate Lauren Chudian uh in the
+
+ align:start position:0%
+>> Delegate Lauren Chudian uh in the
+ 
+
+ align:start position:0%
+>> Delegate Lauren Chudian uh in the
+Maryland General Assembly and I am
+
+ align:start position:0%
+Maryland General Assembly and I am
+ 
+
+ align:start position:0%
+Maryland General Assembly and I am
+sending my greetings and a little bit of
+
+ align:start position:0%
+sending my greetings and a little bit of
+ 
+
+ align:start position:0%
+sending my greetings and a little bit of
+jealousy because I wish I was there with
+
+ align:start position:0%
+jealousy because I wish I was there with
+ 
+
+ align:start position:0%
+jealousy because I wish I was there with
+you.
+
+ align:start position:0%
+you.
+ 
+
+ align:start position:0%
+you.
+>> Um but I'm here in the Maryland General
+
+ align:start position:0%
+>> Um but I'm here in the Maryland General
+ 
+
+ align:start position:0%
+>> Um but I'm here in the Maryland General
+Assembly. We are in full session and I
+
+ align:start position:0%
+Assembly. We are in full session and I
+ 
+
+ align:start position:0%
+Assembly. We are in full session and I
+have bill hearings at the time that you
+
+ align:start position:0%
+have bill hearings at the time that you
+ 
+
+ align:start position:0%
+have bill hearings at the time that you
+all are meeting. So, I know your
+
+ align:start position:0%
+all are meeting. So, I know your
+ 
+
+ align:start position:0%
+all are meeting. So, I know your
+meetings um and your conversations are
+
+ align:start position:0%
+meetings um and your conversations are
+ 
+
+ align:start position:0%
+meetings um and your conversations are
+probably amazing and I look forward to
+
+ align:start position:0%
+probably amazing and I look forward to
+ 
+
+ align:start position:0%
+probably amazing and I look forward to
+hearing about everything that you are
+
+ align:start position:0%
+hearing about everything that you are
+ 
+
+ align:start position:0%
+hearing about everything that you are
+learning from each other as I continue
+
+ align:start position:0%
+learning from each other as I continue
+ 
+
+ align:start position:0%
+learning from each other as I continue
+to be part of this amazing network of
+
+ align:start position:0%
+to be part of this amazing network of
+ 
+
+ align:start position:0%
+to be part of this amazing network of
+people across the country uh who are
+
+ align:start position:0%
+people across the country uh who are
+ 
+
+ align:start position:0%
+people across the country uh who are
+moving legislation and pilots and
+
+ align:start position:0%
+moving legislation and pilots and
+ 
+
+ align:start position:0%
+moving legislation and pilots and
+programs forward to increase um network
+
+ align:start position:0%
+programs forward to increase um network
+ 
+
+ align:start position:0%
+programs forward to increase um network
+geothermal systems across our
+
+ align:start position:0%
+geothermal systems across our
+ 
+
+ align:start position:0%
+geothermal systems across our
+communities. Um last year around this
+
+ align:start position:0%
+communities. Um last year around this
+ 
+
+ align:start position:0%
+communities. Um last year around this
+time I was working to pass the warmth
+
+ align:start position:0%
+time I was working to pass the warmth
+ 
+
+ align:start position:0%
+time I was working to pass the warmth
+act which is the um working for
+
+ align:start position:0%
+act which is the um working for
+ 
+
+ align:start position:0%
+act which is the um working for
+accessible renewable Maryland thermal
+
+ align:start position:0%
+accessible renewable Maryland thermal
+ 
+
+ align:start position:0%
+accessible renewable Maryland thermal
+heat. A bit of a mouthful but really a
+
+ align:start position:0%
+heat. A bit of a mouthful but really a
+ 
+
+ align:start position:0%
+heat. A bit of a mouthful but really a
+brilliant name. Wouldn't you agree? Um
+
+ align:start position:0%
+brilliant name. Wouldn't you agree? Um
+ 
+
+ align:start position:0%
+brilliant name. Wouldn't you agree? Um
+and warmth like who doesn't want to be
+
+ align:start position:0%
+and warmth like who doesn't want to be
+ 
+
+ align:start position:0%
+and warmth like who doesn't want to be
+warm? And so with that as our entry, we
+
+ align:start position:0%
+warm? And so with that as our entry, we
+ 
+
+ align:start position:0%
+warm? And so with that as our entry, we
+were able to educate my colleagues on um
+
+ align:start position:0%
+were able to educate my colleagues on um
+ 
+
+ align:start position:0%
+were able to educate my colleagues on um
+network geothermal systems uh in our
+
+ align:start position:0%
+network geothermal systems uh in our
+ 
+
+ align:start position:0%
+network geothermal systems uh in our
+case utility owned systems and we passed
+
+ align:start position:0%
+case utility owned systems and we passed
+ 
+
+ align:start position:0%
+case utility owned systems and we passed
+the bill in uh 2024. And so now we've
+
+ align:start position:0%
+the bill in uh 2024. And so now we've
+ 
+
+ align:start position:0%
+the bill in uh 2024. And so now we've
+reached a point where the utilities are
+
+ align:start position:0%
+reached a point where the utilities are
+ 
+
+ align:start position:0%
+reached a point where the utilities are
+each putting in um their filings with
+
+ align:start position:0%
+each putting in um their filings with
+ 
+
+ align:start position:0%
+each putting in um their filings with
+working with the community on developing
+
+ align:start position:0%
+working with the community on developing
+ 
+
+ align:start position:0%
+working with the community on developing
+pilot locations um and things are moving
+
+ align:start position:0%
+pilot locations um and things are moving
+ 
+
+ align:start position:0%
+pilot locations um and things are moving
+forward. So I'll back up a little bit
+
+ align:start position:0%
+forward. So I'll back up a little bit
+ 
+
+ align:start position:0%
+forward. So I'll back up a little bit
+and tell you about our process. I became
+
+ align:start position:0%
+and tell you about our process. I became
+ 
+
+ align:start position:0%
+and tell you about our process. I became
+um really interested in geothermal in
+
+ align:start position:0%
+um really interested in geothermal in
+ 
+
+ align:start position:0%
+um really interested in geothermal in
+general when I was working both on
+
+ align:start position:0%
+general when I was working both on
+ 
+
+ align:start position:0%
+general when I was working both on
+building electrification a number of
+
+ align:start position:0%
+building electrification a number of
+ 
+
+ align:start position:0%
+building electrification a number of
+years ago. Working on building
+
+ align:start position:0%
+years ago. Working on building
+ 
+
+ align:start position:0%
+years ago. Working on building
+electrification and also simultaneously
+
+ align:start position:0%
+electrification and also simultaneously
+ 
+
+ align:start position:0%
+electrification and also simultaneously
+on looking at grid issues and and um
+
+ align:start position:0%
+on looking at grid issues and and um
+ 
+
+ align:start position:0%
+on looking at grid issues and and um
+grid stability and the ability of the
+
+ align:start position:0%
+grid stability and the ability of the
+ 
+
+ align:start position:0%
+grid stability and the ability of the
+grid to handle building and and um
+
+ align:start position:0%
+grid to handle building and and um
+ 
+
+ align:start position:0%
+grid to handle building and and um
+transportation electrification. And that
+
+ align:start position:0%
+transportation electrification. And that
+ 
+
+ align:start position:0%
+transportation electrification. And that
+was even before we were looking at load
+
+ align:start position:0%
+was even before we were looking at load
+ 
+
+ align:start position:0%
+was even before we were looking at load
+growth from data centers and other
+
+ align:start position:0%
+growth from data centers and other
+ 
+
+ align:start position:0%
+growth from data centers and other
+manufacturing. Um and it was clear to me
+
+ align:start position:0%
+manufacturing. Um and it was clear to me
+ 
+
+ align:start position:0%
+manufacturing. Um and it was clear to me
+that geothermal had to be part of our uh
+
+ align:start position:0%
+that geothermal had to be part of our uh
+ 
+
+ align:start position:0%
+that geothermal had to be part of our uh
+transition because of the fact that it
+
+ align:start position:0%
+transition because of the fact that it
+ 
+
+ align:start position:0%
+transition because of the fact that it
+has the ability to um to do the
+
+ align:start position:0%
+has the ability to um to do the
+ 
+
+ align:start position:0%
+has the ability to um to do the
+electrification superefficiently um and
+
+ align:start position:0%
+electrification superefficiently um and
+ 
+
+ align:start position:0%
+electrification superefficiently um and
+in a way that really minimizes impact on
+
+ align:start position:0%
+in a way that really minimizes impact on
+ 
+
+ align:start position:0%
+in a way that really minimizes impact on
+the grid and long-term as we've seen
+
+ align:start position:0%
+the grid and long-term as we've seen
+ 
+
+ align:start position:0%
+the grid and long-term as we've seen
+from the DOE studies um really saves an
+
+ align:start position:0%
+from the DOE studies um really saves an
+ 
+
+ align:start position:0%
+from the DOE studies um really saves an
+extraordinary amount of money in terms
+
+ align:start position:0%
+extraordinary amount of money in terms
+ 
+
+ align:start position:0%
+extraordinary amount of money in terms
+of uh infrastructure um and generation.
+
+ align:start position:0%
+of uh infrastructure um and generation.
+ 
+
+ align:start position:0%
+of uh infrastructure um and generation.
+So I got excited about that. I had an
+
+ align:start position:0%
+So I got excited about that. I had an
+ 
+
+ align:start position:0%
+So I got excited about that. I had an
+initial bill um in 2021 uh to create
+
+ align:start position:0%
+initial bill um in 2021 uh to create
+ 
+
+ align:start position:0%
+initial bill um in 2021 uh to create
+geothermal wrecks in the state. But as I
+
+ align:start position:0%
+geothermal wrecks in the state. But as I
+ 
+
+ align:start position:0%
+geothermal wrecks in the state. But as I
+was doing that research, I ran across
+
+ align:start position:0%
+was doing that research, I ran across
+ 
+
+ align:start position:0%
+was doing that research, I ran across
+the work that heat was doing and I
+
+ align:start position:0%
+the work that heat was doing and I
+ 
+
+ align:start position:0%
+the work that heat was doing and I
+absolutely fell in love with the model
+
+ align:start position:0%
+absolutely fell in love with the model
+ 
+
+ align:start position:0%
+absolutely fell in love with the model
+because for a few reasons. Um, one
+
+ align:start position:0%
+because for a few reasons. Um, one
+ 
+
+ align:start position:0%
+because for a few reasons. Um, one
+reason is because um, as I work on
+
+ align:start position:0%
+reason is because um, as I work on
+ 
+
+ align:start position:0%
+reason is because um, as I work on
+energy transition, one of my top
+
+ align:start position:0%
+energy transition, one of my top
+ 
+
+ align:start position:0%
+energy transition, one of my top
+priorities is to make sure that the jobs
+
+ align:start position:0%
+priorities is to make sure that the jobs
+ 
+
+ align:start position:0%
+priorities is to make sure that the jobs
+that are being created in our new energy
+
+ align:start position:0%
+that are being created in our new energy
+ 
+
+ align:start position:0%
+that are being created in our new energy
+economy are good union jobs and are
+
+ align:start position:0%
+economy are good union jobs and are
+ 
+
+ align:start position:0%
+economy are good union jobs and are
+equivalent to the jobs uh, that are
+
+ align:start position:0%
+equivalent to the jobs uh, that are
+ 
+
+ align:start position:0%
+equivalent to the jobs uh, that are
+being lost as we transition away from
+
+ align:start position:0%
+being lost as we transition away from
+ 
+
+ align:start position:0%
+being lost as we transition away from
+fossil fuels. And so network geothermal
+
+ align:start position:0%
+fossil fuels. And so network geothermal
+ 
+
+ align:start position:0%
+fossil fuels. And so network geothermal
+of course is the most perfect of those
+
+ align:start position:0%
+of course is the most perfect of those
+ 
+
+ align:start position:0%
+of course is the most perfect of those
+transitions because um literally the
+
+ align:start position:0%
+transitions because um literally the
+ 
+
+ align:start position:0%
+transitions because um literally the
+very same work working on pipes in the
+
+ align:start position:0%
+very same work working on pipes in the
+ 
+
+ align:start position:0%
+very same work working on pipes in the
+ground that could be done with gas is
+
+ align:start position:0%
+ground that could be done with gas is
+ 
+
+ align:start position:0%
+ground that could be done with gas is
+the very same work working on pipes in
+
+ align:start position:0%
+the very same work working on pipes in
+ 
+
+ align:start position:0%
+the very same work working on pipes in
+the ground that is done with never
+
+ align:start position:0%
+the ground that is done with never
+ 
+
+ align:start position:0%
+the ground that is done with never
+geothermal. So that sort of checked one
+
+ align:start position:0%
+geothermal. So that sort of checked one
+ 
+
+ align:start position:0%
+geothermal. So that sort of checked one
+of my top priority boxes. And then the
+
+ align:start position:0%
+of my top priority boxes. And then the
+ 
+
+ align:start position:0%
+of my top priority boxes. And then the
+idea of, you know, I do spend a lot of
+
+ align:start position:0%
+idea of, you know, I do spend a lot of
+ 
+
+ align:start position:0%
+idea of, you know, I do spend a lot of
+time um with legislation that the
+
+ align:start position:0%
+time um with legislation that the
+ 
+
+ align:start position:0%
+time um with legislation that the
+utilities don't like. Um and it's nice
+
+ align:start position:0%
+utilities don't like. Um and it's nice
+ 
+
+ align:start position:0%
+utilities don't like. Um and it's nice
+to work with the gas utilities and say,
+
+ align:start position:0%
+to work with the gas utilities and say,
+ 
+
+ align:start position:0%
+to work with the gas utilities and say,
+"Look, you know, like if you want a
+
+ align:start position:0%
+"Look, you know, like if you want a
+ 
+
+ align:start position:0%
+"Look, you know, like if you want a
+future, I don't have a problem with your
+
+ align:start position:0%
+future, I don't have a problem with your
+ 
+
+ align:start position:0%
+future, I don't have a problem with your
+future. I just have a problem with your
+
+ align:start position:0%
+future. I just have a problem with your
+ 
+
+ align:start position:0%
+future. I just have a problem with your
+current business model and your past
+
+ align:start position:0%
+current business model and your past
+ 
+
+ align:start position:0%
+current business model and your past
+business model of fossil gas." And so if
+
+ align:start position:0%
+business model of fossil gas." And so if
+ 
+
+ align:start position:0%
+business model of fossil gas." And so if
+you want a future, like let me help you
+
+ align:start position:0%
+you want a future, like let me help you
+ 
+
+ align:start position:0%
+you want a future, like let me help you
+have another kind of a future. and um
+
+ align:start position:0%
+have another kind of a future. and um
+ 
+
+ align:start position:0%
+have another kind of a future. and um
+really an opportunity to take um to take
+
+ align:start position:0%
+really an opportunity to take um to take
+ 
+
+ align:start position:0%
+really an opportunity to take um to take
+what it is that utilities do have, which
+
+ align:start position:0%
+what it is that utilities do have, which
+ 
+
+ align:start position:0%
+what it is that utilities do have, which
+is an ability and expertise on massive
+
+ align:start position:0%
+is an ability and expertise on massive
+ 
+
+ align:start position:0%
+is an ability and expertise on massive
+infrastructure projects and access to
+
+ align:start position:0%
+infrastructure projects and access to
+ 
+
+ align:start position:0%
+infrastructure projects and access to
+capital to do that um and a system that
+
+ align:start position:0%
+capital to do that um and a system that
+ 
+
+ align:start position:0%
+capital to do that um and a system that
+lets us spread the costs and the
+
+ align:start position:0%
+lets us spread the costs and the
+ 
+
+ align:start position:0%
+lets us spread the costs and the
+benefits across all rateayers. And so
+
+ align:start position:0%
+benefits across all rateayers. And so
+ 
+
+ align:start position:0%
+benefits across all rateayers. And so
+all of those things uh made me really
+
+ align:start position:0%
+all of those things uh made me really
+ 
+
+ align:start position:0%
+all of those things uh made me really
+excited about network geothermal. Um so
+
+ align:start position:0%
+excited about network geothermal. Um so
+ 
+
+ align:start position:0%
+excited about network geothermal. Um so
+I went up first and u met with folks at
+
+ align:start position:0%
+I went up first and u met with folks at
+ 
+
+ align:start position:0%
+I went up first and u met with folks at
+HEAT myself. Um learned a bunch of stuff
+
+ align:start position:0%
+HEAT myself. Um learned a bunch of stuff
+ 
+
+ align:start position:0%
+HEAT myself. Um learned a bunch of stuff
+um with um we brought up I went up with
+
+ align:start position:0%
+um with um we brought up I went up with
+ 
+
+ align:start position:0%
+um with um we brought up I went up with
+uh initially sorry first I went up with
+
+ align:start position:0%
+uh initially sorry first I went up with
+ 
+
+ align:start position:0%
+uh initially sorry first I went up with
+uh Washington gas uh and we took a look
+
+ align:start position:0%
+uh Washington gas uh and we took a look
+ 
+
+ align:start position:0%
+uh Washington gas uh and we took a look
+at the systems and then as I got clearer
+
+ align:start position:0%
+at the systems and then as I got clearer
+ 
+
+ align:start position:0%
+at the systems and then as I got clearer
+about the bill that I was putting
+
+ align:start position:0%
+about the bill that I was putting
+ 
+
+ align:start position:0%
+about the bill that I was putting
+together I started a process that I do
+
+ align:start position:0%
+together I started a process that I do
+ 
+
+ align:start position:0%
+together I started a process that I do
+on most of my big energy bills which is
+
+ align:start position:0%
+on most of my big energy bills which is
+ 
+
+ align:start position:0%
+on most of my big energy bills which is
+really bringing together all of the
+
+ align:start position:0%
+really bringing together all of the
+ 
+
+ align:start position:0%
+really bringing together all of the
+potential stakeholders. So, I was
+
+ align:start position:0%
+potential stakeholders. So, I was
+ 
+
+ align:start position:0%
+potential stakeholders. So, I was
+working with um I was working with the
+
+ align:start position:0%
+working with um I was working with the
+ 
+
+ align:start position:0%
+working with um I was working with the
+gas utilities. I was working with the
+
+ align:start position:0%
+gas utilities. I was working with the
+ 
+
+ align:start position:0%
+gas utilities. I was working with the
+labor unions, both the labor unions who
+
+ align:start position:0%
+labor unions, both the labor unions who
+ 
+
+ align:start position:0%
+labor unions, both the labor unions who
+represent gas workers. So, the in-house
+
+ align:start position:0%
+represent gas workers. So, the in-house
+ 
+
+ align:start position:0%
+represent gas workers. So, the in-house
+labor unions uh for Washington gas and
+
+ align:start position:0%
+labor unions uh for Washington gas and
+ 
+
+ align:start position:0%
+labor unions uh for Washington gas and
+BG and then also the building trades. Uh
+
+ align:start position:0%
+BG and then also the building trades. Uh
+ 
+
+ align:start position:0%
+BG and then also the building trades. Uh
+so, work that doesn't get done um by the
+
+ align:start position:0%
+so, work that doesn't get done um by the
+ 
+
+ align:start position:0%
+so, work that doesn't get done um by the
+in-house unions, construction work that
+
+ align:start position:0%
+in-house unions, construction work that
+ 
+
+ align:start position:0%
+in-house unions, construction work that
+gets contracted out could be done um by
+
+ align:start position:0%
+gets contracted out could be done um by
+ 
+
+ align:start position:0%
+gets contracted out could be done um by
+building trades. I was working very
+
+ align:start position:0%
+building trades. I was working very
+ 
+
+ align:start position:0%
+building trades. I was working very
+closely with uh the grassroots groups uh
+
+ align:start position:0%
+closely with uh the grassroots groups uh
+ 
+
+ align:start position:0%
+closely with uh the grassroots groups uh
+the housing justice folks, the climate
+
+ align:start position:0%
+the housing justice folks, the climate
+ 
+
+ align:start position:0%
+the housing justice folks, the climate
+justice folks who are doing really
+
+ align:start position:0%
+justice folks who are doing really
+ 
+
+ align:start position:0%
+justice folks who are doing really
+interesting organizing in my community
+
+ align:start position:0%
+interesting organizing in my community
+ 
+
+ align:start position:0%
+interesting organizing in my community
+where they're going in and measuring NO2
+
+ align:start position:0%
+where they're going in and measuring NO2
+ 
+
+ align:start position:0%
+where they're going in and measuring NO2
+levels associated with gas stoves and
+
+ align:start position:0%
+levels associated with gas stoves and
+ 
+
+ align:start position:0%
+levels associated with gas stoves and
+then they're organizing tenants who are
+
+ align:start position:0%
+then they're organizing tenants who are
+ 
+
+ align:start position:0%
+then they're organizing tenants who are
+then going to their landlords and asking
+
+ align:start position:0%
+then going to their landlords and asking
+ 
+
+ align:start position:0%
+then going to their landlords and asking
+for um asking for electrification um for
+
+ align:start position:0%
+for um asking for electrification um for
+ 
+
+ align:start position:0%
+for um asking for electrification um for
+as a health and safety issue. So working
+
+ align:start position:0%
+as a health and safety issue. So working
+ 
+
+ align:start position:0%
+as a health and safety issue. So working
+with Action in Montgomery, Interfaith
+
+ align:start position:0%
+with Action in Montgomery, Interfaith
+ 
+
+ align:start position:0%
+with Action in Montgomery, Interfaith
+Power and Light, those were some of the
+
+ align:start position:0%
+Power and Light, those were some of the
+ 
+
+ align:start position:0%
+Power and Light, those were some of the
+groups doing that. grassroots housing
+
+ align:start position:0%
+groups doing that. grassroots housing
+ 
+
+ align:start position:0%
+groups doing that. grassroots housing
+justice, climate justice work, and then
+
+ align:start position:0%
+justice, climate justice work, and then
+ 
+
+ align:start position:0%
+justice, climate justice work, and then
+um also bringing into the conversation
+
+ align:start position:0%
+um also bringing into the conversation
+ 
+
+ align:start position:0%
+um also bringing into the conversation
+groups like the Maryland Energy
+
+ align:start position:0%
+groups like the Maryland Energy
+ 
+
+ align:start position:0%
+groups like the Maryland Energy
+Administration, the Public Service
+
+ align:start position:0%
+Administration, the Public Service
+ 
+
+ align:start position:0%
+Administration, the Public Service
+Commission, the Office of People's
+
+ align:start position:0%
+Commission, the Office of People's
+ 
+
+ align:start position:0%
+Commission, the Office of People's
+Council, and then of course all the
+
+ align:start position:0%
+Council, and then of course all the
+ 
+
+ align:start position:0%
+Council, and then of course all the
+climate groups um that do really good
+
+ align:start position:0%
+climate groups um that do really good
+ 
+
+ align:start position:0%
+climate groups um that do really good
+work in the state, Chesby Climate Action
+
+ align:start position:0%
+work in the state, Chesby Climate Action
+ 
+
+ align:start position:0%
+work in the state, Chesby Climate Action
+Network, League of Conservation, Vot
+
+ align:start position:0%
+Network, League of Conservation, Vot
+ 
+
+ align:start position:0%
+Network, League of Conservation, Vot
+Sierra Club, and others. And so, um I
+
+ align:start position:0%
+Sierra Club, and others. And so, um I
+ 
+
+ align:start position:0%
+Sierra Club, and others. And so, um I
+started working with all of those
+
+ align:start position:0%
+started working with all of those
+ 
+
+ align:start position:0%
+started working with all of those
+groups. And um I I um
+
+ align:start position:0%
+groups. And um I I um
+ 
+
+ align:start position:0%
+groups. And um I I um
+brought uh a group of people up to
+
+ align:start position:0%
+brought uh a group of people up to
+ 
+
+ align:start position:0%
+brought uh a group of people up to
+Massachusetts and thanks again to heat
+
+ align:start position:0%
+Massachusetts and thanks again to heat
+ 
+
+ align:start position:0%
+Massachusetts and thanks again to heat
+for hosting us. Um we had a chance to
+
+ align:start position:0%
+for hosting us. Um we had a chance to
+ 
+
+ align:start position:0%
+for hosting us. Um we had a chance to
+see um some of the test board holes. we
+
+ align:start position:0%
+see um some of the test board holes. we
+ 
+
+ align:start position:0%
+see um some of the test board holes. we
+had a chance to sort of stand there and
+
+ align:start position:0%
+had a chance to sort of stand there and
+ 
+
+ align:start position:0%
+had a chance to sort of stand there and
+look at, you know, buildings really,
+
+ align:start position:0%
+look at, you know, buildings really,
+ 
+
+ align:start position:0%
+look at, you know, buildings really,
+right? because um as AB likes to say
+
+ align:start position:0%
+right? because um as AB likes to say
+ 
+
+ align:start position:0%
+right? because um as AB likes to say
+there's not a lot to see but um but to
+
+ align:start position:0%
+there's not a lot to see but um but to
+ 
+
+ align:start position:0%
+there's not a lot to see but um but to
+be able to picture I think for folks who
+
+ align:start position:0%
+be able to picture I think for folks who
+ 
+
+ align:start position:0%
+be able to picture I think for folks who
+were there to be able to you know learn
+
+ align:start position:0%
+were there to be able to you know learn
+ 
+
+ align:start position:0%
+were there to be able to you know learn
+about what's happening but also to
+
+ align:start position:0%
+about what's happening but also to
+ 
+
+ align:start position:0%
+about what's happening but also to
+picture what kind of neighborhoods um uh
+
+ align:start position:0%
+picture what kind of neighborhoods um uh
+ 
+
+ align:start position:0%
+picture what kind of neighborhoods um uh
+this could be really effective in and um
+
+ align:start position:0%
+this could be really effective in and um
+ 
+
+ align:start position:0%
+this could be really effective in and um
+and then we continued to work
+
+ align:start position:0%
+and then we continued to work
+ 
+
+ align:start position:0%
+and then we continued to work
+collaboratively and and it was exciting
+
+ align:start position:0%
+collaboratively and and it was exciting
+ 
+
+ align:start position:0%
+collaboratively and and it was exciting
+to bring folks together who often are
+
+ align:start position:0%
+to bring folks together who often are
+ 
+
+ align:start position:0%
+to bring folks together who often are
+not working um in the same direction on
+
+ align:start position:0%
+not working um in the same direction on
+ 
+
+ align:start position:0%
+not working um in the same direction on
+the same policies um working through
+
+ align:start position:0%
+the same policies um working through
+ 
+
+ align:start position:0%
+the same policies um working through
+building trust across those groups of
+
+ align:start position:0%
+building trust across those groups of
+ 
+
+ align:start position:0%
+building trust across those groups of
+people and making sure that everybody
+
+ align:start position:0%
+people and making sure that everybody
+ 
+
+ align:start position:0%
+people and making sure that everybody
+body felt like the bill that we finally
+
+ align:start position:0%
+body felt like the bill that we finally
+ 
+
+ align:start position:0%
+body felt like the bill that we finally
+produced really um met the needs of of
+
+ align:start position:0%
+produced really um met the needs of of
+ 
+
+ align:start position:0%
+produced really um met the needs of of
+the folks who were going to be required
+
+ align:start position:0%
+the folks who were going to be required
+ 
+
+ align:start position:0%
+the folks who were going to be required
+and and necessary for implementation.
+
+ align:start position:0%
+and and necessary for implementation.
+ 
+
+ align:start position:0%
+and and necessary for implementation.
+And so, uh we had the bill last year in
+
+ align:start position:0%
+And so, uh we had the bill last year in
+ 
+
+ align:start position:0%
+And so, uh we had the bill last year in
+the 2024 session. Um and I'm happy to
+
+ align:start position:0%
+the 2024 session. Um and I'm happy to
+ 
+
+ align:start position:0%
+the 2024 session. Um and I'm happy to
+say it passed in the in the first year
+
+ align:start position:0%
+say it passed in the in the first year
+ 
+
+ align:start position:0%
+say it passed in the in the first year
+we introduced it. Um and really a lot of
+
+ align:start position:0%
+we introduced it. Um and really a lot of
+ 
+
+ align:start position:0%
+we introduced it. Um and really a lot of
+that had to do with the fact that we
+
+ align:start position:0%
+that had to do with the fact that we
+ 
+
+ align:start position:0%
+that had to do with the fact that we
+essentially had no opposition because
+
+ align:start position:0%
+essentially had no opposition because
+ 
+
+ align:start position:0%
+essentially had no opposition because
+everybody was sitting at the table. And
+
+ align:start position:0%
+everybody was sitting at the table. And
+ 
+
+ align:start position:0%
+everybody was sitting at the table. And
+in fact, when we went for our hearing,
+
+ align:start position:0%
+in fact, when we went for our hearing,
+ 
+
+ align:start position:0%
+in fact, when we went for our hearing,
+you know, I had the the climate justice
+
+ align:start position:0%
+you know, I had the the climate justice
+ 
+
+ align:start position:0%
+you know, I had the the climate justice
+groups and the gas workers union and the
+
+ align:start position:0%
+groups and the gas workers union and the
+ 
+
+ align:start position:0%
+groups and the gas workers union and the
+utility and the office of people's
+
+ align:start position:0%
+utility and the office of people's
+ 
+
+ align:start position:0%
+utility and the office of people's
+council and like that's a set of folks
+
+ align:start position:0%
+council and like that's a set of folks
+ 
+
+ align:start position:0%
+council and like that's a set of folks
+that I don't know if they've ever been
+
+ align:start position:0%
+that I don't know if they've ever been
+ 
+
+ align:start position:0%
+that I don't know if they've ever been
+on the same panel before, but I was
+
+ align:start position:0%
+on the same panel before, but I was
+ 
+
+ align:start position:0%
+on the same panel before, but I was
+telling my colleagues, I was like, just
+
+ align:start position:0%
+telling my colleagues, I was like, just
+ 
+
+ align:start position:0%
+telling my colleagues, I was like, just
+go ahead and take a picture of this um
+
+ align:start position:0%
+go ahead and take a picture of this um
+ 
+
+ align:start position:0%
+go ahead and take a picture of this um
+and then move my bill favorable because
+
+ align:start position:0%
+and then move my bill favorable because
+ 
+
+ align:start position:0%
+and then move my bill favorable because
+um obviously there was still work to be
+
+ align:start position:0%
+um obviously there was still work to be
+ 
+
+ align:start position:0%
+um obviously there was still work to be
+done and education and and so on, but
+
+ align:start position:0%
+done and education and and so on, but
+ 
+
+ align:start position:0%
+done and education and and so on, but
+most of the work really was the year and
+
+ align:start position:0%
+most of the work really was the year and
+ 
+
+ align:start position:0%
+most of the work really was the year and
+a half of building coalitions and
+
+ align:start position:0%
+a half of building coalitions and
+ 
+
+ align:start position:0%
+a half of building coalitions and
+connecting people with each and making
+
+ align:start position:0%
+connecting people with each and making
+ 
+
+ align:start position:0%
+connecting people with each and making
+sure that the language really met the
+
+ align:start position:0%
+sure that the language really met the
+ 
+
+ align:start position:0%
+sure that the language really met the
+needs of everybody involved. So that
+
+ align:start position:0%
+needs of everybody involved. So that
+ 
+
+ align:start position:0%
+needs of everybody involved. So that
+bill passed and then soon after we
+
+ align:start position:0%
+bill passed and then soon after we
+ 
+
+ align:start position:0%
+bill passed and then soon after we
+started um you know working with the gas
+
+ align:start position:0%
+started um you know working with the gas
+ 
+
+ align:start position:0%
+started um you know working with the gas
+companies uh to to start to you know
+
+ align:start position:0%
+companies uh to to start to you know
+ 
+
+ align:start position:0%
+companies uh to to start to you know
+connect them to the grassroots groups
+
+ align:start position:0%
+connect them to the grassroots groups
+ 
+
+ align:start position:0%
+connect them to the grassroots groups
+and to start to organize and identify
+
+ align:start position:0%
+and to start to organize and identify
+ 
+
+ align:start position:0%
+and to start to organize and identify
+potential locations. Um and that's
+
+ align:start position:0%
+potential locations. Um and that's
+ 
+
+ align:start position:0%
+potential locations. Um and that's
+really where we are right now. Um we're
+
+ align:start position:0%
+really where we are right now. Um we're
+ 
+
+ align:start position:0%
+really where we are right now. Um we're
+going through that process with
+
+ align:start position:0%
+going through that process with
+ 
+
+ align:start position:0%
+going through that process with
+community groups and the the gas
+
+ align:start position:0%
+community groups and the the gas
+ 
+
+ align:start position:0%
+community groups and the the gas
+companies are working on um some
+
+ align:start position:0%
+companies are working on um some
+ 
+
+ align:start position:0%
+companies are working on um some
+engineering studies and we're excited to
+
+ align:start position:0%
+engineering studies and we're excited to
+ 
+
+ align:start position:0%
+engineering studies and we're excited to
+have um to have something here in the
+
+ align:start position:0%
+have um to have something here in the
+ 
+
+ align:start position:0%
+have um to have something here in the
+next few years. So um I'll stop there.
+
+ align:start position:0%
+next few years. So um I'll stop there.
+ 
+
+ align:start position:0%
+next few years. So um I'll stop there.
+I'm not I may or may not be able to be
+
+ align:start position:0%
+I'm not I may or may not be able to be
+ 
+
+ align:start position:0%
+I'm not I may or may not be able to be
+on there for questions. I'm not sure how
+
+ align:start position:0%
+on there for questions. I'm not sure how
+ 
+
+ align:start position:0%
+on there for questions. I'm not sure how
+that's going to work, but um if anyone's
+
+ align:start position:0%
+that's going to work, but um if anyone's
+ 
+
+ align:start position:0%
+that's going to work, but um if anyone's
+interested in getting in touch with me,
+
+ align:start position:0%
+interested in getting in touch with me,
+ 
+
+ align:start position:0%
+interested in getting in touch with me,
+we'll make sure that you all have my
+
+ align:start position:0%
+we'll make sure that you all have my
+ 
+
+ align:start position:0%
+we'll make sure that you all have my
+contact information. Um so I'm happy to
+
+ align:start position:0%
+contact information. Um so I'm happy to
+ 
+
+ align:start position:0%
+contact information. Um so I'm happy to
+follow up and be supportive um as I am
+
+ align:start position:0%
+follow up and be supportive um as I am
+ 
+
+ align:start position:0%
+follow up and be supportive um as I am
+able. And I do hope to to connect with
+
+ align:start position:0%
+able. And I do hope to to connect with
+ 
+
+ align:start position:0%
+able. And I do hope to to connect with
+folks and and hear more and learn more
+
+ align:start position:0%
+folks and and hear more and learn more
+ 
+
+ align:start position:0%
+folks and and hear more and learn more
+about what you all are doing all across
+
+ align:start position:0%
+about what you all are doing all across
+ 
+
+ align:start position:0%
+about what you all are doing all across
+this country.
\ No newline at end of file
diff --git a/hV5af_07ToE.txt b/hV5af_07ToE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d59e8e076a12fb7fb4a3f59910f33d5b01cab5b4
--- /dev/null
+++ b/hV5af_07ToE.txt
@@ -0,0 +1,3043 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+I'd like us to to work on an example of
+
+ align:start position:0%
+I'd like us to to work on an example of
+ 
+
+ align:start position:0%
+I'd like us to to work on an example of
+something you actually saw in one of the
+
+ align:start position:0%
+something you actually saw in one of the
+ 
+
+ align:start position:0%
+something you actually saw in one of the
+lecture videos and that's about
+
+ align:start position:0%
+lecture videos and that's about
+ 
+
+ align:start position:0%
+lecture videos and that's about
+reduction formulas so what I'd like us
+
+ align:start position:0%
+reduction formulas so what I'd like us
+ 
+
+ align:start position:0%
+reduction formulas so what I'd like us
+to do is to find a reduction formula for
+
+ align:start position:0%
+to do is to find a reduction formula for
+ 
+
+ align:start position:0%
+to do is to find a reduction formula for
+the integral of sin to the NX DX which
+
+ align:start position:0%
+the integral of sin to the NX DX which
+ 
+
+ align:start position:0%
+the integral of sin to the NX DX which
+I'm denoting by f subn of x that's
+
+ align:start position:0%
+I'm denoting by f subn of x that's
+ 
+
+ align:start position:0%
+I'm denoting by f subn of x that's
+actually f subn of x is it's the
+
+ align:start position:0%
+actually f subn of x is it's the
+ 
+
+ align:start position:0%
+actually f subn of x is it's the
+integral of sinx raised to the N DX so
+
+ align:start position:0%
+integral of sinx raised to the N DX so
+ 
+
+ align:start position:0%
+integral of sinx raised to the N DX so
+the object here just to remind you of
+
+ align:start position:0%
+the object here just to remind you of
+ 
+
+ align:start position:0%
+the object here just to remind you of
+what we'd like to do is to be able to
+
+ align:start position:0%
+what we'd like to do is to be able to
+ 
+
+ align:start position:0%
+what we'd like to do is to be able to
+write f subn of x in a form where maybe
+
+ align:start position:0%
+write f subn of x in a form where maybe
+ 
+
+ align:start position:0%
+write f subn of x in a form where maybe
+it involves some functions but any
+
+ align:start position:0%
+it involves some functions but any
+ 
+
+ align:start position:0%
+it involves some functions but any
+integral that it involves is an integral
+
+ align:start position:0%
+integral that it involves is an integral
+ 
+
+ align:start position:0%
+integral that it involves is an integral
+of s to a lower power than n so an
+
+ align:start position:0%
+of s to a lower power than n so an
+ 
+
+ align:start position:0%
+of s to a lower power than n so an
+integral of sin x to a lower power than
+
+ align:start position:0%
+integral of sin x to a lower power than
+ 
+
+ align:start position:0%
+integral of sin x to a lower power than
+n so that's the object the object is to
+
+ align:start position:0%
+n so that's the object the object is to
+ 
+
+ align:start position:0%
+n so that's the object the object is to
+write this down in such a way that this
+
+ align:start position:0%
+write this down in such a way that this
+ 
+
+ align:start position:0%
+write this down in such a way that this
+integral is equal to some some functions
+
+ align:start position:0%
+integral is equal to some some functions
+ 
+
+ align:start position:0%
+integral is equal to some some functions
+maybe uh product of some functions added
+
+ align:start position:0%
+maybe uh product of some functions added
+ 
+
+ align:start position:0%
+maybe uh product of some functions added
+to uh another function that's like f but
+
+ align:start position:0%
+to uh another function that's like f but
+ 
+
+ align:start position:0%
+to uh another function that's like f but
+with a lower
+
+ align:start position:0%
+with a lower
+ 
+
+ align:start position:0%
+with a lower
+subscript so I'm going to give you a
+
+ align:start position:0%
+subscript so I'm going to give you a
+ 
+
+ align:start position:0%
+subscript so I'm going to give you a
+little time to work on it why don't you
+
+ align:start position:0%
+little time to work on it why don't you
+ 
+
+ align:start position:0%
+little time to work on it why don't you
+pause the video take some time to work
+
+ align:start position:0%
+pause the video take some time to work
+ 
+
+ align:start position:0%
+pause the video take some time to work
+on it and when I come back I'll show you
+
+ align:start position:0%
+on it and when I come back I'll show you
+ 
+
+ align:start position:0%
+on it and when I come back I'll show you
+how I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay welcome back well hopefully you
+
+ align:start position:0%
+it okay welcome back well hopefully you
+ 
+
+ align:start position:0%
+it okay welcome back well hopefully you
+were able to make some Headway on this
+
+ align:start position:0%
+were able to make some Headway on this
+ 
+
+ align:start position:0%
+were able to make some Headway on this
+problem so let's take a look again at
+
+ align:start position:0%
+problem so let's take a look again at
+ 
+
+ align:start position:0%
+problem so let's take a look again at
+what we want to do what the goal is and
+
+ align:start position:0%
+what we want to do what the goal is and
+ 
+
+ align:start position:0%
+what we want to do what the goal is and
+then we'll we'll figure out a good
+
+ align:start position:0%
+then we'll we'll figure out a good
+ 
+
+ align:start position:0%
+then we'll we'll figure out a good
+strategy to do that so the goal is to be
+
+ align:start position:0%
+strategy to do that so the goal is to be
+ 
+
+ align:start position:0%
+strategy to do that so the goal is to be
+able to write f subn of x as something
+
+ align:start position:0%
+able to write f subn of x as something
+ 
+
+ align:start position:0%
+able to write f subn of x as something
+that involves a lower a lower numbered
+
+ align:start position:0%
+that involves a lower a lower numbered
+ 
+
+ align:start position:0%
+that involves a lower a lower numbered
+subscript than n right so we'd like to
+
+ align:start position:0%
+subscript than n right so we'd like to
+ 
+
+ align:start position:0%
+subscript than n right so we'd like to
+be able to take this integral that's a
+
+ align:start position:0%
+be able to take this integral that's a
+ 
+
+ align:start position:0%
+be able to take this integral that's a
+power of sinx and reduce the number of
+
+ align:start position:0%
+power of sinx and reduce the number of
+ 
+
+ align:start position:0%
+power of sinx and reduce the number of
+powers you know it'd be great if we
+
+ align:start position:0%
+powers you know it'd be great if we
+ 
+
+ align:start position:0%
+powers you know it'd be great if we
+could just write down a final formula
+
+ align:start position:0%
+could just write down a final formula
+ 
+
+ align:start position:0%
+could just write down a final formula
+but if we're able to to reduce the power
+
+ align:start position:0%
+but if we're able to to reduce the power
+ 
+
+ align:start position:0%
+but if we're able to to reduce the power
+of sinx then we're able to head in a
+
+ align:start position:0%
+of sinx then we're able to head in a
+ 
+
+ align:start position:0%
+of sinx then we're able to head in a
+Direction Where We could start to write
+
+ align:start position:0%
+Direction Where We could start to write
+ 
+
+ align:start position:0%
+Direction Where We could start to write
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+um start to write down this down as as
+
+ align:start position:0%
+um start to write down this down as as
+ 
+
+ align:start position:0%
+um start to write down this down as as
+functions that don't involve integrals
+
+ align:start position:0%
+functions that don't involve integrals
+ 
+
+ align:start position:0%
+functions that don't involve integrals
+so the the first step in these kinds of
+
+ align:start position:0%
+so the the first step in these kinds of
+ 
+
+ align:start position:0%
+so the the first step in these kinds of
+things is finding a reduction formula so
+
+ align:start position:0%
+things is finding a reduction formula so
+ 
+
+ align:start position:0%
+things is finding a reduction formula so
+a couple things I want to remind us um
+
+ align:start position:0%
+a couple things I want to remind us um
+ 
+
+ align:start position:0%
+a couple things I want to remind us um
+we're going to make the common
+
+ align:start position:0%
+we're going to make the common
+ 
+
+ align:start position:0%
+we're going to make the common
+substitution that we that we make uh for
+
+ align:start position:0%
+substitution that we that we make uh for
+ 
+
+ align:start position:0%
+substitution that we that we make uh for
+for powers of sign or powers of cosine
+
+ align:start position:0%
+for powers of sign or powers of cosine
+ 
+
+ align:start position:0%
+for powers of sign or powers of cosine
+that we see a lot um well I guess
+
+ align:start position:0%
+that we see a lot um well I guess
+ 
+
+ align:start position:0%
+that we see a lot um well I guess
+actually there's two when you just see a
+
+ align:start position:0%
+actually there's two when you just see a
+ 
+
+ align:start position:0%
+actually there's two when you just see a
+sign squared sometimes you do this this
+
+ align:start position:0%
+sign squared sometimes you do this this
+ 
+
+ align:start position:0%
+sign squared sometimes you do this this
+half angle formula or double angle
+
+ align:start position:0%
+half angle formula or double angle
+ 
+
+ align:start position:0%
+half angle formula or double angle
+formula that that Joel has mentioned in
+
+ align:start position:0%
+formula that that Joel has mentioned in
+ 
+
+ align:start position:0%
+formula that that Joel has mentioned in
+some videos but in this one we're more
+
+ align:start position:0%
+some videos but in this one we're more
+ 
+
+ align:start position:0%
+some videos but in this one we're more
+interested in uh manipulating the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identity sin^2 X plus cosine squ x equal
+
+ align:start position:0%
+identity sin^2 X plus cosine squ x equal
+ 
+
+ align:start position:0%
+identity sin^2 X plus cosine squ x equal
+1 in particular we're going to replace
+
+ align:start position:0%
+1 in particular we're going to replace
+ 
+
+ align:start position:0%
+1 in particular we're going to replace
+one of the sin squ X's or we're going to
+
+ align:start position:0%
+one of the sin squ X's or we're going to
+ 
+
+ align:start position:0%
+one of the sin squ X's or we're going to
+replace two of the signs by 1 - cosine 2
+
+ align:start position:0%
+replace two of the signs by 1 - cosine 2
+ 
+
+ align:start position:0%
+replace two of the signs by 1 - cosine 2
+x so that'll be our first step so we're
+
+ align:start position:0%
+x so that'll be our first step so we're
+ 
+
+ align:start position:0%
+x so that'll be our first step so we're
+going to do that substitution we'll
+
+ align:start position:0%
+going to do that substitution we'll
+ 
+
+ align:start position:0%
+going to do that substitution we'll
+break it into some pieces we'll see
+
+ align:start position:0%
+break it into some pieces we'll see
+ 
+
+ align:start position:0%
+break it into some pieces we'll see
+where we get okay so let me come over
+
+ align:start position:0%
+where we get okay so let me come over
+ 
+
+ align:start position:0%
+where we get okay so let me come over
+over here and I will start the problem
+
+ align:start position:0%
+over here and I will start the problem
+ 
+
+ align:start position:0%
+over here and I will start the problem
+so I'm starting with f subn of x and I'm
+
+ align:start position:0%
+so I'm starting with f subn of x and I'm
+ 
+
+ align:start position:0%
+so I'm starting with f subn of x and I'm
+going to rewrite it as the integral of
+
+ align:start position:0%
+going to rewrite it as the integral of
+ 
+
+ align:start position:0%
+going to rewrite it as the integral of
+sin to the N - 2
+
+ align:start position:0%
+sin to the N - 2
+ 
+
+ align:start position:0%
+sin to the N - 2
+xan 1 - cosine 2
+
+ align:start position:0%
+xan 1 - cosine 2
+ 
+
+ align:start position:0%
+xan 1 - cosine 2
+x DX so let me take a step back so what
+
+ align:start position:0%
+x DX so let me take a step back so what
+ 
+
+ align:start position:0%
+x DX so let me take a step back so what
+did we do here we took two powers of
+
+ align:start position:0%
+did we do here we took two powers of
+ 
+
+ align:start position:0%
+did we do here we took two powers of
+sign and we replace them by what I said
+
+ align:start position:0%
+sign and we replace them by what I said
+ 
+
+ align:start position:0%
+sign and we replace them by what I said
+earlier we replace them by 1us cosine 2
+
+ align:start position:0%
+earlier we replace them by 1us cosine 2
+ 
+
+ align:start position:0%
+earlier we replace them by 1us cosine 2
+x right so this is a sin^2 x here I have
+
+ align:start position:0%
+x right so this is a sin^2 x here I have
+ 
+
+ align:start position:0%
+x right so this is a sin^2 x here I have
+sin x to the N minus 2 when I multiply
+
+ align:start position:0%
+sin x to the N minus 2 when I multiply
+ 
+
+ align:start position:0%
+sin x to the N minus 2 when I multiply
+those together I get sin x the N so
+
+ align:start position:0%
+those together I get sin x the N so
+ 
+
+ align:start position:0%
+those together I get sin x the N so
+everything's still working out so far
+
+ align:start position:0%
+everything's still working out so far
+ 
+
+ align:start position:0%
+everything's still working out so far
+why is this good well notice the terms
+
+ align:start position:0%
+why is this good well notice the terms
+ 
+
+ align:start position:0%
+why is this good well notice the terms
+we have sign to the nus 2 x
+
+ align:start position:0%
+we have sign to the nus 2 x
+ 
+
+ align:start position:0%
+we have sign to the nus 2 x
+DX minus the
+
+ align:start position:0%
+DX minus the
+ 
+
+ align:start position:0%
+DX minus the
+integral of sin the nus
+
+ align:start position:0%
+integral of sin the nus
+ 
+
+ align:start position:0%
+integral of sin the nus
+2x cine 2 x DX
+
+ align:start position:0%
+2x cine 2 x DX
+ 
+
+ align:start position:0%
+2x cine 2 x DX
+okay this we like why do we like this
+
+ align:start position:0%
+okay this we like why do we like this
+ 
+
+ align:start position:0%
+okay this we like why do we like this
+because it's
+
+ align:start position:0%
+because it's
+ 
+
+ align:start position:0%
+because it's
+actually just like the f subn of x
+
+ align:start position:0%
+actually just like the f subn of x
+ 
+
+ align:start position:0%
+actually just like the f subn of x
+except it has a lower power so this
+
+ align:start position:0%
+except it has a lower power so this
+ 
+
+ align:start position:0%
+except it has a lower power so this
+piece is actually f subn
+
+ align:start position:0%
+piece is actually f subn
+ 
+
+ align:start position:0%
+piece is actually f subn
+min-2 of x so that's something we like
+
+ align:start position:0%
+min-2 of x so that's something we like
+ 
+
+ align:start position:0%
+min-2 of x so that's something we like
+because it's already reduced the power
+
+ align:start position:0%
+because it's already reduced the power
+ 
+
+ align:start position:0%
+because it's already reduced the power
+of sin x by two so that's good that's
+
+ align:start position:0%
+of sin x by two so that's good that's
+ 
+
+ align:start position:0%
+of sin x by two so that's good that's
+part of the reduction idea this one
+
+ align:start position:0%
+part of the reduction idea this one
+ 
+
+ align:start position:0%
+part of the reduction idea this one
+obviously we can't write it in terms of
+
+ align:start position:0%
+obviously we can't write it in terms of
+ 
+
+ align:start position:0%
+obviously we can't write it in terms of
+capital F with some
+
+ align:start position:0%
+capital F with some
+ 
+
+ align:start position:0%
+capital F with some
+subscript and it maybe it doesn't look
+
+ align:start position:0%
+subscript and it maybe it doesn't look
+ 
+
+ align:start position:0%
+subscript and it maybe it doesn't look
+so easy to to integrate right away but
+
+ align:start position:0%
+so easy to to integrate right away but
+ 
+
+ align:start position:0%
+so easy to to integrate right away but
+let's think about it for a second how we
+
+ align:start position:0%
+let's think about it for a second how we
+ 
+
+ align:start position:0%
+let's think about it for a second how we
+could split this thing up and the goal
+
+ align:start position:0%
+could split this thing up and the goal
+ 
+
+ align:start position:0%
+could split this thing up and the goal
+is to use an integration by parts so
+
+ align:start position:0%
+is to use an integration by parts so
+ 
+
+ align:start position:0%
+is to use an integration by parts so
+we're going to examine this integral in
+
+ align:start position:0%
+we're going to examine this integral in
+ 
+
+ align:start position:0%
+we're going to examine this integral in
+particular so let me just write that one
+
+ align:start position:0%
+particular so let me just write that one
+ 
+
+ align:start position:0%
+particular so let me just write that one
+down again here so we need to analyze
+
+ align:start position:0%
+down again here so we need to analyze
+ 
+
+ align:start position:0%
+down again here so we need to analyze
+I'm going to drop the minus sign for the
+
+ align:start position:0%
+I'm going to drop the minus sign for the
+ 
+
+ align:start position:0%
+I'm going to drop the minus sign for the
+moment andus 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so our goal again is to try and write
+
+ align:start position:0%
+so our goal again is to try and write
+ 
+
+ align:start position:0%
+so our goal again is to try and write
+this somehow either manipulate it so it
+
+ align:start position:0%
+this somehow either manipulate it so it
+ 
+
+ align:start position:0%
+this somehow either manipulate it so it
+looks like an a capital f function or
+
+ align:start position:0%
+looks like an a capital f function or
+ 
+
+ align:start position:0%
+looks like an a capital f function or
+manipulate it so that the the integral
+
+ align:start position:0%
+manipulate it so that the the integral
+ 
+
+ align:start position:0%
+manipulate it so that the the integral
+sign is gone okay that's our main goal
+
+ align:start position:0%
+sign is gone okay that's our main goal
+ 
+
+ align:start position:0%
+sign is gone okay that's our main goal
+here so let's look at what what we can
+
+ align:start position:0%
+here so let's look at what what we can
+ 
+
+ align:start position:0%
+here so let's look at what what we can
+do with this well I can split this up
+
+ align:start position:0%
+do with this well I can split this up
+ 
+
+ align:start position:0%
+do with this well I can split this up
+what I'm going to do it's kind of tricky
+
+ align:start position:0%
+what I'm going to do it's kind of tricky
+ 
+
+ align:start position:0%
+what I'm going to do it's kind of tricky
+but what I'm going to do is I'm going to
+
+ align:start position:0%
+but what I'm going to do is I'm going to
+ 
+
+ align:start position:0%
+but what I'm going to do is I'm going to
+take all of the S x's and I'm going to
+
+ align:start position:0%
+take all of the S x's and I'm going to
+ 
+
+ align:start position:0%
+take all of the S x's and I'm going to
+take one of the cosine
+
+ align:start position:0%
+take one of the cosine
+ 
+
+ align:start position:0%
+take one of the cosine
+x's and I'm going to make that one thing
+
+ align:start position:0%
+x's and I'm going to make that one thing
+ 
+
+ align:start position:0%
+x's and I'm going to make that one thing
+and I'm going to make the other cosine X
+
+ align:start position:0%
+and I'm going to make the other cosine X
+ 
+
+ align:start position:0%
+and I'm going to make the other cosine X
+another thing and I'm going to write
+
+ align:start position:0%
+another thing and I'm going to write
+ 
+
+ align:start position:0%
+another thing and I'm going to write
+them down first and then we'll figure
+
+ align:start position:0%
+them down first and then we'll figure
+ 
+
+ align:start position:0%
+them down first and then we'll figure
+out which is a good U and which is a
+
+ align:start position:0%
+out which is a good U and which is a
+ 
+
+ align:start position:0%
+out which is a good U and which is a
+good V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime so that's going to be one thing
+
+ align:start position:0%
+Prime so that's going to be one thing
+ 
+
+ align:start position:0%
+Prime so that's going to be one thing
+and then the other cosine
+
+ align:start position:0%
+and then the other cosine
+ 
+
+ align:start position:0%
+and then the other cosine
+X it's going to be oh does that look
+
+ align:start position:0%
+X it's going to be oh does that look
+ 
+
+ align:start position:0%
+X it's going to be oh does that look
+like an equal sign equals it's going to
+
+ align:start position:0%
+like an equal sign equals it's going to
+ 
+
+ align:start position:0%
+like an equal sign equals it's going to
+be the other thing so again sin the nus
+
+ align:start position:0%
+be the other thing so again sin the nus
+ 
+
+ align:start position:0%
+be the other thing so again sin the nus
+2x * cosine x * cosine X gives me what's
+
+ align:start position:0%
+2x * cosine x * cosine X gives me what's
+ 
+
+ align:start position:0%
+2x * cosine x * cosine X gives me what's
+up here inside the integral and now what
+
+ align:start position:0%
+up here inside the integral and now what
+ 
+
+ align:start position:0%
+up here inside the integral and now what
+I really want to see I'm going to use an
+
+ align:start position:0%
+I really want to see I'm going to use an
+ 
+
+ align:start position:0%
+I really want to see I'm going to use an
+integration by parts well this is easy
+
+ align:start position:0%
+integration by parts well this is easy
+ 
+
+ align:start position:0%
+integration by parts well this is easy
+to integrate or take a derivative of but
+
+ align:start position:0%
+to integrate or take a derivative of but
+ 
+
+ align:start position:0%
+to integrate or take a derivative of but
+the point is that now I can integrate
+
+ align:start position:0%
+the point is that now I can integrate
+ 
+
+ align:start position:0%
+the point is that now I can integrate
+this and why can I integrate this well I
+
+ align:start position:0%
+this and why can I integrate this well I
+ 
+
+ align:start position:0%
+this and why can I integrate this well I
+can do a substitution on this so this is
+
+ align:start position:0%
+can do a substitution on this so this is
+ 
+
+ align:start position:0%
+can do a substitution on this so this is
+kind of complicated because there's
+
+ align:start position:0%
+kind of complicated because there's
+ 
+
+ align:start position:0%
+kind of complicated because there's
+first you have to notice an integration
+
+ align:start position:0%
+first you have to notice an integration
+ 
+
+ align:start position:0%
+first you have to notice an integration
+by parts is a good way to go with this
+
+ align:start position:0%
+by parts is a good way to go with this
+ 
+
+ align:start position:0%
+by parts is a good way to go with this
+and then you have to see oh my goodness
+
+ align:start position:0%
+and then you have to see oh my goodness
+ 
+
+ align:start position:0%
+and then you have to see oh my goodness
+this one of the steps of integration by
+
+ align:start position:0%
+this one of the steps of integration by
+ 
+
+ align:start position:0%
+this one of the steps of integration by
+parts requires substitution so it's a
+
+ align:start position:0%
+parts requires substitution so it's a
+ 
+
+ align:start position:0%
+parts requires substitution so it's a
+little tricky but I'm going to make this
+
+ align:start position:0%
+little tricky but I'm going to make this
+ 
+
+ align:start position:0%
+little tricky but I'm going to make this
+then my V
+
+ align:start position:0%
+then my V
+ 
+
+ align:start position:0%
+then my V
+Prime and I'm going to make this my
+
+ align:start position:0%
+Prime and I'm going to make this my
+ 
+
+ align:start position:0%
+Prime and I'm going to make this my
+U now I'm going to come over to the
+
+ align:start position:0%
+U now I'm going to come over to the
+ 
+
+ align:start position:0%
+U now I'm going to come over to the
+other board to figure out just to make
+
+ align:start position:0%
+other board to figure out just to make
+ 
+
+ align:start position:0%
+other board to figure out just to make
+sure I do the V Prime right okay and
+
+ align:start position:0%
+sure I do the V Prime right okay and
+ 
+
+ align:start position:0%
+sure I do the V Prime right okay and
+then I'm going to finish off this
+
+ align:start position:0%
+then I'm going to finish off this
+ 
+
+ align:start position:0%
+then I'm going to finish off this
+problem so we'll come back here in a
+
+ align:start position:0%
+problem so we'll come back here in a
+ 
+
+ align:start position:0%
+problem so we'll come back here in a
+second so right now this is a question
+
+ align:start position:0%
+second so right now this is a question
+ 
+
+ align:start position:0%
+second so right now this is a question
+mark we're going to make sure we do the
+
+ align:start position:0%
+mark we're going to make sure we do the
+ 
+
+ align:start position:0%
+mark we're going to make sure we do the
+V Prime part right and then we're going
+
+ align:start position:0%
+V Prime part right and then we're going
+ 
+
+ align:start position:0%
+V Prime part right and then we're going
+to write down this should be UV minus
+
+ align:start position:0%
+to write down this should be UV minus
+ 
+
+ align:start position:0%
+to write down this should be UV minus
+the integral of VD okay so let me give
+
+ align:start position:0%
+the integral of VD okay so let me give
+ 
+
+ align:start position:0%
+the integral of VD okay so let me give
+myself some space so I'm trying to
+
+ align:start position:0%
+myself some space so I'm trying to
+ 
+
+ align:start position:0%
+myself some space so I'm trying to
+integrate
+
+ align:start position:0%
+integrate
+ 
+
+ align:start position:0%
+integrate
+now sign the N -
+
+ align:start position:0%
+now sign the N -
+ 
+
+ align:start position:0%
+now sign the N -
+2x cosine
+
+ align:start position:0%
+2x cosine
+ 
+
+ align:start position:0%
+2x cosine
+X DX all right that's my integral of V
+
+ align:start position:0%
+X DX all right that's my integral of V
+ 
+
+ align:start position:0%
+X DX all right that's my integral of V
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+DX okay so this will give me V so let's
+
+ align:start position:0%
+DX okay so this will give me V so let's
+ 
+
+ align:start position:0%
+DX okay so this will give me V so let's
+see what we do we're going to now make I
+
+ align:start position:0%
+see what we do we're going to now make I
+ 
+
+ align:start position:0%
+see what we do we're going to now make I
+don't want to use a u for my
+
+ align:start position:0%
+don't want to use a u for my
+ 
+
+ align:start position:0%
+don't want to use a u for my
+substitution because I already have in
+
+ align:start position:0%
+substitution because I already have in
+ 
+
+ align:start position:0%
+substitution because I already have in
+my mind a u so I'm going to let
+
+ align:start position:0%
+my mind a u so I'm going to let
+ 
+
+ align:start position:0%
+my mind a u so I'm going to let
+W wal
+
+ align:start position:0%
+W wal
+ 
+
+ align:start position:0%
+W wal
+sinx and then DW is equal to cosin X DX
+
+ align:start position:0%
+sinx and then DW is equal to cosin X DX
+ 
+
+ align:start position:0%
+sinx and then DW is equal to cosin X DX
+right what's the what's the point here
+
+ align:start position:0%
+right what's the what's the point here
+ 
+
+ align:start position:0%
+right what's the what's the point here
+why is this do we see this as easy to
+
+ align:start position:0%
+why is this do we see this as easy to
+ 
+
+ align:start position:0%
+why is this do we see this as easy to
+integrate because this is powers of sign
+
+ align:start position:0%
+integrate because this is powers of sign
+ 
+
+ align:start position:0%
+integrate because this is powers of sign
+and the derivative of sign is cosine so
+
+ align:start position:0%
+and the derivative of sign is cosine so
+ 
+
+ align:start position:0%
+and the derivative of sign is cosine so
+that's why This lends itself to a
+
+ align:start position:0%
+that's why This lends itself to a
+ 
+
+ align:start position:0%
+that's why This lends itself to a
+substitution so easily so that should be
+
+ align:start position:0%
+substitution so easily so that should be
+ 
+
+ align:start position:0%
+substitution so easily so that should be
+fairly familiar by now but just to make
+
+ align:start position:0%
+fairly familiar by now but just to make
+ 
+
+ align:start position:0%
+fairly familiar by now but just to make
+sure we're clear so then this is now the
+
+ align:start position:0%
+sure we're clear so then this is now the
+ 
+
+ align:start position:0%
+sure we're clear so then this is now the
+integral of w to the N minus 2
+
+ align:start position:0%
+integral of w to the N minus 2
+ 
+
+ align:start position:0%
+integral of w to the N minus 2
+DW right I have sin x to the nus 2 so
+
+ align:start position:0%
+DW right I have sin x to the nus 2 so
+ 
+
+ align:start position:0%
+DW right I have sin x to the nus 2 so
+that's replaced by W to the N minus 2
+
+ align:start position:0%
+that's replaced by W to the N minus 2
+ 
+
+ align:start position:0%
+that's replaced by W to the N minus 2
+and then DW replaces cosin X DX X and
+
+ align:start position:0%
+and then DW replaces cosin X DX X and
+ 
+
+ align:start position:0%
+and then DW replaces cosin X DX X and
+that is pretty easy to integrate I think
+
+ align:start position:0%
+that is pretty easy to integrate I think
+ 
+
+ align:start position:0%
+that is pretty easy to integrate I think
+that's W
+
+ align:start position:0%
+that's W
+ 
+
+ align:start position:0%
+that's W
+nus1 over nus1 I'm not going to worry
+
+ align:start position:0%
+nus1 over nus1 I'm not going to worry
+ 
+
+ align:start position:0%
+nus1 over nus1 I'm not going to worry
+about my C's right now that that'll come
+
+ align:start position:0%
+about my C's right now that that'll come
+ 
+
+ align:start position:0%
+about my C's right now that that'll come
+up right at the end we'll put in a plus
+
+ align:start position:0%
+up right at the end we'll put in a plus
+ 
+
+ align:start position:0%
+up right at the end we'll put in a plus
+c if we needed to
+
+ align:start position:0%
+c if we needed to
+ 
+
+ align:start position:0%
+c if we needed to
+um but so don't worry about your plus C
+
+ align:start position:0%
+um but so don't worry about your plus C
+ 
+
+ align:start position:0%
+um but so don't worry about your plus C
+I don't want to carry that around okay
+
+ align:start position:0%
+I don't want to carry that around okay
+ 
+
+ align:start position:0%
+I don't want to carry that around okay
+so then when I when I look at this what
+
+ align:start position:0%
+so then when I when I look at this what
+ 
+
+ align:start position:0%
+so then when I when I look at this what
+does this tell me this tells me that if
+
+ align:start position:0%
+does this tell me this tells me that if
+ 
+
+ align:start position:0%
+does this tell me this tells me that if
+this was the integral of V Prime this
+
+ align:start position:0%
+this was the integral of V Prime this
+ 
+
+ align:start position:0%
+this was the integral of V Prime this
+tells me that V is equal to sinx to the
+
+ align:start position:0%
+tells me that V is equal to sinx to the
+ 
+
+ align:start position:0%
+tells me that V is equal to sinx to the
+nus1 sin the n-1 X over
+
+ align:start position:0%
+nus1 sin the n-1 X over
+ 
+
+ align:start position:0%
+nus1 sin the n-1 X over
+nus1 okay this whole bit was to help us
+
+ align:start position:0%
+nus1 okay this whole bit was to help us
+ 
+
+ align:start position:0%
+nus1 okay this whole bit was to help us
+in the middle of the problem so this was
+
+ align:start position:0%
+in the middle of the problem so this was
+ 
+
+ align:start position:0%
+in the middle of the problem so this was
+the V we needed all right so let's come
+
+ align:start position:0%
+the V we needed all right so let's come
+ 
+
+ align:start position:0%
+the V we needed all right so let's come
+back fill in a little piece we needed a
+
+ align:start position:0%
+back fill in a little piece we needed a
+ 
+
+ align:start position:0%
+back fill in a little piece we needed a
+little Gap we had and then we'll finish
+
+ align:start position:0%
+little Gap we had and then we'll finish
+ 
+
+ align:start position:0%
+little Gap we had and then we'll finish
+the problem on the far right so let's
+
+ align:start position:0%
+the problem on the far right so let's
+ 
+
+ align:start position:0%
+the problem on the far right so let's
+come back where was I okay so I was
+
+ align:start position:0%
+come back where was I okay so I was
+ 
+
+ align:start position:0%
+come back where was I okay so I was
+integrating this quantity sin the nus 2x
+
+ align:start position:0%
+integrating this quantity sin the nus 2x
+ 
+
+ align:start position:0%
+integrating this quantity sin the nus 2x
+cosine 2 x DX and I was trying to use
+
+ align:start position:0%
+cosine 2 x DX and I was trying to use
+ 
+
+ align:start position:0%
+cosine 2 x DX and I was trying to use
+integration by parts so I had u and v
+
+ align:start position:0%
+integration by parts so I had u and v
+ 
+
+ align:start position:0%
+integration by parts so I had u and v
+Prime and I've now calculated V and I
+
+ align:start position:0%
+Prime and I've now calculated V and I
+ 
+
+ align:start position:0%
+Prime and I've now calculated V and I
+know what du is so I'm going to write
+
+ align:start position:0%
+know what du is so I'm going to write
+ 
+
+ align:start position:0%
+know what du is so I'm going to write
+down what this equals this is going to
+
+ align:start position:0%
+down what this equals this is going to
+ 
+
+ align:start position:0%
+down what this equals this is going to
+be U which is cosine X and I'll just
+
+ align:start position:0%
+be U which is cosine X and I'll just
+ 
+
+ align:start position:0%
+be U which is cosine X and I'll just
+write down V here so we'll see what it
+
+ align:start position:0%
+write down V here so we'll see what it
+ 
+
+ align:start position:0%
+write down V here so we'll see what it
+is again times sin to the
+
+ align:start position:0%
+is again times sin to the
+ 
+
+ align:start position:0%
+is again times sin to the
+nus1 uh X over
+
+ align:start position:0%
+nus1 uh X over
+ 
+
+ align:start position:0%
+nus1 uh X over
+nus1 and then I have to subtract VD so
+
+ align:start position:0%
+nus1 and then I have to subtract VD so
+ 
+
+ align:start position:0%
+nus1 and then I have to subtract VD so
+this is V and what's du du is or I
+
+ align:start position:0%
+this is V and what's du du is or I
+ 
+
+ align:start position:0%
+this is V and what's du du is or I
+should say U Prime is how you saw it in
+
+ align:start position:0%
+should say U Prime is how you saw it in
+ 
+
+ align:start position:0%
+should say U Prime is how you saw it in
+class U Prime is sinx so what am I going
+
+ align:start position:0%
+class U Prime is sinx so what am I going
+ 
+
+ align:start position:0%
+class U Prime is sinx so what am I going
+to get I'm going to get sinx times the V
+
+ align:start position:0%
+to get I'm going to get sinx times the V
+ 
+
+ align:start position:0%
+to get I'm going to get sinx times the V
+that I had so when I when I subtract I'm
+
+ align:start position:0%
+that I had so when I when I subtract I'm
+ 
+
+ align:start position:0%
+that I had so when I when I subtract I'm
+going to end up with a plus sign and I'm
+
+ align:start position:0%
+going to end up with a plus sign and I'm
+ 
+
+ align:start position:0%
+going to end up with a plus sign and I'm
+going to have plus I'm going to pull out
+
+ align:start position:0%
+going to have plus I'm going to pull out
+ 
+
+ align:start position:0%
+going to have plus I'm going to pull out
+the constant 1/ n minus one integral now
+
+ align:start position:0%
+the constant 1/ n minus one integral now
+ 
+
+ align:start position:0%
+the constant 1/ n minus one integral now
+let's look at the magic that happens
+
+ align:start position:0%
+let's look at the magic that happens
+ 
+
+ align:start position:0%
+let's look at the magic that happens
+here okay let's make sure you agree with
+
+ align:start position:0%
+here okay let's make sure you agree with
+ 
+
+ align:start position:0%
+here okay let's make sure you agree with
+this power it's the nth power of sinx so
+
+ align:start position:0%
+this power it's the nth power of sinx so
+ 
+
+ align:start position:0%
+this power it's the nth power of sinx so
+let's double check
+
+ align:start position:0%
+let's double check
+ 
+
+ align:start position:0%
+let's double check
+I said U was cosine X so U Prime is Nega
+
+ align:start position:0%
+I said U was cosine X so U Prime is Nega
+ 
+
+ align:start position:0%
+I said U was cosine X so U Prime is Nega
+sinx so I have to take U Prime v u Prime
+
+ align:start position:0%
+sinx so I have to take U Prime v u Prime
+ 
+
+ align:start position:0%
+sinx so I have to take U Prime v u Prime
+is negative
+
+ align:start position:0%
+is negative
+ 
+
+ align:start position:0%
+is negative
+sinx if we come over
+
+ align:start position:0%
+sinx if we come over
+ 
+
+ align:start position:0%
+sinx if we come over
+here we see V is sinx to the N minus one
+
+ align:start position:0%
+here we see V is sinx to the N minus one
+ 
+
+ align:start position:0%
+here we see V is sinx to the N minus one
+so U Prime V is
+
+ align:start position:0%
+so U Prime V is
+ 
+
+ align:start position:0%
+so U Prime V is
+indeed uh is indeed negative uh well I
+
+ align:start position:0%
+indeed uh is indeed negative uh well I
+ 
+
+ align:start position:0%
+indeed uh is indeed negative uh well I
+should say V is sinx to the nus1 Over N
+
+ align:start position:0%
+should say V is sinx to the nus1 Over N
+ 
+
+ align:start position:0%
+should say V is sinx to the nus1 Over N
+minus1 so U Prime V in fact has the
+
+ align:start position:0%
+minus1 so U Prime V in fact has the
+ 
+
+ align:start position:0%
+minus1 so U Prime V in fact has the
+power n on sign so that's maybe a little
+
+ align:start position:0%
+power n on sign so that's maybe a little
+ 
+
+ align:start position:0%
+power n on sign so that's maybe a little
+bit complicated in nerve-wracking but
+
+ align:start position:0%
+bit complicated in nerve-wracking but
+ 
+
+ align:start position:0%
+bit complicated in nerve-wracking but
+that's that's okay we're actually headed
+
+ align:start position:0%
+that's that's okay we're actually headed
+ 
+
+ align:start position:0%
+that's that's okay we're actually headed
+in the right direction so I'm going to
+
+ align:start position:0%
+in the right direction so I'm going to
+ 
+
+ align:start position:0%
+in the right direction so I'm going to
+rewrite the stuff we know and we'll see
+
+ align:start position:0%
+rewrite the stuff we know and we'll see
+ 
+
+ align:start position:0%
+rewrite the stuff we know and we'll see
+how we're headed in the right direction
+
+ align:start position:0%
+how we're headed in the right direction
+ 
+
+ align:start position:0%
+how we're headed in the right direction
+okay so again we were trying to find f
+
+ align:start position:0%
+okay so again we were trying to find f
+ 
+
+ align:start position:0%
+okay so again we were trying to find f
+subn of x and I'm going to write out the
+
+ align:start position:0%
+subn of x and I'm going to write out the
+ 
+
+ align:start position:0%
+subn of x and I'm going to write out the
+pieces we already knew so we had an F
+
+ align:start position:0%
+pieces we already knew so we had an F
+ 
+
+ align:start position:0%
+pieces we already knew so we had an F
+subn minus 2 of X that was that was the
+
+ align:start position:0%
+subn minus 2 of X that was that was the
+ 
+
+ align:start position:0%
+subn minus 2 of X that was that was the
+first term we had and then we analyzed
+
+ align:start position:0%
+first term we had and then we analyzed
+ 
+
+ align:start position:0%
+first term we had and then we analyzed
+this second piece and the second piece
+
+ align:start position:0%
+this second piece and the second piece
+ 
+
+ align:start position:0%
+this second piece and the second piece
+is the one that we just spent a little
+
+ align:start position:0%
+is the one that we just spent a little
+ 
+
+ align:start position:0%
+is the one that we just spent a little
+while on and that gave us a cosine
+
+ align:start position:0%
+while on and that gave us a cosine
+ 
+
+ align:start position:0%
+while on and that gave us a cosine
+x s to the nus one of
+
+ align:start position:0%
+x s to the nus one of
+ 
+
+ align:start position:0%
+x s to the nus one of
+X over n
+
+ align:start position:0%
+X over n
+ 
+
+ align:start position:0%
+X over n
+minus1 and then um
+
+ align:start position:0%
+minus1 and then um
+ 
+
+ align:start position:0%
+minus1 and then um
+plus 1 over n minus one and what was our
+
+ align:start position:0%
+plus 1 over n minus one and what was our
+ 
+
+ align:start position:0%
+plus 1 over n minus one and what was our
+thing here our thing here was f subn of
+
+ align:start position:0%
+thing here our thing here was f subn of
+ 
+
+ align:start position:0%
+thing here our thing here was f subn of
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+again okay so this might be a little
+
+ align:start position:0%
+again okay so this might be a little
+ 
+
+ align:start position:0%
+again okay so this might be a little
+complicated so I'm going to I'm going to
+
+ align:start position:0%
+complicated so I'm going to I'm going to
+ 
+
+ align:start position:0%
+complicated so I'm going to I'm going to
+show us where all the pieces come from
+
+ align:start position:0%
+show us where all the pieces come from
+ 
+
+ align:start position:0%
+show us where all the pieces come from
+just to remind us so we start with f
+
+ align:start position:0%
+just to remind us so we start with f
+ 
+
+ align:start position:0%
+just to remind us so we start with f
+subn of x and I'm claiming there are two
+
+ align:start position:0%
+subn of x and I'm claiming there are two
+ 
+
+ align:start position:0%
+subn of x and I'm claiming there are two
+pieces that are of Interest okay the
+
+ align:start position:0%
+pieces that are of Interest okay the
+ 
+
+ align:start position:0%
+pieces that are of Interest okay the
+first piece let's come back
+
+ align:start position:0%
+first piece let's come back
+ 
+
+ align:start position:0%
+first piece let's come back
+over the first piece this was our f subn
+
+ align:start position:0%
+over the first piece this was our f subn
+ 
+
+ align:start position:0%
+over the first piece this was our f subn
+of x we wrote it this way the first
+
+ align:start position:0%
+of x we wrote it this way the first
+ 
+
+ align:start position:0%
+of x we wrote it this way the first
+piece was the F subn minus 2 of X sign
+
+ align:start position:0%
+piece was the F subn minus 2 of X sign
+ 
+
+ align:start position:0%
+piece was the F subn minus 2 of X sign
+the N minus 2 of x no problem then we
+
+ align:start position:0%
+the N minus 2 of x no problem then we
+ 
+
+ align:start position:0%
+the N minus 2 of x no problem then we
+subtracted this integral and so I spent
+
+ align:start position:0%
+subtracted this integral and so I spent
+ 
+
+ align:start position:0%
+subtracted this integral and so I spent
+a little while trying to figure out how
+
+ align:start position:0%
+a little while trying to figure out how
+ 
+
+ align:start position:0%
+a little while trying to figure out how
+to write that integral and that integral
+
+ align:start position:0%
+to write that integral and that integral
+ 
+
+ align:start position:0%
+to write that integral and that integral
+was written right down here so I have to
+
+ align:start position:0%
+was written right down here so I have to
+ 
+
+ align:start position:0%
+was written right down here so I have to
+subtract off all of that that and the
+
+ align:start position:0%
+subtract off all of that that and the
+ 
+
+ align:start position:0%
+subtract off all of that that and the
+point is that this integral here
+
+ align:start position:0%
+point is that this integral here
+ 
+
+ align:start position:0%
+point is that this integral here
+integral of sin x to the N the quantity
+
+ align:start position:0%
+integral of sin x to the N the quantity
+ 
+
+ align:start position:0%
+integral of sin x to the N the quantity
+of sin x to the N is f subn of x again
+
+ align:start position:0%
+of sin x to the N is f subn of x again
+ 
+
+ align:start position:0%
+of sin x to the N is f subn of x again
+now you might be nervous because again
+
+ align:start position:0%
+now you might be nervous because again
+ 
+
+ align:start position:0%
+now you might be nervous because again
+we just said we see the same thing over
+
+ align:start position:0%
+we just said we see the same thing over
+ 
+
+ align:start position:0%
+we just said we see the same thing over
+we see what we want to reduce on the
+
+ align:start position:0%
+we see what we want to reduce on the
+ 
+
+ align:start position:0%
+we see what we want to reduce on the
+right hand side but now all we have to
+
+ align:start position:0%
+right hand side but now all we have to
+ 
+
+ align:start position:0%
+right hand side but now all we have to
+do as a little algebra so I'm going to
+
+ align:start position:0%
+do as a little algebra so I'm going to
+ 
+
+ align:start position:0%
+do as a little algebra so I'm going to
+come over and show you the magic of
+
+ align:start position:0%
+come over and show you the magic of
+ 
+
+ align:start position:0%
+come over and show you the magic of
+algebra okay let's uh let's to make this
+
+ align:start position:0%
+algebra okay let's uh let's to make this
+ 
+
+ align:start position:0%
+algebra okay let's uh let's to make this
+as easy as possible I'm going to erase
+
+ align:start position:0%
+as easy as possible I'm going to erase
+ 
+
+ align:start position:0%
+as easy as possible I'm going to erase
+the parentheses here and put that minus
+
+ align:start position:0%
+the parentheses here and put that minus
+ 
+
+ align:start position:0%
+the parentheses here and put that minus
+sign here so I don't have to rewrite the
+
+ align:start position:0%
+sign here so I don't have to rewrite the
+ 
+
+ align:start position:0%
+sign here so I don't have to rewrite the
+whole line okay so the parentheses are
+
+ align:start position:0%
+whole line okay so the parentheses are
+ 
+
+ align:start position:0%
+whole line okay so the parentheses are
+gone and I've I've distributed the
+
+ align:start position:0%
+gone and I've I've distributed the
+ 
+
+ align:start position:0%
+gone and I've I've distributed the
+negative one to both terms now notice I
+
+ align:start position:0%
+negative one to both terms now notice I
+ 
+
+ align:start position:0%
+negative one to both terms now notice I
+want to figure out what this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is to figure out what that blue thing
+
+ align:start position:0%
+is to figure out what that blue thing
+ 
+
+ align:start position:0%
+is to figure out what that blue thing
+equals well we're back to sort of an
+
+ align:start position:0%
+equals well we're back to sort of an
+ 
+
+ align:start position:0%
+equals well we're back to sort of an
+algebra problem we can isolate the blue
+
+ align:start position:0%
+algebra problem we can isolate the blue
+ 
+
+ align:start position:0%
+algebra problem we can isolate the blue
+things and solve for what's in the blue
+
+ align:start position:0%
+things and solve for what's in the blue
+ 
+
+ align:start position:0%
+things and solve for what's in the blue
+box so that's what we're going to do so
+
+ align:start position:0%
+box so that's what we're going to do so
+ 
+
+ align:start position:0%
+box so that's what we're going to do so
+what do we have to do well we have to
+
+ align:start position:0%
+what do we have to do well we have to
+ 
+
+ align:start position:0%
+what do we have to do well we have to
+add this to the left hand side and what
+
+ align:start position:0%
+add this to the left hand side and what
+ 
+
+ align:start position:0%
+add this to the left hand side and what
+do we get let's see what we get we get 1
+
+ align:start position:0%
+do we get let's see what we get we get 1
+ 
+
+ align:start position:0%
+do we get let's see what we get we get 1
++ 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nus1 f subn of
+
+ align:start position:0%
+nus1 f subn of
+ 
+
+ align:start position:0%
+nus1 f subn of
+x is equal
+
+ align:start position:0%
+x is equal
+ 
+
+ align:start position:0%
+x is equal
+to F subn minus 2 of
+
+ align:start position:0%
+to F subn minus 2 of
+ 
+
+ align:start position:0%
+to F subn minus 2 of
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+minus cine
+
+ align:start position:0%
+minus cine
+ 
+
+ align:start position:0%
+minus cine
+X sin x to the nus1 over
+
+ align:start position:0%
+X sin x to the nus1 over
+ 
+
+ align:start position:0%
+X sin x to the nus1 over
+nus1 so all I did was I added 1 over n
+
+ align:start position:0%
+nus1 so all I did was I added 1 over n
+ 
+
+ align:start position:0%
+nus1 so all I did was I added 1 over n
+minus one time f subn of x to the left
+
+ align:start position:0%
+minus one time f subn of x to the left
+ 
+
+ align:start position:0%
+minus one time f subn of x to the left
+hand side well to both sides so it moved
+
+ align:start position:0%
+hand side well to both sides so it moved
+ 
+
+ align:start position:0%
+hand side well to both sides so it moved
+to the left hand side and there was one
+
+ align:start position:0%
+to the left hand side and there was one
+ 
+
+ align:start position:0%
+to the left hand side and there was one
+of them here and there's one over n
+
+ align:start position:0%
+of them here and there's one over n
+ 
+
+ align:start position:0%
+of them here and there's one over n
+minus one of them here and let's let's
+
+ align:start position:0%
+minus one of them here and let's let's
+ 
+
+ align:start position:0%
+minus one of them here and let's let's
+make sure we can simplify that let's see
+
+ align:start position:0%
+make sure we can simplify that let's see
+ 
+
+ align:start position:0%
+make sure we can simplify that let's see
+we get n minus1 over nus1 + 1 I think it
+
+ align:start position:0%
+we get n minus1 over nus1 + 1 I think it
+ 
+
+ align:start position:0%
+we get n minus1 over nus1 + 1 I think it
+gives me n Over N minus one so that
+
+ align:start position:0%
+gives me n Over N minus one so that
+ 
+
+ align:start position:0%
+gives me n Over N minus one so that
+gives me n Over N minus
+
+ align:start position:0%
+gives me n Over N minus
+ 
+
+ align:start position:0%
+gives me n Over N minus
+one um I guess I'll write it
+
+ align:start position:0%
+one um I guess I'll write it
+ 
+
+ align:start position:0%
+one um I guess I'll write it
+again we're really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close and then this whole mess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again and now we only have one more step
+
+ align:start position:0%
+again and now we only have one more step
+ 
+
+ align:start position:0%
+again and now we only have one more step
+to figure out what f subn of x is and
+
+ align:start position:0%
+to figure out what f subn of x is and
+ 
+
+ align:start position:0%
+to figure out what f subn of x is and
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is to multiply both sides by n minus one
+
+ align:start position:0%
+is to multiply both sides by n minus one
+ 
+
+ align:start position:0%
+is to multiply both sides by n minus one
+/ n nus one over n multiplied here gives
+
+ align:start position:0%
+/ n nus one over n multiplied here gives
+ 
+
+ align:start position:0%
+/ n nus one over n multiplied here gives
+me one and so then I get nus1 / n and F
+
+ align:start position:0%
+me one and so then I get nus1 / n and F
+ 
+
+ align:start position:0%
+me one and so then I get nus1 / n and F
+of nus
+
+ align:start position:0%
+of nus
+ 
+
+ align:start position:0%
+of nus
+2 of
+
+ align:start position:0%
+2 of
+ 
+
+ align:start position:0%
+2 of
+x minus the N minus 1's kill off and I
+
+ align:start position:0%
+x minus the N minus 1's kill off and I
+ 
+
+ align:start position:0%
+x minus the N minus 1's kill off and I
+just get cine X
+
+ align:start position:0%
+just get cine X
+ 
+
+ align:start position:0%
+just get cine X
+sin to the N -1 x over
+
+ align:start position:0%
+sin to the N -1 x over
+ 
+
+ align:start position:0%
+sin to the N -1 x over
+n so this is our is our answer because
+
+ align:start position:0%
+n so this is our is our answer because
+ 
+
+ align:start position:0%
+n so this is our is our answer because
+what is the point why can I say well
+
+ align:start position:0%
+what is the point why can I say well
+ 
+
+ align:start position:0%
+what is the point why can I say well
+I've reduced it I've reduced it because
+
+ align:start position:0%
+I've reduced it I've reduced it because
+ 
+
+ align:start position:0%
+I've reduced it I've reduced it because
+I have the only integral I have is an
+
+ align:start position:0%
+I have the only integral I have is an
+ 
+
+ align:start position:0%
+I have the only integral I have is an
+integral that was a power of sinx X and
+
+ align:start position:0%
+integral that was a power of sinx X and
+ 
+
+ align:start position:0%
+integral that was a power of sinx X and
+that's the goal is that I have it in the
+
+ align:start position:0%
+that's the goal is that I have it in the
+ 
+
+ align:start position:0%
+that's the goal is that I have it in the
+form this is the power of s sin x to the
+
+ align:start position:0%
+form this is the power of s sin x to the
+ 
+
+ align:start position:0%
+form this is the power of s sin x to the
+N integrated this is sin x to the N
+
+ align:start position:0%
+N integrated this is sin x to the N
+ 
+
+ align:start position:0%
+N integrated this is sin x to the N
+minus 2 integrated and this is just a
+
+ align:start position:0%
+minus 2 integrated and this is just a
+ 
+
+ align:start position:0%
+minus 2 integrated and this is just a
+function okay and you know if we want to
+
+ align:start position:0%
+function okay and you know if we want to
+ 
+
+ align:start position:0%
+function okay and you know if we want to
+say what's the true anti-derivative we
+
+ align:start position:0%
+say what's the true anti-derivative we
+ 
+
+ align:start position:0%
+say what's the true anti-derivative we
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+allow we have to allow for a plus c here
+
+ align:start position:0%
+allow we have to allow for a plus c here
+ 
+
+ align:start position:0%
+allow we have to allow for a plus c here
+for a true anti-derivative but uh but
+
+ align:start position:0%
+for a true anti-derivative but uh but
+ 
+
+ align:start position:0%
+for a true anti-derivative but uh but
+we're really interested
+
+ align:start position:0%
+we're really interested
+ 
+
+ align:start position:0%
+we're really interested
+in this part here okay because if we
+
+ align:start position:0%
+in this part here okay because if we
+ 
+
+ align:start position:0%
+in this part here okay because if we
+evaluate this at bounds that's going to
+
+ align:start position:0%
+evaluate this at bounds that's going to
+ 
+
+ align:start position:0%
+evaluate this at bounds that's going to
+go away but I want to just make sure we
+
+ align:start position:0%
+go away but I want to just make sure we
+ 
+
+ align:start position:0%
+go away but I want to just make sure we
+understand I think we understand the
+
+ align:start position:0%
+understand I think we understand the
+ 
+
+ align:start position:0%
+understand I think we understand the
+goal maybe the hardest part of this
+
+ align:start position:0%
+goal maybe the hardest part of this
+ 
+
+ align:start position:0%
+goal maybe the hardest part of this
+problem is once you come over
+
+ align:start position:0%
+problem is once you come over
+ 
+
+ align:start position:0%
+problem is once you come over
+here was once you have these two
+
+ align:start position:0%
+here was once you have these two
+ 
+
+ align:start position:0%
+here was once you have these two
+components so we did the substitution
+
+ align:start position:0%
+components so we did the substitution
+ 
+
+ align:start position:0%
+components so we did the substitution
+that seems natural you have these two
+
+ align:start position:0%
+that seems natural you have these two
+ 
+
+ align:start position:0%
+that seems natural you have these two
+components this one you should be able
+
+ align:start position:0%
+components this one you should be able
+ 
+
+ align:start position:0%
+components this one you should be able
+to recognizes in the form you want this
+
+ align:start position:0%
+to recognizes in the form you want this
+ 
+
+ align:start position:0%
+to recognizes in the form you want this
+one is the hard one to deal with but the
+
+ align:start position:0%
+one is the hard one to deal with but the
+ 
+
+ align:start position:0%
+one is the hard one to deal with but the
+trick is to see that under the right
+
+ align:start position:0%
+trick is to see that under the right
+ 
+
+ align:start position:0%
+trick is to see that under the right
+splitting up of these functions one of
+
+ align:start position:0%
+splitting up of these functions one of
+ 
+
+ align:start position:0%
+splitting up of these functions one of
+them is easy to integrate and one of
+
+ align:start position:0%
+them is easy to integrate and one of
+ 
+
+ align:start position:0%
+them is easy to integrate and one of
+them you know it's easy to integrate or
+
+ align:start position:0%
+them you know it's easy to integrate or
+ 
+
+ align:start position:0%
+them you know it's easy to integrate or
+take a derivative so I have a little bit
+
+ align:start position:0%
+take a derivative so I have a little bit
+ 
+
+ align:start position:0%
+take a derivative so I have a little bit
+of Freedom you don't want to substitute
+
+ align:start position:0%
+of Freedom you don't want to substitute
+ 
+
+ align:start position:0%
+of Freedom you don't want to substitute
+back in for cosine squared with one
+
+ align:start position:0%
+back in for cosine squared with one
+ 
+
+ align:start position:0%
+back in for cosine squared with one
+minus sin squar because it'll get you
+
+ align:start position:0%
+minus sin squar because it'll get you
+ 
+
+ align:start position:0%
+minus sin squar because it'll get you
+right back to where you started you
+
+ align:start position:0%
+right back to where you started you
+ 
+
+ align:start position:0%
+right back to where you started you
+would be like substituting one way and
+
+ align:start position:0%
+would be like substituting one way and
+ 
+
+ align:start position:0%
+would be like substituting one way and
+then substituting the other way so the
+
+ align:start position:0%
+then substituting the other way so the
+ 
+
+ align:start position:0%
+then substituting the other way so the
+goal at this point is to sort of the
+
+ align:start position:0%
+goal at this point is to sort of the
+ 
+
+ align:start position:0%
+goal at this point is to sort of the
+trick with this one I mean is this
+
+ align:start position:0%
+trick with this one I mean is this
+ 
+
+ align:start position:0%
+trick with this one I mean is this
+integration by parts which requires some
+
+ align:start position:0%
+integration by parts which requires some
+ 
+
+ align:start position:0%
+integration by parts which requires some
+substitution so hopefully this was a
+
+ align:start position:0%
+substitution so hopefully this was a
+ 
+
+ align:start position:0%
+substitution so hopefully this was a
+good exercise for you and um and you see
+
+ align:start position:0%
+good exercise for you and um and you see
+ 
+
+ align:start position:0%
+good exercise for you and um and you see
+some of the strategies that one needs to
+
+ align:start position:0%
+some of the strategies that one needs to
+ 
+
+ align:start position:0%
+some of the strategies that one needs to
+reduce the powers of of sinx you could
+
+ align:start position:0%
+reduce the powers of of sinx you could
+ 
+
+ align:start position:0%
+reduce the powers of of sinx you could
+do a very similar type of thing with
+
+ align:start position:0%
+do a very similar type of thing with
+ 
+
+ align:start position:0%
+do a very similar type of thing with
+cosine X to the end so if you felt like
+
+ align:start position:0%
+cosine X to the end so if you felt like
+ 
+
+ align:start position:0%
+cosine X to the end so if you felt like
+I'm not quite sure about this method you
+
+ align:start position:0%
+I'm not quite sure about this method you
+ 
+
+ align:start position:0%
+I'm not quite sure about this method you
+might want to try and do something
+
+ align:start position:0%
+might want to try and do something
+ 
+
+ align:start position:0%
+might want to try and do something
+similar with cosine X to the n as your
+
+ align:start position:0%
+similar with cosine X to the n as your
+ 
+
+ align:start position:0%
+similar with cosine X to the n as your
+as your uh function that you're
+
+ align:start position:0%
+as your uh function that you're
+ 
+
+ align:start position:0%
+as your uh function that you're
+integrating and see if you can reduce
+
+ align:start position:0%
+integrating and see if you can reduce
+ 
+
+ align:start position:0%
+integrating and see if you can reduce
+that and I guarantee you can find a
+
+ align:start position:0%
+that and I guarantee you can find a
+ 
+
+ align:start position:0%
+that and I guarantee you can find a
+formula for that uh in a book or online
+
+ align:start position:0%
+formula for that uh in a book or online
+ 
+
+ align:start position:0%
+formula for that uh in a book or online
+if you wanted to check that answer so I
+
+ align:start position:0%
+if you wanted to check that answer so I
+ 
+
+ align:start position:0%
+if you wanted to check that answer so I
+guess this is where I'll stop
\ No newline at end of file
diff --git a/imywn6EaJxg.txt b/imywn6EaJxg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42ed848bad9deb229977e0ba3157ea447712aa98
--- /dev/null
+++ b/imywn6EaJxg.txt
@@ -0,0 +1,10969 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu yeah so you have Miss two
+
+ align:start position:0%
+ocw.mit.edu yeah so you have Miss two
+ 
+
+ align:start position:0%
+ocw.mit.edu yeah so you have Miss two
+semiconductors to start with uh one n
+
+ align:start position:0%
+semiconductors to start with uh one n
+ 
+
+ align:start position:0%
+semiconductors to start with uh one n
+and one one p typ and um P typ so for
+
+ align:start position:0%
+and one one p typ and um P typ so for
+ 
+
+ align:start position:0%
+and one one p typ and um P typ so for
+example you on the left hand side you
+
+ align:start position:0%
+example you on the left hand side you
+ 
+
+ align:start position:0%
+example you on the left hand side you
+have a p type the right hand side you
+
+ align:start position:0%
+have a p type the right hand side you
+ 
+
+ align:start position:0%
+have a p type the right hand side you
+have n type
+
+ align:start position:0%
+have n type
+ 
+
+ align:start position:0%
+have n type
+and there since you have a high
+
+ align:start position:0%
+and there since you have a high
+ 
+
+ align:start position:0%
+and there since you have a high
+concentration of electr on this side the
+
+ align:start position:0%
+concentration of electr on this side the
+ 
+
+ align:start position:0%
+concentration of electr on this side the
+electr jump to this side and you have a
+
+ align:start position:0%
+electr jump to this side and you have a
+ 
+
+ align:start position:0%
+electr jump to this side and you have a
+higher concentration of H the P type the
+
+ align:start position:0%
+higher concentration of H the P type the
+ 
+
+ align:start position:0%
+higher concentration of H the P type the
+P jump to the other side so you will end
+
+ align:start position:0%
+P jump to the other side so you will end
+ 
+
+ align:start position:0%
+P jump to the other side so you will end
+up with this space charge me that g
+
+ align:start position:0%
+up with this space charge me that g
+ 
+
+ align:start position:0%
+up with this space charge me that g
+talked about last
+
+ align:start position:0%
+talked about last
+ 
+
+ align:start position:0%
+talked about last
+week and um this is basically
+
+ align:start position:0%
+week and um this is basically
+ 
+
+ align:start position:0%
+week and um this is basically
+characteristic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I just I just draw one layer
+
+ align:start position:0%
+I just I just draw one layer
+ 
+
+ align:start position:0%
+I just I just draw one layer
+see so um so B you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have then you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cont impose the solar radiation
+
+ align:start position:0%
+cont impose the solar radiation
+ 
+
+ align:start position:0%
+cont impose the solar radiation
+something to
+
+ align:start position:0%
+something to
+ 
+
+ align:start position:0%
+something to
+this the volage
+
+ align:start position:0%
+this the volage
+ 
+
+ align:start position:0%
+this the volage
+you close the circuit you can generate B
+
+ align:start position:0%
+you close the circuit you can generate B
+ 
+
+ align:start position:0%
+you close the circuit you can generate B
+power for now I just talk about ciruit
+
+ align:start position:0%
+power for now I just talk about ciruit
+ 
+
+ align:start position:0%
+power for now I just talk about ciruit
+voltage so this is the first thing that
+
+ align:start position:0%
+voltage so this is the first thing that
+ 
+
+ align:start position:0%
+voltage so this is the first thing that
+happens space judge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region and um this you basically also
+
+ align:start position:0%
+region and um this you basically also
+ 
+
+ align:start position:0%
+region and um this you basically also
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+generate vol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so you have the space Char right here
+
+ align:start position:0%
+so so you have the space Char right here
+ 
+
+ align:start position:0%
+so so you have the space Char right here
+and then draw for
+
+ align:start position:0%
+and then draw for
+ 
+
+ align:start position:0%
+and then draw for
+example the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concentration and um so for the electron
+
+ align:start position:0%
+concentration and um so for the electron
+ 
+
+ align:start position:0%
+concentration and um so for the electron
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state so basic have
+
+ align:start position:0%
+state so basic have
+ 
+
+ align:start position:0%
+state so basic have
+here um you have
+
+ align:start position:0%
+here um you have
+ 
+
+ align:start position:0%
+here um you have
+ai generat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here in case you have for example comes
+
+ align:start position:0%
+here in case you have for example comes
+ 
+
+ align:start position:0%
+here in case you have for example comes
+in talk
+
+ align:start position:0%
+in talk
+ 
+
+ align:start position:0%
+in talk
+when a comes it's ex so they still very
+
+ align:start position:0%
+when a comes it's ex so they still very
+ 
+
+ align:start position:0%
+when a comes it's ex so they still very
+close to each other these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ex
+
+ align:start position:0%
+ex
+ 
+
+ align:start position:0%
+ex
+um they have
+
+ align:start position:0%
+um they have
+ 
+
+ align:start position:0%
+um they have
+to into this space but they
+
+ align:start position:0%
+to into this space but they
+ 
+
+ align:start position:0%
+to into this space but they
+basic um get separate so for this for
+
+ align:start position:0%
+basic um get separate so for this for
+ 
+
+ align:start position:0%
+basic um get separate so for this for
+this case for example we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have coming um
+
+ align:start position:0%
+have coming um
+ 
+
+ align:start position:0%
+have coming um
+Direction so basically the electron will
+
+ align:start position:0%
+Direction so basically the electron will
+ 
+
+ align:start position:0%
+Direction so basically the electron will
+basically drag through this so the
+
+ align:start position:0%
+basically drag through this so the
+ 
+
+ align:start position:0%
+basically drag through this so the
+electron this direction so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+El get separate from the hole and jumps
+
+ align:start position:0%
+El get separate from the hole and jumps
+ 
+
+ align:start position:0%
+El get separate from the hole and jumps
+on the other side and you you end up
+
+ align:start position:0%
+on the other side and you you end up
+ 
+
+ align:start position:0%
+on the other side and you you end up
+just positive charge here and um to the
+
+ align:start position:0%
+just positive charge here and um to the
+ 
+
+ align:start position:0%
+just positive charge here and um to the
+m region here have Fusion of
+
+ align:start position:0%
+m region here have Fusion of
+ 
+
+ align:start position:0%
+m region here have Fusion of
+your to the Conta here so um further so
+
+ align:start position:0%
+your to the Conta here so um further so
+ 
+
+ align:start position:0%
+your to the Conta here so um further so
+this is uh the car concentration and
+
+ align:start position:0%
+this is uh the car concentration and
+ 
+
+ align:start position:0%
+this is uh the car concentration and
+then you can also can can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there so e is generated inside Space
+
+ align:start position:0%
+there so e is generated inside Space
+ 
+
+ align:start position:0%
+there so e is generated inside Space
+Char this
+
+ align:start position:0%
+Char this
+ 
+
+ align:start position:0%
+Char this
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I think this was also when you
+
+ align:start position:0%
+and I think this was also when you
+ 
+
+ align:start position:0%
+and I think this was also when you
+talked about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+about just
+
+ align:start position:0%
+about just
+ 
+
+ align:start position:0%
+about just
+umal expansion
+
+ align:start position:0%
+umal expansion
+ 
+
+ align:start position:0%
+umal expansion
+um of
+
+ align:start position:0%
+um of
+ 
+
+ align:start position:0%
+um of
+this Bally say
+
+ align:start position:0%
+this Bally say
+ 
+
+ align:start position:0%
+this Bally say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drop just say up to certain point drop
+
+ align:start position:0%
+drop just say up to certain point drop
+ 
+
+ align:start position:0%
+drop just say up to certain point drop
+down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C up to this point exit when it comes it
+
+ align:start position:0%
+C up to this point exit when it comes it
+ 
+
+ align:start position:0%
+C up to this point exit when it comes it
+will start
+
+ align:start position:0%
+will start
+ 
+
+ align:start position:0%
+will start
+feeling space charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I wanted to talk about so in
+
+ align:start position:0%
+and then I wanted to talk about so in
+ 
+
+ align:start position:0%
+and then I wanted to talk about so in
+the real case we actually have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pH the so when we join the when we join
+
+ align:start position:0%
+pH the so when we join the when we join
+ 
+
+ align:start position:0%
+pH the so when we join the when we join
+two the last Le
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we since the
+
+ align:start position:0%
+we since the
+ 
+
+ align:start position:0%
+we since the
+family
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same let see what happens is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it's basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exed at the same I mean gets SE first
+
+ align:start position:0%
+exed at the same I mean gets SE first
+ 
+
+ align:start position:0%
+exed at the same I mean gets SE first
+you have this this state EXC State and
+
+ align:start position:0%
+you have this this state EXC State and
+ 
+
+ align:start position:0%
+you have this this state EXC State and
+then when CL St
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SE um changes with Lev so what you end
+
+ align:start position:0%
+SE um changes with Lev so what you end
+ 
+
+ align:start position:0%
+SE um changes with Lev so what you end
+up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ises and when you remove an El here you
+
+ align:start position:0%
+ises and when you remove an El here you
+ 
+
+ align:start position:0%
+ises and when you remove an El here you
+end up with ho here so you basically
+
+ align:start position:0%
+end up with ho here so you basically
+ 
+
+ align:start position:0%
+end up with ho here so you basically
+decreas so end up
+
+ align:start position:0%
+decreas so end up
+ 
+
+ align:start position:0%
+decreas so end up
+some Med is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is basically the we see so the
+
+ align:start position:0%
+and this is basically the we see so the
+ 
+
+ align:start position:0%
+and this is basically the we see so the
+difference between these two due to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thech the IDE obvious
+
+ align:start position:0%
+thech the IDE obvious
+ 
+
+ align:start position:0%
+thech the IDE obvious
+basically go all the way so maximum
+
+ align:start position:0%
+basically go all the way so maximum
+ 
+
+ align:start position:0%
+basically go all the way so maximum
+open get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the elction go conduction band is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because what was the question uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah that's that's a good question I was
+
+ align:start position:0%
+yeah that's that's a good question I was
+ 
+
+ align:start position:0%
+yeah that's that's a good question I was
+thinking about that too whe it's
+
+ align:start position:0%
+thinking about that too whe it's
+ 
+
+ align:start position:0%
+thinking about that too whe it's
+actually a step like this and then go
+
+ align:start position:0%
+actually a step like this and then go
+ 
+
+ align:start position:0%
+actually a step like this and then go
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um very good question I think I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well it's a it's a distributor so
+
+ align:start position:0%
+yeah well it's a it's a distributor so
+ 
+
+ align:start position:0%
+yeah well it's a it's a distributor so
+this one you should not look at the uh
+
+ align:start position:0%
+this one you should not look at the uh
+ 
+
+ align:start position:0%
+this one you should not look at the uh
+the spaceship so it's locally it could
+
+ align:start position:0%
+the spaceship so it's locally it could
+ 
+
+ align:start position:0%
+the spaceship so it's locally it could
+be anywhere around that
+
+ align:start position:0%
+be anywhere around that
+ 
+
+ align:start position:0%
+be anywhere around that
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+the so uh I I think that's a good place
+
+ align:start position:0%
+the so uh I I think that's a good place
+ 
+
+ align:start position:0%
+the so uh I I think that's a good place
+I I think back same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh that's where we stopped uh the
+
+ align:start position:0%
+so uh that's where we stopped uh the
+ 
+
+ align:start position:0%
+so uh that's where we stopped uh the
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+lecture uh it's about the
+
+ align:start position:0%
+lecture uh it's about the
+ 
+
+ align:start position:0%
+lecture uh it's about the
+compar
+
+ align:start position:0%
+compar
+ 
+
+ align:start position:0%
+compar
+umj a diet
+
+ align:start position:0%
+umj a diet
+ 
+
+ align:start position:0%
+umj a diet
+there a sh barrier sh about on the left
+
+ align:start position:0%
+there a sh barrier sh about on the left
+ 
+
+ align:start position:0%
+there a sh barrier sh about on the left
+is a sh on the
+
+ align:start position:0%
+is a sh on the
+ 
+
+ align:start position:0%
+is a sh on the
+right and when you look at the current
+
+ align:start position:0%
+right and when you look at the current
+ 
+
+ align:start position:0%
+right and when you look at the current
+voltage characteristics looks very
+
+ align:start position:0%
+voltage characteristics looks very
+ 
+
+ align:start position:0%
+voltage characteristics looks very
+similar right except that the
+
+ align:start position:0%
+similar right except that the
+ 
+
+ align:start position:0%
+similar right except that the
+coefficient are different the saturation
+
+ align:start position:0%
+coefficient are different the saturation
+ 
+
+ align:start position:0%
+coefficient are different the saturation
+This Is Us saturation C and saturation
+
+ align:start position:0%
+This Is Us saturation C and saturation
+ 
+
+ align:start position:0%
+This Is Us saturation C and saturation
+for uh this is a metal semiconductor
+
+ align:start position:0%
+for uh this is a metal semiconductor
+ 
+
+ align:start position:0%
+for uh this is a metal semiconductor
+right uh
+
+ align:start position:0%
+right uh
+ 
+
+ align:start position:0%
+right uh
+Junction and in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofation uh and in the case
+
+ align:start position:0%
+ofation uh and in the case
+ 
+
+ align:start position:0%
+ofation uh and in the case
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+thejunction the card include the B Gap
+
+ align:start position:0%
+thejunction the card include the B Gap
+ 
+
+ align:start position:0%
+thejunction the card include the B Gap
+and include the effusivity of hole so on
+
+ align:start position:0%
+and include the effusivity of hole so on
+ 
+
+ align:start position:0%
+and include the effusivity of hole so on
+the P side is a really hole that PR the
+
+ align:start position:0%
+the P side is a really hole that PR the
+ 
+
+ align:start position:0%
+the P side is a really hole that PR the
+car on the inside is the electron so if
+
+ align:start position:0%
+car on the inside is the electron so if
+ 
+
+ align:start position:0%
+car on the inside is the electron so if
+you elect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inside and then we have this one time
+
+ align:start position:0%
+inside and then we have this one time
+ 
+
+ align:start position:0%
+inside and then we have this one time
+the comination time uh this is a uh say
+
+ align:start position:0%
+the comination time uh this is a uh say
+ 
+
+ align:start position:0%
+the comination time uh this is a uh say
+when you create a
+
+ align:start position:0%
+when you create a
+ 
+
+ align:start position:0%
+when you create a
+electron you excite the
+
+ align:start position:0%
+electron you excite the
+ 
+
+ align:start position:0%
+electron you excite the
+electron from Val to conduction
+
+ align:start position:0%
+electron from Val to conduction
+ 
+
+ align:start position:0%
+electron from Val to conduction
+conduction but how long they can be kep
+
+ align:start position:0%
+conduction but how long they can be kep
+ 
+
+ align:start position:0%
+conduction but how long they can be kep
+separate and after amount of time they
+
+ align:start position:0%
+separate and after amount of time they
+ 
+
+ align:start position:0%
+separate and after amount of time they
+will Rec
+
+ align:start position:0%
+will Rec
+ 
+
+ align:start position:0%
+will Rec
+combine and give us the either for
+
+ align:start position:0%
+combine and give us the either for
+ 
+
+ align:start position:0%
+combine and give us the either for
+that's where laser
+
+ align:start position:0%
+that's where laser
+ 
+
+ align:start position:0%
+that's where laser
+or you want or uh give ke uh the general
+
+ align:start position:0%
+or you want or uh give ke uh the general
+ 
+
+ align:start position:0%
+or you want or uh give ke uh the general
+forms so uh this is the recombination
+
+ align:start position:0%
+forms so uh this is the recombination
+ 
+
+ align:start position:0%
+forms so uh this is the recombination
+time for and you can see that the
+
+ align:start position:0%
+time for and you can see that the
+ 
+
+ align:start position:0%
+time for and you can see that the
+difference really in this saturation
+
+ align:start position:0%
+difference really in this saturation
+ 
+
+ align:start position:0%
+difference really in this saturation
+that Cur and sometimes equal
+
+ align:start position:0%
+that Cur and sometimes equal
+ 
+
+ align:start position:0%
+that Cur and sometimes equal
+for matics
+
+ align:start position:0%
+for matics
+ 
+
+ align:start position:0%
+for matics
+but I want to emphasize another
+
+ align:start position:0%
+but I want to emphasize another
+ 
+
+ align:start position:0%
+but I want to emphasize another
+fundamental
+
+ align:start position:0%
+fundamental
+ 
+
+ align:start position:0%
+fundamental
+yes I would sort of intuitively that the
+
+ align:start position:0%
+yes I would sort of intuitively that the
+ 
+
+ align:start position:0%
+yes I would sort of intuitively that the
+longer the recombination time the more
+
+ align:start position:0%
+longer the recombination time the more
+ 
+
+ align:start position:0%
+longer the recombination time the more
+current we would have the longer the the
+
+ align:start position:0%
+current we would have the longer the the
+ 
+
+ align:start position:0%
+current we would have the longer the the
+longer the rec relation time yes let's
+
+ align:start position:0%
+longer the rec relation time yes let's
+ 
+
+ align:start position:0%
+longer the rec relation time yes let's
+see uh recombination is also related to
+
+ align:start position:0%
+see uh recombination is also related to
+ 
+
+ align:start position:0%
+see uh recombination is also related to
+um U
+
+ align:start position:0%
+um U
+ 
+
+ align:start position:0%
+um U
+uh longer Rec
+
+ align:start position:0%
+uh longer Rec
+ 
+
+ align:start position:0%
+uh longer Rec
+comilation uh
+
+ align:start position:0%
+comilation uh
+ 
+
+ align:start position:0%
+comilation uh
+well longer recombination uh uh
+
+ align:start position:0%
+well longer recombination uh uh
+ 
+
+ align:start position:0%
+well longer recombination uh uh
+smaller uh um uh not
+
+ align:start position:0%
+smaller uh um uh not
+ 
+
+ align:start position:0%
+smaller uh um uh not
+C but say I see your point uh where if
+
+ align:start position:0%
+C but say I see your point uh where if
+ 
+
+ align:start position:0%
+C but say I see your point uh where if
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+longer uh is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reculation reculation happens in this
+
+ align:start position:0%
+reculation reculation happens in this
+ 
+
+ align:start position:0%
+reculation reculation happens in this
+region okay so
+
+ align:start position:0%
+region okay so
+ 
+
+ align:start position:0%
+region okay so
+um uh I think in that case what happens
+
+ align:start position:0%
+um uh I think in that case what happens
+ 
+
+ align:start position:0%
+um uh I think in that case what happens
+is the diffusion Supply is also uh limit
+
+ align:start position:0%
+is the diffusion Supply is also uh limit
+ 
+
+ align:start position:0%
+is the diffusion Supply is also uh limit
+your your your uh current flow so this
+
+ align:start position:0%
+your your your uh current flow so this
+ 
+
+ align:start position:0%
+your your your uh current flow so this
+is where I want to emphasize the
+
+ align:start position:0%
+is where I want to emphasize the
+ 
+
+ align:start position:0%
+is where I want to emphasize the
+important difference between this two
+
+ align:start position:0%
+important difference between this two
+ 
+
+ align:start position:0%
+important difference between this two
+formula is a sh barrier when electron go
+
+ align:start position:0%
+formula is a sh barrier when electron go
+ 
+
+ align:start position:0%
+formula is a sh barrier when electron go
+from here to here right it's electron
+
+ align:start position:0%
+from here to here right it's electron
+ 
+
+ align:start position:0%
+from here to here right it's electron
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+elect the way I draw it here is the
+
+ align:start position:0%
+elect the way I draw it here is the
+ 
+
+ align:start position:0%
+elect the way I draw it here is the
+electron and the M side is electron no
+
+ align:start position:0%
+electron and the M side is electron no
+ 
+
+ align:start position:0%
+electron and the M side is electron no
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+now if you look at the K
+
+ align:start position:0%
+now if you look at the K
+ 
+
+ align:start position:0%
+now if you look at the K
+Junction okay on the end Ty is
+
+ align:start position:0%
+Junction okay on the end Ty is
+ 
+
+ align:start position:0%
+Junction okay on the end Ty is
+electron and then T
+
+ align:start position:0%
+electron and then T
+ 
+
+ align:start position:0%
+electron and then T
+typ so if electron go I'm dra here
+
+ align:start position:0%
+typ so if electron go I'm dra here
+ 
+
+ align:start position:0%
+typ so if electron go I'm dra here
+electron go from here to here go through
+
+ align:start position:0%
+electron go from here to here go through
+ 
+
+ align:start position:0%
+electron go from here to here go through
+this space charge
+
+ align:start position:0%
+this space charge
+ 
+
+ align:start position:0%
+this space charge
+region there's no more
+
+ align:start position:0%
+region there's no more
+ 
+
+ align:start position:0%
+region there's no more
+electron right you have to
+
+ align:start position:0%
+electron right you have to
+ 
+
+ align:start position:0%
+electron right you have to
+P so what happens
+
+ align:start position:0%
+P so what happens
+ 
+
+ align:start position:0%
+P so what happens
+and you have to have current continuity
+
+ align:start position:0%
+and you have to have current continuity
+ 
+
+ align:start position:0%
+and you have to have current continuity
+the charge has to be supplied
+
+ align:start position:0%
+the charge has to be supplied
+ 
+
+ align:start position:0%
+the charge has to be supplied
+right so what happens is that the
+
+ align:start position:0%
+right so what happens is that the
+ 
+
+ align:start position:0%
+right so what happens is that the
+hole will Rec combine with this
+
+ align:start position:0%
+hole will Rec combine with this
+ 
+
+ align:start position:0%
+hole will Rec combine with this
+electron okay so the ho we combined with
+
+ align:start position:0%
+electron okay so the ho we combined with
+ 
+
+ align:start position:0%
+electron okay so the ho we combined with
+the electron that means you have to
+
+ align:start position:0%
+the electron that means you have to
+ 
+
+ align:start position:0%
+the electron that means you have to
+supply holes from this side so you draw
+
+ align:start position:0%
+supply holes from this side so you draw
+ 
+
+ align:start position:0%
+supply holes from this side so you draw
+hole from this side we combine with
+
+ align:start position:0%
+hole from this side we combine with
+ 
+
+ align:start position:0%
+hole from this side we combine with
+whatever electron come this side
+
+ align:start position:0%
+whatever electron come this side
+ 
+
+ align:start position:0%
+whatever electron come this side
+and this is the where the recompilation
+
+ align:start position:0%
+and this is the where the recompilation
+ 
+
+ align:start position:0%
+and this is the where the recompilation
+reg happen it's not in the space chart
+
+ align:start position:0%
+reg happen it's not in the space chart
+ 
+
+ align:start position:0%
+reg happen it's not in the space chart
+it's slightly just outside the space
+
+ align:start position:0%
+it's slightly just outside the space
+ 
+
+ align:start position:0%
+it's slightly just outside the space
+chart so it's minority carrier
+
+ align:start position:0%
+chart so it's minority carrier
+ 
+
+ align:start position:0%
+chart so it's minority carrier
+device that's really fundamental
+
+ align:start position:0%
+device that's really fundamental
+ 
+
+ align:start position:0%
+device that's really fundamental
+difference between majority carrier
+
+ align:start position:0%
+difference between majority carrier
+ 
+
+ align:start position:0%
+difference between majority carrier
+device minority device minority device
+
+ align:start position:0%
+device minority device minority device
+ 
+
+ align:start position:0%
+device minority device minority device
+this Rec comilation is crucial and later
+
+ align:start position:0%
+this Rec comilation is crucial and later
+ 
+
+ align:start position:0%
+this Rec comilation is crucial and later
+on we talk about solar cell that's all
+
+ align:start position:0%
+on we talk about solar cell that's all
+ 
+
+ align:start position:0%
+on we talk about solar cell that's all
+people trying to refine solar silicon is
+
+ align:start position:0%
+people trying to refine solar silicon is
+ 
+
+ align:start position:0%
+people trying to refine solar silicon is
+trying to increase
+
+ align:start position:0%
+trying to increase
+ 
+
+ align:start position:0%
+trying to increase
+this Rec
+
+ align:start position:0%
+this Rec
+ 
+
+ align:start position:0%
+this Rec
+combination okay so that's that's a so
+
+ align:start position:0%
+combination okay so that's that's a so
+ 
+
+ align:start position:0%
+combination okay so that's that's a so
+you brought this this is the point
+
+ align:start position:0%
+you brought this this is the point
+ 
+
+ align:start position:0%
+you brought this this is the point
+that's really important to uh to
+
+ align:start position:0%
+that's really important to uh to
+ 
+
+ align:start position:0%
+that's really important to uh to
+appreciate the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minority okay and of course I mention so
+
+ align:start position:0%
+minority okay and of course I mention so
+ 
+
+ align:start position:0%
+minority okay and of course I mention so
+this is what I draw the C you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+diffusion is on this side so whole
+
+ align:start position:0%
+diffusion is on this side so whole
+ 
+
+ align:start position:0%
+diffusion is on this side so whole
+diffus one just this side there's no
+
+ align:start position:0%
+diffus one just this side there's no
+ 
+
+ align:start position:0%
+diffus one just this side there's no
+more electron right so electron will Rec
+
+ align:start position:0%
+more electron right so electron will Rec
+ 
+
+ align:start position:0%
+more electron right so electron will Rec
+combin with so there's next electron FL
+
+ align:start position:0%
+combin with so there's next electron FL
+ 
+
+ align:start position:0%
+combin with so there's next electron FL
+forward so there small so if I look at
+
+ align:start position:0%
+forward so there small so if I look at
+ 
+
+ align:start position:0%
+forward so there small so if I look at
+electron Cur it dease in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+combination and then I look at the whole
+
+ align:start position:0%
+combination and then I look at the whole
+ 
+
+ align:start position:0%
+combination and then I look at the whole
+current right say on this side the whole
+
+ align:start position:0%
+current right say on this side the whole
+ 
+
+ align:start position:0%
+current right say on this side the whole
+difference in this that's where the
+
+ align:start position:0%
+difference in this that's where the
+ 
+
+ align:start position:0%
+difference in this that's where the
+supply we comb
+
+ align:start position:0%
+supply we comb
+ 
+
+ align:start position:0%
+supply we comb
+with so go through the space Char reg
+
+ align:start position:0%
+with so go through the space Char reg
+ 
+
+ align:start position:0%
+with so go through the space Char reg
+space Char
+
+ align:start position:0%
+space Char
+ 
+
+ align:start position:0%
+space Char
+comination so as approximation so it's a
+
+ align:start position:0%
+comination so as approximation so it's a
+ 
+
+ align:start position:0%
+comination so as approximation so it's a
+constant and then after space charge
+
+ align:start position:0%
+constant and then after space charge
+ 
+
+ align:start position:0%
+constant and then after space charge
+they Rec combine with the pole so
+
+ align:start position:0%
+they Rec combine with the pole so
+ 
+
+ align:start position:0%
+they Rec combine with the pole so
+electron diminish now and this side is
+
+ align:start position:0%
+electron diminish now and this side is
+ 
+
+ align:start position:0%
+electron diminish now and this side is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+over right so that's how we go trans
+
+ align:start position:0%
+over right so that's how we go trans
+ 
+
+ align:start position:0%
+over right so that's how we go trans
+from a electron
+
+ align:start position:0%
+from a electron
+ 
+
+ align:start position:0%
+from a electron
+to so K Jun Theory shly uh uh say you
+
+ align:start position:0%
+to so K Jun Theory shly uh uh say you
+ 
+
+ align:start position:0%
+to so K Jun Theory shly uh uh say you
+know injunction was I think I say three
+
+ align:start position:0%
+know injunction was I think I say three
+ 
+
+ align:start position:0%
+know injunction was I think I say three
+people got Rob Price uh one is the sh
+
+ align:start position:0%
+people got Rob Price uh one is the sh
+ 
+
+ align:start position:0%
+people got Rob Price uh one is the sh
+and the other is bin and the third is
+
+ align:start position:0%
+and the other is bin and the third is
+ 
+
+ align:start position:0%
+and the other is bin and the third is
+BR and I think it was sh
+
+ align:start position:0%
+BR and I think it was sh
+ 
+
+ align:start position:0%
+BR and I think it was sh
+and uh shle and Britain did the invation
+
+ align:start position:0%
+and uh shle and Britain did the invation
+ 
+
+ align:start position:0%
+and uh shle and Britain did the invation
+and B was the manager at time
+
+ align:start position:0%
+and B was the manager at time
+ 
+
+ align:start position:0%
+and B was the manager at time
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+develop and if you look at the the
+
+ align:start position:0%
+develop and if you look at the the
+ 
+
+ align:start position:0%
+develop and if you look at the the
+history
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+superity so he was very
+
+ align:start position:0%
+superity so he was very
+ 
+
+ align:start position:0%
+superity so he was very
+history as manager this is so important
+
+ align:start position:0%
+history as manager this is so important
+ 
+
+ align:start position:0%
+history as manager this is so important
+has to do something if you Theory okay
+
+ align:start position:0%
+has to do something if you Theory okay
+ 
+
+ align:start position:0%
+has to do something if you Theory okay
+and but this is really a very ingenious
+
+ align:start position:0%
+and but this is really a very ingenious
+ 
+
+ align:start position:0%
+and but this is really a very ingenious
+Theory to think about how
+
+ align:start position:0%
+Theory to think about how
+ 
+
+ align:start position:0%
+Theory to think about how
+electron on this side know on other
+
+ align:start position:0%
+electron on this side know on other
+ 
+
+ align:start position:0%
+electron on this side know on other
+by the end your curent has to be
+
+ align:start position:0%
+by the end your curent has to be
+ 
+
+ align:start position:0%
+by the end your curent has to be
+continued the summation of electron Cur
+
+ align:start position:0%
+continued the summation of electron Cur
+ 
+
+ align:start position:0%
+continued the summation of electron Cur
+the whole current is Con
+
+ align:start position:0%
+the whole current is Con
+ 
+
+ align:start position:0%
+the whole current is Con
+right okay and uh in the last lecture I
+
+ align:start position:0%
+right okay and uh in the last lecture I
+ 
+
+ align:start position:0%
+right okay and uh in the last lecture I
+also said if you look at the energy
+
+ align:start position:0%
+also said if you look at the energy
+ 
+
+ align:start position:0%
+also said if you look at the energy
+flow and when electron right here yes I
+
+ align:start position:0%
+flow and when electron right here yes I
+ 
+
+ align:start position:0%
+flow and when electron right here yes I
+would like to know what happens the
+
+ align:start position:0%
+would like to know what happens the
+ 
+
+ align:start position:0%
+would like to know what happens the
+whole Curr in the contact because in the
+
+ align:start position:0%
+whole Curr in the contact because in the
+ 
+
+ align:start position:0%
+whole Curr in the contact because in the
+cbles we must have elect right of in the
+
+ align:start position:0%
+cbles we must have elect right of in the
+ 
+
+ align:start position:0%
+cbles we must have elect right of in the
+uh in the
+
+ align:start position:0%
+uh in the
+ 
+
+ align:start position:0%
+uh in the
+contact very so it's a it's a matter of
+
+ align:start position:0%
+contact very so it's a it's a matter of
+ 
+
+ align:start position:0%
+contact very so it's a it's a matter of
+there's no hole again there's no hole so
+
+ align:start position:0%
+there's no hole again there's no hole so
+ 
+
+ align:start position:0%
+there's no hole again there's no hole so
+if typically contact people want to make
+
+ align:start position:0%
+if typically contact people want to make
+ 
+
+ align:start position:0%
+if typically contact people want to make
+an army contact so what what H what
+
+ align:start position:0%
+an army contact so what what H what
+ 
+
+ align:start position:0%
+an army contact so what what H what
+happens is when uh uh uh so the whole
+
+ align:start position:0%
+happens is when uh uh uh so the whole
+ 
+
+ align:start position:0%
+happens is when uh uh uh so the whole
+motion is really majority of electron
+
+ align:start position:0%
+motion is really majority of electron
+ 
+
+ align:start position:0%
+motion is really majority of electron
+Motion in the t region so when po move
+
+ align:start position:0%
+Motion in the t region so when po move
+ 
+
+ align:start position:0%
+Motion in the t region so when po move
+this way go uh from Whole Mo from here
+
+ align:start position:0%
+this way go uh from Whole Mo from here
+ 
+
+ align:start position:0%
+this way go uh from Whole Mo from here
+to here that means this electron goes
+
+ align:start position:0%
+to here that means this electron goes
+ 
+
+ align:start position:0%
+to here that means this electron goes
+out to the
+
+ align:start position:0%
+out to the
+ 
+
+ align:start position:0%
+out to the
+metal so that's what
+
+ align:start position:0%
+metal so that's what
+ 
+
+ align:start position:0%
+metal so that's what
+happens okay and they have full chal
+
+ align:start position:0%
+happens okay and they have full chal
+ 
+
+ align:start position:0%
+happens okay and they have full chal
+potential electral potential that's what
+
+ align:start position:0%
+potential electral potential that's what
+ 
+
+ align:start position:0%
+potential electral potential that's what
+say Junction sort of like the CH bar but
+
+ align:start position:0%
+say Junction sort of like the CH bar but
+ 
+
+ align:start position:0%
+say Junction sort of like the CH bar but
+they want make Armic
+
+ align:start position:0%
+they want make Armic
+ 
+
+ align:start position:0%
+they want make Armic
+Junction those
+
+ align:start position:0%
+Junction those
+ 
+
+ align:start position:0%
+Junction those
+sides and if you think about the C
+
+ align:start position:0%
+sides and if you think about the C
+ 
+
+ align:start position:0%
+sides and if you think about the C
+effect right Pro he is the kinetic
+
+ align:start position:0%
+effect right Pro he is the kinetic
+ 
+
+ align:start position:0%
+effect right Pro he is the kinetic
+energy part which is 2
+
+ align:start position:0%
+energy part which is 2
+ 
+
+ align:start position:0%
+energy part which is 2
+KT of the charge average
+
+ align:start position:0%
+KT of the charge average
+ 
+
+ align:start position:0%
+KT of the charge average
+speaking minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+EA
+
+ align:start position:0%
+EA
+ 
+
+ align:start position:0%
+EA
+EA minus EF right the C
+
+ align:start position:0%
+EA minus EF right the C
+ 
+
+ align:start position:0%
+EA minus EF right the C
+energy and you look at this EC and EF is
+
+ align:start position:0%
+energy and you look at this EC and EF is
+ 
+
+ align:start position:0%
+energy and you look at this EC and EF is
+growing here on the inside e EF is here
+
+ align:start position:0%
+growing here on the inside e EF is here
+ 
+
+ align:start position:0%
+growing here on the inside e EF is here
+in this space charge reg is grow larger
+
+ align:start position:0%
+in this space charge reg is grow larger
+ 
+
+ align:start position:0%
+in this space charge reg is grow larger
+larger so electron is carrying more heat
+
+ align:start position:0%
+larger so electron is carrying more heat
+ 
+
+ align:start position:0%
+larger so electron is carrying more heat
+per charge is carrying more
+
+ align:start position:0%
+per charge is carrying more
+ 
+
+ align:start position:0%
+per charge is carrying more
+heat right it's carrying he out of the
+
+ align:start position:0%
+heat right it's carrying he out of the
+ 
+
+ align:start position:0%
+heat right it's carrying he out of the
+space charge
+
+ align:start position:0%
+space charge
+ 
+
+ align:start position:0%
+space charge
+region that's why space charge region is
+
+ align:start position:0%
+region that's why space charge region is
+ 
+
+ align:start position:0%
+region that's why space charge region is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+a okay and then in outside immediate
+
+ align:start position:0%
+a okay and then in outside immediate
+ 
+
+ align:start position:0%
+a okay and then in outside immediate
+outside space charge region
+
+ align:start position:0%
+outside space charge region
+ 
+
+ align:start position:0%
+outside space charge region
+recompilation happens right
+
+ align:start position:0%
+recompilation happens right
+ 
+
+ align:start position:0%
+recompilation happens right
+recombination dump the H just immediate
+
+ align:start position:0%
+recombination dump the H just immediate
+ 
+
+ align:start position:0%
+recombination dump the H just immediate
+outside space charger we flow back of
+
+ align:start position:0%
+outside space charger we flow back of
+ 
+
+ align:start position:0%
+outside space charger we flow back of
+course Junction heats up but physics is
+
+ align:start position:0%
+course Junction heats up but physics is
+ 
+
+ align:start position:0%
+course Junction heats up but physics is
+it's not the junction the space charge
+
+ align:start position:0%
+it's not the junction the space charge
+ 
+
+ align:start position:0%
+it's not the junction the space charge
+region that really heats up the heat is
+
+ align:start position:0%
+region that really heats up the heat is
+ 
+
+ align:start position:0%
+region that really heats up the heat is
+actually generated
+
+ align:start position:0%
+actually generated
+ 
+
+ align:start position:0%
+actually generated
+outside this space charge in this Rec
+
+ align:start position:0%
+outside this space charge in this Rec
+ 
+
+ align:start position:0%
+outside this space charge in this Rec
+comilation this is where heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that's a fact that most people
+
+ align:start position:0%
+is that's a fact that most people
+ 
+
+ align:start position:0%
+is that's a fact that most people
+probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+okay so uh uh to finish what I was
+
+ align:start position:0%
+okay so uh uh to finish what I was
+ 
+
+ align:start position:0%
+okay so uh uh to finish what I was
+talking last lecture more research this
+
+ align:start position:0%
+talking last lecture more research this
+ 
+
+ align:start position:0%
+talking last lecture more research this
+is the basic physics
+
+ align:start position:0%
+is the basic physics
+ 
+
+ align:start position:0%
+is the basic physics
+and since we're talking about the re
+
+ align:start position:0%
+and since we're talking about the re
+ 
+
+ align:start position:0%
+and since we're talking about the re
+formula emission so uh there are people
+
+ align:start position:0%
+formula emission so uh there are people
+ 
+
+ align:start position:0%
+formula emission so uh there are people
+doing for example in the this is a
+
+ align:start position:0%
+doing for example in the this is a
+ 
+
+ align:start position:0%
+doing for example in the this is a
+conduction F if you don't have a fir
+
+ align:start position:0%
+conduction F if you don't have a fir
+ 
+
+ align:start position:0%
+conduction F if you don't have a fir
+number around this place the energy
+
+ align:start position:0%
+number around this place the energy
+ 
+
+ align:start position:0%
+number around this place the energy
+electron below the fir level is actually
+
+ align:start position:0%
+electron below the fir level is actually
+ 
+
+ align:start position:0%
+electron below the fir level is actually
+carry negative energy and the electron
+
+ align:start position:0%
+carry negative energy and the electron
+ 
+
+ align:start position:0%
+carry negative energy and the electron
+above carry positive energy
+
+ align:start position:0%
+above carry positive energy
+ 
+
+ align:start position:0%
+above carry positive energy
+so one idea is if I do a shock barrier
+
+ align:start position:0%
+so one idea is if I do a shock barrier
+ 
+
+ align:start position:0%
+so one idea is if I do a shock barrier
+or potential barrier right and I just
+
+ align:start position:0%
+or potential barrier right and I just
+ 
+
+ align:start position:0%
+or potential barrier right and I just
+scatter this part of the electron that's
+
+ align:start position:0%
+scatter this part of the electron that's
+ 
+
+ align:start position:0%
+scatter this part of the electron that's
+called Energy filter or depends on if
+
+ align:start position:0%
+called Energy filter or depends on if
+ 
+
+ align:start position:0%
+called Energy filter or depends on if
+you have interface you also call it
+
+ align:start position:0%
+you have interface you also call it
+ 
+
+ align:start position:0%
+you have interface you also call it
+emission so some people call the
+
+ align:start position:0%
+emission so some people call the
+ 
+
+ align:start position:0%
+emission so some people call the
+emission say
+
+ align:start position:0%
+emission say
+ 
+
+ align:start position:0%
+emission say
+thric effect the soal solidate teric but
+
+ align:start position:0%
+thric effect the soal solidate teric but
+ 
+
+ align:start position:0%
+thric effect the soal solidate teric but
+say uh essentially
+
+ align:start position:0%
+say uh essentially
+ 
+
+ align:start position:0%
+say uh essentially
+of the low energy electron or sometimes
+
+ align:start position:0%
+of the low energy electron or sometimes
+ 
+
+ align:start position:0%
+of the low energy electron or sometimes
+carry heat because the electron below
+
+ align:start position:0%
+carry heat because the electron below
+ 
+
+ align:start position:0%
+carry heat because the electron below
+the CH
+
+ align:start position:0%
+the CH
+ 
+
+ align:start position:0%
+the CH
+Po and if I draw the
+
+ align:start position:0%
+Po and if I draw the
+ 
+
+ align:start position:0%
+Po and if I draw the
+stat most I I mentioned before talk
+
+ align:start position:0%
+stat most I I mentioned before talk
+ 
+
+ align:start position:0%
+stat most I I mentioned before talk
+electric stat need a sharp feature the
+
+ align:start position:0%
+electric stat need a sharp feature the
+ 
+
+ align:start position:0%
+electric stat need a sharp feature the
+sharp feature help increases thric
+
+ align:start position:0%
+sharp feature help increases thric
+ 
+
+ align:start position:0%
+sharp feature help increases thric
+effect right so the way I view is okay
+
+ align:start position:0%
+effect right so the way I view is okay
+ 
+
+ align:start position:0%
+effect right so the way I view is okay
+in this I cut it off by transport I cut
+
+ align:start position:0%
+in this I cut it off by transport I cut
+ 
+
+ align:start position:0%
+in this I cut it off by transport I cut
+off transport electrons I still have the
+
+ align:start position:0%
+off transport electrons I still have the
+ 
+
+ align:start position:0%
+off transport electrons I still have the
+electron but they are scatter they don't
+
+ align:start position:0%
+electron but they are scatter they don't
+ 
+
+ align:start position:0%
+electron but they are scatter they don't
+move so then uh the real ones are here
+
+ align:start position:0%
+move so then uh the real ones are here
+ 
+
+ align:start position:0%
+move so then uh the real ones are here
+and I can think this sh so that's the
+
+ align:start position:0%
+and I can think this sh so that's the
+ 
+
+ align:start position:0%
+and I can think this sh so that's the
+way I say okay it's all really coming
+
+ align:start position:0%
+way I say okay it's all really coming
+ 
+
+ align:start position:0%
+way I say okay it's all really coming
+back to the idea if you can create a sh
+
+ align:start position:0%
+back to the idea if you can create a sh
+ 
+
+ align:start position:0%
+back to the idea if you can create a sh
+features in this sub States put a lot of
+
+ align:start position:0%
+features in this sub States put a lot of
+ 
+
+ align:start position:0%
+features in this sub States put a lot of
+electron there and you can potentially
+
+ align:start position:0%
+electron there and you can potentially
+ 
+
+ align:start position:0%
+electron there and you can potentially
+improve the electron um car Factor
+
+ align:start position:0%
+improve the electron um car Factor
+ 
+
+ align:start position:0%
+improve the electron um car Factor
+that's for signal but see the key is you
+
+ align:start position:0%
+that's for signal but see the key is you
+ 
+
+ align:start position:0%
+that's for signal but see the key is you
+don't want you only want to scare this
+
+ align:start position:0%
+don't want you only want to scare this
+ 
+
+ align:start position:0%
+don't want you only want to scare this
+part you don't want to this part do it
+
+ align:start position:0%
+part you don't want to this part do it
+ 
+
+ align:start position:0%
+part you don't want to this part do it
+that's a still a lot of TRS I think that
+
+ align:start position:0%
+that's a still a lot of TRS I think that
+ 
+
+ align:start position:0%
+that's a still a lot of TRS I think that
+this this idea here not fully convincing
+
+ align:start position:0%
+this this idea here not fully convincing
+ 
+
+ align:start position:0%
+this this idea here not fully convincing
+yet
+
+ align:start position:0%
+yet
+ 
+
+ align:start position:0%
+yet
+me and I made a few slides on this
+
+ align:start position:0%
+me and I made a few slides on this
+ 
+
+ align:start position:0%
+me and I made a few slides on this
+that's on my own uh sort of toy baby I I
+
+ align:start position:0%
+that's on my own uh sort of toy baby I I
+ 
+
+ align:start position:0%
+that's on my own uh sort of toy baby I I
+published a paper before uh um there's
+
+ align:start position:0%
+published a paper before uh um there's
+ 
+
+ align:start position:0%
+published a paper before uh um there's
+no experiment maybe some of you
+
+ align:start position:0%
+no experiment maybe some of you
+ 
+
+ align:start position:0%
+no experiment maybe some of you
+interested but this is the issue I what
+
+ align:start position:0%
+interested but this is the issue I what
+ 
+
+ align:start position:0%
+interested but this is the issue I what
+is the evaporation right I said that the
+
+ align:start position:0%
+is the evaporation right I said that the
+ 
+
+ align:start position:0%
+is the evaporation right I said that the
+uh electron no the modle coming out of
+
+ align:start position:0%
+uh electron no the modle coming out of
+ 
+
+ align:start position:0%
+uh electron no the modle coming out of
+the liquid surface that's like a
+
+ align:start position:0%
+the liquid surface that's like a
+ 
+
+ align:start position:0%
+the liquid surface that's like a
+evaporation uh that's equivalent to Ser
+
+ align:start position:0%
+evaporation uh that's equivalent to Ser
+ 
+
+ align:start position:0%
+evaporation uh that's equivalent to Ser
+emission let's say uh the how about I
+
+ align:start position:0%
+emission let's say uh the how about I
+ 
+
+ align:start position:0%
+emission let's say uh the how about I
+have a vacuum here right I got a liquid
+
+ align:start position:0%
+have a vacuum here right I got a liquid
+ 
+
+ align:start position:0%
+have a vacuum here right I got a liquid
+here and sudden a drop of liquid drop
+
+ align:start position:0%
+here and sudden a drop of liquid drop
+ 
+
+ align:start position:0%
+here and sudden a drop of liquid drop
+into the vacuum C every it suddenly
+
+ align:start position:0%
+into the vacuum C every it suddenly
+ 
+
+ align:start position:0%
+into the vacuum C every it suddenly
+expand is that a corresponding to
+
+ align:start position:0%
+expand is that a corresponding to
+ 
+
+ align:start position:0%
+expand is that a corresponding to
+evaporation and I have a s case where
+
+ align:start position:0%
+evaporation and I have a s case where
+ 
+
+ align:start position:0%
+evaporation and I have a s case where
+I'm comparing this two examples and this
+
+ align:start position:0%
+I'm comparing this two examples and this
+ 
+
+ align:start position:0%
+I'm comparing this two examples and this
+two example is one is a cionic barrier
+
+ align:start position:0%
+two example is one is a cionic barrier
+ 
+
+ align:start position:0%
+two example is one is a cionic barrier
+as everybody before when electron flow
+
+ align:start position:0%
+as everybody before when electron flow
+ 
+
+ align:start position:0%
+as everybody before when electron flow
+this way the low energ electron in this
+
+ align:start position:0%
+this way the low energ electron in this
+ 
+
+ align:start position:0%
+this way the low energ electron in this
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SC the other case I consider this was
+
+ align:start position:0%
+SC the other case I consider this was
+ 
+
+ align:start position:0%
+SC the other case I consider this was
+actually Pap General Physics is what
+
+ align:start position:0%
+actually Pap General Physics is what
+ 
+
+ align:start position:0%
+actually Pap General Physics is what
+about I flow electron this way and
+
+ align:start position:0%
+about I flow electron this way and
+ 
+
+ align:start position:0%
+about I flow electron this way and
+suddenly drop a letter and that mean to
+
+ align:start position:0%
+suddenly drop a letter and that mean to
+ 
+
+ align:start position:0%
+suddenly drop a letter and that mean to
+me is more like I take a drop put the
+
+ align:start position:0%
+me is more like I take a drop put the
+ 
+
+ align:start position:0%
+me is more like I take a drop put the
+vacuum suddenly
+
+ align:start position:0%
+vacuum suddenly
+ 
+
+ align:start position:0%
+vacuum suddenly
+evaporate and this one is more like a
+
+ align:start position:0%
+evaporate and this one is more like a
+ 
+
+ align:start position:0%
+evaporate and this one is more like a
+water surface and the water Mo coming
+
+ align:start position:0%
+water surface and the water Mo coming
+ 
+
+ align:start position:0%
+water surface and the water Mo coming
+out of surface like cool water right so
+
+ align:start position:0%
+out of surface like cool water right so
+ 
+
+ align:start position:0%
+out of surface like cool water right so
+um uh that's a solid state analogy that
+
+ align:start position:0%
+um uh that's a solid state analogy that
+ 
+
+ align:start position:0%
+um uh that's a solid state analogy that
+we're trying to make so what I did is I
+
+ align:start position:0%
+we're trying to make so what I did is I
+ 
+
+ align:start position:0%
+we're trying to make so what I did is I
+did some energy balance analysis
+
+ align:start position:0%
+did some energy balance analysis
+ 
+
+ align:start position:0%
+did some energy balance analysis
+essentially a recharge and
+
+ align:start position:0%
+essentially a recharge and
+ 
+
+ align:start position:0%
+essentially a recharge and
+formula high and you can do you can
+
+ align:start position:0%
+formula high and you can do you can
+ 
+
+ align:start position:0%
+formula high and you can do you can
+assume the two sides has different
+
+ align:start position:0%
+assume the two sides has different
+ 
+
+ align:start position:0%
+assume the two sides has different
+temperature even on the both sides and
+
+ align:start position:0%
+temperature even on the both sides and
+ 
+
+ align:start position:0%
+temperature even on the both sides and
+different C
+
+ align:start position:0%
+different C
+ 
+
+ align:start position:0%
+different C
+potential the real way to do this Sol
+
+ align:start position:0%
+potential the real way to do this Sol
+ 
+
+ align:start position:0%
+potential the real way to do this Sol
+equation very complicated don't how to
+
+ align:start position:0%
+equation very complicated don't how to
+ 
+
+ align:start position:0%
+equation very complicated don't how to
+do it so this actually problem even when
+
+ align:start position:0%
+do it so this actually problem even when
+ 
+
+ align:start position:0%
+do it so this actually problem even when
+I tried to do it took a very very detail
+
+ align:start position:0%
+I tried to do it took a very very detail
+ 
+
+ align:start position:0%
+I tried to do it took a very very detail
+a very hard calulation
+
+ align:start position:0%
+a very hard calulation
+ 
+
+ align:start position:0%
+a very hard calulation
+but when I just do statistic you can do
+
+ align:start position:0%
+but when I just do statistic you can do
+ 
+
+ align:start position:0%
+but when I just do statistic you can do
+your deration no for statistics energy
+
+ align:start position:0%
+your deration no for statistics energy
+ 
+
+ align:start position:0%
+your deration no for statistics energy
+balance current balance at the interface
+
+ align:start position:0%
+balance current balance at the interface
+ 
+
+ align:start position:0%
+balance current balance at the interface
+and what I found is that this is the
+
+ align:start position:0%
+and what I found is that this is the
+ 
+
+ align:start position:0%
+and what I found is that this is the
+electron temp on this side electr one
+
+ align:start position:0%
+electron temp on this side electr one
+ 
+
+ align:start position:0%
+electron temp on this side electr one
+and two just right at the interface it
+
+ align:start position:0%
+and two just right at the interface it
+ 
+
+ align:start position:0%
+and two just right at the interface it
+turn out that when I go down a step
+
+ align:start position:0%
+turn out that when I go down a step
+ 
+
+ align:start position:0%
+turn out that when I go down a step
+there is a amplification Factor this is
+
+ align:start position:0%
+there is a amplification Factor this is
+ 
+
+ align:start position:0%
+there is a amplification Factor this is
+the potential High
+
+ align:start position:0%
+the potential High
+ 
+
+ align:start position:0%
+the potential High
+and this is mean free pass so normally
+
+ align:start position:0%
+and this is mean free pass so normally
+ 
+
+ align:start position:0%
+and this is mean free pass so normally
+this is very small because me
+
+ align:start position:0%
+this is very small because me
+ 
+
+ align:start position:0%
+this is very small because me
+pass just temp drop with one that's
+
+ align:start position:0%
+pass just temp drop with one that's
+ 
+
+ align:start position:0%
+pass just temp drop with one that's
+very but what I saw what I saw
+
+ align:start position:0%
+very but what I saw what I saw
+ 
+
+ align:start position:0%
+very but what I saw what I saw
+interesting is if I have this structure
+
+ align:start position:0%
+interesting is if I have this structure
+ 
+
+ align:start position:0%
+interesting is if I have this structure
+I suddenly like the electron expand
+
+ align:start position:0%
+I suddenly like the electron expand
+ 
+
+ align:start position:0%
+I suddenly like the electron expand
+actually raises temperature or create a
+
+ align:start position:0%
+actually raises temperature or create a
+ 
+
+ align:start position:0%
+actually raises temperature or create a
+large temperature there's an
+
+ align:start position:0%
+large temperature there's an
+ 
+
+ align:start position:0%
+large temperature there's an
+amplification factor I
+
+ align:start position:0%
+amplification factor I
+ 
+
+ align:start position:0%
+amplification factor I
+canfy how much electron temperature draw
+
+ align:start position:0%
+canfy how much electron temperature draw
+ 
+
+ align:start position:0%
+canfy how much electron temperature draw
+at the interface so that's what I call
+
+ align:start position:0%
+at the interface so that's what I call
+ 
+
+ align:start position:0%
+at the interface so that's what I call
+potential amplifi on the other hand of
+
+ align:start position:0%
+potential amplifi on the other hand of
+ 
+
+ align:start position:0%
+potential amplifi on the other hand of
+my thisas structure same analysis didn't
+
+ align:start position:0%
+my thisas structure same analysis didn't
+ 
+
+ align:start position:0%
+my thisas structure same analysis didn't
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+that so so I follow up I said this is
+
+ align:start position:0%
+that so so I follow up I said this is
+ 
+
+ align:start position:0%
+that so so I follow up I said this is
+the board my statistic I did fir
+
+ align:start position:0%
+the board my statistic I did fir
+ 
+
+ align:start position:0%
+the board my statistic I did fir
+statistics and solve some equations and
+
+ align:start position:0%
+statistics and solve some equations and
+ 
+
+ align:start position:0%
+statistics and solve some equations and
+this is the equation this is the
+
+ align:start position:0%
+this is the equation this is the
+ 
+
+ align:start position:0%
+this is the equation this is the
+temperature the interface and you can
+
+ align:start position:0%
+temperature the interface and you can
+ 
+
+ align:start position:0%
+temperature the interface and you can
+say you can actually drive therm just
+
+ align:start position:0%
+say you can actually drive therm just
+ 
+
+ align:start position:0%
+say you can actually drive therm just
+with a tempure G you can grab electron
+
+ align:start position:0%
+with a tempure G you can grab electron
+ 
+
+ align:start position:0%
+with a tempure G you can grab electron
+and phon out
+
+ align:start position:0%
+and phon out
+ 
+
+ align:start position:0%
+and phon out
+of and this is the electron temperature
+
+ align:start position:0%
+of and this is the electron temperature
+ 
+
+ align:start position:0%
+of and this is the electron temperature
+jump at the interface but if you do the
+
+ align:start position:0%
+jump at the interface but if you do the
+ 
+
+ align:start position:0%
+jump at the interface but if you do the
+reverse structure there's no
+
+ align:start position:0%
+reverse structure there's no
+ 
+
+ align:start position:0%
+reverse structure there's no
+discontinuity in the interface so this
+
+ align:start position:0%
+discontinuity in the interface so this
+ 
+
+ align:start position:0%
+discontinuity in the interface so this
+this way s can help the efficiency of
+
+ align:start position:0%
+this way s can help the efficiency of
+ 
+
+ align:start position:0%
+this way s can help the efficiency of
+cooling but uh so far I have not like I
+
+ align:start position:0%
+cooling but uh so far I have not like I
+ 
+
+ align:start position:0%
+cooling but uh so far I have not like I
+said this is just a theory no
+
+ align:start position:0%
+said this is just a theory no
+ 
+
+ align:start position:0%
+said this is just a theory no
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+okay now I want to move on that's just
+
+ align:start position:0%
+okay now I want to move on that's just
+ 
+
+ align:start position:0%
+okay now I want to move on that's just
+a example sometimes it's interesting to
+
+ align:start position:0%
+a example sometimes it's interesting to
+ 
+
+ align:start position:0%
+a example sometimes it's interesting to
+TST and think whether you can have new
+
+ align:start position:0%
+TST and think whether you can have new
+ 
+
+ align:start position:0%
+TST and think whether you can have new
+ideas in this
+
+ align:start position:0%
+ideas in this
+ 
+
+ align:start position:0%
+ideas in this
+F now coming back now we talk about the
+
+ align:start position:0%
+F now coming back now we talk about the
+ 
+
+ align:start position:0%
+F now coming back now we talk about the
+the really the fs and this is the the
+
+ align:start position:0%
+the really the fs and this is the the
+ 
+
+ align:start position:0%
+the really the fs and this is the the
+injunction I just show
+
+ align:start position:0%
+injunction I just show
+ 
+
+ align:start position:0%
+injunction I just show
+and the saturation current sometimes
+
+ align:start position:0%
+and the saturation current sometimes
+ 
+
+ align:start position:0%
+and the saturation current sometimes
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+detector and uh now uh we have a photon
+
+ align:start position:0%
+detector and uh now uh we have a photon
+ 
+
+ align:start position:0%
+detector and uh now uh we have a photon
+comes in gener electron over here so if
+
+ align:start position:0%
+comes in gener electron over here so if
+ 
+
+ align:start position:0%
+comes in gener electron over here so if
+the photon energy is larger than the
+
+ align:start position:0%
+the photon energy is larger than the
+ 
+
+ align:start position:0%
+the photon energy is larger than the
+bank Gap the bank Gap is always the same
+
+ align:start position:0%
+bank Gap the bank Gap is always the same
+ 
+
+ align:start position:0%
+bank Gap the bank Gap is always the same
+everywhere Bank Gap is the same so if
+
+ align:start position:0%
+everywhere Bank Gap is the same so if
+ 
+
+ align:start position:0%
+everywhere Bank Gap is the same so if
+the F energy is larger than b you
+
+ align:start position:0%
+the F energy is larger than b you
+ 
+
+ align:start position:0%
+the F energy is larger than b you
+generate lift the one electron from the
+
+ align:start position:0%
+generate lift the one electron from the
+ 
+
+ align:start position:0%
+generate lift the one electron from the
+valance band to the conduction B right
+
+ align:start position:0%
+valance band to the conduction B right
+ 
+
+ align:start position:0%
+valance band to the conduction B right
+and this could happen anywhere in the
+
+ align:start position:0%
+and this could happen anywhere in the
+ 
+
+ align:start position:0%
+and this could happen anywhere in the
+device that depends on how where Fon is
+
+ align:start position:0%
+device that depends on how where Fon is
+ 
+
+ align:start position:0%
+device that depends on how where Fon is
+abor we'll talk about that later right
+
+ align:start position:0%
+abor we'll talk about that later right
+ 
+
+ align:start position:0%
+abor we'll talk about that later right
+so what I'm drawing just okay my Fon
+
+ align:start position:0%
+so what I'm drawing just okay my Fon
+ 
+
+ align:start position:0%
+so what I'm drawing just okay my Fon
+happen to be absorbed within the space
+
+ align:start position:0%
+happen to be absorbed within the space
+ 
+
+ align:start position:0%
+happen to be absorbed within the space
+charge region then the
+
+ align:start position:0%
+charge region then the
+ 
+
+ align:start position:0%
+charge region then the
+electron is generated within space
+
+ align:start position:0%
+electron is generated within space
+ 
+
+ align:start position:0%
+electron is generated within space
+charge don't
+
+ align:start position:0%
+charge don't
+ 
+
+ align:start position:0%
+charge don't
+for right now what happens after this
+
+ align:start position:0%
+for right now what happens after this
+ 
+
+ align:start position:0%
+for right now what happens after this
+generation of course they were they have
+
+ align:start position:0%
+generation of course they were they have
+ 
+
+ align:start position:0%
+generation of course they were they have
+tendency Rec
+
+ align:start position:0%
+tendency Rec
+ 
+
+ align:start position:0%
+tendency Rec
+combine right and if you did Rec combine
+
+ align:start position:0%
+combine right and if you did Rec combine
+ 
+
+ align:start position:0%
+combine right and if you did Rec combine
+your photo cell is affiliate you don't
+
+ align:start position:0%
+your photo cell is affiliate you don't
+ 
+
+ align:start position:0%
+your photo cell is affiliate you don't
+want them to rec combine you want to
+
+ align:start position:0%
+want them to rec combine you want to
+ 
+
+ align:start position:0%
+want them to rec combine you want to
+separate
+
+ align:start position:0%
+separate
+ 
+
+ align:start position:0%
+separate
+it and now if Junction if in the space
+
+ align:start position:0%
+it and now if Junction if in the space
+ 
+
+ align:start position:0%
+it and now if Junction if in the space
+charge there's
+
+ align:start position:0%
+charge there's
+ 
+
+ align:start position:0%
+charge there's
+one because electron now there's a
+
+ align:start position:0%
+one because electron now there's a
+ 
+
+ align:start position:0%
+one because electron now there's a
+electric field inside so electron wants
+
+ align:start position:0%
+electric field inside so electron wants
+ 
+
+ align:start position:0%
+electric field inside so electron wants
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+go lower energy this way whole is the
+
+ align:start position:0%
+go lower energy this way whole is the
+ 
+
+ align:start position:0%
+go lower energy this way whole is the
+higher energy is the whole positive is
+
+ align:start position:0%
+higher energy is the whole positive is
+ 
+
+ align:start position:0%
+higher energy is the whole positive is
+the higher energy electron low say
+
+ align:start position:0%
+the higher energy electron low say
+ 
+
+ align:start position:0%
+the higher energy electron low say
+higher energy so go this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+posi okay just go down the potential
+
+ align:start position:0%
+posi okay just go down the potential
+ 
+
+ align:start position:0%
+posi okay just go down the potential
+H this is the potential H this is
+
+ align:start position:0%
+H this is the potential H this is
+ 
+
+ align:start position:0%
+H this is the potential H this is
+potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+that's and this Lal tenden so now you
+
+ align:start position:0%
+that's and this Lal tenden so now you
+ 
+
+ align:start position:0%
+that's and this Lal tenden so now you
+got more electron this side then I say
+
+ align:start position:0%
+got more electron this side then I say
+ 
+
+ align:start position:0%
+got more electron this side then I say
+uh uh uh in normally equ no voltage
+
+ align:start position:0%
+uh uh uh in normally equ no voltage
+ 
+
+ align:start position:0%
+uh uh uh in normally equ no voltage
+right now you accumulate more electron
+
+ align:start position:0%
+right now you accumulate more electron
+ 
+
+ align:start position:0%
+right now you accumulate more electron
+this side accumulate more hole so you
+
+ align:start position:0%
+this side accumulate more hole so you
+ 
+
+ align:start position:0%
+this side accumulate more hole so you
+generate
+
+ align:start position:0%
+generate
+ 
+
+ align:start position:0%
+generate
+volt
+
+ align:start position:0%
+volt
+ 
+
+ align:start position:0%
+volt
+okay and once you generate voltage this
+
+ align:start position:0%
+okay and once you generate voltage this
+ 
+
+ align:start position:0%
+okay and once you generate voltage this
+voltage will drive your
+
+ align:start position:0%
+voltage will drive your
+ 
+
+ align:start position:0%
+voltage will drive your
+di right just like on this side you have
+
+ align:start position:0%
+di right just like on this side you have
+ 
+
+ align:start position:0%
+di right just like on this side you have
+volage difference you'll have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d so now if I have light comes in this
+
+ align:start position:0%
+d so now if I have light comes in this
+ 
+
+ align:start position:0%
+d so now if I have light comes in this
+is the current the electron ho current
+
+ align:start position:0%
+is the current the electron ho current
+ 
+
+ align:start position:0%
+is the current the electron ho current
+do the absorption of full time and now
+
+ align:start position:0%
+do the absorption of full time and now
+ 
+
+ align:start position:0%
+do the absorption of full time and now
+once I bu the voltage this is the
+
+ align:start position:0%
+once I bu the voltage this is the
+ 
+
+ align:start position:0%
+once I bu the voltage this is the
+current the forward that balance
+
+ align:start position:0%
+current the forward that balance
+ 
+
+ align:start position:0%
+current the forward that balance
+it right this is this is now when I have
+
+ align:start position:0%
+it right this is this is now when I have
+ 
+
+ align:start position:0%
+it right this is this is now when I have
+voltage I drive the DI and this is where
+
+ align:start position:0%
+voltage I drive the DI and this is where
+ 
+
+ align:start position:0%
+voltage I drive the DI and this is where
+I have electron generation the counter
+
+ align:start position:0%
+I have electron generation the counter
+ 
+
+ align:start position:0%
+I have electron generation the counter
+going this way and of course in a solar
+
+ align:start position:0%
+going this way and of course in a solar
+ 
+
+ align:start position:0%
+going this way and of course in a solar
+Cale I want to go this way I don't want
+
+ align:start position:0%
+Cale I want to go this way I don't want
+ 
+
+ align:start position:0%
+Cale I want to go this way I don't want
+I I want right I want this less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay so that's if you understand
+
+ align:start position:0%
+this okay so that's if you understand
+ 
+
+ align:start position:0%
+this okay so that's if you understand
+the DI that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a okay
+
+ align:start position:0%
+a okay
+ 
+
+ align:start position:0%
+a okay
+and you can so this one if you I want
+
+ align:start position:0%
+and you can so this one if you I want
+ 
+
+ align:start position:0%
+and you can so this one if you I want
+call the short C short circuit current
+
+ align:start position:0%
+call the short C short circuit current
+ 
+
+ align:start position:0%
+call the short C short circuit current
+if the Short Circuit the voltage
+
+ align:start position:0%
+if the Short Circuit the voltage
+ 
+
+ align:start position:0%
+if the Short Circuit the voltage
+difference is zero right you
+
+ align:start position:0%
+difference is zero right you
+ 
+
+ align:start position:0%
+difference is zero right you
+surely this there's no no resistance
+
+ align:start position:0%
+surely this there's no no resistance
+ 
+
+ align:start position:0%
+surely this there's no no resistance
+then this has to equal this no voltage
+
+ align:start position:0%
+then this has to equal this no voltage
+ 
+
+ align:start position:0%
+then this has to equal this no voltage
+want that's
+
+ align:start position:0%
+want that's
+ 
+
+ align:start position:0%
+want that's
+short short Circle short Circle both for
+
+ align:start position:0%
+short short Circle short Circle both for
+ 
+
+ align:start position:0%
+short short Circle short Circle both for
+zero that's your JL is your short
+
+ align:start position:0%
+zero that's your JL is your short
+ 
+
+ align:start position:0%
+zero that's your JL is your short
+CC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay now I'm going to with that
+
+ align:start position:0%
+right okay now I'm going to with that
+ 
+
+ align:start position:0%
+right okay now I'm going to with that
+starting from there the rest is simple
+
+ align:start position:0%
+starting from there the rest is simple
+ 
+
+ align:start position:0%
+starting from there the rest is simple
+just MTH I can see what's my open
+
+ align:start position:0%
+just MTH I can see what's my open
+ 
+
+ align:start position:0%
+just MTH I can see what's my open
+circular voltage and my open circular
+
+ align:start position:0%
+circular voltage and my open circular
+ 
+
+ align:start position:0%
+circular voltage and my open circular
+voltage is just to say there's zero
+
+ align:start position:0%
+voltage is just to say there's zero
+ 
+
+ align:start position:0%
+voltage is just to say there's zero
+current so if I set this side zero I
+
+ align:start position:0%
+current so if I set this side zero I
+ 
+
+ align:start position:0%
+current so if I set this side zero I
+find what's the open circle voltage
+
+ align:start position:0%
+find what's the open circle voltage
+ 
+
+ align:start position:0%
+find what's the open circle voltage
+the open circuit voltage and you can
+
+ align:start position:0%
+the open circuit voltage and you can
+ 
+
+ align:start position:0%
+the open circuit voltage and you can
+further simplify because we know GS to
+
+ align:start position:0%
+further simplify because we know GS to
+ 
+
+ align:start position:0%
+further simplify because we know GS to
+that c right look at this called do
+
+ align:start position:0%
+that c right look at this called do
+ 
+
+ align:start position:0%
+that c right look at this called do
+current or saturation
+
+ align:start position:0%
+current or saturation
+ 
+
+ align:start position:0%
+current or saturation
+current and I the high open circular
+
+ align:start position:0%
+current and I the high open circular
+ 
+
+ align:start position:0%
+current and I the high open circular
+voltage what do you do smaller is better
+
+ align:start position:0%
+voltage what do you do smaller is better
+ 
+
+ align:start position:0%
+voltage what do you do smaller is better
+right J smaller is better you look at it
+
+ align:start position:0%
+right J smaller is better you look at it
+ 
+
+ align:start position:0%
+right J smaller is better you look at it
+smaller j i open
+
+ align:start position:0%
+smaller j i open
+ 
+
+ align:start position:0%
+smaller j i open
+circle
+
+ align:start position:0%
+circle
+ 
+
+ align:start position:0%
+circle
+right so JS power
+
+ align:start position:0%
+right so JS power
+ 
+
+ align:start position:0%
+right so JS power
+reculation time is longer JS
+
+ align:start position:0%
+reculation time is longer JS
+ 
+
+ align:start position:0%
+reculation time is longer JS
+smaller right so I don't want the
+
+ align:start position:0%
+smaller right so I don't want the
+ 
+
+ align:start position:0%
+smaller right so I don't want the
+recombination I want the long lifetime
+
+ align:start position:0%
+recombination I want the long lifetime
+ 
+
+ align:start position:0%
+recombination I want the long lifetime
+for the electron basically I want long
+
+ align:start position:0%
+for the electron basically I want long
+ 
+
+ align:start position:0%
+for the electron basically I want long
+life so I can exract
+
+ align:start position:0%
+life so I can exract
+ 
+
+ align:start position:0%
+life so I can exract
+out okay and you put like in the JSA
+
+ align:start position:0%
+out okay and you put like in the JSA
+ 
+
+ align:start position:0%
+out okay and you put like in the JSA
+related to all
+
+ align:start position:0%
+related to all
+ 
+
+ align:start position:0%
+related to all
+diffusivity comilation time wri down out
+
+ align:start position:0%
+diffusivity comilation time wri down out
+ 
+
+ align:start position:0%
+diffusivity comilation time wri down out
+here basically
+
+ align:start position:0%
+here basically
+ 
+
+ align:start position:0%
+here basically
+to the end you approxim drop this one
+
+ align:start position:0%
+to the end you approxim drop this one
+ 
+
+ align:start position:0%
+to the end you approxim drop this one
+that's what you get that's just
+
+ align:start position:0%
+that's what you get that's just
+ 
+
+ align:start position:0%
+that's what you get that's just
+matics on
+
+ align:start position:0%
+matics on
+ 
+
+ align:start position:0%
+matics on
+this now of course open circuit is
+
+ align:start position:0%
+this now of course open circuit is
+ 
+
+ align:start position:0%
+this now of course open circuit is
+useless because there's no power output
+
+ align:start position:0%
+useless because there's no power output
+ 
+
+ align:start position:0%
+useless because there's no power output
+in real operation we always have a load
+
+ align:start position:0%
+in real operation we always have a load
+ 
+
+ align:start position:0%
+in real operation we always have a load
+we have car flowing so uh when we have a
+
+ align:start position:0%
+we have car flowing so uh when we have a
+ 
+
+ align:start position:0%
+we have car flowing so uh when we have a
+car
+
+ align:start position:0%
+car
+ 
+
+ align:start position:0%
+car
+flowing uh uh uh Power and so but before
+
+ align:start position:0%
+flowing uh uh uh Power and so but before
+ 
+
+ align:start position:0%
+flowing uh uh uh Power and so but before
+I do that I want to show you if you draw
+
+ align:start position:0%
+I do that I want to show you if you draw
+ 
+
+ align:start position:0%
+I do that I want to show you if you draw
+this C voltage so this is your short
+
+ align:start position:0%
+this C voltage so this is your short
+ 
+
+ align:start position:0%
+this C voltage so this is your short
+circuit voltage Z short Circ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current right when current is zero open
+
+ align:start position:0%
+current right when current is zero open
+ 
+
+ align:start position:0%
+current right when current is zero open
+Circ okay so it's more like you shifting
+
+ align:start position:0%
+Circ okay so it's more like you shifting
+ 
+
+ align:start position:0%
+Circ okay so it's more like you shifting
+di parall down this if if you don't have
+
+ align:start position:0%
+di parall down this if if you don't have
+ 
+
+ align:start position:0%
+di parall down this if if you don't have
+if you don't have a light
+
+ align:start position:0%
+if you don't have a light
+ 
+
+ align:start position:0%
+if you don't have a light
+illumination it's a DI equation right
+
+ align:start position:0%
+illumination it's a DI equation right
+ 
+
+ align:start position:0%
+illumination it's a DI equation right
+that's a diation you don't have this
+
+ align:start position:0%
+that's a diation you don't have this
+ 
+
+ align:start position:0%
+that's a diation you don't have this
+part sh that cve cve to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+okay and uh of course you can you can
+
+ align:start position:0%
+okay and uh of course you can you can
+ 
+
+ align:start position:0%
+okay and uh of course you can you can
+look at this the power output is voltage
+
+ align:start position:0%
+look at this the power output is voltage
+ 
+
+ align:start position:0%
+look at this the power output is voltage
+times current so
+
+ align:start position:0%
+times current so
+ 
+
+ align:start position:0%
+times current so
+somewhere your voltage that's this squ
+
+ align:start position:0%
+somewhere your voltage that's this squ
+ 
+
+ align:start position:0%
+somewhere your voltage that's this squ
+depends on which point your op
+
+ align:start position:0%
+depends on which point your op
+ 
+
+ align:start position:0%
+depends on which point your op
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+maim and that's how you optimize you you
+
+ align:start position:0%
+maim and that's how you optimize you you
+ 
+
+ align:start position:0%
+maim and that's how you optimize you you
+change your load
+
+ align:start position:0%
+change your load
+ 
+
+ align:start position:0%
+change your load
+resistance okay so that you can control
+
+ align:start position:0%
+resistance okay so that you can control
+ 
+
+ align:start position:0%
+resistance okay so that you can control
+the current and the voltage by changing
+
+ align:start position:0%
+the current and the voltage by changing
+ 
+
+ align:start position:0%
+the current and the voltage by changing
+external L resistance so that's a low me
+
+ align:start position:0%
+external L resistance so that's a low me
+ 
+
+ align:start position:0%
+external L resistance so that's a low me
+you do that for ther elrics you do that
+
+ align:start position:0%
+you do that for ther elrics you do that
+ 
+
+ align:start position:0%
+you do that for ther elrics you do that
+for Sol cells or so you need to optimize
+
+ align:start position:0%
+for Sol cells or so you need to optimize
+ 
+
+ align:start position:0%
+for Sol cells or so you need to optimize
+so some people just design their circuit
+
+ align:start position:0%
+so some people just design their circuit
+ 
+
+ align:start position:0%
+so some people just design their circuit
+to optimize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and very of people don't dra this way
+
+ align:start position:0%
+and very of people don't dra this way
+ 
+
+ align:start position:0%
+and very of people don't dra this way
+just reverse it for convenience so that
+
+ align:start position:0%
+just reverse it for convenience so that
+ 
+
+ align:start position:0%
+just reverse it for convenience so that
+will be another way to draw but that's
+
+ align:start position:0%
+will be another way to draw but that's
+ 
+
+ align:start position:0%
+will be another way to draw but that's
+the real one is actually to be on the
+
+ align:start position:0%
+the real one is actually to be on the
+ 
+
+ align:start position:0%
+the real one is actually to be on the
+side
+
+ align:start position:0%
+side
+ 
+
+ align:start position:0%
+side
+okay now we can uh go to see maximum
+
+ align:start position:0%
+okay now we can uh go to see maximum
+ 
+
+ align:start position:0%
+okay now we can uh go to see maximum
+power when the power output is maximize
+
+ align:start position:0%
+power when the power output is maximize
+ 
+
+ align:start position:0%
+power when the power output is maximize
+is the current times voltage that's the
+
+ align:start position:0%
+is the current times voltage that's the
+ 
+
+ align:start position:0%
+is the current times voltage that's the
+power right so you just take a
+
+ align:start position:0%
+power right so you just take a
+ 
+
+ align:start position:0%
+power right so you just take a
+derivative of your voltage and say when
+
+ align:start position:0%
+derivative of your voltage and say when
+ 
+
+ align:start position:0%
+derivative of your voltage and say when
+it's maximiz when you take
+
+ align:start position:0%
+it's maximiz when you take
+ 
+
+ align:start position:0%
+it's maximiz when you take
+derivative physically what you do is I'm
+
+ align:start position:0%
+derivative physically what you do is I'm
+ 
+
+ align:start position:0%
+derivative physically what you do is I'm
+changing my external load to find out
+
+ align:start position:0%
+changing my external load to find out
+ 
+
+ align:start position:0%
+changing my external load to find out
+where is the optimal volage so that
+
+ align:start position:0%
+where is the optimal volage so that
+ 
+
+ align:start position:0%
+where is the optimal volage so that
+power is
+
+ align:start position:0%
+power is
+ 
+
+ align:start position:0%
+power is
+maximized so so that if you take this
+
+ align:start position:0%
+maximized so so that if you take this
+ 
+
+ align:start position:0%
+maximized so so that if you take this
+derivative you'll find out where is the
+
+ align:start position:0%
+derivative you'll find out where is the
+ 
+
+ align:start position:0%
+derivative you'll find out where is the
+optimum current where is the optimal
+
+ align:start position:0%
+optimum current where is the optimal
+ 
+
+ align:start position:0%
+optimum current where is the optimal
+voltage
+
+ align:start position:0%
+voltage
+ 
+
+ align:start position:0%
+voltage
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+uh again see this is just mathematic
+
+ align:start position:0%
+uh again see this is just mathematic
+ 
+
+ align:start position:0%
+uh again see this is just mathematic
+detail not important but very often in
+
+ align:start position:0%
+detail not important but very often in
+ 
+
+ align:start position:0%
+detail not important but very often in
+the terminology people say what's your
+
+ align:start position:0%
+the terminology people say what's your
+ 
+
+ align:start position:0%
+the terminology people say what's your
+fail
+
+ align:start position:0%
+fail
+ 
+
+ align:start position:0%
+fail
+Factor what is that so this is the
+
+ align:start position:0%
+Factor what is that so this is the
+ 
+
+ align:start position:0%
+Factor what is that so this is the
+rectangular this is where you optimize
+
+ align:start position:0%
+rectangular this is where you optimize
+ 
+
+ align:start position:0%
+rectangular this is where you optimize
+you run your uh Optimum current voltage
+
+ align:start position:0%
+you run your uh Optimum current voltage
+ 
+
+ align:start position:0%
+you run your uh Optimum current voltage
+point right so that's the actual maximum
+
+ align:start position:0%
+point right so that's the actual maximum
+ 
+
+ align:start position:0%
+point right so that's the actual maximum
+power you you have and if you look at if
+
+ align:start position:0%
+power you you have and if you look at if
+ 
+
+ align:start position:0%
+power you you have and if you look at if
+you draw another
+
+ align:start position:0%
+you draw another
+ 
+
+ align:start position:0%
+you draw another
+rectangle where you draw the this set up
+
+ align:start position:0%
+rectangle where you draw the this set up
+ 
+
+ align:start position:0%
+rectangle where you draw the this set up
+uh the the uh uh short circular current
+
+ align:start position:0%
+uh the the uh uh short circular current
+ 
+
+ align:start position:0%
+uh the the uh uh short circular current
+and open Circ voltage you to another
+
+ align:start position:0%
+and open Circ voltage you to another
+ 
+
+ align:start position:0%
+and open Circ voltage you to another
+rectangle right this ratio of this Acra
+
+ align:start position:0%
+rectangle right this ratio of this Acra
+ 
+
+ align:start position:0%
+rectangle right this ratio of this Acra
+power divided by the outer rectangle
+
+ align:start position:0%
+power divided by the outer rectangle
+ 
+
+ align:start position:0%
+power divided by the outer rectangle
+that's your fi factor and you want to
+
+ align:start position:0%
+that's your fi factor and you want to
+ 
+
+ align:start position:0%
+that's your fi factor and you want to
+feel as much as you can you can say to
+
+ align:start position:0%
+feel as much as you can you can say to
+ 
+
+ align:start position:0%
+feel as much as you can you can say to
+get the maximum
+
+ align:start position:0%
+get the maximum
+ 
+
+ align:start position:0%
+get the maximum
+power okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's go to Source term Source this
+
+ align:start position:0%
+now let's go to Source term Source this
+ 
+
+ align:start position:0%
+now let's go to Source term Source this
+is a electron ho generation right so I
+
+ align:start position:0%
+is a electron ho generation right so I
+ 
+
+ align:start position:0%
+is a electron ho generation right so I
+have the radiation coming in only
+
+ align:start position:0%
+have the radiation coming in only
+ 
+
+ align:start position:0%
+have the radiation coming in only
+electrons photons with energy larger
+
+ align:start position:0%
+electrons photons with energy larger
+ 
+
+ align:start position:0%
+electrons photons with energy larger
+than Bap can generate
+
+ align:start position:0%
+than Bap can generate
+ 
+
+ align:start position:0%
+than Bap can generate
+electon so uh and also this let's
+
+ align:start position:0%
+electon so uh and also this let's
+ 
+
+ align:start position:0%
+electon so uh and also this let's
+suppose this is body that's Tre the sign
+
+ align:start position:0%
+suppose this is body that's Tre the sign
+ 
+
+ align:start position:0%
+suppose this is body that's Tre the sign
+as a
+
+ align:start position:0%
+as a
+ 
+
+ align:start position:0%
+as a
+body okay so the solar radiation come
+
+ align:start position:0%
+body okay so the solar radiation come
+ 
+
+ align:start position:0%
+body okay so the solar radiation come
+from s and this is the fraction of solar
+
+ align:start position:0%
+from s and this is the fraction of solar
+ 
+
+ align:start position:0%
+from s and this is the fraction of solar
+radiation actually so you have to look
+
+ align:start position:0%
+radiation actually so you have to look
+ 
+
+ align:start position:0%
+radiation actually so you have to look
+at the distance the fraction of solar
+
+ align:start position:0%
+at the distance the fraction of solar
+ 
+
+ align:start position:0%
+at the distance the fraction of solar
+radiation black body of the sign
+
+ align:start position:0%
+radiation black body of the sign
+ 
+
+ align:start position:0%
+radiation black body of the sign
+58 kin you know it's not just a close
+
+ align:start position:0%
+58 kin you know it's not just a close
+ 
+
+ align:start position:0%
+58 kin you know it's not just a close
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+500 of C right it's verify diver diluted
+
+ align:start position:0%
+500 of C right it's verify diver diluted
+ 
+
+ align:start position:0%
+500 of C right it's verify diver diluted
+so that's this
+
+ align:start position:0%
+so that's this
+ 
+
+ align:start position:0%
+so that's this
+fraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radiation but it's not the radiation
+
+ align:start position:0%
+radiation but it's not the radiation
+ 
+
+ align:start position:0%
+radiation but it's not the radiation
+intensity right it's the number of
+
+ align:start position:0%
+intensity right it's the number of
+ 
+
+ align:start position:0%
+intensity right it's the number of
+photons because each
+
+ align:start position:0%
+photons because each
+ 
+
+ align:start position:0%
+photons because each
+Photon generate one pair of
+
+ align:start position:0%
+Photon generate one pair of
+ 
+
+ align:start position:0%
+Photon generate one pair of
+electron so I'm looking at the energy
+
+ align:start position:0%
+electron so I'm looking at the energy
+ 
+
+ align:start position:0%
+electron so I'm looking at the energy
+because this is the energy that's the
+
+ align:start position:0%
+because this is the energy that's the
+ 
+
+ align:start position:0%
+because this is the energy that's the
+energy of per phot so I divide that
+
+ align:start position:0%
+energy of per phot so I divide that
+ 
+
+ align:start position:0%
+energy of per phot so I divide that
+that's the of photons
+
+ align:start position:0%
+that's the of photons
+ 
+
+ align:start position:0%
+that's the of photons
+coming it's not the flux of energy flux
+
+ align:start position:0%
+coming it's not the flux of energy flux
+ 
+
+ align:start position:0%
+coming it's not the flux of energy flux
+of photon coming
+
+ align:start position:0%
+of photon coming
+ 
+
+ align:start position:0%
+of photon coming
+toward and this is reflectivity I assume
+
+ align:start position:0%
+toward and this is reflectivity I assume
+ 
+
+ align:start position:0%
+toward and this is reflectivity I assume
+that a getting in the cell is absorb the
+
+ align:start position:0%
+that a getting in the cell is absorb the
+ 
+
+ align:start position:0%
+that a getting in the cell is absorb the
+gener electr that's of course
+
+ align:start position:0%
+gener electr that's of course
+ 
+
+ align:start position:0%
+gener electr that's of course
+idealization you got different losses
+
+ align:start position:0%
+idealization you got different losses
+ 
+
+ align:start position:0%
+idealization you got different losses
+this is best case and of course the max
+
+ align:start position:0%
+this is best case and of course the max
+ 
+
+ align:start position:0%
+this is best case and of course the max
+best there no refle that's
+
+ align:start position:0%
+best there no refle that's
+ 
+
+ align:start position:0%
+best there no refle that's
+one okay so this is a source
+
+ align:start position:0%
+one okay so this is a source
+ 
+
+ align:start position:0%
+one okay so this is a source
+term and uh the good thing is the source
+
+ align:start position:0%
+term and uh the good thing is the source
+ 
+
+ align:start position:0%
+term and uh the good thing is the source
+term depends on only the temperature if
+
+ align:start position:0%
+term depends on only the temperature if
+ 
+
+ align:start position:0%
+term depends on only the temperature if
+you idealize depends only on the
+
+ align:start position:0%
+you idealize depends only on the
+ 
+
+ align:start position:0%
+you idealize depends only on the
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+of the source
+
+ align:start position:0%
+of the source
+ 
+
+ align:start position:0%
+of the source
+right and when I come the
+
+ align:start position:0%
+right and when I come the
+ 
+
+ align:start position:0%
+right and when I come the
+efficiency this is the energy of the
+
+ align:start position:0%
+efficiency this is the energy of the
+ 
+
+ align:start position:0%
+efficiency this is the energy of the
+photon coming towards
+
+ align:start position:0%
+photon coming towards
+ 
+
+ align:start position:0%
+photon coming towards
+C and this is the power so of course I
+
+ align:start position:0%
+C and this is the power so of course I
+ 
+
+ align:start position:0%
+C and this is the power so of course I
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+maximize efficiency everybody wants to
+
+ align:start position:0%
+maximize efficiency everybody wants to
+ 
+
+ align:start position:0%
+maximize efficiency everybody wants to
+maximiz and then the question is what's
+
+ align:start position:0%
+maximiz and then the question is what's
+ 
+
+ align:start position:0%
+maximiz and then the question is what's
+the maximum what's what how much you can
+
+ align:start position:0%
+the maximum what's what how much you can
+ 
+
+ align:start position:0%
+the maximum what's what how much you can
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+right second L first the solar cell is
+
+ align:start position:0%
+right second L first the solar cell is
+ 
+
+ align:start position:0%
+right second L first the solar cell is
+limited by second low col you can always
+
+ align:start position:0%
+limited by second low col you can always
+ 
+
+ align:start position:0%
+limited by second low col you can always
+say very safe the maximum efficiency you
+
+ align:start position:0%
+say very safe the maximum efficiency you
+ 
+
+ align:start position:0%
+say very safe the maximum efficiency you
+can get is a heat engine between sand
+
+ align:start position:0%
+can get is a heat engine between sand
+ 
+
+ align:start position:0%
+can get is a heat engine between sand
+and Earth so TC is 300 K T is the
+
+ align:start position:0%
+and Earth so TC is 300 K T is the
+ 
+
+ align:start position:0%
+and Earth so TC is 300 K T is the
+58 so that's that's an
+
+ align:start position:0%
+58 so that's that's an
+ 
+
+ align:start position:0%
+58 so that's that's an
+upper upper can't
+
+ align:start position:0%
+upper upper can't
+ 
+
+ align:start position:0%
+upper upper can't
+get yes I'm just curious what the way
+
+ align:start position:0%
+get yes I'm just curious what the way
+ 
+
+ align:start position:0%
+get yes I'm just curious what the way
+the picture you have on that slide so
+
+ align:start position:0%
+the picture you have on that slide so
+ 
+
+ align:start position:0%
+the picture you have on that slide so
+so it's it's actually inst on the P type
+
+ align:start position:0%
+so it's it's actually inst on the P type
+ 
+
+ align:start position:0%
+so it's it's actually inst on the P type
+and then only want to hit the the space
+
+ align:start position:0%
+and then only want to hit the the space
+ 
+
+ align:start position:0%
+and then only want to hit the the space
+Char
+
+ align:start position:0%
+Char
+ 
+
+ align:start position:0%
+Char
+reg so okay so the the full could be
+
+ align:start position:0%
+reg so okay so the the full could be
+ 
+
+ align:start position:0%
+reg so okay so the the full could be
+absorbed along the UN absorb here so
+
+ align:start position:0%
+absorbed along the UN absorb here so
+ 
+
+ align:start position:0%
+absorbed along the UN absorb here so
+some of them penetrate right yeah
+
+ align:start position:0%
+some of them penetrate right yeah
+ 
+
+ align:start position:0%
+some of them penetrate right yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+Char they have less probability go to
+
+ align:start position:0%
+Char they have less probability go to
+ 
+
+ align:start position:0%
+Char they have less probability go to
+the other side electron they diffuse you
+
+ align:start position:0%
+the other side electron they diffuse you
+ 
+
+ align:start position:0%
+the other side electron they diffuse you
+still diffuse there
+
+ align:start position:0%
+still diffuse there
+ 
+
+ align:start position:0%
+still diffuse there
+Fusion just to take a more the chance of
+
+ align:start position:0%
+Fusion just to take a more the chance of
+ 
+
+ align:start position:0%
+Fusion just to take a more the chance of
+getting there is less so that's why you
+
+ align:start position:0%
+getting there is less so that's why you
+ 
+
+ align:start position:0%
+getting there is less so that's why you
+want it that way and not
+
+ align:start position:0%
+want it that way and not
+ 
+
+ align:start position:0%
+want it that way and not
+like like you see how that is
+
+ align:start position:0%
+like like you see how that is
+ 
+
+ align:start position:0%
+like like you see how that is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+like uhhuh so so so so you want to have
+
+ align:start position:0%
+like uhhuh so so so so you want to have
+ 
+
+ align:start position:0%
+like uhhuh so so so so you want to have
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+longer potential field Drive the
+
+ align:start position:0%
+longer potential field Drive the
+ 
+
+ align:start position:0%
+longer potential field Drive the
+actually use the field right I'm there's
+
+ align:start position:0%
+actually use the field right I'm there's
+ 
+
+ align:start position:0%
+actually use the field right I'm there's
+a picture right there the being thin and
+
+ align:start position:0%
+a picture right there the being thin and
+ 
+
+ align:start position:0%
+a picture right there the being thin and
+flat
+
+ align:start position:0%
+flat
+ 
+
+ align:start position:0%
+flat
+uh really th PN of course the good thing
+
+ align:start position:0%
+uh really th PN of course the good thing
+ 
+
+ align:start position:0%
+uh really th PN of course the good thing
+is your electrod is very
+
+ align:start position:0%
+is your electrod is very
+ 
+
+ align:start position:0%
+is your electrod is very
+close you can get to the two elect but
+
+ align:start position:0%
+close you can get to the two elect but
+ 
+
+ align:start position:0%
+close you can get to the two elect but
+your full not get AB so this is another
+
+ align:start position:0%
+your full not get AB so this is another
+ 
+
+ align:start position:0%
+your full not get AB so this is another
+that we going to talk that's your your
+
+ align:start position:0%
+that we going to talk that's your your
+ 
+
+ align:start position:0%
+that we going to talk that's your your
+battle your
+
+ align:start position:0%
+battle your
+ 
+
+ align:start position:0%
+battle your
+s you want
+
+ align:start position:0%
+s you want
+ 
+
+ align:start position:0%
+s you want
+get two you want to get the charge to
+
+ align:start position:0%
+get two you want to get the charge to
+ 
+
+ align:start position:0%
+get two you want to get the charge to
+the electr before they Rec combine one
+
+ align:start position:0%
+the electr before they Rec combine one
+ 
+
+ align:start position:0%
+the electr before they Rec combine one
+want Center the other one
+
+ align:start position:0%
+want Center the other one
+ 
+
+ align:start position:0%
+want Center the other one
+Zer this is essentially the same people
+
+ align:start position:0%
+Zer this is essentially the same people
+ 
+
+ align:start position:0%
+Zer this is essentially the same people
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+SW
+
+ align:start position:0%
+SW
+ 
+
+ align:start position:0%
+SW
+okay but the question we want to ask is
+
+ align:start position:0%
+okay but the question we want to ask is
+ 
+
+ align:start position:0%
+okay but the question we want to ask is
+what's the maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible okay what's the maximum
+
+ align:start position:0%
+possible okay what's the maximum
+ 
+
+ align:start position:0%
+possible okay what's the maximum
+possible and this one anybody to solar
+
+ align:start position:0%
+possible and this one anybody to solar
+ 
+
+ align:start position:0%
+possible and this one anybody to solar
+cell the first paper you read you should
+
+ align:start position:0%
+cell the first paper you read you should
+ 
+
+ align:start position:0%
+cell the first paper you read you should
+read is this Pap like shop and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sh okay that's what
+
+ align:start position:0%
+Sh okay that's what
+ 
+
+ align:start position:0%
+Sh okay that's what
+Sher limit uh we discuss the
+
+ align:start position:0%
+Sher limit uh we discuss the
+ 
+
+ align:start position:0%
+Sher limit uh we discuss the
+next and uh of course the real di right
+
+ align:start position:0%
+next and uh of course the real di right
+ 
+
+ align:start position:0%
+next and uh of course the real di right
+the real di is hard to get what's
+
+ align:start position:0%
+the real di is hard to get what's
+ 
+
+ align:start position:0%
+the real di is hard to get what's
+maximum the saturation depends on the
+
+ align:start position:0%
+maximum the saturation depends on the
+ 
+
+ align:start position:0%
+maximum the saturation depends on the
+material recation time if you
+
+ align:start position:0%
+material recation time if you
+ 
+
+ align:start position:0%
+material recation time if you
+you it's hard to get
+
+ align:start position:0%
+you it's hard to get
+ 
+
+ align:start position:0%
+you it's hard to get
+the and gen of chocolate I read a few
+
+ align:start position:0%
+the and gen of chocolate I read a few
+ 
+
+ align:start position:0%
+the and gen of chocolate I read a few
+people very very
+
+ align:start position:0%
+people very very
+ 
+
+ align:start position:0%
+people very very
+my and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what what what
+
+ align:start position:0%
+so this is what what what
+ 
+
+ align:start position:0%
+so this is what what what
+sh so if you think
+
+ align:start position:0%
+sh so if you think
+ 
+
+ align:start position:0%
+sh so if you think
+about pin Junction put under side right
+
+ align:start position:0%
+about pin Junction put under side right
+ 
+
+ align:start position:0%
+about pin Junction put under side right
+open
+
+ align:start position:0%
+open
+ 
+
+ align:start position:0%
+open
+circuit of course the solar radiation
+
+ align:start position:0%
+circuit of course the solar radiation
+ 
+
+ align:start position:0%
+circuit of course the solar radiation
+will create the electron HS continuously
+
+ align:start position:0%
+will create the electron HS continuously
+ 
+
+ align:start position:0%
+will create the electron HS continuously
+every Photon will gener electron here if
+
+ align:start position:0%
+every Photon will gener electron here if
+ 
+
+ align:start position:0%
+every Photon will gener electron here if
+there's no rec comination now defects
+
+ align:start position:0%
+there's no rec comination now defects
+ 
+
+ align:start position:0%
+there's no rec comination now defects
+Rec combine what happen you got to have
+
+ align:start position:0%
+Rec combine what happen you got to have
+ 
+
+ align:start position:0%
+Rec combine what happen you got to have
+AAL recombination process
+
+ align:start position:0%
+AAL recombination process
+ 
+
+ align:start position:0%
+AAL recombination process
+right spontaneous recation give about
+
+ align:start position:0%
+right spontaneous recation give about
+ 
+
+ align:start position:0%
+right spontaneous recation give about
+full so that's your maximum limit now
+
+ align:start position:0%
+full so that's your maximum limit now
+ 
+
+ align:start position:0%
+full so that's your maximum limit now
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+recombination only spontaneous
+
+ align:start position:0%
+recombination only spontaneous
+ 
+
+ align:start position:0%
+recombination only spontaneous
+recombination but what's that theous
+
+ align:start position:0%
+recombination but what's that theous
+ 
+
+ align:start position:0%
+recombination but what's that theous
+recation that okay and I'm really
+
+ align:start position:0%
+recation that okay and I'm really
+ 
+
+ align:start position:0%
+recation that okay and I'm really
+impressed I read a few paper this is
+
+ align:start position:0%
+impressed I read a few paper this is
+ 
+
+ align:start position:0%
+impressed I read a few paper this is
+where every time I I do this I have a
+
+ align:start position:0%
+where every time I I do this I have a
+ 
+
+ align:start position:0%
+where every time I I do this I have a
+place where I don't feel comfortable to
+
+ align:start position:0%
+place where I don't feel comfortable to
+ 
+
+ align:start position:0%
+place where I don't feel comfortable to
+tell you and I want to tell you because
+
+ align:start position:0%
+tell you and I want to tell you because
+ 
+
+ align:start position:0%
+tell you and I want to tell you because
+I want go to find
+
+ align:start position:0%
+I want go to find
+ 
+
+ align:start position:0%
+I want go to find
+out and this is not just I read
+
+ align:start position:0%
+out and this is not just I read
+ 
+
+ align:start position:0%
+out and this is not just I read
+yesterday I for many years I tried to
+
+ align:start position:0%
+yesterday I for many years I tried to
+ 
+
+ align:start position:0%
+yesterday I for many years I tried to
+understand this I still fully
+
+ align:start position:0%
+understand this I still fully
+ 
+
+ align:start position:0%
+understand this I still fully
+appr feel fully
+
+ align:start position:0%
+appr feel fully
+ 
+
+ align:start position:0%
+appr feel fully
+compl this is this expression where they
+
+ align:start position:0%
+compl this is this expression where they
+ 
+
+ align:start position:0%
+compl this is this expression where they
+came up and this is actually not in
+
+ align:start position:0%
+came up and this is actually not in
+ 
+
+ align:start position:0%
+came up and this is actually not in
+shock paper this is check paper and had
+
+ align:start position:0%
+shock paper this is check paper and had
+ 
+
+ align:start position:0%
+shock paper this is check paper and had
+another refer another by Ross and they
+
+ align:start position:0%
+another refer another by Ross and they
+ 
+
+ align:start position:0%
+another refer another by Ross and they
+all discuss different three different
+
+ align:start position:0%
+all discuss different three different
+ 
+
+ align:start position:0%
+all discuss different three different
+cherer three different way to write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expression and uh so when the P Junction
+
+ align:start position:0%
+expression and uh so when the P Junction
+ 
+
+ align:start position:0%
+expression and uh so when the P Junction
+has a voltage
+
+ align:start position:0%
+has a voltage
+ 
+
+ align:start position:0%
+has a voltage
+here and what's the uh the so we see the
+
+ align:start position:0%
+here and what's the uh the so we see the
+ 
+
+ align:start position:0%
+here and what's the uh the so we see the
+quom state
+
+ align:start position:0%
+quom state
+ 
+
+ align:start position:0%
+quom state
+the statistics right but what say what
+
+ align:start position:0%
+the statistics right but what say what
+ 
+
+ align:start position:0%
+the statistics right but what say what
+they the phons which oby
+
+ align:start position:0%
+they the phons which oby
+ 
+
+ align:start position:0%
+they the phons which oby
+Einstein in the
+
+ align:start position:0%
+Einstein in the
+ 
+
+ align:start position:0%
+Einstein in the
+injunction everything looks like except
+
+ align:start position:0%
+injunction everything looks like except
+ 
+
+ align:start position:0%
+injunction everything looks like except
+that he add
+
+ align:start position:0%
+that he add
+ 
+
+ align:start position:0%
+that he add
+e okay e is the you look at e is really
+
+ align:start position:0%
+e okay e is the you look at e is really
+ 
+
+ align:start position:0%
+e okay e is the you look at e is really
+the peral over here in N Tye p in this
+
+ align:start position:0%
+the peral over here in N Tye p in this
+ 
+
+ align:start position:0%
+the peral over here in N Tye p in this
+region that's the
+
+ align:start position:0%
+region that's the
+ 
+
+ align:start position:0%
+region that's the
+voltage it's adding this term that I
+
+ align:start position:0%
+voltage it's adding this term that I
+ 
+
+ align:start position:0%
+voltage it's adding this term that I
+just feel
+
+ align:start position:0%
+just feel
+ 
+
+ align:start position:0%
+just feel
+I can't comfortably dve it you can go to
+
+ align:start position:0%
+I can't comfortably dve it you can go to
+ 
+
+ align:start position:0%
+I can't comfortably dve it you can go to
+expand so each paper you start from
+
+ align:start position:0%
+expand so each paper you start from
+ 
+
+ align:start position:0%
+expand so each paper you start from
+different place and and I will encourage
+
+ align:start position:0%
+different place and and I will encourage
+ 
+
+ align:start position:0%
+different place and and I will encourage
+you to read and again if you have any
+
+ align:start position:0%
+you to read and again if you have any
+ 
+
+ align:start position:0%
+you to read and again if you have any
+idea to make my S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comfortable because I I I for many years
+
+ align:start position:0%
+comfortable because I I I for many years
+ 
+
+ align:start position:0%
+comfortable because I I I for many years
+we actually looking into this see how we
+
+ align:start position:0%
+we actually looking into this see how we
+ 
+
+ align:start position:0%
+we actually looking into this see how we
+can really make comfortable D some um
+
+ align:start position:0%
+can really make comfortable D some um
+ 
+
+ align:start position:0%
+can really make comfortable D some um
+nearfield under nearfield where
+
+ align:start position:0%
+nearfield under nearfield where
+ 
+
+ align:start position:0%
+nearfield under nearfield where
+let's see so I can only just say take
+
+ align:start position:0%
+let's see so I can only just say take
+ 
+
+ align:start position:0%
+let's see so I can only just say take
+from here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iier and the
+
+ align:start position:0%
+iier and the
+ 
+
+ align:start position:0%
+iier and the
+reculation
+
+ align:start position:0%
+reculation
+ 
+
+ align:start position:0%
+reculation
+reculation P Junction and if you do
+
+ align:start position:0%
+reculation P Junction and if you do
+ 
+
+ align:start position:0%
+reculation P Junction and if you do
+lasers or let down this is very
+
+ align:start position:0%
+lasers or let down this is very
+ 
+
+ align:start position:0%
+lasers or let down this is very
+important this is very of people
+
+ align:start position:0%
+important this is very of people
+ 
+
+ align:start position:0%
+important this is very of people
+St okay but I Haven seen the one that
+
+ align:start position:0%
+St okay but I Haven seen the one that
+ 
+
+ align:start position:0%
+St okay but I Haven seen the one that
+really to thody
+
+ align:start position:0%
+really to thody
+ 
+
+ align:start position:0%
+really to thody
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+easy so that's promote how
+
+ align:start position:0%
+easy so that's promote how
+ 
+
+ align:start position:0%
+easy so that's promote how
+mechanically promote how many to you
+
+ align:start position:0%
+mechanically promote how many to you
+ 
+
+ align:start position:0%
+mechanically promote how many to you
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and okay now starting from
+
+ align:start position:0%
+and okay now starting from
+ 
+
+ align:start position:0%
+and okay now starting from
+here you can deride what du this
+
+ align:start position:0%
+here you can deride what du this
+ 
+
+ align:start position:0%
+here you can deride what du this
+recombination now you have a voltage the
+
+ align:start position:0%
+recombination now you have a voltage the
+ 
+
+ align:start position:0%
+recombination now you have a voltage the
+arbitrary voltage what recombination
+
+ align:start position:0%
+arbitrary voltage what recombination
+ 
+
+ align:start position:0%
+arbitrary voltage what recombination
+part so you just integrate again uh from
+
+ align:start position:0%
+part so you just integrate again uh from
+ 
+
+ align:start position:0%
+part so you just integrate again uh from
+the band Gap to any energy and if you do
+
+ align:start position:0%
+the band Gap to any energy and if you do
+ 
+
+ align:start position:0%
+the band Gap to any energy and if you do
+static you just neglect one factor one
+
+ align:start position:0%
+static you just neglect one factor one
+ 
+
+ align:start position:0%
+static you just neglect one factor one
+and this is the uh L I didn't write the
+
+ align:start position:0%
+and this is the uh L I didn't write the
+ 
+
+ align:start position:0%
+and this is the uh L I didn't write the
+equation copy from paper and this is
+
+ align:start position:0%
+equation copy from paper and this is
+ 
+
+ align:start position:0%
+equation copy from paper and this is
+angular integration so that's
+
+ align:start position:0%
+angular integration so that's
+ 
+
+ align:start position:0%
+angular integration so that's
+essentially the full density of
+
+ align:start position:0%
+essentially the full density of
+ 
+
+ align:start position:0%
+essentially the full density of
+States inside
+
+ align:start position:0%
+States inside
+ 
+
+ align:start position:0%
+States inside
+the so
+
+ align:start position:0%
+the so
+ 
+
+ align:start position:0%
+the so
+it's statistics integrated
+
+ align:start position:0%
+it's statistics integrated
+ 
+
+ align:start position:0%
+it's statistics integrated
+kind so this is the spontaneous emission
+
+ align:start position:0%
+kind so this is the spontaneous emission
+ 
+
+ align:start position:0%
+kind so this is the spontaneous emission
+due to the current that can create
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at and is very similar to what we had
+
+ align:start position:0%
+at and is very similar to what we had
+ 
+
+ align:start position:0%
+at and is very similar to what we had
+before except a is longer that due to if
+
+ align:start position:0%
+before except a is longer that due to if
+ 
+
+ align:start position:0%
+before except a is longer that due to if
+you look at the DI a right this is the a
+
+ align:start position:0%
+you look at the DI a right this is the a
+ 
+
+ align:start position:0%
+you look at the DI a right this is the a
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+DI that's determined by action mat
+
+ align:start position:0%
+DI that's determined by action mat
+ 
+
+ align:start position:0%
+DI that's determined by action mat
+recation and then here
+
+ align:start position:0%
+recation and then here
+ 
+
+ align:start position:0%
+recation and then here
+here theity is no this is really just DC
+
+ align:start position:0%
+here theity is no this is really just DC
+ 
+
+ align:start position:0%
+here theity is no this is really just DC
+constant refractive
+
+ align:start position:0%
+constant refractive
+ 
+
+ align:start position:0%
+constant refractive
+index B on material so this is the
+
+ align:start position:0%
+index B on material so this is the
+ 
+
+ align:start position:0%
+index B on material so this is the
+maximum you can have the best you can
+
+ align:start position:0%
+maximum you can have the best you can
+ 
+
+ align:start position:0%
+maximum you can have the best you can
+have as re recombination no no other
+
+ align:start position:0%
+have as re recombination no no other
+ 
+
+ align:start position:0%
+have as re recombination no no other
+defect so because of that it's free of
+
+ align:start position:0%
+defect so because of that it's free of
+ 
+
+ align:start position:0%
+defect so because of that it's free of
+any material so now you can derive
+
+ align:start position:0%
+any material so now you can derive
+ 
+
+ align:start position:0%
+any material so now you can derive
+the but in see of one material that's
+
+ align:start position:0%
+the but in see of one material that's
+ 
+
+ align:start position:0%
+the but in see of one material that's
+the EG right
+
+ align:start position:0%
+the EG right
+ 
+
+ align:start position:0%
+the EG right
+this is the only other material you have
+
+ align:start position:0%
+this is the only other material you have
+ 
+
+ align:start position:0%
+this is the only other material you have
+but while I talk you can also say ah how
+
+ align:start position:0%
+but while I talk you can also say ah how
+ 
+
+ align:start position:0%
+but while I talk you can also say ah how
+about the photonic crystal inside
+
+ align:start position:0%
+about the photonic crystal inside
+ 
+
+ align:start position:0%
+about the photonic crystal inside
+photonic Crystal this Factor we
+
+ align:start position:0%
+photonic Crystal this Factor we
+ 
+
+ align:start position:0%
+photonic Crystal this Factor we
+check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spontaneous and maybe you got a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different so now I have translated that
+
+ align:start position:0%
+different so now I have translated that
+ 
+
+ align:start position:0%
+different so now I have translated that
+if you look at the term this is the C
+
+ align:start position:0%
+if you look at the term this is the C
+ 
+
+ align:start position:0%
+if you look at the term this is the C
+ter the dial equation right one is the
+
+ align:start position:0%
+ter the dial equation right one is the
+ 
+
+ align:start position:0%
+ter the dial equation right one is the
+dial C the other is the full generator C
+
+ align:start position:0%
+dial C the other is the full generator C
+ 
+
+ align:start position:0%
+dial C the other is the full generator C
+this is the phon gener C in the best
+
+ align:start position:0%
+this is the phon gener C in the best
+ 
+
+ align:start position:0%
+this is the phon gener C in the best
+case this is one so I put in the best
+
+ align:start position:0%
+case this is one so I put in the best
+ 
+
+ align:start position:0%
+case this is one so I put in the best
+scenario and the AR is independent
+
+ align:start position:0%
+scenario and the AR is independent
+ 
+
+ align:start position:0%
+scenario and the AR is independent
+material except the b g only the B Gap
+
+ align:start position:0%
+material except the b g only the B Gap
+ 
+
+ align:start position:0%
+material except the b g only the B Gap
+so that's where shly to derive what's
+
+ align:start position:0%
+so that's where shly to derive what's
+ 
+
+ align:start position:0%
+so that's where shly to derive what's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+m and this is the U the curve not cop
+
+ align:start position:0%
+m and this is the U the curve not cop
+ 
+
+ align:start position:0%
+m and this is the U the curve not cop
+from Chate
+
+ align:start position:0%
+from Chate
+ 
+
+ align:start position:0%
+from Chate
+paper and using this comination
+
+ align:start position:0%
+paper and using this comination
+ 
+
+ align:start position:0%
+paper and using this comination
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+generated this
+
+ align:start position:0%
+generated this
+ 
+
+ align:start position:0%
+generated this
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the gener and the rest just we did
+
+ align:start position:0%
+the gener and the rest just we did
+ 
+
+ align:start position:0%
+the gener and the rest just we did
+before find out what's the maximum power
+
+ align:start position:0%
+before find out what's the maximum power
+ 
+
+ align:start position:0%
+before find out what's the maximum power
+and what's
+
+ align:start position:0%
+and what's
+ 
+
+ align:start position:0%
+and what's
+maximum and this is what uh uh
+
+ align:start position:0%
+maximum and this is what uh uh
+ 
+
+ align:start position:0%
+maximum and this is what uh uh
+calculated and here C is the
+
+ align:start position:0%
+calculated and here C is the
+ 
+
+ align:start position:0%
+calculated and here C is the
+concentration what concentration op
+
+ align:start position:0%
+concentration what concentration op
+ 
+
+ align:start position:0%
+concentration what concentration op
+concentration what what it does change
+
+ align:start position:0%
+concentration what what it does change
+ 
+
+ align:start position:0%
+concentration what what it does change
+JL right if you concentrate more you
+
+ align:start position:0%
+JL right if you concentrate more you
+ 
+
+ align:start position:0%
+JL right if you concentrate more you
+generate more un pair for un body so
+
+ align:start position:0%
+generate more un pair for un body so
+ 
+
+ align:start position:0%
+generate more un pair for un body so
+this is if you concentrate you get this
+
+ align:start position:0%
+this is if you concentrate you get this
+ 
+
+ align:start position:0%
+this is if you concentrate you get this
+larger you get a larger open circuit
+
+ align:start position:0%
+larger you get a larger open circuit
+ 
+
+ align:start position:0%
+larger you get a larger open circuit
+voltage so concentration actually can
+
+ align:start position:0%
+voltage so concentration actually can
+ 
+
+ align:start position:0%
+voltage so concentration actually can
+help you increase
+
+ align:start position:0%
+help you increase
+ 
+
+ align:start position:0%
+help you increase
+efficiency okay so uh not too much
+
+ align:start position:0%
+efficiency okay so uh not too much
+ 
+
+ align:start position:0%
+efficiency okay so uh not too much
+increase but
+
+ align:start position:0%
+increase but
+ 
+
+ align:start position:0%
+increase but
+and what's interesting you look at it
+
+ align:start position:0%
+and what's interesting you look at it
+ 
+
+ align:start position:0%
+and what's interesting you look at it
+under one
+
+ align:start position:0%
+under one
+ 
+
+ align:start position:0%
+under one
+condition right where is the op
+
+ align:start position:0%
+condition right where is the op
+ 
+
+ align:start position:0%
+condition right where is the op
+Bank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.5 look at Material where is about
+
+ align:start position:0%
+1.5 look at Material where is about
+ 
+
+ align:start position:0%
+1.5 look at Material where is about
+what's that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+1.1 not too far from the out so this is
+
+ align:start position:0%
+1.1 not too far from the out so this is
+ 
+
+ align:start position:0%
+1.1 not too far from the out so this is
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that c you if you build the
+
+ align:start position:0%
+okay so that c you if you build the
+ 
+
+ align:start position:0%
+okay so that c you if you build the
+same this is about best you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do uh you mean the uh how many phon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have what happens for
+
+ align:start position:0%
+have what happens for
+ 
+
+ align:start position:0%
+have what happens for
+examp they
+
+ align:start position:0%
+examp they
+ 
+
+ align:start position:0%
+examp they
+absal energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as64 right exactly so so this is a this
+
+ align:start position:0%
+as64 right exactly so so this is a this
+ 
+
+ align:start position:0%
+as64 right exactly so so this is a this
+is black body C right this is your your
+
+ align:start position:0%
+is black body C right this is your your
+ 
+
+ align:start position:0%
+is black body C right this is your your
+B Gap somewhere here okay and uh really
+
+ align:start position:0%
+B Gap somewhere here okay and uh really
+ 
+
+ align:start position:0%
+B Gap somewhere here okay and uh really
+what's use for energy because this above
+
+ align:start position:0%
+what's use for energy because this above
+ 
+
+ align:start position:0%
+what's use for energy because this above
+the Gap energy is lost so if I look at
+
+ align:start position:0%
+the Gap energy is lost so if I look at
+ 
+
+ align:start position:0%
+the Gap energy is lost so if I look at
+this is the B structure if I haveon
+
+ align:start position:0%
+this is the B structure if I haveon
+ 
+
+ align:start position:0%
+this is the B structure if I haveon
+generate electron this way this energ
+
+ align:start position:0%
+generate electron this way this energ
+ 
+
+ align:start position:0%
+generate electron this way this energ
+electron relax bottom very fast okay
+
+ align:start position:0%
+electron relax bottom very fast okay
+ 
+
+ align:start position:0%
+electron relax bottom very fast okay
+whole relax to here very fast so this is
+
+ align:start position:0%
+whole relax to here very fast so this is
+ 
+
+ align:start position:0%
+whole relax to here very fast so this is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+heat and in fact people have been
+
+ align:start position:0%
+heat and in fact people have been
+ 
+
+ align:start position:0%
+heat and in fact people have been
+seizing how the electron C if you can
+
+ align:start position:0%
+seizing how the electron C if you can
+ 
+
+ align:start position:0%
+seizing how the electron C if you can
+extract this electron out with this kind
+
+ align:start position:0%
+extract this electron out with this kind
+ 
+
+ align:start position:0%
+extract this electron out with this kind
+of energy that's how ELR question how
+
+ align:start position:0%
+of energy that's how ELR question how
+ 
+
+ align:start position:0%
+of energy that's how ELR question how
+you get it out before relax this is
+
+ align:start position:0%
+you get it out before relax this is
+ 
+
+ align:start position:0%
+you get it out before relax this is
+about P second so P second is very fast
+
+ align:start position:0%
+about P second so P second is very fast
+ 
+
+ align:start position:0%
+about P second so P second is very fast
+if you times 10 time diffusivity just
+
+ align:start position:0%
+if you times 10 time diffusivity just
+ 
+
+ align:start position:0%
+if you times 10 time diffusivity just
+travel n or n just have no way to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get if you have good ideas that's
+
+ align:start position:0%
+get if you have good ideas that's
+ 
+
+ align:start position:0%
+get if you have good ideas that's
+something people thinking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's a simple Junction Maxim
+
+ align:start position:0%
+okay so that's a simple Junction Maxim
+ 
+
+ align:start position:0%
+okay so that's a simple Junction Maxim
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+get and exactly on this
+
+ align:start position:0%
+get and exactly on this
+ 
+
+ align:start position:0%
+get and exactly on this
+issue right how about we do multi-
+
+ align:start position:0%
+issue right how about we do multi-
+ 
+
+ align:start position:0%
+issue right how about we do multi-
+Junction right one C so multi- Junction
+
+ align:start position:0%
+Junction right one C so multi- Junction
+ 
+
+ align:start position:0%
+Junction right one C so multi- Junction
+like show here the first one absorb blue
+
+ align:start position:0%
+like show here the first one absorb blue
+ 
+
+ align:start position:0%
+like show here the first one absorb blue
+so larger B Gap the top most layer
+
+ align:start position:0%
+so larger B Gap the top most layer
+ 
+
+ align:start position:0%
+so larger B Gap the top most layer
+and the lower longer we lower energy can
+
+ align:start position:0%
+and the lower longer we lower energy can
+ 
+
+ align:start position:0%
+and the lower longer we lower energy can
+transmit so get absorbed second and get
+
+ align:start position:0%
+transmit so get absorbed second and get
+ 
+
+ align:start position:0%
+transmit so get absorbed second and get
+also third that's the idea and of course
+
+ align:start position:0%
+also third that's the idea and of course
+ 
+
+ align:start position:0%
+also third that's the idea and of course
+you can see with this
+
+ align:start position:0%
+you can see with this
+ 
+
+ align:start position:0%
+you can see with this
+stacking each car each one generate a
+
+ align:start position:0%
+stacking each car each one generate a
+ 
+
+ align:start position:0%
+stacking each car each one generate a
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+right if you look at this the case your
+
+ align:start position:0%
+right if you look at this the case your
+ 
+
+ align:start position:0%
+right if you look at this the case your
+current has to be continuous because you
+
+ align:start position:0%
+current has to be continuous because you
+ 
+
+ align:start position:0%
+current has to be continuous because you
+put the on top on bottom so this C has
+
+ align:start position:0%
+put the on top on bottom so this C has
+ 
+
+ align:start position:0%
+put the on top on bottom so this C has
+to generate the same on the C that's a
+
+ align:start position:0%
+to generate the same on the C that's a
+ 
+
+ align:start position:0%
+to generate the same on the C that's a
+design right
+
+ align:start position:0%
+design right
+ 
+
+ align:start position:0%
+design right
+almost right and uh uh but people have
+
+ align:start position:0%
+almost right and uh uh but people have
+ 
+
+ align:start position:0%
+almost right and uh uh but people have
+done that it's a material liare and
+
+ align:start position:0%
+done that it's a material liare and
+ 
+
+ align:start position:0%
+done that it's a material liare and
+design
+
+ align:start position:0%
+design
+ 
+
+ align:start position:0%
+design
+liare and design in a sense you have to
+
+ align:start position:0%
+liare and design in a sense you have to
+ 
+
+ align:start position:0%
+liare and design in a sense you have to
+get a c match so the electron go come
+
+ align:start position:0%
+get a c match so the electron go come
+ 
+
+ align:start position:0%
+get a c match so the electron go come
+from the top layer has to go to the hole
+
+ align:start position:0%
+from the top layer has to go to the hole
+ 
+
+ align:start position:0%
+from the top layer has to go to the hole
+of the next layer or hole of the top
+
+ align:start position:0%
+of the next layer or hole of the top
+ 
+
+ align:start position:0%
+of the next layer or hole of the top
+layer has to merge with
+
+ align:start position:0%
+layer has to merge with
+ 
+
+ align:start position:0%
+layer has to merge with
+theayer right Cent is
+
+ align:start position:0%
+theayer right Cent is
+ 
+
+ align:start position:0%
+theayer right Cent is
+continuous and and uh you have to grou
+
+ align:start position:0%
+continuous and and uh you have to grou
+ 
+
+ align:start position:0%
+continuous and and uh you have to grou
+different materials because
+
+ align:start position:0%
+different materials because
+ 
+
+ align:start position:0%
+different materials because
+recompilation is a killer right so so
+
+ align:start position:0%
+recompilation is a killer right so so
+ 
+
+ align:start position:0%
+recompilation is a killer right so so
+that's why people do
+
+ align:start position:0%
+that's why people do
+ 
+
+ align:start position:0%
+that's why people do
+Mo match you generate defect you
+
+ align:start position:0%
+Mo match you generate defect you
+ 
+
+ align:start position:0%
+Mo match you generate defect you
+generate
+
+ align:start position:0%
+generate
+ 
+
+ align:start position:0%
+generate
+dislocations this were just centers for
+
+ align:start position:0%
+dislocations this were just centers for
+ 
+
+ align:start position:0%
+dislocations this were just centers for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+recombination and then you kill that you
+
+ align:start position:0%
+recombination and then you kill that you
+ 
+
+ align:start position:0%
+recombination and then you kill that you
+kill the electrons before you take
+
+ align:start position:0%
+kill the electrons before you take
+ 
+
+ align:start position:0%
+kill the electrons before you take
+out so to gr this material people
+
+ align:start position:0%
+out so to gr this material people
+ 
+
+ align:start position:0%
+out so to gr this material people
+done like a spectral dial spectral of
+
+ align:start position:0%
+done like a spectral dial spectral of
+ 
+
+ align:start position:0%
+done like a spectral dial spectral of
+down lab they were doing laser before
+
+ align:start position:0%
+down lab they were doing laser before
+ 
+
+ align:start position:0%
+down lab they were doing laser before
+now they're doing probably 40 41% for
+
+ align:start position:0%
+now they're doing probably 40 41% for
+ 
+
+ align:start position:0%
+now they're doing probably 40 41% for
+sales people
+
+ align:start position:0%
+sales people
+ 
+
+ align:start position:0%
+sales people
+Junction Junctions that R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's and so this is I got one from
+
+ align:start position:0%
+that's and so this is I got one from
+ 
+
+ align:start position:0%
+that's and so this is I got one from
+internet I think give some IDE City real
+
+ align:start position:0%
+internet I think give some IDE City real
+ 
+
+ align:start position:0%
+internet I think give some IDE City real
+15% to
+
+ align:start position:0%
+15% to
+ 
+
+ align:start position:0%
+15% to
+18% our
+
+ align:start position:0%
+18% our
+ 
+
+ align:start position:0%
+18% our
+skill and then uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+30% and now this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+junction4 or matal you have to look at
+
+ align:start position:0%
+junction4 or matal you have to look at
+ 
+
+ align:start position:0%
+junction4 or matal you have to look at
+matal C and you can grow so you have to
+
+ align:start position:0%
+matal C and you can grow so you have to
+ 
+
+ align:start position:0%
+matal C and you can grow so you have to
+look at both material and band Gap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+device
+
+ align:start position:0%
+device
+ 
+
+ align:start position:0%
+device
+and how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the paper it shows 72% if you
+
+ align:start position:0%
+so this is the paper it shows 72% if you
+ 
+
+ align:start position:0%
+so this is the paper it shows 72% if you
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+36 say m spectral each 36 stage okay and
+
+ align:start position:0%
+36 say m spectral each 36 stage okay and
+ 
+
+ align:start position:0%
+36 say m spectral each 36 stage okay and
+if you have a infinite stage the Ser is
+
+ align:start position:0%
+if you have a infinite stage the Ser is
+ 
+
+ align:start position:0%
+if you have a infinite stage the Ser is
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+86% that's the
+
+ align:start position:0%
+86% that's the
+ 
+
+ align:start position:0%
+86% that's the
+best around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+86% c lower than the col
+
+ align:start position:0%
+86% c lower than the col
+ 
+
+ align:start position:0%
+86% c lower than the col
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+30000 that's
+
+ align:start position:0%
+30000 that's
+ 
+
+ align:start position:0%
+30000 that's
+L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's
+
+ align:start position:0%
+okay so that's
+ 
+
+ align:start position:0%
+okay so that's
+the what people can do say Theory say
+
+ align:start position:0%
+the what people can do say Theory say
+ 
+
+ align:start position:0%
+the what people can do say Theory say
+now you look at practice in the lab this
+
+ align:start position:0%
+now you look at practice in the lab this
+ 
+
+ align:start position:0%
+now you look at practice in the lab this
+is the best in the lab it's not best
+
+ align:start position:0%
+is the best in the lab it's not best
+ 
+
+ align:start position:0%
+is the best in the lab it's not best
+deploy C where is the first time
+
+ align:start position:0%
+deploy C where is the first time
+ 
+
+ align:start position:0%
+deploy C where is the first time
+C uh
+
+ align:start position:0%
+C uh
+ 
+
+ align:start position:0%
+C uh
+silicon yeah here this
+
+ align:start position:0%
+silicon yeah here this
+ 
+
+ align:start position:0%
+silicon yeah here this
+isic function right best is about
+
+ align:start position:0%
+isic function right best is about
+ 
+
+ align:start position:0%
+isic function right best is about
+56% I remember I this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is probably the biggest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy told me about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+27 that's remember shop reisor gives you
+
+ align:start position:0%
+27 that's remember shop reisor gives you
+ 
+
+ align:start position:0%
+27 that's remember shop reisor gives you
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+31% so do really
+
+ align:start position:0%
+31% so do really
+ 
+
+ align:start position:0%
+31% so do really
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+amazing and uh uh also so that's why all
+
+ align:start position:0%
+amazing and uh uh also so that's why all
+ 
+
+ align:start position:0%
+amazing and uh uh also so that's why all
+your your potential is also Li that's
+
+ align:start position:0%
+your your potential is also Li that's
+ 
+
+ align:start position:0%
+your your potential is also Li that's
+the best you do right but in fact you
+
+ align:start position:0%
+the best you do right but in fact you
+ 
+
+ align:start position:0%
+the best you do right but in fact you
+you can really do that at low cost I
+
+ align:start position:0%
+you can really do that at low cost I
+ 
+
+ align:start position:0%
+you can really do that at low cost I
+think your problem
+
+ align:start position:0%
+think your problem
+ 
+
+ align:start position:0%
+think your problem
+solve you can always work in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+betterine is only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power and so the best multi-
+
+ align:start position:0%
+power and so the best multi-
+ 
+
+ align:start position:0%
+power and so the best multi-
+Junction right
+
+ align:start position:0%
+Junction right
+ 
+
+ align:start position:0%
+Junction right
+spe uh here is less than but I think
+
+ align:start position:0%
+spe uh here is less than but I think
+ 
+
+ align:start position:0%
+spe uh here is less than but I think
+that now the best about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+41%
+
+ align:start position:0%
+41%
+ 
+
+ align:start position:0%
+41%
+okay and uh this is a
+
+ align:start position:0%
+okay and uh this is a
+ 
+
+ align:start position:0%
+okay and uh this is a
+multi this is a single multi
+
+ align:start position:0%
+multi this is a single multi
+ 
+
+ align:start position:0%
+multi this is a single multi
+and let's look at a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mic okay it's well the real world is
+
+ align:start position:0%
+mic okay it's well the real world is
+ 
+
+ align:start position:0%
+mic okay it's well the real world is
+about 6 to 8%
+
+ align:start position:0%
+about 6 to 8%
+ 
+
+ align:start position:0%
+about 6 to 8%
+deploy in the lab about 12% that's
+
+ align:start position:0%
+deploy in the lab about 12% that's
+ 
+
+ align:start position:0%
+deploy in the lab about 12% that's
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not and this is a uh say coer eum uh the
+
+ align:start position:0%
+not and this is a uh say coer eum uh the
+ 
+
+ align:start position:0%
+not and this is a uh say coer eum uh the
+six coer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+medum and so the best is about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+19%
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and said is dark because most people
+
+ align:start position:0%
+and and said is dark because most people
+ 
+
+ align:start position:0%
+and and said is dark because most people
+talk about 6 before and now is probably
+
+ align:start position:0%
+talk about 6 before and now is probably
+ 
+
+ align:start position:0%
+talk about 6 before and now is probably
+best most profitable
+
+ align:start position:0%
+best most profitable
+ 
+
+ align:start position:0%
+best most profitable
+compy and near SE I think
+
+ align:start position:0%
+compy and near SE I think
+ 
+
+ align:start position:0%
+compy and near SE I think
+from Lab to real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+production and then uh uh this one is
+
+ align:start position:0%
+production and then uh uh this one is
+ 
+
+ align:start position:0%
+production and then uh uh this one is
+the I think
+
+ align:start position:0%
+the I think
+ 
+
+ align:start position:0%
+the I think
+organic and then there's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's so this will give to work not the
+
+ align:start position:0%
+that's so this will give to work not the
+ 
+
+ align:start position:0%
+that's so this will give to work not the
+most of years but pretty
+
+ align:start position:0%
+most of years but pretty
+ 
+
+ align:start position:0%
+most of years but pretty
+close what are the problems right
+
+ align:start position:0%
+close what are the problems right
+ 
+
+ align:start position:0%
+close what are the problems right
+mention one for solar cell the L one
+
+ align:start position:0%
+mention one for solar cell the L one
+ 
+
+ align:start position:0%
+mention one for solar cell the L one
+device
+
+ align:start position:0%
+device
+ 
+
+ align:start position:0%
+device
+that's myar device very sensitive to
+
+ align:start position:0%
+that's myar device very sensitive to
+ 
+
+ align:start position:0%
+that's myar device very sensitive to
+recombination so what are the creation
+
+ align:start position:0%
+recombination so what are the creation
+ 
+
+ align:start position:0%
+recombination so what are the creation
+what are this uh what are the reason for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recombination impurities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deep in the bank deep level those
+
+ align:start position:0%
+deep in the bank deep level those
+ 
+
+ align:start position:0%
+deep in the bank deep level those
+areation bombs attack
+
+ align:start position:0%
+areation bombs attack
+ 
+
+ align:start position:0%
+areation bombs attack
+sh
+
+ align:start position:0%
+sh
+ 
+
+ align:start position:0%
+sh
+right and uh bom where you got a lot
+
+ align:start position:0%
+right and uh bom where you got a lot
+ 
+
+ align:start position:0%
+right and uh bom where you got a lot
+of those regions where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recation and that's why people purify
+
+ align:start position:0%
+recation and that's why people purify
+ 
+
+ align:start position:0%
+recation and that's why people purify
+cic CH cic example
+
+ align:start position:0%
+cic CH cic example
+ 
+
+ align:start position:0%
+cic CH cic example
+G is about $2 per per gr per kilogram
+
+ align:start position:0%
+G is about $2 per per gr per kilogram
+ 
+
+ align:start position:0%
+G is about $2 per per gr per kilogram
+C if you want to make a solar Cale you
+
+ align:start position:0%
+C if you want to make a solar Cale you
+ 
+
+ align:start position:0%
+C if you want to make a solar Cale you
+can you re crystalize purify and got to
+
+ align:start position:0%
+can you re crystalize purify and got to
+ 
+
+ align:start position:0%
+can you re crystalize purify and got to
+$40 and of course during process
+
+ align:start position:0%
+$40 and of course during process
+ 
+
+ align:start position:0%
+$40 and of course during process
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+out and in fact that last year before
+
+ align:start position:0%
+out and in fact that last year before
+ 
+
+ align:start position:0%
+out and in fact that last year before
+the market crashed everybody was on 6
+
+ align:start position:0%
+the market crashed everybody was on 6
+ 
+
+ align:start position:0%
+the market crashed everybody was on 6
+so the C of short and that's got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$40 okay so that's a one that's say
+
+ align:start position:0%
+$40 okay so that's a one that's say
+ 
+
+ align:start position:0%
+$40 okay so that's a one that's say
+minity device is and in that sense
+
+ align:start position:0%
+minity device is and in that sense
+ 
+
+ align:start position:0%
+minity device is and in that sense
+IC good because it's majority character
+
+ align:start position:0%
+IC good because it's majority character
+ 
+
+ align:start position:0%
+IC good because it's majority character
+doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have and the other problem this is
+
+ align:start position:0%
+have and the other problem this is
+ 
+
+ align:start position:0%
+have and the other problem this is
+AB in fact this is to me I say okay full
+
+ align:start position:0%
+AB in fact this is to me I say okay full
+ 
+
+ align:start position:0%
+AB in fact this is to me I say okay full
+company First Step
+
+ align:start position:0%
+company First Step
+ 
+
+ align:start position:0%
+company First Step
+absorb second step is charge where it
+
+ align:start position:0%
+absorb second step is charge where it
+ 
+
+ align:start position:0%
+absorb second step is charge where it
+goes so this is really the first step
+
+ align:start position:0%
+goes so this is really the first step
+ 
+
+ align:start position:0%
+goes so this is really the first step
+and look at word goes right of course
+
+ align:start position:0%
+and look at word goes right of course
+ 
+
+ align:start position:0%
+and look at word goes right of course
+the interface reflection you don't want
+
+ align:start position:0%
+the interface reflection you don't want
+ 
+
+ align:start position:0%
+the interface reflection you don't want
+refle minimize that verse C Surface
+
+ align:start position:0%
+refle minimize that verse C Surface
+ 
+
+ align:start position:0%
+refle minimize that verse C Surface
+equipment and once you get a input
+
+ align:start position:0%
+equipment and once you get a input
+ 
+
+ align:start position:0%
+equipment and once you get a input
+material you don't have almost no other
+
+ align:start position:0%
+material you don't have almost no other
+ 
+
+ align:start position:0%
+material you don't have almost no other
+ways to control this profile it's
+
+ align:start position:0%
+ways to control this profile it's
+ 
+
+ align:start position:0%
+ways to control this profile it's
+material inite absorption so this is the
+
+ align:start position:0%
+material inite absorption so this is the
+ 
+
+ align:start position:0%
+material inite absorption so this is the
+absor
+
+ align:start position:0%
+absor
+ 
+
+ align:start position:0%
+absor
+coefficient and decas the intensity
+
+ align:start position:0%
+coefficient and decas the intensity
+ 
+
+ align:start position:0%
+coefficient and decas the intensity
+decase
+
+ align:start position:0%
+decase
+ 
+
+ align:start position:0%
+decase
+exponentially so now you think about
+
+ align:start position:0%
+exponentially so now you think about
+ 
+
+ align:start position:0%
+exponentially so now you think about
+your most generated electron let's say
+
+ align:start position:0%
+your most generated electron let's say
+ 
+
+ align:start position:0%
+your most generated electron let's say
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+region and you want your space charge in
+
+ align:start position:0%
+region and you want your space charge in
+ 
+
+ align:start position:0%
+region and you want your space charge in
+this reg to overlap it so that you can
+
+ align:start position:0%
+this reg to overlap it so that you can
+ 
+
+ align:start position:0%
+this reg to overlap it so that you can
+separate you can use your field to drive
+
+ align:start position:0%
+separate you can use your field to drive
+ 
+
+ align:start position:0%
+separate you can use your field to drive
+electron to one side hold to the other
+
+ align:start position:0%
+electron to one side hold to the other
+ 
+
+ align:start position:0%
+electron to one side hold to the other
+side right so the dep of this 1 R gives
+
+ align:start position:0%
+side right so the dep of this 1 R gives
+ 
+
+ align:start position:0%
+side right so the dep of this 1 R gives
+you oneus one so that's called
+
+ align:start position:0%
+you oneus one so that's called
+ 
+
+ align:start position:0%
+you oneus one so that's called
+cation so this is where you look at
+
+ align:start position:0%
+cation so this is where you look at
+ 
+
+ align:start position:0%
+cation so this is where you look at
+Material what I should
+
+ align:start position:0%
+Material what I should
+ 
+
+ align:start position:0%
+Material what I should
+choose absorption
+
+ align:start position:0%
+choose absorption
+ 
+
+ align:start position:0%
+choose absorption
+Coe absortion happens above the band Gap
+
+ align:start position:0%
+Coe absortion happens above the band Gap
+ 
+
+ align:start position:0%
+Coe absortion happens above the band Gap
+so band Gap is the first step and then
+
+ align:start position:0%
+so band Gap is the first step and then
+ 
+
+ align:start position:0%
+so band Gap is the first step and then
+you look at Material you say oh silicon
+
+ align:start position:0%
+you look at Material you say oh silicon
+ 
+
+ align:start position:0%
+you look at Material you say oh silicon
+we know so much that's the of cic why
+
+ align:start position:0%
+we know so much that's the of cic why
+ 
+
+ align:start position:0%
+we know so much that's the of cic why
+cicon is a problem because it's really
+
+ align:start position:0%
+cicon is a problem because it's really
+ 
+
+ align:start position:0%
+cicon is a problem because it's really
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+because this
+
+ align:start position:0%
+because this
+ 
+
+ align:start position:0%
+because this
+absortion you see here absorption this
+
+ align:start position:0%
+absortion you see here absorption this
+ 
+
+ align:start position:0%
+absortion you see here absorption this
+is the energy right back is about 1.1
+
+ align:start position:0%
+is the energy right back is about 1.1
+ 
+
+ align:start position:0%
+is the energy right back is about 1.1
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+Vol it's a very slow curve and it's one
+
+ align:start position:0%
+Vol it's a very slow curve and it's one
+ 
+
+ align:start position:0%
+Vol it's a very slow curve and it's one
+over R so this is CM so here is about 10
+
+ align:start position:0%
+over R so this is CM so here is about 10
+ 
+
+ align:start position:0%
+over R so this is CM so here is about 10
+micr so if I use 10 micr so the energy
+
+ align:start position:0%
+micr so if I use 10 micr so the energy
+ 
+
+ align:start position:0%
+micr so if I use 10 micr so the energy
+below
+
+ align:start position:0%
+below
+ 
+
+ align:start position:0%
+below
+1.6 those part of the energy is AB very
+
+ align:start position:0%
+1.6 those part of the energy is AB very
+ 
+
+ align:start position:0%
+1.6 those part of the energy is AB very
+we go through this
+
+ align:start position:0%
+we go through this
+ 
+
+ align:start position:0%
+we go through this
+right it don't
+
+ align:start position:0%
+right it don't
+ 
+
+ align:start position:0%
+right it don't
+get so if it's to this go
+
+ align:start position:0%
+get so if it's to this go
+ 
+
+ align:start position:0%
+get so if it's to this go
+out so that's the the absortion and
+
+ align:start position:0%
+out so that's the the absortion and
+ 
+
+ align:start position:0%
+out so that's the the absortion and
+that's why some say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like6 turn
+
+ align:start position:0%
+like6 turn
+ 
+
+ align:start position:0%
+like6 turn
+right right you have very SP F power so
+
+ align:start position:0%
+right right you have very SP F power so
+ 
+
+ align:start position:0%
+right right you have very SP F power so
+if you have one mic this is the inverse
+
+ align:start position:0%
+if you have one mic this is the inverse
+ 
+
+ align:start position:0%
+if you have one mic this is the inverse
+is One
+
+ align:start position:0%
+is One
+ 
+
+ align:start position:0%
+is One
+mic 10 the
+
+ align:start position:0%
+mic 10 the
+ 
+
+ align:start position:0%
+mic 10 the
+force you m
+
+ align:start position:0%
+force you m
+ 
+
+ align:start position:0%
+force you m
+c okay so with if you want use fil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direct and that's why when people make a
+
+ align:start position:0%
+direct and that's why when people make a
+ 
+
+ align:start position:0%
+direct and that's why when people make a
+cic it's pretty good
+
+ align:start position:0%
+cic it's pretty good
+ 
+
+ align:start position:0%
+cic it's pretty good
+here this is usess
+
+ align:start position:0%
+here this is usess
+ 
+
+ align:start position:0%
+here this is usess
+here right you can generate but you
+
+ align:start position:0%
+here right you can generate but you
+ 
+
+ align:start position:0%
+here right you can generate but you
+don't have much so solar is always first
+
+ align:start position:0%
+don't have much so solar is always first
+ 
+
+ align:start position:0%
+don't have much so solar is always first
+you want to absorb it second you want to
+
+ align:start position:0%
+you want to absorb it second you want to
+ 
+
+ align:start position:0%
+you want to absorb it second you want to
+get the charge to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elect right so why so different from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+directly right this is what I mentioned
+
+ align:start position:0%
+directly right this is what I mentioned
+ 
+
+ align:start position:0%
+directly right this is what I mentioned
+before whether it's a direct
+
+ align:start position:0%
+before whether it's a direct
+ 
+
+ align:start position:0%
+before whether it's a direct
+semiconductor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gap like all the others that have sh
+
+ align:start position:0%
+Gap like all the others that have sh
+ 
+
+ align:start position:0%
+Gap like all the others that have sh
+increase direct
+
+ align:start position:0%
+increase direct
+ 
+
+ align:start position:0%
+increase direct
+G so the
+
+ align:start position:0%
+G so the
+ 
+
+ align:start position:0%
+G so the
+full go from here to here leave the
+
+ align:start position:0%
+full go from here to here leave the
+ 
+
+ align:start position:0%
+full go from here to here leave the
+electron to from valus to conduction B
+
+ align:start position:0%
+electron to from valus to conduction B
+ 
+
+ align:start position:0%
+electron to from valus to conduction B
+you need to satisfy satisfy the energy
+
+ align:start position:0%
+you need to satisfy satisfy the energy
+ 
+
+ align:start position:0%
+you need to satisfy satisfy the energy
+conservation so the fullon energy give
+
+ align:start position:0%
+conservation so the fullon energy give
+ 
+
+ align:start position:0%
+conservation so the fullon energy give
+the difference of electron energy so
+
+ align:start position:0%
+the difference of electron energy so
+ 
+
+ align:start position:0%
+the difference of electron energy so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+energy and second is a
+
+ align:start position:0%
+energy and second is a
+ 
+
+ align:start position:0%
+energy and second is a
+momentum so you have to
+
+ align:start position:0%
+momentum so you have to
+ 
+
+ align:start position:0%
+momentum so you have to
+momentum is H over
+
+ align:start position:0%
+momentum is H over
+ 
+
+ align:start position:0%
+momentum is H over
+Lambda right Lambda of phon is
+
+ align:start position:0%
+Lambda right Lambda of phon is
+ 
+
+ align:start position:0%
+Lambda right Lambda of phon is
+M well Lambda of electron is that
+
+ align:start position:0%
+M well Lambda of electron is that
+ 
+
+ align:start position:0%
+M well Lambda of electron is that
+concept
+
+ align:start position:0%
+concept
+ 
+
+ align:start position:0%
+concept
+Armstrong so the is one over Armstrong
+
+ align:start position:0%
+Armstrong so the is one over Armstrong
+ 
+
+ align:start position:0%
+Armstrong so the is one over Armstrong
+but so one more Lambda is essentially
+
+ align:start position:0%
+but so one more Lambda is essentially
+ 
+
+ align:start position:0%
+but so one more Lambda is essentially
+vertical so the phot don't give you much
+
+ align:start position:0%
+vertical so the phot don't give you much
+ 
+
+ align:start position:0%
+vertical so the phot don't give you much
+momentum that's the problem in indirect
+
+ align:start position:0%
+momentum that's the problem in indirect
+ 
+
+ align:start position:0%
+momentum that's the problem in indirect
+semiconductor right the B Gap is here
+
+ align:start position:0%
+semiconductor right the B Gap is here
+ 
+
+ align:start position:0%
+semiconductor right the B Gap is here
+when you want those
+
+ align:start position:0%
+when you want those
+ 
+
+ align:start position:0%
+when you want those
+the the momentum doesn't match
+
+ align:start position:0%
+the the momentum doesn't match
+ 
+
+ align:start position:0%
+the the momentum doesn't match
+between so if you want to leave this
+
+ align:start position:0%
+between so if you want to leave this
+ 
+
+ align:start position:0%
+between so if you want to leave this
+electron here the photon don't have
+
+ align:start position:0%
+electron here the photon don't have
+ 
+
+ align:start position:0%
+electron here the photon don't have
+enough momentum it has energy doesn't
+
+ align:start position:0%
+enough momentum it has energy doesn't
+ 
+
+ align:start position:0%
+enough momentum it has energy doesn't
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+momentum it has to have like something
+
+ align:start position:0%
+momentum it has to have like something
+ 
+
+ align:start position:0%
+momentum it has to have like something
+else that's Fon can a f or absorb a f
+
+ align:start position:0%
+else that's Fon can a f or absorb a f
+ 
+
+ align:start position:0%
+else that's Fon can a f or absorb a f
+Fon doesn't have much energy but it has
+
+ align:start position:0%
+Fon doesn't have much energy but it has
+ 
+
+ align:start position:0%
+Fon doesn't have much energy but it has
+momentum so this is a why they say so
+
+ align:start position:0%
+momentum so this is a why they say so
+ 
+
+ align:start position:0%
+momentum so this is a why they say so
+you got to have either emission or
+
+ align:start position:0%
+you got to have either emission or
+ 
+
+ align:start position:0%
+you got to have either emission or
+absorption of colon so you have three
+
+ align:start position:0%
+absorption of colon so you have three
+ 
+
+ align:start position:0%
+absorption of colon so you have three
+people now like I said very hard to
+
+ align:start position:0%
+people now like I said very hard to
+ 
+
+ align:start position:0%
+people now like I said very hard to
+schedule three people
+
+ align:start position:0%
+schedule three people
+ 
+
+ align:start position:0%
+schedule three people
+together so the absortion is weaker
+
+ align:start position:0%
+together so the absortion is weaker
+ 
+
+ align:start position:0%
+together so the absortion is weaker
+because when the Fon wants to do it
+
+ align:start position:0%
+because when the Fon wants to do it
+ 
+
+ align:start position:0%
+because when the Fon wants to do it
+there's no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+full okay so that's the Dilemma why the
+
+ align:start position:0%
+full okay so that's the Dilemma why the
+ 
+
+ align:start position:0%
+full okay so that's the Dilemma why the
+don't have there and near the back Gap
+
+ align:start position:0%
+don't have there and near the back Gap
+ 
+
+ align:start position:0%
+don't have there and near the back Gap
+and of course once you move to this
+
+ align:start position:0%
+and of course once you move to this
+ 
+
+ align:start position:0%
+and of course once you move to this
+region go up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go okay so that's what I say Soler sale
+
+ align:start position:0%
+go okay so that's what I say Soler sale
+ 
+
+ align:start position:0%
+go okay so that's what I say Soler sale
+essentially you solve one problem make
+
+ align:start position:0%
+essentially you solve one problem make
+ 
+
+ align:start position:0%
+essentially you solve one problem make
+the other problem see or how you can
+
+ align:start position:0%
+the other problem see or how you can
+ 
+
+ align:start position:0%
+the other problem see or how you can
+address those issues that they really
+
+ align:start position:0%
+address those issues that they really
+ 
+
+ align:start position:0%
+address those issues that they really
+electron thing is better you just take
+
+ align:start position:0%
+electron thing is better you just take
+ 
+
+ align:start position:0%
+electron thing is better you just take
+it out before they Rec combine you
+
+ align:start position:0%
+it out before they Rec combine you
+ 
+
+ align:start position:0%
+it out before they Rec combine you
+send four
+
+ align:start position:0%
+send four
+ 
+
+ align:start position:0%
+send four
+times get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay of course that's related to
+
+ align:start position:0%
+okay of course that's related to
+ 
+
+ align:start position:0%
+okay of course that's related to
+efficiency and the S directly to how
+
+ align:start position:0%
+efficiency and the S directly to how
+ 
+
+ align:start position:0%
+efficiency and the S directly to how
+much material you use that's a cost isue
+
+ align:start position:0%
+much material you use that's a cost isue
+ 
+
+ align:start position:0%
+much material you use that's a cost isue
+also right to have a low cost you need
+
+ align:start position:0%
+also right to have a low cost you need
+ 
+
+ align:start position:0%
+also right to have a low cost you need
+the CER less material always the
+
+ align:start position:0%
+the CER less material always the
+ 
+
+ align:start position:0%
+the CER less material always the
+material cost is
+
+ align:start position:0%
+material cost is
+ 
+
+ align:start position:0%
+material cost is
+better and look at the cost now the
+
+ align:start position:0%
+better and look at the cost now the
+ 
+
+ align:start position:0%
+better and look at the cost now the
+lowest solar cell is from First Solar
+
+ align:start position:0%
+lowest solar cell is from First Solar
+ 
+
+ align:start position:0%
+lowest solar cell is from First Solar
+Bic they have manufacturing cost is
+
+ align:start position:0%
+Bic they have manufacturing cost is
+ 
+
+ align:start position:0%
+Bic they have manufacturing cost is
+about $1 per one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this is where the the back
+
+ align:start position:0%
+okay and this is where the the back
+ 
+
+ align:start position:0%
+okay and this is where the the back
+three assuming certain amount of year
+
+ align:start position:0%
+three assuming certain amount of year
+ 
+
+ align:start position:0%
+three assuming certain amount of year
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+use you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have1 it's good it's good good curve
+
+ align:start position:0%
+have1 it's good it's good good curve
+ 
+
+ align:start position:0%
+have1 it's good it's good good curve
+here in terms of the cost but see look
+
+ align:start position:0%
+here in terms of the cost but see look
+ 
+
+ align:start position:0%
+here in terms of the cost but see look
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get takes a long time right right now
+
+ align:start position:0%
+get takes a long time right right now
+ 
+
+ align:start position:0%
+get takes a long time right right now
+they work expolation per year about 67
+
+ align:start position:0%
+they work expolation per year about 67
+ 
+
+ align:start position:0%
+they work expolation per year about 67
+Gatt 67 G China put a 100 G Ste every
+
+ align:start position:0%
+Gatt 67 G China put a 100 G Ste every
+ 
+
+ align:start position:0%
+Gatt 67 G China put a 100 G Ste every
+year okay just a BL really just a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+BL a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lot okay different type of Sol sales
+
+ align:start position:0%
+lot okay different type of Sol sales
+ 
+
+ align:start position:0%
+lot okay different type of Sol sales
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and uh city
+
+ align:start position:0%
+and uh city
+ 
+
+ align:start position:0%
+and uh city
+con is the most
+
+ align:start position:0%
+con is the most
+ 
+
+ align:start position:0%
+con is the most
+predominant is cost right single Crystal
+
+ align:start position:0%
+predominant is cost right single Crystal
+ 
+
+ align:start position:0%
+predominant is cost right single Crystal
+mul crystal is
+
+ align:start position:0%
+mul crystal is
+ 
+
+ align:start position:0%
+mul crystal is
+considered GRE almost
+
+ align:start position:0%
+considered GRE almost
+ 
+
+ align:start position:0%
+considered GRE almost
+right and uh what's interesting is all
+
+ align:start position:0%
+right and uh what's interesting is all
+ 
+
+ align:start position:0%
+right and uh what's interesting is all
+the cryst surface has
+
+ align:start position:0%
+the cryst surface has
+ 
+
+ align:start position:0%
+the cryst surface has
+Tex and that's the the light so that
+
+ align:start position:0%
+Tex and that's the the light so that
+ 
+
+ align:start position:0%
+Tex and that's the the light so that
+reduce
+
+ align:start position:0%
+reduce
+ 
+
+ align:start position:0%
+reduce
+reflection reduce reflection not only
+
+ align:start position:0%
+reflection reduce reflection not only
+ 
+
+ align:start position:0%
+reflection reduce reflection not only
+refraction once it get in so the back
+
+ align:start position:0%
+refraction once it get in so the back
+ 
+
+ align:start position:0%
+refraction once it get in so the back
+side is a metal you back you don't want
+
+ align:start position:0%
+side is a metal you back you don't want
+ 
+
+ align:start position:0%
+side is a metal you back you don't want
+to go out some of the pH so the more
+
+ align:start position:0%
+to go out some of the pH so the more
+ 
+
+ align:start position:0%
+to go out some of the pH so the more
+light and the difference between single
+
+ align:start position:0%
+light and the difference between single
+ 
+
+ align:start position:0%
+light and the difference between single
+or mod is SLE you can get a regular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+texture manufactur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process and then you got
+
+ align:start position:0%
+process and then you got
+ 
+
+ align:start position:0%
+process and then you got
+say and C here you can see this question
+
+ align:start position:0%
+say and C here you can see this question
+ 
+
+ align:start position:0%
+say and C here you can see this question
+here if you generate here here it has to
+
+ align:start position:0%
+here if you generate here here it has to
+ 
+
+ align:start position:0%
+here if you generate here here it has to
+diffuse you can go both ways right you
+
+ align:start position:0%
+diffuse you can go both ways right you
+ 
+
+ align:start position:0%
+diffuse you can go both ways right you
+don't have a field you have to design so
+
+ align:start position:0%
+don't have a field you have to design so
+ 
+
+ align:start position:0%
+don't have a field you have to design so
+that field can help you go One
+
+ align:start position:0%
+that field can help you go One
+ 
+
+ align:start position:0%
+that field can help you go One
+Direction Why P type is much secret than
+
+ align:start position:0%
+Direction Why P type is much secret than
+ 
+
+ align:start position:0%
+Direction Why P type is much secret than
+the F Tye I don't know it must be
+
+ align:start position:0%
+the F Tye I don't know it must be
+ 
+
+ align:start position:0%
+the F Tye I don't know it must be
+related to the mature par I would
+
+ align:start position:0%
+related to the mature par I would
+ 
+
+ align:start position:0%
+related to the mature par I would
+imagine probably P has combination
+
+ align:start position:0%
+imagine probably P has combination
+ 
+
+ align:start position:0%
+imagine probably P has combination
+together I didn't check
+
+ align:start position:0%
+together I didn't check
+ 
+
+ align:start position:0%
+together I didn't check
+most time people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huh I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't right and you can see here t plus
+
+ align:start position:0%
+don't right and you can see here t plus
+ 
+
+ align:start position:0%
+don't right and you can see here t plus
+trying to make a all
+
+ align:start position:0%
+trying to make a all
+ 
+
+ align:start position:0%
+trying to make a all
+contact right reduce that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sh and uh you have top
+
+ align:start position:0%
+sh and uh you have top
+ 
+
+ align:start position:0%
+sh and uh you have top
+el another
+
+ align:start position:0%
+el another
+ 
+
+ align:start position:0%
+el another
+bre that's a Shel effect met bre they pH
+
+ align:start position:0%
+bre that's a Shel effect met bre they pH
+ 
+
+ align:start position:0%
+bre that's a Shel effect met bre they pH
+on get through that's not good so
+
+ align:start position:0%
+on get through that's not good so
+ 
+
+ align:start position:0%
+on get through that's not good so
+sometimes people even bury the GD down
+
+ align:start position:0%
+sometimes people even bury the GD down
+ 
+
+ align:start position:0%
+sometimes people even bury the GD down
+or make it on the back side through V so
+
+ align:start position:0%
+or make it on the back side through V so
+ 
+
+ align:start position:0%
+or make it on the back side through V so
+there are lot
+
+ align:start position:0%
+there are lot
+ 
+
+ align:start position:0%
+there are lot
+of improvement little bit Improvement
+
+ align:start position:0%
+of improvement little bit Improvement
+ 
+
+ align:start position:0%
+of improvement little bit Improvement
+down over the years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+here say most Early One MA
+
+ align:start position:0%
+here say most Early One MA
+ 
+
+ align:start position:0%
+here say most Early One MA
+silicon MAA silicon we should before is
+
+ align:start position:0%
+silicon MAA silicon we should before is
+ 
+
+ align:start position:0%
+silicon MAA silicon we should before is
+pretty good so you can
+
+ align:start position:0%
+pretty good so you can
+ 
+
+ align:start position:0%
+pretty good so you can
+use but the electron mat electron very
+
+ align:start position:0%
+use but the electron mat electron very
+ 
+
+ align:start position:0%
+use but the electron mat electron very
+hard to move lot of dnic bond
+
+ align:start position:0%
+hard to move lot of dnic bond
+ 
+
+ align:start position:0%
+hard to move lot of dnic bond
+recombination so you got to use really
+
+ align:start position:0%
+recombination so you got to use really
+ 
+
+ align:start position:0%
+recombination so you got to use really
+thin silic about 200 NM
+
+ align:start position:0%
+thin silic about 200 NM
+ 
+
+ align:start position:0%
+thin silic about 200 NM
+and if you can reduce that the UN ther
+
+ align:start position:0%
+and if you can reduce that the UN ther
+ 
+
+ align:start position:0%
+and if you can reduce that the UN ther
+it's probably better two thing your
+
+ align:start position:0%
+it's probably better two thing your
+ 
+
+ align:start position:0%
+it's probably better two thing your
+manufacturing is a problem
+
+ align:start position:0%
+manufacturing is a problem
+ 
+
+ align:start position:0%
+manufacturing is a problem
+P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always but this is actually showing you
+
+ align:start position:0%
+always but this is actually showing you
+ 
+
+ align:start position:0%
+always but this is actually showing you
+just Al Junction I say they if you look
+
+ align:start position:0%
+just Al Junction I say they if you look
+ 
+
+ align:start position:0%
+just Al Junction I say they if you look
+at it this is on steel and top is a
+
+ align:start position:0%
+at it this is on steel and top is a
+ 
+
+ align:start position:0%
+at it this is on steel and top is a
+transparent elect so unlike silicon
+
+ align:start position:0%
+transparent elect so unlike silicon
+ 
+
+ align:start position:0%
+transparent elect so unlike silicon
+silicon you look at the electrode on the
+
+ align:start position:0%
+silicon you look at the electrode on the
+ 
+
+ align:start position:0%
+silicon you look at the electrode on the
+top right it's space across so electron
+
+ align:start position:0%
+top right it's space across so electron
+ 
+
+ align:start position:0%
+top right it's space across so electron
+go here actually diffuse to the
+
+ align:start position:0%
+go here actually diffuse to the
+ 
+
+ align:start position:0%
+go here actually diffuse to the
+elect going to the elect right silicon
+
+ align:start position:0%
+elect going to the elect right silicon
+ 
+
+ align:start position:0%
+elect going to the elect right silicon
+is reason good
+
+ align:start position:0%
+is reason good
+ 
+
+ align:start position:0%
+is reason good
+teration silicon don't work so you got
+
+ align:start position:0%
+teration silicon don't work so you got
+ 
+
+ align:start position:0%
+teration silicon don't work so you got
+have the elect right on top of
+
+ align:start position:0%
+have the elect right on top of
+ 
+
+ align:start position:0%
+have the elect right on top of
+it right so it's transparent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conduction and uh this is the
+
+ align:start position:0%
+conduction and uh this is the
+ 
+
+ align:start position:0%
+conduction and uh this is the
+right the active
+
+ align:start position:0%
+right the active
+ 
+
+ align:start position:0%
+right the active
+reg 6
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mic and this is six
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SP it's a between reculation and
+
+ align:start position:0%
+SP it's a between reculation and
+ 
+
+ align:start position:0%
+SP it's a between reculation and
+absorption to increase absortion using S
+
+ align:start position:0%
+absorption to increase absortion using S
+ 
+
+ align:start position:0%
+absorption to increase absortion using S
+it's always better if you can the better
+
+ align:start position:0%
+it's always better if you can the better
+ 
+
+ align:start position:0%
+it's always better if you can the better
+if you can use the S the first step you
+
+ align:start position:0%
+if you can use the S the first step you
+ 
+
+ align:start position:0%
+if you can use the S the first step you
+can prop light we're doing some
+
+ align:start position:0%
+can prop light we're doing some
+ 
+
+ align:start position:0%
+can prop light we're doing some
+research capitalize
+
+ align:start position:0%
+research capitalize
+ 
+
+ align:start position:0%
+research capitalize
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+uh here is
+
+ align:start position:0%
+uh here is
+ 
+
+ align:start position:0%
+uh here is
+about I'm not sure whether that's
+
+ align:start position:0%
+about I'm not sure whether that's
+ 
+
+ align:start position:0%
+about I'm not sure whether that's
+best just just copy from find to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+show people are doing transparent
+
+ align:start position:0%
+show people are doing transparent
+ 
+
+ align:start position:0%
+show people are doing transparent
+conductor also trying to improve the
+
+ align:start position:0%
+conductor also trying to improve the
+ 
+
+ align:start position:0%
+conductor also trying to improve the
+conductivity basically you want a very
+
+ align:start position:0%
+conductivity basically you want a very
+ 
+
+ align:start position:0%
+conductivity basically you want a very
+highly conduct it so if you highly
+
+ align:start position:0%
+highly conduct it so if you highly
+ 
+
+ align:start position:0%
+highly conduct it so if you highly
+conducted the CER is better because the
+
+ align:start position:0%
+conducted the CER is better because the
+ 
+
+ align:start position:0%
+conducted the CER is better because the
+free electron in this material
+
+ align:start position:0%
+free electron in this material
+ 
+
+ align:start position:0%
+free electron in this material
+also which generally you don't want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that right
+
+ align:start position:0%
+that right
+ 
+
+ align:start position:0%
+that right
+ideally if you you reduce cost by your
+
+ align:start position:0%
+ideally if you you reduce cost by your
+ 
+
+ align:start position:0%
+ideally if you you reduce cost by your
+situation the problem of thiser is that
+
+ align:start position:0%
+situation the problem of thiser is that
+ 
+
+ align:start position:0%
+situation the problem of thiser is that
+it's even worse than M of
+
+ align:start position:0%
+it's even worse than M of
+ 
+
+ align:start position:0%
+it's even worse than M of
+cicon right you generate a immediate Rec
+
+ align:start position:0%
+cicon right you generate a immediate Rec
+ 
+
+ align:start position:0%
+cicon right you generate a immediate Rec
+combine the combination is very fast in
+
+ align:start position:0%
+combine the combination is very fast in
+ 
+
+ align:start position:0%
+combine the combination is very fast in
+fact when first gener they bond it
+
+ align:start position:0%
+fact when first gener they bond it
+ 
+
+ align:start position:0%
+fact when first gener they bond it
+together they not even separate electon
+
+ align:start position:0%
+together they not even separate electon
+ 
+
+ align:start position:0%
+together they not even separate electon
+or hold this B state is called Aon so
+
+ align:start position:0%
+or hold this B state is called Aon so
+ 
+
+ align:start position:0%
+or hold this B state is called Aon so
+MIT has a Aon Center Center M we have I
+
+ align:start position:0%
+MIT has a Aon Center Center M we have I
+ 
+
+ align:start position:0%
+MIT has a Aon Center Center M we have I
+have saying a solar thermal Center
+
+ align:start position:0%
+have saying a solar thermal Center
+ 
+
+ align:start position:0%
+have saying a solar thermal Center
+ACC there is the whole issue to find how
+
+ align:start position:0%
+ACC there is the whole issue to find how
+ 
+
+ align:start position:0%
+ACC there is the whole issue to find how
+I can separate this
+
+ align:start position:0%
+I can separate this
+ 
+
+ align:start position:0%
+I can separate this
+X and make electron go one way and the
+
+ align:start position:0%
+X and make electron go one way and the
+ 
+
+ align:start position:0%
+X and make electron go one way and the
+hole go the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other right so in that case you look at
+
+ align:start position:0%
+other right so in that case you look at
+ 
+
+ align:start position:0%
+other right so in that case you look at
+this really thin uh 220
+
+ align:start position:0%
+this really thin uh 220
+ 
+
+ align:start position:0%
+this really thin uh 220
+NM try to
+
+ align:start position:0%
+NM try to
+ 
+
+ align:start position:0%
+NM try to
+separate but that's still difficult so
+
+ align:start position:0%
+separate but that's still difficult so
+ 
+
+ align:start position:0%
+separate but that's still difficult so
+people now doing the soal bul junction
+
+ align:start position:0%
+people now doing the soal bul junction
+ 
+
+ align:start position:0%
+people now doing the soal bul junction
+sales so put the two type of molecule
+
+ align:start position:0%
+sales so put the two type of molecule
+ 
+
+ align:start position:0%
+sales so put the two type of molecule
+one conduct electron one conduct so
+
+ align:start position:0%
+one conduct electron one conduct so
+ 
+
+ align:start position:0%
+one conduct electron one conduct so
+locally you gener electron righta you
+
+ align:start position:0%
+locally you gener electron righta you
+ 
+
+ align:start position:0%
+locally you gener electron righta you
+want to IM separate the go one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one gra cell right so this is not a
+
+ align:start position:0%
+one gra cell right so this is not a
+ 
+
+ align:start position:0%
+one gra cell right so this is not a
+solid cell it's act a liquid
+
+ align:start position:0%
+solid cell it's act a liquid
+ 
+
+ align:start position:0%
+solid cell it's act a liquid
+C and uh what it has is tianium dioxide
+
+ align:start position:0%
+C and uh what it has is tianium dioxide
+ 
+
+ align:start position:0%
+C and uh what it has is tianium dioxide
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay dioxide has B three electron Vols
+
+ align:start position:0%
+okay dioxide has B three electron Vols
+ 
+
+ align:start position:0%
+okay dioxide has B three electron Vols
+to L not much more
+
+ align:start position:0%
+to L not much more
+ 
+
+ align:start position:0%
+to L not much more
+full
+
+ align:start position:0%
+full
+ 
+
+ align:start position:0%
+full
+right and so
+
+ align:start position:0%
+right and so
+ 
+
+ align:start position:0%
+right and so
+what does you put a d on top of
+
+ align:start position:0%
+what does you put a d on top of
+ 
+
+ align:start position:0%
+what does you put a d on top of
+that and this D is called photosynth so
+
+ align:start position:0%
+that and this D is called photosynth so
+ 
+
+ align:start position:0%
+that and this D is called photosynth so
+this is where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phot and photons
+
+ align:start position:0%
+phot and photons
+ 
+
+ align:start position:0%
+phot and photons
+absorb time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more gener
+
+ align:start position:0%
+more gener
+ 
+
+ align:start position:0%
+more gener
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+ex before they dissociate they are and
+
+ align:start position:0%
+ex before they dissociate they are and
+ 
+
+ align:start position:0%
+ex before they dissociate they are and
+you one thing
+
+ align:start position:0%
+you one thing
+ 
+
+ align:start position:0%
+you one thing
+dissociate separate into electron hole
+
+ align:start position:0%
+dissociate separate into electron hole
+ 
+
+ align:start position:0%
+dissociate separate into electron hole
+and electron go into
+
+ align:start position:0%
+and electron go into
+ 
+
+ align:start position:0%
+and electron go into
+nle so the nle diffuse now there's no
+
+ align:start position:0%
+nle so the nle diffuse now there's no
+ 
+
+ align:start position:0%
+nle so the nle diffuse now there's no
+field really diffusion
+
+ align:start position:0%
+field really diffusion
+ 
+
+ align:start position:0%
+field really diffusion
+process okay so see the WR out so that's
+
+ align:start position:0%
+process okay so see the WR out so that's
+ 
+
+ align:start position:0%
+process okay so see the WR out so that's
+why people try to do n wires so that
+
+ align:start position:0%
+why people try to do n wires so that
+ 
+
+ align:start position:0%
+why people try to do n wires so that
+give a better pass to electr rather than
+
+ align:start position:0%
+give a better pass to electr rather than
+ 
+
+ align:start position:0%
+give a better pass to electr rather than
+n but the problem is when you put n wire
+
+ align:start position:0%
+n but the problem is when you put n wire
+ 
+
+ align:start position:0%
+n but the problem is when you put n wire
+your surface area for abortion also
+
+ align:start position:0%
+your surface area for abortion also
+ 
+
+ align:start position:0%
+your surface area for abortion also
+change right here you can have this area
+
+ align:start position:0%
+change right here you can have this area
+ 
+
+ align:start position:0%
+change right here you can have this area
+surface area
+
+ align:start position:0%
+surface area
+ 
+
+ align:start position:0%
+surface area
+one your your your not aware is only
+
+ align:start position:0%
+one your your your not aware is only
+ 
+
+ align:start position:0%
+one your your your not aware is only
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+surface right vertical so the surface
+
+ align:start position:0%
+surface right vertical so the surface
+ 
+
+ align:start position:0%
+surface right vertical so the surface
+area of absortion
+
+ align:start position:0%
+area of absortion
+ 
+
+ align:start position:0%
+area of absortion
+so has Advantage is just almost like 3D
+
+ align:start position:0%
+so has Advantage is just almost like 3D
+ 
+
+ align:start position:0%
+so has Advantage is just almost like 3D
+W around the
+
+ align:start position:0%
+W around the
+ 
+
+ align:start position:0%
+W around the
+more there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always and
+
+ align:start position:0%
+always and
+ 
+
+ align:start position:0%
+always and
+the ho go to the
+
+ align:start position:0%
+the ho go to the
+ 
+
+ align:start position:0%
+the ho go to the
+liquid and this is a chemical reaction
+
+ align:start position:0%
+liquid and this is a chemical reaction
+ 
+
+ align:start position:0%
+liquid and this is a chemical reaction
+noise not just a whole diffus theid
+
+ align:start position:0%
+noise not just a whole diffus theid
+ 
+
+ align:start position:0%
+noise not just a whole diffus theid
+there no
+
+ align:start position:0%
+there no
+ 
+
+ align:start position:0%
+there no
+can so so the ho
+
+ align:start position:0%
+can so so the ho
+ 
+
+ align:start position:0%
+can so so the ho
+oxidize the Moes in the case very often
+
+ align:start position:0%
+oxidize the Moes in the case very often
+ 
+
+ align:start position:0%
+oxidize the Moes in the case very often
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+iodine
+
+ align:start position:0%
+iodine
+ 
+
+ align:start position:0%
+iodine
+iodine say iodine 3
+
+ align:start position:0%
+iodine say iodine 3
+ 
+
+ align:start position:0%
+iodine say iodine 3
+and this charged molecule diffus to
+
+ align:start position:0%
+and this charged molecule diffus to
+ 
+
+ align:start position:0%
+and this charged molecule diffus to
+the again
+
+ align:start position:0%
+the again
+ 
+
+ align:start position:0%
+the again
+diffus so electron diffuse to one elect
+
+ align:start position:0%
+diffus so electron diffuse to one elect
+ 
+
+ align:start position:0%
+diffus so electron diffuse to one elect
+whole diffuse to the other elect where
+
+ align:start position:0%
+whole diffuse to the other elect where
+ 
+
+ align:start position:0%
+whole diffuse to the other elect where
+they reduce and they reduce the diffuse
+
+ align:start position:0%
+they reduce and they reduce the diffuse
+ 
+
+ align:start position:0%
+they reduce and they reduce the diffuse
+back sounds like a very cool process
+
+ align:start position:0%
+back sounds like a very cool process
+ 
+
+ align:start position:0%
+back sounds like a very cool process
+right the idea is again this you can
+
+ align:start position:0%
+right the idea is again this you can
+ 
+
+ align:start position:0%
+right the idea is again this you can
+pound see was pretty good getting that
+
+ align:start position:0%
+pound see was pretty good getting that
+ 
+
+ align:start position:0%
+pound see was pretty good getting that
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+this and see the so this
+
+ align:start position:0%
+this and see the so this
+ 
+
+ align:start position:0%
+this and see the so this
+is a flat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface so that's pretty much what I
+
+ align:start position:0%
+surface so that's pretty much what I
+ 
+
+ align:start position:0%
+surface so that's pretty much what I
+want to say and on time and this is the
+
+ align:start position:0%
+want to say and on time and this is the
+ 
+
+ align:start position:0%
+want to say and on time and this is the
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+dream okay the dream in the sense here's
+
+ align:start position:0%
+dream okay the dream in the sense here's
+ 
+
+ align:start position:0%
+dream okay the dream in the sense here's
+the cost here is efficiency you want the
+
+ align:start position:0%
+the cost here is efficiency you want the
+ 
+
+ align:start position:0%
+the cost here is efficiency you want the
+low cost high efficiency right
+
+ align:start position:0%
+low cost high efficiency right
+ 
+
+ align:start position:0%
+low cost high efficiency right
+silicon in the first generation called
+
+ align:start position:0%
+silicon in the first generation called
+ 
+
+ align:start position:0%
+silicon in the first generation called
+gen
+
+ align:start position:0%
+gen
+ 
+
+ align:start position:0%
+gen
+one fil is here lower efficiency but
+
+ align:start position:0%
+one fil is here lower efficiency but
+ 
+
+ align:start position:0%
+one fil is here lower efficiency but
+lower cost and in fact they make a good
+
+ align:start position:0%
+lower cost and in fact they make a good
+ 
+
+ align:start position:0%
+lower cost and in fact they make a good
+business at least
+
+ align:start position:0%
+business at least
+ 
+
+ align:start position:0%
+business at least
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+B and people go to
+
+ align:start position:0%
+B and people go to
+ 
+
+ align:start position:0%
+B and people go to
+G no winner in gen 3 okay this is where
+
+ align:start position:0%
+G no winner in gen 3 okay this is where
+ 
+
+ align:start position:0%
+G no winner in gen 3 okay this is where
+you guys could be win
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I think that's it
\ No newline at end of file
diff --git a/jcvxkX2V-SM.txt b/jcvxkX2V-SM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0c226d97fcb9143dafe45fc7965e1c51b7ba39a3
--- /dev/null
+++ b/jcvxkX2V-SM.txt
@@ -0,0 +1,787 @@
+align:start position:0%
+ 
+so we saw in the previous video that the
+
+ align:start position:0%
+so we saw in the previous video that the
+ 
+
+ align:start position:0%
+so we saw in the previous video that the
+house prices were distributed over the
+
+ align:start position:0%
+house prices were distributed over the
+ 
+
+ align:start position:0%
+house prices were distributed over the
+area in an interesting way it's
+
+ align:start position:0%
+area in an interesting way it's
+ 
+
+ align:start position:0%
+area in an interesting way it's
+certainly not a kind of linear way and
+
+ align:start position:0%
+certainly not a kind of linear way and
+ 
+
+ align:start position:0%
+certainly not a kind of linear way and
+we wouldn't in searly expect linear
+
+ align:start position:0%
+we wouldn't in searly expect linear
+ 
+
+ align:start position:0%
+we wouldn't in searly expect linear
+regression to do very well at predicting
+
+ align:start position:0%
+regression to do very well at predicting
+ 
+
+ align:start position:0%
+regression to do very well at predicting
+house price just given latitude and
+
+ align:start position:0%
+house price just given latitude and
+ 
+
+ align:start position:0%
+house price just given latitude and
+longitude we can kind of develop that
+
+ align:start position:0%
+longitude we can kind of develop that
+ 
+
+ align:start position:0%
+longitude we can kind of develop that
+intuition more by plotting the
+
+ align:start position:0%
+intuition more by plotting the
+ 
+
+ align:start position:0%
+intuition more by plotting the
+relationship between latitude and house
+
+ align:start position:0%
+relationship between latitude and house
+ 
+
+ align:start position:0%
+relationship between latitude and house
+prices which doesn't look very linear or
+
+ align:start position:0%
+prices which doesn't look very linear or
+ 
+
+ align:start position:0%
+prices which doesn't look very linear or
+the longitude and the house prices which
+
+ align:start position:0%
+the longitude and the house prices which
+ 
+
+ align:start position:0%
+the longitude and the house prices which
+also looks pretty non non linear so
+
+ align:start position:0%
+also looks pretty non non linear so
+ 
+
+ align:start position:0%
+also looks pretty non non linear so
+we'll fit we'll try fitting a linear
+
+ align:start position:0%
+we'll fit we'll try fitting a linear
+ 
+
+ align:start position:0%
+we'll fit we'll try fitting a linear
+regression anyway so let's call it lat
+
+ align:start position:0%
+regression anyway so let's call it lat
+ 
+
+ align:start position:0%
+regression anyway so let's call it lat
+lon LM and we'll use the Eliam command
+
+ align:start position:0%
+lon LM and we'll use the Eliam command
+ 
+
+ align:start position:0%
+lon LM and we'll use the Eliam command
+the linear model to predict house prices
+
+ align:start position:0%
+the linear model to predict house prices
+ 
+
+ align:start position:0%
+the linear model to predict house prices
+based on latitude and longitude using
+
+ align:start position:0%
+based on latitude and longitude using
+ 
+
+ align:start position:0%
+based on latitude and longitude using
+the Boston data set and if we take a
+
+ align:start position:0%
+the Boston data set and if we take a
+ 
+
+ align:start position:0%
+the Boston data set and if we take a
+look at our linear regression we see the
+
+ align:start position:0%
+look at our linear regression we see the
+ 
+
+ align:start position:0%
+look at our linear regression we see the
+a squared is around 0.1 which is not
+
+ align:start position:0%
+a squared is around 0.1 which is not
+ 
+
+ align:start position:0%
+a squared is around 0.1 which is not
+great the latitude is not significant
+
+ align:start position:0%
+great the latitude is not significant
+ 
+
+ align:start position:0%
+great the latitude is not significant
+which means the north-south differences
+
+ align:start position:0%
+which means the north-south differences
+ 
+
+ align:start position:0%
+which means the north-south differences
+and going to be really used at all
+
+ align:start position:0%
+and going to be really used at all
+ 
+
+ align:start position:0%
+and going to be really used at all
+longitude is significant and it's
+
+ align:start position:0%
+longitude is significant and it's
+ 
+
+ align:start position:0%
+longitude is significant and it's
+negative which we can interpret as as we
+
+ align:start position:0%
+negative which we can interpret as as we
+ 
+
+ align:start position:0%
+negative which we can interpret as as we
+go towards the ocean as we go towards
+
+ align:start position:0%
+go towards the ocean as we go towards
+ 
+
+ align:start position:0%
+go towards the ocean as we go towards
+the East house prices decrease linearly
+
+ align:start position:0%
+the East house prices decrease linearly
+ 
+
+ align:start position:0%
+the East house prices decrease linearly
+so this all seems kind of unlikely but
+
+ align:start position:0%
+so this all seems kind of unlikely but
+ 
+
+ align:start position:0%
+so this all seems kind of unlikely but
+let's work with it so let's see how this
+
+ align:start position:0%
+let's work with it so let's see how this
+ 
+
+ align:start position:0%
+let's work with it so let's see how this
+linear regression model looks on a plot
+
+ align:start position:0%
+linear regression model looks on a plot
+ 
+
+ align:start position:0%
+linear regression model looks on a plot
+so let's plot the since the strikes
+
+ align:start position:0%
+so let's plot the since the strikes
+ 
+
+ align:start position:0%
+so let's plot the since the strikes
+again okay now Brenda before we had from
+
+ align:start position:0%
+again okay now Brenda before we had from
+ 
+
+ align:start position:0%
+again okay now Brenda before we had from
+the previous video we plotted the above
+
+ align:start position:0%
+the previous video we plotted the above
+ 
+
+ align:start position:0%
+the previous video we plotted the above
+median house prices so we're gonna do
+
+ align:start position:0%
+median house prices so we're gonna do
+ 
+
+ align:start position:0%
+median house prices so we're gonna do
+that one more time
+
+ align:start position:0%
+that one more time
+ 
+
+ align:start position:0%
+that one more time
+the meeting was twenty one point two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we had the color was red and we used
+
+ align:start position:0%
+we had the color was red and we used
+ 
+
+ align:start position:0%
+we had the color was red and we used
+solid dots ha whoops see you wrote it
+
+ align:start position:0%
+solid dots ha whoops see you wrote it
+ 
+
+ align:start position:0%
+solid dots ha whoops see you wrote it
+down I use the plot command instead of
+
+ align:start position:0%
+down I use the plot command instead of
+ 
+
+ align:start position:0%
+down I use the plot command instead of
+the points command and it plotted just
+
+ align:start position:0%
+the points command and it plotted just
+ 
+
+ align:start position:0%
+the points command and it plotted just
+some new points I meant to do
+
+ align:start position:0%
+some new points I meant to do
+ 
+
+ align:start position:0%
+some new points I meant to do
+plot the original points and use the
+
+ align:start position:0%
+plot the original points and use the
+ 
+
+ align:start position:0%
+plot the original points and use the
+points command to plot it on top of the
+
+ align:start position:0%
+points command to plot it on top of the
+ 
+
+ align:start position:0%
+points command to plot it on top of the
+existing plot okay so that's more like
+
+ align:start position:0%
+existing plot okay so that's more like
+ 
+
+ align:start position:0%
+existing plot okay so that's more like
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so now we have the median values we have
+
+ align:start position:0%
+so now we have the median values we have
+ 
+
+ align:start position:0%
+so now we have the median values we have
+the above median value census tracks so
+
+ align:start position:0%
+the above median value census tracks so
+ 
+
+ align:start position:0%
+the above median value census tracks so
+okay we want to see now the question
+
+ align:start position:0%
+okay we want to see now the question
+ 
+
+ align:start position:0%
+okay we want to see now the question
+we're going to ask and then plot is what
+
+ align:start position:0%
+we're going to ask and then plot is what
+ 
+
+ align:start position:0%
+we're going to ask and then plot is what
+does the linear regression model think
+
+ align:start position:0%
+does the linear regression model think
+ 
+
+ align:start position:0%
+does the linear regression model think
+is above median so we could just do this
+
+ align:start position:0%
+is above median so we could just do this
+ 
+
+ align:start position:0%
+is above median so we could just do this
+pretty easily
+
+ align:start position:0%
+pretty easily
+ 
+
+ align:start position:0%
+pretty easily
+we have lat lon LM has a field fitted
+
+ align:start position:0%
+we have lat lon LM has a field fitted
+ 
+
+ align:start position:0%
+we have lat lon LM has a field fitted
+values and this is what the linear
+
+ align:start position:0%
+values and this is what the linear
+ 
+
+ align:start position:0%
+values and this is what the linear
+regression model predicts for each of a
+
+ align:start position:0%
+regression model predicts for each of a
+ 
+
+ align:start position:0%
+regression model predicts for each of a
+506 census tracts so we'll plot these on
+
+ align:start position:0%
+506 census tracts so we'll plot these on
+ 
+
+ align:start position:0%
+506 census tracts so we'll plot these on
+top Boston lon
+
+ align:start position:0%
+top Boston lon
+ 
+
+ align:start position:0%
+top Boston lon
+take all the census tracts such that the
+
+ align:start position:0%
+take all the census tracts such that the
+ 
+
+ align:start position:0%
+take all the census tracts such that the
+lat/long alliums
+
+ align:start position:0%
+lat/long alliums
+ 
+
+ align:start position:0%
+lat/long alliums
+fitted values are above the median take
+
+ align:start position:0%
+fitted values are above the median take
+ 
+
+ align:start position:0%
+fitted values are above the median take
+the ladder shoes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm gonna make them blue but let's
+
+ align:start position:0%
+and I'm gonna make them blue but let's
+ 
+
+ align:start position:0%
+and I'm gonna make them blue but let's
+pause for a moment and think if we use
+
+ align:start position:0%
+pause for a moment and think if we use
+ 
+
+ align:start position:0%
+pause for a moment and think if we use
+the dots again we'll cover up the red
+
+ align:start position:0%
+the dots again we'll cover up the red
+ 
+
+ align:start position:0%
+the dots again we'll cover up the red
+dots and cover up some of the black dots
+
+ align:start position:0%
+dots and cover up some of the black dots
+ 
+
+ align:start position:0%
+dots and cover up some of the black dots
+what we won't be able to see is where
+
+ align:start position:0%
+what we won't be able to see is where
+ 
+
+ align:start position:0%
+what we won't be able to see is where
+the red dots and the blue dots match up
+
+ align:start position:0%
+the red dots and the blue dots match up
+ 
+
+ align:start position:0%
+the red dots and the blue dots match up
+you know we're interesting seeing how
+
+ align:start position:0%
+you know we're interesting seeing how
+ 
+
+ align:start position:0%
+you know we're interesting seeing how
+the linear regression matches up with
+
+ align:start position:0%
+the linear regression matches up with
+ 
+
+ align:start position:0%
+the linear regression matches up with
+the truth so it'd be ideal if we could
+
+ align:start position:0%
+the truth so it'd be ideal if we could
+ 
+
+ align:start position:0%
+the truth so it'd be ideal if we could
+plot the linear regression blue dots on
+
+ align:start position:0%
+plot the linear regression blue dots on
+ 
+
+ align:start position:0%
+plot the linear regression blue dots on
+top of the red dots in some way that we
+
+ align:start position:0%
+top of the red dots in some way that we
+ 
+
+ align:start position:0%
+top of the red dots in some way that we
+can still see the red does it turns out
+
+ align:start position:0%
+can still see the red does it turns out
+ 
+
+ align:start position:0%
+can still see the red does it turns out
+that you can actually pass in characters
+
+ align:start position:0%
+that you can actually pass in characters
+ 
+
+ align:start position:0%
+that you can actually pass in characters
+to this PCH option so since we're
+
+ align:start position:0%
+to this PCH option so since we're
+ 
+
+ align:start position:0%
+to this PCH option so since we're
+talking about money
+
+ align:start position:0%
+talking about money
+ 
+
+ align:start position:0%
+talking about money
+let's plot dollar signs instead of
+
+ align:start position:0%
+let's plot dollar signs instead of
+ 
+
+ align:start position:0%
+let's plot dollar signs instead of
+points and there you have it so the
+
+ align:start position:0%
+points and there you have it so the
+ 
+
+ align:start position:0%
+points and there you have it so the
+linear regression model has plotted a
+
+ align:start position:0%
+linear regression model has plotted a
+ 
+
+ align:start position:0%
+linear regression model has plotted a
+dollar sign for every time that things
+
+ align:start position:0%
+dollar sign for every time that things
+ 
+
+ align:start position:0%
+dollar sign for every time that things
+are census tract as above median value
+
+ align:start position:0%
+are census tract as above median value
+ 
+
+ align:start position:0%
+are census tract as above median value
+and you can see that indeed there's
+
+ align:start position:0%
+and you can see that indeed there's
+ 
+
+ align:start position:0%
+and you can see that indeed there's
+almost you can see the sharp line that
+
+ align:start position:0%
+almost you can see the sharp line that
+ 
+
+ align:start position:0%
+almost you can see the sharp line that
+the linear regression defines and how
+
+ align:start position:0%
+the linear regression defines and how
+ 
+
+ align:start position:0%
+the linear regression defines and how
+it's pretty much vertical because
+
+ align:start position:0%
+it's pretty much vertical because
+ 
+
+ align:start position:0%
+it's pretty much vertical because
+remember before the latitude variable
+
+ align:start position:0%
+remember before the latitude variable
+ 
+
+ align:start position:0%
+remember before the latitude variable
+was not very significant in the
+
+ align:start position:0%
+was not very significant in the
+ 
+
+ align:start position:0%
+was not very significant in the
+regression so that's interesting and
+
+ align:start position:0%
+regression so that's interesting and
+ 
+
+ align:start position:0%
+regression so that's interesting and
+pretty wrong one thing that really
+
+ align:start position:0%
+pretty wrong one thing that really
+ 
+
+ align:start position:0%
+pretty wrong one thing that really
+stands out is how it says Boston is
+
+ align:start position:0%
+stands out is how it says Boston is
+ 
+
+ align:start position:0%
+stands out is how it says Boston is
+mostly above median even though we we
+
+ align:start position:0%
+mostly above median even though we we
+ 
+
+ align:start position:0%
+mostly above median even though we we
+saw a right from the step is a big non
+
+ align:start position:0%
+saw a right from the step is a big non
+ 
+
+ align:start position:0%
+saw a right from the step is a big non
+red spot right in the middle of Boston
+
+ align:start position:0%
+red spot right in the middle of Boston
+ 
+
+ align:start position:0%
+red spot right in the middle of Boston
+where the the house prices were below
+
+ align:start position:0%
+where the the house prices were below
+ 
+
+ align:start position:0%
+where the the house prices were below
+the median so the linear regression
+
+ align:start position:0%
+the median so the linear regression
+ 
+
+ align:start position:0%
+the median so the linear regression
+model isn't really doing a good job and
+
+ align:start position:0%
+model isn't really doing a good job and
+ 
+
+ align:start position:0%
+model isn't really doing a good job and
+it's completely ignored everything to
+
+ align:start position:0%
+it's completely ignored everything to
+ 
+
+ align:start position:0%
+it's completely ignored everything to
+the right side of a picture
\ No newline at end of file
diff --git a/kphOAvHVy0E.txt b/kphOAvHVy0E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b31640cbc0de638e9862a17a2f0362b6689755bf
--- /dev/null
+++ b/kphOAvHVy0E.txt
@@ -0,0 +1,595 @@
+align:start position:0%
+ 
+currents induced in a conducting shell
+
+ align:start position:0%
+currents induced in a conducting shell
+ 
+
+ align:start position:0%
+currents induced in a conducting shell
+oppose the penetration of a suddenly
+
+ align:start position:0%
+oppose the penetration of a suddenly
+ 
+
+ align:start position:0%
+oppose the penetration of a suddenly
+applied magnetic field
+
+ align:start position:0%
+applied magnetic field
+ 
+
+ align:start position:0%
+applied magnetic field
+and cause a force that tends to crush
+
+ align:start position:0%
+and cause a force that tends to crush
+ 
+
+ align:start position:0%
+and cause a force that tends to crush
+the shell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here again is edgerton's boomer
+
+ align:start position:0%
+here again is edgerton's boomer
+ 
+
+ align:start position:0%
+here again is edgerton's boomer
+apparatus composed of the driver coil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and large capacitor bank with total
+
+ align:start position:0%
+and large capacitor bank with total
+ 
+
+ align:start position:0%
+and large capacitor bank with total
+capacitance of 48 microfarads
+
+ align:start position:0%
+capacitance of 48 microfarads
+ 
+
+ align:start position:0%
+capacitance of 48 microfarads
+the capacitor bank is charged to 4
+
+ align:start position:0%
+the capacitor bank is charged to 4
+ 
+
+ align:start position:0%
+the capacitor bank is charged to 4
+kilovolts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discharging the capacitor into the coil
+
+ align:start position:0%
+discharging the capacitor into the coil
+ 
+
+ align:start position:0%
+discharging the capacitor into the coil
+with this trigger
+
+ align:start position:0%
+with this trigger
+ 
+
+ align:start position:0%
+with this trigger
+generates a large transient current in
+
+ align:start position:0%
+generates a large transient current in
+ 
+
+ align:start position:0%
+generates a large transient current in
+the coil which in turn generates a large
+
+ align:start position:0%
+the coil which in turn generates a large
+ 
+
+ align:start position:0%
+the coil which in turn generates a large
+magnetic field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+currents induced in the thin foil
+
+ align:start position:0%
+currents induced in the thin foil
+ 
+
+ align:start position:0%
+currents induced in the thin foil
+cylinder to oppose the penetration of
+
+ align:start position:0%
+cylinder to oppose the penetration of
+ 
+
+ align:start position:0%
+cylinder to oppose the penetration of
+magnetic field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cause a radial inwards force on the
+
+ align:start position:0%
+cause a radial inwards force on the
+ 
+
+ align:start position:0%
+cause a radial inwards force on the
+cylinder but tends to crush it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see that again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with this time constant in mind let's
+
+ align:start position:0%
+with this time constant in mind let's
+ 
+
+ align:start position:0%
+with this time constant in mind let's
+see what the actual fields are
+
+ align:start position:0%
+see what the actual fields are
+ 
+
+ align:start position:0%
+see what the actual fields are
+because this is a single shot experiment
+
+ align:start position:0%
+because this is a single shot experiment
+ 
+
+ align:start position:0%
+because this is a single shot experiment
+we use the storage oscilloscope to
+
+ align:start position:0%
+we use the storage oscilloscope to
+ 
+
+ align:start position:0%
+we use the storage oscilloscope to
+record and store measured waveforms
+
+ align:start position:0%
+record and store measured waveforms
+ 
+
+ align:start position:0%
+record and store measured waveforms
+we use this current probe to record the
+
+ align:start position:0%
+we use this current probe to record the
+ 
+
+ align:start position:0%
+we use this current probe to record the
+current in the coil
+
+ align:start position:0%
+current in the coil
+ 
+
+ align:start position:0%
+current in the coil
+in the upper oscilloscope trace its gain
+
+ align:start position:0%
+in the upper oscilloscope trace its gain
+ 
+
+ align:start position:0%
+in the upper oscilloscope trace its gain
+has been adjusted to 500 amps per
+
+ align:start position:0%
+has been adjusted to 500 amps per
+ 
+
+ align:start position:0%
+has been adjusted to 500 amps per
+centimeter
+
+ align:start position:0%
+centimeter
+ 
+
+ align:start position:0%
+centimeter
+this small 200 turn coil is placed just
+
+ align:start position:0%
+this small 200 turn coil is placed just
+ 
+
+ align:start position:0%
+this small 200 turn coil is placed just
+above the driver coil to record the time
+
+ align:start position:0%
+above the driver coil to record the time
+ 
+
+ align:start position:0%
+above the driver coil to record the time
+derivative of magnetic flux on the lower
+
+ align:start position:0%
+derivative of magnetic flux on the lower
+ 
+
+ align:start position:0%
+derivative of magnetic flux on the lower
+oscilloscope trace
+
+ align:start position:0%
+oscilloscope trace
+ 
+
+ align:start position:0%
+oscilloscope trace
+we charge the capacitor to four
+
+ align:start position:0%
+we charge the capacitor to four
+ 
+
+ align:start position:0%
+we charge the capacitor to four
+kilovolts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as we discharge the capacitor bank we
+
+ align:start position:0%
+as we discharge the capacitor bank we
+ 
+
+ align:start position:0%
+as we discharge the capacitor bank we
+record the current oscillations in the
+
+ align:start position:0%
+record the current oscillations in the
+ 
+
+ align:start position:0%
+record the current oscillations in the
+driver coil on the upper scope trace
+
+ align:start position:0%
+driver coil on the upper scope trace
+ 
+
+ align:start position:0%
+driver coil on the upper scope trace
+and the time derivative of the magnetic
+
+ align:start position:0%
+and the time derivative of the magnetic
+ 
+
+ align:start position:0%
+and the time derivative of the magnetic
+flux on the lower scope trace
+
+ align:start position:0%
+flux on the lower scope trace
+ 
+
+ align:start position:0%
+flux on the lower scope trace
+we see decaying oscillations
+
+ align:start position:0%
+we see decaying oscillations
+ 
+
+ align:start position:0%
+we see decaying oscillations
+characteristic of the rlc circuit
+
+ align:start position:0%
+characteristic of the rlc circuit
+ 
+
+ align:start position:0%
+characteristic of the rlc circuit
+for our circuit parameters the frequency
+
+ align:start position:0%
+for our circuit parameters the frequency
+ 
+
+ align:start position:0%
+for our circuit parameters the frequency
+of oscillation is about four kilohertz
+
+ align:start position:0%
+of oscillation is about four kilohertz
+ 
+
+ align:start position:0%
+of oscillation is about four kilohertz
+we store these waveforms and reset the
+
+ align:start position:0%
+we store these waveforms and reset the
+ 
+
+ align:start position:0%
+we store these waveforms and reset the
+scope trigger
+
+ align:start position:0%
+scope trigger
+ 
+
+ align:start position:0%
+scope trigger
+we now place the foil cylinder around
+
+ align:start position:0%
+we now place the foil cylinder around
+ 
+
+ align:start position:0%
+we now place the foil cylinder around
+the magnetic flux sensing coil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember the upper trace records the
+
+ align:start position:0%
+remember the upper trace records the
+ 
+
+ align:start position:0%
+remember the upper trace records the
+driver coil current
+
+ align:start position:0%
+driver coil current
+ 
+
+ align:start position:0%
+driver coil current
+which imposes the magnetic field while
+
+ align:start position:0%
+which imposes the magnetic field while
+ 
+
+ align:start position:0%
+which imposes the magnetic field while
+the lower trace records the sensing coil
+
+ align:start position:0%
+the lower trace records the sensing coil
+ 
+
+ align:start position:0%
+the lower trace records the sensing coil
+signal
+
+ align:start position:0%
+signal
+ 
+
+ align:start position:0%
+signal
+now inside the cylinder
+
+ align:start position:0%
+now inside the cylinder
+ 
+
+ align:start position:0%
+now inside the cylinder
+we see that the driver coil current
+
+ align:start position:0%
+we see that the driver coil current
+ 
+
+ align:start position:0%
+we see that the driver coil current
+waveform has diminished somewhat
+
+ align:start position:0%
+waveform has diminished somewhat
+ 
+
+ align:start position:0%
+waveform has diminished somewhat
+but that the sensing coil waveform
+
+ align:start position:0%
+but that the sensing coil waveform
+ 
+
+ align:start position:0%
+but that the sensing coil waveform
+within the foil cylinder has decreased
+
+ align:start position:0%
+within the foil cylinder has decreased
+ 
+
+ align:start position:0%
+within the foil cylinder has decreased
+even more
+
+ align:start position:0%
+even more
+ 
+
+ align:start position:0%
+even more
+the magnetic field has been shielded out
+
+ align:start position:0%
+the magnetic field has been shielded out
+ 
+
+ align:start position:0%
+the magnetic field has been shielded out
+of the cylinder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's measure the field inside another
+
+ align:start position:0%
+let's measure the field inside another
+ 
+
+ align:start position:0%
+let's measure the field inside another
+aluminum cylinder that is about a
+
+ align:start position:0%
+aluminum cylinder that is about a
+ 
+
+ align:start position:0%
+aluminum cylinder that is about a
+hundred times thicker
+
+ align:start position:0%
+hundred times thicker
+ 
+
+ align:start position:0%
+hundred times thicker
+the bottom scope trace shows the field
+
+ align:start position:0%
+the bottom scope trace shows the field
+ 
+
+ align:start position:0%
+the bottom scope trace shows the field
+without the cylinder
+
+ align:start position:0%
+without the cylinder
+ 
+
+ align:start position:0%
+without the cylinder
+let's reset the scope and put the thick
+
+ align:start position:0%
+let's reset the scope and put the thick
+ 
+
+ align:start position:0%
+let's reset the scope and put the thick
+cylinder around the sensing coil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the new lower trace is essentially zero
+
+ align:start position:0%
+the new lower trace is essentially zero
+ 
+
+ align:start position:0%
+the new lower trace is essentially zero
+for a mega tau
+
+ align:start position:0%
+for a mega tau
+ 
+
+ align:start position:0%
+for a mega tau
+m of order a hundred the magnetic field
+
+ align:start position:0%
+m of order a hundred the magnetic field
+ 
+
+ align:start position:0%
+m of order a hundred the magnetic field
+inside the cylinder is greatly reduced
\ No newline at end of file
diff --git a/lbtrbE_kK_Q.txt b/lbtrbE_kK_Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cf17b2cb4d54fd5231f026d9f8bcb7c81a9094d7
--- /dev/null
+++ b/lbtrbE_kK_Q.txt
@@ -0,0 +1,7715 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I wanted to use this final time our we
+
+ align:start position:0%
+I wanted to use this final time our we
+ 
+
+ align:start position:0%
+I wanted to use this final time our we
+have together to summarize a few of this
+
+ align:start position:0%
+have together to summarize a few of this
+ 
+
+ align:start position:0%
+have together to summarize a few of this
+what I take to be the central themes of
+
+ align:start position:0%
+what I take to be the central themes of
+ 
+
+ align:start position:0%
+what I take to be the central themes of
+the course the the organizing ideas that
+
+ align:start position:0%
+the course the the organizing ideas that
+ 
+
+ align:start position:0%
+the course the the organizing ideas that
+that then at least have seemed to me to
+
+ align:start position:0%
+that then at least have seemed to me to
+ 
+
+ align:start position:0%
+that then at least have seemed to me to
+structure our our argument and our
+
+ align:start position:0%
+structure our our argument and our
+ 
+
+ align:start position:0%
+structure our our argument and our
+progress through these Oh through this
+
+ align:start position:0%
+progress through these Oh through this
+ 
+
+ align:start position:0%
+progress through these Oh through this
+almost a hundred years of movies the
+
+ align:start position:0%
+almost a hundred years of movies the
+ 
+
+ align:start position:0%
+almost a hundred years of movies the
+first idea at one that we've come back
+
+ align:start position:0%
+first idea at one that we've come back
+ 
+
+ align:start position:0%
+first idea at one that we've come back
+to I think again and again has to do
+
+ align:start position:0%
+to I think again and again has to do
+ 
+
+ align:start position:0%
+to I think again and again has to do
+with what we might call film in its
+
+ align:start position:0%
+with what we might call film in its
+ 
+
+ align:start position:0%
+with what we might call film in its
+anthropological or sociological aspect
+
+ align:start position:0%
+anthropological or sociological aspect
+ 
+
+ align:start position:0%
+anthropological or sociological aspect
+film as a cultural form as an expression
+
+ align:start position:0%
+film as a cultural form as an expression
+ 
+
+ align:start position:0%
+film as a cultural form as an expression
+of a culture as something that grows out
+
+ align:start position:0%
+of a culture as something that grows out
+ 
+
+ align:start position:0%
+of a culture as something that grows out
+of a culture that expresses the values
+
+ align:start position:0%
+of a culture that expresses the values
+ 
+
+ align:start position:0%
+of a culture that expresses the values
+and prejudices and weirdnesses of a
+
+ align:start position:0%
+and prejudices and weirdnesses of a
+ 
+
+ align:start position:0%
+and prejudices and weirdnesses of a
+culture from this angle questions of
+
+ align:start position:0%
+culture from this angle questions of
+ 
+
+ align:start position:0%
+culture from this angle questions of
+aesthetic value questions of artistic
+
+ align:start position:0%
+aesthetic value questions of artistic
+ 
+
+ align:start position:0%
+aesthetic value questions of artistic
+excellence are irrelevant in some sense
+
+ align:start position:0%
+excellence are irrelevant in some sense
+ 
+
+ align:start position:0%
+excellence are irrelevant in some sense
+within it from this angle we're thinking
+
+ align:start position:0%
+within it from this angle we're thinking
+ 
+
+ align:start position:0%
+within it from this angle we're thinking
+about film simply as a as a central
+
+ align:start position:0%
+about film simply as a as a central
+ 
+
+ align:start position:0%
+about film simply as a as a central
+expression as a central habit of culture
+
+ align:start position:0%
+expression as a central habit of culture
+ 
+
+ align:start position:0%
+expression as a central habit of culture
+itself and we might we might recognize
+
+ align:start position:0%
+itself and we might we might recognize
+ 
+
+ align:start position:0%
+itself and we might we might recognize
+that in the 20th century film where film
+
+ align:start position:0%
+that in the 20th century film where film
+ 
+
+ align:start position:0%
+that in the 20th century film where film
+was the dominant narrative form the film
+
+ align:start position:0%
+was the dominant narrative form the film
+ 
+
+ align:start position:0%
+was the dominant narrative form the film
+performed functions in the 20th century
+
+ align:start position:0%
+performed functions in the 20th century
+ 
+
+ align:start position:0%
+performed functions in the 20th century
+that earlier forms of storytelling of
+
+ align:start position:0%
+that earlier forms of storytelling of
+ 
+
+ align:start position:0%
+that earlier forms of storytelling of
+narrative and drama had played in
+
+ align:start position:0%
+narrative and drama had played in
+ 
+
+ align:start position:0%
+narrative and drama had played in
+earlier cultures and one of my deep
+
+ align:start position:0%
+earlier cultures and one of my deep
+ 
+
+ align:start position:0%
+earlier cultures and one of my deep
+desires in the course one of my implicit
+
+ align:start position:0%
+desires in the course one of my implicit
+ 
+
+ align:start position:0%
+desires in the course one of my implicit
+ambitions all the way through was to
+
+ align:start position:0%
+ambitions all the way through was to
+ 
+
+ align:start position:0%
+ambitions all the way through was to
+encourage you to think about movies in
+
+ align:start position:0%
+encourage you to think about movies in
+ 
+
+ align:start position:0%
+encourage you to think about movies in
+this way as an as a as as an expression
+
+ align:start position:0%
+this way as an as a as as an expression
+ 
+
+ align:start position:0%
+this way as an as a as as an expression
+of the values and assumptions of 20th
+
+ align:start position:0%
+of the values and assumptions of 20th
+ 
+
+ align:start position:0%
+of the values and assumptions of 20th
+century cultures which might in earlier
+
+ align:start position:0%
+century cultures which might in earlier
+ 
+
+ align:start position:0%
+century cultures which might in earlier
+times have been expressed in other media
+
+ align:start position:0%
+times have been expressed in other media
+ 
+
+ align:start position:0%
+times have been expressed in other media
+and was I it was important for me to
+
+ align:start position:0%
+and was I it was important for me to
+ 
+
+ align:start position:0%
+and was I it was important for me to
+have you recognize that our 20th and
+
+ align:start position:0%
+have you recognize that our 20th and
+ 
+
+ align:start position:0%
+have you recognize that our 20th and
+21st century although it's somewhat
+
+ align:start position:0%
+21st century although it's somewhat
+ 
+
+ align:start position:0%
+21st century although it's somewhat
+different in the 21st century because
+
+ align:start position:0%
+different in the 21st century because
+ 
+
+ align:start position:0%
+different in the 21st century because
+films are film is undergoing such a
+
+ align:start position:0%
+films are film is undergoing such a
+ 
+
+ align:start position:0%
+films are film is undergoing such a
+profound transformation in the digital
+
+ align:start position:0%
+profound transformation in the digital
+ 
+
+ align:start position:0%
+profound transformation in the digital
+age nonetheless in the 20th and the 21st
+
+ align:start position:0%
+age nonetheless in the 20th and the 21st
+ 
+
+ align:start position:0%
+age nonetheless in the 20th and the 21st
+century audio-visual narrative is a
+
+ align:start position:0%
+century audio-visual narrative is a
+ 
+
+ align:start position:0%
+century audio-visual narrative is a
+dominant experience for virtue
+
+ align:start position:0%
+dominant experience for virtue
+ 
+
+ align:start position:0%
+dominant experience for virtue
+everyone in the in the world in earlier
+
+ align:start position:0%
+everyone in the in the world in earlier
+ 
+
+ align:start position:0%
+everyone in the in the world in earlier
+societies we had didn't have this option
+
+ align:start position:0%
+societies we had didn't have this option
+ 
+
+ align:start position:0%
+societies we had didn't have this option
+but it didn't mean that the functions
+
+ align:start position:0%
+but it didn't mean that the functions
+ 
+
+ align:start position:0%
+but it didn't mean that the functions
+played by the movies weren't played by
+
+ align:start position:0%
+played by the movies weren't played by
+ 
+
+ align:start position:0%
+played by the movies weren't played by
+earlier forms so that's one of it that's
+
+ align:start position:0%
+earlier forms so that's one of it that's
+ 
+
+ align:start position:0%
+earlier forms so that's one of it that's
+been one of the deepest umph shion's one
+
+ align:start position:0%
+been one of the deepest umph shion's one
+ 
+
+ align:start position:0%
+been one of the deepest umph shion's one
+of the recurring principles to which
+
+ align:start position:0%
+of the recurring principles to which
+ 
+
+ align:start position:0%
+of the recurring principles to which
+I've recurred through the through the
+
+ align:start position:0%
+I've recurred through the through the
+ 
+
+ align:start position:0%
+I've recurred through the through the
+through the course and another aspect of
+
+ align:start position:0%
+through the course and another aspect of
+ 
+
+ align:start position:0%
+through the course and another aspect of
+this idea something I've come back to I
+
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+ align:start position:0%
+of collaboration in which they're
+constantly borrowing forms and arguments
+
+ align:start position:0%
+constantly borrowing forms and arguments
+ 
+
+ align:start position:0%
+constantly borrowing forms and arguments
+and principles and symbols from the vast
+
+ align:start position:0%
+and principles and symbols from the vast
+ 
+
+ align:start position:0%
+and principles and symbols from the vast
+body of shared knowledge that a culture
+
+ align:start position:0%
+body of shared knowledge that a culture
+ 
+
+ align:start position:0%
+body of shared knowledge that a culture
+might have and so that but what this
+
+ align:start position:0%
+might have and so that but what this
+ 
+
+ align:start position:0%
+might have and so that but what this
+might actually lead to or some what one
+
+ align:start position:0%
+might actually lead to or some what one
+ 
+
+ align:start position:0%
+might actually lead to or some what one
+thing this leads to is the recognition
+
+ align:start position:0%
+thing this leads to is the recognition
+ 
+
+ align:start position:0%
+thing this leads to is the recognition
+that these cultural forms are not always
+
+ align:start position:0%
+that these cultural forms are not always
+ 
+
+ align:start position:0%
+that these cultural forms are not always
+Noble or wonderful that they carry
+
+ align:start position:0%
+Noble or wonderful that they carry
+ 
+
+ align:start position:0%
+Noble or wonderful that they carry
+prejudices that they carry racism that
+
+ align:start position:0%
+prejudices that they carry racism that
+ 
+
+ align:start position:0%
+prejudices that they carry racism that
+they carry misogyny that they're going
+
+ align:start position:0%
+they carry misogyny that they're going
+ 
+
+ align:start position:0%
+they carry misogyny that they're going
+to embody that that that the that the
+
+ align:start position:0%
+to embody that that that the that the
+ 
+
+ align:start position:0%
+to embody that that that the that the
+study of these Texas not as necessarily
+
+ align:start position:0%
+study of these Texas not as necessarily
+ 
+
+ align:start position:0%
+study of these Texas not as necessarily
+it shouldn't that never should be a
+
+ align:start position:0%
+it shouldn't that never should be a
+ 
+
+ align:start position:0%
+it shouldn't that never should be a
+totally celebratory experience even
+
+ align:start position:0%
+totally celebratory experience even
+ 
+
+ align:start position:0%
+totally celebratory experience even
+though many of these texts are want
+
+ align:start position:0%
+though many of these texts are want
+ 
+
+ align:start position:0%
+though many of these texts are want
+valuable and lasting and and speak to us
+
+ align:start position:0%
+valuable and lasting and and speak to us
+ 
+
+ align:start position:0%
+valuable and lasting and and speak to us
+in deep and powerful and useful ways
+
+ align:start position:0%
+in deep and powerful and useful ways
+ 
+
+ align:start position:0%
+in deep and powerful and useful ways
+it's also true that these texts carry
+
+ align:start position:0%
+it's also true that these texts carry
+ 
+
+ align:start position:0%
+it's also true that these texts carry
+the lies and prejudices of the cultures
+
+ align:start position:0%
+the lies and prejudices of the cultures
+ 
+
+ align:start position:0%
+the lies and prejudices of the cultures
+from which they come as I've said a
+
+ align:start position:0%
+from which they come as I've said a
+ 
+
+ align:start position:0%
+from which they come as I've said a
+number of times in the course perhaps
+
+ align:start position:0%
+number of times in the course perhaps
+ 
+
+ align:start position:0%
+number of times in the course perhaps
+too many times but there's a nut but I
+
+ align:start position:0%
+too many times but there's a nut but I
+ 
+
+ align:start position:0%
+too many times but there's a nut but I
+meant but I mentioned again in in this
+
+ align:start position:0%
+meant but I mentioned again in in this
+ 
+
+ align:start position:0%
+meant but I mentioned again in in this
+last lecture because I want to also
+
+ align:start position:0%
+last lecture because I want to also
+ 
+
+ align:start position:0%
+last lecture because I want to also
+mention that there's a way in which not
+
+ align:start position:0%
+mention that there's a way in which not
+ 
+
+ align:start position:0%
+mention that there's a way in which not
+just the evils and the limitations of a
+
+ align:start position:0%
+just the evils and the limitations of a
+ 
+
+ align:start position:0%
+just the evils and the limitations of a
+society that get expressed in the in the
+
+ align:start position:0%
+society that get expressed in the in the
+ 
+
+ align:start position:0%
+society that get expressed in the in the
+color in the in the collaborative
+
+ align:start position:0%
+color in the in the collaborative
+ 
+
+ align:start position:0%
+color in the in the collaborative
+consensus forms that emerge from them
+
+ align:start position:0%
+consensus forms that emerge from them
+ 
+
+ align:start position:0%
+consensus forms that emerge from them
+but also sometimes the wisdom of a
+
+ align:start position:0%
+but also sometimes the wisdom of a
+ 
+
+ align:start position:0%
+but also sometimes the wisdom of a
+society does - in other words what I
+
+ align:start position:0%
+society does - in other words what I
+ 
+
+ align:start position:0%
+society does - in other words what I
+want to suggest you is that the
+
+ align:start position:0%
+want to suggest you is that the
+ 
+
+ align:start position:0%
+want to suggest you is that the
+collaboration has to do not only with
+
+ align:start position:0%
+collaboration has to do not only with
+ 
+
+ align:start position:0%
+collaboration has to do not only with
+with with inherited values and inherited
+
+ align:start position:0%
+with with inherited values and inherited
+ 
+
+ align:start position:0%
+with with inherited values and inherited
+beliefs and inherited story forms they
+
+ align:start position:0%
+beliefs and inherited story forms they
+ 
+
+ align:start position:0%
+beliefs and inherited story forms they
+also have they also have to do sort of
+
+ align:start position:0%
+also have they also have to do sort of
+ 
+
+ align:start position:0%
+also have they also have to do sort of
+with a cut whether with a cut with the
+
+ align:start position:0%
+with a cut whether with a cut with the
+ 
+
+ align:start position:0%
+with a cut whether with a cut with the
+kind of inheritance of them of wisdom
+
+ align:start position:0%
+kind of inheritance of them of wisdom
+ 
+
+ align:start position:0%
+kind of inheritance of them of wisdom
+and I have a particularly exciting way
+
+ align:start position:0%
+and I have a particularly exciting way
+ 
+
+ align:start position:0%
+and I have a particularly exciting way
+of distilling this for you there's a
+
+ align:start position:0%
+of distilling this for you there's a
+ 
+
+ align:start position:0%
+of distilling this for you there's a
+passage one of my favorite passages from
+
+ align:start position:0%
+passage one of my favorite passages from
+ 
+
+ align:start position:0%
+passage one of my favorite passages from
+Shakespeare from his from his great late
+
+ align:start position:0%
+Shakespeare from his from his great late
+ 
+
+ align:start position:0%
+Shakespeare from his from his great late
+play Cymbeline from act 4
+
+ align:start position:0%
+play Cymbeline from act 4
+ 
+
+ align:start position:0%
+play Cymbeline from act 4
+- in which a group of characters gather
+
+ align:start position:0%
+- in which a group of characters gather
+ 
+
+ align:start position:0%
+- in which a group of characters gather
+around a body they think the body
+
+ align:start position:0%
+around a body they think the body
+ 
+
+ align:start position:0%
+around a body they think the body
+actually comes alive later in the play
+
+ align:start position:0%
+actually comes alive later in the play
+ 
+
+ align:start position:0%
+actually comes alive later in the play
+because there's a lot of wonderful magic
+
+ align:start position:0%
+because there's a lot of wonderful magic
+ 
+
+ align:start position:0%
+because there's a lot of wonderful magic
+in the play it's a play about Redemption
+
+ align:start position:0%
+in the play it's a play about Redemption
+ 
+
+ align:start position:0%
+in the play it's a play about Redemption
+and rebirth but at this moment in the
+
+ align:start position:0%
+and rebirth but at this moment in the
+ 
+
+ align:start position:0%
+and rebirth but at this moment in the
+play they think this person is dead and
+
+ align:start position:0%
+play they think this person is dead and
+ 
+
+ align:start position:0%
+play they think this person is dead and
+they sing a dirge it's one of the most
+
+ align:start position:0%
+they sing a dirge it's one of the most
+ 
+
+ align:start position:0%
+they sing a dirge it's one of the most
+uh dirt assault a funeral song a song a
+
+ align:start position:0%
+uh dirt assault a funeral song a song a
+ 
+
+ align:start position:0%
+uh dirt assault a funeral song a song a
+song or a poem to be sung or recited at
+
+ align:start position:0%
+song or a poem to be sung or recited at
+ 
+
+ align:start position:0%
+song or a poem to be sung or recited at
+a graveside and there's a maybe the
+
+ align:start position:0%
+a graveside and there's a maybe the
+ 
+
+ align:start position:0%
+a graveside and there's a maybe the
+greatest of all such churches in English
+
+ align:start position:0%
+greatest of all such churches in English
+ 
+
+ align:start position:0%
+greatest of all such churches in English
+is in Cymbeline and this is the first
+
+ align:start position:0%
+is in Cymbeline and this is the first
+ 
+
+ align:start position:0%
+is in Cymbeline and this is the first
+stanza and the greatest stanza
+
+ align:start position:0%
+stanza and the greatest stanza
+ 
+
+ align:start position:0%
+stanza and the greatest stanza
+fear no more right there people are
+
+ align:start position:0%
+fear no more right there people are
+ 
+
+ align:start position:0%
+fear no more right there people are
+standing over a corpse right fear no
+
+ align:start position:0%
+standing over a corpse right fear no
+ 
+
+ align:start position:0%
+standing over a corpse right fear no
+more the heat of the Sun nor the Furious
+
+ align:start position:0%
+more the heat of the Sun nor the Furious
+ 
+
+ align:start position:0%
+more the heat of the Sun nor the Furious
+winters rages val by worldly tasks hath
+
+ align:start position:0%
+winters rages val by worldly tasks hath
+ 
+
+ align:start position:0%
+winters rages val by worldly tasks hath
+done home art gone and taken thy wages
+
+ align:start position:0%
+done home art gone and taken thy wages
+ 
+
+ align:start position:0%
+done home art gone and taken thy wages
+very interesting to me - to image to
+
+ align:start position:0%
+very interesting to me - to image to
+ 
+
+ align:start position:0%
+very interesting to me - to image to
+embrace a metaphor of working of were a
+
+ align:start position:0%
+embrace a metaphor of working of were a
+ 
+
+ align:start position:0%
+embrace a metaphor of working of were a
+working-class metaphor right you've got
+
+ align:start position:0%
+working-class metaphor right you've got
+ 
+
+ align:start position:0%
+working-class metaphor right you've got
+you're dying when and the metaphor is
+
+ align:start position:0%
+you're dying when and the metaphor is
+ 
+
+ align:start position:0%
+you're dying when and the metaphor is
+you've taken I what you you've taken
+
+ align:start position:0%
+you've taken I what you you've taken
+ 
+
+ align:start position:0%
+you've taken I what you you've taken
+your last wages you've finished your
+
+ align:start position:0%
+your last wages you've finished your
+ 
+
+ align:start position:0%
+your last wages you've finished your
+your work home art gone and taking my
+
+ align:start position:0%
+your work home art gone and taking my
+ 
+
+ align:start position:0%
+your work home art gone and taking my
+wages and here comes the couplet that I
+
+ align:start position:0%
+wages and here comes the couplet that I
+ 
+
+ align:start position:0%
+wages and here comes the couplet that I
+think is most powerful golden lads and
+
+ align:start position:0%
+think is most powerful golden lads and
+ 
+
+ align:start position:0%
+think is most powerful golden lads and
+girls all must as chimney sweepers come
+
+ align:start position:0%
+girls all must as chimney sweepers come
+ 
+
+ align:start position:0%
+girls all must as chimney sweepers come
+to dust let me say it again so you get
+
+ align:start position:0%
+to dust let me say it again so you get
+ 
+
+ align:start position:0%
+to dust let me say it again so you get
+the whole stanza it's quite beautiful I
+
+ align:start position:0%
+the whole stanza it's quite beautiful I
+ 
+
+ align:start position:0%
+the whole stanza it's quite beautiful I
+think fear no more the heat of the Sun
+
+ align:start position:0%
+think fear no more the heat of the Sun
+ 
+
+ align:start position:0%
+think fear no more the heat of the Sun
+nor the Furious winters rages thou thy
+
+ align:start position:0%
+nor the Furious winters rages thou thy
+ 
+
+ align:start position:0%
+nor the Furious winters rages thou thy
+worldly task hath done home art gone and
+
+ align:start position:0%
+worldly task hath done home art gone and
+ 
+
+ align:start position:0%
+worldly task hath done home art gone and
+taken thy wages golden lads and girls
+
+ align:start position:0%
+taken thy wages golden lads and girls
+ 
+
+ align:start position:0%
+taken thy wages golden lads and girls
+all must as chimney sweepers come to
+
+ align:start position:0%
+all must as chimney sweepers come to
+ 
+
+ align:start position:0%
+all must as chimney sweepers come to
+dust now think about those last lines
+
+ align:start position:0%
+dust now think about those last lines
+ 
+
+ align:start position:0%
+dust now think about those last lines
+for a minute they're very powerful even
+
+ align:start position:0%
+for a minute they're very powerful even
+ 
+
+ align:start position:0%
+for a minute they're very powerful even
+if you don't exactly get them golden
+
+ align:start position:0%
+if you don't exactly get them golden
+ 
+
+ align:start position:0%
+if you don't exactly get them golden
+lads and girls right
+
+ align:start position:0%
+lads and girls right
+ 
+
+ align:start position:0%
+lads and girls right
+the implication is highborn wealthy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+golden in their youth and in their
+
+ align:start position:0%
+golden in their youth and in their
+ 
+
+ align:start position:0%
+golden in their youth and in their
+energy and in their and in their and
+
+ align:start position:0%
+energy and in their and in their and
+ 
+
+ align:start position:0%
+energy and in their and in their and
+then in their vitality no matter how
+
+ align:start position:0%
+then in their vitality no matter how
+ 
+
+ align:start position:0%
+then in their vitality no matter how
+golden whether in wealth or in vitality
+
+ align:start position:0%
+golden whether in wealth or in vitality
+ 
+
+ align:start position:0%
+golden whether in wealth or in vitality
+even even golden golden lads and girls
+
+ align:start position:0%
+even even golden golden lads and girls
+ 
+
+ align:start position:0%
+even even golden golden lads and girls
+end up in the grave like all of us and
+
+ align:start position:0%
+end up in the grave like all of us and
+ 
+
+ align:start position:0%
+end up in the grave like all of us and
+there's a the implication of course is
+
+ align:start position:0%
+there's a the implication of course is
+ 
+
+ align:start position:0%
+there's a the implication of course is
+there's a kind of consolation in the
+
+ align:start position:0%
+there's a kind of consolation in the
+ 
+
+ align:start position:0%
+there's a kind of consolation in the
+fact that its death is our shared fate
+
+ align:start position:0%
+fact that its death is our shared fate
+ 
+
+ align:start position:0%
+fact that its death is our shared fate
+there's a it's a console an attempt to
+
+ align:start position:0%
+there's a it's a console an attempt to
+ 
+
+ align:start position:0%
+there's a it's a console an attempt to
+console us although the older I get the
+
+ align:start position:0%
+console us although the older I get the
+ 
+
+ align:start position:0%
+console us although the older I get the
+less consolation they get but I I find
+
+ align:start position:0%
+less consolation they get but I I find
+ 
+
+ align:start position:0%
+less consolation they get but I I find
+myself taking from this insight
+
+ align:start position:0%
+myself taking from this insight
+ 
+
+ align:start position:0%
+myself taking from this insight
+nonetheless it is a great poem and the
+
+ align:start position:0%
+nonetheless it is a great poem and the
+ 
+
+ align:start position:0%
+nonetheless it is a great poem and the
+stanza is a particularly remarkable poem
+
+ align:start position:0%
+stanza is a particularly remarkable poem
+ 
+
+ align:start position:0%
+stanza is a particularly remarkable poem
+because of one element in it
+
+ align:start position:0%
+because of one element in it
+ 
+
+ align:start position:0%
+because of one element in it
+the phrase golden lads for those of you
+
+ align:start position:0%
+the phrase golden lads for those of you
+ 
+
+ align:start position:0%
+the phrase golden lads for those of you
+very few Americans know this but some
+
+ align:start position:0%
+very few Americans know this but some
+ 
+
+ align:start position:0%
+very few Americans know this but some
+Brits know this
+
+ align:start position:0%
+Brits know this
+ 
+
+ align:start position:0%
+Brits know this
+in Shakespeare's native Warwickshire the
+
+ align:start position:0%
+in Shakespeare's native Warwickshire the
+ 
+
+ align:start position:0%
+in Shakespeare's native Warwickshire the
+phrase golden lad referred to something
+
+ align:start position:0%
+phrase golden lad referred to something
+ 
+
+ align:start position:0%
+phrase golden lad referred to something
+very specific it referred to the
+
+ align:start position:0%
+very specific it referred to the
+ 
+
+ align:start position:0%
+very specific it referred to the
+condition of the common ordinary flower
+
+ align:start position:0%
+condition of the common ordinary flower
+ 
+
+ align:start position:0%
+condition of the common ordinary flower
+that we call the dandelion and it's a
+
+ align:start position:0%
+that we call the dandelion and it's a
+ 
+
+ align:start position:0%
+that we call the dandelion and it's a
+it's a flower that that that has a gold
+
+ align:start position:0%
+it's a flower that that that has a gold
+ 
+
+ align:start position:0%
+it's a flower that that that has a gold
+cap when it's when it's young and then
+
+ align:start position:0%
+cap when it's when it's young and then
+ 
+
+ align:start position:0%
+cap when it's when it's young and then
+when it goes to seed and you've all seen
+
+ align:start position:0%
+when it goes to seed and you've all seen
+ 
+
+ align:start position:0%
+when it goes to seed and you've all seen
+them because they're native to North
+
+ align:start position:0%
+them because they're native to North
+ 
+
+ align:start position:0%
+them because they're native to North
+America as well as England they're the
+
+ align:start position:0%
+America as well as England they're the
+ 
+
+ align:start position:0%
+America as well as England they're the
+the top of the cap
+
+ align:start position:0%
+the top of the cap
+ 
+
+ align:start position:0%
+the top of the cap
+turns into a kind of rounded series of
+
+ align:start position:0%
+turns into a kind of rounded series of
+ 
+
+ align:start position:0%
+turns into a kind of rounded series of
+filaments a beautiful round cap and get
+
+ align:start position:0%
+filaments a beautiful round cap and get
+ 
+
+ align:start position:0%
+filaments a beautiful round cap and get
+when when you're a lot of children pick
+
+ align:start position:0%
+when when you're a lot of children pick
+ 
+
+ align:start position:0%
+when when you're a lot of children pick
+them and blow them and you could the
+
+ align:start position:0%
+them and blow them and you could the
+ 
+
+ align:start position:0%
+them and blow them and you could the
+seeds blow although one of the reasons
+
+ align:start position:0%
+seeds blow although one of the reasons
+ 
+
+ align:start position:0%
+seeds blow although one of the reasons
+that these that these common weedy
+
+ align:start position:0%
+that these that these common weedy
+ 
+
+ align:start position:0%
+that these that these common weedy
+flowers are so common is that they're so
+
+ align:start position:0%
+flowers are so common is that they're so
+ 
+
+ align:start position:0%
+flowers are so common is that they're so
+they're so brilliantly designed by
+
+ align:start position:0%
+they're so brilliantly designed by
+ 
+
+ align:start position:0%
+they're so brilliantly designed by
+nature to propagate because the wind
+
+ align:start position:0%
+nature to propagate because the wind
+ 
+
+ align:start position:0%
+nature to propagate because the wind
+blows their their seeds all over the
+
+ align:start position:0%
+blows their their seeds all over the
+ 
+
+ align:start position:0%
+blows their their seeds all over the
+place do you all have an image of this
+
+ align:start position:0%
+place do you all have an image of this
+ 
+
+ align:start position:0%
+place do you all have an image of this
+so when they're young the flowers have
+
+ align:start position:0%
+so when they're young the flowers have
+ 
+
+ align:start position:0%
+so when they're young the flowers have
+these golden caps and then when they go
+
+ align:start position:0%
+these golden caps and then when they go
+ 
+
+ align:start position:0%
+these golden caps and then when they go
+to seed they become these rat they have
+
+ align:start position:0%
+to seed they become these rat they have
+ 
+
+ align:start position:0%
+to seed they become these rat they have
+these rounded filaments on the top and
+
+ align:start position:0%
+these rounded filaments on the top and
+ 
+
+ align:start position:0%
+these rounded filaments on the top and
+these rounded filaments in Shakespeare's
+
+ align:start position:0%
+these rounded filaments in Shakespeare's
+ 
+
+ align:start position:0%
+these rounded filaments in Shakespeare's
+day were called golden lads when they
+
+ align:start position:0%
+day were called golden lads when they
+ 
+
+ align:start position:0%
+day were called golden lads when they
+they were actually called these flowers
+
+ align:start position:0%
+they were actually called these flowers
+ 
+
+ align:start position:0%
+they were actually called these flowers
+were called golden lads when they were
+
+ align:start position:0%
+were called golden lads when they were
+ 
+
+ align:start position:0%
+were called golden lads when they were
+in bloom and they were called Chimney
+
+ align:start position:0%
+in bloom and they were called Chimney
+ 
+
+ align:start position:0%
+in bloom and they were called Chimney
+Sweeps
+
+ align:start position:0%
+Sweeps
+ 
+
+ align:start position:0%
+Sweeps
+when they when they went to seed because
+
+ align:start position:0%
+when they when they went to seed because
+ 
+
+ align:start position:0%
+when they when they went to seed because
+they looked exactly like the chimney
+
+ align:start position:0%
+they looked exactly like the chimney
+ 
+
+ align:start position:0%
+they looked exactly like the chimney
+sweepers broom chimney sweepers would
+
+ align:start position:0%
+sweepers broom chimney sweepers would
+ 
+
+ align:start position:0%
+sweepers broom chimney sweepers would
+take these rounded brooms and put them
+
+ align:start position:0%
+take these rounded brooms and put them
+ 
+
+ align:start position:0%
+take these rounded brooms and put them
+up in chimneys to clean them so when
+
+ align:start position:0%
+up in chimneys to clean them so when
+ 
+
+ align:start position:0%
+up in chimneys to clean them so when
+Shakespeare writes in the in the end
+
+ align:start position:0%
+Shakespeare writes in the in the end
+ 
+
+ align:start position:0%
+Shakespeare writes in the in the end
+there he says golden lads and girls all
+
+ align:start position:0%
+there he says golden lads and girls all
+ 
+
+ align:start position:0%
+there he says golden lads and girls all
+must as chimney sweepers come to dust
+
+ align:start position:0%
+must as chimney sweepers come to dust
+ 
+
+ align:start position:0%
+must as chimney sweepers come to dust
+he's describing literally the
+
+ align:start position:0%
+he's describing literally the
+ 
+
+ align:start position:0%
+he's describing literally the
+raises of life in a flower why is that
+
+ align:start position:0%
+raises of life in a flower why is that
+ 
+
+ align:start position:0%
+raises of life in a flower why is that
+wonderful can you see why that's
+
+ align:start position:0%
+wonderful can you see why that's
+ 
+
+ align:start position:0%
+wonderful can you see why that's
+wonderful why that's what art is because
+
+ align:start position:0%
+wonderful why that's what art is because
+ 
+
+ align:start position:0%
+wonderful why that's what art is because
+of course what's happened is that what
+
+ align:start position:0%
+of course what's happened is that what
+ 
+
+ align:start position:0%
+of course what's happened is that what
+shakes we did was turning will create a
+
+ align:start position:0%
+shakes we did was turning will create a
+ 
+
+ align:start position:0%
+shakes we did was turning will create a
+brilliant metaphor out of something
+
+ align:start position:0%
+brilliant metaphor out of something
+ 
+
+ align:start position:0%
+brilliant metaphor out of something
+that's profoundly concrete right and but
+
+ align:start position:0%
+that's profoundly concrete right and but
+ 
+
+ align:start position:0%
+that's profoundly concrete right and but
+but so the phrase golden lad and chimney
+
+ align:start position:0%
+but so the phrase golden lad and chimney
+ 
+
+ align:start position:0%
+but so the phrase golden lad and chimney
+sweeper actually refers to the life
+
+ align:start position:0%
+sweeper actually refers to the life
+ 
+
+ align:start position:0%
+sweeper actually refers to the life
+cycle of a flower we'll think of how
+
+ align:start position:0%
+cycle of a flower we'll think of how
+ 
+
+ align:start position:0%
+cycle of a flower we'll think of how
+much more consoling how profoundly
+
+ align:start position:0%
+much more consoling how profoundly
+ 
+
+ align:start position:0%
+much more consoling how profoundly
+brilliant the lines become when actually
+
+ align:start position:0%
+brilliant the lines become when actually
+ 
+
+ align:start position:0%
+brilliant the lines become when actually
+Shakespeare's metaphor is literally
+
+ align:start position:0%
+Shakespeare's metaphor is literally
+ 
+
+ align:start position:0%
+Shakespeare's metaphor is literally
+linked to the passages of nature to the
+
+ align:start position:0%
+linked to the passages of nature to the
+ 
+
+ align:start position:0%
+linked to the passages of nature to the
+progress of nature right so what I'm
+
+ align:start position:0%
+progress of nature right so what I'm
+ 
+
+ align:start position:0%
+progress of nature right so what I'm
+what I'm calling your attention to is a
+
+ align:start position:0%
+what I'm calling your attention to is a
+ 
+
+ align:start position:0%
+what I'm calling your attention to is a
+brilliant piece of poetry is a piece of
+
+ align:start position:0%
+brilliant piece of poetry is a piece of
+ 
+
+ align:start position:0%
+brilliant piece of poetry is a piece of
+poetry that has a kind of richness and
+
+ align:start position:0%
+poetry that has a kind of richness and
+ 
+
+ align:start position:0%
+poetry that has a kind of richness and
+complexity that's all that that almost
+
+ align:start position:0%
+complexity that's all that that almost
+ 
+
+ align:start position:0%
+complexity that's all that that almost
+couldn't be better
+
+ align:start position:0%
+couldn't be better
+ 
+
+ align:start position:0%
+couldn't be better
+right I mean and even when we don't know
+
+ align:start position:0%
+right I mean and even when we don't know
+ 
+
+ align:start position:0%
+right I mean and even when we don't know
+that about the flower we get the meaning
+
+ align:start position:0%
+that about the flower we get the meaning
+ 
+
+ align:start position:0%
+that about the flower we get the meaning
+of the lines but think how the lines
+
+ align:start position:0%
+of the lines but think how the lines
+ 
+
+ align:start position:0%
+of the lines but think how the lines
+come alive once we recognize that the
+
+ align:start position:0%
+come alive once we recognize that the
+ 
+
+ align:start position:0%
+come alive once we recognize that the
+progress of human life in those couplets
+
+ align:start position:0%
+progress of human life in those couplets
+ 
+
+ align:start position:0%
+progress of human life in those couplets
+is being explicitly associated with with
+
+ align:start position:0%
+is being explicitly associated with with
+ 
+
+ align:start position:0%
+is being explicitly associated with with
+the life cycle of a natural object of a
+
+ align:start position:0%
+the life cycle of a natural object of a
+ 
+
+ align:start position:0%
+the life cycle of a natural object of a
+flower right now this is a great act of
+
+ align:start position:0%
+flower right now this is a great act of
+ 
+
+ align:start position:0%
+flower right now this is a great act of
+poet poetic genius isn't it but where
+
+ align:start position:0%
+poet poetic genius isn't it but where
+ 
+
+ align:start position:0%
+poet poetic genius isn't it but where
+does the genius lie where does it come
+
+ align:start position:0%
+does the genius lie where does it come
+ 
+
+ align:start position:0%
+does the genius lie where does it come
+experience collaborating with the wisdom
+
+ align:start position:0%
+experience collaborating with the wisdom
+ 
+
+ align:start position:0%
+experience collaborating with the wisdom
+of his culture he it takes Shakespeare
+
+ align:start position:0%
+of his culture he it takes Shakespeare
+ 
+
+ align:start position:0%
+of his culture he it takes Shakespeare
+to figure it out I mean I'm not saying
+
+ align:start position:0%
+to figure it out I mean I'm not saying
+ 
+
+ align:start position:0%
+to figure it out I mean I'm not saying
+that it isn't an act of genius for
+
+ align:start position:0%
+that it isn't an act of genius for
+ 
+
+ align:start position:0%
+that it isn't an act of genius for
+Shakespeare to realize the metaphoric
+
+ align:start position:0%
+Shakespeare to realize the metaphoric
+ 
+
+ align:start position:0%
+Shakespeare to realize the metaphoric
+implications of this he did but the
+
+ align:start position:0%
+implications of this he did but the
+ 
+
+ align:start position:0%
+implications of this he did but the
+metaphor is embedded in the way ordinary
+
+ align:start position:0%
+metaphor is embedded in the way ordinary
+ 
+
+ align:start position:0%
+metaphor is embedded in the way ordinary
+people named that flower for hundreds
+
+ align:start position:0%
+people named that flower for hundreds
+ 
+
+ align:start position:0%
+people named that flower for hundreds
+and perhaps thousands of years
+
+ align:start position:0%
+and perhaps thousands of years
+ 
+
+ align:start position:0%
+and perhaps thousands of years
+Shakespeare is collaborating there with
+
+ align:start position:0%
+Shakespeare is collaborating there with
+ 
+
+ align:start position:0%
+Shakespeare is collaborating there with
+the wisdom of his culture with the
+
+ align:start position:0%
+the wisdom of his culture with the
+ 
+
+ align:start position:0%
+the wisdom of his culture with the
+shared understanding of his society in
+
+ align:start position:0%
+shared understanding of his society in
+ 
+
+ align:start position:0%
+shared understanding of his society in
+order to make that brilliant line of
+
+ align:start position:0%
+order to make that brilliant line of
+ 
+
+ align:start position:0%
+order to make that brilliant line of
+poetry so we can take the that idea that
+
+ align:start position:0%
+poetry so we can take the that idea that
+ 
+
+ align:start position:0%
+poetry so we can take the that idea that
+the notion of golden lads as a kind of
+
+ align:start position:0%
+the notion of golden lads as a kind of
+ 
+
+ align:start position:0%
+the notion of golden lads as a kind of
+emblem for the collaborative energies
+
+ align:start position:0%
+emblem for the collaborative energies
+ 
+
+ align:start position:0%
+emblem for the collaborative energies
+that are sometimes released when artists
+
+ align:start position:0%
+that are sometimes released when artists
+ 
+
+ align:start position:0%
+that are sometimes released when artists
+collaborate with the traditions of their
+
+ align:start position:0%
+collaborate with the traditions of their
+ 
+
+ align:start position:0%
+collaborate with the traditions of their
+culture with the traditions of naming
+
+ align:start position:0%
+culture with the traditions of naming
+ 
+
+ align:start position:0%
+culture with the traditions of naming
+with the traditions of understanding
+
+ align:start position:0%
+with the traditions of understanding
+ 
+
+ align:start position:0%
+with the traditions of understanding
+that are embedded and so therefore the
+
+ align:start position:0%
+that are embedded and so therefore the
+ 
+
+ align:start position:0%
+that are embedded and so therefore the
+collaboration is a deep one it's an
+
+ align:start position:0%
+collaboration is a deep one it's an
+ 
+
+ align:start position:0%
+collaboration is a deep one it's an
+intellectual and a menace and a and an
+
+ align:start position:0%
+intellectual and a menace and a and an
+ 
+
+ align:start position:0%
+intellectual and a menace and a and an
+expressive and a creative collaboration
+
+ align:start position:0%
+expressive and a creative collaboration
+ 
+
+ align:start position:0%
+expressive and a creative collaboration
+between the societies understanding of
+
+ align:start position:0%
+between the societies understanding of
+ 
+
+ align:start position:0%
+between the societies understanding of
+the of things of the cultures underst
+
+ align:start position:0%
+the of things of the cultures underst
+ 
+
+ align:start position:0%
+the of things of the cultures underst
+ending of things and the artists
+
+ align:start position:0%
+ending of things and the artists
+ 
+
+ align:start position:0%
+ending of things and the artists
+interaction with those that's an aspect
+
+ align:start position:0%
+interaction with those that's an aspect
+ 
+
+ align:start position:0%
+interaction with those that's an aspect
+of an even deeper aspect of what I mean
+
+ align:start position:0%
+of an even deeper aspect of what I mean
+ 
+
+ align:start position:0%
+of an even deeper aspect of what I mean
+when I say that consensus narrative and
+
+ align:start position:0%
+when I say that consensus narrative and
+ 
+
+ align:start position:0%
+when I say that consensus narrative and
+that movies are a collaborative art form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I've also tried to suggest again and
+
+ align:start position:0%
+I've also tried to suggest again and
+ 
+
+ align:start position:0%
+I've also tried to suggest again and
+again in the course that there are films
+
+ align:start position:0%
+again in the course that there are films
+ 
+
+ align:start position:0%
+again in the course that there are films
+and many of most of the films we've seen
+
+ align:start position:0%
+and many of most of the films we've seen
+ 
+
+ align:start position:0%
+and many of most of the films we've seen
+in this semester also deserve the
+
+ align:start position:0%
+in this semester also deserve the
+ 
+
+ align:start position:0%
+in this semester also deserve the
+designation art and I don't want I've
+
+ align:start position:0%
+designation art and I don't want I've
+ 
+
+ align:start position:0%
+designation art and I don't want I've
+not really wanted to turn the term art
+
+ align:start position:0%
+not really wanted to turn the term art
+ 
+
+ align:start position:0%
+not really wanted to turn the term art
+into a kind of elitist category which
+
+ align:start position:0%
+into a kind of elitist category which
+ 
+
+ align:start position:0%
+into a kind of elitist category which
+sort of in which we from which we must
+
+ align:start position:0%
+sort of in which we from which we must
+ 
+
+ align:start position:0%
+sort of in which we from which we must
+sort of retreat in awe and bow before it
+
+ align:start position:0%
+sort of retreat in awe and bow before it
+ 
+
+ align:start position:0%
+sort of retreat in awe and bow before it
+I want us to think of art in a simpler
+
+ align:start position:0%
+I want us to think of art in a simpler
+ 
+
+ align:start position:0%
+I want us to think of art in a simpler
+and I think more useful way as a form of
+
+ align:start position:0%
+and I think more useful way as a form of
+ 
+
+ align:start position:0%
+and I think more useful way as a form of
+intelligence and competence right in
+
+ align:start position:0%
+intelligence and competence right in
+ 
+
+ align:start position:0%
+intelligence and competence right in
+other words when things are done well in
+
+ align:start position:0%
+other words when things are done well in
+ 
+
+ align:start position:0%
+other words when things are done well in
+a work of art when the thing when when a
+
+ align:start position:0%
+a work of art when the thing when when a
+ 
+
+ align:start position:0%
+a work of art when the thing when when a
+movie is well made when a poem is well
+
+ align:start position:0%
+movie is well made when a poem is well
+ 
+
+ align:start position:0%
+movie is well made when a poem is well
+made we we admire it and we respect it
+
+ align:start position:0%
+made we we admire it and we respect it
+ 
+
+ align:start position:0%
+made we we admire it and we respect it
+and we don't have to get mystical about
+
+ align:start position:0%
+and we don't have to get mystical about
+ 
+
+ align:start position:0%
+and we don't have to get mystical about
+the qualities of art in order to
+
+ align:start position:0%
+the qualities of art in order to
+ 
+
+ align:start position:0%
+the qualities of art in order to
+recognize that intelligence and
+
+ align:start position:0%
+recognize that intelligence and
+ 
+
+ align:start position:0%
+recognize that intelligence and
+competence are are are qualities that
+
+ align:start position:0%
+competence are are are qualities that
+ 
+
+ align:start position:0%
+competence are are are qualities that
+that we value in other aspects of
+
+ align:start position:0%
+that we value in other aspects of
+ 
+
+ align:start position:0%
+that we value in other aspects of
+experience as well as in art itself and
+
+ align:start position:0%
+experience as well as in art itself and
+ 
+
+ align:start position:0%
+experience as well as in art itself and
+what what do I mean specifically by
+
+ align:start position:0%
+what what do I mean specifically by
+ 
+
+ align:start position:0%
+what what do I mean specifically by
+intelligence and competence the most
+
+ align:start position:0%
+intelligence and competence the most
+ 
+
+ align:start position:0%
+intelligence and competence the most
+profound way of understanding this
+
+ align:start position:0%
+profound way of understanding this
+ 
+
+ align:start position:0%
+profound way of understanding this
+argument has to do with what I've spoken
+
+ align:start position:0%
+argument has to do with what I've spoken
+ 
+
+ align:start position:0%
+argument has to do with what I've spoken
+about a number of times in the course
+
+ align:start position:0%
+about a number of times in the course
+ 
+
+ align:start position:0%
+about a number of times in the course
+I've sometimes used the phrase organic
+
+ align:start position:0%
+I've sometimes used the phrase organic
+ 
+
+ align:start position:0%
+I've sometimes used the phrase organic
+form to explain what I meant in that in
+
+ align:start position:0%
+form to explain what I meant in that in
+ 
+
+ align:start position:0%
+form to explain what I meant in that in
+this regard but essentially the idea has
+
+ align:start position:0%
+this regard but essentially the idea has
+ 
+
+ align:start position:0%
+this regard but essentially the idea has
+to do with the sense with the
+
+ align:start position:0%
+to do with the sense with the
+ 
+
+ align:start position:0%
+to do with the sense with the
+recognition that a serious artist will
+
+ align:start position:0%
+recognition that a serious artist will
+ 
+
+ align:start position:0%
+recognition that a serious artist will
+use instruments that further his or her
+
+ align:start position:0%
+use instruments that further his or her
+ 
+
+ align:start position:0%
+use instruments that further his or her
+intentions effectively and fully that is
+
+ align:start position:0%
+intentions effectively and fully that is
+ 
+
+ align:start position:0%
+intentions effectively and fully that is
+to say that there's a connection between
+
+ align:start position:0%
+to say that there's a connection between
+ 
+
+ align:start position:0%
+to say that there's a connection between
+the formal or stylistic choices that an
+
+ align:start position:0%
+the formal or stylistic choices that an
+ 
+
+ align:start position:0%
+the formal or stylistic choices that an
+artist makes and the content that is
+
+ align:start position:0%
+artist makes and the content that is
+ 
+
+ align:start position:0%
+artist makes and the content that is
+part of the artwork that is to say that
+
+ align:start position:0%
+part of the artwork that is to say that
+ 
+
+ align:start position:0%
+part of the artwork that is to say that
+there's a that there's a link or a bora
+
+ align:start position:0%
+there's a that there's a link or a bora
+ 
+
+ align:start position:0%
+there's a that there's a link or a bora
+ora ora or a connection between the
+
+ align:start position:0%
+ora ora or a connection between the
+ 
+
+ align:start position:0%
+ora ora or a connection between the
+formal choices that a writer or a
+
+ align:start position:0%
+formal choices that a writer or a
+ 
+
+ align:start position:0%
+formal choices that a writer or a
+filmmaker makes and the content intended
+
+ align:start position:0%
+filmmaker makes and the content intended
+ 
+
+ align:start position:0%
+filmmaker makes and the content intended
+to be to be communicated from and we can
+
+ align:start position:0%
+to be to be communicated from and we can
+ 
+
+ align:start position:0%
+to be to be communicated from and we can
+we can think of the term competence
+
+ align:start position:0%
+we can think of the term competence
+ 
+
+ align:start position:0%
+we can think of the term competence
+having to do simply with wit with with
+
+ align:start position:0%
+having to do simply with wit with with
+ 
+
+ align:start position:0%
+having to do simply with wit with with
+the idea of technical mastery in other
+
+ align:start position:0%
+the idea of technical mastery in other
+ 
+
+ align:start position:0%
+the idea of technical mastery in other
+words a competent poet is a master of
+
+ align:start position:0%
+words a competent poet is a master of
+ 
+
+ align:start position:0%
+words a competent poet is a master of
+language is a master of metaphor is a
+
+ align:start position:0%
+language is a master of metaphor is a
+ 
+
+ align:start position:0%
+language is a master of metaphor is a
+master of grammar you can't be a great
+
+ align:start position:0%
+master of grammar you can't be a great
+ 
+
+ align:start position:0%
+master of grammar you can't be a great
+poet if you have no understanding of
+
+ align:start position:0%
+poet if you have no understanding of
+ 
+
+ align:start position:0%
+poet if you have no understanding of
+grammar or whatever because you'd be
+
+ align:start position:0%
+grammar or whatever because you'd be
+ 
+
+ align:start position:0%
+grammar or whatever because you'd be
+you'd be throwing away one of the great
+
+ align:start position:0%
+you'd be throwing away one of the great
+ 
+
+ align:start position:0%
+you'd be throwing away one of the great
+technical resources of the language
+
+ align:start position:0%
+technical resources of the language
+ 
+
+ align:start position:0%
+technical resources of the language
+which is which is the group the
+
+ align:start position:0%
+which is which is the group the
+ 
+
+ align:start position:0%
+which is which is the group the
+complexity that grows out of a mastery
+
+ align:start position:0%
+complexity that grows out of a mastery
+ 
+
+ align:start position:0%
+complexity that grows out of a mastery
+of grammar by the same token you
+
+ align:start position:0%
+of grammar by the same token you
+ 
+
+ align:start position:0%
+of grammar by the same token you
+couldn't have a serious filmmaker who
+
+ align:start position:0%
+couldn't have a serious filmmaker who
+ 
+
+ align:start position:0%
+couldn't have a serious filmmaker who
+didn't have a deep profound sense of
+
+ align:start position:0%
+didn't have a deep profound sense of
+ 
+
+ align:start position:0%
+didn't have a deep profound sense of
+what it meant to create a visual story
+
+ align:start position:0%
+what it meant to create a visual story
+ 
+
+ align:start position:0%
+what it meant to create a visual story
+what it meant to try to embody meaning
+
+ align:start position:0%
+what it meant to try to embody meaning
+ 
+
+ align:start position:0%
+what it meant to try to embody meaning
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+
+ align:start position:0%
+in in audio-visual ways right you
+ 
+
+ align:start position:0%
+in in audio-visual ways right you
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+
+ align:start position:0%
+couldn't have a great filmmaker who was
+ 
+
+ align:start position:0%
+couldn't have a great filmmaker who was
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+
+ align:start position:0%
+oblivious entirely to the visual nature
+ 
+
+ align:start position:0%
+oblivious entirely to the visual nature
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+
+ align:start position:0%
+of his experience he'd have to eat yeah
+ 
+
+ align:start position:0%
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+
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+what any serious filmmaker has to be
+ 
+
+ align:start position:0%
+what any serious filmmaker has to be
+always aware of the special qualities
+
+ align:start position:0%
+always aware of the special qualities
+ 
+
+ align:start position:0%
+always aware of the special qualities
+and properties of the medium in which he
+
+ align:start position:0%
+and properties of the medium in which he
+ 
+
+ align:start position:0%
+and properties of the medium in which he
+or she is working so if we think of art
+
+ align:start position:0%
+or she is working so if we think of art
+ 
+
+ align:start position:0%
+or she is working so if we think of art
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+
+ align:start position:0%
+then not as not as a mystical category
+ 
+
+ align:start position:0%
+then not as not as a mystical category
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+
+ align:start position:0%
+but as as as an expression of
+ 
+
+ align:start position:0%
+but as as as an expression of
+intelligence and mastery intelligence
+
+ align:start position:0%
+intelligence and mastery intelligence
+ 
+
+ align:start position:0%
+intelligence and mastery intelligence
+and competence perhaps we've demystified
+
+ align:start position:0%
+and competence perhaps we've demystified
+ 
+
+ align:start position:0%
+and competence perhaps we've demystified
+it a bit and given us grounds for
+
+ align:start position:0%
+it a bit and given us grounds for
+ 
+
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+it a bit and given us grounds for
+actually making judgments about
+
+ align:start position:0%
+actually making judgments about
+ 
+
+ align:start position:0%
+actually making judgments about
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+
+ align:start position:0%
+particular films and particular passages
+ 
+
+ align:start position:0%
+particular films and particular passages
+and moments in film and let me remind
+
+ align:start position:0%
+and moments in film and let me remind
+ 
+
+ align:start position:0%
+and moments in film and let me remind
+you again that a second version of this
+
+ align:start position:0%
+you again that a second version of this
+ 
+
+ align:start position:0%
+you again that a second version of this
+argument about the relationship of at
+
+ align:start position:0%
+argument about the relationship of at
+ 
+
+ align:start position:0%
+argument about the relationship of at
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+
+ align:start position:0%
+least in part about the relationship
+ 
+
+ align:start position:0%
+least in part about the relationship
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+
+ align:start position:0%
+between art and its and what what I had
+ 
+
+ align:start position:0%
+between art and its and what what I had
+sometimes called entertainment the
+
+ align:start position:0%
+sometimes called entertainment the
+ 
+
+ align:start position:0%
+sometimes called entertainment the
+greater complexity or richness of art
+
+ align:start position:0%
+greater complexity or richness of art
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+can be embodied also not only in this
+ 
+
+ align:start position:0%
+can be embodied also not only in this
+first principle of a connection between
+
+ align:start position:0%
+first principle of a connection between
+ 
+
+ align:start position:0%
+first principle of a connection between
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+
+ align:start position:0%
+the stylistic and formal choices and the
+ 
+
+ align:start position:0%
+the stylistic and formal choices and the
+content but in this second way in the
+
+ align:start position:0%
+content but in this second way in the
+ 
+
+ align:start position:0%
+content but in this second way in the
+second category or second perspective as
+
+ align:start position:0%
+second category or second perspective as
+ 
+
+ align:start position:0%
+second category or second perspective as
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+
+ align:start position:0%
+well in terms of what I've called
+ 
+
+ align:start position:0%
+well in terms of what I've called
+texture or multiplicity right the
+
+ align:start position:0%
+texture or multiplicity right the
+ 
+
+ align:start position:0%
+texture or multiplicity right the
+multiplicity principles let me just
+
+ align:start position:0%
+multiplicity principles let me just
+ 
+
+ align:start position:0%
+multiplicity principles let me just
+quickly remind you of a couple of
+
+ align:start position:0%
+quickly remind you of a couple of
+ 
+
+ align:start position:0%
+quickly remind you of a couple of
+examples we've looked at in the course
+
+ align:start position:0%
+examples we've looked at in the course
+ 
+
+ align:start position:0%
+examples we've looked at in the course
+just as a way of giving you some
+
+ align:start position:0%
+just as a way of giving you some
+ 
+
+ align:start position:0%
+just as a way of giving you some
+instances from which you can look from
+
+ align:start position:0%
+instances from which you can look from
+ 
+
+ align:start position:0%
+instances from which you can look from
+which you can extrapolate your your own
+
+ align:start position:0%
+which you can extrapolate your your own
+ 
+
+ align:start position:0%
+which you can extrapolate your your own
+responses to other texts
+
+ align:start position:0%
+responses to other texts
+ 
+
+ align:start position:0%
+responses to other texts
+do you remember for example the scene of
+
+ align:start position:0%
+do you remember for example the scene of
+ 
+
+ align:start position:0%
+do you remember for example the scene of
+that that we that we looked at fairly
+
+ align:start position:0%
+that that we that we looked at fairly
+ 
+
+ align:start position:0%
+that that we that we looked at fairly
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+
+ align:start position:0%
+closely in McCabe and mrs. Miller that
+ 
+
+ align:start position:0%
+closely in McCabe and mrs. Miller that
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+
+ align:start position:0%
+disturbing ironic shootout on the bridge
+ 
+
+ align:start position:0%
+disturbing ironic shootout on the bridge
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+
+ align:start position:0%
+in which a murderous young killer goods
+ 
+
+ align:start position:0%
+in which a murderous young killer goods
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+
+ align:start position:0%
+a young farmer into taking the gun out
+ 
+
+ align:start position:0%
+a young farmer into taking the gun out
+of his holster and shoots him down in
+
+ align:start position:0%
+of his holster and shoots him down in
+ 
+
+ align:start position:0%
+of his holster and shoots him down in
+cold blood would simply remind you about
+
+ align:start position:0%
+cold blood would simply remind you about
+ 
+
+ align:start position:0%
+cold blood would simply remind you about
+the way in which what Gaytan part of
+
+ align:start position:0%
+the way in which what Gaytan part of
+ 
+
+ align:start position:0%
+the way in which what Gaytan part of
+what gave that scene its power
+
+ align:start position:0%
+what gave that scene its power
+ 
+
+ align:start position:0%
+what gave that scene its power
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+
+ align:start position:0%
+had to do with the fact that there was a
+ 
+
+ align:start position:0%
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+psychological dimension to it
+
+ align:start position:0%
+psychological dimension to it
+ 
+
+ align:start position:0%
+psychological dimension to it
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+
+ align:start position:0%
+the young murderer was committing the
+ 
+
+ align:start position:0%
+the young murderer was committing the
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+
+ align:start position:0%
+murder had been frustrated because he
+ 
+
+ align:start position:0%
+murder had been frustrated because he
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+
+ align:start position:0%
+tried to show off earlier and not
+ 
+
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+tried to show off earlier and not
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+succeeded and that imparted a terrible
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+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+horrible irony to the scene because you
+realize that this boy this murder is
+
+ align:start position:0%
+realize that this boy this murder is
+ 
+
+ align:start position:0%
+realize that this boy this murder is
+completely fortuitous it's completely
+
+ align:start position:0%
+completely fortuitous it's completely
+ 
+
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+completely fortuitous it's completely
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+
+ align:start position:0%
+accidental if that if that little
+ 
+
+ align:start position:0%
+accidental if that if that little
+murderer had succeeded earlier in
+
+ align:start position:0%
+murderer had succeeded earlier in
+ 
+
+ align:start position:0%
+murderer had succeeded earlier in
+shooting the bottle that was floating
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+shooting the bottle that was floating
+ 
+
+ align:start position:0%
+shooting the bottle that was floating
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+
+ align:start position:0%
+around on the on the frozen on the
+ 
+
+ align:start position:0%
+around on the on the frozen on the
+frozen pond he probably would not have
+
+ align:start position:0%
+frozen pond he probably would not have
+ 
+
+ align:start position:0%
+frozen pond he probably would not have
+child he definitely would not have
+
+ align:start position:0%
+child he definitely would not have
+ 
+
+ align:start position:0%
+child he definitely would not have
+challenged this young farmer to try to
+
+ align:start position:0%
+challenged this young farmer to try to
+ 
+
+ align:start position:0%
+challenged this young farmer to try to
+get back his mojo and show the people
+
+ align:start position:0%
+get back his mojo and show the people
+ 
+
+ align:start position:0%
+get back his mojo and show the people
+around him that he knew how to handle a
+
+ align:start position:0%
+around him that he knew how to handle a
+ 
+
+ align:start position:0%
+around him that he knew how to handle a
+gun so it made this is and and of course
+
+ align:start position:0%
+gun so it made this is and and of course
+ 
+
+ align:start position:0%
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+ align:start position:0%
+that and then so that that already
+ 
+
+ align:start position:0%
+that and then so that that already
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+
+ align:start position:0%
+created a kind of complexity and texture
+ 
+
+ align:start position:0%
+created a kind of complexity and texture
+but then when we add in the fact that
+
+ align:start position:0%
+but then when we add in the fact that
+ 
+
+ align:start position:0%
+but then when we add in the fact that
+this scene itself is one of the central
+
+ align:start position:0%
+this scene itself is one of the central
+ 
+
+ align:start position:0%
+this scene itself is one of the central
+iconic scenes in all westerns two males
+
+ align:start position:0%
+iconic scenes in all westerns two males
+ 
+
+ align:start position:0%
+iconic scenes in all westerns two males
+stand with facing off against each other
+
+ align:start position:0%
+stand with facing off against each other
+ 
+
+ align:start position:0%
+stand with facing off against each other
+ready to shoot we come to realize that
+
+ align:start position:0%
+ready to shoot we come to realize that
+ 
+
+ align:start position:0%
+ready to shoot we come to realize that
+the I various anti-heroic and and ironic
+
+ align:start position:0%
+the I various anti-heroic and and ironic
+ 
+
+ align:start position:0%
+the I various anti-heroic and and ironic
+ways in which this shootout is handled
+
+ align:start position:0%
+ways in which this shootout is handled
+ 
+
+ align:start position:0%
+ways in which this shootout is handled
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+
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+throws a profoundly critical and
+ 
+
+ align:start position:0%
+throws a profoundly critical and
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+
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+disturbing light on dozens and perhaps
+ 
+
+ align:start position:0%
+disturbing light on dozens and perhaps
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+
+ align:start position:0%
+hundreds of earlier such scenes that
+ 
+
+ align:start position:0%
+hundreds of earlier such scenes that
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+
+ align:start position:0%
+have occurred in westerns that the very
+ 
+
+ align:start position:0%
+have occurred in westerns that the very
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+
+ align:start position:0%
+basis of the westerns embrace of
+ 
+
+ align:start position:0%
+basis of the westerns embrace of
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+
+ align:start position:0%
+violence its notion that you can achieve
+ 
+
+ align:start position:0%
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+regeneration through violence is put in
+
+ align:start position:0%
+regeneration through violence is put in
+ 
+
+ align:start position:0%
+regeneration through violence is put in
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+question by that scene so there's a
+ 
+
+ align:start position:0%
+question by that scene so there's a
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+
+ align:start position:0%
+texture or multiplicity in the scene
+ 
+
+ align:start position:0%
+texture or multiplicity in the scene
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+
+ align:start position:0%
+it's not if forwards the story it shows
+ 
+
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+it's not if forwards the story it shows
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+
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+ 
+
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+
+ align:start position:0%
+something about the psychology of the
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+ align:start position:0%
+murderer but even more than that it
+ 
+
+ align:start position:0%
+murderer but even more than that it
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+
+ align:start position:0%
+resonates through the whole history of
+ 
+
+ align:start position:0%
+resonates through the whole history of
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+
+ align:start position:0%
+the Western because the shootout itself
+ 
+
+ align:start position:0%
+the Western because the shootout itself
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+
+ align:start position:0%
+has been shown in such an anti heroic
+ 
+
+ align:start position:0%
+has been shown in such an anti heroic
+such an ironic light texture
+
+ align:start position:0%
+such an ironic light texture
+ 
+
+ align:start position:0%
+such an ironic light texture
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+
+ align:start position:0%
+multiplicity remember the moment in
+ 
+
+ align:start position:0%
+multiplicity remember the moment in
+cabaret where the Joel gray character
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+cabaret where the Joel gray character
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+
+ align:start position:0%
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+the the interlocutor the the at one
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+
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+
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+point kneels down while he's talking and
+ 
+
+ align:start position:0%
+point kneels down while he's talking and
+during the mud wrestling scene and picks
+
+ align:start position:0%
+during the mud wrestling scene and picks
+ 
+
+ align:start position:0%
+during the mud wrestling scene and picks
+up a piece of mud on his finger rubs it
+
+ align:start position:0%
+up a piece of mud on his finger rubs it
+ 
+
+ align:start position:0%
+up a piece of mud on his finger rubs it
+on his face like this and gives a Hitler
+
+ align:start position:0%
+on his face like this and gives a Hitler
+ 
+
+ align:start position:0%
+on his face like this and gives a Hitler
+gives himself a Hitler mustache I mean
+
+ align:start position:0%
+gives himself a Hitler mustache I mean
+ 
+
+ align:start position:0%
+gives himself a Hitler mustache I mean
+it's a rich comic moment but isn't it
+
+ align:start position:0%
+it's a rich comic moment but isn't it
+ 
+
+ align:start position:0%
+it's a rich comic moment but isn't it
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+
+ align:start position:0%
+more than that especially in the context
+ 
+
+ align:start position:0%
+more than that especially in the context
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+
+ align:start position:0%
+of as the film proceeds we understand
+ 
+
+ align:start position:0%
+of as the film proceeds we understand
+from that moment that the Nazis are
+
+ align:start position:0%
+from that moment that the Nazis are
+ 
+
+ align:start position:0%
+from that moment that the Nazis are
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+
+ align:start position:0%
+objects of fun and mockery not that
+ 
+
+ align:start position:0%
+objects of fun and mockery not that
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+
+ align:start position:0%
+dangerous it would seem at least that
+ 
+
+ align:start position:0%
+dangerous it would seem at least that
+the Cabaret feels superior to it and of
+
+ align:start position:0%
+the Cabaret feels superior to it and of
+ 
+
+ align:start position:0%
+the Cabaret feels superior to it and of
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+
+ align:start position:0%
+course when we think about the course of
+ 
+
+ align:start position:0%
+course when we think about the course of
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+
+ align:start position:0%
+the film when we think about how the
+ 
+
+ align:start position:0%
+the film when we think about how the
+Nazis moved from the periphery to the
+
+ align:start position:0%
+Nazis moved from the periphery to the
+ 
+
+ align:start position:0%
+Nazis moved from the periphery to the
+center of the movie we come to recognize
+
+ align:start position:0%
+center of the movie we come to recognize
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+
+ align:start position:0%
+center of the movie we come to recognize
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+
+ align:start position:0%
+that that moment especially in
+ 
+
+ align:start position:0%
+that that moment especially in
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+
+ align:start position:0%
+retrospect that moment has a particular
+ 
+
+ align:start position:0%
+retrospect that moment has a particular
+kind of ironic richness that's partly a
+
+ align:start position:0%
+kind of ironic richness that's partly a
+ 
+
+ align:start position:0%
+kind of ironic richness that's partly a
+function of the obliviousness that
+
+ align:start position:0%
+function of the obliviousness that
+ 
+
+ align:start position:0%
+function of the obliviousness that
+everyone in the Cabaret and even the
+
+ align:start position:0%
+everyone in the Cabaret and even the
+ 
+
+ align:start position:0%
+everyone in the Cabaret and even the
+Joel Grey characters despite his
+
+ align:start position:0%
+Joel Grey characters despite his
+ 
+
+ align:start position:0%
+Joel Grey characters despite his
+apparent cynicism and worldliness seems
+
+ align:start position:0%
+apparent cynicism and worldliness seems
+ 
+
+ align:start position:0%
+apparent cynicism and worldliness seems
+to have about they were all they're
+
+ align:start position:0%
+to have about they were all they're
+ 
+
+ align:start position:0%
+to have about they were all they're
+innocent they're naive about the power
+
+ align:start position:0%
+innocent they're naive about the power
+ 
+
+ align:start position:0%
+innocent they're naive about the power
+and danger of the rise of the Nazis and
+
+ align:start position:0%
+and danger of the rise of the Nazis and
+ 
+
+ align:start position:0%
+and danger of the rise of the Nazis and
+let me give you one last example
+
+ align:start position:0%
+let me give you one last example
+ 
+
+ align:start position:0%
+let me give you one last example
+although there are many others that we
+
+ align:start position:0%
+although there are many others that we
+ 
+
+ align:start position:0%
+although there are many others that we
+mentioned do you remember the moment in
+
+ align:start position:0%
+mentioned do you remember the moment in
+ 
+
+ align:start position:0%
+mentioned do you remember the moment in
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+
+ align:start position:0%
+the passage I showed you from from the
+ 
+
+ align:start position:0%
+the passage I showed you from from the
+De Sica movie Umberto D that very brief
+
+ align:start position:0%
+De Sica movie Umberto D that very brief
+ 
+
+ align:start position:0%
+De Sica movie Umberto D that very brief
+moment where we see a man get on a get
+
+ align:start position:0%
+moment where we see a man get on a get
+ 
+
+ align:start position:0%
+moment where we see a man get on a get
+on a tram a bus and sit next to someone
+
+ align:start position:0%
+on a tram a bus and sit next to someone
+ 
+
+ align:start position:0%
+on a tram a bus and sit next to someone
+on the bus and the bus moves there it's
+
+ align:start position:0%
+on the bus and the bus moves there it's
+ 
+
+ align:start position:0%
+on the bus and the bus moves there it's
+a completely wordless sequence and
+
+ align:start position:0%
+a completely wordless sequence and
+ 
+
+ align:start position:0%
+a completely wordless sequence and
+there's a character we've never seen in
+
+ align:start position:0%
+there's a character we've never seen in
+ 
+
+ align:start position:0%
+there's a character we've never seen in
+the film before who sits down next to
+
+ align:start position:0%
+the film before who sits down next to
+ 
+
+ align:start position:0%
+the film before who sits down next to
+the protagonist no words exchanged when
+
+ align:start position:0%
+the protagonist no words exchanged when
+ 
+
+ align:start position:0%
+the protagonist no words exchanged when
+our protagonist gets up and gets off the
+
+ align:start position:0%
+our protagonist gets up and gets off the
+ 
+
+ align:start position:0%
+our protagonist gets up and gets off the
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+
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+
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+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
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+ align:start position:0%
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+
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+
+ align:start position:0%
+for one brief instant in the course of
+ 
+
+ align:start position:0%
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+
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+
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+
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+ 
+
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+our hero Umberto D who was now leaving
+
+ align:start position:0%
+our hero Umberto D who was now leaving
+ 
+
+ align:start position:0%
+our hero Umberto D who was now leaving
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+
+ align:start position:0%
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+
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+shortly be following him so again a
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+
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+ 
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+
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+laxity or richness that that embodies
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+
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+I have a final example of this kind of
+
+ align:start position:0%
+I have a final example of this kind of
+ 
+
+ align:start position:0%
+I have a final example of this kind of
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+
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+ 
+
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+I had hoped to show you when we talked
+
+ align:start position:0%
+I had hoped to show you when we talked
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+
+ align:start position:0%
+I had hoped to show you when we talked
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+
+ align:start position:0%
+about Kurosawa last week but I didn't
+ 
+
+ align:start position:0%
+about Kurosawa last week but I didn't
+quite make enough time in my in my
+
+ align:start position:0%
+quite make enough time in my in my
+ 
+
+ align:start position:0%
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+lecture and I want to show it here as a
+
+ align:start position:0%
+lecture and I want to show it here as a
+ 
+
+ align:start position:0%
+lecture and I want to show it here as a
+kind of final homage to that great
+
+ align:start position:0%
+kind of final homage to that great
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+of the variety of performances that the
+ 
+
+ align:start position:0%
+of the variety of performances that the
+great actor Toshiro Mifune who plays the
+
+ align:start position:0%
+great actor Toshiro Mifune who plays the
+ 
+
+ align:start position:0%
+great actor Toshiro Mifune who plays the
+rapist in Rashomon was capable of so
+
+ align:start position:0%
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+
+ align:start position:0%
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+here is a scene a very minor scene
+
+ align:start position:0%
+here is a scene a very minor scene
+ 
+
+ align:start position:0%
+here is a scene a very minor scene
+actually from the film from the great
+
+ align:start position:0%
+actually from the film from the great
+ 
+
+ align:start position:0%
+actually from the film from the great
+Kurosawa film Seven Samurai which I
+
+ align:start position:0%
+Kurosawa film Seven Samurai which I
+ 
+
+ align:start position:0%
+Kurosawa film Seven Samurai which I
+mentioned last time let me set the
+
+ align:start position:0%
+mentioned last time let me set the
+ 
+
+ align:start position:0%
+mentioned last time let me set the
+context for you before I show it to you
+
+ align:start position:0%
+context for you before I show it to you
+ 
+
+ align:start position:0%
+context for you before I show it to you
+it's a very brief scene Seven Samurai
+
+ align:start position:0%
+it's a very brief scene Seven Samurai
+ 
+
+ align:start position:0%
+it's a very brief scene Seven Samurai
+which I've sometimes shown in this
+
+ align:start position:0%
+which I've sometimes shown in this
+ 
+
+ align:start position:0%
+which I've sometimes shown in this
+course I actually toyed with the idea of
+
+ align:start position:0%
+course I actually toyed with the idea of
+ 
+
+ align:start position:0%
+course I actually toyed with the idea of
+having you watch both but they're both
+
+ align:start position:0%
+having you watch both but they're both
+ 
+
+ align:start position:0%
+having you watch both but they're both
+Rashomon and seven samurai but Seven
+
+ align:start position:0%
+Rashomon and seven samurai but Seven
+ 
+
+ align:start position:0%
+Rashomon and seven samurai but Seven
+Samurai is a very long movie and I
+
+ align:start position:0%
+Samurai is a very long movie and I
+ 
+
+ align:start position:0%
+Samurai is a very long movie and I
+sometimes warn students about it when I
+
+ align:start position:0%
+sometimes warn students about it when I
+ 
+
+ align:start position:0%
+sometimes warn students about it when I
+show it in the class I decided not to do
+
+ align:start position:0%
+show it in the class I decided not to do
+ 
+
+ align:start position:0%
+show it in the class I decided not to do
+it but I hope all of you over the
+
+ align:start position:0%
+it but I hope all of you over the
+ 
+
+ align:start position:0%
+it but I hope all of you over the
+Christmas break soon we'll look at Seven
+
+ align:start position:0%
+Christmas break soon we'll look at Seven
+ 
+
+ align:start position:0%
+Christmas break soon we'll look at Seven
+Samurai it will resonate especially for
+
+ align:start position:0%
+Samurai it will resonate especially for
+ 
+
+ align:start position:0%
+Samurai it will resonate especially for
+you it since you've just seen an earlier
+
+ align:start position:0%
+you it since you've just seen an earlier
+ 
+
+ align:start position:0%
+you it since you've just seen an earlier
+Kurosawa film
+
+ align:start position:0%
+Kurosawa film
+ 
+
+ align:start position:0%
+Kurosawa film
+well this immensely long film has a
+
+ align:start position:0%
+well this immensely long film has a
+ 
+
+ align:start position:0%
+well this immensely long film has a
+wonderful epic amplitude and the long
+
+ align:start position:0%
+wonderful epic amplitude and the long
+ 
+
+ align:start position:0%
+wonderful epic amplitude and the long
+first section of the film involves
+
+ align:start position:0%
+first section of the film involves
+ 
+
+ align:start position:0%
+first section of the film involves
+essentially the assembling of a group of
+
+ align:start position:0%
+essentially the assembling of a group of
+ 
+
+ align:start position:0%
+essentially the assembling of a group of
+samurai who are going to go to a village
+
+ align:start position:0%
+samurai who are going to go to a village
+ 
+
+ align:start position:0%
+samurai who are going to go to a village
+to defend this village of farmers from
+
+ align:start position:0%
+to defend this village of farmers from
+ 
+
+ align:start position:0%
+to defend this village of farmers from
+the depredations of bandits when the
+
+ align:start position:0%
+the depredations of bandits when the
+ 
+
+ align:start position:0%
+the depredations of bandits when the
+film opens some farmers are make their
+
+ align:start position:0%
+film opens some farmers are make their
+ 
+
+ align:start position:0%
+film opens some farmers are make their
+way to a great city trying to find
+
+ align:start position:0%
+way to a great city trying to find
+ 
+
+ align:start position:0%
+way to a great city trying to find
+samurai who will come and defend them
+
+ align:start position:0%
+samurai who will come and defend them
+ 
+
+ align:start position:0%
+samurai who will come and defend them
+and they're the and this the first
+
+ align:start position:0%
+and they're the and this the first
+ 
+
+ align:start position:0%
+and they're the and this the first
+section of the film shows that the this
+
+ align:start position:0%
+section of the film shows that the this
+ 
+
+ align:start position:0%
+section of the film shows that the this
+group of samurai slowly coming together
+
+ align:start position:0%
+group of samurai slowly coming together
+ 
+
+ align:start position:0%
+group of samurai slowly coming together
+but only six of them are in the group
+
+ align:start position:0%
+but only six of them are in the group
+ 
+
+ align:start position:0%
+but only six of them are in the group
+because there was a seventh who tried to
+
+ align:start position:0%
+because there was a seventh who tried to
+ 
+
+ align:start position:0%
+because there was a seventh who tried to
+join them the Toshiro Mifune character
+
+ align:start position:0%
+join them the Toshiro Mifune character
+ 
+
+ align:start position:0%
+join them the Toshiro Mifune character
+but he was rejected in
+
+ align:start position:0%
+but he was rejected in
+ 
+
+ align:start position:0%
+but he was rejected in
+earlier part of the film that we haven't
+
+ align:start position:0%
+earlier part of the film that we haven't
+ 
+
+ align:start position:0%
+earlier part of the film that we haven't
+yet seen that would that you that that
+
+ align:start position:0%
+yet seen that would that you that that
+ 
+
+ align:start position:0%
+yet seen that would that you that that
+we have seen but when you look at the
+
+ align:start position:0%
+we have seen but when you look at the
+ 
+
+ align:start position:0%
+we have seen but when you look at the
+clip you will not have seen yet because
+
+ align:start position:0%
+clip you will not have seen yet because
+ 
+
+ align:start position:0%
+clip you will not have seen yet because
+he's not really a samurai he's he's a
+
+ align:start position:0%
+he's not really a samurai he's he's a
+ 
+
+ align:start position:0%
+he's not really a samurai he's he's a
+he's a commoner who was trying to think
+
+ align:start position:0%
+he's a commoner who was trying to think
+ 
+
+ align:start position:0%
+he's a commoner who was trying to think
+that he was a samurai he grew up top not
+
+ align:start position:0%
+that he was a samurai he grew up top not
+ 
+
+ align:start position:0%
+that he was a samurai he grew up top not
+he can handle the sword but they could
+
+ align:start position:0%
+he can handle the sword but they could
+ 
+
+ align:start position:0%
+he can handle the sword but they could
+tell in various ways he didn't know the
+
+ align:start position:0%
+tell in various ways he didn't know the
+ 
+
+ align:start position:0%
+tell in various ways he didn't know the
+poetry that samurai knew a lot of ways
+
+ align:start position:0%
+poetry that samurai knew a lot of ways
+ 
+
+ align:start position:0%
+poetry that samurai knew a lot of ways
+in which they figured out that the
+
+ align:start position:0%
+in which they figured out that the
+ 
+
+ align:start position:0%
+in which they figured out that the
+Mifune character really was not a
+
+ align:start position:0%
+Mifune character really was not a
+ 
+
+ align:start position:0%
+Mifune character really was not a
+samurai so they didn't let him join them
+
+ align:start position:0%
+samurai so they didn't let him join them
+ 
+
+ align:start position:0%
+samurai so they didn't let him join them
+and in this theme we're going to say
+
+ align:start position:0%
+and in this theme we're going to say
+ 
+
+ align:start position:0%
+and in this theme we're going to say
+it's two or two and a half minutes long
+
+ align:start position:0%
+it's two or two and a half minutes long
+ 
+
+ align:start position:0%
+it's two or two and a half minutes long
+and this is one reason I wanted you to
+
+ align:start position:0%
+and this is one reason I wanted you to
+ 
+
+ align:start position:0%
+and this is one reason I wanted you to
+look at it because it's it's so brief
+
+ align:start position:0%
+look at it because it's it's so brief
+ 
+
+ align:start position:0%
+look at it because it's it's so brief
+and its basic function is so simple the
+
+ align:start position:0%
+and its basic function is so simple the
+ 
+
+ align:start position:0%
+and its basic function is so simple the
+point of the scene is to get the samurai
+
+ align:start position:0%
+point of the scene is to get the samurai
+ 
+
+ align:start position:0%
+point of the scene is to get the samurai
+to the village where the central aspect
+
+ align:start position:0%
+to the village where the central aspect
+ 
+
+ align:start position:0%
+to the village where the central aspect
+with a where the central adventure of
+
+ align:start position:0%
+with a where the central adventure of
+ 
+
+ align:start position:0%
+with a where the central adventure of
+the film will take place right so we can
+
+ align:start position:0%
+the film will take place right so we can
+ 
+
+ align:start position:0%
+the film will take place right so we can
+almost think of part one as a kind of
+
+ align:start position:0%
+almost think of part one as a kind of
+ 
+
+ align:start position:0%
+almost think of part one as a kind of
+prologue or or at least an introductory
+
+ align:start position:0%
+prologue or or at least an introductory
+ 
+
+ align:start position:0%
+prologue or or at least an introductory
+preparation the film really isn't going
+
+ align:start position:0%
+preparation the film really isn't going
+ 
+
+ align:start position:0%
+preparation the film really isn't going
+to get going in it in one sense until
+
+ align:start position:0%
+to get going in it in one sense until
+ 
+
+ align:start position:0%
+to get going in it in one sense until
+after this transition moment there so
+
+ align:start position:0%
+after this transition moment there so
+ 
+
+ align:start position:0%
+after this transition moment there so
+the sequence we're looking at it as a
+
+ align:start position:0%
+the sequence we're looking at it as a
+ 
+
+ align:start position:0%
+the sequence we're looking at it as a
+very simple narrative function it's to
+
+ align:start position:0%
+very simple narrative function it's to
+ 
+
+ align:start position:0%
+very simple narrative function it's to
+get the samurai from the city to the
+
+ align:start position:0%
+get the samurai from the city to the
+ 
+
+ align:start position:0%
+get the samurai from the city to the
+rural village and we see them making
+
+ align:start position:0%
+rural village and we see them making
+ 
+
+ align:start position:0%
+rural village and we see them making
+this trip but as you'll see the scene
+
+ align:start position:0%
+this trip but as you'll see the scene
+ 
+
+ align:start position:0%
+this trip but as you'll see the scene
+has a much greater multiplicity a much a
+
+ align:start position:0%
+has a much greater multiplicity a much a
+ 
+
+ align:start position:0%
+has a much greater multiplicity a much a
+much greater significance than simply
+
+ align:start position:0%
+much greater significance than simply
+ 
+
+ align:start position:0%
+much greater significance than simply
+this simple narrative significance of
+
+ align:start position:0%
+this simple narrative significance of
+ 
+
+ align:start position:0%
+this simple narrative significance of
+moving the actors to a new location here
+
+ align:start position:0%
+moving the actors to a new location here
+ 
+
+ align:start position:0%
+moving the actors to a new location here
+we go and see he's following them in the
+
+ align:start position:0%
+we go and see he's following them in the
+ 
+
+ align:start position:0%
+we go and see he's following them in the
+back there and they say go away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so I've seen a scene of
+
+ align:start position:0%
+all right so I've seen a scene of
+ 
+
+ align:start position:0%
+all right so I've seen a scene of
+unexpected comedy right but what else
+
+ align:start position:0%
+unexpected comedy right but what else
+ 
+
+ align:start position:0%
+unexpected comedy right but what else
+can you see how much is going on there
+
+ align:start position:0%
+can you see how much is going on there
+ 
+
+ align:start position:0%
+can you see how much is going on there
+if we if we think about the scene for a
+
+ align:start position:0%
+if we if we think about the scene for a
+ 
+
+ align:start position:0%
+if we if we think about the scene for a
+moment we can see okay the first
+
+ align:start position:0%
+moment we can see okay the first
+ 
+
+ align:start position:0%
+moment we can see okay the first
+function of the scene is to get them to
+
+ align:start position:0%
+function of the scene is to get them to
+ 
+
+ align:start position:0%
+function of the scene is to get them to
+the village right but it's a wonderful
+
+ align:start position:0%
+the village right but it's a wonderful
+ 
+
+ align:start position:0%
+the village right but it's a wonderful
+example of the multiplicity principle it
+
+ align:start position:0%
+example of the multiplicity principle it
+ 
+
+ align:start position:0%
+example of the multiplicity principle it
+seems to me okay it forwards the story
+
+ align:start position:0%
+seems to me okay it forwards the story
+ 
+
+ align:start position:0%
+seems to me okay it forwards the story
+and in some simple sense but what does
+
+ align:start position:0%
+and in some simple sense but what does
+ 
+
+ align:start position:0%
+and in some simple sense but what does
+it also do it defines the samurai in
+
+ align:start position:0%
+it also do it defines the samurai in
+ 
+
+ align:start position:0%
+it also do it defines the samurai in
+some basic way first of all there's the
+
+ align:start position:0%
+some basic way first of all there's the
+ 
+
+ align:start position:0%
+some basic way first of all there's the
+legitimate samurai have a sense of humor
+
+ align:start position:0%
+legitimate samurai have a sense of humor
+ 
+
+ align:start position:0%
+legitimate samurai have a sense of humor
+and the they but even more than that
+
+ align:start position:0%
+and the they but even more than that
+ 
+
+ align:start position:0%
+and the they but even more than that
+when we went as we're watching this
+
+ align:start position:0%
+when we went as we're watching this
+ 
+
+ align:start position:0%
+when we went as we're watching this
+scene what do we see among other things
+
+ align:start position:0%
+scene what do we see among other things
+ 
+
+ align:start position:0%
+scene what do we see among other things
+a wonderful very brief dramatization of
+
+ align:start position:0%
+a wonderful very brief dramatization of
+ 
+
+ align:start position:0%
+a wonderful very brief dramatization of
+the conflict between man and nature
+
+ align:start position:0%
+the conflict between man and nature
+ 
+
+ align:start position:0%
+the conflict between man and nature
+think of how raw that natural look those
+
+ align:start position:0%
+think of how raw that natural look those
+ 
+
+ align:start position:0%
+think of how raw that natural look those
+natural environments are in that's in
+
+ align:start position:0%
+natural environments are in that's in
+ 
+
+ align:start position:0%
+natural environments are in that's in
+that sequence and the extent to which we
+
+ align:start position:0%
+that sequence and the extent to which we
+ 
+
+ align:start position:0%
+that sequence and the extent to which we
+also so that the the film itself is in
+
+ align:start position:0%
+also so that the the film itself is in
+ 
+
+ align:start position:0%
+also so that the the film itself is in
+many ways a sub-theme in the film is the
+
+ align:start position:0%
+many ways a sub-theme in the film is the
+ 
+
+ align:start position:0%
+many ways a sub-theme in the film is the
+relationship between human beings and
+
+ align:start position:0%
+relationship between human beings and
+ 
+
+ align:start position:0%
+relationship between human beings and
+natural forces this scene implicitly
+
+ align:start position:0%
+natural forces this scene implicitly
+ 
+
+ align:start position:0%
+natural forces this scene implicitly
+sets that theme up without doing
+
+ align:start position:0%
+sets that theme up without doing
+ 
+
+ align:start position:0%
+sets that theme up without doing
+anything fancy or calling our attention
+
+ align:start position:0%
+anything fancy or calling our attention
+ 
+
+ align:start position:0%
+anything fancy or calling our attention
+to it what else does it do it defines
+
+ align:start position:0%
+to it what else does it do it defines
+ 
+
+ align:start position:0%
+to it what else does it do it defines
+the Mifune character really richly and
+
+ align:start position:0%
+the Mifune character really richly and
+ 
+
+ align:start position:0%
+the Mifune character really richly and
+fully he's something of a clown isn't he
+
+ align:start position:0%
+fully he's something of a clown isn't he
+ 
+
+ align:start position:0%
+fully he's something of a clown isn't he
+he likes attention he knew very there's
+
+ align:start position:0%
+he likes attention he knew very there's
+ 
+
+ align:start position:0%
+he likes attention he knew very there's
+something deeply theatrical about him
+
+ align:start position:0%
+something deeply theatrical about him
+ 
+
+ align:start position:0%
+something deeply theatrical about him
+see the way he he knew those that the
+
+ align:start position:0%
+see the way he he knew those that the
+ 
+
+ align:start position:0%
+see the way he he knew those that the
+other samurai were watching him and then
+
+ align:start position:0%
+other samurai were watching him and then
+ 
+
+ align:start position:0%
+other samurai were watching him and then
+when he when he caught but he's also
+
+ align:start position:0%
+when he when he caught but he's also
+ 
+
+ align:start position:0%
+when he when he caught but he's also
+what else do we learn about he's
+
+ align:start position:0%
+what else do we learn about he's
+ 
+
+ align:start position:0%
+what else do we learn about he's
+unbelievably competent he jumps in that
+
+ align:start position:0%
+unbelievably competent he jumps in that
+ 
+
+ align:start position:0%
+unbelievably competent he jumps in that
+freezing water and he catches a fish
+
+ align:start position:0%
+freezing water and he catches a fish
+ 
+
+ align:start position:0%
+freezing water and he catches a fish
+with his bare hands right and one
+
+ align:start position:0%
+with his bare hands right and one
+ 
+
+ align:start position:0%
+with his bare hands right and one
+implication of the scene may very well
+
+ align:start position:0%
+implication of the scene may very well
+ 
+
+ align:start position:0%
+implication of the scene may very well
+be that one of the things the muthoni
+
+ align:start position:0%
+be that one of the things the muthoni
+ 
+
+ align:start position:0%
+be that one of the things the muthoni
+characters trying to do is show the
+
+ align:start position:0%
+characters trying to do is show the
+ 
+
+ align:start position:0%
+characters trying to do is show the
+samurai how competent he is right and he
+
+ align:start position:0%
+samurai how competent he is right and he
+ 
+
+ align:start position:0%
+samurai how competent he is right and he
+led you to see Ben Healy ends up leading
+
+ align:start position:0%
+led you to see Ben Healy ends up leading
+ 
+
+ align:start position:0%
+led you to see Ben Healy ends up leading
+them to the villain of course you might
+
+ align:start position:0%
+them to the villain of course you might
+ 
+
+ align:start position:0%
+them to the villain of course you might
+guess do you think he remains excluded
+
+ align:start position:0%
+guess do you think he remains excluded
+ 
+
+ align:start position:0%
+guess do you think he remains excluded
+no of course not he ends up joining me
+
+ align:start position:0%
+no of course not he ends up joining me
+ 
+
+ align:start position:0%
+no of course not he ends up joining me
+he is the Seven Samurai and becomes the
+
+ align:start position:0%
+he is the Seven Samurai and becomes the
+ 
+
+ align:start position:0%
+he is the Seven Samurai and becomes the
+seventh as the film as the film goes on
+
+ align:start position:0%
+seventh as the film as the film goes on
+ 
+
+ align:start position:0%
+seventh as the film as the film goes on
+so we do so
+
+ align:start position:0%
+so we do so
+ 
+
+ align:start position:0%
+so we do so
+so the buffoon is nature is defined for
+
+ align:start position:0%
+so the buffoon is nature is defined for
+ 
+
+ align:start position:0%
+so the buffoon is nature is defined for
+us in in in action more than in words we
+
+ align:start position:0%
+us in in in action more than in words we
+ 
+
+ align:start position:0%
+us in in in action more than in words we
+have the theme of nature versus man
+
+ align:start position:0%
+have the theme of nature versus man
+ 
+
+ align:start position:0%
+have the theme of nature versus man
+have the broader definition of the
+
+ align:start position:0%
+have the broader definition of the
+ 
+
+ align:start position:0%
+have the broader definition of the
+nature of the samurai group itself and
+
+ align:start position:0%
+nature of the samurai group itself and
+ 
+
+ align:start position:0%
+nature of the samurai group itself and
+we get an action that also moves the
+
+ align:start position:0%
+we get an action that also moves the
+ 
+
+ align:start position:0%
+we get an action that also moves the
+story to a new location and exists this
+
+ align:start position:0%
+story to a new location and exists this
+ 
+
+ align:start position:0%
+story to a new location and exists this
+is the one reason that I find this
+
+ align:start position:0%
+is the one reason that I find this
+ 
+
+ align:start position:0%
+is the one reason that I find this
+example such a powerful one is that many
+
+ align:start position:0%
+example such a powerful one is that many
+ 
+
+ align:start position:0%
+example such a powerful one is that many
+people watching this movie never even
+
+ align:start position:0%
+people watching this movie never even
+ 
+
+ align:start position:0%
+people watching this movie never even
+remember this scene because it's hardly
+
+ align:start position:0%
+remember this scene because it's hardly
+ 
+
+ align:start position:0%
+remember this scene because it's hardly
+even though it is very dramatic scene
+
+ align:start position:0%
+even though it is very dramatic scene
+ 
+
+ align:start position:0%
+even though it is very dramatic scene
+isn't it
+
+ align:start position:0%
+isn't it
+ 
+
+ align:start position:0%
+isn't it
+the fact is there are so many
+
+ align:start position:0%
+the fact is there are so many
+ 
+
+ align:start position:0%
+the fact is there are so many
+astonishing dramatic visually memorable
+
+ align:start position:0%
+astonishing dramatic visually memorable
+ 
+
+ align:start position:0%
+astonishing dramatic visually memorable
+scenes in the film that almost most
+
+ align:start position:0%
+scenes in the film that almost most
+ 
+
+ align:start position:0%
+scenes in the film that almost most
+viewers who who don't have the advantage
+
+ align:start position:0%
+viewers who who don't have the advantage
+ 
+
+ align:start position:0%
+viewers who who don't have the advantage
+of having this scene singled out for
+
+ align:start position:0%
+of having this scene singled out for
+ 
+
+ align:start position:0%
+of having this scene singled out for
+them would never even remember it and
+
+ align:start position:0%
+them would never even remember it and
+ 
+
+ align:start position:0%
+them would never even remember it and
+that's exactly why it's so valuable it
+
+ align:start position:0%
+that's exactly why it's so valuable it
+ 
+
+ align:start position:0%
+that's exactly why it's so valuable it
+seems to me because it it plays a
+
+ align:start position:0%
+seems to me because it it plays a
+ 
+
+ align:start position:0%
+seems to me because it it plays a
+relatively minor role in the film its
+
+ align:start position:0%
+relatively minor role in the film its
+ 
+
+ align:start position:0%
+relatively minor role in the film its
+role in the film is fairly simple and
+
+ align:start position:0%
+role in the film is fairly simple and
+ 
+
+ align:start position:0%
+role in the film is fairly simple and
+structural but even in that simple
+
+ align:start position:0%
+structural but even in that simple
+ 
+
+ align:start position:0%
+structural but even in that simple
+two-and-a-half minute sequence a great
+
+ align:start position:0%
+two-and-a-half minute sequence a great
+ 
+
+ align:start position:0%
+two-and-a-half minute sequence a great
+deal is going on it's a wonderful
+
+ align:start position:0%
+deal is going on it's a wonderful
+ 
+
+ align:start position:0%
+deal is going on it's a wonderful
+instance it seems to me of what we mean
+
+ align:start position:0%
+instance it seems to me of what we mean
+ 
+
+ align:start position:0%
+instance it seems to me of what we mean
+by texture or multiplicity if you're
+
+ align:start position:0%
+by texture or multiplicity if you're
+ 
+
+ align:start position:0%
+by texture or multiplicity if you're
+aware of this principle when you look at
+
+ align:start position:0%
+aware of this principle when you look at
+ 
+
+ align:start position:0%
+aware of this principle when you look at
+other forms of art not just films I
+
+ align:start position:0%
+other forms of art not just films I
+ 
+
+ align:start position:0%
+other forms of art not just films I
+think you'll find your sense of what is
+
+ align:start position:0%
+think you'll find your sense of what is
+ 
+
+ align:start position:0%
+think you'll find your sense of what is
+going on in a particular text or a
+
+ align:start position:0%
+going on in a particular text or a
+ 
+
+ align:start position:0%
+going on in a particular text or a
+particular expressive form will be
+
+ align:start position:0%
+particular expressive form will be
+ 
+
+ align:start position:0%
+particular expressive form will be
+immensely enlarged and I hope you apply
+
+ align:start position:0%
+immensely enlarged and I hope you apply
+ 
+
+ align:start position:0%
+immensely enlarged and I hope you apply
+these ideas not just to movies in the
+
+ align:start position:0%
+these ideas not just to movies in the
+ 
+
+ align:start position:0%
+these ideas not just to movies in the
+future but to other but to other forms
+
+ align:start position:0%
+future but to other but to other forms
+ 
+
+ align:start position:0%
+future but to other but to other forms
+of expressive experience as well I also
+
+ align:start position:0%
+of expressive experience as well I also
+ 
+
+ align:start position:0%
+of expressive experience as well I also
+at the end of this course as at the end
+
+ align:start position:0%
+at the end of this course as at the end
+ 
+
+ align:start position:0%
+at the end of this course as at the end
+of every semester I'm afflicted by a
+
+ align:start position:0%
+of every semester I'm afflicted by a
+ 
+
+ align:start position:0%
+of every semester I'm afflicted by a
+sense of gratitude that I can't always
+
+ align:start position:0%
+sense of gratitude that I can't always
+ 
+
+ align:start position:0%
+sense of gratitude that I can't always
+fully Express to my students I've been
+
+ align:start position:0%
+fully Express to my students I've been
+ 
+
+ align:start position:0%
+fully Express to my students I've been
+doing this for a long time I was
+
+ align:start position:0%
+doing this for a long time I was
+ 
+
+ align:start position:0%
+doing this for a long time I was
+thinking as the class opened this
+
+ align:start position:0%
+thinking as the class opened this
+ 
+
+ align:start position:0%
+thinking as the class opened this
+afternoon looking out at your faces I
+
+ align:start position:0%
+afternoon looking out at your faces I
+ 
+
+ align:start position:0%
+afternoon looking out at your faces I
+real is one of the most amazing things
+
+ align:start position:0%
+real is one of the most amazing things
+ 
+
+ align:start position:0%
+real is one of the most amazing things
+about being a professor is that your
+
+ align:start position:0%
+about being a professor is that your
+ 
+
+ align:start position:0%
+about being a professor is that your
+basic clients stay young and they keep
+
+ align:start position:0%
+basic clients stay young and they keep
+ 
+
+ align:start position:0%
+basic clients stay young and they keep
+you young they keep you young even
+
+ align:start position:0%
+you young they keep you young even
+ 
+
+ align:start position:0%
+you young they keep you young even
+though they also in some ways make you
+
+ align:start position:0%
+though they also in some ways make you
+ 
+
+ align:start position:0%
+though they also in some ways make you
+more and more conscious of the gap
+
+ align:start position:0%
+more and more conscious of the gap
+ 
+
+ align:start position:0%
+more and more conscious of the gap
+between you and your students in some
+
+ align:start position:0%
+between you and your students in some
+ 
+
+ align:start position:0%
+between you and your students in some
+respects I have no doubt that part of
+
+ align:start position:0%
+respects I have no doubt that part of
+ 
+
+ align:start position:0%
+respects I have no doubt that part of
+what has made my career as a satisfying
+
+ align:start position:0%
+what has made my career as a satisfying
+ 
+
+ align:start position:0%
+what has made my career as a satisfying
+one and certainly what has made me a
+
+ align:start position:0%
+one and certainly what has made me a
+ 
+
+ align:start position:0%
+one and certainly what has made me a
+much much better teacher that I might
+
+ align:start position:0%
+much much better teacher that I might
+ 
+
+ align:start position:0%
+much much better teacher that I might
+otherwise have been
+
+ align:start position:0%
+otherwise have been
+ 
+
+ align:start position:0%
+otherwise have been
+has been the enthusiasm and welcoming
+
+ align:start position:0%
+has been the enthusiasm and welcoming
+ 
+
+ align:start position:0%
+has been the enthusiasm and welcoming
+interest that I've felt from virtually
+
+ align:start position:0%
+interest that I've felt from virtually
+ 
+
+ align:start position:0%
+interest that I've felt from virtually
+every student I've ever taught and
+
+ align:start position:0%
+every student I've ever taught and
+ 
+
+ align:start position:0%
+every student I've ever taught and
+that's been especially true in this
+
+ align:start position:0%
+that's been especially true in this
+ 
+
+ align:start position:0%
+that's been especially true in this
+course and it's been especially true in
+
+ align:start position:0%
+course and it's been especially true in
+ 
+
+ align:start position:0%
+course and it's been especially true in
+this semester so I want to end then by
+
+ align:start position:0%
+this semester so I want to end then by
+ 
+
+ align:start position:0%
+this semester so I want to end then by
+saying thank you in a way symbolically
+
+ align:start position:0%
+saying thank you in a way symbolically
+ 
+
+ align:start position:0%
+saying thank you in a way symbolically
+I'd like to say thank you to the
+
+ align:start position:0%
+I'd like to say thank you to the
+ 
+
+ align:start position:0%
+I'd like to say thank you to the
+students to the students I've been
+
+ align:start position:0%
+students to the students I've been
+ 
+
+ align:start position:0%
+students to the students I've been
+teaching for more than 35 years at MIT
+
+ align:start position:0%
+teaching for more than 35 years at MIT
+ 
+
+ align:start position:0%
+teaching for more than 35 years at MIT
+for whom you are stand-ins but most of
+
+ align:start position:0%
+for whom you are stand-ins but most of
+ 
+
+ align:start position:0%
+for whom you are stand-ins but most of
+all I want to thank you
+
+ align:start position:0%
+all I want to thank you
+ 
+
+ align:start position:0%
+all I want to thank you
+you make me teaching makes me feel
+
+ align:start position:0%
+you make me teaching makes me feel
+ 
+
+ align:start position:0%
+you make me teaching makes me feel
+serious being able to introduce students
+
+ align:start position:0%
+serious being able to introduce students
+ 
+
+ align:start position:0%
+serious being able to introduce students
+to these astonishing works of art has
+
+ align:start position:0%
+to these astonishing works of art has
+ 
+
+ align:start position:0%
+to these astonishing works of art has
+always has always seemed to me to be a
+
+ align:start position:0%
+always has always seemed to me to be a
+ 
+
+ align:start position:0%
+always has always seemed to me to be a
+privilege for which I was unable to
+
+ align:start position:0%
+privilege for which I was unable to
+ 
+
+ align:start position:0%
+privilege for which I was unable to
+express fully my gratitude so thank you
+
+ align:start position:0%
+express fully my gratitude so thank you
+ 
+
+ align:start position:0%
+express fully my gratitude so thank you
+very much have a wonderful life
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/oTNwGuI7Wic.txt b/oTNwGuI7Wic.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b3dcc94cd7c02e0e796135137af174001026eb52
--- /dev/null
+++ b/oTNwGuI7Wic.txt
@@ -0,0 +1,2998 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Today I want to
+talk a little bit about
+
+designing control systems.
+
+This will finish up
+our discussions
+
+on signals and systems.
+
+Let me then just briefly
+review where we are.
+
+Hopefully this might help you
+also for perspective with
+
+regard to thinking about
+the exam tonight.
+
+We've looked at a bunch
+of different kinds of
+
+representations for discrete
+time systems.
+
+The easiest, most concise method
+we looked at was the
+
+representation using a
+difference equation.
+
+That's mathematically as
+concise as you can get.
+
+But it doesn't tell you
+important things like who's
+
+the input and who's the output
+and what are all the different
+
+ways that you can get
+through the system
+
+from input to output?
+
+So for that question block
+diagrams are nice.
+
+Block diagrams are graphical.
+
+It makes it very easy to see
+when there is, for example, a
+
+cyclic path through
+the network.
+
+But they're graphic.
+
+They're not nearly so concise
+as difference equations.
+
+So then we went on
+to operators.
+
+Operators are just as concise
+as difference equations but
+
+they contain additional
+information because the
+
+operators have an implicit
+argument.
+
+So there's an input, which is
+the argument to the operator,
+
+and there's an output, which is
+the output of the operator.
+
+So you can tell who is the input
+and who is the output.
+
+So that's good.
+
+That sort of combines the
+strengths of difference
+
+equations and block diagrams.
+
+You end up with a concise
+representation that has
+
+complete information about
+the signal flow paths.
+
+Furthermore, you can analyze
+the operators by using
+
+polynomial mathematics and that
+gives rise to the notion
+
+of a system functional.
+
+And that's a very nice closure
+because that represents an
+
+abstraction that lets us think
+about a whole system as though
+
+it were just one part, one
+thing, one operator.
+
+So we use that structure then,
+all of those representations,
+
+to try to learn about
+feedback.
+
+And first off, in the block
+diagram it's very easy to see
+
+that any time you have feedback
+-- feedback so
+
+enormously powerful that we want
+to use it in design --
+
+but you can see immediately
+from the structure of the
+
+block diagram that if you have
+feedback then you have cycles.
+
+Why is that interesting?
+
+Well, that's interesting because
+if you have cycles
+
+then even transient inputs can
+generate persistent outputs.
+
+So that's a kind of behavior
+that we would like to
+
+understand.
+
+From the nature of feedback
+it generates cycles.
+
+From the nature of cycles it
+generates persistent responses
+
+even if there's no input.
+
+And we saw that we could
+characterize those by thinking
+
+about those responses for
+one part at a time.
+
+And those parts we thought of as
+poles and the responses to
+
+a single pole we called modes.
+
+So we thought through a way of
+decomposing the response of a
+
+complicated system in terms
+of a number of additive
+
+components that are
+based on poles.
+
+Poles are just the base of
+a geometric sequence.
+
+So today then what I want to
+do is use that framework to
+
+think about design.
+
+How would you optimize the
+design of a controller?
+
+Looking back to where we've
+been, way back in Lab 4,
+
+ancient history, we looked at
+how you could program the
+
+robot to approach a wall.
+
+And we saw that depending on how
+you set up that system you
+
+could get very different
+performances.
+
+And what we'd like to do is have
+a way that we can design
+
+for performance without
+actually building it.
+
+The kind of thing that we built
+in the lab, Lab 4, was
+
+so easy that building it to
+determine its behaviors was
+
+not a bad problem.
+
+But In general if you were
+building a 777, there's more
+
+than one pole.
+
+And you wouldn't necessarily
+want to test drive all of the
+
+bad configurations.
+
+So we'd like to be able to
+understand that kind of a
+
+problem analytically.
+
+We'd like to be able
+to analyze it.
+
+So using the different
+representations you can
+
+generate a very concise
+representation just thinking
+
+in terms of difference
+equations.
+
+You all did this in Lab 4.
+
+And you get a single difference
+equation that tells
+
+you in principle everything
+there is that you could know,
+
+but not in a form that's
+very easy to analyze.
+
+It's a bit better if you
+translate the difference
+
+equation into a block diagram
+because now you can see that
+
+this system of equations
+has in fact two
+
+feedback loops in it.
+
+Two cycles.
+
+Two things that might
+potentially generate
+
+persistent responses to
+transient signals, which could
+
+then degrade performance.
+
+If the transient signal lasts
+ten years it might be a bad
+
+controller.
+
+If the 777 hits turbulence
+and never stabilizes
+
+that would be bad.
+
+If small disturbances got bigger
+with time that might be
+
+bad, right?
+
+So we can see that this simple
+controller described by these
+
+difference equations has
+the potential to do
+
+that sort of stuff.
+
+And we'd like to understand,
+when does it?
+
+The easiest way to think about
+analyzing this is to focus
+
+first on the inner loop and ask
+the question, what's the
+
+functional representation for
+that box which we would call
+
+an accumulator?
+
+This box, this thing,
+accumulates at its output, the
+
+sum of all the things that ever
+came in so we call it an
+
+accumulator.
+
+So what's the functional
+representation of an
+
+accumulator?
+
+Well, we just do polynomial
+math.
+
+Easy so we can recognize from
+the block diagram that the
+
+signal Y could be constructed
+by applying R to W.
+
+But we can also see in the block
+diagram that W is the
+
+sum of X and Y. And then if we
+take the left hand side and
+
+the right hand side of this
+double equation we get
+
+something that involves just X
+and Y, which we can solve for
+
+the ratio Y over X. Which then
+says that the ratio is R over
+
+(1 minus R).
+
+That's a functional
+representation for the effect
+
+of the accumulation.
+
+That's also something that comes
+up so frequently in the
+
+design of control systems
+that we give it a name.
+
+We call this Black's Equation.
+
+And it's especially useful to
+avoid these little trivial
+
+steps in algebra, to just
+jump to the answer.
+
+So let's see that everybody's
+following me.
+
+The equation for this box is
+the thing that we will call
+
+Black's Equation.
+
+It's not mysterious.
+
+It's something that you could
+derive, so derive it.
+
+Figure out the functional form
+for the system that goes from
+
+X to Y and figure out which
+of these forms is correct.
+
+(1) through (4), or (5) if none
+of the above applies.
+
+So take 30 seconds, figure
+out the answer.
+
+I'm going to ask you
+to raise your hand.
+
+You're free to talk
+to your neighbors.
+
+OK.
+
+So everybody who raised your
+hands tell me what the
+
+right answer is.
+
+OK, wonderful.
+
+It's about 95%.
+
+No.
+
+It's about 100% correct out of
+about 95% participation.
+
+So the answer you can form just
+like we did before, no
+
+particular tricks, using
+simple algebra.
+
+Simple algebra you get
+F over (1 minus FG).
+
+The thing I want you to
+recognize is kind of a
+
+graphical way of thinking
+about that.
+
+And you can just memorize
+F over (1 minus
+
+FG) and that's fine.
+
+But there's some interesting
+things that the designer
+
+thinks about.
+
+This functional form is F,
+that's the forward gain.
+
+That's the gain through the
+system starting at the input
+
+and going directly
+to the output.
+
+So this form says that the
+closed loop gain, the system
+
+function that results when the
+loop is closed, is just the
+
+forward gain, F, divided by
+(1 minus the loop gain).
+
+The loop gain is the product
+around the loop once.
+
+So that's just a convenient
+way of thinking about it.
+
+Any time you have a feedback
+system of this type you can
+
+think about the closed loop
+response as being the forward
+
+path F divided by (1 minus
+loop gain FG).
+
+So the answer was 1.
+
+And generally we'll see two
+different ways of representing
+
+the system.
+
+Sometimes we'll represent it
+with a plus as we did with the
+
+accumulator.
+
+Many times we'll represent
+it with a minus.
+
+That's the way we think about
+control problems.
+
+We put in the minus because we'd
+like to think about the
+
+controller as trying to make
+something go to 0.
+
+So when you take the difference,
+that gives us an
+
+error signal.
+
+And then we can think about the
+controller being the thing
+
+that drives that error to 0.
+
+But however you think about it,
+there's two forms that are
+
+very closely related.
+
+They really differ by just a
+minus sign which you could
+
+think of as just multiplying
+G. So it's sort of like the
+
+right hand side is just
+a minus G plugged into
+
+the left hand side.
+
+So then the way you use this
+idea, you think about the
+
+block diagram and you say, OK I
+can replace this thing with
+
+an equivalent system
+which is R over (1
+
+minus R) and then repeat.
+
+So the R over (1 minus R) means
+that, if you think about
+
+Black's Equation now for this
+loop, you should think about
+
+the forward gain, K minus T, R
+over (1 minus R), that's this.
+
+Divided by (1 plus
+the loop gain).
+
+So 1 plus, and the loop gain,
+well, the wire down here just
+
+has a gain of 1.
+
+So the loop gain and
+the forward gain
+
+are the same thing.
+
+So you get this kind
+of expression which
+
+simplifies to this.
+
+There's two things I want
+you to see about this.
+
+First off, I want you to see
+that even though the
+
+simple-minded way of plugging
+in said that we should have
+
+got a quotient of quotients N
+over D over N over D, it's
+
+simplified to a single ratio.
+
+If you design a system out of
+just adders, gains and delays,
+
+that will always be true.
+
+There's a closure.
+
+It will always be the case
+that the functional that
+
+represents a system of that
+form will always have the
+
+property that it's a polynomial
+in R divided by
+
+another polynomial in R,
+that's just the way
+
+polynomials work.
+
+The other thing is that you
+can now start to interpret
+
+what the behavior of this could
+represent in a simpler
+
+form than thinking about this.
+
+So this kind of a representation
+that leads to
+
+intuition about what the
+behavior should be is very
+
+helpful when you're thinking
+about design.
+
+And in particular this
+particular thing says that if
+
+we think about a simpler system
+that could generate
+
+that same response we can
+generate some intuition for
+
+how we would like to set
+the parameter k.
+
+So in particular this system
+functional which we generated
+
+for this system could equally
+apply to that system.
+
+Is that clear?
+
+So there's a numerator, which
+I've represented here.
+
+There's a numerator, which
+has an R in it and has
+
+a minus kT in it.
+
+I'm going to, for reasons that
+you'll see in a minute, I'm
+
+going to call something P0
+because it's the pole.
+
+So the numerator I've
+represented here and this
+
+denominator has this form.
+
+And I wrote it that way because
+this is the canonical
+
+form for the way of thinking
+about a pole.
+
+So what I showed is that even
+though this was a more
+
+complicated system you can think
+about it as the cascade
+
+of a delay, a gain,
+and a pole.
+
+The pole can be calculated from
+the gain, the pole is the
+
+multiplier for R, so the
+pole is (1 plus kT).
+
+So if I were to choose kT to
+be minus 0.2 then the pole
+
+would be at 0.8.
+
+If the pole is at 0.8 then the
+mode, the natural response to
+
+the pole, would have the
+form P to the n.
+
+They always have the form
+geometric P to the n, so it
+
+would look like 0.8 to the n.
+
+Because of the pre-multiplier of
+1 minus P0 the whole thing
+
+gets multiplied by 0.2 and
+because of the delay the whole
+
+thing gets shifted
+to the right.
+
+The important thing is that by
+thinking about manipulating
+
+this as an operator we can
+recognize and simplify the
+
+form of the behavior.
+
+That gives us an intuitive
+grasp over how
+
+to best choose kT.
+
+It's all clear?
+
+Now, the behaviors that we're
+interested in are not always
+
+unit-sample responses.
+
+We do unit-sample responses
+because they're the easiest
+
+possible thing we could
+think of, right?
+
+A unit-sample is the simplest
+non-zero signal.
+
+A unit-sample is the signal that
+is different from 0 in
+
+exactly one place --
+
+the easiest possible place, 0.
+
+And it has its easy-as-possible
+
+non-zero value --
+
+1.
+
+So we focus on the unit-sample
+signal because it's the
+
+easiest possible signal
+we could think about.
+
+But when we're thinking about
+behaviors we're often thinking
+
+about other things.
+
+Often we'll think about
+the step response.
+
+Here I have illustrated
+the way you would
+
+measure a step response.
+
+A step response is what would
+happen if the output were
+
+initially 0, if we were at rest,
+and suddenly we turned
+
+on a signal that was
+constant at 1.
+
+That would happen in the robot
+case if we started the robot
+
+close to the wall, at
+rest, near 0 --
+
+so that the output signal is
+close to 0, but the desired
+
+input was a meter behind.
+
+Then that would be an input
+signal that started at time
+
+equals 0 equal to 1 and
+persisted forever at 1.
+
+And the result then
+would be what we
+
+call the step response.
+
+The step response is typically
+easier to measure in the lab
+
+than is the unit-sample
+response.
+
+So we use the unit-sample
+response when we're thinking
+
+analytically, when we're doing
+calculations, and we use the
+
+step response when
+we're in the lab
+
+trying to measure something.
+
+And the whole theory wouldn't
+be very useful if there
+
+weren't a close relationship
+between those two things.
+
+This diagram illustrates
+the relationship.
+
+If we think about a system H
+for which we would like to
+
+find the step response, the step
+response to that system
+
+is what would the system
+do if you put the
+
+unit-step into the system.
+
+I've represented the unit-step
+here as u[n].
+
+u[n], the signal that is 0 for
+n less than 0, and 1 for n
+
+bigger than or equal to 0 --
+
+is just the accumulation of
+the delta function, the
+
+unit-sample.
+
+So this system, the cascade of
+an accumulator with H, would
+
+measure the step response of H
+if it were driven with the
+
+sample signal.
+
+Because of the properties of
+polynomials and because block
+
+diagrams follow the rules for
+polynomials, we can flip these
+
+whenever the systems both start
+at rest, and if we flip
+
+those we get a different
+interpretation.
+
+What this says is that if you
+were to take H and stimulate
+
+it with the unit-sample you
+would get h, little h, which
+
+we would call the unit-sample
+response because it's the
+
+response to the system when the
+input is the unit-sample.
+
+So if you measured h with the
+unit-sample rather then with
+
+the unit-step you would get the
+unit-sample response from
+
+which you could generate the
+step response by running it
+
+through an accumulator.
+
+So what that says is there's a
+close association, there's a
+
+close relationship, between the
+unit-sample response and
+
+the unit-step response.
+
+One is the accumulation
+of the other.
+
+The unit-step response is the
+accumulated response to the
+
+unit-sample response.
+
+So that means that in that
+previous example where we saw
+
+that setting kT equal to minus
+0.2 resulted in this
+
+unit-sample response, that
+would correspond to this
+
+unit-step response.
+
+All you do is for every sample
+you calculate, for this
+
+response you calculate the sum
+of say, n equals 0, you would
+
+take the sum of all of the
+previous answers in H[n].
+
+It's the accumulation.
+
+So it starts at 0 since the sum
+of all those numbers is 0.
+
+Then at time 1 it becomes the
+sum from here back so it
+
+becomes 0.2.
+
+Then here it's the sum
+from here back.
+
+And if you add these all up
+it becomes a number that
+
+approaches 1.
+
+Not surprisingly, right?
+
+If you've got a feedback system
+and if you started the
+
+robot up against the wall and
+the desired position was one
+
+meter behind you would
+monotonically approach 1, OK?
+
+And what you can see is that if
+you change the value of the
+
+pole, here I've changed the kT
+from minus 0.2 which is what
+
+the previous answer was, to
+minus 0.8, I've changed the
+
+value of the pole,
+the unit-sample
+
+response got faster.
+
+And the unit-step response
+also got faster.
+
+The point is there are different
+kinds of performance
+
+metrics that we might want to
+use, unit-sample response,
+
+unit-step response, but the
+responses of all of them, you
+
+can tell something about the
+response to all of them from
+
+the response of the unit-sample
+signal.
+
+That's why we focus so much
+on the unit-sample signal.
+
+It's not because it's the
+most popular thing
+
+to use in the lab.
+
+It's because it's the easiest
+thing to calculate with and it
+
+gives us insight into things
+that we would like to measure
+
+in the lab.
+
+So for this very simple system
+what you can show is that
+
+there's only a few possible
+behaviors, a few
+
+categories of behaviors.
+
+If you were to choose kT to be
+between 0 and 1, then the
+
+pole, which is (1 plus kT) would
+also be between 0 and 1.
+
+Since the system has a single
+pole you can say a lot about
+
+the response from the numerical
+value of the pole.
+
+If the pole is between 0 and 1
+then the response is going to
+
+be monotonic and converging.
+
+That results because the
+unit-sample response was
+
+positive only and decayed
+towards 0.
+
+Because it's positive only
+it means monotonic --
+
+goes to 0 and makes
+it converge.
+
+So you can infer properties
+about the unit-step's response
+
+from properties of the pole
+just like we could infer
+
+properties of the unit-sample
+response.
+
+If you changed kT to be between
+minus 2 and 1 you get
+
+a P0 that's between
+minus 1 and 0.
+
+Again that's just
+that equation.
+
+That says that the response
+will be alternating.
+
+So the sign of the unit-sample
+response goes
+
+positive then negative.
+
+It still converges in the sense
+that the unit sample
+
+response approaches 0.
+
+And what that means for the unit
+step-response is that the
+
+unit-step response will
+converge toward 1.
+
+The sign doesn't alternate
+around 0, the sign
+
+alternates around 1.
+
+So again, you can infer the
+properties of the unit-step
+
+response from the properties of
+the unit-sample response.
+
+And if you have kT that is less
+than minus 2 then you get
+
+a P0 that's less than
+minus 1 and
+
+that's a divergent response.
+
+So the point is you can infer
+properties about the control
+
+system by thinking about the
+poles of the system where here
+
+I've illustrated it for
+a simple system that
+
+only has one pole.
+
+OK.
+
+I told you a bunch of facts.
+
+Now you figure out something.
+
+How would I choose k for this
+system to get the quote, "best
+
+performance?"
+
+So which value of kT would give
+the fastest convergence
+
+for the unit-sample signal?
+
+OK, participation is down but
+the hit rate is still good.
+
+Virtually everybody who
+volunteered to answer got the
+
+right answer.
+
+The most popular
+answer was (2).
+
+Why is the answer (2)?
+
+What's the range of
+possibilities
+
+that we could get?
+
+If we choose k, or kT, we
+could choose kT to be--
+
+what's the range of kT
+that we could use?
+
+Minus 2 to 0?
+
+[INAUDIBLE] we could use kT,
+any real number, right?
+
+We couldn't use imaginary
+numbers because that doesn't
+
+sort of make sense for
+a real system.
+
+But we could choose
+any real number.
+
+The real numbers map, according
+to this chart, the
+
+real numbers map to a different
+real number.
+
+If you choose kT you can figure
+out where is the pole
+
+by that mapping.
+
+Where would you put the pole to
+get the fastest response?
+
+If you have your choice of
+putting the pole anywhere on
+
+this red line, that red line or
+that red line, where would
+
+you put it and why?
+
+AUDIENCE: Just inside
+the [INAUDIBLE]
+
+PROFESSOR: Putting it inside the
+unit circle would probably
+
+be a good idea because?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: Yeah.
+
+If you didn't put it
+inside the unit
+
+circle it wouldn't converge.
+
+That's right.
+
+So you like [UNINTELLIGIBLE]
+the inside.
+
+Given the choice of anywhere
+here and anywhere here which
+
+would you choose?
+
+How would you choose it?
+
+Yeah.
+
+AUDIENCE: Derive.
+
+PROFESSOR: Derive.
+
+And how do you get that?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: What would happen
+if it was close to
+
+[UNINTELLIGIBLE]?
+
+It converges quite
+quickly, right?
+
+Poles always converge
+geometrically.
+
+The base of the geometric
+is the pole value.
+
+So you'd like the pole to be
+as small as possible to get
+
+the convergence as
+fast as possible.
+
+That make sense to everybody?
+
+So in particular for this
+example if you chose kT to be
+
+minus 1 in that limit then this
+entire factor goes away.
+
+So the entire response
+degenerates to R and R is not
+
+instantaneous but it's
+pretty fast.
+
+What that says is that
+you get to the final
+
+value in one step.
+
+So if the input consisted of
+a unit sample, which has
+
+non-zero value only at 0, the
+output would have non-zero
+
+value only at 1, right?
+
+Thinking about the way that
+works in practice, think about
+
+the robot and think about
+we're trying to
+
+drive toward the wall.
+
+If we made kT be minus one, and
+just for the sake of being
+
+concrete let me say that
+T is about 1/10.
+
+That's what the sampling period
+is for the robots we
+
+use in the lab.
+
+If T were 1/10 then the best
+k would be minus 10.
+
+And what that says is that if
+we were 1 meter away from
+
+where we want to be we would set
+the velocity to 10 meters
+
+per second.
+
+What that says is that if we
+started 1 meter away from
+
+where we want to be, so this
+is intended to represent
+
+position on the same axis that
+this has showed, so if we
+
+started here and we wanted to be
+here, time is plotted down.
+
+If we use the rule that we just
+specified then we would
+
+set the velocity given this
+condition which is 1 meter
+
+away from where we want to be.
+
+We would set the velocity
+to be 10.
+
+If we set the velocity to be 10
+then after 1 unit of time,
+
+after 1/10 of a second, we are
+1 meter to the right, which
+
+just happens to be exactly
+where we want to be.
+
+Had we chosen k to be bigger
+we would have overshot.
+
+Had we chosen k to be smaller
+we would have undershot.
+
+k equals 10 gave us precisely
+the right answer so that we
+
+get there in one fell swoop.
+
+Then on the very next step we
+would compute a velocity of 0
+
+because we are at where
+we want to be so
+
+we would stay there.
+
+And that condition would
+persist forever.
+
+The idea would be this simple
+system provides a way that we
+
+could set the gain so we could
+get to where we want
+
+to be in one step.
+
+It's hard to beat that.
+
+The problem that results and the
+reason you didn't see that
+
+good behavior in the lab was
+that the sensors in the robot
+
+don't work instantaneously.
+
+They introduce delay.
+
+And as an idealization of that
+delay I want to think through
+
+the same problem.
+
+But now let's say that the
+sensor delays the input to the
+
+sensor which is the output
+of the system.
+
+Let's say that the sensor
+introduces a delay of 1, so
+
+now instead of reporting d
+sensed, which was d0[n], it
+
+reports d0[n minus 1].
+
+So now what would happen?
+
+Now with the delay, if I started
+here and if by some
+
+mysterious process I was here
+at time n equals 1, then I
+
+would calculate my
+new velocity.
+
+What would be my new
+velocity here?
+
+I'm right where I want to be.
+
+What would be my new velocity
+if I assume that the sensor
+
+has a delay of [UNINTELLIGIBLE]?
+
+AUDIENCE: 10.
+
+PROFESSOR: 10.
+
+Because of the delay the sensor
+is reporting that I'm a
+
+meter away from where
+I want to be.
+
+So the controller calculates,
+oh, I need to
+
+go forward a meter.
+
+I'll set the velocity to 10.
+
+So having set the velocity to 10
+and then one step goes by,
+
+now we're completely
+on the wrong side.
+
+That's what happens when you
+put delay into the system.
+
+So because we're basing this
+decision on where we were last
+
+time we go to the wrong place.
+
+So now we're here.
+
+What will the controller
+say next?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: Stay here.
+
+You're in a great place.
+
+I'm really 1 meter too close.
+
+In fact I banged
+into the wall.
+
+But the sensor is telling me I'm
+exactly where I want to be
+
+so stay here.
+
+Say I didn't kill myself, what
+will the velocity next be?
+
+Minus 10.
+
+So now I tell myself
+to go back.
+
+That's probably a good move.
+
+But now I still think I'm too
+close to the wall so I tell
+
+myself to continue to back up.
+
+The idea is that I get
+poor performance.
+
+The delay had a devastating
+effect on the way that the
+
+controller worked.
+
+Even though it's a tiny change
+to the way the system works it
+
+has a devastating effect
+on behavior.
+
+We'd like to be able to predict
+that without having to
+
+measure it.
+
+Here's the same equations except
+that I put a delay in
+
+the sensor.
+
+Here is the same block diagram
+but I've represented a delay
+
+in the sensor path.
+
+So now the question is, what's
+the new functional
+
+representation for that
+control system?
+
+So what's the answer?
+
+Can you rate the functional form
+for this system as one of
+
+(1), (2), (3), or (4), or
+is it none of the above?
+
+About 1/3 participation and
+about 100% correct.
+
+The answer's four.
+
+You get to use Black's Equation
+or however you'd like
+
+to think about that.
+
+You can think about reducing the
+inner loop the same as we
+
+did before and then think about
+this as forward over (1
+
+plus loop gain) but now the loop
+gain has R squared in it
+
+instead of R. We
+get this form.
+
+How does this form differ from
+when the R wasn't here?
+
+What's the difference between
+R not there and R is there?
+
+What's the answer?
+
+Anyone?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: The squared term.
+
+So this term in the previous
+form was just an R and in this
+
+form is a square and
+so what's that do?
+
+What's the importance
+of the fact that
+
+there's a square there?
+
+Two poles, right?
+
+We now have a polynomial in
+the denominator that is
+
+quadratic in R.
+
+And what that's going to do is
+it's going to give us two
+
+poles instead of one.
+
+The importance of that is that
+now we're going to have to
+
+think through-- we previously
+categorized what were all the
+
+behaviors you could
+get from one pole.
+
+The behaviors you can get from
+one pole were monotonic
+
+divergence, non-monotonic
+alternating divergence,
+
+monotonic convergence,
+alternating convergence.
+
+So there were four behaviors
+that were
+
+possible with one pole.
+
+Now we have to think through
+what are all the possible
+
+behaviors that we could
+get with two poles.
+
+Different problem.
+
+Hopefully they're related.
+
+So here, the way we would find
+out what the poles are is take
+
+this expression, substitute for
+every R, 1 over z, turn
+
+the ratio of polynomials
+in R into a ratio of
+
+polynomials in z.
+
+To do that in this case I had
+to multiply numerator and
+
+denominator by z squared.
+
+Having done that I get a second
+order polynomial in z
+
+in the bottom so there's two
+poles which are the roots of
+
+that polynomial.
+
+And that's just a quadratic
+equation.
+
+The interesting thing now is
+to map out what are all the
+
+possible behaviors that that
+system can give us.
+
+It's important to realize that's
+a simple generalization
+
+of what we saw before.
+
+It will be the case that any
+system that we construct out
+
+of adders, gains and delays will
+have the property that we
+
+can write the system functional
+as a ratio of
+
+polynomials in R. By the factor
+theorem we will always
+
+be able to factor
+the denominator.
+
+And by the notion of partial
+fractions we'll always be able
+
+to write some complicated
+expression like that in terms
+
+of a sum of parts.
+
+Each part being first order.
+
+The intuition we get from this
+is that what we ought to do is
+
+factor the denominator, find
+the poles, and associate a
+
+behavior with each
+of those poles.
+
+Here's what the problem looks
+like for the two pole problem.
+
+If we have the general form
+given here and if we start by
+
+thinking about kT having a small
+magnitude, if kT has a
+
+small magnitude then we have 1/2
+plus or minus the square
+
+root of 1/2 squared.
+
+So that's 1/2 plus
+or minus 1/2.
+
+That's 0 or 1.
+
+So the poles for this system,
+if you make k be very small,
+
+the poles are at 0,
+near 0 and near 1.
+
+Is that a good system response
+or a bad system response?
+
+Bad.
+
+Why?
+
+Well, we're trying to think
+through the behavior of the
+
+second order system by thinking
+about the separate
+
+behaviors of each
+of the poles.
+
+Is this a good pole
+or a bad pole?
+
+Why?
+
+The response is always pole
+[UNINTELLIGIBLE].
+
+The mode associated with the
+response at a pole near one is
+
+something near one to the end.
+
+That never converges.
+
+If you start with some error
+the error persists forever.
+
+Well, that's not good.
+
+If wind turbulence knocks you
+into a decline in your
+
+airplane and it persists
+forever, that's not good.
+
+You would like those
+things to damp out.
+
+So this pole is bad.
+
+How about that pole?
+
+That one has a response
+that decays quickly.
+
+But the problem is that when
+you add the two pieces
+
+together, that was the reason
+I showed you this
+
+decomposition, you can think
+about the polynomial being
+
+factored and being broken
+into a number of parts.
+
+The part that's associated with
+the pole near one has a
+
+response that goes
+for a long time.
+
+So that will asymptotically
+dominate your response.
+
+So we refer to this as
+a dominant pole.
+
+This pole dominates
+the response.
+
+That's a way of inferring the
+behavior of two poles from the
+
+sum of single poles.
+
+In this particular case there's
+one pole that matters
+
+more than the other one.
+
+So we call that pole
+the dominant pole.
+
+If you were to make kT more
+negative, So here's the
+
+general form.
+
+If you make kT negative, you can
+make the thing under the
+
+radical sign go towards 0.
+
+If you made the thing under the
+radical sign go to 0 then
+
+you would get two
+poles at 1/2.
+
+So here we would see that if kT
+were minus 1/4, if kT were
+
+minus 1/4 we would have 1/2
+squared, which is plus 1/4.
+
+Minus 1/4 would give us
+0 under the radical.
+
+So we would get two
+poles at 1/2.
+
+Is that good or bad?
+
+Well, it's better than the
+previous example, right?
+
+Because each of those poles is
+associated with the response
+
+where the error gets half what
+it used to be on every step.
+
+So it converges.
+
+If going from 0 to minus 1/4 is
+good, then going to minus
+
+1/2 might be better, right?
+
+If you continue that trend, say
+you make kT be minus 1, if
+
+kT is minus 1 then you get
+1/2 squared minus one.
+
+So 1/2 squared is 1/4, minus
+1 would be minus 3/4.
+
+That gives us a complex
+pole here.
+
+So we get two poles that are
+right on the unit circle.
+
+What's that mean?
+
+That means oscillations.
+
+Oscillations is something you
+can't get with one pole with a
+
+real system.
+
+Oscillations result from
+a poll that has
+
+an imaginary component.
+
+If the system is real
+you could only get
+
+such poles in pairs.
+
+So it's this pair that
+makes sense for
+
+a real valued system.
+
+And that gives rise to
+oscillations and that's
+
+exactly what we saw here.
+
+So we can associate the
+oscillations that we saw in
+
+the simulated lab experiment
+with poles that have imaginary
+
+components.
+
+So what would be the period of
+the oscillation in the system
+
+given by 1/2 plus
+j root 3 over 2?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Excuse me?
+
+Excuse me?
+
+AUDIENCE: Where did the
+root three come from?
+
+PROFESSOR: The previous page.
+
+If you substitute minus 1.
+
+So what's the period
+of the oscillation?
+
+So the period's represented
+by 5 converged into 6.
+
+So how do you get 6?
+
+The easiest way to think about
+that is to think about the
+
+poles being expressed
+in polar notation.
+
+The poles we previously said
+were 1/2 plus or minus
+
+j root 3 over 2.
+
+That's the same as e plus
+or minus j pi over 3.
+
+It's easier to use that form
+because if you take that form,
+
+so if you think about e to the
+j, what was it, 2 pi over 3?
+
+Pi over 3.
+
+So if you think about that form,
+that's the pole, we can
+
+write that that way.
+
+Then the inside has
+a magnitude of 1.
+
+So we can think about that just
+being a magnitude of 1
+
+and an angle of pi over 3.
+
+So when you raise that to the n,
+the magnitude to the n, one
+
+to the n is always 1, and the
+angle raised to the n, it just
+
+increases linearly with n.
+
+So the angle goes from pi over
+3 to 2pi over 3 to pi to 4pi
+
+over 3, et cetera.
+
+So you can think about this
+going from pi over 3, 2pi over
+
+3, pi, 4, 5, 6.
+
+It takes n equals 6 to get
+around to where it started so
+
+the period is 6.
+
+If you were to further change
+the game, if you were to make
+
+it even more negative, the poles
+would go outside the
+
+unit circle.
+
+And then what would happen?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: Right.
+
+So that's completely
+unacceptable.
+
+The point is that by changing
+the gain you can get any
+
+behavior on this figure which
+is called the root locus.
+
+So root meaning the root
+of a polynomial.
+
+Locus meaning the acceptable
+values of points.
+
+So the root locus shows you
+all the possible behaviors
+
+they could result from
+this system.
+
+So given that root locus, how
+would you choose k to make
+
+your system response as
+fast as you could?
+
+So what value of kT
+would you want?
+
+Everyone raise your hands.
+
+That's very good.
+
+So the most popular answer
+is number (2).
+
+So why would the answer
+be number (2)?
+
+What do you look at?
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Remember what
+we're trying to do.
+
+We're trying to infer properties
+of the behavior of
+
+this second order system from
+the pole locations.
+
+We know that there's an
+expansion that lets us expand
+
+the system in terms of the sum
+of two first order responses.
+
+The slowest of the first order
+responses will dominate
+
+eventually.
+
+So what we need to
+look at is the
+
+slowest of the two responses.
+
+We would like to know
+of the two poles
+
+which one is the slowest?
+
+The slowest is the one that's
+closest to the unit circle.
+
+So we would get the fastest
+response when the slowest one
+
+is as fast as possible.
+
+As the poles initially go toward
+each other from 0 to 1
+
+this one is getting faster, this
+one is getting slower.
+
+So the slowest one
+is this one.
+
+So the slowest one is fastest
+when they meet.
+
+And then when they diverge
+does the slowest one get
+
+faster or slower?
+
+It's already slower
+because it gets
+
+closer to the unit circle.
+
+So you get the fastest response
+whenever you get the
+
+two poles both colliding at 1/2
+and that was the case that
+
+happened when kT was minus 1/4
+from two or three slides ago.
+
+So the idea then is to try to
+infer what would be the
+
+behavior of this higher order
+system by thinking about the
+
+behaviors of the individual
+components, here the poles.
+
+And what we saw was something
+that's in fact a very
+
+important general trend.
+
+What we saw was that we first
+analyzed the wall finder
+
+system assuming there was
+no delay in the sensor.
+
+And we found that that system
+was characterized by a single
+
+pole and we had the design
+freedom of putting that pole
+
+anywhere we wanted to
+on the real axis.
+
+And that allowed us to choose
+the pole to be at 0 which gave
+
+terrific performance.
+
+The interesting thing that
+happened when you add just one
+
+more pole by putting a delay
+in the sensor, you make the
+
+system more complicated and
+now you can't possibly get
+
+nearly so good behavior.
+
+The behavior is a lot worse
+than it was before.
+
+And in fact, if you were to do
+the same kind of analysis by
+
+putting yet another delay in the
+sensor you would find even
+
+worse behavior.
+
+The idea then, the
+generalization of the way the
+
+behaviors is working, generally
+speaking adding
+
+delays inside a feedback loop
+is a destabilizing thing.
+
+Generally as the number of
+delays increases you end up
+
+having to back off on the
+maximum gain that you can use
+
+because the system becomes
+less stable.
+
+So the overall moral is that
+delays are bad generally.
+
+I mean, you could concoct some
+kind of a weird scheme where
+
+that wouldn't be true.
+
+But it's actually hard to
+concoct such a weird scheme.
+
+In general, and in virtually
+every physical system that
+
+you'll run into, adding
+delays makes the
+
+system harder to stabilize.
+
+And that's the big message.
+
+And the system that we looked at
+in the lab, the wall finder
+
+was actually quite hard
+because the number
+
+of delays was large.
+
+If you try to track where delays
+can enter the robot
+
+system they get in at very
+many different places.
+
+In the physical sensor, in the
+microprocessor, in the
+
+conversion from analog to
+digital, there's a number of
+
+delays in that system.
+
+And that's why it becomes
+hard to stabilize.
+
+OK.
+
+So that's the main content
+for today.
+
+What I want to do is give you
+one more practice question.
+
+The big problem that I want you
+to think about from today
+
+is how do you characterize
+performance?
+
+When we had a single pole
+performance was easy to talk
+
+about because performance was
+diverging monotonically,
+
+diverging alternating,
+converging monotonically,
+
+converging alternating.
+
+There were four kinds
+of behaviors.
+
+When we went to second order
+we saw some new behaviors.
+
+It could become oscillatory.
+
+What I'd like you to do now is
+think not just about those
+
+properties but many
+other properties.
+
+So here's some questions.
+
+Think about the system on the
+top and I'd like you to infer
+
+properties about that system.
+
+In particular, does this system
+have three poles?
+
+Is the unit sample response, is
+there a way to write that
+
+as the sum of three geometric
+sequences?
+
+What's the unit sample
+response?
+
+And is one of the poles
+that z equals 1?
+
+So think about the system,
+think about five ways of
+
+characterizing it and tell
+me how many of those five
+
+characterizations is correct.
+
+So how many of the properties
+are true?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+Probably 2/3 correct?
+
+PROFESSOR: How many poles?
+
+How do you get three?
+
+Where are the poles?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: How do
+I find poles?
+
+What do I do?
+
+Yes?
+
+AUDIENCE: You use Black's
+Equation [UNINTELLIGIBLE]
+
+the top you can express
+[UNINTELLIGIBLE]
+
+so use Black's Equation to
+express the system function as
+
+R cubed over (1 minus
+R-cubed) then--
+
+PROFESSOR: That's right.
+
+AUDIENCE: --the denominator
+as an order of 3 and
+
+you combine the 3s.
+
+PROFESSOR: So a little more
+formally, we would take this
+
+thing and we would rewrite that
+with R goes to 1 over z.
+
+So we get 1 over z cubed, 1
+minus (1 over z cubed), which
+
+is then, clearing the z cubes
+we would get 1 over
+
+(z cubed minus 1).
+
+How many poles?
+
+Three.
+
+What are the poles of
+z cubed minus 1?
+
+Three poles in what?
+
+AUDIENCE: 0 [UNINTELLIGIBLE]
+
+PROFESSOR: And so let's vote.
+
+Let's take a vote.
+
+There's two poles
+at z equals 1.
+
+Yes?
+
+No?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: Why not?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: So there's
+two poles.
+
+I made a [UNINTELLIGIBLE]
+plane.
+
+Where's the poles?
+
+Well, you could factor
+it, right?
+
+If you factored it you'd
+find that there is
+
+a pole at 1, right?
+
+But then there's two more
+poles like that.
+
+So the poles are the three
+roots of 1, which can be
+
+written like 1 e to the j, 2pi
+over 3, and e to the j minus
+
+2pi over 3.
+
+Which pole was the
+dominant pole?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: OK, bad question.
+
+What's a better question?
+
+AUDIENCE: How many dominant
+poles are there?
+
+PROFESSOR: How many dominant
+poles are there?
+
+That's a much better
+question, yes.
+
+There's sort of three
+poles that are
+
+equally dominant, right?
+
+They all have the
+same magnitude.
+
+Why do we talk about
+dominant poles?
+
+What are dominant
+poles good for?
+
+If I told you that I had a pole
+at 3 and a pole at minus
+
+1, which one's the
+dominant pole?
+
+AUDIENCE: 3.
+
+PROFESSOR: Why?
+
+AUDIENCE: Greater magnitude.
+
+PROFESSOR: Greater magnitude.
+
+Why do we care?
+
+We don't care, right?
+
+What's good about the
+dominant pole?
+
+Well, we can write this response
+as something that
+
+looks like three to the n
+plus minus 1 to the n.
+
+If you let n get big enough
+the only one that
+
+matters is 3 to the n.
+
+So if all you care about is
+exactly how the plane was
+
+flying the instant before it hit
+the ground then you would
+
+only need to worry
+about long time.
+
+And if you only worry about
+long time you only need to
+
+worry about the pole that's
+worst behaved.
+
+That's where the concept
+comes from.
+
+So none of these poles are
+particularly worse behaved
+
+than the others.
+
+What's the unit-sample response
+
+associated with that pole?
+
+We have a name for that
+[INAUDIBLE] right?
+
+AUDIENCE: It's huge.
+
+PROFESSOR: It's
+[UNINTELLIGIBLE].
+
+What's the unit-sample response
+
+associated with this pole?
+
+Well, it's got a complex
+value right?
+
+So the unit-sample response
+associated with that pole is e
+
+to the j 2 pi over 3 n.
+
+That's a complex number.
+
+That's 1 at time 0 and e to the
+j 2 pi over 3n at time 1
+
+and e to the j 4 pi over
+3 at time two.
+
+So it goes from here at 0 to
+here at 1 to here at 2,3, 4,
+
+5, 6, 7, 8.
+
+What's the period
+of this pole?
+
+What's the period of the
+unit-sample responses
+
+associated with that pole?
+
+3.
+
+Because it takes 3
+to get around to
+
+where you started again.
+
+What's the period
+of this pole?
+
+3.
+
+You just spin around backward.
+
+What's the period
+of the response
+
+associated with that pole?
+
+Bad question.
+
+All right, what's a
+better question?
+
+Is there a period associated
+with it?
+
+You could say that period
+1 [UNINTELLIGIBLE]
+
+definition of period.
+
+What's the period
+of this pole?
+
+Dumb question, right?
+
+Period implies repeat.
+
+If the response repeats itself
+after some time then we would
+
+say the response is periodic.
+
+Neither of those poles,
+well, the minus 1 is.
+
+Is the minus 1 pole periodic?
+
+Yes.
+
+What's the difference between
+periodic and alternation?
+
+Does a [UNINTELLIGIBLE]
+
+alternate?
+
+AUDIENCE: Yes.
+
+PROFESSOR: Does it oscillate?
+
+AUDIENCE: No.
+
+PROFESSOR: Bad question.
+
+Alternate is a word that we
+invented for one pole.
+
+Because the response
+alternated in sine.
+
+The unit-sample response in one
+pole, where the pole is a
+
+negative number, alternated
+in sine.
+
+So we gave that a name.
+
+Alternation is not necessarily
+something that we would like
+
+to associate with a higher
+order system.
+
+Periodic is perfectly reasonable
+to talk about for a
+
+higher order system.
+
+Periodic merely means that if y
+of n were a periodic signal
+
+that I could express y of
+n plus n as y of n.
+
+That would be periodic.
+
+If the thing repeats itself we
+would say it's periodic.
+
+So the point of going over this
+stuff is just to give you
+
+some exercise in thinking
+about how to think about
+
+properties of systems.
+
+We develop properties initially
+
+thinking about one pole.
+
+Those properties were easy.
+
+Converging, diverging,
+monotonic, alternating.
+
+When we try to think about
+corresponding properties of
+
+higher order systems we can't
+simply map the simple
+
+properties of first order
+systems into the other.
+
+We have to think about more
+complicated things.
+
+Then we think about things
+like dominant.
+
+If one of the poles has a bigger
+magnitude than the
+
+other then for large times we
+can ignore the smaller one.
+
+What happens for short time?
+
+Does this response monotonically
+increase with
+
+time for all time?
+
+No.
+
+Since the response associated
+with minus 1 alternates in
+
+sine, for short times, for times
+with n close to 0, that
+
+can be just as important
+as this one.
+
+So the dominant pole idea tells
+you how things work when
+
+you have large times.
+
+It doesn't necessarily tell you
+how things work when you
+
+have small times.
+
+How about, the unit sample
+response is the sum of three
+
+geometrics.
+
+Yes or no?
+
+What are the three geometrics?
+
+And the answer to that's yes.
+
+That's very important.
+
+The three geometrics over here
+are this pole to the n plus
+
+this pole to the n plus
+something that goes with this
+
+other pole to the n.
+
+Now it's a weighted sum but
+the weights are not
+
+necessarily 0.
+
+The slide that I showed you
+for the partial fraction
+
+decomposition, you can always
+write a higher order system as
+
+a sum of first order factors.
+
+That's the partial fraction
+expansion.
+
+That doesn't mean the weights
+are all unity.
+
+Number (2), can you write the
+unit-sample response as the
+
+sum of three geometric
+signals?
+
+Yes.
+
+There it is.
+
+And if you're really good at
+complex math you could find
+
+out a, b and c.
+
+And that would tell you the
+unit-sample response and that
+
+would tell you the answer
+to (3) and (4).
+
+Is the unit-sample response 0,
+0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
+
+1, 0, 0, 0, 1?
+
+Or 1, 0, 0, 0, 1, 1 --
+
+whatever.
+
+Is it one of those two or
+something different?
+
+And how do you figure it out?
+
+How do you figure
+out the unit?
+
+Is the unit-sample response--
+
+Is number (2) correct?
+
+Is the unit-sample response
+0, 0, 0, 1, 0, 0,
+
+0, 1, 0, 0, 0, 1--
+
+Yes?
+
+How do you know that?
+
+You could solve that equation.
+
+Is there an easier way?
+
+Yeah?
+
+AUDIENCE: I wrote it as
+a difference equation.
+
+PROFESSOR: Just write the
+difference equation.
+
+Exactly.
+
+So even though I bad-mouth
+difference equations a lot,
+
+here it's easy.
+
+In fact, you can see
+it in the network.
+
+Thinking about the difference
+equation would be easy.
+
+Thinking about the network
+would be easy.
+
+If we think about the
+unit-sample response of this
+
+thing started at rest, rest
+means this is 0, this is 0,
+
+and this is 0 initially.
+
+Unit-sample response means
+this becomes 1 at time 0.
+
+At time 0 this is 1, this is
+0, this is 0, this is 0.
+
+So if I think about what's the
+time response look like and I
+
+did plus, this is
+0, 1, 0, 0, 0.
+
+The first answer is 0.
+
+Clock ticks.
+
+What happens?
+
+This is 1.
+
+This becomes 1.
+
+This doesn't change.
+
+That doesn't change.
+
+This goes to 0.
+
+0 comes around here.
+
+That goes to 0.
+
+So that's the answer
+at time 1.
+
+What happens at time 2?
+
+Just keep working it.
+
+The clock ticks, this goes to 1,
+this goes to 0, these stay
+
+0, this stays 0.
+
+That's the answer at
+time equals 2.
+
+Now the clock ticks.
+
+Now this comes over to here,
+that means it comes back here.
+
+This is still 0.
+
+That comes to 1.
+
+That's the answer for time 3.
+
+Now the clock ticks.
+
+And you can see the whole
+thing would just
+
+repeat itself now.
+
+Is the response periodic?
+
+Yes.
+
+The response is periodic.
+
+What's the period?
+
+3.
+
+And I can see [INAUDIBLE] if
+the [INAUDIBLE] there it's
+
+going to have be related to
+the period over here.
+
+These periods are not same.
+
+This period is 3, this period is
+3, this period is 1, if you
+
+want to call that a period.
+
+But they are related.
+
+OK.
+
+The point of this exercise is
+to illustrate two things.
+
+We inferred properties of first
+order systems by looking
+
+at a single pole which for a
+real system could only behave
+
+in one of four different ways.
+
+Second order system introduced
+new behaviors.
+
+Now we can oscillate, which
+we couldn't do before.
+
+Having got to oscillation,
+oscillation came about because
+
+of complex numbers.
+
+If you go to higher order
+systems nothing
+
+new happens in algebra.
+
+There's no such thing as
+meta-complex numbers, right?
+
+Complex is as bad as it gets.
+
+So you can have complex
+numbers.
+
+The higher order behaviors can
+still have complex numbers but
+
+you have to think when we ask
+you, what's the property of a
+
+higher order system.
+
+You can think about it in terms
+of the individual parts
+
+but it requires some thinking.
+
+OK.
+
+Good luck tonight.
+
+See you then.
\ No newline at end of file
diff --git a/p5ro4x1r16Q.txt b/p5ro4x1r16Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ab2c0cd47e1a13180326789472a34e8d95262cdc
--- /dev/null
+++ b/p5ro4x1r16Q.txt
@@ -0,0 +1,2920 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: We ended last time
+kind of without really a
+
+resolution in the sense that we
+looked at this example of
+
+these vendors in India and the
+Philippines, and these vendors
+
+were somehow--
+
+they seem to be unable to save
+their way out of something
+
+that seems extremely costly
+to keep bearing.
+
+They were paying 5% a day, and
+even when somebody paid down
+
+their entire debt so that they
+didn't have to borrow any
+
+more, they slipped back into
+debt within about three weeks.
+
+So it was a sense in which these
+people seem to find it
+
+difficult to stay out of debt
+and, in particular, to hold
+
+onto their savings.
+
+So here's another experiment,
+which sort of brings out some
+
+more off it.
+
+It's in Busia, Kenya, a
+letter missing there.
+
+So the way it started
+is that--
+
+the experiment is by Esther
+Duflo, Michael Kremer, and
+
+John Robinson.
+
+What they had done was they
+started by actually giving
+
+farmers some fertilizer.
+
+One of the enduring kind of
+puzzles in agricultural and
+
+economics is why farmers in
+Africa don't use more
+
+fertilizer given that fertilizer
+is something that
+
+basically makes money
+for people.
+
+So why don't they use
+fertilizer, and their various
+
+possible answers would
+talk about those.
+
+But to demonstrate that it
+really does seem to work--
+
+what they started by doing is
+making sure that it's true
+
+that it works, so what they did
+was they had people give
+
+farmers fertilizer and told
+them, this is your plot, just
+
+go ahead and use fertilizer,
+and they give them free
+
+fertilizer.
+
+So they took a bunch of plots
+and gave them free fertilizer.
+
+So very simple, you give people
+free fertilizer, they
+
+do use it, not surprisingly,
+especially if you make sure
+
+they can't sell it, and
+they do use it.
+
+When they use it,
+their incomes go
+
+up by 27%, and that's--
+
+Oh, their incomes go
+up by 27%, which is
+
+100% increase annually.
+
+So that's like three months,
+three months, you bought the
+
+fertilizer, you laid it in the
+ground, you waited for three
+
+months, you would get
+27% more back.
+
+So they were pretty convinced
+that fertilizer was a very
+
+useful thing to use.
+
+And this, they did it many
+times, so it varies.
+
+Fertilizer is, in fact,
+not predictable.
+
+Sometimes it works better than
+others, but the range of these
+
+returns, where you never got
+less than 80%, I think,
+
+basically, on your money, and
+that's a very good investment
+
+if you get 80% on your money.
+
+Sometimes, you get 500%, but
+even if you got a 80% on your
+
+money, that would be
+a good investment.
+
+So question is why
+don't they do it?
+
+So the various theories,
+obviously, on why
+
+people don't do it.
+
+One is that they don't
+know about it.
+
+That seems implausible, partly
+because fertilizer's not a new
+
+technology.
+
+It's been around for
+a very long time.
+
+And second, because take those
+farmers who were given free
+
+fertilizer.
+
+They used it, they got 100%
+return, annualized return, go
+
+back to those people at the
+end of the year and the
+
+beginning of next season and
+ask them do you want to use
+
+fertilizer.
+
+98% say yes, of course, we
+want to use fertilizer.
+
+Only 37% actually use it.
+
+So these are people who clearly
+know fertilizer works
+
+because they did it.
+
+It worked.
+
+There's no two ways about the
+fact that they know it
+
+because, the fertilizer, they
+had used it, they saw the
+
+results, they saw
+it's working.
+
+Why didn't the farmers who had
+seen that the fertilizer
+
+generates these massive returns
+not go back to using
+
+fertilizer?
+
+Yeah?
+
+AUDIENCE: Beause they said
+couldn't really afford it, and
+
+then also the fact was when
+they did have the money,
+
+fertilizer generally
+wasn't there.
+
+And when they didn't have
+the money it was there.
+
+So it's difficult.
+
+PROFESSOR: OK, so that's
+sort of the--
+
+but before we come there,
+lets rule out some other
+
+explanations.
+
+So one other explanation is
+credit constraint, so we
+
+already discussed it's hard
+for the poor to borrow.
+
+Interest rates are very high.
+
+That would be a good explanation
+if fertilizer were
+
+indivisible, so if you had to
+use a certain minimal amount
+
+to make money.
+
+But fertilizer is extremely
+divisible.
+
+You can buy it in like You could
+buy 500 grams of it, put
+
+it on a small plot, and
+you'll make more money
+
+on that small plot.
+
+If you bought two kilos,
+you make more
+
+money on a bigger plot.
+
+If you bought 10 kilos,
+you'd have even more.
+
+So the question is why don't
+people use fertilizer?
+
+If they have less money,
+why don't they use it
+
+on a smaller plot?
+
+It's not enough to say that they
+don't have money because
+
+money just--
+
+if you're less money, you
+can use it on less land.
+
+The main point is that whenever
+you use it, you make
+
+money, so even if you use it on
+a smaller plot, the output
+
+on that plot would still go up
+by a lot, and the returns
+
+would be 100% a year on
+the money you put in.
+
+Yeah?
+
+AUDIENCE: So I understand what
+you're saying, but on the
+
+other hand, they can only afford
+to fertilize a very
+
+small amount of land, that their
+returns might just not
+
+be worth it to make this
+tiny investment.
+
+You would have to wait for
+several months to get an extra
+
+several rupees whereas you have
+this money now, you might
+
+as well spend it now
+[INAUDIBLE].
+
+PROFESSOR: I guess that might
+be right, but it's sort of--
+
+in the end, it's why aren't they
+thinking, look, it's 100
+
+Kenyan shillings now.
+
+I'm going to get 200
+in three months.
+
+If it's 100 shillings, and
+that's very little, that's a
+
+dollar and a bit, it's still
+you get twice as much.
+
+So why aren't people thinking
+in proportion?
+
+Why aren't they thinking that
+twice as much is a lot more?
+
+Yeah?
+
+AUDIENCE: Wouldn't fertilizer
+be more viable for bigger
+
+farmers because they have
+irrigation, which is required
+
+for fertilizer to really work.
+
+PROFESSOR: Not in
+Kenya, actually.
+
+I mean, fertilizer is--
+
+it's true that it would
+be more useful.
+
+But mostly even, Kenya
+has especially--
+
+this is the what they call
+the short rain season.
+
+Most of agriculture in the short
+rain season is rain fed,
+
+so I think people don't--
+
+it's true that I'm sure
+fertilizer would reduce risk,
+
+but there isn't much of risk.
+
+Even when the rains are not
+great, you still make money.
+
+So if you ask farmers, they do
+tell you the answer that they
+
+don't have any money.
+
+So they're answer is we
+don't have any money.
+
+It's exactly what you
+said, which is that
+
+they don't have money.
+
+Well, how would we
+buy fertilizer?
+
+The fact is that, as you'll see
+in a minute, they do have
+
+money, especially when
+they harvest.
+
+Farming is a cyclical
+business.
+
+You make money at some point.
+
+You plant, you wait for three
+months, your crops come out,
+
+you sell your crops,
+you get money, then
+
+you wait for a while.
+
+You buy some seeds.
+
+You plant again, so it's
+kind of a cycle.
+
+So if you think of the point
+when they have sold the crops,
+
+they certainly, at that point,
+certainly do have money.
+
+It's not true that they don't,
+and we'll see in a minute
+
+evidence that they
+do have money.
+
+And in particular,
+they seem to--
+
+I mean, even if they can't save
+all of it because they
+
+need to eat most of it, they
+could have saved a little bit
+
+of it, so they could have
+saved the money.
+
+Alternatively, they could just
+buy fertilizer then, when they
+
+have the money.
+
+Fertilizer it is very durable.
+
+You just buy fertilizer.
+
+You keep it in a bag.
+
+It'll stay for three months.
+
+It's not that you need to buy
+fertilizer on the day when you
+
+need to go farming.
+
+You could have bought fertilizer
+ahead of time and
+
+kept it in your home.
+
+So we'll see that they do have
+money at some point, and when
+
+they do have money, they
+don't necessarily buy
+
+fertilizer with it.
+
+In fact, they did a small
+survey, and they asked did you
+
+buy fertilizer at harvest
+time when you had money.
+
+The answer is, no, almost
+no one did that.
+
+So if you look at the
+population, about 30% of them
+
+use fertilizer at any point of
+time, but of that 30%, only
+
+about 3% had bought it early
+when they had money.
+
+Most of them bought it at the
+point of planting, so they had
+
+either managed to save
+or they had borrowed.
+
+But in any case, they had--
+
+[INAUDIBLE]
+
+Let me remove Skype.
+
+Yep.
+
+So what is true is that, so
+basically, no one buys
+
+fertilizer early even though--
+
+if you think that it's
+a problem to--
+
+maybe you don't have money at
+planting time, then you should
+
+just buy it early.
+
+So here's a nice experiment,
+which is sort of exactly
+
+trying to figure out what's
+going on here.
+
+So what they did was they went
+to different farmers, and
+
+since some farmers had already
+had some experience using
+
+fertilizer and others had not,
+they stratified by that.
+
+What does it mean to stratify?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Right, they're
+randomized within the group of
+
+people who had used it before,
+and within the group of people
+
+who had used it before.
+
+So they divided up the
+population and randomized
+
+within each group, and then they
+came to the household and
+
+offered them fertilizer and
+said, look, you pay for it.
+
+We will sell it to you, and
+we'll bring it to you so you
+
+don't have to go to a
+market to buy it.
+
+And that saves a trip, saves
+trouble, but it also--
+
+so this was done at harvest
+time, and it basically forced
+
+them to make a decision then.
+
+So you couldn't say, well,
+maybe I'll buy it.
+
+Maybe I won't.
+
+I'll wait until when
+I need it.
+
+It was kind of a all or nothing
+decision, where they
+
+had to take a decision right
+now when they had money.
+
+This was the first experiment.
+
+Then they follow it up a second
+experiment where they
+
+took another set of people,
+and then in the second
+
+experiment, they offered people
+an additional choice.
+
+You can either choose
+when you'll get--
+
+we'll come to sell
+you fertilizer.
+
+This was done before harvest, so
+they didn't have any money
+
+at that time.
+
+So they said you can either tell
+us, and we'll come right
+
+after harvest, or we'll
+come when you plant.
+
+Just tell us what to do.
+
+So the first experiment, they
+were not given the choice.
+
+They said you want it now, we'll
+bring it to you free.
+
+You don't have to go collect.
+
+If not, that's it.
+
+Then you're on your own.
+
+Now, it's you can either
+buy now or later.
+
+You're offered a choice.
+
+And the other thing that they
+did was other people who were
+
+not given any offer like this,
+when it came to the actual
+
+time of the planting, they came
+to these people and said
+
+do you want to buy fertilizer.
+
+We'll bring it to you, and then
+some people, they offered
+
+a 50% discount.
+
+So they actually said if
+we give you a discount,
+
+will you buy it?
+
+So these were the treatments, so
+think of the treatments as
+
+the first treatment, all or
+nothing at harvest time, you
+
+want to buy fertilizer; second
+treatment, before harvest, do
+
+you want to buy fertilizer at
+harvest or later; third
+
+treatment, at planting time, do
+you want to buy fertilizer
+
+from us if we deliver
+it to you free.
+
+That's the experiment.
+
+Before we get into
+the experiment,
+
+suppose people were--
+
+what's the disadvantage
+of saying that you
+
+can only buy it--
+
+we'll offer it to you
+now, but not later?
+
+What's the downside of that?
+
+Why did they go to the second
+treatment, do you think, where
+
+they give you a choice
+when to buy?
+
+What's the advantage of giving
+you this choice?
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Right, exactly, I
+mean, typically we think that
+
+buying things early
+is a bad idea.
+
+Why?
+
+Because you're locking
+up your money.
+
+I mean, fertilizer's not that
+easy to sell, whereas if
+
+somebody got sick, you
+had money, you'd
+
+be able to buy medicine.
+
+Now, instead you have
+fertilizer.
+
+So why would you
+lock up money?
+
+So in general, the standard
+intuition would be that
+
+locking up money is a bad
+idea, not a good idea.
+
+So in the first treatment,
+they were
+
+forced to lock up money.
+
+The second one, they
+give them a choice.
+
+So we take the first one,
+basically, there was a 50%--
+
+so about, as I said, 25% to 30%
+of them use fertilizer.
+
+That went up by 11 to 14
+percentage points, so that's
+
+like a 46% to 63% increase
+in fertilizer use.
+
+So you get more than 50%, more
+than 50% increase in
+
+fertilizer use when you just
+tell people, look, we'll bring
+
+it to you for free.
+
+Do you want it at
+harvest time?
+
+This did not change--
+
+so then what they looked at is
+this season, of course, you
+
+getting it delivered to
+you, so you buy it.
+
+It doesn't have any
+persistent effect.
+
+You saw that it was
+a good idea.
+
+Did you start saving money
+or finding a way to
+
+buy ahead of time?
+
+The answer's no.
+
+People seem to be--
+
+when you offer it to them for
+free at harvest time, a
+
+substantial number
+of them buy it.
+
+But if you said, look, last
+year you did this,
+
+look, it was good.
+
+You got much more output.
+
+This time, why don't you
+buy on your own?
+
+Just buy it at harvest time.
+
+We won't help you.
+
+You can do it on your own.
+
+Nobody does it.
+
+So it's not the case that
+people learn from this
+
+experience to buy fertilizer
+to use at harvest time.
+
+They go back to not using
+it, basically.
+
+So when you give people a
+choice, that's experiment two,
+
+you get bigger effects.
+
+Instead of getting 11 to 14
+percentage points, you get 18
+
+percentage points.
+
+That's almost 75% increase in
+fertilizer use, so if you give
+
+them a choice, then you get
+more people taking it up.
+
+On the other hand, if you show
+up at harvest time--
+
+so this is not mainly an effect
+of offering it to them,
+
+just bringing it to them.
+
+It's not because they're getting
+free transportation.
+
+It's not because they don't have
+to go buy it that they're
+
+doing it because if you came to
+them at planting time and
+
+said do you want to buy it,
+we'll get it to you free, that
+
+has no impact.
+
+If you bring it to people at
+planting time free, then they
+
+don't buy it, so it's not the
+case that you get the same
+
+effect by just delivering it
+to them free at any time.
+
+You have to deliver
+it to them free
+
+typically at planting time--
+
+sorry, at harvest time.
+
+When they have money, you have
+to deliver it to them free,
+
+then they buy it.
+
+If you bring it to them when
+they are planting, and you
+
+offer free delivery, that
+doesn't have the same impact.
+
+So it's not that whenever
+you offer it to them
+
+free, they buy a lot.
+
+They only buy a lot if
+you offer it free
+
+when they have money.
+
+The 50% discount does have a
+significant effect, maybe not
+
+surprisingly.
+
+On the other hand, it's not
+really smaller than just
+
+offering people to get free
+delivery with no discount.
+
+No discount is better than
+giving people a discount if
+
+you give them the discount
+at the right time--
+
+sorry, the free--
+
+the delivery at the
+right time.
+
+So if I go to you at harvest
+time, and I say I won't give
+
+you a discount, when do you
+want it, you get a bigger
+
+effect than if I tell you I'll
+give you 50% discount, but
+
+that I offer that to you
+only at planting time.
+
+So just those magnitudes are
+what's worth looking at
+
+because you're getting
+people--
+
+it's not that people, even if
+you offer them a 50% discount,
+
+you don't get as big an effect
+as just finding the right time
+
+to make an offer without
+a discount.
+
+Yeah?
+
+AUDIENCE: How do people get this
+if it wasn't delivered?
+
+PROFESSOR: You just go to the
+local town and you buy--
+
+AUDIENCE: --drag it back
+or pull it back--
+
+PROFESSOR: Oh, you
+bring it on a--
+
+they have all these three-wheel
+taxis and little
+
+trucks in Kenya.
+
+You put it in the back of
+one, and you bring it.
+
+It's like--
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: No, it's a small
+cost, actually.
+
+That's the usual.
+
+Now, you notice that
+there was this 18
+
+percentage point increase.
+
+That came from a bunch of those
+people said, look, it's
+
+free delivery, but
+we just want it
+
+delivered at planting time.
+
+So some people behaved as if
+they had no worries about
+
+having the money later, and the
+other half said bring it
+
+to us now, so a bunch
+of people said
+
+bring it to us now.
+
+The reason why this one gives
+you a bigger effect than
+
+forcing people to buy early is
+because a bunch of those
+
+people actually prefer
+to get it late.
+
+So it's clear that the economics
+we described before
+
+is working for some people, but
+it's also striking that
+
+about half of those people
+say, no, we want it now.
+
+We want to lock up our money.
+
+We want our money to
+not be spendable.
+
+We want it in fertilizer now.
+
+So what's quite striking is
+that people are willing to
+
+lock up their money,
+even though it's--
+
+So what could be going on?
+
+So here's a story that
+seems to mostly work.
+
+So these people have money
+at harvest time and want
+
+fertilizer, but somehow, they
+don't manage to buy
+
+fertilizer.
+
+So the reason why the experiment
+works is that these
+
+people basically say, look,
+we will buy fertilizer.
+
+So what seems to be going on
+is that, as we said, 98% of
+
+those people who had plots where
+fertilizer was used said
+
+they wanted to buy it again.
+
+Only 37% actually did.
+
+So at harvest time, it seems
+most people plan to use
+
+fertilizer, and then only
+a small fraction of them
+
+actually managed to get there.
+
+So what seems to happen
+is that they
+
+don't manage to implement.
+
+So they think that they're going
+to buy fertilizer, but
+
+then somehow end up spending the
+money before they get to
+
+the fertilizer.
+
+So one way to think about what
+could be happening is that
+
+people say, look, today I really
+want to buy fertilizer,
+
+but right now, I really like a
+drink or I'd really like to
+
+have a barbecue.
+
+So they go to the market, they
+buy something, and they say,
+
+look, it doesn't really matter
+because tomorrow,
+
+I'm going to save.
+
+Today, let me have a barbecue,
+but tomorrow, I'm definitely
+
+going to save.
+
+So they say that so it doesn't
+really matter.
+
+It's going to be in three months
+that we're going to
+
+plant, so even if I don't save
+today, I'll save tomorrow.
+
+So sometimes, this is
+represented by this formula.
+
+These kind of preferences are
+sometimes [INAUDIBLE]
+
+by this formula.
+
+So the U function is the
+utility you get or the
+
+pleasure you get out
+of eating today or
+
+tomorrow or day after.
+
+Today is c0, tomorrow's c1, day
+after is c2, the day after
+
+that is c3.
+
+Or we could think of months,
+c0 this month, c1 is next
+
+month, et cetera.
+
+What's important is that U of
+c1 is multiplied by two
+
+numbers, both less than 1.
+
+U of c2 is multiplied by
+beta delta squared.
+
+If delta's less than 1, delta
+squared is less than 1, but I
+
+didn't multiply by beta
+squared delta squared.
+
+I multiplied by beta
+delta squared.
+
+The day after that is multiplied
+by beta delta
+
+cubed, so I didn't multiply
+by beta cubed delta cubed.
+
+Why am I doing that?
+
+What's the point being made
+by having that structure?
+
+This is sometimes called a
+quasi hyperbolic model.
+
+Why did I put that
+structure there?
+
+Yeah?
+
+AUDIENCE: Maybe like delta is
+something that [INAUDIBLE]
+
+whereas beta is a variable that
+probably won't happen.
+
+Like, [INAUDIBLE].
+
+PROFESSOR: Well, specifically,
+these are constant, so think
+
+of them as being numbers.
+
+Beta's like a number, like--
+
+maybe delta is 0.9, and beta's
+something like 0.6.
+
+That's the sort of numbers
+people often throw
+
+around over a month.
+
+What does this preference
+specifically say?
+
+Yeah?
+
+AUDIENCE: Seems like it's just
+saying that if more importance
+
+is given to c0, and anything
+in the future as a discount
+
+factor of beta.
+
+But the further into the future
+you go, you go from
+
+delta to delta squared
+so [INAUDIBLE].
+
+PROFESSOR: Right, but
+specifically what it's saying
+
+is that today versus tomorrow
+is very different from
+
+tomorrow versus day
+after or day after
+
+versus day after that.
+
+It's saying specifically that
+when I offer you a choice
+
+between today and tomorrow,
+you want it today, but you
+
+don't care as much about day
+after versus day after that.
+
+So beta and delta both numbers
+less than 1, then what this
+
+preference is exactly
+saying is that I
+
+would take one today.
+
+I'll give up two tomorrow to
+get one today, but when I
+
+compare tomorrow with day after,
+I'm not going to take
+
+one tomorrow instead
+of two day after.
+
+So people are very short--
+
+they want things now, but they
+don't really care about when
+
+they get it if they
+don't get it now.
+
+Why is that an interesting
+set of preferences?
+
+Well, if you believe those set
+of preferences, then this
+
+behavior seems to start
+to make sense.
+
+So what I really want
+is I want tomorrow--
+
+since I don't care about whether
+I consume tomorrow or
+
+day after, I want tomorrow
+to do the saving.
+
+Today, I don't want to save
+because today is much more
+
+important to me than tomorrow.
+
+Tomorrow is not that much more
+important than day after, so
+
+if I want some money for day
+after, the best way to get
+
+there is by eating a lot today,
+saving a lot tomorrow,
+
+and then ending up with
+the money day after.
+
+I would rather do that than eat
+little today and also a
+
+little tomorrow.
+
+I would rather save by binging
+today and then waiting, and
+
+then implementing
+saving tomorrow.
+
+The problem is that when
+you get around to
+
+tomorrow, what happens?
+
+If your plan is I will save more
+tomorrow, I'll eat more
+
+today, save more tomorrow,
+what's the
+
+problem with that plan?
+
+AUDIENCE: Tomorrow
+becomes today.
+
+PROFESSOR: Tomorrow
+becomes today.
+
+Once tomorrow becomes today, you
+start thinking, OK, well,
+
+I have the same preferences.
+
+c0 then becomes tomorrow's c0.
+
+I want to implement the
+same plan tomorrow.
+
+I want to eat a lot tomorrow,
+and get day after to do the
+
+savings, and you can
+keep doing that.
+
+That's the problem.
+
+OK, so that's the idea.
+
+Now do people actually
+behave in such a way?
+
+So here's an experiment.
+
+Ashraf, Karlan, and Win asked
+1,700 subjects in the
+
+Philippines the following
+questions.
+
+So they asked them, first, would
+you prefer 200 pesos now
+
+or 250 pesos later?
+
+Some people said I'd prefer
+250 later, in
+
+which case, they stopped.
+
+If they said that they would
+prefer 200 now rather than 250
+
+in a month, then they were
+asked how about 300?
+
+If they said they'll even take
+300, then they were asked how
+
+much would it take to stop you
+from wanting 200 today?
+
+Somebody might say 400.
+
+I'll take 200 today
+and 400 a month.
+
+So there are people who could
+say 250 I'll take in a month.
+
+Some people say I'll take
+300 in a month.
+
+Some people will say
+name a number.
+
+So do you see how it goes?
+
+Then they are given a break.
+
+They went and wander around,
+then came back, and 15 minutes
+
+later, they were asked the same
+set of questions, but
+
+with one change, which is that
+instead of asking them about
+
+today versus in a month, they
+were asked in six months
+
+versus in seven months.
+
+Same thing, but notice
+what we're doing is
+
+exactly this exercise.
+
+We are exactly trying to
+pinpoint whether or not people
+
+have a different view of today
+versus tomorrow versus one
+
+month later at any other
+point of time.
+
+That's exactly the idea, that
+am I someone who thinks that
+
+tomorrow is going to be--
+
+do I think that tomorrow
+it's going to be it
+
+really doesn't matter.
+
+I can cut back tomorrow,
+but I really don't
+
+want to cut back today.
+
+So this is what they found.
+
+This is a complicated
+table, but we can
+
+go through it slowly.
+
+So the way to think about
+it is that the--
+
+each square in a matrix is how
+much money would you take
+
+today versus 200--
+
+so how much money in the future
+versus 200 today.
+
+Along the vertical dimension,
+we're increasing the amount of
+
+money in a month from today.
+
+On the horizontal dimension,
+we increasing the amount of
+
+money in a month from
+six months.
+
+And those are the fraction of
+people who make those choices.
+
+So some people are
+just patient.
+
+Those people say, you offer
+me 200 today, I'll
+
+take 250 in a month.
+
+You offer me 200 in six
+months, I'll take
+
+250 in seven months.
+
+Some people say you offer
+me 200 today, I
+
+take 250 in a month--
+
+or more than 250, but less than
+300 in a month, and they
+
+express the same preference
+in the future as well.
+
+But then interesting people
+are the people who seem to
+
+have different preferences, and
+we see that there are both
+
+kinds of people.
+
+There are some people
+who are--
+
+So what is the dark squares?
+
+What are the dark squares
+telling you?
+
+Who are those people?
+
+The really dark ones.
+
+What are their preferences?
+
+AUDIENCE: They'll take less
+money, one month from now then
+
+require more money
+in the future.
+
+PROFESSOR: The really daft, daft
+ones are the ones who are
+
+saying I'll take less than 250
+for 200 in one month, but six
+
+months or seven months, it'll
+take me more than 250 to
+
+compensate.
+
+So they seem to be the opposite
+of the kind of people
+
+who you're talking about.
+
+They seem to be impatient
+in the future but
+
+patient in the present.
+
+Yeah?
+
+AUDIENCE: All right,
+I have a question.
+
+Could it be that it's not so
+much about money today versus
+
+money tomorrow, and preferences
+for consumption
+
+versus investment?
+
+So if you're waiting for the 250
+in a month, you're putting
+
+your income towards investment
+as opposed to [INAUDIBLE]
+
+consumption.
+
+PROFESSOR: Sure.
+
+AUDIENCE: Does that
+make sense?
+
+PROFESSOR: I mean,
+it makes sense.
+
+It's just I don't understand
+why that's different.
+
+It's the same thing.
+
+I'm going to get money
+in the future.
+
+Investment is just a way to
+get money in the future.
+
+I think it's the same thing.
+
+What's not visible, but I can
+tell you, is that those three
+
+dark squares, which are people
+who are patient now but
+
+impatient in the future--
+
+that's about 15% of the
+population seem to be patient
+
+now, impatient in the future.
+
+Now, the ones who are in the
+kind of what I call hyperbolic
+
+squares, that's about 25% of
+the population, they're
+
+impatient now, patient later.
+
+They are the people
+who are impatient.
+
+They're saying I'll take 200
+now over 300 later, but--
+
+or was it 250 later?
+
+But in a month, I'll reverse
+that preferences.
+
+I'll take 200 in six
+months rather than
+
+250 in seven months.
+
+Sorry, the other way.
+
+I'll take 250 in seven months,
+but 200 in six months, and
+
+that's about 25% of
+the population.
+
+And then there is another 17%
+of the population who are in
+
+that other box, and they're
+people for whom--
+
+about half of those are actually
+more patient now than
+
+they were in the future than
+the other way around.
+
+So basically, what this
+shows is that it's not
+
+everybody's like that.
+
+Some people are just
+very impatient.
+
+Who are the very impatient
+people?
+
+Which box would they be?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Those people, we--
+
+You're right, they are
+the people who are--
+
+I guess they're the people who
+are most impatient, but some
+
+of those people are more
+impatient now.
+
+Some people are more impatient
+in the future.
+
+Who are the most
+patient people?
+
+Which box?
+
+AUDIENCE: Require 250
+now or later?
+
+PROFESSOR: Yeah, so the top
+left-hand boxes were the most
+
+patient people.
+
+So basically, what this says
+there's about a third of the
+
+population who are
+very patient.
+
+Yeah?
+
+AUDIENCE: What were
+the incomes of the
+
+people in this survey?
+
+Like is 250 a lot for them,
+relative to 300 or--
+
+PROFESSOR: No, these
+are actually
+
+small amounts of money.
+
+Not very cvalued.
+
+These are not very big
+amounts of money.
+
+AUDIENCE: But in terms of part
+of their income, would that be
+
+significant or not?
+
+PROFESSOR: Significant per
+billion, but really not.
+
+So the point that we want to
+take away from this is that
+
+people seem to vary a lot.
+
+It's not that there's one kind
+of people in the world.
+
+Some people are patient now and
+impatient in the future.
+
+A lot more people are impatient
+now and patient in
+
+the future.
+
+But there's a whole bunch of
+people who are both impatient
+
+now and impatient in the future,
+and a whole bunch of
+
+people who are patient now and
+patient in the future.
+
+So there are all kinds
+of different
+
+behaviors in this table.
+
+Yeah?
+
+AUDIENCE: Does this table change
+for people in developed
+
+countries who are making
+lots of money?
+
+PROFESSOR: So here's
+another experiment.
+
+It's not here.
+
+Let's look at another one.
+
+This is actually interesting.
+
+I think I have it here.
+
+I'll show it to you.
+
+Actually not--
+
+it's quite interesting.
+
+This one was done in the
+US, and it's kind of
+
+interesting to see.
+
+[INAUDIBLE], OK, good.
+
+It is something funny.
+
+This is not going to get
+recorded, but it's this--
+
+yeah.
+
+So this is a very famous
+experiment on the US.
+
+Exactly the same kind
+of question, but
+
+now, people were asked--
+
+so this is the median
+response.
+
+So people were asked how much
+money would you take in x
+
+months, where x is either three
+months, one year, or
+
+three years, relative to
+that much money today.
+
+OK, so this is in the US with
+college students, and then
+
+these were Cornell students
+if I remember right.
+
+So you can see, this
+is the answer--
+
+it's interesting.
+
+So if I offer you $15 today
+versus $30 in three months,
+
+the median response--
+
+many people were asked this
+question, and this is the
+
+answer to the question, what's
+the median response.
+
+So if you take half
+the people--
+
+so for example, for $15, half
+the people said I'll take less
+
+than $30, half the people said
+I'll take more than $30, so
+
+the median response was $30.
+
+So you can see that, basically,
+the US in three
+
+months, the trade off
+is basically people
+
+want twice the money.
+
+That's a yearly discount
+factor of 277%.
+
+For one year, they say $60.
+
+For three years,
+they say $100.
+
+Now, the point is that that
+number is getting, relatively,
+
+you're getting more patient as
+you look into the future.
+
+So it's today versus the future
+always, but as I may
+
+force you to look further into
+the future, you become
+
+actually more patient.
+
+And that sort of phenomenon I
+was alluding to, which is that
+
+as people really want it today,
+but the difference
+
+between tomorrow and in
+one year later is
+
+not that much more.
+
+AUDIENCE: So the amount
+increase, right?
+
+It's not [INAUDIBLE]
+
+more patient just because you
+are talking about $3,000
+
+versus $15.
+
+Then you say [INAUDIBLE].
+
+PROFESSOR: Yeah, so that's
+exactly right.
+
+That's to make the other
+point, that as amounts
+
+increase, people look like
+they're more patient.
+
+So if this was a lot of money--
+so in the US, they're
+
+going to look actually more
+impatient than in the
+
+Philippines.
+
+The Philippines, they were
+looking much more patient
+
+because these were actually big
+amounts of money in the
+
+Philippines.
+
+In the US, for those
+amounts of money,
+
+they look more impatient.
+
+So it's when the amounts of
+money are bigger, people seem
+
+to look more patient.
+
+That's the bottom
+line of that.
+
+The bottom of that says that
+once you go to $3,000, people
+
+really don't want
+twice as much.
+
+They'll take much less than
+twice as much to wait three
+
+months, so people get much more
+patient as you increase
+
+the amount of money.
+
+I think that's a very kind
+of interesting fact.
+
+I need to go back to where
+I was, but this is a--
+
+so that's kind of the answer to
+your question, is that this
+
+is actually relatively--
+
+people are actually-- no,
+this is the wrong--
+
+I need to go back to the PDF.
+
+So actually, they are relatively
+patient here
+
+because these are amounts of
+money that are relatively
+
+large for them.
+
+If you make the amount of money
+smaller, people become
+
+less patient, not
+more patient.
+
+So in the US, with these
+choices, they look more
+
+impatient actually, not
+less impatient.
+
+OK, so the question is can this
+is really explain the
+
+fertilizer puzzle?
+
+So we can see that there are
+people, about a quarter of the
+
+population, do behave
+in this funny way.
+
+They want it now, and they think
+in the future they're
+
+going to be very patient,
+so they want to
+
+postpone their savings.
+
+They want to say I will consume
+now and save later.
+
+That's a kind of a natural
+instinct for about a quarter
+
+of the population.
+
+The problem is that this
+requires people
+
+to be pretty naive.
+
+What do I mean by naive?
+
+I mean they need to actually not
+realize that this is what
+
+they're doing because otherwise
+they should be able
+
+to say, look, but I'll do that
+tomorrow as well, and day
+
+after and the day after that, so
+I'll never buy fertilizer.
+
+I want to buy fertilizer.
+
+So if you were sophisticated
+and, you fully understood what
+
+you were doing, what
+would you do?
+
+Yeah?
+
+AUDIENCE: You force yourself
+to save [INAUDIBLE].
+
+PROFESSOR: You'll buy now.
+
+You just buy now.
+
+You know that you can
+never really--
+
+Yeah, or you save now, whatever
+you need to do.
+
+You know that you'll never win
+the game by postponing because
+
+you know tomorrow you'll
+have the same problem.
+
+So basically, if you're
+sophisticated,
+
+you would buy now.
+
+So you never want to do it, so
+you really need people to be
+
+pretty naive to be able to--
+
+In other words, sophisticated
+people should not react to
+
+this program.
+
+They would buy in any case.
+
+The only advantage this program
+offers is that they're
+
+getting free delivery, but free
+delivery, as we saw, is
+
+not worth that much.
+
+When you give people just free
+delivery, that doesn't have a
+
+big effect.
+
+So in other words, if these guys
+are really sophisticated,
+
+they shouldn't need this program
+to get them to buy
+
+fertilizer.
+
+They would buy it in any case
+because they'll realize that
+
+this is what's going on and
+say, look, if I can try to
+
+fool myself and say I'm going
+to buy it tomorrow, but I'm
+
+not going to buy it tomorrow.
+
+I'm always going to
+do the same thing.
+
+Yeah?
+
+AUDIENCE: Didn't they say that
+the fertilizer wasn't
+
+available [INAUDIBLE]
+
+back to the city to check
+it, so that's why they
+
+[INAUDIBLE]?
+
+PROFESSOR: I'm sure that's also
+true, but just take this
+
+particular experiment.
+
+I'm sure there are other costs,
+like there is some
+
+transportation costs of finding
+fertilizer, et cetera,
+
+but it's hard to imagine that's
+the only problem.
+
+However, here's a problem with
+saying that they are
+
+sophisticated.
+
+Suppose people were
+sophisticated, then they
+
+wouldn't want the fertilizer--
+
+the program would not have an
+effect because, basically,
+
+they would buy it in any case.
+
+Now, suppose they're not
+sophisticated, so they don't
+
+understand they do this.
+
+Suppose they come and tell you
+do you want to buy now or in
+
+the future?
+
+What would you say?
+
+You all would say in the future
+because why would
+
+[INAUDIBLE]?
+
+I don't realize I'm going to
+do this, so then I have no
+
+reason to say lock
+up my money.
+
+I should always ask to spend
+it in the future.
+
+You cannot have them being
+completely fully
+
+sophisticated, in which case the
+program would not have an
+
+effect, because they're
+sophisticated.
+
+They don't need the program.
+
+They'll buy in any case.
+
+But if you assume that they was
+not sophisticated at all,
+
+then they would say,
+look, bring it
+
+back at planting time.
+
+I'll buy it then.
+
+Why would I lockup my money?
+
+Because I don't understand
+that I have this problem.
+
+So these people must be
+halfway between being
+
+sophisticated and not
+being sophisticated.
+
+They cannot be either
+fully sophisticated.
+
+If they were fully
+sophisticated, they would not
+
+need this program.
+
+If they were fully
+unsophisticated, they would
+
+not respond to when you offer
+them and ask them do you want
+
+to buy it now or later, they
+would all say later, and half
+
+of them say they want it now
+even though they don't need
+
+the fertilizer now.
+
+So some of those people must
+realize that later, they're
+
+going to not have the money,
+so somehow there is some
+
+combination of sophistication
+and naivete that's driving
+
+this behavior.
+
+So one way to look at this
+question of how sophisticated
+
+is go back to that experiment
+that we were talking about,
+
+the Ashraf, Karlan, and Yin.
+
+What they do is they offer their
+subjects a lock-box.
+
+A lock-box is just a box where
+the key is usually kept with
+
+someone else, so you don't
+have access to the key.
+
+You can put money into it.
+
+It's just a money box.
+
+And they were told that
+you can set you goal.
+
+Your goal can be either a date,
+so I'll break the box,
+
+I'll open the box
+at Christmas.
+
+Or it could be an
+amount of money.
+
+I'll open the box once
+I have $200 in it.
+
+So if you look at what people
+say, most people want it on a
+
+date, so a huge fraction say
+I want it on Christmas, my
+
+wife's birthday, my husband's
+birthday, my son's birthday,
+
+my child's graduation,
+something like that.
+
+Then some people have an
+amount based goal.
+
+They say that I need it for
+buying a house, so I need this
+
+much money.
+
+But most people seemed to
+set time-based goals.
+
+Now, out of 1,7000 people,
+only 200 people
+
+wanted these boxes.
+
+So not everybody wanted it.
+
+In fact, only one out of eight,
+roughly, wanted one of
+
+these boxes.
+
+But among those who did, there's
+a massive effect of
+
+being hyperbolic.
+
+Hyperbolic are those people who
+are patient in the future
+
+but impatient now.
+
+Those are the people who really
+wanted the lock-boxes,
+
+so that's what you'd expect.
+
+You'd expect that somebody who
+is fundamentally patient, but
+
+is impatient right now, is the
+one who wants a lock-box
+
+because they do see the
+value of saving.
+
+They're patient fundamentally,
+but they're impatient right
+
+now in the moment.
+
+Those are the people who would
+want a lock-box, and that's
+
+exactly what you find.
+
+You find that the people who
+want the lock-box tend to be
+
+people who are patient in
+general, in the future are
+
+patient, but are less
+patient right now.
+
+They want the lock-box to kind
+of bind their hands.
+
+So they seem to know that
+they're hyperbolic, so a lot
+
+of these people seem to know
+they're hyperbolic.
+
+They seem to realize that they
+have this problem, so they're
+
+not unsophisticated.
+
+They seem to be relatively aware
+of their-- they're not,
+
+at least, totally
+unsophisticated.
+
+They seem to have some
+awareness of their
+
+self-control problem.
+
+The other striking thing is
+only women are effected.
+
+Men don't seem to understand
+they have this problem, even
+
+though they do, actually.
+
+So women seem to understand
+they have a problem.
+
+Men also have the same problem,
+but they don't seem
+
+to understand it.
+
+Now, here's another experiment,
+last experiment we
+
+will talk about, which gives a
+different take to this men
+
+versus women question.
+
+We've been talking a lot about
+this kind of hyperbolic view,
+
+which says that I'm worried that
+I won't be able to save.
+
+An alternative view of why
+people don't save is they feel
+
+like I want to save, but I
+know that I can't because
+
+somebody else will come and
+take the money away.
+
+My husband will spend it, or my
+brother will come and beg
+
+me money, and I'll have to give
+it to him or something.
+
+So one other reason for not
+saving, which is related, and
+
+one reason why women might want
+a lock-box more might not
+
+be because just that
+they're hyperbolic.
+
+They might also worry about the
+fact that their husbands
+
+will just take away the money,
+and that might explain their
+
+demand for lock-boxes, that they
+want to keep the money
+
+away from their husband and say
+that we can't get at the
+
+money right now.
+
+So this is an experiment
+in a bank.
+
+This one was done by Simone
+Schaner, who was a
+
+PhD Student at MIT.
+
+So this is a bank, and
+basically, she invited a bunch
+
+of married couples to the bank
+and said do you want to open
+
+an account.
+
+And the accounts she offered
+had came in three types.
+
+I mean, everybody was offered
+one joint account for two
+
+spouses, one wife's account,
+and one husband's account.
+
+The reason why they did that,
+she was trying to get at this
+
+idea that maybe if I have a
+joint account with my husband,
+
+that's not very good because
+he can take out the money.
+
+If I want to have an account,
+I want full control of it.
+
+So what she's interested in is
+this question, are people
+
+sufficiently aware of this
+problem that they're willing
+
+to give up a high return
+account to
+
+have their own account?
+
+So the design of the experiment
+is one where,
+
+sometimes, randomly, the joint
+account has the highest
+
+interest rate, and your own
+account has a very low
+
+interest rate.
+
+And what she's interested in is
+whether you would give up
+
+getting a high interest
+rate account to
+
+get your own account.
+
+So for the whole family, it
+would be better to get a joint
+
+account in terms of returns.
+
+So the returns can vary between
+0% to 10%, so you
+
+could be getting 10% on the
+account instead of zero, but
+
+you might choose zero because
+you don't want your wife or
+
+husband to get at it.
+
+So I'll skip this.
+
+This just explain the point.
+
+The point is that people got
+different accounts offered, so
+
+some people were offered a
+joint account with the
+
+interest rate zero, a man's
+account with interest rate
+
+zero, but a joint account
+with interest rate two.
+
+So this is sort of just to
+understand the experiment, you
+
+might be someone who gets the
+joint account interest rates
+
+could be 10, but the man's
+account interest rate could be
+
+zero, and the woman's account
+interest rate could be two.
+
+So what's in the squares are
+the excess interest rate on
+
+the account you're choosing, so
+maybe you choose an account
+
+which gives you 4%.
+
+You could have gotten the best
+account you could have got
+
+would have interest
+rate of 10.
+
+Your excess interest rate is
+negative in that case.
+
+You are getting a -6%
+on the interest.
+
+So the question here, the reason
+why this experiment is
+
+interesting, you're trying to
+figure out do people give up
+
+getting lots of extra money
+to make sure that somebody
+
+doesn't have access
+to their account.
+
+So first thing she did
+was to figure out--
+
+she'll administer
+these questions
+
+where they ask them--
+
+it's kind of like the questions
+we were asking.
+
+How much money would you give
+up today for 290 Kenyan
+
+shillings tomorrow?
+
+So these are questions basically
+aimed to measure how
+
+impatient people.
+
+Would you take 20 today or 200
+tomorrow, and if you say 20
+
+today, you're very impatient,
+obviously.
+
+So that's the kind of question
+she was asking.
+
+So what she did, by using that,
+what she figured out was
+
+who are the couples who
+are well matched.
+
+So if I'm impatient and my wife
+is impatient, that's no
+
+problem because neither
+of us want to save.
+
+So I don't have to tie my
+husband's hands or my wife's
+
+hands because I have the same
+preferences as she does, and
+
+therefore, if she wants to
+spend, I also want to spend.
+
+Then there are couple which are
+both parties are patient,
+
+so if one wants to save, the
+other wants to save.
+
+And then there are people
+who were given--
+
+the couples which
+are ill matched.
+
+Ill matched couples are where
+one says I want to save now,
+
+the other says I want
+to spend now.
+
+So they're ill matched
+couples.
+
+Now, it's the ill matched
+couples that are going to
+
+choose accounts that
+have low returns.
+
+If you're well matched, it
+really doesn't matter who's
+
+name the account is in because
+we have the same objectives.
+
+We both want to spend now.
+
+We both want to spend
+in the future.
+
+Whatever we want to do,
+we both want to do.
+
+But if one of the spouses is
+patient, and the other's
+
+impatient, you have a problem.
+
+Now, it turns out, she went
+with the hypothesis that
+
+she'll find that only the
+men are impatient.
+
+Turns out it was about 50/50,
+about men and women are
+
+equally likely to be less
+patient than their spouse.
+
+But a lot of these households
+were ill matched, so a lot of
+
+the households had one spouse
+who was very patient and the
+
+other spouse who was
+very impatient.
+
+That's a setting where you'd
+imagine going back to the
+
+issue we were raising, as we
+said, maybe people don't save
+
+because they feel that
+they can't save.
+
+If they try to save, the spouse
+will just spend it.
+
+So if one of the spouses is
+patient, but the other's
+
+impatient, the impatient
+spouse kind of has an
+
+advantage because once the
+money's spent, it's gone.
+
+The patient spouse will keep
+guarding the money, but the
+
+impatient spouse, all she has
+to do is to spend it.
+
+Once it's spent, it's gone, so
+in a sense, the impatience
+
+spouse always has
+an advantage.
+
+So you're always fighting
+against the impatience spouse.
+
+The patient spouse is always
+trying to save it and can't do
+
+much about it once the
+money's spent.
+
+But as a patient spouse
+is always--
+
+if she's saved it through today,
+she has to save it
+
+through tomorrow.
+
+In some sense, it's kind of
+an asymmetric problem.
+
+So what she's looking for is
+what happens to these ill
+
+matched couples.
+
+So this is sort of just to give
+a sense of how many are
+
+ill matched.
+
+Yeah, Melissa?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: We'll be done
+in two minutes.
+
+So this is a graph of
+ill matched couples.
+
+A lot of these are at zero.
+
+You can see zero means you have
+the same discount factor.
+
+You're equally patient.
+
+But you can see that there are
+people who are difference of
+
+-0.5, so that means
+that I want it--
+
+my discount factor is maybe
+0.9, and my spouse is 0.4.
+
+And look, it's basically
+symmetrical.
+
+Men and women are
+not different.
+
+It's just one of the
+spouses is more
+
+impatient than the other.
+
+And then what she looks at--
+
+I'll skip these and show
+you the picture.
+
+So on the horizontal axis
+is excess interest rate.
+
+How much are you giving up?
+
+When the wife's account has,
+let's say, the highest
+
+interest rate over the
+other account--
+
+what fraction of the people
+use the account more?
+
+And you can see that basically,
+for well matched
+
+couples, the shared saving in
+that account is clearly
+
+increasing with interest rate.
+
+If the interest rate
+is higher, you save
+
+more in that account.
+
+For ill matched couples, they
+see no relationship.
+
+You don't save more because the
+account is more rewarding.
+
+Why?
+
+Because it doesn't matter if
+it's more rewarding or not.
+
+You just don't want that on
+the other guy to have that
+
+access to that account.
+
+So ill matched couples don't
+react to the interest rate.
+
+Their priority is
+something else.
+
+They want their own account.
+
+Doesn't matter whether that's
+a low interest account.
+
+The well matched couples, you
+see this, and you can see the
+
+same thing for the
+joint accounts.
+
+The joint accounts, again, it's
+the same question, excess
+
+interest rate, share saving.
+
+The well matched couples, as the
+interest rate goes up, you
+
+save more in that account.
+
+In the badly matched couples,
+it doesn't matter.
+
+Interest rate doesn't matter.
+
+If you're badly matched, you
+choose the one that you will
+
+keep the other guy out.
+
+You're not the one that has
+the highest interest rate.
\ No newline at end of file
diff --git a/rhNKncraJMk.txt b/rhNKncraJMk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ed195456098d13a9007f8036dc135399d6e51e72
--- /dev/null
+++ b/rhNKncraJMk.txt
@@ -0,0 +1,1427 @@
+align:start position:0%
+ 
+Hi, I'm Ben. Today we are going to do an
+
+ align:start position:0%
+Hi, I'm Ben. Today we are going to do an
+ 
+
+ align:start position:0%
+Hi, I'm Ben. Today we are going to do an
+LU decomposition problem. Here's the
+
+ align:start position:0%
+LU decomposition problem. Here's the
+ 
+
+ align:start position:0%
+LU decomposition problem. Here's the
+problem right here. Find the LU
+
+ align:start position:0%
+problem right here. Find the LU
+ 
+
+ align:start position:0%
+problem right here. Find the LU
+decomposition of this matrix A. Now
+
+ align:start position:0%
+decomposition of this matrix A. Now
+ 
+
+ align:start position:0%
+decomposition of this matrix A. Now
+notice that this matrix A has variables
+
+ align:start position:0%
+notice that this matrix A has variables
+ 
+
+ align:start position:0%
+notice that this matrix A has variables
+as well as numbers. So
+
+ align:start position:0%
+as well as numbers. So
+ 
+
+ align:start position:0%
+as well as numbers. So
+uh the sentence ends when it exists. And
+
+ align:start position:0%
+uh the sentence ends when it exists. And
+ 
+
+ align:start position:0%
+uh the sentence ends when it exists. And
+the second part of the question asks you
+
+ align:start position:0%
+the second part of the question asks you
+ 
+
+ align:start position:0%
+the second part of the question asks you
+for which real numbers A and B does the
+
+ align:start position:0%
+for which real numbers A and B does the
+ 
+
+ align:start position:0%
+for which real numbers A and B does the
+LU decomposition of this matrix actually
+
+ align:start position:0%
+LU decomposition of this matrix actually
+ 
+
+ align:start position:0%
+LU decomposition of this matrix actually
+exist. Now uh you can hit pause now and
+
+ align:start position:0%
+exist. Now uh you can hit pause now and
+ 
+
+ align:start position:0%
+exist. Now uh you can hit pause now and
+I'll get you uh give you a few seconds.
+
+ align:start position:0%
+I'll get you uh give you a few seconds.
+ 
+
+ align:start position:0%
+I'll get you uh give you a few seconds.
+You can try to solve this on your own
+
+ align:start position:0%
+You can try to solve this on your own
+ 
+
+ align:start position:0%
+You can try to solve this on your own
+and then we'll be back and we can do it
+
+ align:start position:0%
+and then we'll be back and we can do it
+ 
+
+ align:start position:0%
+and then we'll be back and we can do it
+together.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we're
+
+ align:start position:0%
+And we're
+ 
+
+ align:start position:0%
+And we're
+back. Now, what do you have to remember
+
+ align:start position:0%
+back. Now, what do you have to remember
+ 
+
+ align:start position:0%
+back. Now, what do you have to remember
+when doing an LU decomposition
+
+ align:start position:0%
+when doing an LU decomposition
+ 
+
+ align:start position:0%
+when doing an LU decomposition
+problem? Well, it's we do elimination in
+
+ align:start position:0%
+problem? Well, it's we do elimination in
+ 
+
+ align:start position:0%
+problem? Well, it's we do elimination in
+the same way that we
+
+ align:start position:0%
+the same way that we
+ 
+
+ align:start position:0%
+the same way that we
+uh um did before in order to find U. But
+
+ align:start position:0%
+uh um did before in order to find U. But
+ 
+
+ align:start position:0%
+uh um did before in order to find U. But
+with this question, we need to find L as
+
+ align:start position:0%
+with this question, we need to find L as
+ 
+
+ align:start position:0%
+with this question, we need to find L as
+well. So, we need to do elimination, but
+
+ align:start position:0%
+well. So, we need to do elimination, but
+ 
+
+ align:start position:0%
+well. So, we need to do elimination, but
+we also need to keep track of the
+
+ align:start position:0%
+we also need to keep track of the
+ 
+
+ align:start position:0%
+we also need to keep track of the
+elimination matrices along the way.
+
+ align:start position:0%
+elimination matrices along the way.
+ 
+
+ align:start position:0%
+elimination matrices along the way.
+Good. So, let's let's do that. So, let
+
+ align:start position:0%
+Good. So, let's let's do that. So, let
+ 
+
+ align:start position:0%
+Good. So, let's let's do that. So, let
+me put my matrix up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here. Okay. And we want to do
+
+ align:start position:0%
+here. Okay. And we want to do
+ 
+
+ align:start position:0%
+here. Okay. And we want to do
+elimination. So, which entry do we
+
+ align:start position:0%
+elimination. So, which entry do we
+ 
+
+ align:start position:0%
+elimination. So, which entry do we
+eliminate
+
+ align:start position:0%
+eliminate
+ 
+
+ align:start position:0%
+eliminate
+first? That's right. It's it's this 21
+
+ align:start position:0%
+first? That's right. It's it's this 21
+ 
+
+ align:start position:0%
+first? That's right. It's it's this 21
+entry.
+
+ align:start position:0%
+entry.
+ 
+
+ align:start position:0%
+entry.
+We so we replace the second row by the
+
+ align:start position:0%
+We so we replace the second row by the
+ 
+
+ align:start position:0%
+We so we replace the second row by the
+second row minus a times the the first
+
+ align:start position:0%
+second row minus a times the the first
+ 
+
+ align:start position:0%
+second row minus a times the the first
+row and we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this. Okay, but we're not just doing
+
+ align:start position:0%
+this. Okay, but we're not just doing
+ 
+
+ align:start position:0%
+this. Okay, but we're not just doing
+elimination. We're finding an LU
+
+ align:start position:0%
+elimination. We're finding an LU
+ 
+
+ align:start position:0%
+elimination. We're finding an LU
+decomposition. So, we need to keep track
+
+ align:start position:0%
+decomposition. So, we need to keep track
+ 
+
+ align:start position:0%
+decomposition. So, we need to keep track
+of the matrix that I multiplied the uh
+
+ align:start position:0%
+of the matrix that I multiplied the uh
+ 
+
+ align:start position:0%
+of the matrix that I multiplied the uh
+elimination matrix that I multiplied
+
+ align:start position:0%
+elimination matrix that I multiplied
+ 
+
+ align:start position:0%
+elimination matrix that I multiplied
+this matrix A by on the left to get this
+
+ align:start position:0%
+this matrix A by on the left to get this
+ 
+
+ align:start position:0%
+this matrix A by on the left to get this
+matrix. So, what is that? That's this
+
+ align:start position:0%
+matrix. So, what is that? That's this
+ 
+
+ align:start position:0%
+matrix. So, what is that? That's this
+E21. Since I eliminated the 21 entry,
+
+ align:start position:0%
+E21. Since I eliminated the 21 entry,
+ 
+
+ align:start position:0%
+E21. Since I eliminated the 21 entry,
+I'll call it
+
+ align:start position:0%
+I'll call it
+ 
+
+ align:start position:0%
+I'll call it
+E21. And it's this
+
+ align:start position:0%
+E21. And it's this
+ 
+
+ align:start position:0%
+E21. And it's this
+matrix. Why is it this matrix? Well,
+
+ align:start position:0%
+matrix. Why is it this matrix? Well,
+ 
+
+ align:start position:0%
+matrix. Why is it this matrix? Well,
+remember how multiplication on the left
+
+ align:start position:0%
+remember how multiplication on the left
+ 
+
+ align:start position:0%
+remember how multiplication on the left
+works? I replace the first row by just
+
+ align:start position:0%
+works? I replace the first row by just
+ 
+
+ align:start position:0%
+works? I replace the first row by just
+the first row. I replace the second row
+
+ align:start position:0%
+the first row. I replace the second row
+ 
+
+ align:start position:0%
+the first row. I replace the second row
+by the second row minus a times the f
+
+ align:start position:0%
+by the second row minus a times the f
+ 
+
+ align:start position:0%
+by the second row minus a times the f
+the first row. So you can just read off
+
+ align:start position:0%
+the first row. So you can just read off
+ 
+
+ align:start position:0%
+the first row. So you can just read off
+from these rows which operations I did.
+
+ align:start position:0%
+from these rows which operations I did.
+ 
+
+ align:start position:0%
+from these rows which operations I did.
+Good. Now which entry should we
+
+ align:start position:0%
+Good. Now which entry should we
+ 
+
+ align:start position:0%
+Good. Now which entry should we
+eliminate next? We need to eliminate
+
+ align:start position:0%
+eliminate next? We need to eliminate
+ 
+
+ align:start position:0%
+eliminate next? We need to eliminate
+this B. So we
+
+ align:start position:0%
+this B. So we
+ 
+
+ align:start position:0%
+this B. So we
+will replace the third row by the third
+
+ align:start position:0%
+will replace the third row by the third
+ 
+
+ align:start position:0%
+will replace the third row by the third
+row minus B * the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row. And which elimination matrix did we
+
+ align:start position:0%
+row. And which elimination matrix did we
+ 
+
+ align:start position:0%
+row. And which elimination matrix did we
+use?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, note we replace the third row by
+
+ align:start position:0%
+Well, note we replace the third row by
+ 
+
+ align:start position:0%
+Well, note we replace the third row by
+the third row minus B times the first
+
+ align:start position:0%
+the third row minus B times the first
+ 
+
+ align:start position:0%
+the third row minus B times the first
+row. That's exactly what you should read
+
+ align:start position:0%
+row. That's exactly what you should read
+ 
+
+ align:start position:0%
+row. That's exactly what you should read
+off this elimination
+
+ align:start position:0%
+off this elimination
+ 
+
+ align:start position:0%
+off this elimination
+matrix. Good. Now, we only have one one
+
+ align:start position:0%
+matrix. Good. Now, we only have one one
+ 
+
+ align:start position:0%
+matrix. Good. Now, we only have one one
+step left, right? We only need to
+
+ align:start position:0%
+step left, right? We only need to
+ 
+
+ align:start position:0%
+step left, right? We only need to
+eliminate one last entry. But this one's
+
+ align:start position:0%
+eliminate one last entry. But this one's
+ 
+
+ align:start position:0%
+eliminate one last entry. But this one's
+a little tricky. So, let's be
+
+ align:start position:0%
+a little tricky. So, let's be
+ 
+
+ align:start position:0%
+a little tricky. So, let's be
+careful. In order to eliminate this uh
+
+ align:start position:0%
+careful. In order to eliminate this uh
+ 
+
+ align:start position:0%
+careful. In order to eliminate this uh
+B, we need A to be a pivot. In
+
+ align:start position:0%
+B, we need A to be a pivot. In
+ 
+
+ align:start position:0%
+B, we need A to be a pivot. In
+particular, we need a to be non zero. If
+
+ align:start position:0%
+particular, we need a to be non zero. If
+ 
+
+ align:start position:0%
+particular, we need a to be non zero. If
+if a were zero here, then we would have
+
+ align:start position:0%
+if a were zero here, then we would have
+ 
+
+ align:start position:0%
+if a were zero here, then we would have
+to do a row exchange. And that's no
+
+ align:start position:0%
+to do a row exchange. And that's no
+ 
+
+ align:start position:0%
+to do a row exchange. And that's no
+good. You can't find an LU decomposition
+
+ align:start position:0%
+good. You can't find an LU decomposition
+ 
+
+ align:start position:0%
+good. You can't find an LU decomposition
+if you have to do a row exchange in
+
+ align:start position:0%
+if you have to do a row exchange in
+ 
+
+ align:start position:0%
+if you have to do a row exchange in
+elimination. So, we need to
+
+ align:start position:0%
+elimination. So, we need to
+ 
+
+ align:start position:0%
+elimination. So, we need to
+assume that a is non
+
+ align:start position:0%
+assume that a is non
+ 
+
+ align:start position:0%
+assume that a is non
+zero in order to keep
+
+ align:start position:0%
+zero in order to keep
+ 
+
+ align:start position:0%
+zero in order to keep
+going. Okay. So, let's just assume there
+
+ align:start position:0%
+going. Okay. So, let's just assume there
+ 
+
+ align:start position:0%
+going. Okay. So, let's just assume there
+that a is non zero.
+
+ align:start position:0%
+that a is non zero.
+ 
+
+ align:start position:0%
+that a is non zero.
+Now what do we do? Well, we can replace
+
+ align:start position:0%
+Now what do we do? Well, we can replace
+ 
+
+ align:start position:0%
+Now what do we do? Well, we can replace
+the third row by the third row minus b /
+
+ align:start position:0%
+the third row by the third row minus b /
+ 
+
+ align:start position:0%
+the third row by the third row minus b /
+a * the the uh second
+
+ align:start position:0%
+a * the the uh second
+ 
+
+ align:start position:0%
+a * the the uh second
+row.
+
+ align:start position:0%
+row.
+ 
+
+ align:start position:0%
+row.
+And we just get this
+
+ align:start position:0%
+And we just get this
+ 
+
+ align:start position:0%
+And we just get this
+uh a minus b. Good. And let's write down
+
+ align:start position:0%
+uh a minus b. Good. And let's write down
+ 
+
+ align:start position:0%
+uh a minus b. Good. And let's write down
+our elimination
+
+ align:start position:0%
+our elimination
+ 
+
+ align:start position:0%
+our elimination
+matrix e uh
+
+ align:start position:0%
+matrix e uh
+ 
+
+ align:start position:0%
+matrix e uh
+32 now.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There's our elimination matrix. We
+
+ align:start position:0%
+There's our elimination matrix. We
+ 
+
+ align:start position:0%
+There's our elimination matrix. We
+replace the third row by the third row
+
+ align:start position:0%
+replace the third row by the third row
+ 
+
+ align:start position:0%
+replace the third row by the third row
+minus B / A * the second row.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Good. Good. So, we found our U matrix.
+
+ align:start position:0%
+Good. Good. So, we found our U matrix.
+ 
+
+ align:start position:0%
+Good. Good. So, we found our U matrix.
+That's what elimination does. It gives
+
+ align:start position:0%
+That's what elimination does. It gives
+ 
+
+ align:start position:0%
+That's what elimination does. It gives
+us our U matrix. So, let me write it up
+
+ align:start position:0%
+us our U matrix. So, let me write it up
+ 
+
+ align:start position:0%
+us our U matrix. So, let me write it up
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 0
+
+ align:start position:0%
+1 0
+ 
+
+ align:start position:0%
+1 0
+1 0 a
+
+ align:start position:0%
+1 0 a
+ 
+
+ align:start position:0%
+1 0 a
+0 0 uh a minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b. Good. Okay. Now we have to find our L
+
+ align:start position:0%
+b. Good. Okay. Now we have to find our L
+ 
+
+ align:start position:0%
+b. Good. Okay. Now we have to find our L
+matrix and we need to use these
+
+ align:start position:0%
+matrix and we need to use these
+ 
+
+ align:start position:0%
+matrix and we need to use these
+elimination matrices that we've been
+
+ align:start position:0%
+elimination matrices that we've been
+ 
+
+ align:start position:0%
+elimination matrices that we've been
+recording along the way in order to do
+
+ align:start position:0%
+recording along the way in order to do
+ 
+
+ align:start position:0%
+recording along the way in order to do
+that. Okay. So remember that we started
+
+ align:start position:0%
+that. Okay. So remember that we started
+ 
+
+ align:start position:0%
+that. Okay. So remember that we started
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+A and we got U. And how did we do that?
+
+ align:start position:0%
+A and we got U. And how did we do that?
+ 
+
+ align:start position:0%
+A and we got U. And how did we do that?
+Well, we multiplied on the left by all
+
+ align:start position:0%
+Well, we multiplied on the left by all
+ 
+
+ align:start position:0%
+Well, we multiplied on the left by all
+of these elimination matrices.
+
+ align:start position:0%
+of these elimination matrices.
+ 
+
+ align:start position:0%
+of these elimination matrices.
+E21,
+
+ align:start position:0%
+E21,
+ 
+
+ align:start position:0%
+E21,
+E31, and
+
+ align:start position:0%
+E31, and
+ 
+
+ align:start position:0%
+E31, and
+E32. Sorry if that's scrunching together
+
+ align:start position:0%
+E32. Sorry if that's scrunching together
+ 
+
+ align:start position:0%
+E32. Sorry if that's scrunching together
+there. Now, if we move these elimination
+
+ align:start position:0%
+there. Now, if we move these elimination
+ 
+
+ align:start position:0%
+there. Now, if we move these elimination
+matrices to the other side, then we'll
+
+ align:start position:0%
+matrices to the other side, then we'll
+ 
+
+ align:start position:0%
+matrices to the other side, then we'll
+get L
+
+ align:start position:0%
+get L
+ 
+
+ align:start position:0%
+get L
+So what do we have? We have a
+
+ align:start position:0%
+So what do we have? We have a
+ 
+
+ align:start position:0%
+So what do we have? We have a
+equ= e21 inverse e31
+
+ align:start position:0%
+equ= e21 inverse e31
+ 
+
+ align:start position:0%
+equ= e21 inverse e31
+inverse e 32 inverse time u and this is
+
+ align:start position:0%
+inverse e 32 inverse time u and this is
+ 
+
+ align:start position:0%
+inverse e 32 inverse time u and this is
+our l this product of these three
+
+ align:start position:0%
+our l this product of these three
+ 
+
+ align:start position:0%
+our l this product of these three
+matrices. Good. So let's compute it
+
+ align:start position:0%
+matrices. Good. So let's compute it
+ 
+
+ align:start position:0%
+matrices. Good. So let's compute it
+now. Right? So L is the product of three
+
+ align:start position:0%
+now. Right? So L is the product of three
+ 
+
+ align:start position:0%
+now. Right? So L is the product of three
+matrices. I need to get them by going
+
+ align:start position:0%
+matrices. I need to get them by going
+ 
+
+ align:start position:0%
+matrices. I need to get them by going
+back and looking at these three
+
+ align:start position:0%
+back and looking at these three
+ 
+
+ align:start position:0%
+back and looking at these three
+elimination matrices and taking their
+
+ align:start position:0%
+elimination matrices and taking their
+ 
+
+ align:start position:0%
+elimination matrices and taking their
+inverses. Well, the nice thing about
+
+ align:start position:0%
+inverses. Well, the nice thing about
+ 
+
+ align:start position:0%
+inverses. Well, the nice thing about
+taking an inverse of this of an
+
+ align:start position:0%
+taking an inverse of this of an
+ 
+
+ align:start position:0%
+taking an inverse of this of an
+elementary matrix like this is we just
+
+ align:start position:0%
+elementary matrix like this is we just
+ 
+
+ align:start position:0%
+elementary matrix like this is we just
+make a minus a plus or a plus a minus.
+
+ align:start position:0%
+make a minus a plus or a plus a minus.
+ 
+
+ align:start position:0%
+make a minus a plus or a plus a minus.
+So that's
+
+ align:start position:0%
+So that's
+ 
+
+ align:start position:0%
+So that's
+easy
+
+ align:start position:0%
+easy
+ 
+
+ align:start position:0%
+easy
+enough. We just change the off diagonal
+
+ align:start position:0%
+enough. We just change the off diagonal
+ 
+
+ align:start position:0%
+enough. We just change the off diagonal
+entries. We just change their signs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You can check that that uh does what we
+
+ align:start position:0%
+You can check that that uh does what we
+ 
+
+ align:start position:0%
+You can check that that uh does what we
+wanted it
+
+ align:start position:0%
+wanted it
+ 
+
+ align:start position:0%
+wanted it
+to. Gives us the
+
+ align:start position:0%
+to. Gives us the
+ 
+
+ align:start position:0%
+to. Gives us the
+inverse. Good. And the last comment is
+
+ align:start position:0%
+inverse. Good. And the last comment is
+ 
+
+ align:start position:0%
+inverse. Good. And the last comment is
+that multiplying these three matrices is
+
+ align:start position:0%
+that multiplying these three matrices is
+ 
+
+ align:start position:0%
+that multiplying these three matrices is
+really easy in this order. Turns out it
+
+ align:start position:0%
+really easy in this order. Turns out it
+ 
+
+ align:start position:0%
+really easy in this order. Turns out it
+just all you do is you just plop these
+
+ align:start position:0%
+just all you do is you just plop these
+ 
+
+ align:start position:0%
+just all you do is you just plop these
+entries right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in one. One. Good. So this is our L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix. Good. So now we have our U
+
+ align:start position:0%
+matrix. Good. So now we have our U
+ 
+
+ align:start position:0%
+matrix. Good. So now we have our U
+matrix and our L matrix. And we're done
+
+ align:start position:0%
+matrix and our L matrix. And we're done
+ 
+
+ align:start position:0%
+matrix and our L matrix. And we're done
+with the first part of the question. The
+
+ align:start position:0%
+with the first part of the question. The
+ 
+
+ align:start position:0%
+with the first part of the question. The
+second part asks us for which real
+
+ align:start position:0%
+second part asks us for which real
+ 
+
+ align:start position:0%
+second part asks us for which real
+numbers A and B does this decomposition
+
+ align:start position:0%
+numbers A and B does this decomposition
+ 
+
+ align:start position:0%
+numbers A and B does this decomposition
+exist. Now let's go back and remember
+
+ align:start position:0%
+exist. Now let's go back and remember
+ 
+
+ align:start position:0%
+exist. Now let's go back and remember
+that at one point we had to assume that
+
+ align:start position:0%
+that at one point we had to assume that
+ 
+
+ align:start position:0%
+that at one point we had to assume that
+A was non zero. That was the only
+
+ align:start position:0%
+A was non zero. That was the only
+ 
+
+ align:start position:0%
+A was non zero. That was the only
+assumption we had to make to get this
+
+ align:start position:0%
+assumption we had to make to get this
+ 
+
+ align:start position:0%
+assumption we had to make to get this
+decomposition.
+
+ align:start position:0%
+decomposition.
+ 
+
+ align:start position:0%
+decomposition.
+So it
+
+ align:start position:0%
+So it
+ 
+
+ align:start position:0%
+So it
+exists it being this decomposition when
+
+ align:start position:0%
+exists it being this decomposition when
+ 
+
+ align:start position:0%
+exists it being this decomposition when
+a is non
+
+ align:start position:0%
+a is non
+ 
+
+ align:start position:0%
+a is non
+zero and that's the answer to the second
+
+ align:start position:0%
+zero and that's the answer to the second
+ 
+
+ align:start position:0%
+zero and that's the answer to the second
+part. Good. So we have our LU
+
+ align:start position:0%
+part. Good. So we have our LU
+ 
+
+ align:start position:0%
+part. Good. So we have our LU
+decomposition and we we know when it
+
+ align:start position:0%
+decomposition and we we know when it
+ 
+
+ align:start position:0%
+decomposition and we we know when it
+exists. Before I end, two
+
+ align:start position:0%
+exists. Before I end, two
+ 
+
+ align:start position:0%
+exists. Before I end, two
+comments.
+
+ align:start position:0%
+comments.
+ 
+
+ align:start position:0%
+comments.
+First, always check your work. always go
+
+ align:start position:0%
+First, always check your work. always go
+ 
+
+ align:start position:0%
+First, always check your work. always go
+back and multiply L times U and make
+
+ align:start position:0%
+back and multiply L times U and make
+ 
+
+ align:start position:0%
+back and multiply L times U and make
+sure it's A because it's easy to screw
+
+ align:start position:0%
+sure it's A because it's easy to screw
+ 
+
+ align:start position:0%
+sure it's A because it's easy to screw
+up the elimination process and uh it's
+
+ align:start position:0%
+up the elimination process and uh it's
+ 
+
+ align:start position:0%
+up the elimination process and uh it's
+easy to check your work. So you should
+
+ align:start position:0%
+easy to check your work. So you should
+ 
+
+ align:start position:0%
+easy to check your work. So you should
+go back and make sure things are uh as
+
+ align:start position:0%
+go back and make sure things are uh as
+ 
+
+ align:start position:0%
+go back and make sure things are uh as
+they should be. Second comment is that
+
+ align:start position:0%
+they should be. Second comment is that
+ 
+
+ align:start position:0%
+they should be. Second comment is that
+you might be worried when you do this
+
+ align:start position:0%
+you might be worried when you do this
+ 
+
+ align:start position:0%
+you might be worried when you do this
+elimination process that well okay we
+
+ align:start position:0%
+elimination process that well okay we
+ 
+
+ align:start position:0%
+elimination process that well okay we
+had to assume a is non zero because we
+
+ align:start position:0%
+had to assume a is non zero because we
+ 
+
+ align:start position:0%
+had to assume a is non zero because we
+wanted a non-zero pivot. You might worry
+
+ align:start position:0%
+wanted a non-zero pivot. You might worry
+ 
+
+ align:start position:0%
+wanted a non-zero pivot. You might worry
+that we might have to have a minus b be
+
+ align:start position:0%
+that we might have to have a minus b be
+ 
+
+ align:start position:0%
+that we might have to have a minus b be
+non zero but in fact a minus b can be
+
+ align:start position:0%
+non zero but in fact a minus b can be
+ 
+
+ align:start position:0%
+non zero but in fact a minus b can be
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+It's not a problem uh for this this
+
+ align:start position:0%
+It's not a problem uh for this this
+ 
+
+ align:start position:0%
+It's not a problem uh for this this
+entry to be zero because we don't have
+
+ align:start position:0%
+entry to be zero because we don't have
+ 
+
+ align:start position:0%
+entry to be zero because we don't have
+to do a row exchange to get U. That's
+
+ align:start position:0%
+to do a row exchange to get U. That's
+ 
+
+ align:start position:0%
+to do a row exchange to get U. That's
+the only time when we can't do the LU
+
+ align:start position:0%
+the only time when we can't do the LU
+ 
+
+ align:start position:0%
+the only time when we can't do the LU
+decomposition. In particular, singular
+
+ align:start position:0%
+decomposition. In particular, singular
+ 
+
+ align:start position:0%
+decomposition. In particular, singular
+matrices can have LU
+
+ align:start position:0%
+matrices can have LU
+ 
+
+ align:start position:0%
+matrices can have LU
+decompositions. Good.
+
+ align:start position:0%
+decompositions. Good.
+ 
+
+ align:start position:0%
+decompositions. Good.
+Okay. Thanks.
\ No newline at end of file
diff --git a/sd-ZVAw8qB0.txt b/sd-ZVAw8qB0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..be1af225903b157c7682d49bf9552482efab20f7
--- /dev/null
+++ b/sd-ZVAw8qB0.txt
@@ -0,0 +1,267 @@
+Computer systems bring together many technologies
+and harness them to provide fast execution
+
+of programs.
+
+Some of these technologies are relatively
+new, others have been with us for decades.
+
+Each of the system components comes with a
+detailed specification of their functionality
+
+and interface.
+
+The expectation is that system designers can
+engineer the system based on the component
+
+specifications without having to know the
+details of the implementations of each component.
+
+This is good since many of the underlying
+technologies change, often in ways that allow
+
+the components to become smaller, faster,
+cheaper, more energy efficient, and so on.
+
+Assuming the new components still implement
+same interfaces, they can be integrated into
+
+the system with very little effort.
+
+The moral of this story is that the important
+part of the system architecture is the interfaces.
+
+Our goal is to design interface specifications
+that can survive many generations of technological
+
+change.
+
+One approach to long-term survival is to base
+the specification on a useful abstraction
+
+that hides most, if not all, of the low-level
+implementation details.
+
+Operating systems provide many interfaces
+that have remained stable for many years.
+
+For example, network interfaces that reliably
+deliver streams of bytes to named hosts, hiding
+
+the details of packets, sockets, error detection
+and recovery, etc.
+
+Or windowing and graphics systems that render
+complex images, shielding the application
+
+from details about the underlying graphics
+engine.
+
+Or journaled file systems that behind-the-scenes
+defend against corruption in the secondary
+
+storage arrays.
+
+Basically, we're long since past the point
+where we can afford to start from scratch
+
+each time the integrated circuit gurus are
+able to double the number of transistors on
+
+a chip,
+or the communication wizards figure out how
+
+to go from 1GHz networks to 10GHz networks,
+or the memory mavens are able to increase
+
+the size of main memory by a factor of 4.
+
+The interfaces that insulate us from technological
+change are critical to ensure that improved
+
+technology isn't a constant source of disruption.
+
+There are some famous examples of where an
+apparently convenient choice of interface
+
+has had embarrassing long-term consequences.
+
+For example, back in the days of stand-alone
+computing, different ISAs made different choices
+
+on how to store multi-byte numeric values
+in main memory.
+
+IBM architectures store the most-significant
+byte in the lowest address (so called "big
+
+endian"), while Intel's x86 architectures
+store the least-significant byte first (so
+
+called "little endian").
+
+But this leads to all sorts of complications
+in a networked world where numeric data is
+
+often transferred from system to system.
+
+This is a prime example of a locally-optimal
+choice having an unfortunate global impact.
+
+As the phrase goes: "a moment of convenience,
+a lifetime of regret."
+
+Another example is the system-level communication
+strategy chosen for the first IBM PC, the
+
+original personal computer based Intel CPU
+chips.
+
+IBM built their expansion bus for adding I/O
+peripherals, memory cards, etc., by simply
+
+using the interface signals provided by then-current
+x86 CPU.
+
+So the width of the data bus, the number of
+address pins, the data-transfer protocol,
+
+etc. where are exactly as designed for interfacing
+to that particular CPU.
+
+A logical choice since it got the job done
+while keeping costs as low a possible.
+
+But that choice quickly proved unfortunate
+as newer, higher-performance CPUs were introduced,
+
+capable of addressing more memory or providing
+32-bit instead of 16-bit external data paths.
+
+So system architects were forced into offering
+customers the Hobson's choice of crippling
+
+system throughput for the sake of backward
+compatibility,
+
+or discarding the networking card they bought
+last year since it was now incompatible with
+
+this year's system.
+
+But there are success stories too.
+
+The System/360 interfaces chosen by IBM in
+the early 1960s carried over to the System/370
+
+in the 70's and 80's and to the Enterprise
+System Architecture/390 of the 90's.
+
+Customers had the expectation that software
+written for the earlier machines would continue
+
+to work on the newer systems and IBM was able
+to fulfill that expectation.
+
+Maybe the most notable long-term interface
+success is the design the TCP and IP network
+
+protocols in the early 70's, which formed
+the basis for most packet-based network communication.
+
+A recent refresh expanded the network addresses
+from 32 to 128 bits, but that was largely
+
+invisible to applications using the network.
+
+It was a remarkably prescient set of engineering
+choices that stood the test of time for over
+
+four decades of exponential growth in network
+connectivity.
+
+Today's lecture topic is figuring out the
+appropriate interface choices for interconnecting
+
+system components.
+
+In the earliest systems these connections
+were very ad hoc in the sense that the protocols
+
+and physical implementation were chosen independently
+for each connection that had to be made.
+
+The cable connecting the CPU box to the memory
+box (yes, in those days, they lived in separate
+
+19" racks!) was different than the cable connecting
+the CPU to the disk.
+
+Improving circuit technologies allowed system
+components to shrink from cabinet-size to
+
+board-size
+and system engineers designed a modular packaging
+
+scheme that allowed users to mix-and-match
+board types that plugged into a communication
+
+backplane.
+
+The protocols and signals on the backplane
+reflected the different choices made by each
+
+vendor - IBM boards didn't plug into Digital
+Equipment backplanes, and vice versa.
+
+This evolved into some standardized communication
+backplanes that allowed users to do their
+
+own system integration, choosing different
+vendors for their CPU, memory, networking,
+
+etc.
+
+Healthy competition quickly brought prices
+down and drove innovation.
+
+However this promising development was overtaken
+by rapidly improving performance, which required
+
+communication bandwidths that simply could
+not be supported across a multi-board backplane.
+
+These demands for higher performance and the
+ability to integrate many different communication
+
+channels into a single chip, lead to a proliferation
+of different channels.
+
+In many ways, the system architecture was
+reminiscent of the original systems - ad-hoc
+
+purpose-built communication channels specialized
+to a specific task.
+
+As we'll see, engineering considerations have
+led to the widespread adoption of general-purpose
+
+unidirectional point-to-point communication
+channels.
+
+There are still several types of channels
+depending on the required performance, the
+
+distance travelled, etc.,
+but asynchronous point-to-point channels have
+
+mostly replaced the synchronous multi-signal
+channels of earlier systems.
+
+Most system-level communications involve signaling
+over wires, so next we'll look into some the
+
+engineering issues we've had to deal with
+as communication speeds have increased from
+
+kHz to GHz.
\ No newline at end of file
diff --git a/seBwiL9InII.txt b/seBwiL9InII.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c731981fb6dbc0ff7a17f9124bee05c7a64fa6aa
--- /dev/null
+++ b/seBwiL9InII.txt
@@ -0,0 +1,3218 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu
+
+PROFESSOR: As you know,
+Professor Guth is away.
+
+I'm substituting for
+today, he didn't leave me
+
+with a particularly
+coherent game plan,
+
+so I'm going to begin with
+where he thinks we should start.
+
+Please jump in if I am
+just repeating something
+
+that he has already
+described to you guys,
+
+or if there's anything you
+like me go over a little bit
+
+more detail, I will
+do my best here.
+
+So, I'm working off of
+a fairly rough plan.
+
+But let me just
+quickly describe what--
+
+based on what Alan has explained
+to me --what we're planning
+
+to talk about today,
+and if there's
+
+any adjustments
+you think I should
+
+be making that would be great.
+
+So, the game plan for today.
+
+What I want to do
+very quickly is
+
+hit on a couple of
+the key points which
+
+I believe you talked
+about last week,
+
+which is a quick review
+of the essential features
+
+of symmetries of
+the gauge fields
+
+the make up the standard model.
+
+Now, I believe you
+guys did in fact talk
+
+about this last week,
+at least briefly.
+
+And you talked about how
+you can take these things
+
+and embed them in a larger
+gauge group, the group SU(5).
+
+I'm not going to talk
+about that too much,
+
+but I want to just quickly
+hit on a few elements related
+
+to this before we get into that.
+
+From this we'll then talk about
+the Higgs mechanism-- really
+
+I'm going to talk
+about the Higgs field,
+
+I'm not going to talk
+about the Higgs mechanism
+
+quite so much as motivate
+why it is necessary--
+
+and then talk about how
+the Higgs field behaves
+
+and why it's important for
+the next problem, which
+
+is what is called the
+cosmological monopole problem.
+
+To be more specific
+magnetic monopole problem.
+
+I confess I feel a little
+bit awkward talking
+
+about this problem
+on behalf of Alan.
+
+This would be kind of
+like if you were planning
+
+on studying Hamlet and there
+was this guy W. Shakespeare who
+
+was listed as the
+instructor and you walk in
+
+and discover there's this
+guy Warren Shackspeare, who's
+
+actually going to be teaching
+or something like that.
+
+I kind of feel like Warren here.
+
+This stuff really is Allen's
+thing, so it's sort of,
+
+I'm probably going to leave this
+at the denouement of all this
+
+when you actually get
+into inflation to him.
+
+I may have a little bit of time
+at the end to just motivate
+
+it a little bit, but the grand
+summary will come from him.
+
+OK, so, as discussed by
+Alan the standard model
+
+describes all the
+fundamental interactions
+
+between particles
+via gauge theories.
+
+OK, and these gauge theories
+all have a combined symmetry
+
+group that is traditionally
+written in a somewhat
+
+awkward form, SU(3)
+cross SU(2) cross U(1).
+
+U(1) could be an
+SU(1) for reasons
+
+which I'll elucidate
+a little bit more
+
+clearly in just a moment.
+
+There's really no point in
+putting the S on that one.
+
+So each of these
+things essentially
+
+labels the particular
+symmetry group.
+
+So, the "S" an
+element of SU(n) is
+
+a matrix that is n x n, that
+is unitary-- that's the U.
+
+Unitary just means that the
+inverse and the transpose
+
+of the matrix at the same,
+actually the Hermitian
+
+conjugate because they
+can be complex, in fact,
+
+they generally are.
+
+And it has determinant of 1.
+
+That's what the special refers
+to, special, the S in SU(n)
+
+stands for special unitary n.
+
+So, the S means
+that the determinant
+
+is one-- that's what's
+special about it-- unitary
+
+is this idea that the inverse
+Hermitian conjugate are
+
+the same, and then n
+refers to all these things.
+
+So, that tells us that the
+gauge degrees of freedom
+
+are related by a symmetry
+that looks like a 3
+
+by 3 matrix with
+these properties,
+
+as listed there for the
+SU(3) piece of the symmetry.
+
+SU(2) means it's
+a 2 by 2 matrix.
+
+And U(1) means it's a one by one
+matrix, what's a 1 by 1 matrix?
+
+It's a number, its
+a complex number.
+
+And that's why we
+don't really need
+
+to put an "s" in front of it.
+
+If it's a complex
+number its determinant
+
+is 1 if it's just a complex
+number whose modules is one.
+
+That's why we don't bother
+with the S on the U(1).
+
+So, I think you've already
+hit on some of this
+
+but this is sort of useful
+to review because it's
+
+going to set up why we
+need to introduce a Higgs
+
+mechanism in a little bit.
+
+Let me just quickly
+hit on what the details
+
+structure of this looks
+like for you want to think
+
+is the easiest one understand,
+So, as I just said,
+
+a one by one matrix is
+just a complex number.
+
+So that means that any
+element of this group
+
+is a complex number, which
+we can write in the form z
+
+equals ei theta, where
+theta is a real number.
+
+Now, the thing which
+is I want to hit on
+
+in this, the reason I want to
+describe this a little bit is,
+
+this may not smell
+like the gauge symmetry
+
+that you're used to if you
+study classical E&M. Some of you
+
+here are in 807
+with me right now,
+
+and we've gone over this
+quite a bit recently.
+
+How is this akin to the gauge
+group that we are normally
+
+used to when we
+talk about the gauge
+
+freedom of electricity
+and magnetism?
+
+Well, it turns out
+there's actually
+
+a very simple relationship
+between one and the other,
+
+rather between this view
+of it and the way we learn
+
+about it when we study
+classical E&M. It's simply
+
+that we use a somewhat different
+language, because when we talk
+
+about it in this group
+theoretic picture we're doing it
+
+in the way that is sort of
+tuned to a quantum field theory.
+
+So, the way we have learned
+about electromagnetic gauge
+
+symmetry in terms of the
+fields sort of goes as follows.
+
+We actually work with the
+potentials, and so what we do
+
+is we note that the potentials
+Amu, which you can write
+
+as a four vector, whose
+time-like component is
+
+the negative of the
+scalar potential,
+
+and whose spatial
+components are just
+
+the three components of
+the vector potential.
+
+So, this potential and
+this potential-- --okay
+
+this is possibly module of
+factor of c somewhere in here
+
+but I'm going to imagine
+the speed of light
+
+has been set equal to 1.
+
+Both of those potentials
+generate the same E&B fields.
+
+OK, again you still
+should be looking at this
+
+and thinking to yourself
+what the hell does
+
+this have to do with the
+U(1) as we presented it here.
+
+I've given you a
+bunch of operations
+
+that involve some kind of
+a scale or function of time
+
+and space.
+
+And I've added particular
+components of this four vector
+
+in this way, what does that
+to do with this multiplication
+
+by a complex number?
+
+Well, where it comes
+from is that when
+
+we study E&M, not as a
+classical field theory
+
+but as a quantum
+field theory, we
+
+have a field that
+describes the electron.
+
+So, where it comes
+from is that when
+
+you examine the Dirac field,
+which is the quantum field
+
+theory that governs the
+electron, when you change gauge
+
+the electron field acquires
+a local phase change.
+
+So in particular,
+what we find is
+
+that if we have a field
+5x, which those of you who
+
+have taken a little bit
+of quantum field theory
+
+should know this is
+actually a spinner field,
+
+but for now, just think of it
+as some kind of a field that
+
+under the field
+equations of quantum
+
+electrodynamics-- the Dirac
+equation or high order
+
+ones that have been developed
+by Feynman, Schwinger,
+
+and others-- under
+a change of gauge
+
+this goes over to
+si prime of x, which
+
+equals e to the--
+terrible notation
+
+I realized-- 1e is obviously
+the root of natural logs,
+
+e sub 0 is the fundamental
+electric charge.
+
+OK, can everyone read that?
+
+I didn't block it too badly here
+I'm not used to this classroom.
+
+So, here's the thing to note,
+is that this field lambda, which
+
+we learned about
+in classical E&M
+
+directly connects to the phase
+function of the Dirac field
+
+in quantum electrodynamics.
+
+So, our gauge symmetry
+is simply expressed
+
+in the quantum version
+of electrodynamics
+
+by a function of the form e
+to the i real number, where
+
+that real number is the
+fundamental electric charge
+
+times the classical
+gauge generator.
+
+So, this is what is meant when
+people say that electrodynamics
+
+is a U(1) gauge theory.
+
+Now, I'm not going to go
+into this level of detail
+
+for the other two
+gauge symmetry that
+
+are built into the
+standard model.
+
+But, what I want
+you to understand
+
+is that the root idea
+is very, very similar.
+
+It's just now, instead of my
+gauge functions looking like e
+
+to the i, some kind of a local
+gauge phase of x multiplying
+
+my functions, my
+quantities which
+
+generate the gauge
+transformation are going
+
+to become complex
+value matrices.
+
+So that makes them a
+lot more complicated,
+
+and it's responsible
+for the fact
+
+that the weak and the
+strong interactions
+
+are non-abelian paid which
+order you perform the gauge
+
+transformation in matters.
+
+Question.
+
+AUDIENCE: What's the
+physical significance
+
+of them being non-abelian?
+
+PROFESSOR: Yes.
+
+So, what is a
+physical significance
+
+of them being non-abelian?
+
+I'm trying think of a really
+simple way to put this,
+
+it's-- Alan would have an
+answer to this right off the top
+
+of his head, so I
+apologize for this--
+
+this isn't the kind of thing
+that I work on every day so I
+
+don't have an answer right
+at the very top of my head,
+
+unfortunately.
+
+Let me get back to
+you on that one, OK,
+
+that's something I can't
+give you a quick answer to.
+
+It's an excellent question and
+it's an important question.
+
+Any other questions?
+
+OK, so, here's a basic
+picture that we have.
+
+So, we find is that the
+strong interactions have
+
+a similar structure where
+my need to e to the i factor
+
+goes over to a 3 by 3 matrix,
+and the weak interactions
+
+in a similar structure with my
+e to the i factor going over
+
+to a 2 by 2 complex matrix.
+
+OK, what does this have
+to do with cosmology?
+
+In fact, as an enormous
+amount to do with cosmology,
+
+as we'll see over the course
+of the rest of course.
+
+Part of the thing which is
+interesting about all this
+
+is that we have strong
+experimental reasons,
+
+and theoretical
+reasons to believe,
+
+that the different symmetries
+that these interactions
+
+participate in, the
+different symmetries that we
+
+see them having, that isn't the
+way things have always been.
+
+So, in particular when the
+universe was a lot hotter
+
+and denser these different
+symmetries actually
+
+all began to look the same.
+
+In particular the one which
+is particularly important,
+
+and you guys have surely heard
+of this, is that the SU(2)--
+
+if we just focus on electric
+and the weak piece of this--
+
+SU(2) cross U(1).
+
+So, this is associated
+with the gauge boson that
+
+carry the weak force, OK, the
+z boson, the w plus, and the w
+
+minus.
+
+And your U(1) ends up being
+associated with the photon.
+
+In many ways, when
+you actually look
+
+at the equations that
+govern these things,
+
+they seem very,
+very similar to one
+
+another except that
+the-- here's partly
+
+an answer to your
+question I just
+
+realized-- the gauge
+generators of these things
+
+have a mass
+associated with them.
+
+That mass ends up
+being connected
+
+to the non-abelian
+nature of these things.
+
+That's not the whole answer,
+but it has a connection to that.
+
+That's one thing
+which I do remember,
+
+like I said I feel
+this is really
+
+Alan's perfect framework
+here and I'm just
+
+a posture in bad shoes.
+
+So if we look at this
+thing, what we see
+
+is that these symmetry groups,
+what's particularly interesting
+
+is that U(1) can be regarded
+as a piece of SU(2).
+
+And we would expect
+that in a perfect world
+
+they would actually
+be SU(2) governing
+
+both the electric and
+the weak interactions.
+
+Whereby perfect
+I mean everything
+
+is a nice balmy 10 to the 16th
+GeV throughout all of space
+
+time, and all the different
+vector bosons happily
+
+exchange with one another,
+not caring with who is who.
+
+It's actually not
+very perfect if you
+
+want to teach a physics class
+and have a nice conversation,
+
+but if you are interested in
+perfect symmetry among gauge
+
+interactions it's
+very, very nice.
+
+So, the fact that
+these are separate
+
+is now-- I was about to use the
+word believed but it's stronger
+
+and that, we now know
+this for sure thanks
+
+to all the exciting work
+that happened at the LHC
+
+over the past year or two-- the
+fact that these symmetries are
+
+separate is due to what is
+called spontaneous symmetry
+
+breaking.
+
+So, let's talk very
+briefly about what
+
+goes into this spontaneous
+symmetry breaking.
+
+So SU(2) turns
+out to actually be
+
+isomorphic to the group
+of rotations on a sphere.
+
+So, when you think
+about something
+
+that has perfect
+SU(2) symmetry it's
+
+as though you have perfect
+symmetry when you move around
+
+through a whole host
+of different angles.
+
+OK, so you move through all
+of your different angles
+
+and everyone looks exactly
+identical to all the others.
+
+If you break that
+symmetry it may
+
+mean you're picking out
+one angle as being special,
+
+and then you only retain
+a symmetry with respect
+
+to the other angle.
+
+And essentially, that is what
+happens when SU(2) breaks off
+
+in a U(1) piece of it.
+
+Something has occurred
+that picked out
+
+one of these directions.
+
+And by the way, you have to
+think very abstractly here.
+
+This is not necessarily a
+direction in physical space
+
+we're talking
+about here but it's
+
+a direction in the
+space of gauge fields.
+
+So, if we imagine that all of
+these, my gauge fields in some
+
+sense the different
+components of them defined
+
+in some abstract
+space direction,
+
+initially these
+things are completely
+
+symmetric with
+respect to rotations
+
+in some kind of an abstract
+notion of a sphere.
+
+And then something
+happens to freeze
+
+one of the directions
+and only symmetries
+
+with respect to one of the
+angles remains the same.
+
+Let's just write that
+out, when SU(2)'s symmetry
+
+is broken so one of the
+directions in the space
+
+of gauge fields is
+picked out as special.
+
+That direction
+then ends up being
+
+associated with
+your U(1) symmetry.
+
+So, what is the mechanism that
+actually breaks the symmetry
+
+and causes this to happen.
+
+Well, this is what the
+Higgs field is all about.
+
+The idea is there is some field
+that fills all of space time.
+
+It has the property that
+at very high energies
+
+it is extremely symmetric,
+with to respect all these gauge
+
+fields, all directions and
+sort of gauge field space
+
+look exactly the same.
+
+And then as things cool, as
+the energy density goes down
+
+by the temperature of the
+expanding universe, cooling
+
+everything off, the Higgs field
+moves to a particular place
+
+that picks out some direction
+in the space of gauge fields
+
+as being special.
+
+So let's make this a
+little bit more concrete.
+
+OK.
+
+You guys have probably heard
+quite a lot about the Higgs
+
+field over the
+past couple years,
+
+months-- what actually is it?
+
+Well, the field itself is
+described by a complex doublet.
+
+So, if you actually see someone
+write down a Higgs field what
+
+they will actually
+write down is h,
+
+being a two components
+spinner, whose components are
+
+h1 of x, h2 of
+x-- where x really
+
+stands for space time
+coordinates, so that's time
+
+and all of your
+spatial coordinates--
+
+and both h1 and h2
+are complex fields.
+
+The thing which is particularly
+key to understanding
+
+the importance of this
+thing is that h transforms,
+
+under gauge transformations,
+with elements of SU(2).
+
+So, if you want to
+change gauge the way
+
+you're going to do it is you're
+going to have some new Higgs
+
+field.
+
+So remember, if U(2)
+is an element of SU(2)
+
+we call it the
+two by two matrix.
+
+This is what they look like
+in a new gauge OK-- pardon me
+
+a second I don't see
+a clock in this room,
+
+I just want to make sure I
+know the time, thank you.
+
+OK, so, what are we
+going to do with this?
+
+Well, there's a couple
+features which it must have,
+
+so the Higgs field
+fills all of space time
+
+and it has an energy
+density associated
+
+with it, which we will call
+just the potential energy.
+
+It's really an energy
+density, but, whatever.
+
+The energy density that is
+associated with this thing
+
+must be gauge invariant.
+
+OK, even when you're
+working with strong fields
+
+and weak fields, the lesson
+of gauge invariance from E&M
+
+still holds.
+
+OK, one of the key points was
+that the gauge fields affect
+
+potentials, they allow us
+to manipulate our equations
+
+to put things into a form where
+the calculation may be easier.
+
+But at the end of the day, there
+are certain things it actually
+
+exert forces that
+cause things to happen,
+
+those must be invariant to
+the gauge transformation.
+
+Energy density is
+of those things.
+
+If you were to get
+into your spaceship
+
+and go back to
+the early universe
+
+and actually take a little
+scoop of early universe out
+
+and measure the energy density,
+A, that would be cool, but B
+
+it would be something
+that couldn't actually
+
+depend on what
+gauge you were using
+
+to make your measurements.
+
+That is something that is
+a complete artifice of how
+
+you want to set
+up the convenience
+
+of your calculation.
+
+So, in order for the energy
+density to be gauge invariant
+
+we have to find a gauge
+invariant quantity that
+
+is constructed from this, which
+is the only thing the energy
+
+density can depend on.
+
+This means, let's call
+our energy density V,
+
+it's the potential
+energy density.
+
+So, it can only depend on
+the following combination
+
+of the fundamental fields Pretty
+much just what you'd expect.
+
+This is sort of the
+equivalent to saying
+
+that if you're working
+in spherical symmetry
+
+the electrostatic
+potential can only
+
+depend on the distance
+from a point charge.
+
+This is a very similar
+kind of construct
+
+here, where I'm taking
+the only quantity that
+
+follows in a fully
+symmetric way, of calling
+
+the fact that this is a
+special unitary matrix that I
+
+can construct from these things.
+
+So then, where all
+the magic comes
+
+in is in how the Higgs field
+potential energy density
+
+varies as a function of
+this h, this magnitude of h.
+
+So, as I plot v as
+a function of h,
+
+in order to get your
+spontaneous symmetry breaking
+
+to happen what you want
+is for the minimum of V,
+
+the minimum potential
+energy, to occur somewhere
+
+out at a non-zero value
+of the Higgs field H.
+
+Now, why is that so special?
+
+The thing that is so
+special about that
+
+is that when I constructed
+this magnitude of h,
+
+I actually lost a
+lot of information
+
+about the Higgs field.
+
+OK, let's just say for
+the sake of argument
+
+that this minimum
+occurs at a place where
+
+the Higgs field in some system
+of units has a value of 1.
+
+So, all I need to do
+is as my universe cools
+
+what I'm going to
+want is energetically,
+
+my potential is going to want
+to go down to its minimum.
+
+So, that just means that as
+the universe is cooling, maybe
+
+at very, very early times
+when everything is extremely
+
+hot and dense, I'm up here
+where the potential energy is
+
+very high.
+
+As the universe expands,
+as everything cools,
+
+it moves over to
+here, it just moves
+
+to someplace where the Higgs
+field takes on a value of 1.
+
+And that's exactly correct,
+that is what ends up happening.
+
+But remember, the minimum
+occurs at some value
+
+in which the magnitude
+of this field
+
+does not equal zero, but given
+that value-- where again let's
+
+just say for this for
+sake of specificity
+
+that we set it equal to
+the magnitude of this thing
+
+equal to 1 in some
+units-- there's actually
+
+an infinite number of
+configurations that correspond
+
+to that because this
+is a complex number,
+
+this is a complex number.
+
+I could put it all
+into little h1,
+
+and I could set into the value
+where that thing is completely
+
+real, or I could put it all
+into little h2 being completely
+
+imaginary or all on to h1 being
+all imaginary, halfway into h1,
+
+halfway into h2.
+
+There are literally an
+infinite number of combinations
+
+that I can choose
+which are consistent
+
+with this value of the
+magnitude of H. So, yeah--
+
+AUDIENCE: So, I
+don't know if I'm
+
+putting too much physical
+significance on the gauge,
+
+but with the other cases
+of spontaneous symmetry,
+
+briefly, that we discussed
+you can always measure.
+
+OK, I've broken my symmetry,
+and now it's lined up this way,
+
+or there's something measurable.
+
+Now, the field
+has to be physical
+
+because the fact that
+you have gauge symmetry
+
+gives you some concerned
+quantity, right?
+
+But, how can I measure what
+direction in gauge space
+
+that I picked out?
+
+PROFESSOR: So, that
+is, let me talk
+
+about this just a
+little bit more.
+
+I think answering your
+question completely
+
+is not really
+possible, but there
+
+is a residue of that is
+in fact very interesting,
+
+and let me just lay out a couple
+more facts about what actually
+
+happens with this
+gauge symmetry,
+
+and it's not going to
+answer your question
+
+but it's going to give you
+something to think about.
+
+OK, so that's an excellent
+and very deep question,
+
+and there are really
+interesting consequences.
+
+And this is a case
+where my failure
+
+to answer the previous
+one is because there's
+
+details I can't
+remember, in this case,
+
+I think it's because
+there's details we actually
+
+don't understand fully.
+
+Research into the mechanism of
+electroweak symmetry breaking,
+
+which is what this
+is all about, is
+
+one of the hot topics in
+particle physics right now.
+
+AUDIENCE: I was just
+wondering if gravity
+
+has any gauge symmetry
+associated with it.
+
+PROFESSOR: It does, but it fits
+in a very, very different way,
+
+and with the exception of the
+fairly speculative framework
+
+of string theory-- which I
+think is very, very promising,
+
+but it's just
+sufficiently removed
+
+from experimental
+verification that I'm
+
+going to have to label it
+speculative-- it doesn't quite
+
+tie in in the same way.
+
+And that's the best
+I can say right now.
+
+The gauge symmetries
+of general relativity
+
+are, at the classical
+level, they correspond
+
+to coordinate transformations,
+at a quantum level,
+
+there's not such a
+simple way to put it.
+
+All right, where
+was I, OK, sorry
+
+I didn't get to your question.
+
+So, the point we made here is
+that we have spontaneously,
+
+when we actually choose which
+one of these infinite number
+
+of values we're going
+to have, we just
+
+randomly break the symmetry.
+
+OK, and you guys
+apparently have already
+
+talked a little bit about
+spontaneous symmetry breaking.
+
+The analogy that
+people often make
+
+is to the freezing
+of water, OK, prior
+
+to the water entering its
+solid phase its completely
+
+rotationally symmetric,
+then at a certain point
+
+crystalline planes
+start to form,
+
+the water forms,
+all the molecules
+
+get set into a
+particular orientation,
+
+you lose that
+rotational symmetry.
+
+In this case, we started
+out with a theory,
+
+with a set of interactions
+that were completely symmetric
+
+in sort of gauge field space.
+
+And now by settling
+down and picking
+
+a particular special
+value of h1 and h2
+
+we have at least nailed
+down one direction.
+
+It's like we've defined
+a crystalline plane,
+
+and so now things, suddenly,
+aren't as symmetric.
+
+And we start to pick
+out preferred directions
+
+in our gauge fields.
+
+What we can do
+with this is really
+
+a topic for a
+whole other course,
+
+and that course is called
+quantum field theory,
+
+but I will sketch a
+couple of the consequences
+
+and this gets directly to
+the answer your questions.
+
+So, one of the
+consequences of this
+
+is that once we have picked
+out a particular direction,
+
+electrons and neutrinos
+are different.
+
+When the Higgs field
+is equal to zero
+
+there is no difference between
+an electron and a neutrino.
+
+They obey exactly
+the same equation,
+
+there's literally no
+difference between them.
+
+Once we have actually
+settled on an h1 and an h2
+
+some combination of the
+fundamental underlying fields
+
+comes together, acquires a mass,
+acquires an electric charge,
+
+and we say A-HA thou
+beist an electron.
+
+It wasn't like that in the
+original unbroken symmetry.
+
+AUDIENCE: Also, [INAUDIBLE]?
+
+PROFESSOR: Presumably,
+but I'm going
+
+to stick with just
+these for now,
+
+but I've I'm pretty sure
+that's the case, yeah.
+
+That gets into even more
+complications of course
+
+because the additional
+generations are actually
+
+consequence presumably of some
+broken higher level symmetry,
+
+which is even poorly,
+more poorly understood.
+
+But you raise a good point.
+
+So, that's one partial
+answer your question.
+
+How one can actually
+walk that backwards
+
+to understand this thing
+about the initial state?
+
+That's hard to say.
+
+I actually think
+this particular one
+
+is one of the profound
+and interesting aspects
+
+of this, in part because we now
+know the neutrino has a mass.
+
+We have no idea what that is,
+and in fact we only really
+
+have bounds on the mass, such
+that we know it is non-zero,
+
+and we have upper
+limits that are
+
+set by very indirect
+measurements.
+
+But the actual
+values of the mass
+
+are very, very
+poorly constrained.
+
+Within the standard
+model you just
+
+take the electroweak
+interaction,
+
+introduce a Higgs coupling
+and allow the symmetry
+
+to be spontaneously broken,
+the neutrino mass is zero.
+
+Full stop zero.
+
+So something's not
+right, we're actually
+
+missing something here.
+
+People have kind of jury
+rigged the standard model
+
+to put in the masses by
+hand, and it works OK,
+
+but it's not
+completely satisfying.
+
+And a lot of experiments
+going on right now
+
+to explore the neutrino
+sector are hopefully
+
+going to open us up to a
+deeper understanding of this
+
+and may say a lot about all this
+physics, which is at present,
+
+pretty poorly understood.
+
+The consequence, which has
+received the most popular
+
+press, and what you
+guys have certainly
+
+seen about in newspapers,
+given the results that came out
+
+from the LHC over the past year
+is that quarks and leptons have
+
+mass, or put more
+specifically, rest mass.
+
+To understand what
+this actually means
+
+I think you really need to
+ask yourself what is mass
+
+meant to be.
+
+Well, the idea is you calculate
+the spectrum of oscillations
+
+associated with the
+fields of your theory,
+
+and then if your theory
+predicts a discrete spectrum
+
+of oscillations, it doesn't
+even have to be discrete
+
+but predict some
+spectrum of oscillations,
+
+then for every oscillation
+frequency omega
+
+there's an associated
+mass that is just
+
+H bar omega over c squared.
+
+If your omega has
+some lower bound that
+
+is greater than zero,
+then your theory
+
+has particles with
+nonzero rest mass.
+
+Without going into the
+details-- and this again
+
+is something which
+those of you who
+
+are going to go on to study
+this in more detail in a higher
+
+level course, which is
+fairly standard stuff is done
+
+in probably the first or maybe
+late in the first or early
+
+in the second semester of a
+typical quantum field theory
+
+course-- what you'll find is
+that when the Higgs field is
+
+zero then quarks
+and leptons have,
+
+the field that describes quarks
+and leptons-- and yes including
+
+mu and tau, so including
+all the leptons, this one
+
+I'm very confident
+on-- the spectrum
+
+goes all the way to zero
+if the Higgs field is zero.
+
+But when the Higgs field becomes
+non-zero, roughly speaking,
+
+it shifts the spectrum
+over for these particles.
+
+There's an interaction between
+the things like the electron
+
+field in the Higgs field or the
+up quark field and the Higgs
+
+field, which shifts the
+spectrum over just enough
+
+so that the frequency
+is never allowed
+
+to go below some minimum.
+
+AUDIENCE: Going back
+a bit, I'm confused
+
+about how picking a specific
+value to the Higgs field
+
+is breaking SU(2)
+symmetry and not U(1),
+
+because it seems like we're
+fixed on a circle, right?
+
+PROFESSOR: That's right what
+U(1) is a symmetry on a circle,
+
+SU(2) is kind of like symmetry
+on a sphere, essentially.
+
+AUDIENCE: Right, so how are we
+not picking a specific value
+
+[INAUDIBLE] circle [INAUDIBLE]?
+
+PROFESSOR: Well, what we're
+doing is, think of it this way,
+
+imagine SU(2) is a
+symmetry on a sphere,
+
+and then when we break
+the SU(2) symmetry
+
+it's like we're picking
+some circle on that sphere.
+
+So, we've broken one circle,
+we've picked one circle,
+
+but now we're allowed
+to go anywhere
+
+on that remaining circle,
+which is a U(1) symmetry.
+
+Does that help?
+
+Yeah, OK good.
+
+And it comes down to the
+fact if you sort of count up
+
+your degrees of freedom,
+it has to do with the fact
+
+you you've got four, you
+have two complex numbers,
+
+so there's four real parameters
+associated with this thing,
+
+and they are isomorphic to sort
+of rotations in a three space
+
+and you're adding
+one constraint.
+
+OK, so let me just finish
+making this point here again.
+
+So, when h does not
+equal zero, spectrum
+
+get shifted for the
+quarks and leptons,
+
+so everything picks up
+a little bit of a mass.
+
+And the final one,
+final consequence
+
+which we're going
+to talk about today,
+
+is that the universe is filled
+with magnetic monopoles.
+
+We all remember studying
+Maxwell's equations
+
+learning that del dot
+b is equal to 4 pi
+
+times the density
+of magnetic charge--
+
+this all makes
+perfect sense, right?
+
+Well, this is actually something
+that when it first sort of came
+
+out and people begin to
+appreciate this thing with sort
+
+of a "Um, well everything
+else works so well,
+
+maybe we're just not
+looking hard enough. " So,
+
+it was a bit of a surprise.
+
+So, where do these magnetic
+monopoles come from?
+
+And essentially, the
+magnetic monopoles
+
+are going to turn out to be
+a consequence of the fact
+
+that when spontaneous
+symmetry breaking happens
+
+it doesn't happen
+everywhere simultaneously.
+
+So, think again about-- yeah?
+
+AUDIENCE: Doesn't that
+bring up possibility
+
+that the symmetry could
+break in different ways
+
+in different places?
+
+PROFESSOR: That is in
+fact exactly what this
+
+is going to be.
+
+Magnetic monopoles are in
+fact exactly a consequence
+
+of this, yes.
+
+Give me a few
+moments to step ahead
+
+to fill in a couple of the
+gaps, but you're basically
+
+already there.
+
+So, think about crystalline
+crystal formation again.
+
+Imagine you have,
+we could do ice
+
+if you like or choose something
+that's got a little bit more
+
+of an interesting
+crystalline structure.
+
+Imagine you have a big bucket
+full of molten quarts, OK.
+
+So, if you have a
+big thing of quartz
+
+that you want to sort of freeze
+into a single gigantic crystal,
+
+what you typically do if
+you'd like to do this is
+
+you actually seed
+it with a little bit
+
+of a starter crystal.
+
+So, you put a little bit
+of crystal into this thing,
+
+and what that does is it sort of
+defines a preferred orientation
+
+of the crystal axes,
+so that as things
+
+start to cool in the
+vicinity of that they have
+
+a preferred orientation
+to grab on to.
+
+And that seed then
+gradually gets
+
+bigger and bigger and bigger,
+and all the little crystals
+
+as they form near
+it tend to latch
+
+onto the preexisting
+crystalline structure,
+
+and that allows you
+to grow actually
+
+extremely large crystals.
+
+I don't know if anyone here is
+doing a year off with the LIGO
+
+project but these guys have to
+make these sort of 100 kilogram
+
+mirrors of very pure either
+Sapphire or silicon dioxide,
+
+and when you make 100
+kilograms of crystal
+
+you need to build it
+really, really carefully.
+
+It's extremely important
+for the optical purposes
+
+that all the axes
+associated with the crystal
+
+will be pointing in
+the right direction.
+
+Otherwise you spend
+$100,000 on this thing
+
+and it ends up being the
+world's prettiest paperweight.
+
+So, similar things happen
+when the Higgs field cools.
+
+Let's imagine that
+we've got our universe,
+
+time going forward like this,
+and at some point over here
+
+the universe cools enough
+that's the Higgs field condenses
+
+into some particular direction.
+
+And symmetry is spontaneously
+broken right at this one point
+
+over here.
+
+So, I'm going to draw
+my diagram over there
+
+and put some words over here.
+
+I shouldn't say Higgs
+field cools enough,
+
+the universe cools
+enough so that the Higgs
+
+field breaks the symmetry.
+
+So, just to be concrete, let's
+imagine that at 0.1 over here
+
+it takes on a field of the
+value one for h1 and I for h2.
+
+So just for concreteness
+imagine it looks something
+
+like this at this point.
+
+And so what happens is as
+the university continues
+
+to expand other areas
+are going to cool off.
+
+The bits that are
+closest to it are
+
+going to see that
+there is already
+
+a preferred orientation
+defined by the Higgs field.
+
+And so it's energetically
+favorable for those regions
+
+of the universe to fall
+into the same alignment
+
+and so there'll be a
+region in space times
+
+that grows here as the universe
+cools, in which the Higgs
+
+field all falls into
+this configuration, which
+
+I will call h1.
+
+But suppose somewhere
+over here at 0.2,
+
+and the key thing is
+that initially 0.2
+
+is going to be so far away
+from 0.1 that these points are
+
+out of causal contact
+with one another.
+
+I can not send a message
+from event one to event two.
+
+The Higgs field
+also reaches a point
+
+that the universe cools enough
+that at 0.2, just you know,
+
+it's a system that's not
+in thermal equilibrium.
+
+So, some places are
+going to be a little bit
+
+hotter than others,
+some are going
+
+to be a little bit cooler.
+
+And so, at these two
+points it just so happened
+
+that the Higgs field
+got to the point
+
+where it could spontaneously
+break the symmetry.
+
+So at 0.2 the Higgs field
+also got to the point
+
+where it could spontaneously
+break its symmetry.
+
+And the only thing
+that's got to happen
+
+is, remember the only
+constraint we have is
+
+that the magnitude
+of the Higgs field
+
+be equals to some value-- I
+should normalize that to root 2
+
+in units I want to
+use but whatever.
+
+Let's say on this one
+my h1 is equal to y,
+
+and h2 is equal to minus 1.
+
+So, it's basically
+the same thing
+
+but all the fields
+are multiplied by i.
+
+It's the same
+magnitude, so it's going
+
+to have the same
+potential energy.
+
+So that's cool.
+
+Clearly this is allowed,
+and now all the regions
+
+in the universe that
+are close to the this
+
+are going to sort of smell
+this particular arrangement
+
+of the Higgs field
+and say OK, that's
+
+preferred arrangement
+I want to go into.
+
+So, we have two separate
+values of the Higgs field
+
+that are happily swooping
+out space time here.
+
+This gets to the
+excellent question
+
+I was just asked a moment ago--
+what happens when they collide?
+
+As the universe expands
+and gets cooler, all of it
+
+is going to end
+up getting swooped
+
+into either the field that
+was seeded at event one,
+
+or the field that was
+seeded in to event two,
+
+but at a certain
+point we're going
+
+to get the bits where they're
+smashing into one another.
+
+So what happens when these
+different domains come
+
+into contact with one another?
+
+The absolutely full
+and probably correct
+
+answer is we don't know.
+
+The reason is that we don't
+really, to be perfectly blunt,
+
+fully understand every little
+detail about the symmetry
+
+breaking, or about the
+structure of whatever
+
+grand unified theory brings
+all these things together
+
+at the temperatures at
+which this is happening.
+
+Because this is happening
+when the universe has
+
+a temperature of like
+10 to the 16th GeV.
+
+And so it's way
+beyond the domain
+
+of where we can push things.
+
+But we can, as physicists
+are fond of doing,
+
+we can paramaterize
+our ignorance,
+
+and we can ask
+ourselves, well what
+
+happens if these various
+parameters that characterize
+
+my grand unified theory take on
+the following plausible kinds
+
+of parameters.
+
+And what we find is
+that generically,
+
+when you have two different
+domains where the Higgs
+
+field takes on different
+values like this, when
+
+these domains come
+into contact you
+
+get what are called
+topological defects.
+
+The topological defects come
+in three different flavors.
+
+To understand something
+about those flavors
+
+you have to know a
+little bit about what
+
+happens in general when
+you have phase transitions,
+
+and different regions
+of your medium
+
+go through a phase transition
+with different values
+
+of the parameters.
+
+So, it's a general
+case that whenever
+
+you have some kind
+of a phase transition
+
+and you have domains
+of different phase
+
+that come into contact
+with one another,
+
+your field will attempt
+to smoothly match itself
+
+across the boundary.
+
+But that can be very difficult.
+
+So if you imagine these
+particular two cases
+
+that I have here,
+that's essentially
+
+saying that when
+these two domains
+
+coming to contact
+with one another
+
+there's going to be sort
+of a transition zone
+
+where the field is
+attempting to rotate
+
+from one value of the
+Higgs to the other.
+
+And it's going to pick some
+value that is in some sense
+
+intermediate to
+those two things.
+
+So that, let's say we
+continue these up here,
+
+so that the collision is
+occurring right in this place
+
+here, in this little locus
+of events in space time.
+
+I have Higgs field 2 over
+here, Higgs field 1 over here,
+
+and I've got some crazy
+intermediate field that
+
+goes between the
+two of them, which
+
+is trying to sort of force
+itself to smoothly transition
+
+from one to the other.
+
+In so doing, I might end
+up pushing my field away
+
+from the minimum, in
+which case there will then
+
+be some energy
+trapped in that layer.
+
+And there's a reason we
+do this level the class
+
+in a bit of a hand
+wavy way, I mean
+
+it's very, very complicated
+to get the details right.
+
+But the key thing we see is
+that in doing this match,
+
+the field has to do some
+pretty silly shenanigans order
+
+to make everything
+kind of match up
+
+and we can be left with
+odd observable consequences
+
+from the energy associated
+with the Higgs field getting
+
+pinned down at
+that boundary here.
+
+Now, the details of the
+forms of this boundary
+
+vary a lot depending upon
+to the specific assumptions
+
+you make about your underlying
+grand unified theory.
+
+OK, so I should
+back up for a bit.
+
+I'm sort of assuming here when
+I discuss all this that there
+
+is some underlying SU(5)
+theory which describes
+
+the strong weak and
+electromagnetic interactions
+
+are very, very high temperatures
+as one gigantic thing.
+
+And we're getting
+to the point now
+
+where all the different
+interactions are beginning
+
+to just sort of
+crystallize out of it.
+
+There's a lot of different ways
+you can pack your underlying,
+
+fundamental, what we now think
+of as our standard model,
+
+into SU(5) grand
+unified theories.
+
+And so the ways in
+which we can get
+
+different topological
+defects depend
+
+upon how we choose to do that.
+
+So defect flavor one is you get
+something called a domain wall.
+
+When we do this
+the fields attempts
+
+to make itself smoothly match
+from one region of Higgs field,
+
+say from Higgs 1 to Higgs 2.
+
+It succeeds, but
+you end up with kind
+
+of a two dimensional structure--
+a wall-- in which there's
+
+some kind of anomalous field
+that is just pinned down there.
+
+And so we end up
+with a big sheet.
+
+So in a theory
+like this, it would
+
+predict that somewhere out
+in the universe if there were
+
+regions in which the
+Higgs field had taken
+
+on a different
+value than the one
+
+that we encounter
+around us right now,
+
+it could be somewhere out
+gigaparsecs away, essentially
+
+a giant sheet of some kind.
+
+And there would be
+weird, anomalous behavior
+
+associated with it.
+
+People have really
+looked long and hard
+
+to try to find things
+like this and in fact it
+
+would be expected to leave
+interesting residuals
+
+in the cause of
+microwave background.
+
+My understanding
+of the literature
+
+is that there are
+actually now very
+
+strong bounds on the
+possibility of having
+
+a grand unified theory
+that leads to domain walls.
+
+And so this kind of
+a topological defect
+
+is observationally disfavored.
+
+So this, I should
+mention, only occurs
+
+in some grand unified theories.
+
+Basically, As we move on to
+the other flavors of defects
+
+we end up just going down a step
+in dimensionality associated
+
+with the little kinks
+that are left over when
+
+the different domains come
+into contact with one another.
+
+Flavor two, we would get
+what's called a cosmic string.
+
+Some of you may
+have heard of this.
+
+This is essentially, at its
+core, just a one dimensional,
+
+it could be gigparsecs long,
+but one dimensional, truly
+
+one dimensional--
+essentially just
+
+a point in the other two
+dimensions-- string of mismatch
+
+Higgs field with some kind of
+an energy density associated
+
+with it when the different
+domains get in contact.
+
+AUDIENCE: Do we
+have any estimate
+
+of how close in actual space
+these different regions would
+
+have started?
+
+PROFESSOR: We do and I'm
+actually going to get to that.
+
+So, let me give you
+two answers to that.
+
+One of them is you are going
+to estimate that apparently
+
+on PSET 10, according to the
+notes that Alan left for me.
+
+But I'm going to spell out
+for you the arguments that
+
+go into it in the last
+10 minutes of a class.
+
+But yeah, so let me just quickly
+finish up this one because this
+
+again-- so a cosmic string is
+sort of like a one dimensional
+
+analog of a domain wall.
+
+And because it would be
+this sort of long one
+
+dimensional structure, that
+has actually up a lot of energy
+
+sort of pinned down to it
+by the fact it has a Higgs
+
+anomaly associated with it, it
+would be strongly gravitating
+
+and so it would leave really
+interesting signatures.
+
+It was thought for a while
+that cosmic strings might
+
+have been the sort of original
+gravitational anomalies
+
+that seeded some of
+the structures we see
+
+in the universe today.
+
+Again, it's now pretty
+highly disfavored.
+
+If cosmic strings
+exist, they don't
+
+appear to contribute very
+much to the budget of mass
+
+in our universe.
+
+I should also mention
+that this is only
+
+predicted by some grand
+unifying theories.
+
+If you guys are
+curious about this
+
+I suggest when Alice
+back you ask him
+
+what the difference
+between these sums,
+
+why some predict a
+domain wall, some
+
+predict the cosmic strings.
+
+Flavor three is where
+you end up with the Higgs
+
+field essentially being
+able to smoothly transition
+
+without leaving any defect
+anywhere except at a zero
+
+dimensional point.
+
+So you end up with just a
+little knot in the Higgs field.
+
+And for reasons that I
+will outline very soon,
+
+it turns out that this little
+not must carry magnetic charge,
+
+and so it must be a
+magnetic monopole.
+
+The domain walls and
+the cosmic strings
+
+are, as I've emphasized,
+only predicted
+
+by certain specific
+grand unified theories.
+
+Magnetic monopoles are actually
+predicted by all of them.
+
+Question.
+
+AUDIENCE: What does it mean to
+have a one dimensional domain
+
+wall, because there's no
+different region separated
+
+by one [INAUDIBLE].
+
+PROFESSOR: That's right.
+
+So what ends up
+happening, and this
+
+is where I think
+you're going to have
+
+to ask Alan to sort of follow
+up on this a little bit.
+
+So, as the domains come into
+contact with one another.
+
+The fields do their best to
+smoothly transition from one
+
+to the other.
+
+And grand unified theories
+that predict a cosmic string,
+
+they succeed pretty
+much everywhere.
+
+They're able to actually
+smoothly make it all go away
+
+so you don't end up with
+feel being pinned down
+
+anywhere, except in a little
+one dimensional singularity that
+
+is somewhere along where the two
+dimensional services originally
+
+met.
+
+And that is--
+there's details there
+
+that I'm not even
+pretending to explain.
+
+And as I say, those
+are only predicted
+
+by certain kinds of
+grand unified theories.
+
+All of them will then predict
+that even if you don't have
+
+that, that cosmic string
+will then shrink itself down
+
+and it'll just be left with
+a little knot of Higgs field,
+
+where there's a little
+bit of residual mismatch
+
+between the two regions.
+
+AUDIENCE: Do all three
+types of defects carry
+
+a magnetic charge,
+or only the knots?
+
+PROFESSOR: I think
+only the knots.
+
+They do carry other
+kinds of fields,
+
+though, in particular the
+other ones gravitate, in fact
+
+all them gravitate,
+and so that's
+
+one of the ways in
+which people have
+
+tried to set observational
+limits on these things.
+
+In particular
+there have recently
+
+been a fair amount of
+work of people trying
+
+to set limits on cosmic strings
+from gravitational lensing,
+
+and there was really
+a lot of excitement
+
+because people thought they
+discovered want a couple
+
+years ago.
+
+And they saw
+basically two quasars
+
+that looked absolutely
+identical, that were separated
+
+or scale that was just
+right to be a cosmic string.
+
+And then people actually looked
+at with better telescopes,
+
+and saw they had absolutely
+nothing to do with one another.
+
+They were not cosmic, they were
+not lenses, it's just every now
+
+and then God is
+screwing with you.
+
+OK, so without going into some
+of the details what you have,
+
+these little point like
+defects-- and I'm short on time
+
+so I'm going to kind of go
+through this a little bit
+
+in a sketchy way enough so
+that I can pay for you how
+
+to do some calculations
+you're going to need to do.
+
+So the point like defects
+end up being regions,
+
+where at that point the
+Higgs field actually takes
+
+the value zero.
+
+So remember I was describing how
+when you have two regions where
+
+the Higgs fields are both
+taking on values such as there
+
+at the minimum of the
+Higgs potential energy,
+
+and they come in to
+match one another,
+
+and what we have a
+boundary condition
+
+that very far away the
+Higgs field has values
+
+such as the energy is minimized.
+
+And there is a theorem, which
+in his notes Alan-- the way
+
+he describes it is
+he gives you a figure
+
+and outlines the
+various things that
+
+are necessary for the
+theorem to be true,
+
+and invites you to think
+deeply for a moment
+
+and until insight
+comes to you, I guess.
+
+And when you put this ingredient
+that the Higgs field has
+
+this asymptotic, very far
+away value that drives you
+
+to the minimum of the field,
+and yet it must change value
+
+somewhere in the
+middle, the theorem
+
+requires that there be one
+point at which H equals 0.
+
+And apparently, this
+is a consequence
+
+in all grand unified theories.
+
+So, recall, H equals 0.
+
+This is a point at which
+the potential energy
+
+density can be huge.
+
+So, when you have a little
+point like defect like this,
+
+it looks like a massive nugget,
+little massive particle.
+
+You can in fact calculate
+the total amount
+
+of energy associated
+with this particle.
+
+If you do so just including the
+influence of the Higgs field,
+
+the calculation
+basically goes like this.
+
+It's very similar to the way we
+calculate the energy associated
+
+with electric and magnetic
+fields in electrodynamics.
+
+Ask yourself, how much
+energy is contained
+
+in a sphere of
+radius, capital R,
+
+centered on this little
+knot of Higgs field.
+
+Well, it's going to
+look like 4pi times
+
+an integral of the
+gradient of the Higgs field
+
+squared r squared
+dr It turns out,
+
+when you calculate the
+[INAUDIBLE] of the Higgs field
+
+around one of these
+little defects,
+
+it's actually very complicated
+close to the defect,
+
+but as you get far away
+it has a very simple form.
+
+The gradient goes
+as 1 over r, it
+
+tells you the field
+itself actually
+
+goes something like log.
+
+That means your energy looks
+something like, R squared,
+
+1 over R squared dr which goes
+as R, which diverges as you
+
+make the sphere bigger
+and bigger and bigger.
+
+So, what's the mistake we made?
+
+Well, the Higgs
+field doesn't always
+
+just sit there and
+operate on itself.
+
+The Higgs field actually
+couples pretty strongly
+
+to all of our vector bosons.
+
+Particularly, it
+couples pretty strongly
+
+to electric and magnetic fields.
+
+So, we have to repeat
+this calculation including
+
+the interaction of the Higgs
+field with the E&D field.
+
+And in Alan's notes he
+gives you some references
+
+on this because this is not
+the kind of calculation you
+
+can really sketch
+out very easily
+
+in an undergraduate class.
+
+To make this
+integral convergent,
+
+the only way it can be done
+is if that little nugget
+
+of Higgs field is endowed
+with magnetic charge.
+
+You need to have a monopolar
+magnetic field that ends up
+
+putting in interaction
+terms, that
+
+make the divergence of
+this integral go away.
+
+So, I at last get to the
+punchline of all this,
+
+we are left inevitably, if we
+accept the whole foundation
+
+story of particle physics that
+the different interactions were
+
+unified in some high energy
+scale and then froze out.
+
+We are driven
+inevitably to the story
+
+that defects in the Higgs field
+create magnetic monopoles.
+
+Now, I realize I'm out of time,
+so let me just quickly sketch
+
+a few interesting
+facts about this
+
+and there's a few exercises
+that you guys are apparently
+
+going to look at in your
+homework assignment.
+
+When we do this
+calculation, one which
+
+is I believe just
+referenced in the notes
+
+that Alan has for the
+class, we learn a couple
+
+of things about this
+magnetic charge.
+
+One of them is that if you
+work in the fundamental unit,
+
+say CGS units, the value
+of the magnetic charge,
+
+we'll call that g,
+is exactly 1 over
+
+2 alpha where alpha
+is a fine structure
+
+constant, times the
+electric charge.
+
+So if you have two
+magnetic monopoles
+
+they attract each
+other with a force
+
+that is-- so 1 over 2 alpha is
+approximately 68.5 I think--
+
+and so it would be 68.5
+squared times the force of two
+
+electric charges at
+that same distance.
+
+We also end up
+learning the mass.
+
+It turns out to be 1 over alpha
+times the scale of GUT symmetry
+
+breaking.
+
+Anyone recall what the scale
+of GUT symmetry breaking is?
+
+10 to the 16 GeV.
+
+So, this is a particle, 1
+over alpha is approximately 10
+
+to the two, so this
+is a particle that
+
+has a mass of about
+10 to the 18th GeV,
+
+in other words it's a single
+particle with a mass of 10
+
+to the 18th protons.
+
+This is approximately
+one microgram.
+
+If you put one of these things
+on a scale it could measure it,
+
+that's bloody big.
+
+So getting to the last bit
+of the class, which I am just
+
+going to very basically
+quote the answer.
+
+The question becomes how often
+do these things get created
+
+and here I'm going to
+refer to Alan's notes.
+
+What you'll find
+is that, remember
+
+when we sketched our original
+picture of this thing
+
+we looked at regions
+of the universe
+
+where the Higgs
+field was initially
+
+seeded with different values.
+
+In order for the Higgs field
+to take on different values,
+
+initially, these regions had
+to be out of causal contact
+
+with one another.
+
+So we are going to require
+that the initial seed areas be
+
+separated by a distance,
+which is the correlation
+
+length, which has to
+be less than or of
+
+order the horizon distance.
+
+You can get a lower bound on
+this thing by imagining that
+
+it's-- sorry let me
+say one other thing.
+
+If you do that, then you
+can estimate that the number
+
+density associated
+with these things,
+
+the number density
+of these monopoles
+
+will be 1 over the
+correlation length cubed.
+
+To get a lower
+bound on the number
+
+density of these things, set
+the correlation length exactly
+
+to the horizon distance, and
+then do the following exercise.
+
+So first, let's set
+up the correlation
+
+length equal to the
+horizon distance.
+
+Set the density in monopoles
+equal to the mass of a monopole
+
+over rH cubed, normalized
+to the critical density.
+
+If you do this,
+you will find that
+
+just due to magnetic
+monopoles alone,
+
+the density of the universe.
+
+PROFESSOR 2: Excuse
+me, professor
+
+PROFESSOR: Yes, I'm wrapping
+up right this second.
+
+PROFESSOR 2: It's seven minutes.
+
+You were supposed
+to end at 10:55.
+
+PROFESSOR: I'm substitute
+teaching, I'm sorry.
+
+OK, so this tells
+us that we are at 10
+
+to the 20 of the
+critical density.
+
+And a consequence
+is that the universe
+
+is approximately two years old.
+
+I will let Alan pick
+it up from there.
\ No newline at end of file
diff --git a/sfH3Jw6LZm8.txt b/sfH3Jw6LZm8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f31c02e967146927c871cafb1a588a094ad1111b
--- /dev/null
+++ b/sfH3Jw6LZm8.txt
@@ -0,0 +1,787 @@
+align:start position:0%
+ 
+where do forces come from all forces
+
+ align:start position:0%
+where do forces come from all forces
+ 
+
+ align:start position:0%
+where do forces come from all forces
+arise from the interaction of two
+
+ align:start position:0%
+arise from the interaction of two
+ 
+
+ align:start position:0%
+arise from the interaction of two
+objects with each other in this example
+
+ align:start position:0%
+objects with each other in this example
+ 
+
+ align:start position:0%
+objects with each other in this example
+we have two objects one and two
+
+ align:start position:0%
+we have two objects one and two
+ 
+
+ align:start position:0%
+we have two objects one and two
+interacting with each other in this case
+
+ align:start position:0%
+interacting with each other in this case
+ 
+
+ align:start position:0%
+interacting with each other in this case
+because there are surfaces are in
+
+ align:start position:0%
+because there are surfaces are in
+ 
+
+ align:start position:0%
+because there are surfaces are in
+contact with each other one sitting on
+
+ align:start position:0%
+contact with each other one sitting on
+ 
+
+ align:start position:0%
+contact with each other one sitting on
+top of the other and the interaction
+
+ align:start position:0%
+top of the other and the interaction
+ 
+
+ align:start position:0%
+top of the other and the interaction
+between the two objects gives rise to a
+
+ align:start position:0%
+between the two objects gives rise to a
+ 
+
+ align:start position:0%
+between the two objects gives rise to a
+pair of forces I have one force that's
+
+ align:start position:0%
+pair of forces I have one force that's
+ 
+
+ align:start position:0%
+pair of forces I have one force that's
+acting from object two down on object
+
+ align:start position:0%
+acting from object two down on object
+ 
+
+ align:start position:0%
+acting from object two down on object
+one and the other force that's acting
+
+ align:start position:0%
+one and the other force that's acting
+ 
+
+ align:start position:0%
+one and the other force that's acting
+from object one back up onto object two
+
+ align:start position:0%
+from object one back up onto object two
+ 
+
+ align:start position:0%
+from object one back up onto object two
+and these forces following Newton's
+
+ align:start position:0%
+and these forces following Newton's
+ 
+
+ align:start position:0%
+and these forces following Newton's
+third law are equal in magnitude and
+
+ align:start position:0%
+third law are equal in magnitude and
+ 
+
+ align:start position:0%
+third law are equal in magnitude and
+opposite in direction what if we now
+
+ align:start position:0%
+opposite in direction what if we now
+ 
+
+ align:start position:0%
+opposite in direction what if we now
+push these blocks horizontally in
+
+ align:start position:0%
+push these blocks horizontally in
+ 
+
+ align:start position:0%
+push these blocks horizontally in
+opposite directions at their interface
+
+ align:start position:0%
+opposite directions at their interface
+ 
+
+ align:start position:0%
+opposite directions at their interface
+there is a frictional interaction this
+
+ align:start position:0%
+there is a frictional interaction this
+ 
+
+ align:start position:0%
+there is a frictional interaction this
+interaction gives rise to a pair of
+
+ align:start position:0%
+interaction gives rise to a pair of
+ 
+
+ align:start position:0%
+interaction gives rise to a pair of
+frictional forces that are parallel to
+
+ align:start position:0%
+frictional forces that are parallel to
+ 
+
+ align:start position:0%
+frictional forces that are parallel to
+the interface the friction force on the
+
+ align:start position:0%
+the interface the friction force on the
+ 
+
+ align:start position:0%
+the interface the friction force on the
+top block from the bottom block is
+
+ align:start position:0%
+top block from the bottom block is
+ 
+
+ align:start position:0%
+top block from the bottom block is
+opposite and direction but equal in
+
+ align:start position:0%
+opposite and direction but equal in
+ 
+
+ align:start position:0%
+opposite and direction but equal in
+magnitude to the friction from the
+
+ align:start position:0%
+magnitude to the friction from the
+ 
+
+ align:start position:0%
+magnitude to the friction from the
+bottom block due to the top block let's
+
+ align:start position:0%
+bottom block due to the top block let's
+ 
+
+ align:start position:0%
+bottom block due to the top block let's
+look at some of the common
+
+ align:start position:0%
+look at some of the common
+ 
+
+ align:start position:0%
+look at some of the common
+misconceptions about forces first of all
+
+ align:start position:0%
+misconceptions about forces first of all
+ 
+
+ align:start position:0%
+misconceptions about forces first of all
+motion is not a force if I have a block
+
+ align:start position:0%
+motion is not a force if I have a block
+ 
+
+ align:start position:0%
+motion is not a force if I have a block
+that's moving at a constant velocity
+
+ align:start position:0%
+that's moving at a constant velocity
+ 
+
+ align:start position:0%
+that's moving at a constant velocity
+along a frictionless plane then there is
+
+ align:start position:0%
+along a frictionless plane then there is
+ 
+
+ align:start position:0%
+along a frictionless plane then there is
+no horizontal force that's acting on
+
+ align:start position:0%
+no horizontal force that's acting on
+ 
+
+ align:start position:0%
+no horizontal force that's acting on
+this block because there is no
+
+ align:start position:0%
+this block because there is no
+ 
+
+ align:start position:0%
+this block because there is no
+interaction that would give rise to a
+
+ align:start position:0%
+interaction that would give rise to a
+ 
+
+ align:start position:0%
+interaction that would give rise to a
+horizontal force the fact that it has a
+
+ align:start position:0%
+horizontal force the fact that it has a
+ 
+
+ align:start position:0%
+horizontal force the fact that it has a
+velocity does not necessarily mean that
+
+ align:start position:0%
+velocity does not necessarily mean that
+ 
+
+ align:start position:0%
+velocity does not necessarily mean that
+there is a force acting on it another
+
+ align:start position:0%
+there is a force acting on it another
+ 
+
+ align:start position:0%
+there is a force acting on it another
+common mistake is to think that forces
+
+ align:start position:0%
+common mistake is to think that forces
+ 
+
+ align:start position:0%
+common mistake is to think that forces
+transfer through objects for example if
+
+ align:start position:0%
+transfer through objects for example if
+ 
+
+ align:start position:0%
+transfer through objects for example if
+I'm pushing a book against a wall it
+
+ align:start position:0%
+I'm pushing a book against a wall it
+ 
+
+ align:start position:0%
+I'm pushing a book against a wall it
+might seem like the force from my hand
+
+ align:start position:0%
+might seem like the force from my hand
+ 
+
+ align:start position:0%
+might seem like the force from my hand
+is being transferred to the wall but
+
+ align:start position:0%
+is being transferred to the wall but
+ 
+
+ align:start position:0%
+is being transferred to the wall but
+what is really happening is that there
+
+ align:start position:0%
+what is really happening is that there
+ 
+
+ align:start position:0%
+what is really happening is that there
+are two independent interactions the
+
+ align:start position:0%
+are two independent interactions the
+ 
+
+ align:start position:0%
+are two independent interactions the
+interaction of my hand with the book and
+
+ align:start position:0%
+interaction of my hand with the book and
+ 
+
+ align:start position:0%
+interaction of my hand with the book and
+the interaction of the book with the
+
+ align:start position:0%
+the interaction of the book with the
+ 
+
+ align:start position:0%
+the interaction of the book with the
+wall and these are separate interactions
+
+ align:start position:0%
+wall and these are separate interactions
+ 
+
+ align:start position:0%
+wall and these are separate interactions
+the forces might happen to have the same
+
+ align:start position:0%
+the forces might happen to have the same
+ 
+
+ align:start position:0%
+the forces might happen to have the same
+magnitude in some cases but it's not
+
+ align:start position:0%
+magnitude in some cases but it's not
+ 
+
+ align:start position:0%
+magnitude in some cases but it's not
+because the force from my hand is being
+
+ align:start position:0%
+because the force from my hand is being
+ 
+
+ align:start position:0%
+because the force from my hand is being
+transferred forces arise between pairs
+
+ align:start position:0%
+transferred forces arise between pairs
+ 
+
+ align:start position:0%
+transferred forces arise between pairs
+of objects and those horses can only act
+
+ align:start position:0%
+of objects and those horses can only act
+ 
+
+ align:start position:0%
+of objects and those horses can only act
+on those two objects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look more closely at Newton's
+
+ align:start position:0%
+let's look more closely at Newton's
+ 
+
+ align:start position:0%
+let's look more closely at Newton's
+third law so Newton's third law says
+
+ align:start position:0%
+third law so Newton's third law says
+ 
+
+ align:start position:0%
+third law so Newton's third law says
+that when there are two objects that are
+
+ align:start position:0%
+that when there are two objects that are
+ 
+
+ align:start position:0%
+that when there are two objects that are
+interacting there will be two forces
+
+ align:start position:0%
+interacting there will be two forces
+ 
+
+ align:start position:0%
+interacting there will be two forces
+that arise from that interaction and
+
+ align:start position:0%
+that arise from that interaction and
+ 
+
+ align:start position:0%
+that arise from that interaction and
+these two forces are always equal in
+
+ align:start position:0%
+these two forces are always equal in
+ 
+
+ align:start position:0%
+these two forces are always equal in
+magnitude and opposite in direction
+
+ align:start position:0%
+magnitude and opposite in direction
+ 
+
+ align:start position:0%
+magnitude and opposite in direction
+these two forces this Newton's third law
+
+ align:start position:0%
+these two forces this Newton's third law
+ 
+
+ align:start position:0%
+these two forces this Newton's third law
+pair of forces never act on the same
+
+ align:start position:0%
+pair of forces never act on the same
+ 
+
+ align:start position:0%
+pair of forces never act on the same
+object but instead one force acts on the
+
+ align:start position:0%
+object but instead one force acts on the
+ 
+
+ align:start position:0%
+object but instead one force acts on the
+first object and one on the second
+
+ align:start position:0%
+first object and one on the second
+ 
+
+ align:start position:0%
+first object and one on the second
+because these forces arise out of the
+
+ align:start position:0%
+because these forces arise out of the
+ 
+
+ align:start position:0%
+because these forces arise out of the
+same interaction they have to be the
+
+ align:start position:0%
+same interaction they have to be the
+ 
+
+ align:start position:0%
+same interaction they have to be the
+same type of force so they could be
+
+ align:start position:0%
+same type of force so they could be
+ 
+
+ align:start position:0%
+same type of force so they could be
+gravitational forces frictional forces
+
+ align:start position:0%
+gravitational forces frictional forces
+ 
+
+ align:start position:0%
+gravitational forces frictional forces
+normal forces etc let's look at an
+
+ align:start position:0%
+normal forces etc let's look at an
+ 
+
+ align:start position:0%
+normal forces etc let's look at an
+example of a book sitting on a table
+
+ align:start position:0%
+example of a book sitting on a table
+ 
+
+ align:start position:0%
+example of a book sitting on a table
+it's being pulled down by the
+
+ align:start position:0%
+it's being pulled down by the
+ 
+
+ align:start position:0%
+it's being pulled down by the
+gravitational force and it's being held
+
+ align:start position:0%
+gravitational force and it's being held
+ 
+
+ align:start position:0%
+gravitational force and it's being held
+up by the normal force are these two
+
+ align:start position:0%
+up by the normal force are these two
+ 
+
+ align:start position:0%
+up by the normal force are these two
+forces a news third law pair the book is
+
+ align:start position:0%
+forces a news third law pair the book is
+ 
+
+ align:start position:0%
+forces a news third law pair the book is
+not accelerating so these forces are
+
+ align:start position:0%
+not accelerating so these forces are
+ 
+
+ align:start position:0%
+not accelerating so these forces are
+equal in magnitude and opposite in
+
+ align:start position:0%
+equal in magnitude and opposite in
+ 
+
+ align:start position:0%
+equal in magnitude and opposite in
+direction but they cannot be a Newton's
+
+ align:start position:0%
+direction but they cannot be a Newton's
+ 
+
+ align:start position:0%
+direction but they cannot be a Newton's
+third law pair for two different reasons
+
+ align:start position:0%
+third law pair for two different reasons
+ 
+
+ align:start position:0%
+third law pair for two different reasons
+first of all they both act on the same
+
+ align:start position:0%
+first of all they both act on the same
+ 
+
+ align:start position:0%
+first of all they both act on the same
+object the book and second of all they
+
+ align:start position:0%
+object the book and second of all they
+ 
+
+ align:start position:0%
+object the book and second of all they
+arise from different interactions the
+
+ align:start position:0%
+arise from different interactions the
+ 
+
+ align:start position:0%
+arise from different interactions the
+normal force on the book is part of a
+
+ align:start position:0%
+normal force on the book is part of a
+ 
+
+ align:start position:0%
+normal force on the book is part of a
+Newton's third law pair that comes from
+
+ align:start position:0%
+Newton's third law pair that comes from
+ 
+
+ align:start position:0%
+Newton's third law pair that comes from
+the interaction between the book and the
+
+ align:start position:0%
+the interaction between the book and the
+ 
+
+ align:start position:0%
+the interaction between the book and the
+table
+
+ align:start position:0%
+table
+ 
+
+ align:start position:0%
+table
+what's the Newton's third law pair of
+
+ align:start position:0%
+what's the Newton's third law pair of
+ 
+
+ align:start position:0%
+what's the Newton's third law pair of
+the gravitational force on the book well
+
+ align:start position:0%
+the gravitational force on the book well
+ 
+
+ align:start position:0%
+the gravitational force on the book well
+because the gravitational forces arises
+
+ align:start position:0%
+because the gravitational forces arises
+ 
+
+ align:start position:0%
+because the gravitational forces arises
+from the interaction between the book
+
+ align:start position:0%
+from the interaction between the book
+ 
+
+ align:start position:0%
+from the interaction between the book
+and the earth the other force in the
+
+ align:start position:0%
+and the earth the other force in the
+ 
+
+ align:start position:0%
+and the earth the other force in the
+Newton's third law pair is actually the
+
+ align:start position:0%
+Newton's third law pair is actually the
+ 
+
+ align:start position:0%
+Newton's third law pair is actually the
+force that the book exerts on the earth
+
+ align:start position:0%
+force that the book exerts on the earth
+ 
+
+ align:start position:0%
+force that the book exerts on the earth
+you might not think about the book
+
+ align:start position:0%
+you might not think about the book
+ 
+
+ align:start position:0%
+you might not think about the book
+acting on the earth but the force is
+
+ align:start position:0%
+acting on the earth but the force is
+ 
+
+ align:start position:0%
+acting on the earth but the force is
+actually equal and opposite to the
+
+ align:start position:0%
+actually equal and opposite to the
+ 
+
+ align:start position:0%
+actually equal and opposite to the
+Earth's force on the book it's just that
+
+ align:start position:0%
+Earth's force on the book it's just that
+ 
+
+ align:start position:0%
+Earth's force on the book it's just that
+the earth is so much more massive the
+
+ align:start position:0%
+the earth is so much more massive the
+ 
+
+ align:start position:0%
+the earth is so much more massive the
+force has no detectable influence on the
+
+ align:start position:0%
+force has no detectable influence on the
+ 
+
+ align:start position:0%
+force has no detectable influence on the
+Earth's behavior behavior at all
\ No newline at end of file
diff --git a/u72VF_VDp2k.txt b/u72VF_VDp2k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..68025a4ee544406d7729049301a9d2e12fa602fb
--- /dev/null
+++ b/u72VF_VDp2k.txt
@@ -0,0 +1,10259 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay shall we begin so on the syllabus
+
+ align:start position:0%
+okay shall we begin so on the syllabus
+ 
+
+ align:start position:0%
+okay shall we begin so on the syllabus
+today's class is supposed to be a review
+
+ align:start position:0%
+today's class is supposed to be a review
+ 
+
+ align:start position:0%
+today's class is supposed to be a review
+for the next quiz and I'm happy to
+
+ align:start position:0%
+for the next quiz and I'm happy to
+ 
+
+ align:start position:0%
+for the next quiz and I'm happy to
+answer any questions you have about the
+
+ align:start position:0%
+answer any questions you have about the
+ 
+
+ align:start position:0%
+answer any questions you have about the
+material or about the quiz to the best
+
+ align:start position:0%
+material or about the quiz to the best
+ 
+
+ align:start position:0%
+material or about the quiz to the best
+of my ability and when we've exhausted
+
+ align:start position:0%
+of my ability and when we've exhausted
+ 
+
+ align:start position:0%
+of my ability and when we've exhausted
+those questions I have some notes on
+
+ align:start position:0%
+those questions I have some notes on
+ 
+
+ align:start position:0%
+those questions I have some notes on
+another method for solving partial
+
+ align:start position:0%
+another method for solving partial
+ 
+
+ align:start position:0%
+another method for solving partial
+differential equations we didn't really
+
+ align:start position:0%
+differential equations we didn't really
+ 
+
+ align:start position:0%
+differential equations we didn't really
+cover in class but I think it's quite
+
+ align:start position:0%
+cover in class but I think it's quite
+ 
+
+ align:start position:0%
+cover in class but I think it's quite
+quite interesting and applicable for
+
+ align:start position:0%
+quite interesting and applicable for
+ 
+
+ align:start position:0%
+quite interesting and applicable for
+chemical engineers in particular because
+
+ align:start position:0%
+chemical engineers in particular because
+ 
+
+ align:start position:0%
+chemical engineers in particular because
+of the classes of problems that we study
+
+ align:start position:0%
+of the classes of problems that we study
+ 
+
+ align:start position:0%
+of the classes of problems that we study
+and then notes on how to construct a
+
+ align:start position:0%
+and then notes on how to construct a
+ 
+
+ align:start position:0%
+and then notes on how to construct a
+simulation of a PDE that follow from
+
+ align:start position:0%
+simulation of a PDE that follow from
+ 
+
+ align:start position:0%
+simulation of a PDE that follow from
+what Professor Green discussed during
+
+ align:start position:0%
+what Professor Green discussed during
+ 
+
+ align:start position:0%
+what Professor Green discussed during
+your last PDE lecture and we'll do do an
+
+ align:start position:0%
+your last PDE lecture and we'll do do an
+ 
+
+ align:start position:0%
+your last PDE lecture and we'll do do an
+example where we actually develop a code
+
+ align:start position:0%
+example where we actually develop a code
+ 
+
+ align:start position:0%
+example where we actually develop a code
+to solve the PDE and maybe refine it so
+
+ align:start position:0%
+to solve the PDE and maybe refine it so
+ 
+
+ align:start position:0%
+to solve the PDE and maybe refine it so
+that it runs more quickly by noticing
+
+ align:start position:0%
+that it runs more quickly by noticing
+ 
+
+ align:start position:0%
+that it runs more quickly by noticing
+certain things about the structure of
+
+ align:start position:0%
+certain things about the structure of
+ 
+
+ align:start position:0%
+certain things about the structure of
+the problem okay I have your your gift
+
+ align:start position:0%
+the problem okay I have your your gift
+ 
+
+ align:start position:0%
+the problem okay I have your your gift
+cards I remembered them
+
+ align:start position:0%
+cards I remembered them
+ 
+
+ align:start position:0%
+cards I remembered them
+so I'll hand those out at the end of
+
+ align:start position:0%
+so I'll hand those out at the end of
+ 
+
+ align:start position:0%
+so I'll hand those out at the end of
+class just in case more people trickle
+
+ align:start position:0%
+class just in case more people trickle
+ 
+
+ align:start position:0%
+class just in case more people trickle
+in but it doesn't look like there's 53
+
+ align:start position:0%
+in but it doesn't look like there's 53
+ 
+
+ align:start position:0%
+in but it doesn't look like there's 53
+people here so maybe the TAS are gonna
+
+ align:start position:0%
+people here so maybe the TAS are gonna
+ 
+
+ align:start position:0%
+people here so maybe the TAS are gonna
+be eating burritos for a while this is
+
+ align:start position:0%
+be eating burritos for a while this is
+ 
+
+ align:start position:0%
+be eating burritos for a while this is
+for me a lot left over we'll see I'll
+
+ align:start position:0%
+for me a lot left over we'll see I'll
+ 
+
+ align:start position:0%
+for me a lot left over we'll see I'll
+hold on to them try to make sure
+
+ align:start position:0%
+hold on to them try to make sure
+ 
+
+ align:start position:0%
+hold on to them try to make sure
+everyone gets their gets their reward
+
+ align:start position:0%
+everyone gets their gets their reward
+ 
+
+ align:start position:0%
+everyone gets their gets their reward
+for responding to the class survey so
+
+ align:start position:0%
+for responding to the class survey so
+ 
+
+ align:start position:0%
+for responding to the class survey so
+let's let's start with questions about
+
+ align:start position:0%
+let's let's start with questions about
+ 
+
+ align:start position:0%
+let's let's start with questions about
+the quiz about the material that we've
+
+ align:start position:0%
+the quiz about the material that we've
+ 
+
+ align:start position:0%
+the quiz about the material that we've
+covered up to this point I'm really
+
+ align:start position:0%
+covered up to this point I'm really
+ 
+
+ align:start position:0%
+covered up to this point I'm really
+gonna leave it to you to point out
+
+ align:start position:0%
+gonna leave it to you to point out
+ 
+
+ align:start position:0%
+gonna leave it to you to point out
+things so you feel like you need help
+
+ align:start position:0%
+things so you feel like you need help
+ 
+
+ align:start position:0%
+things so you feel like you need help
+with you think need to be reviewed I
+
+ align:start position:0%
+with you think need to be reviewed I
+ 
+
+ align:start position:0%
+with you think need to be reviewed I
+know you've had a review session with
+
+ align:start position:0%
+know you've had a review session with
+ 
+
+ align:start position:0%
+know you've had a review session with
+the TAS already maybe that's been
+
+ align:start position:0%
+the TAS already maybe that's been
+ 
+
+ align:start position:0%
+the TAS already maybe that's been
+sufficient okay questions it's up to you
+
+ align:start position:0%
+sufficient okay questions it's up to you
+ 
+
+ align:start position:0%
+sufficient okay questions it's up to you
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ooh good question so so I'll tell you
+
+ align:start position:0%
+ooh good question so so I'll tell you
+ 
+
+ align:start position:0%
+ooh good question so so I'll tell you
+that I believe the problems on the quiz
+
+ align:start position:0%
+that I believe the problems on the quiz
+ 
+
+ align:start position:0%
+that I believe the problems on the quiz
+this year are motivated by chemical
+
+ align:start position:0%
+this year are motivated by chemical
+ 
+
+ align:start position:0%
+this year are motivated by chemical
+engineering problems okay the reason for
+
+ align:start position:0%
+engineering problems okay the reason for
+ 
+
+ align:start position:0%
+engineering problems okay the reason for
+that is unlike linear algebra problems
+
+ align:start position:0%
+that is unlike linear algebra problems
+ 
+
+ align:start position:0%
+that is unlike linear algebra problems
+or optimization problems those those can
+
+ align:start position:0%
+or optimization problems those those can
+ 
+
+ align:start position:0%
+or optimization problems those those can
+be crafted out of whole cloth but
+
+ align:start position:0%
+be crafted out of whole cloth but
+ 
+
+ align:start position:0%
+be crafted out of whole cloth but
+workable right boundary value problems
+
+ align:start position:0%
+workable right boundary value problems
+ 
+
+ align:start position:0%
+workable right boundary value problems
+workable initial value problems really
+
+ align:start position:0%
+workable initial value problems really
+ 
+
+ align:start position:0%
+workable initial value problems really
+really neat to stem from something
+
+ align:start position:0%
+really neat to stem from something
+ 
+
+ align:start position:0%
+really neat to stem from something
+physical you are not asked to derive
+
+ align:start position:0%
+physical you are not asked to derive
+ 
+
+ align:start position:0%
+physical you are not asked to derive
+anything from your extensive chemical
+
+ align:start position:0%
+anything from your extensive chemical
+ 
+
+ align:start position:0%
+anything from your extensive chemical
+engineering knowledge is not a qualifier
+
+ align:start position:0%
+engineering knowledge is not a qualifier
+ 
+
+ align:start position:0%
+engineering knowledge is not a qualifier
+for reactors or thermo or transport we
+
+ align:start position:0%
+for reactors or thermo or transport we
+ 
+
+ align:start position:0%
+for reactors or thermo or transport we
+provide you with those details okay but
+
+ align:start position:0%
+provide you with those details okay but
+ 
+
+ align:start position:0%
+provide you with those details okay but
+they are I think they they are of a
+
+ align:start position:0%
+they are I think they they are of a
+ 
+
+ align:start position:0%
+they are I think they they are of a
+chemical engineering origin so you have
+
+ align:start position:0%
+chemical engineering origin so you have
+ 
+
+ align:start position:0%
+chemical engineering origin so you have
+equations that are reasonable to work
+
+ align:start position:0%
+equations that are reasonable to work
+ 
+
+ align:start position:0%
+equations that are reasonable to work
+with okay more questions yes okay sure
+
+ align:start position:0%
+with okay more questions yes okay sure
+ 
+
+ align:start position:0%
+with okay more questions yes okay sure
+so okay so let's let's let's just
+
+ align:start position:0%
+so okay so let's let's let's just
+ 
+
+ align:start position:0%
+so okay so let's let's let's just
+discuss boundary value problems first
+
+ align:start position:0%
+discuss boundary value problems first
+ 
+
+ align:start position:0%
+discuss boundary value problems first
+turns out PDEs are a class of boundary
+
+ align:start position:0%
+turns out PDEs are a class of boundary
+ 
+
+ align:start position:0%
+turns out PDEs are a class of boundary
+value problem to largely at least the
+
+ align:start position:0%
+value problem to largely at least the
+ 
+
+ align:start position:0%
+value problem to largely at least the
+ones that chemical engineers are
+
+ align:start position:0%
+ones that chemical engineers are
+ 
+
+ align:start position:0%
+ones that chemical engineers are
+interested in so if we understand
+
+ align:start position:0%
+interested in so if we understand
+ 
+
+ align:start position:0%
+interested in so if we understand
+boundary value problems in general we
+
+ align:start position:0%
+boundary value problems in general we
+ 
+
+ align:start position:0%
+boundary value problems in general we
+should understand how to solve partial
+
+ align:start position:0%
+should understand how to solve partial
+ 
+
+ align:start position:0%
+should understand how to solve partial
+differential equations to many classes
+
+ align:start position:0%
+differential equations to many classes
+ 
+
+ align:start position:0%
+differential equations to many classes
+of partial differential equations that
+
+ align:start position:0%
+of partial differential equations that
+ 
+
+ align:start position:0%
+of partial differential equations that
+we're interested in can also be solved
+
+ align:start position:0%
+we're interested in can also be solved
+ 
+
+ align:start position:0%
+we're interested in can also be solved
+in these ways so we talked about
+
+ align:start position:0%
+in these ways so we talked about
+ 
+
+ align:start position:0%
+in these ways so we talked about
+relaxation methods in general okay which
+
+ align:start position:0%
+relaxation methods in general okay which
+ 
+
+ align:start position:0%
+relaxation methods in general okay which
+were these methods that rely on somehow
+
+ align:start position:0%
+were these methods that rely on somehow
+ 
+
+ align:start position:0%
+were these methods that rely on somehow
+disk utilizing the continuous function
+
+ align:start position:0%
+disk utilizing the continuous function
+ 
+
+ align:start position:0%
+disk utilizing the continuous function
+that we're trying to describe in this
+
+ align:start position:0%
+that we're trying to describe in this
+ 
+
+ align:start position:0%
+that we're trying to describe in this
+boundary value problem so usually you've
+
+ align:start position:0%
+boundary value problem so usually you've
+ 
+
+ align:start position:0%
+boundary value problem so usually you've
+got some we've got some linear function
+
+ align:start position:0%
+got some we've got some linear function
+ 
+
+ align:start position:0%
+got some we've got some linear function
+okay some linear operator that operates
+
+ align:start position:0%
+okay some linear operator that operates
+ 
+
+ align:start position:0%
+okay some linear operator that operates
+on some variable that we're trying to
+
+ align:start position:0%
+on some variable that we're trying to
+ 
+
+ align:start position:0%
+on some variable that we're trying to
+understand and evaluate boundary value
+
+ align:start position:0%
+understand and evaluate boundary value
+ 
+
+ align:start position:0%
+understand and evaluate boundary value
+from maybe it's temperature right equals
+
+ align:start position:0%
+from maybe it's temperature right equals
+ 
+
+ align:start position:0%
+from maybe it's temperature right equals
+zero so this would be something like
+
+ align:start position:0%
+zero so this would be something like
+ 
+
+ align:start position:0%
+zero so this would be something like
+write thermal diffusion range this
+
+ align:start position:0%
+write thermal diffusion range this
+ 
+
+ align:start position:0%
+write thermal diffusion range this
+equation could represent that could
+
+ align:start position:0%
+equation could represent that could
+ 
+
+ align:start position:0%
+equation could represent that could
+represent some advection diffusion
+
+ align:start position:0%
+represent some advection diffusion
+ 
+
+ align:start position:0%
+represent some advection diffusion
+problem in some bounded domain it can be
+
+ align:start position:0%
+problem in some bounded domain it can be
+ 
+
+ align:start position:0%
+problem in some bounded domain it can be
+a PDE it could be a it could just be a
+
+ align:start position:0%
+a PDE it could be a it could just be a
+ 
+
+ align:start position:0%
+a PDE it could be a it could just be a
+an ordinary differential equation right
+
+ align:start position:0%
+an ordinary differential equation right
+ 
+
+ align:start position:0%
+an ordinary differential equation right
+but a boundary value problem and with
+
+ align:start position:0%
+but a boundary value problem and with
+ 
+
+ align:start position:0%
+but a boundary value problem and with
+this relaxation with these class of
+
+ align:start position:0%
+this relaxation with these class of
+ 
+
+ align:start position:0%
+this relaxation with these class of
+relaxation methods we try not to exactly
+
+ align:start position:0%
+relaxation methods we try not to exactly
+ 
+
+ align:start position:0%
+relaxation methods we try not to exactly
+satisfy this equation we relax that
+
+ align:start position:0%
+satisfy this equation we relax that
+ 
+
+ align:start position:0%
+satisfy this equation we relax that
+assumption we try to somehow discretize
+
+ align:start position:0%
+assumption we try to somehow discretize
+ 
+
+ align:start position:0%
+assumption we try to somehow discretize
+this function could be temperature could
+
+ align:start position:0%
+this function could be temperature could
+ 
+
+ align:start position:0%
+this function could be temperature could
+be energy could be velocity or momentum
+
+ align:start position:0%
+be energy could be velocity or momentum
+ 
+
+ align:start position:0%
+be energy could be velocity or momentum
+be lots of different things try to relax
+
+ align:start position:0%
+be lots of different things try to relax
+ 
+
+ align:start position:0%
+be lots of different things try to relax
+the constraint this is satisfied
+
+ align:start position:0%
+the constraint this is satisfied
+ 
+
+ align:start position:0%
+the constraint this is satisfied
+everywhere and we try to satisfy in some
+
+ align:start position:0%
+everywhere and we try to satisfy in some
+ 
+
+ align:start position:0%
+everywhere and we try to satisfy in some
+approximate sense instead so we
+
+ align:start position:0%
+approximate sense instead so we
+ 
+
+ align:start position:0%
+approximate sense instead so we
+discussed collocation methods where we
+
+ align:start position:0%
+discussed collocation methods where we
+ 
+
+ align:start position:0%
+discussed collocation methods where we
+take the domain we're interested in then
+
+ align:start position:0%
+take the domain we're interested in then
+ 
+
+ align:start position:0%
+take the domain we're interested in then
+we divide it up into a series of points
+
+ align:start position:0%
+we divide it up into a series of points
+ 
+
+ align:start position:0%
+we divide it up into a series of points
+ok and we try to satisfy this equation
+
+ align:start position:0%
+ok and we try to satisfy this equation
+ 
+
+ align:start position:0%
+ok and we try to satisfy this equation
+at those points and we have some
+
+ align:start position:0%
+at those points and we have some
+ 
+
+ align:start position:0%
+at those points and we have some
+approximation for the function its
+
+ align:start position:0%
+approximation for the function its
+ 
+
+ align:start position:0%
+approximation for the function its
+representation at those points that
+
+ align:start position:0%
+representation at those points that
+ 
+
+ align:start position:0%
+representation at those points that
+approximation could be a finite
+
+ align:start position:0%
+approximation could be a finite
+ 
+
+ align:start position:0%
+approximation could be a finite
+difference approximation okay that
+
+ align:start position:0%
+difference approximation okay that
+ 
+
+ align:start position:0%
+difference approximation okay that
+approximation could be a basis set
+
+ align:start position:0%
+approximation could be a basis set
+ 
+
+ align:start position:0%
+approximation could be a basis set
+expansion it could be a finite volume
+
+ align:start position:0%
+expansion it could be a finite volume
+ 
+
+ align:start position:0%
+expansion it could be a finite volume
+approximation we could expand in terms
+
+ align:start position:0%
+approximation we could expand in terms
+ 
+
+ align:start position:0%
+approximation we could expand in terms
+of local basis functions
+
+ align:start position:0%
+of local basis functions
+ 
+
+ align:start position:0%
+of local basis functions
+that's the finite element method we
+
+ align:start position:0%
+that's the finite element method we
+ 
+
+ align:start position:0%
+that's the finite element method we
+covered all these different methods that
+
+ align:start position:0%
+covered all these different methods that
+ 
+
+ align:start position:0%
+covered all these different methods that
+involves chopping the domain up into a
+
+ align:start position:0%
+involves chopping the domain up into a
+ 
+
+ align:start position:0%
+involves chopping the domain up into a
+series of points and trying to satisfy
+
+ align:start position:0%
+series of points and trying to satisfy
+ 
+
+ align:start position:0%
+series of points and trying to satisfy
+the function at each of those points
+
+ align:start position:0%
+the function at each of those points
+ 
+
+ align:start position:0%
+the function at each of those points
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there was an alternative method right
+
+ align:start position:0%
+there was an alternative method right
+ 
+
+ align:start position:0%
+there was an alternative method right
+this sort of glurk in method where
+
+ align:start position:0%
+this sort of glurk in method where
+ 
+
+ align:start position:0%
+this sort of glurk in method where
+instead of trying to satisfy the
+
+ align:start position:0%
+instead of trying to satisfy the
+ 
+
+ align:start position:0%
+instead of trying to satisfy the
+function at each of those points we have
+
+ align:start position:0%
+function at each of those points we have
+ 
+
+ align:start position:0%
+function at each of those points we have
+some basis set expansion okay so we have
+
+ align:start position:0%
+some basis set expansion okay so we have
+ 
+
+ align:start position:0%
+some basis set expansion okay so we have
+some approximate representation of our
+
+ align:start position:0%
+some approximate representation of our
+ 
+
+ align:start position:0%
+some approximate representation of our
+function in terms of these basis sets in
+
+ align:start position:0%
+function in terms of these basis sets in
+ 
+
+ align:start position:0%
+function in terms of these basis sets in
+terms of this basis set and instead we
+
+ align:start position:0%
+terms of this basis set and instead we
+ 
+
+ align:start position:0%
+terms of this basis set and instead we
+try to make it be the case that the
+
+ align:start position:0%
+try to make it be the case that the
+ 
+
+ align:start position:0%
+try to make it be the case that the
+integral okay of our operator applied to
+
+ align:start position:0%
+integral okay of our operator applied to
+ 
+
+ align:start position:0%
+integral okay of our operator applied to
+our approximation brake chalk multiplied
+
+ align:start position:0%
+our approximation brake chalk multiplied
+ 
+
+ align:start position:0%
+our approximation brake chalk multiplied
+by each of the basis functions and then
+
+ align:start position:0%
+by each of the basis functions and then
+ 
+
+ align:start position:0%
+by each of the basis functions and then
+integrated over this entire domain okay
+
+ align:start position:0%
+integrated over this entire domain okay
+ 
+
+ align:start position:0%
+integrated over this entire domain okay
+is equal to zero okay so we try to
+
+ align:start position:0%
+is equal to zero okay so we try to
+ 
+
+ align:start position:0%
+is equal to zero okay so we try to
+satisfy this equation right with respect
+
+ align:start position:0%
+satisfy this equation right with respect
+ 
+
+ align:start position:0%
+satisfy this equation right with respect
+to each of these basis functions
+
+ align:start position:0%
+to each of these basis functions
+ 
+
+ align:start position:0%
+to each of these basis functions
+essentially right there's some this
+
+ align:start position:0%
+essentially right there's some this
+ 
+
+ align:start position:0%
+essentially right there's some this
+isn't going to exactly satisfy the
+
+ align:start position:0%
+isn't going to exactly satisfy the
+ 
+
+ align:start position:0%
+isn't going to exactly satisfy the
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+this is an approximation so I can
+
+ align:start position:0%
+this is an approximation so I can
+ 
+
+ align:start position:0%
+this is an approximation so I can
+exactly satisfy the boundary value
+
+ align:start position:0%
+exactly satisfy the boundary value
+ 
+
+ align:start position:0%
+exactly satisfy the boundary value
+problem we were after okay but the
+
+ align:start position:0%
+problem we were after okay but the
+ 
+
+ align:start position:0%
+problem we were after okay but the
+projection of the residual or how far
+
+ align:start position:0%
+projection of the residual or how far
+ 
+
+ align:start position:0%
+projection of the residual or how far
+off we are with this operator on each of
+
+ align:start position:0%
+off we are with this operator on each of
+ 
+
+ align:start position:0%
+off we are with this operator on each of
+the basis functions we're gonna try to
+
+ align:start position:0%
+the basis functions we're gonna try to
+ 
+
+ align:start position:0%
+the basis functions we're gonna try to
+force to be zero so rather than trying
+
+ align:start position:0%
+force to be zero so rather than trying
+ 
+
+ align:start position:0%
+force to be zero so rather than trying
+to get a point wise solution of the
+
+ align:start position:0%
+to get a point wise solution of the
+ 
+
+ align:start position:0%
+to get a point wise solution of the
+problem we're gonna try to sort of
+
+ align:start position:0%
+problem we're gonna try to sort of
+ 
+
+ align:start position:0%
+problem we're gonna try to sort of
+smooth out the air with respect to the
+
+ align:start position:0%
+smooth out the air with respect to the
+ 
+
+ align:start position:0%
+smooth out the air with respect to the
+basis functions and make it make this
+
+ align:start position:0%
+basis functions and make it make this
+ 
+
+ align:start position:0%
+basis functions and make it make this
+equation as satisfied as it possibly can
+
+ align:start position:0%
+equation as satisfied as it possibly can
+ 
+
+ align:start position:0%
+equation as satisfied as it possibly can
+with respect to these basis functions
+
+ align:start position:0%
+with respect to these basis functions
+ 
+
+ align:start position:0%
+with respect to these basis functions
+and that's the that's the glurk and view
+
+ align:start position:0%
+and that's the that's the glurk and view
+ 
+
+ align:start position:0%
+and that's the that's the glurk and view
+okay so it's different it's like a
+
+ align:start position:0%
+okay so it's different it's like a
+ 
+
+ align:start position:0%
+okay so it's different it's like a
+you're trying to minimize sort of a
+
+ align:start position:0%
+you're trying to minimize sort of a
+ 
+
+ align:start position:0%
+you're trying to minimize sort of a
+global air with respect to the basis
+
+ align:start position:0%
+global air with respect to the basis
+ 
+
+ align:start position:0%
+global air with respect to the basis
+functions as what as opposed to a point
+
+ align:start position:0%
+functions as what as opposed to a point
+ 
+
+ align:start position:0%
+functions as what as opposed to a point
+wise air okay and again these these
+
+ align:start position:0%
+wise air okay and again these these
+ 
+
+ align:start position:0%
+wise air okay and again these these
+basis functions can be chosen in a lot
+
+ align:start position:0%
+basis functions can be chosen in a lot
+ 
+
+ align:start position:0%
+basis functions can be chosen in a lot
+of different ways they can be chosen as
+
+ align:start position:0%
+of different ways they can be chosen as
+ 
+
+ align:start position:0%
+of different ways they can be chosen as
+sort of global functions they could be
+
+ align:start position:0%
+sort of global functions they could be
+ 
+
+ align:start position:0%
+sort of global functions they could be
+things like sines and cosines right we
+
+ align:start position:0%
+things like sines and cosines right we
+ 
+
+ align:start position:0%
+things like sines and cosines right we
+may know that the solution to this
+
+ align:start position:0%
+may know that the solution to this
+ 
+
+ align:start position:0%
+may know that the solution to this
+equation looks a lot like sines and
+
+ align:start position:0%
+equation looks a lot like sines and
+ 
+
+ align:start position:0%
+equation looks a lot like sines and
+cosines so that makes sense or we may
+
+ align:start position:0%
+cosines so that makes sense or we may
+ 
+
+ align:start position:0%
+cosines so that makes sense or we may
+choose local basis functions and set
+
+ align:start position:0%
+choose local basis functions and set
+ 
+
+ align:start position:0%
+choose local basis functions and set
+little tent functions in 1d okay
+
+ align:start position:0%
+little tent functions in 1d okay
+ 
+
+ align:start position:0%
+little tent functions in 1d okay
+actually tent functions in many
+
+ align:start position:0%
+actually tent functions in many
+ 
+
+ align:start position:0%
+actually tent functions in many
+dimensions as well you can imagine sort
+
+ align:start position:0%
+dimensions as well you can imagine sort
+ 
+
+ align:start position:0%
+dimensions as well you can imagine sort
+of extending that to look like a tent in
+
+ align:start position:0%
+of extending that to look like a tent in
+ 
+
+ align:start position:0%
+of extending that to look like a tent in
+many dimensions that's the finite
+
+ align:start position:0%
+many dimensions that's the finite
+ 
+
+ align:start position:0%
+many dimensions that's the finite
+element method okay so we can choose
+
+ align:start position:0%
+element method okay so we can choose
+ 
+
+ align:start position:0%
+element method okay so we can choose
+those basis functions however we want
+
+ align:start position:0%
+those basis functions however we want
+ 
+
+ align:start position:0%
+those basis functions however we want
+and the goal is to just minimize write
+
+ align:start position:0%
+and the goal is to just minimize write
+ 
+
+ align:start position:0%
+and the goal is to just minimize write
+this residual with respect to each of
+
+ align:start position:0%
+this residual with respect to each of
+ 
+
+ align:start position:0%
+this residual with respect to each of
+the basis functions that we include in
+
+ align:start position:0%
+the basis functions that we include in
+ 
+
+ align:start position:0%
+the basis functions that we include in
+our approximate solution we would call
+
+ align:start position:0%
+our approximate solution we would call
+ 
+
+ align:start position:0%
+our approximate solution we would call
+that a reasonable approximation
+
+ align:start position:0%
+that a reasonable approximation
+ 
+
+ align:start position:0%
+that a reasonable approximation
+presumably as the number of basis
+
+ align:start position:0%
+presumably as the number of basis
+ 
+
+ align:start position:0%
+presumably as the number of basis
+functions goes to infinity this is going
+
+ align:start position:0%
+functions goes to infinity this is going
+ 
+
+ align:start position:0%
+functions goes to infinity this is going
+to converge right that's the applied
+
+ align:start position:0%
+to converge right that's the applied
+ 
+
+ align:start position:0%
+to converge right that's the applied
+mathematicians job to show us that it's
+
+ align:start position:0%
+mathematicians job to show us that it's
+ 
+
+ align:start position:0%
+mathematicians job to show us that it's
+going to converge to the true solution
+
+ align:start position:0%
+going to converge to the true solution
+ 
+
+ align:start position:0%
+going to converge to the true solution
+of the equations okay so those are those
+
+ align:start position:0%
+of the equations okay so those are those
+ 
+
+ align:start position:0%
+of the equations okay so those are those
+those are the methods that we those are
+
+ align:start position:0%
+those are the methods that we those are
+ 
+
+ align:start position:0%
+those are the methods that we those are
+the methods that we apply right good
+
+ align:start position:0%
+the methods that we apply right good
+ 
+
+ align:start position:0%
+the methods that we apply right good
+choice is a basis function are important
+
+ align:start position:0%
+choice is a basis function are important
+ 
+
+ align:start position:0%
+choice is a basis function are important
+so there was a discussion about sort of
+
+ align:start position:0%
+so there was a discussion about sort of
+ 
+
+ align:start position:0%
+so there was a discussion about sort of
+quantum chemistry where you're trying to
+
+ align:start position:0%
+quantum chemistry where you're trying to
+ 
+
+ align:start position:0%
+quantum chemistry where you're trying to
+solve the you're trying to solve the
+
+ align:start position:0%
+solve the you're trying to solve the
+ 
+
+ align:start position:0%
+solve the you're trying to solve the
+Schrodinger equation for n electrons
+
+ align:start position:0%
+Schrodinger equation for n electrons
+ 
+
+ align:start position:0%
+Schrodinger equation for n electrons
+there's three n degrees of freedom so
+
+ align:start position:0%
+there's three n degrees of freedom so
+ 
+
+ align:start position:0%
+there's three n degrees of freedom so
+it's a very high dimensional space
+
+ align:start position:0%
+it's a very high dimensional space
+ 
+
+ align:start position:0%
+it's a very high dimensional space
+how you going to do that you do with
+
+ align:start position:0%
+how you going to do that you do with
+ 
+
+ align:start position:0%
+how you going to do that you do with
+basis set expansions and the choice of
+
+ align:start position:0%
+basis set expansions and the choice of
+ 
+
+ align:start position:0%
+basis set expansions and the choice of
+those basis functions is really
+
+ align:start position:0%
+those basis functions is really
+ 
+
+ align:start position:0%
+those basis functions is really
+important so when you if you read a
+
+ align:start position:0%
+important so when you if you read a
+ 
+
+ align:start position:0%
+important so when you if you read a
+quantum chemistry paper you'll see they
+
+ align:start position:0%
+quantum chemistry paper you'll see they
+ 
+
+ align:start position:0%
+quantum chemistry paper you'll see they
+give a they have a long series of digits
+
+ align:start position:0%
+give a they have a long series of digits
+ 
+
+ align:start position:0%
+give a they have a long series of digits
+and numbers that are meant to indicate
+
+ align:start position:0%
+and numbers that are meant to indicate
+ 
+
+ align:start position:0%
+and numbers that are meant to indicate
+which which basis set expansion they
+
+ align:start position:0%
+which which basis set expansion they
+ 
+
+ align:start position:0%
+which which basis set expansion they
+used and for certain classes a problem
+
+ align:start position:0%
+used and for certain classes a problem
+ 
+
+ align:start position:0%
+used and for certain classes a problem
+some are better than others and they
+
+ align:start position:0%
+some are better than others and they
+ 
+
+ align:start position:0%
+some are better than others and they
+make the
+
+ align:start position:0%
+make the
+ 
+
+ align:start position:0%
+make the
+the problem actually solvable when it's
+
+ align:start position:0%
+the problem actually solvable when it's
+ 
+
+ align:start position:0%
+the problem actually solvable when it's
+when it's not if you were to just choose
+
+ align:start position:0%
+when it's not if you were to just choose
+ 
+
+ align:start position:0%
+when it's not if you were to just choose
+your basis functions you know with
+
+ align:start position:0%
+your basis functions you know with
+ 
+
+ align:start position:0%
+your basis functions you know with
+without care for the physics of the
+
+ align:start position:0%
+without care for the physics of the
+ 
+
+ align:start position:0%
+without care for the physics of the
+problem Sam yeah right well it should
+
+ align:start position:0%
+problem Sam yeah right well it should
+ 
+
+ align:start position:0%
+problem Sam yeah right well it should
+have been right here okay so technically
+
+ align:start position:0%
+have been right here okay so technically
+ 
+
+ align:start position:0%
+have been right here okay so technically
+the basis functions don't have to be
+
+ align:start position:0%
+the basis functions don't have to be
+ 
+
+ align:start position:0%
+the basis functions don't have to be
+real valued functions they could be
+
+ align:start position:0%
+real valued functions they could be
+ 
+
+ align:start position:0%
+real valued functions they could be
+complex valued functions and then this
+
+ align:start position:0%
+complex valued functions and then this
+ 
+
+ align:start position:0%
+complex valued functions and then this
+is this is in some sense a dot product
+
+ align:start position:0%
+is this is in some sense a dot product
+ 
+
+ align:start position:0%
+is this is in some sense a dot product
+okay an inner product in the space of
+
+ align:start position:0%
+okay an inner product in the space of
+ 
+
+ align:start position:0%
+okay an inner product in the space of
+these basis functions and the proper
+
+ align:start position:0%
+these basis functions and the proper
+ 
+
+ align:start position:0%
+these basis functions and the proper
+form for an inner product when we have
+
+ align:start position:0%
+form for an inner product when we have
+ 
+
+ align:start position:0%
+form for an inner product when we have
+complex valued things is to take the
+
+ align:start position:0%
+complex valued things is to take the
+ 
+
+ align:start position:0%
+complex valued things is to take the
+real part of one and multiply it with
+
+ align:start position:0%
+real part of one and multiply it with
+ 
+
+ align:start position:0%
+real part of one and multiply it with
+the complex part of another right so
+
+ align:start position:0%
+the complex part of another right so
+ 
+
+ align:start position:0%
+the complex part of another right so
+that's should have been great here this
+
+ align:start position:0%
+that's should have been great here this
+ 
+
+ align:start position:0%
+that's should have been great here this
+should be the complex conjugate okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes that's right well in the in the
+
+ align:start position:0%
+yes yes that's right well in the in the
+ 
+
+ align:start position:0%
+yes yes that's right well in the in the
+you know if we have a if we have a an
+
+ align:start position:0%
+you know if we have a if we have a an
+ 
+
+ align:start position:0%
+you know if we have a if we have a an
+expansion of our of the sort of
+
+ align:start position:0%
+expansion of our of the sort of
+ 
+
+ align:start position:0%
+expansion of our of the sort of
+objective that we're trying to calculate
+
+ align:start position:0%
+objective that we're trying to calculate
+ 
+
+ align:start position:0%
+objective that we're trying to calculate
+in terms of those basis functions L is
+
+ align:start position:0%
+in terms of those basis functions L is
+ 
+
+ align:start position:0%
+in terms of those basis functions L is
+the real L right it is what it is this
+
+ align:start position:0%
+the real L right it is what it is this
+ 
+
+ align:start position:0%
+the real L right it is what it is this
+is the model equation to be solved we
+
+ align:start position:0%
+is the model equation to be solved we
+ 
+
+ align:start position:0%
+is the model equation to be solved we
+operate on our approximate solution with
+
+ align:start position:0%
+operate on our approximate solution with
+ 
+
+ align:start position:0%
+operate on our approximate solution with
+the real L in the collocation method
+
+ align:start position:0%
+the real L in the collocation method
+ 
+
+ align:start position:0%
+the real L in the collocation method
+that may be the real L or may be some
+
+ align:start position:0%
+that may be the real L or may be some
+ 
+
+ align:start position:0%
+that may be the real L or may be some
+approximation for L if we do finite
+
+ align:start position:0%
+approximation for L if we do finite
+ 
+
+ align:start position:0%
+approximation for L if we do finite
+differences we're approximating all
+
+ align:start position:0%
+differences we're approximating all
+ 
+
+ align:start position:0%
+differences we're approximating all
+these derivatives okay if we do a basis
+
+ align:start position:0%
+these derivatives okay if we do a basis
+ 
+
+ align:start position:0%
+these derivatives okay if we do a basis
+set expansion and we try to satisfy that
+
+ align:start position:0%
+set expansion and we try to satisfy that
+ 
+
+ align:start position:0%
+set expansion and we try to satisfy that
+at a certain number of points
+
+ align:start position:0%
+at a certain number of points
+ 
+
+ align:start position:0%
+at a certain number of points
+we're not approximating L we're
+
+ align:start position:0%
+we're not approximating L we're
+ 
+
+ align:start position:0%
+we're not approximating L we're
+approximating T instead okay so they're
+
+ align:start position:0%
+approximating T instead okay so they're
+ 
+
+ align:start position:0%
+approximating T instead okay so they're
+a little bit they're a little bit
+
+ align:start position:0%
+a little bit they're a little bit
+ 
+
+ align:start position:0%
+a little bit they're a little bit
+different more questions so it's B VP's
+
+ align:start position:0%
+different more questions so it's B VP's
+ 
+
+ align:start position:0%
+different more questions so it's B VP's
+this picture applies for PDE stew okay
+
+ align:start position:0%
+this picture applies for PDE stew okay
+ 
+
+ align:start position:0%
+this picture applies for PDE stew okay
+so this you know this is the integral
+
+ align:start position:0%
+so this you know this is the integral
+ 
+
+ align:start position:0%
+so this you know this is the integral
+over the domain of interest the domain
+
+ align:start position:0%
+over the domain of interest the domain
+ 
+
+ align:start position:0%
+over the domain of interest the domain
+that's bound
+
+ align:start position:0%
+that's bound
+ 
+
+ align:start position:0%
+that's bound
+did right by our boundary conditions
+
+ align:start position:0%
+did right by our boundary conditions
+ 
+
+ align:start position:0%
+did right by our boundary conditions
+these basis functions don't have to be
+
+ align:start position:0%
+these basis functions don't have to be
+ 
+
+ align:start position:0%
+these basis functions don't have to be
+in one dimension they can be in any
+
+ align:start position:0%
+in one dimension they can be in any
+ 
+
+ align:start position:0%
+in one dimension they can be in any
+number of dimensions we want we just
+
+ align:start position:0%
+number of dimensions we want we just
+ 
+
+ align:start position:0%
+number of dimensions we want we just
+want them to be good basis functions in
+
+ align:start position:0%
+want them to be good basis functions in
+ 
+
+ align:start position:0%
+want them to be good basis functions in
+principle okay so for finite elements
+
+ align:start position:0%
+principle okay so for finite elements
+ 
+
+ align:start position:0%
+principle okay so for finite elements
+you use little tents okay a
+
+ align:start position:0%
+you use little tents okay a
+ 
+
+ align:start position:0%
+you use little tents okay a
+multi-dimensional tents but they're
+
+ align:start position:0%
+multi-dimensional tents but they're
+ 
+
+ align:start position:0%
+multi-dimensional tents but they're
+still tents the same as these have
+
+ align:start position:0%
+still tents the same as these have
+ 
+
+ align:start position:0%
+still tents the same as these have
+functions that Professor Green talked
+
+ align:start position:0%
+functions that Professor Green talked
+ 
+
+ align:start position:0%
+functions that Professor Green talked
+about in 1d just do them in many
+
+ align:start position:0%
+about in 1d just do them in many
+ 
+
+ align:start position:0%
+about in 1d just do them in many
+dimensions okay they work exactly the
+
+ align:start position:0%
+dimensions okay they work exactly the
+ 
+
+ align:start position:0%
+dimensions okay they work exactly the
+same way they're easy to take the
+
+ align:start position:0%
+same way they're easy to take the
+ 
+
+ align:start position:0%
+same way they're easy to take the
+derivatives of these integrals are for
+
+ align:start position:0%
+derivatives of these integrals are for
+ 
+
+ align:start position:0%
+derivatives of these integrals are for
+the most part simple to calculate that's
+
+ align:start position:0%
+the most part simple to calculate that's
+ 
+
+ align:start position:0%
+the most part simple to calculate that's
+that's why COMSOL for example uses uses
+
+ align:start position:0%
+that's why COMSOL for example uses uses
+ 
+
+ align:start position:0%
+that's why COMSOL for example uses uses
+that methodology it's based on this sort
+
+ align:start position:0%
+that methodology it's based on this sort
+ 
+
+ align:start position:0%
+that methodology it's based on this sort
+of glurk in picture so P DS be VPS
+
+ align:start position:0%
+of glurk in picture so P DS be VPS
+ 
+
+ align:start position:0%
+of glurk in picture so P DS be VPS
+look very similar okay usually we're
+
+ align:start position:0%
+look very similar okay usually we're
+ 
+
+ align:start position:0%
+look very similar okay usually we're
+talking about spatial dimensions that
+
+ align:start position:0%
+talking about spatial dimensions that
+ 
+
+ align:start position:0%
+talking about spatial dimensions that
+look very similar when we go to the time
+
+ align:start position:0%
+look very similar when we go to the time
+ 
+
+ align:start position:0%
+look very similar when we go to the time
+domain things get a little more
+
+ align:start position:0%
+domain things get a little more
+ 
+
+ align:start position:0%
+domain things get a little more
+confusing right that mixes together what
+
+ align:start position:0%
+confusing right that mixes together what
+ 
+
+ align:start position:0%
+confusing right that mixes together what
+we know from oti VPS with what we know
+
+ align:start position:0%
+we know from oti VPS with what we know
+ 
+
+ align:start position:0%
+we know from oti VPS with what we know
+from boundary value problems down so you
+
+ align:start position:0%
+from boundary value problems down so you
+ 
+
+ align:start position:0%
+from boundary value problems down so you
+talked about the method of lines last
+
+ align:start position:0%
+talked about the method of lines last
+ 
+
+ align:start position:0%
+talked about the method of lines last
+time is one way of studying for example
+
+ align:start position:0%
+time is one way of studying for example
+ 
+
+ align:start position:0%
+time is one way of studying for example
+parabolic partial differential equations
+
+ align:start position:0%
+parabolic partial differential equations
+ 
+
+ align:start position:0%
+parabolic partial differential equations
+you have the spatial discretization like
+
+ align:start position:0%
+you have the spatial discretization like
+ 
+
+ align:start position:0%
+you have the spatial discretization like
+this and then in time you have some ODI
+
+ align:start position:0%
+this and then in time you have some ODI
+ 
+
+ align:start position:0%
+this and then in time you have some ODI
+VP technique that you integrate forward
+
+ align:start position:0%
+VP technique that you integrate forward
+ 
+
+ align:start position:0%
+VP technique that you integrate forward
+right you rely on these robust OD
+
+ align:start position:0%
+right you rely on these robust OD
+ 
+
+ align:start position:0%
+right you rely on these robust OD
+methods that know how to control the
+
+ align:start position:0%
+methods that know how to control the
+ 
+
+ align:start position:0%
+methods that know how to control the
+numerical air can detect maybe when
+
+ align:start position:0%
+numerical air can detect maybe when
+ 
+
+ align:start position:0%
+numerical air can detect maybe when
+there's some sort of an instability and
+
+ align:start position:0%
+there's some sort of an instability and
+ 
+
+ align:start position:0%
+there's some sort of an instability and
+try to damp it out by altering the time
+
+ align:start position:0%
+try to damp it out by altering the time
+ 
+
+ align:start position:0%
+try to damp it out by altering the time
+step so that things stay stable yes sure
+
+ align:start position:0%
+step so that things stay stable yes sure
+ 
+
+ align:start position:0%
+step so that things stay stable yes sure
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first of all there are a lot of local
+
+ align:start position:0%
+so first of all there are a lot of local
+ 
+
+ align:start position:0%
+so first of all there are a lot of local
+basis functions we could write down okay
+
+ align:start position:0%
+basis functions we could write down okay
+ 
+
+ align:start position:0%
+basis functions we could write down okay
+there are many of them so yes so let's
+
+ align:start position:0%
+there are many of them so yes so let's
+ 
+
+ align:start position:0%
+there are many of them so yes so let's
+do the Hat okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's suppose I have this line right in
+
+ align:start position:0%
+let's suppose I have this line right in
+ 
+
+ align:start position:0%
+let's suppose I have this line right in
+X and I target in my collocation method
+
+ align:start position:0%
+X and I target in my collocation method
+ 
+
+ align:start position:0%
+X and I target in my collocation method
+a series of points column X I minus 1
+
+ align:start position:0%
+a series of points column X I minus 1
+ 
+
+ align:start position:0%
+a series of points column X I minus 1
+xixi plus 1 and they extend well beyond
+
+ align:start position:0%
+xixi plus 1 and they extend well beyond
+ 
+
+ align:start position:0%
+xixi plus 1 and they extend well beyond
+here it doesn't matter where they are
+
+ align:start position:0%
+here it doesn't matter where they are
+ 
+
+ align:start position:0%
+here it doesn't matter where they are
+okay I choose where they are based on
+
+ align:start position:0%
+okay I choose where they are based on
+ 
+
+ align:start position:0%
+okay I choose where they are based on
+the physics of the problem I'll put them
+
+ align:start position:0%
+the physics of the problem I'll put them
+ 
+
+ align:start position:0%
+the physics of the problem I'll put them
+where I want them to go and in fact you
+
+ align:start position:0%
+where I want them to go and in fact you
+ 
+
+ align:start position:0%
+where I want them to go and in fact you
+might even try to optimize where they go
+
+ align:start position:0%
+might even try to optimize where they go
+ 
+
+ align:start position:0%
+might even try to optimize where they go
+so you might start with some
+
+ align:start position:0%
+so you might start with some
+ 
+
+ align:start position:0%
+so you might start with some
+distribution of them and then move them
+
+ align:start position:0%
+distribution of them and then move them
+ 
+
+ align:start position:0%
+distribution of them and then move them
+around in some way to improve the
+
+ align:start position:0%
+around in some way to improve the
+ 
+
+ align:start position:0%
+around in some way to improve the
+quality of your solution right maybe you
+
+ align:start position:0%
+quality of your solution right maybe you
+ 
+
+ align:start position:0%
+quality of your solution right maybe you
+maybe you distribute them uniformly
+
+ align:start position:0%
+maybe you distribute them uniformly
+ 
+
+ align:start position:0%
+maybe you distribute them uniformly
+first and then you notice so my solution
+
+ align:start position:0%
+first and then you notice so my solution
+ 
+
+ align:start position:0%
+first and then you notice so my solution
+is changing very quickly over here I
+
+ align:start position:0%
+is changing very quickly over here I
+ 
+
+ align:start position:0%
+is changing very quickly over here I
+would like more points in this region
+
+ align:start position:0%
+would like more points in this region
+ 
+
+ align:start position:0%
+would like more points in this region
+live it in MATLAB there's a function
+
+ align:start position:0%
+live it in MATLAB there's a function
+ 
+
+ align:start position:0%
+live it in MATLAB there's a function
+called be VP for C which is a boundary
+
+ align:start position:0%
+called be VP for C which is a boundary
+ 
+
+ align:start position:0%
+called be VP for C which is a boundary
+value problem solver solves 1d boundary
+
+ align:start position:0%
+value problem solver solves 1d boundary
+ 
+
+ align:start position:0%
+value problem solver solves 1d boundary
+value problems and it does precisely
+
+ align:start position:0%
+value problems and it does precisely
+ 
+
+ align:start position:0%
+value problems and it does precisely
+this uses finite differences in
+
+ align:start position:0%
+this uses finite differences in
+ 
+
+ align:start position:0%
+this uses finite differences in
+collocation and the good thing about it
+
+ align:start position:0%
+collocation and the good thing about it
+ 
+
+ align:start position:0%
+collocation and the good thing about it
+is it's trying to adaptively change
+
+ align:start position:0%
+is it's trying to adaptively change
+ 
+
+ align:start position:0%
+is it's trying to adaptively change
+where these points are positioned so it
+
+ align:start position:0%
+where these points are positioned so it
+ 
+
+ align:start position:0%
+where these points are positioned so it
+solves it
+
+ align:start position:0%
+solves it
+ 
+
+ align:start position:0%
+solves it
+it looks where things are changing
+
+ align:start position:0%
+it looks where things are changing
+ 
+
+ align:start position:0%
+it looks where things are changing
+quickly and tries to shift its shift its
+
+ align:start position:0%
+quickly and tries to shift its shift its
+ 
+
+ align:start position:0%
+quickly and tries to shift its shift its
+points around and Reese all've it right
+
+ align:start position:0%
+points around and Reese all've it right
+ 
+
+ align:start position:0%
+points around and Reese all've it right
+in order to improve the quality of the
+
+ align:start position:0%
+in order to improve the quality of the
+ 
+
+ align:start position:0%
+in order to improve the quality of the
+solution hit certain certain targets for
+
+ align:start position:0%
+solution hit certain certain targets for
+ 
+
+ align:start position:0%
+solution hit certain certain targets for
+the air okay so what do these what would
+
+ align:start position:0%
+the air okay so what do these what would
+ 
+
+ align:start position:0%
+the air okay so what do these what would
+these local basis functions look like so
+
+ align:start position:0%
+these local basis functions look like so
+ 
+
+ align:start position:0%
+these local basis functions look like so
+we talked about these hats right there
+
+ align:start position:0%
+we talked about these hats right there
+ 
+
+ align:start position:0%
+we talked about these hats right there
+one here right they're going to be 0 on
+
+ align:start position:0%
+one here right they're going to be 0 on
+ 
+
+ align:start position:0%
+one here right they're going to be 0 on
+either side at this point we could call
+
+ align:start position:0%
+either side at this point we could call
+ 
+
+ align:start position:0%
+either side at this point we could call
+this our hat I okay which is centered at
+
+ align:start position:0%
+this our hat I okay which is centered at
+ 
+
+ align:start position:0%
+this our hat I okay which is centered at
+point X I and it's going to raise it's
+
+ align:start position:0%
+point X I and it's going to raise it's
+ 
+
+ align:start position:0%
+point X I and it's going to raise it's
+going to be a piecewise sort of function
+
+ align:start position:0%
+going to be a piecewise sort of function
+ 
+
+ align:start position:0%
+going to be a piecewise sort of function
+ok it's going to be an increasing linear
+
+ align:start position:0%
+ok it's going to be an increasing linear
+ 
+
+ align:start position:0%
+ok it's going to be an increasing linear
+function between X I minus 1 and X I so
+
+ align:start position:0%
+function between X I minus 1 and X I so
+ 
+
+ align:start position:0%
+function between X I minus 1 and X I so
+for X between X I and X I minus 1 it'll
+
+ align:start position:0%
+for X between X I and X I minus 1 it'll
+ 
+
+ align:start position:0%
+for X between X I and X I minus 1 it'll
+have one form and it's got a switch it's
+
+ align:start position:0%
+have one form and it's got a switch it's
+ 
+
+ align:start position:0%
+have one form and it's got a switch it's
+going to be a decreasing function on the
+
+ align:start position:0%
+going to be a decreasing function on the
+ 
+
+ align:start position:0%
+going to be a decreasing function on the
+other side so between X I and X I plus 1
+
+ align:start position:0%
+other side so between X I and X I plus 1
+ 
+
+ align:start position:0%
+other side so between X I and X I plus 1
+it'll have a different form so here
+
+ align:start position:0%
+it'll have a different form so here
+ 
+
+ align:start position:0%
+it'll have a different form so here
+right it's going to increase between 0
+
+ align:start position:0%
+right it's going to increase between 0
+ 
+
+ align:start position:0%
+right it's going to increase between 0
+and 1 so it's gonna have to look
+
+ align:start position:0%
+and 1 so it's gonna have to look
+ 
+
+ align:start position:0%
+and 1 so it's gonna have to look
+something like X
+
+ align:start position:0%
+something like X
+ 
+
+ align:start position:0%
+something like X
+- X I minus 1 divided by X I minus X I
+
+ align:start position:0%
+- X I minus 1 divided by X I minus X I
+ 
+
+ align:start position:0%
+- X I minus 1 divided by X I minus X I
+minus 1 okay so it goes from 0 to 1 okay
+
+ align:start position:0%
+minus 1 okay so it goes from 0 to 1 okay
+ 
+
+ align:start position:0%
+minus 1 okay so it goes from 0 to 1 okay
+and then the other side it's gonna have
+
+ align:start position:0%
+and then the other side it's gonna have
+ 
+
+ align:start position:0%
+and then the other side it's gonna have
+to have the opposite sign okay so this
+
+ align:start position:0%
+to have the opposite sign okay so this
+ 
+
+ align:start position:0%
+to have the opposite sign okay so this
+is gonna have to look like let's see X
+
+ align:start position:0%
+is gonna have to look like let's see X
+ 
+
+ align:start position:0%
+is gonna have to look like let's see X
+minus X I plus 1 divided by X I minus X
+
+ align:start position:0%
+minus X I plus 1 divided by X I minus X
+ 
+
+ align:start position:0%
+minus X I plus 1 divided by X I minus X
+I plus 1 well that'd do it
+
+ align:start position:0%
+I plus 1 well that'd do it
+ 
+
+ align:start position:0%
+I plus 1 well that'd do it
+I think so okay you are gonna make it
+
+ align:start position:0%
+I think so okay you are gonna make it
+ 
+
+ align:start position:0%
+I think so okay you are gonna make it
+look like this one so you could do a
+
+ align:start position:0%
+look like this one so you could do a
+ 
+
+ align:start position:0%
+look like this one so you could do a
+plus 1 X I and then put a minus sign in
+
+ align:start position:0%
+plus 1 X I and then put a minus sign in
+ 
+
+ align:start position:0%
+plus 1 X I and then put a minus sign in
+front of it if you want okay
+
+ align:start position:0%
+front of it if you want okay
+ 
+
+ align:start position:0%
+front of it if you want okay
+you decide how you want to write it okay
+
+ align:start position:0%
+you decide how you want to write it okay
+ 
+
+ align:start position:0%
+you decide how you want to write it okay
+but it describes this line here and this
+
+ align:start position:0%
+but it describes this line here and this
+ 
+
+ align:start position:0%
+but it describes this line here and this
+line here but there are other choices
+
+ align:start position:0%
+line here but there are other choices
+ 
+
+ align:start position:0%
+line here but there are other choices
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this doesn't have to be piecewise linear
+
+ align:start position:0%
+this doesn't have to be piecewise linear
+ 
+
+ align:start position:0%
+this doesn't have to be piecewise linear
+necessarily right a lot of times people
+
+ align:start position:0%
+necessarily right a lot of times people
+ 
+
+ align:start position:0%
+necessarily right a lot of times people
+choose different different types of
+
+ align:start position:0%
+choose different different types of
+ 
+
+ align:start position:0%
+choose different different types of
+splines
+
+ align:start position:0%
+splines
+ 
+
+ align:start position:0%
+splines
+okay different types of interpolating
+
+ align:start position:0%
+okay different types of interpolating
+ 
+
+ align:start position:0%
+okay different types of interpolating
+functions they might not be localized to
+
+ align:start position:0%
+functions they might not be localized to
+ 
+
+ align:start position:0%
+functions they might not be localized to
+one point they might be localized over a
+
+ align:start position:0%
+one point they might be localized over a
+ 
+
+ align:start position:0%
+one point they might be localized over a
+few points okay
+
+ align:start position:0%
+few points okay
+ 
+
+ align:start position:0%
+few points okay
+maybe something about the physics of a
+
+ align:start position:0%
+maybe something about the physics of a
+ 
+
+ align:start position:0%
+maybe something about the physics of a
+particular problem that tell you right
+
+ align:start position:0%
+particular problem that tell you right
+ 
+
+ align:start position:0%
+particular problem that tell you right
+you can't get away with these piecewise
+
+ align:start position:0%
+you can't get away with these piecewise
+ 
+
+ align:start position:0%
+you can't get away with these piecewise
+linear functions that they're not good
+
+ align:start position:0%
+linear functions that they're not good
+ 
+
+ align:start position:0%
+linear functions that they're not good
+enough to describe say higher-order
+
+ align:start position:0%
+enough to describe say higher-order
+ 
+
+ align:start position:0%
+enough to describe say higher-order
+derivatives in your equation okay so you
+
+ align:start position:0%
+derivatives in your equation okay so you
+ 
+
+ align:start position:0%
+derivatives in your equation okay so you
+might instead interpolate with I don't
+
+ align:start position:0%
+might instead interpolate with I don't
+ 
+
+ align:start position:0%
+might instead interpolate with I don't
+know like a quadratic basis function
+
+ align:start position:0%
+know like a quadratic basis function
+ 
+
+ align:start position:0%
+know like a quadratic basis function
+that spans a few more points I'll be
+
+ align:start position:0%
+that spans a few more points I'll be
+ 
+
+ align:start position:0%
+that spans a few more points I'll be
+fine it would be easy to do the
+
+ align:start position:0%
+fine it would be easy to do the
+ 
+
+ align:start position:0%
+fine it would be easy to do the
+integration and your glucan method uses
+
+ align:start position:0%
+integration and your glucan method uses
+ 
+
+ align:start position:0%
+integration and your glucan method uses
+do these integrals out they're
+
+ align:start position:0%
+do these integrals out they're
+ 
+
+ align:start position:0%
+do these integrals out they're
+complicated but you do them do them once
+
+ align:start position:0%
+complicated but you do them do them once
+ 
+
+ align:start position:0%
+complicated but you do them do them once
+for a generic point X I and you know
+
+ align:start position:0%
+for a generic point X I and you know
+ 
+
+ align:start position:0%
+for a generic point X I and you know
+their value for every point in the
+
+ align:start position:0%
+their value for every point in the
+ 
+
+ align:start position:0%
+their value for every point in the
+domain okay so you choose them you
+
+ align:start position:0%
+domain okay so you choose them you
+ 
+
+ align:start position:0%
+domain okay so you choose them you
+choose the basis set okay but that's
+
+ align:start position:0%
+choose the basis set okay but that's
+ 
+
+ align:start position:0%
+choose the basis set okay but that's
+that W mean equation for the tenth
+
+ align:start position:0%
+that W mean equation for the tenth
+ 
+
+ align:start position:0%
+that W mean equation for the tenth
+function centered at X I that's the
+
+ align:start position:0%
+function centered at X I that's the
+ 
+
+ align:start position:0%
+function centered at X I that's the
+tenth function centered at any point in
+
+ align:start position:0%
+tenth function centered at any point in
+ 
+
+ align:start position:0%
+tenth function centered at any point in
+the domain in principle in many
+
+ align:start position:0%
+the domain in principle in many
+ 
+
+ align:start position:0%
+the domain in principle in many
+dimensions right so if I have two
+
+ align:start position:0%
+dimensions right so if I have two
+ 
+
+ align:start position:0%
+dimensions right so if I have two
+dimensions you see in COMSOL right you
+
+ align:start position:0%
+dimensions you see in COMSOL right you
+ 
+
+ align:start position:0%
+dimensions you see in COMSOL right you
+have a sort of a triangular mesh and
+
+ align:start position:0%
+have a sort of a triangular mesh and
+ 
+
+ align:start position:0%
+have a sort of a triangular mesh and
+what does my tenth function do it sort
+
+ align:start position:0%
+what does my tenth function do it sort
+ 
+
+ align:start position:0%
+what does my tenth function do it sort
+of stands up right stands up above the
+
+ align:start position:0%
+of stands up right stands up above the
+ 
+
+ align:start position:0%
+of stands up right stands up above the
+triangle it's a real tenth no it's
+
+ align:start position:0%
+triangle it's a real tenth no it's
+ 
+
+ align:start position:0%
+triangle it's a real tenth no it's
+coming out of the board can you see it
+
+ align:start position:0%
+coming out of the board can you see it
+ 
+
+ align:start position:0%
+coming out of the board can you see it
+put on your 3d glasses you'll see it
+
+ align:start position:0%
+put on your 3d glasses you'll see it
+ 
+
+ align:start position:0%
+put on your 3d glasses you'll see it
+then it's coming out of the board okay
+
+ align:start position:0%
+then it's coming out of the board okay
+ 
+
+ align:start position:0%
+then it's coming out of the board okay
+it has height one above this triangular
+
+ align:start position:0%
+it has height one above this triangular
+ 
+
+ align:start position:0%
+it has height one above this triangular
+domain right it sits at the center of
+
+ align:start position:0%
+domain right it sits at the center of
+ 
+
+ align:start position:0%
+domain right it sits at the center of
+the triangle for exams one way to draw
+
+ align:start position:0%
+the triangle for exams one way to draw
+ 
+
+ align:start position:0%
+the triangle for exams one way to draw
+these elements actually many ways to
+
+ align:start position:0%
+these elements actually many ways to
+ 
+
+ align:start position:0%
+these elements actually many ways to
+draw these offices just one way of
+
+ align:start position:0%
+draw these offices just one way of
+ 
+
+ align:start position:0%
+draw these offices just one way of
+drawing these oh that's okay
+
+ align:start position:0%
+drawing these oh that's okay
+ 
+
+ align:start position:0%
+drawing these oh that's okay
+good other questions
+
+ align:start position:0%
+good other questions
+ 
+
+ align:start position:0%
+good other questions
+oh good question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good question so why is central
+
+ align:start position:0%
+good question so why is central
+ 
+
+ align:start position:0%
+good question so why is central
+differencing second order accurate so
+
+ align:start position:0%
+differencing second order accurate so
+ 
+
+ align:start position:0%
+differencing second order accurate so
+the central difference formula says that
+
+ align:start position:0%
+the central difference formula says that
+ 
+
+ align:start position:0%
+the central difference formula says that
+the derivative of a function X could be
+
+ align:start position:0%
+the derivative of a function X could be
+ 
+
+ align:start position:0%
+the derivative of a function X could be
+written as its f at X I plus 1 minus F
+
+ align:start position:0%
+written as its f at X I plus 1 minus F
+ 
+
+ align:start position:0%
+written as its f at X I plus 1 minus F
+at X I minus 1/2 Delta X or let's say
+
+ align:start position:0%
+at X I minus 1/2 Delta X or let's say
+ 
+
+ align:start position:0%
+at X I minus 1/2 Delta X or let's say
+these aren't equally spaced points well
+
+ align:start position:0%
+these aren't equally spaced points well
+ 
+
+ align:start position:0%
+these aren't equally spaced points well
+let's make these equally spaced points
+
+ align:start position:0%
+let's make these equally spaced points
+ 
+
+ align:start position:0%
+let's make these equally spaced points
+for now let's make it easy okay so let's
+
+ align:start position:0%
+for now let's make it easy okay so let's
+ 
+
+ align:start position:0%
+for now let's make it easy okay so let's
+say X I plus Delta X and X I - day it'll
+
+ align:start position:0%
+say X I plus Delta X and X I - day it'll
+ 
+
+ align:start position:0%
+say X I plus Delta X and X I - day it'll
+make our lives easier if we do it this
+
+ align:start position:0%
+make our lives easier if we do it this
+ 
+
+ align:start position:0%
+make our lives easier if we do it this
+way it can be generalized but let's
+
+ align:start position:0%
+way it can be generalized but let's
+ 
+
+ align:start position:0%
+way it can be generalized but let's
+let's let's do it the easiest possible
+
+ align:start position:0%
+let's let's do it the easiest possible
+ 
+
+ align:start position:0%
+let's let's do it the easiest possible
+way and this is the derivative at the
+
+ align:start position:0%
+way and this is the derivative at the
+ 
+
+ align:start position:0%
+way and this is the derivative at the
+point X I write graphically okay here's
+
+ align:start position:0%
+point X I write graphically okay here's
+ 
+
+ align:start position:0%
+point X I write graphically okay here's
+X here's X I right here's my function
+
+ align:start position:0%
+X here's X I right here's my function
+ 
+
+ align:start position:0%
+X here's X I right here's my function
+okay I want to know what the slope here
+
+ align:start position:0%
+okay I want to know what the slope here
+ 
+
+ align:start position:0%
+okay I want to know what the slope here
+is okay and I'm gonna proximate it by
+
+ align:start position:0%
+is okay and I'm gonna proximate it by
+ 
+
+ align:start position:0%
+is okay and I'm gonna proximate it by
+looking one point upstream and one point
+
+ align:start position:0%
+looking one point upstream and one point
+ 
+
+ align:start position:0%
+looking one point upstream and one point
+downstream okay and I'm gonna connect
+
+ align:start position:0%
+downstream okay and I'm gonna connect
+ 
+
+ align:start position:0%
+downstream okay and I'm gonna connect
+those points with a line you would agree
+
+ align:start position:0%
+those points with a line you would agree
+ 
+
+ align:start position:0%
+those points with a line you would agree
+that is the one as this spacing gets
+
+ align:start position:0%
+that is the one as this spacing gets
+ 
+
+ align:start position:0%
+that is the one as this spacing gets
+smaller and smaller it'll be a good
+
+ align:start position:0%
+smaller and smaller it'll be a good
+ 
+
+ align:start position:0%
+smaller and smaller it'll be a good
+approximation for what the derivative is
+
+ align:start position:0%
+approximation for what the derivative is
+ 
+
+ align:start position:0%
+approximation for what the derivative is
+so why is it second-order accurate so
+
+ align:start position:0%
+so why is it second-order accurate so
+ 
+
+ align:start position:0%
+so why is it second-order accurate so
+you can show that it's not too hard okay
+
+ align:start position:0%
+you can show that it's not too hard okay
+ 
+
+ align:start position:0%
+you can show that it's not too hard okay
+you can show that using Taylor series
+
+ align:start position:0%
+you can show that using Taylor series
+ 
+
+ align:start position:0%
+you can show that using Taylor series
+expansion like everything else in this
+
+ align:start position:0%
+expansion like everything else in this
+ 
+
+ align:start position:0%
+expansion like everything else in this
+course right the Taylor series is really
+
+ align:start position:0%
+course right the Taylor series is really
+ 
+
+ align:start position:0%
+course right the Taylor series is really
+a key so let's let's look at it okay
+
+ align:start position:0%
+a key so let's let's look at it okay
+ 
+
+ align:start position:0%
+a key so let's let's look at it okay
+so f at X I plus Delta X I want to write
+
+ align:start position:0%
+so f at X I plus Delta X I want to write
+ 
+
+ align:start position:0%
+so f at X I plus Delta X I want to write
+this as a Taylor series expansion about
+
+ align:start position:0%
+this as a Taylor series expansion about
+ 
+
+ align:start position:0%
+this as a Taylor series expansion about
+the point X I okay so tell me the first
+
+ align:start position:0%
+the point X I okay so tell me the first
+ 
+
+ align:start position:0%
+the point X I okay so tell me the first
+term f of X I okay tell me the second
+
+ align:start position:0%
+term f of X I okay tell me the second
+ 
+
+ align:start position:0%
+term f of X I okay tell me the second
+term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f Prime at X I times Delta X tell me the
+
+ align:start position:0%
+f Prime at X I times Delta X tell me the
+ 
+
+ align:start position:0%
+f Prime at X I times Delta X tell me the
+third term 1/2 F double Prime at times
+
+ align:start position:0%
+third term 1/2 F double Prime at times
+ 
+
+ align:start position:0%
+third term 1/2 F double Prime at times
+how big is the third term okay this is
+
+ align:start position:0%
+how big is the third term okay this is
+ 
+
+ align:start position:0%
+how big is the third term okay this is
+always true by the way this not always
+
+ align:start position:0%
+always true by the way this not always
+ 
+
+ align:start position:0%
+always true by the way this not always
+right there are lots of functions non
+
+ align:start position:0%
+right there are lots of functions non
+ 
+
+ align:start position:0%
+right there are lots of functions non
+analytic functions that don't have these
+
+ align:start position:0%
+analytic functions that don't have these
+ 
+
+ align:start position:0%
+analytic functions that don't have these
+sorts of expansions so we're sort of we
+
+ align:start position:0%
+sorts of expansions so we're sort of we
+ 
+
+ align:start position:0%
+sorts of expansions so we're sort of we
+got to have a function that has these
+
+ align:start position:0%
+got to have a function that has these
+ 
+
+ align:start position:0%
+got to have a function that has these
+derivatives they need to exist at the
+
+ align:start position:0%
+derivatives they need to exist at the
+ 
+
+ align:start position:0%
+derivatives they need to exist at the
+point X I let's assume that's true
+
+ align:start position:0%
+point X I let's assume that's true
+ 
+
+ align:start position:0%
+point X I let's assume that's true
+ok good ok now I'm going to do something
+
+ align:start position:0%
+ok good ok now I'm going to do something
+ 
+
+ align:start position:0%
+ok good ok now I'm going to do something
+really simple let's let's write F at X X
+
+ align:start position:0%
+really simple let's let's write F at X X
+ 
+
+ align:start position:0%
+really simple let's let's write F at X X
+I'm minus Delta X ok and let's just
+
+ align:start position:0%
+I'm minus Delta X ok and let's just
+ 
+
+ align:start position:0%
+I'm minus Delta X ok and let's just
+point out the differences between these
+
+ align:start position:0%
+point out the differences between these
+ 
+
+ align:start position:0%
+point out the differences between these
+two formulas ok so this is the same ok
+
+ align:start position:0%
+two formulas ok so this is the same ok
+ 
+
+ align:start position:0%
+two formulas ok so this is the same ok
+this switches sign because Delta X which
+
+ align:start position:0%
+this switches sign because Delta X which
+ 
+
+ align:start position:0%
+this switches sign because Delta X which
+signs was plus Delta X now it's minus
+
+ align:start position:0%
+signs was plus Delta X now it's minus
+ 
+
+ align:start position:0%
+signs was plus Delta X now it's minus
+Delta X ok this is the same Delta x
+
+ align:start position:0%
+Delta X ok this is the same Delta x
+ 
+
+ align:start position:0%
+Delta X ok this is the same Delta x
+squared same as minus Delta x squared
+
+ align:start position:0%
+squared same as minus Delta x squared
+ 
+
+ align:start position:0%
+squared same as minus Delta x squared
+doesn't matter ok this one down here
+
+ align:start position:0%
+doesn't matter ok this one down here
+ 
+
+ align:start position:0%
+doesn't matter ok this one down here
+well ok its order Delta X cubed ok it'll
+
+ align:start position:0%
+well ok its order Delta X cubed ok it'll
+ 
+
+ align:start position:0%
+well ok its order Delta X cubed ok it'll
+actually look the same but have the
+
+ align:start position:0%
+actually look the same but have the
+ 
+
+ align:start position:0%
+actually look the same but have the
+opposite sign ok we can't resolve it
+
+ align:start position:0%
+opposite sign ok we can't resolve it
+ 
+
+ align:start position:0%
+opposite sign ok we can't resolve it
+though that's sort of the tricky part
+
+ align:start position:0%
+though that's sort of the tricky part
+ 
+
+ align:start position:0%
+though that's sort of the tricky part
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+we don't know ok we don't know for sure
+
+ align:start position:0%
+we don't know ok we don't know for sure
+ 
+
+ align:start position:0%
+we don't know ok we don't know for sure
+what value that takes on this just gives
+
+ align:start position:0%
+what value that takes on this just gives
+ 
+
+ align:start position:0%
+what value that takes on this just gives
+us a bound for how big the air is in
+
+ align:start position:0%
+us a bound for how big the air is in
+ 
+
+ align:start position:0%
+us a bound for how big the air is in
+this expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's now compute what's in that
+
+ align:start position:0%
+so let's now compute what's in that
+ 
+
+ align:start position:0%
+so let's now compute what's in that
+formula so if we take the difference
+
+ align:start position:0%
+formula so if we take the difference
+ 
+
+ align:start position:0%
+formula so if we take the difference
+between this and this ok these two will
+
+ align:start position:0%
+between this and this ok these two will
+ 
+
+ align:start position:0%
+between this and this ok these two will
+cancel ok these two will combine I'll
+
+ align:start position:0%
+cancel ok these two will combine I'll
+ 
+
+ align:start position:0%
+cancel ok these two will combine I'll
+get to F prime X I times Delta X these
+
+ align:start position:0%
+get to F prime X I times Delta X these
+ 
+
+ align:start position:0%
+get to F prime X I times Delta X these
+two will cancel ok so I'll get 0
+
+ align:start position:0%
+two will cancel ok so I'll get 0
+ 
+
+ align:start position:0%
+two will cancel ok so I'll get 0
+these two okay I can't rely on them
+
+ align:start position:0%
+these two okay I can't rely on them
+ 
+
+ align:start position:0%
+these two okay I can't rely on them
+necessarily necessarily cancelling each
+
+ align:start position:0%
+necessarily necessarily cancelling each
+ 
+
+ align:start position:0%
+necessarily necessarily cancelling each
+other out in fact they want to combine
+
+ align:start position:0%
+other out in fact they want to combine
+ 
+
+ align:start position:0%
+other out in fact they want to combine
+in principle right we've just bounded
+
+ align:start position:0%
+in principle right we've just bounded
+ 
+
+ align:start position:0%
+in principle right we've just bounded
+the air here we don't really know what
+
+ align:start position:0%
+the air here we don't really know what
+ 
+
+ align:start position:0%
+the air here we don't really know what
+it is but it gives me something that's
+
+ align:start position:0%
+it is but it gives me something that's
+ 
+
+ align:start position:0%
+it is but it gives me something that's
+order Delta X cubed in size okay so this
+
+ align:start position:0%
+order Delta X cubed in size okay so this
+ 
+
+ align:start position:0%
+order Delta X cubed in size okay so this
+is the this is one minus one minus two
+
+ align:start position:0%
+is the this is one minus one minus two
+ 
+
+ align:start position:0%
+is the this is one minus one minus two
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it's two F prime X I times Delta X plus
+
+ align:start position:0%
+it's two F prime X I times Delta X plus
+ 
+
+ align:start position:0%
+it's two F prime X I times Delta X plus
+the air which is order Delta X cubed if
+
+ align:start position:0%
+the air which is order Delta X cubed if
+ 
+
+ align:start position:0%
+the air which is order Delta X cubed if
+I divide by two Delta X ok I know you
+
+ align:start position:0%
+I divide by two Delta X ok I know you
+ 
+
+ align:start position:0%
+I divide by two Delta X ok I know you
+guys hate it when the instructor does
+
+ align:start position:0%
+guys hate it when the instructor does
+ 
+
+ align:start position:0%
+guys hate it when the instructor does
+this but you know you can't can't help
+
+ align:start position:0%
+this but you know you can't can't help
+ 
+
+ align:start position:0%
+this but you know you can't can't help
+it divided by Delta X the error becomes
+
+ align:start position:0%
+it divided by Delta X the error becomes
+ 
+
+ align:start position:0%
+it divided by Delta X the error becomes
+order Delta x squared okay so have the
+
+ align:start position:0%
+order Delta x squared okay so have the
+ 
+
+ align:start position:0%
+order Delta x squared okay so have the
+derivative is this thing plus some order
+
+ align:start position:0%
+derivative is this thing plus some order
+ 
+
+ align:start position:0%
+derivative is this thing plus some order
+Delta x squared peace its second order
+
+ align:start position:0%
+Delta x squared peace its second order
+ 
+
+ align:start position:0%
+Delta x squared peace its second order
+accurate we would say great the air is
+
+ align:start position:0%
+accurate we would say great the air is
+ 
+
+ align:start position:0%
+accurate we would say great the air is
+going to be reduced like the square of
+
+ align:start position:0%
+going to be reduced like the square of
+ 
+
+ align:start position:0%
+going to be reduced like the square of
+the spacing now you can imagine all the
+
+ align:start position:0%
+the spacing now you can imagine all the
+ 
+
+ align:start position:0%
+the spacing now you can imagine all the
+finite difference formulas out there in
+
+ align:start position:0%
+finite difference formulas out there in
+ 
+
+ align:start position:0%
+finite difference formulas out there in
+the world are constructed in this way
+
+ align:start position:0%
+the world are constructed in this way
+ 
+
+ align:start position:0%
+the world are constructed in this way
+right you use Taylor series expansions
+
+ align:start position:0%
+right you use Taylor series expansions
+ 
+
+ align:start position:0%
+right you use Taylor series expansions
+you got as many terms as you need to go
+
+ align:start position:0%
+you got as many terms as you need to go
+ 
+
+ align:start position:0%
+you got as many terms as you need to go
+for the level of accuracy you're trying
+
+ align:start position:0%
+for the level of accuracy you're trying
+ 
+
+ align:start position:0%
+for the level of accuracy you're trying
+to achieve for different points spaced
+
+ align:start position:0%
+to achieve for different points spaced
+ 
+
+ align:start position:0%
+to achieve for different points spaced
+in different ways and you you try to try
+
+ align:start position:0%
+in different ways and you you try to try
+ 
+
+ align:start position:0%
+in different ways and you you try to try
+to dream up some linear combination of
+
+ align:start position:0%
+to dream up some linear combination of
+ 
+
+ align:start position:0%
+to dream up some linear combination of
+these things so that you get a certain
+
+ align:start position:0%
+these things so that you get a certain
+ 
+
+ align:start position:0%
+these things so that you get a certain
+certain level of accuracy okay they're
+
+ align:start position:0%
+certain level of accuracy okay they're
+ 
+
+ align:start position:0%
+certain level of accuracy okay they're
+also not unique right I can construct
+
+ align:start position:0%
+also not unique right I can construct
+ 
+
+ align:start position:0%
+also not unique right I can construct
+these in a lot of different ways okay
+
+ align:start position:0%
+these in a lot of different ways okay
+ 
+
+ align:start position:0%
+these in a lot of different ways okay
+and have the same same sort of error
+
+ align:start position:0%
+and have the same same sort of error
+ 
+
+ align:start position:0%
+and have the same same sort of error
+level out here okay but different
+
+ align:start position:0%
+level out here okay but different
+ 
+
+ align:start position:0%
+level out here okay but different
+coefficients associated with the air but
+
+ align:start position:0%
+coefficients associated with the air but
+ 
+
+ align:start position:0%
+coefficients associated with the air but
+the same overall scaling and then you
+
+ align:start position:0%
+the same overall scaling and then you
+ 
+
+ align:start position:0%
+the same overall scaling and then you
+might choose different approximations
+
+ align:start position:0%
+might choose different approximations
+ 
+
+ align:start position:0%
+might choose different approximations
+for other reasons Sam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I mean yeah so if let's say you go
+
+ align:start position:0%
+well I mean yeah so if let's say you go
+ 
+
+ align:start position:0%
+well I mean yeah so if let's say you go
+out further right what's the next term
+
+ align:start position:0%
+out further right what's the next term
+ 
+
+ align:start position:0%
+out further right what's the next term
+here it's gonna be one over six F triple
+
+ align:start position:0%
+here it's gonna be one over six F triple
+ 
+
+ align:start position:0%
+here it's gonna be one over six F triple
+prime X I Delta X cubed okay and here
+
+ align:start position:0%
+prime X I Delta X cubed okay and here
+ 
+
+ align:start position:0%
+prime X I Delta X cubed okay and here
+you'll have minus that because I cube
+
+ align:start position:0%
+you'll have minus that because I cube
+ 
+
+ align:start position:0%
+you'll have minus that because I cube
+the Delta X so when I combine them right
+
+ align:start position:0%
+the Delta X so when I combine them right
+ 
+
+ align:start position:0%
+the Delta X so when I combine them right
+I'll actually get 1 over 3 F triple
+
+ align:start position:0%
+I'll actually get 1 over 3 F triple
+ 
+
+ align:start position:0%
+I'll actually get 1 over 3 F triple
+prime and so I could I could do a little
+
+ align:start position:0%
+prime and so I could I could do a little
+ 
+
+ align:start position:0%
+prime and so I could I could do a little
+better if I knew what my function was I
+
+ align:start position:0%
+better if I knew what my function was I
+ 
+
+ align:start position:0%
+better if I knew what my function was I
+can tell you exactly how big the air was
+
+ align:start position:0%
+can tell you exactly how big the air was
+ 
+
+ align:start position:0%
+can tell you exactly how big the air was
+right I can tell you that it was as big
+
+ align:start position:0%
+right I can tell you that it was as big
+ 
+
+ align:start position:0%
+right I can tell you that it was as big
+as the third derivative of F my function
+
+ align:start position:0%
+as the third derivative of F my function
+ 
+
+ align:start position:0%
+as the third derivative of F my function
+doesn't have a third derivative at that
+
+ align:start position:0%
+doesn't have a third derivative at that
+ 
+
+ align:start position:0%
+doesn't have a third derivative at that
+point the air might be huge and it's
+
+ align:start position:0%
+point the air might be huge and it's
+ 
+
+ align:start position:0%
+point the air might be huge and it's
+possible to construct functions that
+
+ align:start position:0%
+possible to construct functions that
+ 
+
+ align:start position:0%
+possible to construct functions that
+that lack that particular property ok so
+
+ align:start position:0%
+that lack that particular property ok so
+ 
+
+ align:start position:0%
+that lack that particular property ok so
+you can go out further and you can use
+
+ align:start position:0%
+you can go out further and you can use
+ 
+
+ align:start position:0%
+you can go out further and you can use
+it to sort of quantify exactly exactly
+
+ align:start position:0%
+it to sort of quantify exactly exactly
+ 
+
+ align:start position:0%
+it to sort of quantify exactly exactly
+how big you think the air might be in
+
+ align:start position:0%
+how big you think the air might be in
+ 
+
+ align:start position:0%
+how big you think the air might be in
+the approximation it's all constructed
+
+ align:start position:0%
+the approximation it's all constructed
+ 
+
+ align:start position:0%
+the approximation it's all constructed
+from linear combinations of different
+
+ align:start position:0%
+from linear combinations of different
+ 
+
+ align:start position:0%
+from linear combinations of different
+Taylor expansions ok about nearby points
+
+ align:start position:0%
+Taylor expansions ok about nearby points
+ 
+
+ align:start position:0%
+Taylor expansions ok about nearby points
+and and the related problem actually the
+
+ align:start position:0%
+and and the related problem actually the
+ 
+
+ align:start position:0%
+and and the related problem actually the
+equivalent problem is polynomial
+
+ align:start position:0%
+equivalent problem is polynomial
+ 
+
+ align:start position:0%
+equivalent problem is polynomial
+interpolation ok
+
+ align:start position:0%
+interpolation ok
+ 
+
+ align:start position:0%
+interpolation ok
+so the sort of if you can somehow in
+
+ align:start position:0%
+so the sort of if you can somehow in
+ 
+
+ align:start position:0%
+so the sort of if you can somehow in
+your mind transpose this problem it
+
+ align:start position:0%
+your mind transpose this problem it
+ 
+
+ align:start position:0%
+your mind transpose this problem it
+looks a lot like polynomial
+
+ align:start position:0%
+looks a lot like polynomial
+ 
+
+ align:start position:0%
+looks a lot like polynomial
+interpolation so these two are
+
+ align:start position:0%
+interpolation so these two are
+ 
+
+ align:start position:0%
+interpolation so these two are
+intimately related to each other yeah
+
+ align:start position:0%
+intimately related to each other yeah
+ 
+
+ align:start position:0%
+intimately related to each other yeah
+yes how much do you have to know about
+
+ align:start position:0%
+yes how much do you have to know about
+ 
+
+ align:start position:0%
+yes how much do you have to know about
+polynomial interpolation well say that
+
+ align:start position:0%
+polynomial interpolation well say that
+ 
+
+ align:start position:0%
+polynomial interpolation well say that
+again what do I want to say about that I
+
+ align:start position:0%
+again what do I want to say about that I
+ 
+
+ align:start position:0%
+again what do I want to say about that I
+wouldn't expect that level of detail I
+
+ align:start position:0%
+wouldn't expect that level of detail I
+ 
+
+ align:start position:0%
+wouldn't expect that level of detail I
+think it's quite difficult to construct
+
+ align:start position:0%
+think it's quite difficult to construct
+ 
+
+ align:start position:0%
+think it's quite difficult to construct
+Lagrange polynomial expansions by hand I
+
+ align:start position:0%
+Lagrange polynomial expansions by hand I
+ 
+
+ align:start position:0%
+Lagrange polynomial expansions by hand I
+don't know anyone who does that
+
+ align:start position:0%
+don't know anyone who does that
+ 
+
+ align:start position:0%
+don't know anyone who does that
+professionally or for pleasure I think
+
+ align:start position:0%
+professionally or for pleasure I think
+ 
+
+ align:start position:0%
+professionally or for pleasure I think
+I think that's a I think that's a bad
+
+ align:start position:0%
+I think that's a I think that's a bad
+ 
+
+ align:start position:0%
+I think that's a I think that's a bad
+idea you should understand polynomial
+
+ align:start position:0%
+idea you should understand polynomial
+ 
+
+ align:start position:0%
+idea you should understand polynomial
+interpolation you should understand the
+
+ align:start position:0%
+interpolation you should understand the
+ 
+
+ align:start position:0%
+interpolation you should understand the
+contexts in which it's important right
+
+ align:start position:0%
+contexts in which it's important right
+ 
+
+ align:start position:0%
+contexts in which it's important right
+when is Paulette what is polynomial
+
+ align:start position:0%
+when is Paulette what is polynomial
+ 
+
+ align:start position:0%
+when is Paulette what is polynomial
+interpolation for important for
+
+ align:start position:0%
+interpolation for important for
+ 
+
+ align:start position:0%
+interpolation for important for
+numerically do you recall her sure
+
+ align:start position:0%
+numerically do you recall her sure
+ 
+
+ align:start position:0%
+numerically do you recall her sure
+numerical integration right so this was
+
+ align:start position:0%
+numerical integration right so this was
+ 
+
+ align:start position:0%
+numerical integration right so this was
+this was really the key to numerical
+
+ align:start position:0%
+this was really the key to numerical
+ 
+
+ align:start position:0%
+this was really the key to numerical
+integration was trying to construct
+
+ align:start position:0%
+integration was trying to construct
+ 
+
+ align:start position:0%
+integration was trying to construct
+appropriate approximations of our
+
+ align:start position:0%
+appropriate approximations of our
+ 
+
+ align:start position:0%
+appropriate approximations of our
+function from a finite set of data and
+
+ align:start position:0%
+function from a finite set of data and
+ 
+
+ align:start position:0%
+function from a finite set of data and
+figure out the area under the curve so
+
+ align:start position:0%
+figure out the area under the curve so
+ 
+
+ align:start position:0%
+figure out the area under the curve so
+you should you should understand how one
+
+ align:start position:0%
+you should you should understand how one
+ 
+
+ align:start position:0%
+you should you should understand how one
+uses polynomial interpolation to do
+
+ align:start position:0%
+uses polynomial interpolation to do
+ 
+
+ align:start position:0%
+uses polynomial interpolation to do
+numerical integration but I wouldn't
+
+ align:start position:0%
+numerical integration but I wouldn't
+ 
+
+ align:start position:0%
+numerical integration but I wouldn't
+expect us to ask you to to actually
+
+ align:start position:0%
+expect us to ask you to to actually
+ 
+
+ align:start position:0%
+expect us to ask you to to actually
+compute polynomial interpolant and and
+
+ align:start position:0%
+compute polynomial interpolant and and
+ 
+
+ align:start position:0%
+compute polynomial interpolant and and
+numerically integrate it by hand I think
+
+ align:start position:0%
+numerically integrate it by hand I think
+ 
+
+ align:start position:0%
+numerically integrate it by hand I think
+that didn't exist that's too much okay
+
+ align:start position:0%
+that didn't exist that's too much okay
+ 
+
+ align:start position:0%
+that didn't exist that's too much okay
+okay four questions first sure for OTE
+
+ align:start position:0%
+okay four questions first sure for OTE
+ 
+
+ align:start position:0%
+okay four questions first sure for OTE
+OTE IBP okay okay so we have to have an
+
+ align:start position:0%
+OTE IBP okay okay so we have to have an
+ 
+
+ align:start position:0%
+OTE IBP okay okay so we have to have an
+OD we want to solve can I just do can I
+
+ align:start position:0%
+OD we want to solve can I just do can I
+ 
+
+ align:start position:0%
+OD we want to solve can I just do can I
+do one one dimensional unknown do I need
+
+ align:start position:0%
+do one one dimensional unknown do I need
+ 
+
+ align:start position:0%
+do one one dimensional unknown do I need
+to do a vector here can I just would you
+
+ align:start position:0%
+to do a vector here can I just would you
+ 
+
+ align:start position:0%
+to do a vector here can I just would you
+be satisfied if I wrote this as F of yn
+
+ align:start position:0%
+be satisfied if I wrote this as F of yn
+ 
+
+ align:start position:0%
+be satisfied if I wrote this as F of yn
+T and that it's sufficiently general
+
+ align:start position:0%
+T and that it's sufficiently general
+ 
+
+ align:start position:0%
+T and that it's sufficiently general
+that wait out that blame me when I
+
+ align:start position:0%
+that wait out that blame me when I
+ 
+
+ align:start position:0%
+that wait out that blame me when I
+forget to underscore things along the
+
+ align:start position:0%
+forget to underscore things along the
+ 
+
+ align:start position:0%
+forget to underscore things along the
+way and we don't have to think about
+
+ align:start position:0%
+way and we don't have to think about
+ 
+
+ align:start position:0%
+way and we don't have to think about
+such Akopian or anything like that okay
+
+ align:start position:0%
+such Akopian or anything like that okay
+ 
+
+ align:start position:0%
+such Akopian or anything like that okay
+so oh time derivative right so there's
+
+ align:start position:0%
+so oh time derivative right so there's
+ 
+
+ align:start position:0%
+so oh time derivative right so there's
+the OD we're gonna solve the trapezoid
+
+ align:start position:0%
+the OD we're gonna solve the trapezoid
+ 
+
+ align:start position:0%
+the OD we're gonna solve the trapezoid
+rule okay so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do this the following way especially I
+
+ align:start position:0%
+do this the following way especially I
+ 
+
+ align:start position:0%
+do this the following way especially I
+wind up looking very similar to what we
+
+ align:start position:0%
+wind up looking very similar to what we
+ 
+
+ align:start position:0%
+wind up looking very similar to what we
+just did which is useful I might even be
+
+ align:start position:0%
+just did which is useful I might even be
+ 
+
+ align:start position:0%
+just did which is useful I might even be
+able to pull that board down and reuse
+
+ align:start position:0%
+able to pull that board down and reuse
+ 
+
+ align:start position:0%
+able to pull that board down and reuse
+it at a certain point so that'll be good
+
+ align:start position:0%
+it at a certain point so that'll be good
+ 
+
+ align:start position:0%
+it at a certain point so that'll be good
+let's do this so what is ultimately what
+
+ align:start position:0%
+let's do this so what is ultimately what
+ 
+
+ align:start position:0%
+let's do this so what is ultimately what
+is ODI VP solving like what are you
+
+ align:start position:0%
+is ODI VP solving like what are you
+ 
+
+ align:start position:0%
+is ODI VP solving like what are you
+trying to do when you solve one of these
+
+ align:start position:0%
+trying to do when you solve one of these
+ 
+
+ align:start position:0%
+trying to do when you solve one of these
+things it's extrapolation right I don't
+
+ align:start position:0%
+things it's extrapolation right I don't
+ 
+
+ align:start position:0%
+things it's extrapolation right I don't
+I know the value of y initially I'm
+
+ align:start position:0%
+I know the value of y initially I'm
+ 
+
+ align:start position:0%
+I know the value of y initially I'm
+trying to figure out where the hell this
+
+ align:start position:0%
+trying to figure out where the hell this
+ 
+
+ align:start position:0%
+trying to figure out where the hell this
+thing is going okay I've gotta
+
+ align:start position:0%
+thing is going okay I've gotta
+ 
+
+ align:start position:0%
+thing is going okay I've gotta
+extrapolate forward and you should be
+
+ align:start position:0%
+extrapolate forward and you should be
+ 
+
+ align:start position:0%
+extrapolate forward and you should be
+very uncomfortable with the notion that
+
+ align:start position:0%
+very uncomfortable with the notion that
+ 
+
+ align:start position:0%
+very uncomfortable with the notion that
+I can do that right how good a job can I
+
+ align:start position:0%
+I can do that right how good a job can I
+ 
+
+ align:start position:0%
+I can do that right how good a job can I
+do predicting the future knowing how
+
+ align:start position:0%
+do predicting the future knowing how
+ 
+
+ align:start position:0%
+do predicting the future knowing how
+things are now it's really quite quite
+
+ align:start position:0%
+things are now it's really quite quite
+ 
+
+ align:start position:0%
+things are now it's really quite quite
+complicated in fact it's so complicated
+
+ align:start position:0%
+complicated in fact it's so complicated
+ 
+
+ align:start position:0%
+complicated in fact it's so complicated
+right there are certain circumstances in
+
+ align:start position:0%
+right there are certain circumstances in
+ 
+
+ align:start position:0%
+right there are certain circumstances in
+which it's not really possible
+
+ align:start position:0%
+which it's not really possible
+ 
+
+ align:start position:0%
+which it's not really possible
+discovered here at MIT actually right so
+
+ align:start position:0%
+discovered here at MIT actually right so
+ 
+
+ align:start position:0%
+discovered here at MIT actually right so
+there was weather research going on at a
+
+ align:start position:0%
+there was weather research going on at a
+ 
+
+ align:start position:0%
+there was weather research going on at a
+certain point at MIT right it's a very
+
+ align:start position:0%
+certain point at MIT right it's a very
+ 
+
+ align:start position:0%
+certain point at MIT right it's a very
+famous case researcher a very famous
+
+ align:start position:0%
+famous case researcher a very famous
+ 
+
+ align:start position:0%
+famous case researcher a very famous
+researcher was doing numerical
+
+ align:start position:0%
+researcher was doing numerical
+ 
+
+ align:start position:0%
+researcher was doing numerical
+simulations of a weather model in Eau de
+
+ align:start position:0%
+simulations of a weather model in Eau de
+ 
+
+ align:start position:0%
+simulations of a weather model in Eau de
+IVP okay he ran it for a while and he
+
+ align:start position:0%
+IVP okay he ran it for a while and he
+ 
+
+ align:start position:0%
+IVP okay he ran it for a while and he
+stopped he looked at his end state right
+
+ align:start position:0%
+stopped he looked at his end state right
+ 
+
+ align:start position:0%
+stopped he looked at his end state right
+the last value of y in his simulation
+
+ align:start position:0%
+the last value of y in his simulation
+ 
+
+ align:start position:0%
+the last value of y in his simulation
+he put in three digits used that as the
+
+ align:start position:0%
+he put in three digits used that as the
+ 
+
+ align:start position:0%
+he put in three digits used that as the
+initial condition and started a
+
+ align:start position:0%
+initial condition and started a
+ 
+
+ align:start position:0%
+initial condition and started a
+simulation again and it went wacky right
+
+ align:start position:0%
+simulation again and it went wacky right
+ 
+
+ align:start position:0%
+simulation again and it went wacky right
+didn't look anything like the initial
+
+ align:start position:0%
+didn't look anything like the initial
+ 
+
+ align:start position:0%
+didn't look anything like the initial
+solution okay
+
+ align:start position:0%
+solution okay
+ 
+
+ align:start position:0%
+solution okay
+how did that happen right it seemed fine
+
+ align:start position:0%
+how did that happen right it seemed fine
+ 
+
+ align:start position:0%
+how did that happen right it seemed fine
+up to that point solutions cranking
+
+ align:start position:0%
+up to that point solutions cranking
+ 
+
+ align:start position:0%
+up to that point solutions cranking
+along he stopped okay he took three
+
+ align:start position:0%
+along he stopped okay he took three
+ 
+
+ align:start position:0%
+along he stopped okay he took three
+digits accuracy out of the computer and
+
+ align:start position:0%
+digits accuracy out of the computer and
+ 
+
+ align:start position:0%
+digits accuracy out of the computer and
+he started again and it did something
+
+ align:start position:0%
+he started again and it did something
+ 
+
+ align:start position:0%
+he started again and it did something
+else okay all right so there they're
+
+ align:start position:0%
+else okay all right so there they're
+ 
+
+ align:start position:0%
+else okay all right so there they're
+problems that are inherently chaotic and
+
+ align:start position:0%
+problems that are inherently chaotic and
+ 
+
+ align:start position:0%
+problems that are inherently chaotic and
+very sensitive to their initial
+
+ align:start position:0%
+very sensitive to their initial
+ 
+
+ align:start position:0%
+very sensitive to their initial
+conditions right they're hard to resolve
+
+ align:start position:0%
+conditions right they're hard to resolve
+ 
+
+ align:start position:0%
+conditions right they're hard to resolve
+so the entire point of doing this sort
+
+ align:start position:0%
+so the entire point of doing this sort
+ 
+
+ align:start position:0%
+so the entire point of doing this sort
+of analysis of OD IV pieces at least in
+
+ align:start position:0%
+of analysis of OD IV pieces at least in
+ 
+
+ align:start position:0%
+of analysis of OD IV pieces at least in
+the best case scenarios right we want to
+
+ align:start position:0%
+the best case scenarios right we want to
+ 
+
+ align:start position:0%
+the best case scenarios right we want to
+try to manage the error associated with
+
+ align:start position:0%
+try to manage the error associated with
+ 
+
+ align:start position:0%
+try to manage the error associated with
+these kinds of extrapolation in some
+
+ align:start position:0%
+these kinds of extrapolation in some
+ 
+
+ align:start position:0%
+these kinds of extrapolation in some
+cases it's really not it's really not
+
+ align:start position:0%
+cases it's really not it's really not
+ 
+
+ align:start position:0%
+cases it's really not it's really not
+very possible okay you don't know the
+
+ align:start position:0%
+very possible okay you don't know the
+ 
+
+ align:start position:0%
+very possible okay you don't know the
+initial conditions well enough to
+
+ align:start position:0%
+initial conditions well enough to
+ 
+
+ align:start position:0%
+initial conditions well enough to
+predict what the final state is so there
+
+ align:start position:0%
+predict what the final state is so there
+ 
+
+ align:start position:0%
+predict what the final state is so there
+are problems that are inherently
+
+ align:start position:0%
+are problems that are inherently
+ 
+
+ align:start position:0%
+are problems that are inherently
+unstable or sensitive to their initial
+
+ align:start position:0%
+unstable or sensitive to their initial
+ 
+
+ align:start position:0%
+unstable or sensitive to their initial
+conditions they don't have to blow up
+
+ align:start position:0%
+conditions they don't have to blow up
+ 
+
+ align:start position:0%
+conditions they don't have to blow up
+either they can find themselves moving
+
+ align:start position:0%
+either they can find themselves moving
+ 
+
+ align:start position:0%
+either they can find themselves moving
+through the phase space
+
+ align:start position:0%
+through the phase space
+ 
+
+ align:start position:0%
+through the phase space
+in some way that's very very sensitive
+
+ align:start position:0%
+in some way that's very very sensitive
+ 
+
+ align:start position:0%
+in some way that's very very sensitive
+and two points that start very close
+
+ align:start position:0%
+and two points that start very close
+ 
+
+ align:start position:0%
+and two points that start very close
+together can wind up very part of a far
+
+ align:start position:0%
+together can wind up very part of a far
+ 
+
+ align:start position:0%
+together can wind up very part of a far
+apart from each other okay so it's
+
+ align:start position:0%
+apart from each other okay so it's
+ 
+
+ align:start position:0%
+apart from each other okay so it's
+deterministic chaos but outside of those
+
+ align:start position:0%
+deterministic chaos but outside of those
+ 
+
+ align:start position:0%
+deterministic chaos but outside of those
+problems right we try to do this
+
+ align:start position:0%
+problems right we try to do this
+ 
+
+ align:start position:0%
+problems right we try to do this
+extrapolation and figure out figure out
+
+ align:start position:0%
+extrapolation and figure out figure out
+ 
+
+ align:start position:0%
+extrapolation and figure out figure out
+sort of a best approximation for where
+
+ align:start position:0%
+sort of a best approximation for where
+ 
+
+ align:start position:0%
+sort of a best approximation for where
+we think right our target function is
+
+ align:start position:0%
+we think right our target function is
+ 
+
+ align:start position:0%
+we think right our target function is
+going so what are we trying to do
+
+ align:start position:0%
+going so what are we trying to do
+ 
+
+ align:start position:0%
+going so what are we trying to do
+in principle okay we know why at a
+
+ align:start position:0%
+in principle okay we know why at a
+ 
+
+ align:start position:0%
+in principle okay we know why at a
+certain point okay and we want to know
+
+ align:start position:0%
+certain point okay and we want to know
+ 
+
+ align:start position:0%
+certain point okay and we want to know
+where it's where it's gonna go okay and
+
+ align:start position:0%
+where it's where it's gonna go okay and
+ 
+
+ align:start position:0%
+where it's where it's gonna go okay and
+so you might say well maybe I know dy DT
+
+ align:start position:0%
+so you might say well maybe I know dy DT
+ 
+
+ align:start position:0%
+so you might say well maybe I know dy DT
+initially and so I should just move a
+
+ align:start position:0%
+initially and so I should just move a
+ 
+
+ align:start position:0%
+initially and so I should just move a
+small increment along that slope and
+
+ align:start position:0%
+small increment along that slope and
+ 
+
+ align:start position:0%
+small increment along that slope and
+that's a good approximation let's the
+
+ align:start position:0%
+that's a good approximation let's the
+ 
+
+ align:start position:0%
+that's a good approximation let's the
+forward Euler approximation and
+
+ align:start position:0%
+forward Euler approximation and
+ 
+
+ align:start position:0%
+forward Euler approximation and
+trapezoid rule or equivalently the
+
+ align:start position:0%
+trapezoid rule or equivalently the
+ 
+
+ align:start position:0%
+trapezoid rule or equivalently the
+midpoint rule
+
+ align:start position:0%
+midpoint rule
+ 
+
+ align:start position:0%
+midpoint rule
+okay says well maybe maybe that initial
+
+ align:start position:0%
+okay says well maybe maybe that initial
+ 
+
+ align:start position:0%
+okay says well maybe maybe that initial
+slope isn't really the right one to use
+
+ align:start position:0%
+slope isn't really the right one to use
+ 
+
+ align:start position:0%
+slope isn't really the right one to use
+okay maybe why this something like this
+
+ align:start position:0%
+okay maybe why this something like this
+ 
+
+ align:start position:0%
+okay maybe why this something like this
+and we should actually look sort of
+
+ align:start position:0%
+and we should actually look sort of
+ 
+
+ align:start position:0%
+and we should actually look sort of
+halfway between the point we're trying
+
+ align:start position:0%
+halfway between the point we're trying
+ 
+
+ align:start position:0%
+halfway between the point we're trying
+to extrapolate to and the current point
+
+ align:start position:0%
+to extrapolate to and the current point
+ 
+
+ align:start position:0%
+to extrapolate to and the current point
+right and use that value right as the
+
+ align:start position:0%
+right and use that value right as the
+ 
+
+ align:start position:0%
+right and use that value right as the
+best approximation of the derivative and
+
+ align:start position:0%
+best approximation of the derivative and
+ 
+
+ align:start position:0%
+best approximation of the derivative and
+extrapolate forward along that and it
+
+ align:start position:0%
+extrapolate forward along that and it
+ 
+
+ align:start position:0%
+extrapolate forward along that and it
+turns out that's more accurate okay so
+
+ align:start position:0%
+turns out that's more accurate okay so
+ 
+
+ align:start position:0%
+turns out that's more accurate okay so
+what does that look like
+
+ align:start position:0%
+what does that look like
+ 
+
+ align:start position:0%
+what does that look like
+so one typically says you know why I
+
+ align:start position:0%
+so one typically says you know why I
+ 
+
+ align:start position:0%
+so one typically says you know why I
+plus 1 is equal to okay why I plus delta
+
+ align:start position:0%
+plus 1 is equal to okay why I plus delta
+ 
+
+ align:start position:0%
+plus 1 is equal to okay why I plus delta
+T times F why I plus 1/2 comma and we
+
+ align:start position:0%
+T times F why I plus 1/2 comma and we
+ 
+
+ align:start position:0%
+T times F why I plus 1/2 comma and we
+won't worry about the T here but it's
+
+ align:start position:0%
+won't worry about the T here but it's
+ 
+
+ align:start position:0%
+won't worry about the T here but it's
+gonna have to be TI plus 1/2 so I look
+
+ align:start position:0%
+gonna have to be TI plus 1/2 so I look
+ 
+
+ align:start position:0%
+gonna have to be TI plus 1/2 so I look
+halfway forward in time and I say that's
+
+ align:start position:0%
+halfway forward in time and I say that's
+ 
+
+ align:start position:0%
+halfway forward in time and I say that's
+the slope that's the derivative of Y so
+
+ align:start position:0%
+the slope that's the derivative of Y so
+ 
+
+ align:start position:0%
+the slope that's the derivative of Y so
+let me step forward along that line okay
+
+ align:start position:0%
+let me step forward along that line okay
+ 
+
+ align:start position:0%
+let me step forward along that line okay
+let's turn up this is going to be this
+
+ align:start position:0%
+let's turn up this is going to be this
+ 
+
+ align:start position:0%
+let's turn up this is going to be this
+is gonna be reasonably accurate if I can
+
+ align:start position:0%
+is gonna be reasonably accurate if I can
+ 
+
+ align:start position:0%
+is gonna be reasonably accurate if I can
+get a good approximation for y I plus a
+
+ align:start position:0%
+get a good approximation for y I plus a
+ 
+
+ align:start position:0%
+get a good approximation for y I plus a
+half okay okay so let's excuse me yeah
+
+ align:start position:0%
+half okay okay so let's excuse me yeah
+ 
+
+ align:start position:0%
+half okay okay so let's excuse me yeah
+they're there they're functionally
+
+ align:start position:0%
+they're there they're functionally
+ 
+
+ align:start position:0%
+they're there they're functionally
+equivalent to each other they work they
+
+ align:start position:0%
+equivalent to each other they work they
+ 
+
+ align:start position:0%
+equivalent to each other they work they
+work in precisely the same fashion okay
+
+ align:start position:0%
+work in precisely the same fashion okay
+ 
+
+ align:start position:0%
+work in precisely the same fashion okay
+so whether it's the trapezoidal world
+
+ align:start position:0%
+so whether it's the trapezoidal world
+ 
+
+ align:start position:0%
+so whether it's the trapezoidal world
+the midpoint method they they have
+
+ align:start position:0%
+the midpoint method they they have
+ 
+
+ align:start position:0%
+the midpoint method they they have
+fundamentally the same fundamentally the
+
+ align:start position:0%
+fundamentally the same fundamentally the
+ 
+
+ align:start position:0%
+fundamentally the same fundamentally the
+same picture is there okay here right if
+
+ align:start position:0%
+same picture is there okay here right if
+ 
+
+ align:start position:0%
+same picture is there okay here right if
+you do forward Euler you're doing
+
+ align:start position:0%
+you do forward Euler you're doing
+ 
+
+ align:start position:0%
+you do forward Euler you're doing
+numerical integration assuming the slope
+
+ align:start position:0%
+numerical integration assuming the slope
+ 
+
+ align:start position:0%
+numerical integration assuming the slope
+is the value at this point if you're
+
+ align:start position:0%
+is the value at this point if you're
+ 
+
+ align:start position:0%
+is the value at this point if you're
+doing the midpoint method or the
+
+ align:start position:0%
+doing the midpoint method or the
+ 
+
+ align:start position:0%
+doing the midpoint method or the
+trapezoid rule you're trying to get a
+
+ align:start position:0%
+trapezoid rule you're trying to get a
+ 
+
+ align:start position:0%
+trapezoid rule you're trying to get a
+better approximation for this slope
+
+ align:start position:0%
+better approximation for this slope
+ 
+
+ align:start position:0%
+better approximation for this slope
+right so you're trying to build a
+
+ align:start position:0%
+right so you're trying to build a
+ 
+
+ align:start position:0%
+right so you're trying to build a
+trapezoid and integrate the area under
+
+ align:start position:0%
+trapezoid and integrate the area under
+ 
+
+ align:start position:0%
+trapezoid and integrate the area under
+that trapezoid okay so they're
+
+ align:start position:0%
+that trapezoid okay so they're
+ 
+
+ align:start position:0%
+that trapezoid okay so they're
+fundamentally the same thing okay now
+
+ align:start position:0%
+fundamentally the same thing okay now
+ 
+
+ align:start position:0%
+fundamentally the same thing okay now
+the question becomes
+
+ align:start position:0%
+the question becomes
+ 
+
+ align:start position:0%
+the question becomes
+I don't know F at Y I plus two so I need
+
+ align:start position:0%
+I don't know F at Y I plus two so I need
+ 
+
+ align:start position:0%
+I don't know F at Y I plus two so I need
+to use a Taylor expansion of this
+
+ align:start position:0%
+to use a Taylor expansion of this
+ 
+
+ align:start position:0%
+to use a Taylor expansion of this
+quantity in terms of the value of f that
+
+ align:start position:0%
+quantity in terms of the value of f that
+ 
+
+ align:start position:0%
+quantity in terms of the value of f that
+I know so I need to expand this in terms
+
+ align:start position:0%
+I know so I need to expand this in terms
+ 
+
+ align:start position:0%
+I know so I need to expand this in terms
+of F at Y I okay and I'll know the
+
+ align:start position:0%
+of F at Y I okay and I'll know the
+ 
+
+ align:start position:0%
+of F at Y I okay and I'll know the
+derivative of Y with respect to T at Y I
+
+ align:start position:0%
+derivative of Y with respect to T at Y I
+ 
+
+ align:start position:0%
+derivative of Y with respect to T at Y I
+I know from this formula so if I take
+
+ align:start position:0%
+I know from this formula so if I take
+ 
+
+ align:start position:0%
+I know from this formula so if I take
+this Taylor expansion okay and I carry
+
+ align:start position:0%
+this Taylor expansion okay and I carry
+ 
+
+ align:start position:0%
+this Taylor expansion okay and I carry
+it out to the first term I don't know
+
+ align:start position:0%
+it out to the first term I don't know
+ 
+
+ align:start position:0%
+it out to the first term I don't know
+okay which is the order delta T squared
+
+ align:start position:0%
+okay which is the order delta T squared
+ 
+
+ align:start position:0%
+okay which is the order delta T squared
+term okay and a carry through all of the
+
+ align:start position:0%
+term okay and a carry through all of the
+ 
+
+ align:start position:0%
+term okay and a carry through all of the
+airs right I'll find out that there's a
+
+ align:start position:0%
+airs right I'll find out that there's a
+ 
+
+ align:start position:0%
+airs right I'll find out that there's a
+numerical error proportional to order
+
+ align:start position:0%
+numerical error proportional to order
+ 
+
+ align:start position:0%
+numerical error proportional to order
+delta T squared
+
+ align:start position:0%
+delta T squared
+ 
+
+ align:start position:0%
+delta T squared
+yes I need to do exactly this okay and
+
+ align:start position:0%
+yes I need to do exactly this okay and
+ 
+
+ align:start position:0%
+yes I need to do exactly this okay and
+substitute in terms of quantities I know
+
+ align:start position:0%
+substitute in terms of quantities I know
+ 
+
+ align:start position:0%
+substitute in terms of quantities I know
+when quantities I don't know okay and
+
+ align:start position:0%
+when quantities I don't know okay and
+ 
+
+ align:start position:0%
+when quantities I don't know okay and
+the leading order contribution of the
+
+ align:start position:0%
+the leading order contribution of the
+ 
+
+ align:start position:0%
+the leading order contribution of the
+quantities I don't know will give me
+
+ align:start position:0%
+quantities I don't know will give me
+ 
+
+ align:start position:0%
+quantities I don't know will give me
+this order delta T squared piece that'll
+
+ align:start position:0%
+this order delta T squared piece that'll
+ 
+
+ align:start position:0%
+this order delta T squared piece that'll
+give me the local truncation error in
+
+ align:start position:0%
+give me the local truncation error in
+ 
+
+ align:start position:0%
+give me the local truncation error in
+the solution that makes sense so it's
+
+ align:start position:0%
+the solution that makes sense so it's
+ 
+
+ align:start position:0%
+the solution that makes sense so it's
+still Taylor expansions good other
+
+ align:start position:0%
+still Taylor expansions good other
+ 
+
+ align:start position:0%
+still Taylor expansions good other
+questions yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why is the central difference I don't
+
+ align:start position:0%
+why is the central difference I don't
+ 
+
+ align:start position:0%
+why is the central difference I don't
+think I said anything like that so
+
+ align:start position:0%
+think I said anything like that so
+ 
+
+ align:start position:0%
+think I said anything like that so
+implicit versus explicit really depends
+
+ align:start position:0%
+implicit versus explicit really depends
+ 
+
+ align:start position:0%
+implicit versus explicit really depends
+on on what you're trying to do okay so
+
+ align:start position:0%
+on on what you're trying to do okay so
+ 
+
+ align:start position:0%
+on on what you're trying to do okay so
+if I'm trying to use a central
+
+ align:start position:0%
+if I'm trying to use a central
+ 
+
+ align:start position:0%
+if I'm trying to use a central
+difference formula of some sort to solve
+
+ align:start position:0%
+difference formula of some sort to solve
+ 
+
+ align:start position:0%
+difference formula of some sort to solve
+an OD e which progresses forward in time
+
+ align:start position:0%
+an OD e which progresses forward in time
+ 
+
+ align:start position:0%
+an OD e which progresses forward in time
+right it has a direction associated with
+
+ align:start position:0%
+right it has a direction associated with
+ 
+
+ align:start position:0%
+right it has a direction associated with
+it that things always progress in then
+
+ align:start position:0%
+it that things always progress in then
+ 
+
+ align:start position:0%
+it that things always progress in then
+this this might be an explicit formula
+
+ align:start position:0%
+this this might be an explicit formula
+ 
+
+ align:start position:0%
+this this might be an explicit formula
+because I could solve right for F at X I
+
+ align:start position:0%
+because I could solve right for F at X I
+ 
+
+ align:start position:0%
+because I could solve right for F at X I
+plus one in terms of what's going on in
+
+ align:start position:0%
+plus one in terms of what's going on in
+ 
+
+ align:start position:0%
+plus one in terms of what's going on in
+the past if we tried to do finite
+
+ align:start position:0%
+the past if we tried to do finite
+ 
+
+ align:start position:0%
+the past if we tried to do finite
+differences in a boundary value problem
+
+ align:start position:0%
+differences in a boundary value problem
+ 
+
+ align:start position:0%
+differences in a boundary value problem
+instead okay and that boundary value
+
+ align:start position:0%
+instead okay and that boundary value
+ 
+
+ align:start position:0%
+instead okay and that boundary value
+from doesn't have some direction
+
+ align:start position:0%
+from doesn't have some direction
+ 
+
+ align:start position:0%
+from doesn't have some direction
+associated with it anymore right so it's
+
+ align:start position:0%
+associated with it anymore right so it's
+ 
+
+ align:start position:0%
+associated with it anymore right so it's
+not like space has some preferred
+
+ align:start position:0%
+not like space has some preferred
+ 
+
+ align:start position:0%
+not like space has some preferred
+direction Ty and goes in a preferred
+
+ align:start position:0%
+direction Ty and goes in a preferred
+ 
+
+ align:start position:0%
+direction Ty and goes in a preferred
+direction space does not okay you may
+
+ align:start position:0%
+direction space does not okay you may
+ 
+
+ align:start position:0%
+direction space does not okay you may
+find that the point-wise equations you
+
+ align:start position:0%
+find that the point-wise equations you
+ 
+
+ align:start position:0%
+find that the point-wise equations you
+write down cannot be solved right
+
+ align:start position:0%
+write down cannot be solved right
+ 
+
+ align:start position:0%
+write down cannot be solved right
+strictly in terms of one of these you
+
+ align:start position:0%
+strictly in terms of one of these you
+ 
+
+ align:start position:0%
+strictly in terms of one of these you
+can't can't just move this to the other
+
+ align:start position:0%
+can't can't just move this to the other
+ 
+
+ align:start position:0%
+can't can't just move this to the other
+side of the equation and solve in terms
+
+ align:start position:0%
+side of the equation and solve in terms
+ 
+
+ align:start position:0%
+side of the equation and solve in terms
+of everything else you'll have a coupled
+
+ align:start position:0%
+of everything else you'll have a coupled
+ 
+
+ align:start position:0%
+of everything else you'll have a coupled
+set of equations that can't be can't be
+
+ align:start position:0%
+set of equations that can't be can't be
+ 
+
+ align:start position:0%
+set of equations that can't be can't be
+diagonalized can't be simply simply
+
+ align:start position:0%
+diagonalized can't be simply simply
+ 
+
+ align:start position:0%
+diagonalized can't be simply simply
+reduced they won't have the form of save
+
+ align:start position:0%
+reduced they won't have the form of save
+ 
+
+ align:start position:0%
+reduced they won't have the form of save
+triangular matrix for example okay this
+
+ align:start position:0%
+triangular matrix for example okay this
+ 
+
+ align:start position:0%
+triangular matrix for example okay this
+this will happen okay and in that case
+
+ align:start position:0%
+this will happen okay and in that case
+ 
+
+ align:start position:0%
+this will happen okay and in that case
+this you would say this formulas
+
+ align:start position:0%
+this you would say this formulas
+ 
+
+ align:start position:0%
+this you would say this formulas
+implicit okay so it really depends on
+
+ align:start position:0%
+implicit okay so it really depends on
+ 
+
+ align:start position:0%
+implicit okay so it really depends on
+which problem you're trying to solve
+
+ align:start position:0%
+which problem you're trying to solve
+ 
+
+ align:start position:0%
+which problem you're trying to solve
+whether you label them explicit or
+
+ align:start position:0%
+whether you label them explicit or
+ 
+
+ align:start position:0%
+whether you label them explicit or
+implicit explicit is going to mean that
+
+ align:start position:0%
+implicit explicit is going to mean that
+ 
+
+ align:start position:0%
+implicit explicit is going to mean that
+the data I want okay can be found with a
+
+ align:start position:0%
+the data I want okay can be found with a
+ 
+
+ align:start position:0%
+the data I want okay can be found with a
+simple equation solve in terms of the
+
+ align:start position:0%
+simple equation solve in terms of the
+ 
+
+ align:start position:0%
+simple equation solve in terms of the
+data I know in places' can mean I've got
+
+ align:start position:0%
+data I know in places' can mean I've got
+ 
+
+ align:start position:0%
+data I know in places' can mean I've got
+to do some complicated equation solving
+
+ align:start position:0%
+to do some complicated equation solving
+ 
+
+ align:start position:0%
+to do some complicated equation solving
+methodology right I've got to I've got
+
+ align:start position:0%
+methodology right I've got to I've got
+ 
+
+ align:start position:0%
+methodology right I've got to I've got
+to go do Gaussian elimination I need to
+
+ align:start position:0%
+to go do Gaussian elimination I need to
+ 
+
+ align:start position:0%
+to go do Gaussian elimination I need to
+go to F solve and solve this thing right
+
+ align:start position:0%
+go to F solve and solve this thing right
+ 
+
+ align:start position:0%
+go to F solve and solve this thing right
+the data that I want is not not
+
+ align:start position:0%
+the data that I want is not not
+ 
+
+ align:start position:0%
+the data that I want is not not
+available through some simple some
+
+ align:start position:0%
+available through some simple some
+ 
+
+ align:start position:0%
+available through some simple some
+simple scheme where I can just write
+
+ align:start position:0%
+simple scheme where I can just write
+ 
+
+ align:start position:0%
+simple scheme where I can just write
+explicit
+
+ align:start position:0%
+explicit
+ 
+
+ align:start position:0%
+explicit
+the thing I want equals some function of
+
+ align:start position:0%
+the thing I want equals some function of
+ 
+
+ align:start position:0%
+the thing I want equals some function of
+things I know okay other questions okay
+
+ align:start position:0%
+things I know okay other questions okay
+ 
+
+ align:start position:0%
+things I know okay other questions okay
+yeah yeah oh man
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the question was how many questions and
+
+ align:start position:0%
+the question was how many questions and
+ 
+
+ align:start position:0%
+the question was how many questions and
+how many sub questions on the quiz yeah
+
+ align:start position:0%
+how many sub questions on the quiz yeah
+ 
+
+ align:start position:0%
+how many sub questions on the quiz yeah
+the quiz is it's it's in my opinion it's
+
+ align:start position:0%
+the quiz is it's it's in my opinion it's
+ 
+
+ align:start position:0%
+the quiz is it's it's in my opinion it's
+now shorter than the last one that you
+
+ align:start position:0%
+now shorter than the last one that you
+ 
+
+ align:start position:0%
+now shorter than the last one that you
+took we've been pretty sensitive to time
+
+ align:start position:0%
+took we've been pretty sensitive to time
+ 
+
+ align:start position:0%
+took we've been pretty sensitive to time
+concerns we know that was something that
+
+ align:start position:0%
+concerns we know that was something that
+ 
+
+ align:start position:0%
+concerns we know that was something that
+was an issue on the previous quiz I
+
+ align:start position:0%
+was an issue on the previous quiz I
+ 
+
+ align:start position:0%
+was an issue on the previous quiz I
+think there is only going to be two
+
+ align:start position:0%
+think there is only going to be two
+ 
+
+ align:start position:0%
+think there is only going to be two
+problems on it okay
+
+ align:start position:0%
+problems on it okay
+ 
+
+ align:start position:0%
+problems on it okay
+they have many parts but we've really
+
+ align:start position:0%
+they have many parts but we've really
+ 
+
+ align:start position:0%
+they have many parts but we've really
+tried to refine the questions in those
+
+ align:start position:0%
+tried to refine the questions in those
+ 
+
+ align:start position:0%
+tried to refine the questions in those
+parts okay that's that's that's what you
+
+ align:start position:0%
+parts okay that's that's that's what you
+ 
+
+ align:start position:0%
+parts okay that's that's that's what you
+should expect it's comprehensive covers
+
+ align:start position:0%
+should expect it's comprehensive covers
+ 
+
+ align:start position:0%
+should expect it's comprehensive covers
+all the things from this section okay
+
+ align:start position:0%
+all the things from this section okay
+ 
+
+ align:start position:0%
+all the things from this section okay
+yes yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes sure sure so so higher index daes
+
+ align:start position:0%
+yes sure sure so so higher index daes
+ 
+
+ align:start position:0%
+yes sure sure so so higher index daes
+okay come up all the time and the
+
+ align:start position:0%
+okay come up all the time and the
+ 
+
+ align:start position:0%
+okay come up all the time and the
+degrees of freedom refers to your
+
+ align:start position:0%
+degrees of freedom refers to your
+ 
+
+ align:start position:0%
+degrees of freedom refers to your
+ability to choose initial conditions for
+
+ align:start position:0%
+ability to choose initial conditions for
+ 
+
+ align:start position:0%
+ability to choose initial conditions for
+the problem and we saw several examples
+
+ align:start position:0%
+the problem and we saw several examples
+ 
+
+ align:start position:0%
+the problem and we saw several examples
+in which if we try to convert that da e
+
+ align:start position:0%
+in which if we try to convert that da e
+ 
+
+ align:start position:0%
+in which if we try to convert that da e
+to an OD e we found along the way that
+
+ align:start position:0%
+to an OD e we found along the way that
+ 
+
+ align:start position:0%
+to an OD e we found along the way that
+there were certain hidden conditions
+
+ align:start position:0%
+there were certain hidden conditions
+ 
+
+ align:start position:0%
+there were certain hidden conditions
+that all the initial conditions would
+
+ align:start position:0%
+that all the initial conditions would
+ 
+
+ align:start position:0%
+that all the initial conditions would
+need to satisfy in order for this OD the
+
+ align:start position:0%
+need to satisfy in order for this OD the
+ 
+
+ align:start position:0%
+need to satisfy in order for this OD the
+system of Odie's that we built from the
+
+ align:start position:0%
+system of Odie's that we built from the
+ 
+
+ align:start position:0%
+system of Odie's that we built from the
+da's to follow the same solution path or
+
+ align:start position:0%
+da's to follow the same solution path or
+ 
+
+ align:start position:0%
+da's to follow the same solution path or
+solution manifold as the original da
+
+ align:start position:0%
+solution manifold as the original da
+ 
+
+ align:start position:0%
+solution manifold as the original da
+system would follow okay the higher the
+
+ align:start position:0%
+system would follow okay the higher the
+ 
+
+ align:start position:0%
+system would follow okay the higher the
+index is the more of these hidden
+
+ align:start position:0%
+index is the more of these hidden
+ 
+
+ align:start position:0%
+index is the more of these hidden
+constraints you find okay
+
+ align:start position:0%
+constraints you find okay
+ 
+
+ align:start position:0%
+constraints you find okay
+and those hidden constraints tell you
+
+ align:start position:0%
+and those hidden constraints tell you
+ 
+
+ align:start position:0%
+and those hidden constraints tell you
+that the initial conditions have to be
+
+ align:start position:0%
+that the initial conditions have to be
+ 
+
+ align:start position:0%
+that the initial conditions have to be
+very particular so there were there I've
+
+ align:start position:0%
+very particular so there were there I've
+ 
+
+ align:start position:0%
+very particular so there were there I've
+encouraged you to look at look at the
+
+ align:start position:0%
+encouraged you to look at look at the
+ 
+
+ align:start position:0%
+encouraged you to look at look at the
+specific examples in the notes and
+
+ align:start position:0%
+specific examples in the notes and
+ 
+
+ align:start position:0%
+specific examples in the notes and
+you'll see there was there was a simple
+
+ align:start position:0%
+you'll see there was there was a simple
+ 
+
+ align:start position:0%
+you'll see there was there was a simple
+CSTR example that was index 1 and almost
+
+ align:start position:0%
+CSTR example that was index 1 and almost
+ 
+
+ align:start position:0%
+CSTR example that was index 1 and almost
+almost unconstrained basically there was
+
+ align:start position:0%
+almost unconstrained basically there was
+ 
+
+ align:start position:0%
+almost unconstrained basically there was
+an index to Dae in which the consistent
+
+ align:start position:0%
+an index to Dae in which the consistent
+ 
+
+ align:start position:0%
+an index to Dae in which the consistent
+initial conditions you actually couldn't
+
+ align:start position:0%
+initial conditions you actually couldn't
+ 
+
+ align:start position:0%
+initial conditions you actually couldn't
+specify any of the initial conditions
+
+ align:start position:0%
+specify any of the initial conditions
+ 
+
+ align:start position:0%
+specify any of the initial conditions
+they were they were fixed by the
+
+ align:start position:0%
+they were they were fixed by the
+ 
+
+ align:start position:0%
+they were they were fixed by the
+equations themselves right
+
+ align:start position:0%
+equations themselves right
+ 
+
+ align:start position:0%
+equations themselves right
+remember that sort of happened because
+
+ align:start position:0%
+remember that sort of happened because
+ 
+
+ align:start position:0%
+remember that sort of happened because
+certain certain days are pathological in
+
+ align:start position:0%
+certain certain days are pathological in
+ 
+
+ align:start position:0%
+certain certain days are pathological in
+nature they often ask us to do something
+
+ align:start position:0%
+nature they often ask us to do something
+ 
+
+ align:start position:0%
+nature they often ask us to do something
+we can't do physically like you know try
+
+ align:start position:0%
+we can't do physically like you know try
+ 
+
+ align:start position:0%
+we can't do physically like you know try
+to control the input by or try to
+
+ align:start position:0%
+to control the input by or try to
+ 
+
+ align:start position:0%
+to control the input by or try to
+predict let's say how do I say this it's
+
+ align:start position:0%
+predict let's say how do I say this it's
+ 
+
+ align:start position:0%
+predict let's say how do I say this it's
+easy for us to predict the output
+
+ align:start position:0%
+easy for us to predict the output
+ 
+
+ align:start position:0%
+easy for us to predict the output
+knowing the input it's very hard for us
+
+ align:start position:0%
+knowing the input it's very hard for us
+ 
+
+ align:start position:0%
+knowing the input it's very hard for us
+to predict the input knowing the output
+
+ align:start position:0%
+to predict the input knowing the output
+ 
+
+ align:start position:0%
+to predict the input knowing the output
+right and these higher index Dae s were
+
+ align:start position:0%
+right and these higher index Dae s were
+ 
+
+ align:start position:0%
+right and these higher index Dae s were
+essentially asking us to do that right
+
+ align:start position:0%
+essentially asking us to do that right
+ 
+
+ align:start position:0%
+essentially asking us to do that right
+there's a lag in how we measure things
+
+ align:start position:0%
+there's a lag in how we measure things
+ 
+
+ align:start position:0%
+there's a lag in how we measure things
+and it's easier to go forward through a
+
+ align:start position:0%
+and it's easier to go forward through a
+ 
+
+ align:start position:0%
+and it's easier to go forward through a
+process than backwards through a process
+
+ align:start position:0%
+process than backwards through a process
+ 
+
+ align:start position:0%
+process than backwards through a process
+and make these predictions there's
+
+ align:start position:0%
+and make these predictions there's
+ 
+
+ align:start position:0%
+and make these predictions there's
+inherent sensitivity in doing the former
+
+ align:start position:0%
+inherent sensitivity in doing the former
+ 
+
+ align:start position:0%
+inherent sensitivity in doing the former
+it's the same sort of sensitivity you
+
+ align:start position:0%
+it's the same sort of sensitivity you
+ 
+
+ align:start position:0%
+it's the same sort of sensitivity you
+get from these systems of Odie's in fact
+
+ align:start position:0%
+get from these systems of Odie's in fact
+ 
+
+ align:start position:0%
+get from these systems of Odie's in fact
+right that's just small change in the
+
+ align:start position:0%
+right that's just small change in the
+ 
+
+ align:start position:0%
+right that's just small change in the
+initial conditions can lead to big
+
+ align:start position:0%
+initial conditions can lead to big
+ 
+
+ align:start position:0%
+initial conditions can lead to big
+changes in the outlet so if I measure
+
+ align:start position:0%
+changes in the outlet so if I measure
+ 
+
+ align:start position:0%
+changes in the outlet so if I measure
+the outlet it's hard to predict the
+
+ align:start position:0%
+the outlet it's hard to predict the
+ 
+
+ align:start position:0%
+the outlet it's hard to predict the
+inlet ok so it's just very inherently
+
+ align:start position:0%
+inlet ok so it's just very inherently
+ 
+
+ align:start position:0%
+inlet ok so it's just very inherently
+difficult to do and so formulating a
+
+ align:start position:0%
+difficult to do and so formulating a
+ 
+
+ align:start position:0%
+difficult to do and so formulating a
+model which has this high index right
+
+ align:start position:0%
+model which has this high index right
+ 
+
+ align:start position:0%
+model which has this high index right
+you will naturally find that your choice
+
+ align:start position:0%
+you will naturally find that your choice
+ 
+
+ align:start position:0%
+you will naturally find that your choice
+of initial conditions for the solution
+
+ align:start position:0%
+of initial conditions for the solution
+ 
+
+ align:start position:0%
+of initial conditions for the solution
+of that model are constrained and their
+
+ align:start position:0%
+of that model are constrained and their
+ 
+
+ align:start position:0%
+of that model are constrained and their
+constraint because of the way you
+
+ align:start position:0%
+constraint because of the way you
+ 
+
+ align:start position:0%
+constraint because of the way you
+formulated the model ok if you're
+
+ align:start position:0%
+formulated the model ok if you're
+ 
+
+ align:start position:0%
+formulated the model ok if you're
+actually trying to do control ok of a
+
+ align:start position:0%
+actually trying to do control ok of a
+ 
+
+ align:start position:0%
+actually trying to do control ok of a
+chemical process is gonna be very
+
+ align:start position:0%
+chemical process is gonna be very
+ 
+
+ align:start position:0%
+chemical process is gonna be very
+difficult ok to try to somehow control
+
+ align:start position:0%
+difficult ok to try to somehow control
+ 
+
+ align:start position:0%
+difficult ok to try to somehow control
+the you know try to make the input be a
+
+ align:start position:0%
+the you know try to make the input be a
+ 
+
+ align:start position:0%
+the you know try to make the input be a
+certain thing by controlling the output
+
+ align:start position:0%
+certain thing by controlling the output
+ 
+
+ align:start position:0%
+certain thing by controlling the output
+ok this is that doesn't make sense
+
+ align:start position:0%
+ok this is that doesn't make sense
+ 
+
+ align:start position:0%
+ok this is that doesn't make sense
+almost right it seems very very strange
+
+ align:start position:0%
+almost right it seems very very strange
+ 
+
+ align:start position:0%
+almost right it seems very very strange
+you would really want to change the
+
+ align:start position:0%
+you would really want to change the
+ 
+
+ align:start position:0%
+you would really want to change the
+input in order to hit a target in the
+
+ align:start position:0%
+input in order to hit a target in the
+ 
+
+ align:start position:0%
+input in order to hit a target in the
+output how do you change the output and
+
+ align:start position:0%
+output how do you change the output and
+ 
+
+ align:start position:0%
+output how do you change the output and
+hit a target in the input right the
+
+ align:start position:0%
+hit a target in the input right the
+ 
+
+ align:start position:0%
+hit a target in the input right the
+process doesn't actually care about
+
+ align:start position:0%
+process doesn't actually care about
+ 
+
+ align:start position:0%
+process doesn't actually care about
+things in that way and you saw that
+
+ align:start position:0%
+things in that way and you saw that
+ 
+
+ align:start position:0%
+things in that way and you saw that
+in that in that particular CSTR example
+
+ align:start position:0%
+in that in that particular CSTR example
+ 
+
+ align:start position:0%
+in that in that particular CSTR example
+you couldn't you couldn't fix any of the
+
+ align:start position:0%
+you couldn't you couldn't fix any of the
+ 
+
+ align:start position:0%
+you couldn't you couldn't fix any of the
+initial conditions actually right there
+
+ align:start position:0%
+initial conditions actually right there
+ 
+
+ align:start position:0%
+initial conditions actually right there
+was no free choice in the problem
+
+ align:start position:0%
+was no free choice in the problem
+ 
+
+ align:start position:0%
+was no free choice in the problem
+everything was automatically fixed
+
+ align:start position:0%
+everything was automatically fixed
+ 
+
+ align:start position:0%
+everything was automatically fixed
+they'd had to have perfect knowledge of
+
+ align:start position:0%
+they'd had to have perfect knowledge of
+ 
+
+ align:start position:0%
+they'd had to have perfect knowledge of
+everything in the system
+
+ align:start position:0%
+everything in the system
+ 
+
+ align:start position:0%
+everything in the system
+I wasn't actually able to do control in
+
+ align:start position:0%
+I wasn't actually able to do control in
+ 
+
+ align:start position:0%
+I wasn't actually able to do control in
+a sense there I just measure the output
+
+ align:start position:0%
+a sense there I just measure the output
+ 
+
+ align:start position:0%
+a sense there I just measure the output
+I could tell you what the input was
+
+ align:start position:0%
+I could tell you what the input was
+ 
+
+ align:start position:0%
+I could tell you what the input was
+supposed to be and it was super
+
+ align:start position:0%
+supposed to be and it was super
+ 
+
+ align:start position:0%
+supposed to be and it was super
+sensitive to my measurement okay so
+
+ align:start position:0%
+sensitive to my measurement okay so
+ 
+
+ align:start position:0%
+sensitive to my measurement okay so
+these high index problems tend to come
+
+ align:start position:0%
+these high index problems tend to come
+ 
+
+ align:start position:0%
+these high index problems tend to come
+up when we when we want to constrain
+
+ align:start position:0%
+up when we when we want to constrain
+ 
+
+ align:start position:0%
+up when we when we want to constrain
+things in a way that's it's a physically
+
+ align:start position:0%
+things in a way that's it's a physically
+ 
+
+ align:start position:0%
+things in a way that's it's a physically
+quite challenging okay high index
+
+ align:start position:0%
+quite challenging okay high index
+ 
+
+ align:start position:0%
+quite challenging okay high index
+problems are incredibly common in
+
+ align:start position:0%
+problems are incredibly common in
+ 
+
+ align:start position:0%
+problems are incredibly common in
+mechanical engineering things like
+
+ align:start position:0%
+mechanical engineering things like
+ 
+
+ align:start position:0%
+mechanical engineering things like
+robotics okay we you know you want to
+
+ align:start position:0%
+robotics okay we you know you want to
+ 
+
+ align:start position:0%
+robotics okay we you know you want to
+make sure the the robots arm doesn't
+
+ align:start position:0%
+make sure the the robots arm doesn't
+ 
+
+ align:start position:0%
+make sure the the robots arm doesn't
+whack someone in the head right this is
+
+ align:start position:0%
+whack someone in the head right this is
+ 
+
+ align:start position:0%
+whack someone in the head right this is
+important and so you're trying to
+
+ align:start position:0%
+important and so you're trying to
+ 
+
+ align:start position:0%
+important and so you're trying to
+constrain all these degrees of freedom
+
+ align:start position:0%
+constrain all these degrees of freedom
+ 
+
+ align:start position:0%
+constrain all these degrees of freedom
+and the paths that it's going to move on
+
+ align:start position:0%
+and the paths that it's going to move on
+ 
+
+ align:start position:0%
+and the paths that it's going to move on
+and all those constraints mean there's
+
+ align:start position:0%
+and all those constraints mean there's
+ 
+
+ align:start position:0%
+and all those constraints mean there's
+actually a very narrow envelope in which
+
+ align:start position:0%
+actually a very narrow envelope in which
+ 
+
+ align:start position:0%
+actually a very narrow envelope in which
+this thing gets to operate so accurately
+
+ align:start position:0%
+this thing gets to operate so accurately
+ 
+
+ align:start position:0%
+this thing gets to operate so accurately
+accurately simulating the motion and
+
+ align:start position:0%
+accurately simulating the motion and
+ 
+
+ align:start position:0%
+accurately simulating the motion and
+then making making the robot move that
+
+ align:start position:0%
+then making making the robot move that
+ 
+
+ align:start position:0%
+then making making the robot move that
+way is very important chemical processes
+
+ align:start position:0%
+way is very important chemical processes
+ 
+
+ align:start position:0%
+way is very important chemical processes
+that's true too but oftentimes we you
+
+ align:start position:0%
+that's true too but oftentimes we you
+ 
+
+ align:start position:0%
+that's true too but oftentimes we you
+can make choices in model formulation
+
+ align:start position:0%
+can make choices in model formulation
+ 
+
+ align:start position:0%
+can make choices in model formulation
+right like how you try to control the
+
+ align:start position:0%
+right like how you try to control the
+ 
+
+ align:start position:0%
+right like how you try to control the
+process that can ease the ease those
+
+ align:start position:0%
+process that can ease the ease those
+ 
+
+ align:start position:0%
+process that can ease the ease those
+constraints right if I had some
+
+ align:start position:0%
+constraints right if I had some
+ 
+
+ align:start position:0%
+constraints right if I had some
+controller it doesn't control in an
+
+ align:start position:0%
+controller it doesn't control in an
+ 
+
+ align:start position:0%
+controller it doesn't control in an
+instantaneous fashion even if it's a
+
+ align:start position:0%
+instantaneous fashion even if it's a
+ 
+
+ align:start position:0%
+instantaneous fashion even if it's a
+very high bandwidth controller so finite
+
+ align:start position:0%
+very high bandwidth controller so finite
+ 
+
+ align:start position:0%
+very high bandwidth controller so finite
+time for signals to propagate there's
+
+ align:start position:0%
+time for signals to propagate there's
+ 
+
+ align:start position:0%
+time for signals to propagate there's
+dynamics associated with the controller
+
+ align:start position:0%
+dynamics associated with the controller
+ 
+
+ align:start position:0%
+dynamics associated with the controller
+that can convert that da system into a
+
+ align:start position:0%
+that can convert that da system into a
+ 
+
+ align:start position:0%
+that can convert that da system into a
+system of Odie's for example then you
+
+ align:start position:0%
+system of Odie's for example then you
+ 
+
+ align:start position:0%
+system of Odie's for example then you
+don't have they may be stiff Odie's okay
+
+ align:start position:0%
+don't have they may be stiff Odie's okay
+ 
+
+ align:start position:0%
+don't have they may be stiff Odie's okay
+days are the limit of sort of infinite
+
+ align:start position:0%
+days are the limit of sort of infinite
+ 
+
+ align:start position:0%
+days are the limit of sort of infinite
+stiffness in Odie's but they're not they
+
+ align:start position:0%
+stiffness in Odie's but they're not they
+ 
+
+ align:start position:0%
+stiffness in Odie's but they're not they
+may not be as troublesome to solve as
+
+ align:start position:0%
+may not be as troublesome to solve as
+ 
+
+ align:start position:0%
+may not be as troublesome to solve as
+the da e system would be okay it's about
+
+ align:start position:0%
+the da e system would be okay it's about
+ 
+
+ align:start position:0%
+the da e system would be okay it's about
+model formulation okay can I can I talk
+
+ align:start position:0%
+model formulation okay can I can I talk
+ 
+
+ align:start position:0%
+model formulation okay can I can I talk
+briefly about PD es is that okay I'll
+
+ align:start position:0%
+briefly about PD es is that okay I'll
+ 
+
+ align:start position:0%
+briefly about PD es is that okay I'll
+tell you it tell you a bit about I like
+
+ align:start position:0%
+tell you it tell you a bit about I like
+ 
+
+ align:start position:0%
+tell you it tell you a bit about I like
+this finite volume method I think is
+
+ align:start position:0%
+this finite volume method I think is
+ 
+
+ align:start position:0%
+this finite volume method I think is
+very interesting okay you've got some
+
+ align:start position:0%
+very interesting okay you've got some
+ 
+
+ align:start position:0%
+very interesting okay you've got some
+notes on it I think I like it because I
+
+ align:start position:0%
+notes on it I think I like it because I
+ 
+
+ align:start position:0%
+notes on it I think I like it because I
+think it comes very naturally actually
+
+ align:start position:0%
+think it comes very naturally actually
+ 
+
+ align:start position:0%
+think it comes very naturally actually
+to chemical engineers because the
+
+ align:start position:0%
+to chemical engineers because the
+ 
+
+ align:start position:0%
+to chemical engineers because the
+problems we like to solve are of the
+
+ align:start position:0%
+problems we like to solve are of the
+ 
+
+ align:start position:0%
+problems we like to solve are of the
+type that finite finite volume eats for
+
+ align:start position:0%
+type that finite finite volume eats for
+ 
+
+ align:start position:0%
+type that finite finite volume eats for
+breakfast okay these are problems of
+
+ align:start position:0%
+breakfast okay these are problems of
+ 
+
+ align:start position:0%
+breakfast okay these are problems of
+conservation okay so we have a conserved
+
+ align:start position:0%
+conservation okay so we have a conserved
+ 
+
+ align:start position:0%
+conservation okay so we have a conserved
+quantity B right Saladin uses isn't in
+
+ align:start position:0%
+quantity B right Saladin uses isn't in
+ 
+
+ align:start position:0%
+quantity B right Saladin uses isn't in
+his book the new version still uses bees
+
+ align:start position:0%
+his book the new version still uses bees
+ 
+
+ align:start position:0%
+his book the new version still uses bees
+for me right so the time rate of change
+
+ align:start position:0%
+for me right so the time rate of change
+ 
+
+ align:start position:0%
+for me right so the time rate of change
+of B is equal to minus the gradient in
+
+ align:start position:0%
+of B is equal to minus the gradient in
+ 
+
+ align:start position:0%
+of B is equal to minus the gradient in
+the flux plus some I don't know some
+
+ align:start position:0%
+the flux plus some I don't know some
+ 
+
+ align:start position:0%
+the flux plus some I don't know some
+volumetric change maybe a reaction maybe
+
+ align:start position:0%
+volumetric change maybe a reaction maybe
+ 
+
+ align:start position:0%
+volumetric change maybe a reaction maybe
+there's some injection somewhere of mass
+
+ align:start position:0%
+there's some injection somewhere of mass
+ 
+
+ align:start position:0%
+there's some injection somewhere of mass
+or momentum or you know it's some source
+
+ align:start position:0%
+or momentum or you know it's some source
+ 
+
+ align:start position:0%
+or momentum or you know it's some source
+okay and our numerical solution
+
+ align:start position:0%
+okay and our numerical solution
+ 
+
+ align:start position:0%
+okay and our numerical solution
+oftentimes we would like it to also
+
+ align:start position:0%
+oftentimes we would like it to also
+ 
+
+ align:start position:0%
+oftentimes we would like it to also
+conserve B right conserve mass conserve
+
+ align:start position:0%
+conserve B right conserve mass conserve
+ 
+
+ align:start position:0%
+conserve B right conserve mass conserve
+momentum conserve energy conserve
+
+ align:start position:0%
+momentum conserve energy conserve
+ 
+
+ align:start position:0%
+momentum conserve energy conserve
+species these collocation methods in
+
+ align:start position:0%
+species these collocation methods in
+ 
+
+ align:start position:0%
+species these collocation methods in
+general a relaxation methods in general
+
+ align:start position:0%
+general a relaxation methods in general
+ 
+
+ align:start position:0%
+general a relaxation methods in general
+don't do that okay they're not designed
+
+ align:start position:0%
+don't do that okay they're not designed
+ 
+
+ align:start position:0%
+don't do that okay they're not designed
+to do that you might be able to
+
+ align:start position:0%
+to do that you might be able to
+ 
+
+ align:start position:0%
+to do that you might be able to
+construct for example basis functions
+
+ align:start position:0%
+construct for example basis functions
+ 
+
+ align:start position:0%
+construct for example basis functions
+that have that property that they will
+
+ align:start position:0%
+that have that property that they will
+ 
+
+ align:start position:0%
+that have that property that they will
+satisfy conservation okay you might be
+
+ align:start position:0%
+satisfy conservation okay you might be
+ 
+
+ align:start position:0%
+satisfy conservation okay you might be
+able to construct certain meshing
+
+ align:start position:0%
+able to construct certain meshing
+ 
+
+ align:start position:0%
+able to construct certain meshing
+methods
+
+ align:start position:0%
+methods
+ 
+
+ align:start position:0%
+methods
+okay certain collocation methods and
+
+ align:start position:0%
+okay certain collocation methods and
+ 
+
+ align:start position:0%
+okay certain collocation methods and
+this is one of them the finite volume
+
+ align:start position:0%
+this is one of them the finite volume
+ 
+
+ align:start position:0%
+this is one of them the finite volume
+method that respects conservation and
+
+ align:start position:0%
+method that respects conservation and
+ 
+
+ align:start position:0%
+method that respects conservation and
+here's how you do it okay so you worked
+
+ align:start position:0%
+here's how you do it okay so you worked
+ 
+
+ align:start position:0%
+here's how you do it okay so you worked
+you worked really hard and transport to
+
+ align:start position:0%
+you worked really hard and transport to
+ 
+
+ align:start position:0%
+you worked really hard and transport to
+derive these differential forms of the
+
+ align:start position:0%
+derive these differential forms of the
+ 
+
+ align:start position:0%
+derive these differential forms of the
+transport equations but finite volume
+
+ align:start position:0%
+transport equations but finite volume
+ 
+
+ align:start position:0%
+transport equations but finite volume
+actually likes the integral form so you
+
+ align:start position:0%
+actually likes the integral form so you
+ 
+
+ align:start position:0%
+actually likes the integral form so you
+got to go back okay so you got to take
+
+ align:start position:0%
+got to go back okay so you got to take
+ 
+
+ align:start position:0%
+got to go back okay so you got to take
+the integral of these equations over
+
+ align:start position:0%
+the integral of these equations over
+ 
+
+ align:start position:0%
+the integral of these equations over
+some volume V and then the time
+
+ align:start position:0%
+some volume V and then the time
+ 
+
+ align:start position:0%
+some volume V and then the time
+derivative okay of the amount of B in
+
+ align:start position:0%
+derivative okay of the amount of B in
+ 
+
+ align:start position:0%
+derivative okay of the amount of B in
+this volume is related to the flux of V
+
+ align:start position:0%
+this volume is related to the flux of V
+ 
+
+ align:start position:0%
+this volume is related to the flux of V
+of B through the surfaces of that volume
+
+ align:start position:0%
+of B through the surfaces of that volume
+ 
+
+ align:start position:0%
+of B through the surfaces of that volume
+plus the amount of generation or
+
+ align:start position:0%
+plus the amount of generation or
+ 
+
+ align:start position:0%
+plus the amount of generation or
+consumption of the conserved quantity
+
+ align:start position:0%
+consumption of the conserved quantity
+ 
+
+ align:start position:0%
+consumption of the conserved quantity
+within that volume V right and this
+
+ align:start position:0%
+within that volume V right and this
+ 
+
+ align:start position:0%
+within that volume V right and this
+volume is my finite volume I take the
+
+ align:start position:0%
+volume is my finite volume I take the
+ 
+
+ align:start position:0%
+volume is my finite volume I take the
+domain of interest and I chop it up into
+
+ align:start position:0%
+domain of interest and I chop it up into
+ 
+
+ align:start position:0%
+domain of interest and I chop it up into
+all these little volumes okay and then I
+
+ align:start position:0%
+all these little volumes okay and then I
+ 
+
+ align:start position:0%
+all these little volumes okay and then I
+just need to conserve B within that
+
+ align:start position:0%
+just need to conserve B within that
+ 
+
+ align:start position:0%
+just need to conserve B within that
+volume so I have the class you know the
+
+ align:start position:0%
+volume so I have the class you know the
+ 
+
+ align:start position:0%
+volume so I have the class you know the
+first equation you learned in chemical
+
+ align:start position:0%
+first equation you learned in chemical
+ 
+
+ align:start position:0%
+first equation you learned in chemical
+engineering right the amount of
+
+ align:start position:0%
+engineering right the amount of
+ 
+
+ align:start position:0%
+engineering right the amount of
+accumulation of the conserved quantity
+
+ align:start position:0%
+accumulation of the conserved quantity
+ 
+
+ align:start position:0%
+accumulation of the conserved quantity
+is related to the fluxes in and out of
+
+ align:start position:0%
+is related to the fluxes in and out of
+ 
+
+ align:start position:0%
+is related to the fluxes in and out of
+the control volume plus the amount of
+
+ align:start position:0%
+the control volume plus the amount of
+ 
+
+ align:start position:0%
+the control volume plus the amount of
+generation or consumption within the
+
+ align:start position:0%
+generation or consumption within the
+ 
+
+ align:start position:0%
+generation or consumption within the
+control arms this comes very naturally
+
+ align:start position:0%
+control arms this comes very naturally
+ 
+
+ align:start position:0%
+control arms this comes very naturally
+to chemical engineers it fits perfectly
+
+ align:start position:0%
+to chemical engineers it fits perfectly
+ 
+
+ align:start position:0%
+to chemical engineers it fits perfectly
+in the problems we like to solve yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it all depends on how we choose to
+
+ align:start position:0%
+well it all depends on how we choose to
+ 
+
+ align:start position:0%
+well it all depends on how we choose to
+write J actually right so is J the flux
+
+ align:start position:0%
+write J actually right so is J the flux
+ 
+
+ align:start position:0%
+write J actually right so is J the flux
+into or out of this volume so I won't i
+
+ align:start position:0%
+into or out of this volume so I won't i
+ 
+
+ align:start position:0%
+into or out of this volume so I won't i
+won't i won't prescribe that here
+
+ align:start position:0%
+won't i won't prescribe that here
+ 
+
+ align:start position:0%
+won't i won't prescribe that here
+right okay it depends on what you chose
+
+ align:start position:0%
+right okay it depends on what you chose
+ 
+
+ align:start position:0%
+right okay it depends on what you chose
+as the flux so maybe I don't know what
+
+ align:start position:0%
+as the flux so maybe I don't know what
+ 
+
+ align:start position:0%
+as the flux so maybe I don't know what
+does Dean writes the stress tensor with
+
+ align:start position:0%
+does Dean writes the stress tensor with
+ 
+
+ align:start position:0%
+does Dean writes the stress tensor with
+the opposite sign of like bird Stewart
+
+ align:start position:0%
+the opposite sign of like bird Stewart
+ 
+
+ align:start position:0%
+the opposite sign of like bird Stewart
+and Lightfoot right so these guys that's
+
+ align:start position:0%
+and Lightfoot right so these guys that's
+ 
+
+ align:start position:0%
+and Lightfoot right so these guys that's
+the flux of momentum right they choose a
+
+ align:start position:0%
+the flux of momentum right they choose a
+ 
+
+ align:start position:0%
+the flux of momentum right they choose a
+sign and then the normals have to
+
+ align:start position:0%
+sign and then the normals have to
+ 
+
+ align:start position:0%
+sign and then the normals have to
+respect that sign doesn't really matter
+
+ align:start position:0%
+respect that sign doesn't really matter
+ 
+
+ align:start position:0%
+respect that sign doesn't really matter
+the physics doesn't care okay you just
+
+ align:start position:0%
+the physics doesn't care okay you just
+ 
+
+ align:start position:0%
+the physics doesn't care okay you just
+have to choose the flux in the right
+
+ align:start position:0%
+have to choose the flux in the right
+ 
+
+ align:start position:0%
+have to choose the flux in the right
+direction if we think of J is the flux
+
+ align:start position:0%
+direction if we think of J is the flux
+ 
+
+ align:start position:0%
+direction if we think of J is the flux
+into the volume and you should point in
+
+ align:start position:0%
+into the volume and you should point in
+ 
+
+ align:start position:0%
+into the volume and you should point in
+okay right okay so you have this
+
+ align:start position:0%
+okay right okay so you have this
+ 
+
+ align:start position:0%
+okay right okay so you have this
+conservation equation you've got to
+
+ align:start position:0%
+conservation equation you've got to
+ 
+
+ align:start position:0%
+conservation equation you've got to
+solve for each of your finite volumes
+
+ align:start position:0%
+solve for each of your finite volumes
+ 
+
+ align:start position:0%
+solve for each of your finite volumes
+and the finite volumes are coupled
+
+ align:start position:0%
+and the finite volumes are coupled
+ 
+
+ align:start position:0%
+and the finite volumes are coupled
+together because the flux out of one
+
+ align:start position:0%
+together because the flux out of one
+ 
+
+ align:start position:0%
+together because the flux out of one
+volume is a flux into another volume
+
+ align:start position:0%
+volume is a flux into another volume
+ 
+
+ align:start position:0%
+volume is a flux into another volume
+right so you can think of these volumes
+
+ align:start position:0%
+right so you can think of these volumes
+ 
+
+ align:start position:0%
+right so you can think of these volumes
+as being little cstr's right they're all
+
+ align:start position:0%
+as being little cstr's right they're all
+ 
+
+ align:start position:0%
+as being little cstr's right they're all
+sitting next to each other and they're
+
+ align:start position:0%
+sitting next to each other and they're
+ 
+
+ align:start position:0%
+sitting next to each other and they're
+all linked together by these volumetric
+
+ align:start position:0%
+all linked together by these volumetric
+ 
+
+ align:start position:0%
+all linked together by these volumetric
+flows from one to another and that's in
+
+ align:start position:0%
+flows from one to another and that's in
+ 
+
+ align:start position:0%
+flows from one to another and that's in
+fact what they are right the key is how
+
+ align:start position:0%
+fact what they are right the key is how
+ 
+
+ align:start position:0%
+fact what they are right the key is how
+do i model these fluxes basically right
+
+ align:start position:0%
+do i model these fluxes basically right
+ 
+
+ align:start position:0%
+do i model these fluxes basically right
+the accuracy the method is gonna be set
+
+ align:start position:0%
+the accuracy the method is gonna be set
+ 
+
+ align:start position:0%
+the accuracy the method is gonna be set
+by how big a volume am I gonna model
+
+ align:start position:0%
+by how big a volume am I gonna model
+ 
+
+ align:start position:0%
+by how big a volume am I gonna model
+right can't have infinitely small
+
+ align:start position:0%
+right can't have infinitely small
+ 
+
+ align:start position:0%
+right can't have infinitely small
+volumes gonna be too many of them in my
+
+ align:start position:0%
+volumes gonna be too many of them in my
+ 
+
+ align:start position:0%
+volumes gonna be too many of them in my
+domain to solve the problem accurately
+
+ align:start position:0%
+domain to solve the problem accurately
+ 
+
+ align:start position:0%
+domain to solve the problem accurately
+okay and then do I have good models for
+
+ align:start position:0%
+okay and then do I have good models for
+ 
+
+ align:start position:0%
+okay and then do I have good models for
+these fluxes you think about these terms
+
+ align:start position:0%
+these fluxes you think about these terms
+ 
+
+ align:start position:0%
+these fluxes you think about these terms
+in this way okay so sometimes it's
+
+ align:start position:0%
+in this way okay so sometimes it's
+ 
+
+ align:start position:0%
+in this way okay so sometimes it's
+useful so there's big be the amount of B
+
+ align:start position:0%
+useful so there's big be the amount of B
+ 
+
+ align:start position:0%
+useful so there's big be the amount of B
+in the volume is like the volume times
+
+ align:start position:0%
+in the volume is like the volume times
+ 
+
+ align:start position:0%
+in the volume is like the volume times
+the density of B the volumetric density
+
+ align:start position:0%
+the density of B the volumetric density
+ 
+
+ align:start position:0%
+the density of B the volumetric density
+of B and the volume right the average
+
+ align:start position:0%
+of B and the volume right the average
+ 
+
+ align:start position:0%
+of B and the volume right the average
+density in the volume R is like the
+
+ align:start position:0%
+density in the volume R is like the
+ 
+
+ align:start position:0%
+density in the volume R is like the
+volume multiplied by the average rate of
+
+ align:start position:0%
+volume multiplied by the average rate of
+ 
+
+ align:start position:0%
+volume multiplied by the average rate of
+generation or consumption okay F is the
+
+ align:start position:0%
+generation or consumption okay F is the
+ 
+
+ align:start position:0%
+generation or consumption okay F is the
+flux in or out it's the sum over all the
+
+ align:start position:0%
+flux in or out it's the sum over all the
+ 
+
+ align:start position:0%
+flux in or out it's the sum over all the
+phases of the flux through each of the
+
+ align:start position:0%
+phases of the flux through each of the
+ 
+
+ align:start position:0%
+phases of the flux through each of the
+phases which is the area of the face
+
+ align:start position:0%
+phases which is the area of the face
+ 
+
+ align:start position:0%
+phases which is the area of the face
+multiplied by the average flux through
+
+ align:start position:0%
+multiplied by the average flux through
+ 
+
+ align:start position:0%
+multiplied by the average flux through
+the face so this is the normal to the
+
+ align:start position:0%
+the face so this is the normal to the
+ 
+
+ align:start position:0%
+the face so this is the normal to the
+face and this is the flux through the
+
+ align:start position:0%
+face and this is the flux through the
+ 
+
+ align:start position:0%
+face and this is the flux through the
+face okay and so I just are gonna solve
+
+ align:start position:0%
+face okay and so I just are gonna solve
+ 
+
+ align:start position:0%
+face okay and so I just are gonna solve
+this equation right I try to figure out
+
+ align:start position:0%
+this equation right I try to figure out
+ 
+
+ align:start position:0%
+this equation right I try to figure out
+in each volume what's the average be
+
+ align:start position:0%
+in each volume what's the average be
+ 
+
+ align:start position:0%
+in each volume what's the average be
+okay that's what this tells me right
+
+ align:start position:0%
+okay that's what this tells me right
+ 
+
+ align:start position:0%
+okay that's what this tells me right
+well on average what is B on average
+
+ align:start position:0%
+well on average what is B on average
+ 
+
+ align:start position:0%
+well on average what is B on average
+what is the concentration on average
+
+ align:start position:0%
+what is the concentration on average
+ 
+
+ align:start position:0%
+what is the concentration on average
+what is the amount of momentum on
+
+ align:start position:0%
+what is the amount of momentum on
+ 
+
+ align:start position:0%
+what is the amount of momentum on
+average what is the total energy right
+
+ align:start position:0%
+average what is the total energy right
+ 
+
+ align:start position:0%
+average what is the total energy right
+it's fine
+
+ align:start position:0%
+it's fine
+ 
+
+ align:start position:0%
+it's fine
+okay so finite volume very simple okay
+
+ align:start position:0%
+okay so finite volume very simple okay
+ 
+
+ align:start position:0%
+okay so finite volume very simple okay
+what's nice about it
+
+ align:start position:0%
+what's nice about it
+ 
+
+ align:start position:0%
+what's nice about it
+well you know it's really suitable to
+
+ align:start position:0%
+well you know it's really suitable to
+ 
+
+ align:start position:0%
+well you know it's really suitable to
+any sort of geometry we want to look at
+
+ align:start position:0%
+any sort of geometry we want to look at
+ 
+
+ align:start position:0%
+any sort of geometry we want to look at
+we want to solve this equation say in
+
+ align:start position:0%
+we want to solve this equation say in
+ 
+
+ align:start position:0%
+we want to solve this equation say in
+this square domain we divide the domain
+
+ align:start position:0%
+this square domain we divide the domain
+ 
+
+ align:start position:0%
+this square domain we divide the domain
+up into a bunch of little square volumes
+
+ align:start position:0%
+up into a bunch of little square volumes
+ 
+
+ align:start position:0%
+up into a bunch of little square volumes
+and in each volume we just make sure
+
+ align:start position:0%
+and in each volume we just make sure
+ 
+
+ align:start position:0%
+and in each volume we just make sure
+that the amount of this be right
+
+ align:start position:0%
+that the amount of this be right
+ 
+
+ align:start position:0%
+that the amount of this be right
+balances the fluxes coming through the
+
+ align:start position:0%
+balances the fluxes coming through the
+ 
+
+ align:start position:0%
+balances the fluxes coming through the
+volume and the amount of consumption or
+
+ align:start position:0%
+volume and the amount of consumption or
+ 
+
+ align:start position:0%
+volume and the amount of consumption or
+generation of that quantity within the
+
+ align:start position:0%
+generation of that quantity within the
+ 
+
+ align:start position:0%
+generation of that quantity within the
+volume but it didn't have to be a square
+
+ align:start position:0%
+volume but it didn't have to be a square
+ 
+
+ align:start position:0%
+volume but it didn't have to be a square
+domain right square domain it's okay but
+
+ align:start position:0%
+domain right square domain it's okay but
+ 
+
+ align:start position:0%
+domain right square domain it's okay but
+maybe I want to solve it on some
+
+ align:start position:0%
+maybe I want to solve it on some
+ 
+
+ align:start position:0%
+maybe I want to solve it on some
+circular domain well I can divide that
+
+ align:start position:0%
+circular domain well I can divide that
+ 
+
+ align:start position:0%
+circular domain well I can divide that
+up into volumes too and actually this
+
+ align:start position:0%
+up into volumes too and actually this
+ 
+
+ align:start position:0%
+up into volumes too and actually this
+these equations are the same right they
+
+ align:start position:0%
+these equations are the same right they
+ 
+
+ align:start position:0%
+these equations are the same right they
+look identical I just got to calculate
+
+ align:start position:0%
+look identical I just got to calculate
+ 
+
+ align:start position:0%
+look identical I just got to calculate
+the flux through each of the phases okay
+
+ align:start position:0%
+the flux through each of the phases okay
+ 
+
+ align:start position:0%
+the flux through each of the phases okay
+but maybe I'm interested in I don't know
+
+ align:start position:0%
+but maybe I'm interested in I don't know
+ 
+
+ align:start position:0%
+but maybe I'm interested in I don't know
+pollution and one of the Great Lakes and
+
+ align:start position:0%
+pollution and one of the Great Lakes and
+ 
+
+ align:start position:0%
+pollution and one of the Great Lakes and
+I want to know how concentration is some
+
+ align:start position:0%
+I want to know how concentration is some
+ 
+
+ align:start position:0%
+I want to know how concentration is some
+pollutant is trans transformed well
+
+ align:start position:0%
+pollutant is trans transformed well
+ 
+
+ align:start position:0%
+pollutant is trans transformed well
+divide this up into a bunch of little
+
+ align:start position:0%
+divide this up into a bunch of little
+ 
+
+ align:start position:0%
+divide this up into a bunch of little
+volumes too and now I got to calculate
+
+ align:start position:0%
+volumes too and now I got to calculate
+ 
+
+ align:start position:0%
+volumes too and now I got to calculate
+the flux through each of these phases
+
+ align:start position:0%
+the flux through each of these phases
+ 
+
+ align:start position:0%
+the flux through each of these phases
+and that links all these domains
+
+ align:start position:0%
+and that links all these domains
+ 
+
+ align:start position:0%
+and that links all these domains
+together okay maybe I'm interested in
+
+ align:start position:0%
+together okay maybe I'm interested in
+ 
+
+ align:start position:0%
+together okay maybe I'm interested in
+transport within some porous medium say
+
+ align:start position:0%
+transport within some porous medium say
+ 
+
+ align:start position:0%
+transport within some porous medium say
+a bone I think it's someone's hip joint
+
+ align:start position:0%
+a bone I think it's someone's hip joint
+ 
+
+ align:start position:0%
+a bone I think it's someone's hip joint
+here okay well I divide that up into a
+
+ align:start position:0%
+here okay well I divide that up into a
+ 
+
+ align:start position:0%
+here okay well I divide that up into a
+bunch of volumes and I still sound solve
+
+ align:start position:0%
+bunch of volumes and I still sound solve
+ 
+
+ align:start position:0%
+bunch of volumes and I still sound solve
+the exact same conservation equation so
+
+ align:start position:0%
+the exact same conservation equation so
+ 
+
+ align:start position:0%
+the exact same conservation equation so
+I'm sort of decoupled the problem of
+
+ align:start position:0%
+I'm sort of decoupled the problem of
+ 
+
+ align:start position:0%
+I'm sort of decoupled the problem of
+meshing and equations okay the governing
+
+ align:start position:0%
+meshing and equations okay the governing
+ 
+
+ align:start position:0%
+meshing and equations okay the governing
+equations associated with the meshes as
+
+ align:start position:0%
+equations associated with the meshes as
+ 
+
+ align:start position:0%
+equations associated with the meshes as
+long as I have a way to divide the
+
+ align:start position:0%
+long as I have a way to divide the
+ 
+
+ align:start position:0%
+long as I have a way to divide the
+domain up may be very complicated okay
+
+ align:start position:0%
+domain up may be very complicated okay
+ 
+
+ align:start position:0%
+domain up may be very complicated okay
+I'm gonna go ask a buddy in applied math
+
+ align:start position:0%
+I'm gonna go ask a buddy in applied math
+ 
+
+ align:start position:0%
+I'm gonna go ask a buddy in applied math
+to do that
+
+ align:start position:0%
+to do that
+ 
+
+ align:start position:0%
+to do that
+well I'm gonna come to them with the
+
+ align:start position:0%
+well I'm gonna come to them with the
+ 
+
+ align:start position:0%
+well I'm gonna come to them with the
+right engineering equations for each of
+
+ align:start position:0%
+right engineering equations for each of
+ 
+
+ align:start position:0%
+right engineering equations for each of
+those domains a little equation for a
+
+ align:start position:0%
+those domains a little equation for a
+ 
+
+ align:start position:0%
+those domains a little equation for a
+CSTR okay it turns out this you know one
+
+ align:start position:0%
+CSTR okay it turns out this you know one
+ 
+
+ align:start position:0%
+CSTR okay it turns out this you know one
+of the one one of the most common say
+
+ align:start position:0%
+of the one one of the most common say
+ 
+
+ align:start position:0%
+of the one one of the most common say
+fluid mechanical codes out there that
+
+ align:start position:0%
+fluid mechanical codes out there that
+ 
+
+ align:start position:0%
+fluid mechanical codes out there that
+people use now is open foam okay this is
+
+ align:start position:0%
+people use now is open foam okay this is
+ 
+
+ align:start position:0%
+people use now is open foam okay this is
+very common
+
+ align:start position:0%
+very common
+ 
+
+ align:start position:0%
+very common
+lots of people use it it's very general
+
+ align:start position:0%
+lots of people use it it's very general
+ 
+
+ align:start position:0%
+lots of people use it it's very general
+solver does finite volume that's the
+
+ align:start position:0%
+solver does finite volume that's the
+ 
+
+ align:start position:0%
+solver does finite volume that's the
+method it chooses to use why does it
+
+ align:start position:0%
+method it chooses to use why does it
+ 
+
+ align:start position:0%
+method it chooses to use why does it
+choose to use because it wants to
+
+ align:start position:0%
+choose to use because it wants to
+ 
+
+ align:start position:0%
+choose to use because it wants to
+convert conserve momentum okay i
+
+ align:start position:0%
+convert conserve momentum okay i
+ 
+
+ align:start position:0%
+convert conserve momentum okay i
+guaranteed momentum conservation can't
+
+ align:start position:0%
+guaranteed momentum conservation can't
+ 
+
+ align:start position:0%
+guaranteed momentum conservation can't
+lose momentum can't lose energy okay
+
+ align:start position:0%
+lose momentum can't lose energy okay
+ 
+
+ align:start position:0%
+lose momentum can't lose energy okay
+can't lose mass I just have to pass the
+
+ align:start position:0%
+can't lose mass I just have to pass the
+ 
+
+ align:start position:0%
+can't lose mass I just have to pass the
+right amount between each of these
+
+ align:start position:0%
+right amount between each of these
+ 
+
+ align:start position:0%
+right amount between each of these
+spaces as long as my calculation of that
+
+ align:start position:0%
+spaces as long as my calculation of that
+ 
+
+ align:start position:0%
+spaces as long as my calculation of that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+accurate I've conserved the quantity it
+
+ align:start position:0%
+accurate I've conserved the quantity it
+ 
+
+ align:start position:0%
+accurate I've conserved the quantity it
+never evaporates find a difference
+
+ align:start position:0%
+never evaporates find a difference
+ 
+
+ align:start position:0%
+never evaporates find a difference
+finite element different basis set
+
+ align:start position:0%
+finite element different basis set
+ 
+
+ align:start position:0%
+finite element different basis set
+expansions they they will have this
+
+ align:start position:0%
+expansions they they will have this
+ 
+
+ align:start position:0%
+expansions they they will have this
+problem that at low levels of accuracy
+
+ align:start position:0%
+problem that at low levels of accuracy
+ 
+
+ align:start position:0%
+problem that at low levels of accuracy
+you can have sort of artificial constant
+
+ align:start position:0%
+you can have sort of artificial constant
+ 
+
+ align:start position:0%
+you can have sort of artificial constant
+consumption of save the quantity or
+
+ align:start position:0%
+consumption of save the quantity or
+ 
+
+ align:start position:0%
+consumption of save the quantity or
+artificial production of the quantity
+
+ align:start position:0%
+artificial production of the quantity
+ 
+
+ align:start position:0%
+artificial production of the quantity
+conserved quantity of interest okay so
+
+ align:start position:0%
+conserved quantity of interest okay so
+ 
+
+ align:start position:0%
+conserved quantity of interest okay so
+this is gonna be very nice way to solve
+
+ align:start position:0%
+this is gonna be very nice way to solve
+ 
+
+ align:start position:0%
+this is gonna be very nice way to solve
+these problems too
+
+ align:start position:0%
+these problems too
+ 
+
+ align:start position:0%
+these problems too
+it's another relaxation method it's a
+
+ align:start position:0%
+it's another relaxation method it's a
+ 
+
+ align:start position:0%
+it's another relaxation method it's a
+type of collocation I divide the domain
+
+ align:start position:0%
+type of collocation I divide the domain
+ 
+
+ align:start position:0%
+type of collocation I divide the domain
+up right and I try to satisfy
+
+ align:start position:0%
+up right and I try to satisfy
+ 
+
+ align:start position:0%
+up right and I try to satisfy
+conservation equations on each of these
+
+ align:start position:0%
+conservation equations on each of these
+ 
+
+ align:start position:0%
+conservation equations on each of these
+little volumes since finite volume okay
+
+ align:start position:0%
+little volumes since finite volume okay
+ 
+
+ align:start position:0%
+little volumes since finite volume okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how do you solve Pease by hand or
+
+ align:start position:0%
+so how do you solve Pease by hand or
+ 
+
+ align:start position:0%
+so how do you solve Pease by hand or
+write your own code there's a nice
+
+ align:start position:0%
+write your own code there's a nice
+ 
+
+ align:start position:0%
+write your own code there's a nice
+little tutorial here we'll see how far
+
+ align:start position:0%
+little tutorial here we'll see how far
+ 
+
+ align:start position:0%
+little tutorial here we'll see how far
+we're able to get through it before I
+
+ align:start position:0%
+we're able to get through it before I
+ 
+
+ align:start position:0%
+we're able to get through it before I
+gotta give you guys your cards but I'll
+
+ align:start position:0%
+gotta give you guys your cards but I'll
+ 
+
+ align:start position:0%
+gotta give you guys your cards but I'll
+illustrate some key points okay that I
+
+ align:start position:0%
+illustrate some key points okay that I
+ 
+
+ align:start position:0%
+illustrate some key points okay that I
+think are really important so step one
+
+ align:start position:0%
+think are really important so step one
+ 
+
+ align:start position:0%
+think are really important so step one
+okay no matter what what method you
+
+ align:start position:0%
+okay no matter what what method you
+ 
+
+ align:start position:0%
+okay no matter what what method you
+choose right whether you choose
+
+ align:start position:0%
+choose right whether you choose
+ 
+
+ align:start position:0%
+choose right whether you choose
+collocation whether you choose galerkin
+
+ align:start position:0%
+collocation whether you choose galerkin
+ 
+
+ align:start position:0%
+collocation whether you choose galerkin
+right whether using basis sets or you're
+
+ align:start position:0%
+right whether using basis sets or you're
+ 
+
+ align:start position:0%
+right whether using basis sets or you're
+using finite elements or finite volumes
+
+ align:start position:0%
+using finite elements or finite volumes
+ 
+
+ align:start position:0%
+using finite elements or finite volumes
+you've got some domain you're trying to
+
+ align:start position:0%
+you've got some domain you're trying to
+ 
+
+ align:start position:0%
+you've got some domain you're trying to
+solve your PDE and then you've got to
+
+ align:start position:0%
+solve your PDE and then you've got to
+ 
+
+ align:start position:0%
+solve your PDE and then you've got to
+discretize it okay you've got to figure
+
+ align:start position:0%
+discretize it okay you've got to figure
+ 
+
+ align:start position:0%
+discretize it okay you've got to figure
+out how to decompose the domain so for
+
+ align:start position:0%
+out how to decompose the domain so for
+ 
+
+ align:start position:0%
+out how to decompose the domain so for
+finite differences you might decompose
+
+ align:start position:0%
+finite differences you might decompose
+ 
+
+ align:start position:0%
+finite differences you might decompose
+it into a series of nodes at which you
+
+ align:start position:0%
+it into a series of nodes at which you
+ 
+
+ align:start position:0%
+it into a series of nodes at which you
+want to know the value of your function
+
+ align:start position:0%
+want to know the value of your function
+ 
+
+ align:start position:0%
+want to know the value of your function
+whatever that function is for finite
+
+ align:start position:0%
+whatever that function is for finite
+ 
+
+ align:start position:0%
+whatever that function is for finite
+volume you decompose it into cells in
+
+ align:start position:0%
+volume you decompose it into cells in
+ 
+
+ align:start position:0%
+volume you decompose it into cells in
+which you would like to know the average
+
+ align:start position:0%
+which you would like to know the average
+ 
+
+ align:start position:0%
+which you would like to know the average
+value of your conserved quantity for
+
+ align:start position:0%
+value of your conserved quantity for
+ 
+
+ align:start position:0%
+value of your conserved quantity for
+finite elements right you divide the
+
+ align:start position:0%
+finite elements right you divide the
+ 
+
+ align:start position:0%
+finite elements right you divide the
+domain up into into some points across
+
+ align:start position:0%
+domain up into into some points across
+ 
+
+ align:start position:0%
+domain up into into some points across
+which low-salt local basis functions
+
+ align:start position:0%
+which low-salt local basis functions
+ 
+
+ align:start position:0%
+which low-salt local basis functions
+span right the region you would like to
+
+ align:start position:0%
+span right the region you would like to
+ 
+
+ align:start position:0%
+span right the region you would like to
+know the weighting of these local basis
+
+ align:start position:0%
+know the weighting of these local basis
+ 
+
+ align:start position:0%
+know the weighting of these local basis
+functions near each of these points okay
+
+ align:start position:0%
+functions near each of these points okay
+ 
+
+ align:start position:0%
+functions near each of these points okay
+but you've got to divide the domain up
+
+ align:start position:0%
+but you've got to divide the domain up
+ 
+
+ align:start position:0%
+but you've got to divide the domain up
+and the most important thing okay is you
+
+ align:start position:0%
+and the most important thing okay is you
+ 
+
+ align:start position:0%
+and the most important thing okay is you
+always choose the spacing the nodes okay
+
+ align:start position:0%
+always choose the spacing the nodes okay
+ 
+
+ align:start position:0%
+always choose the spacing the nodes okay
+there are the dimensions of the cells to
+
+ align:start position:0%
+there are the dimensions of the cells to
+ 
+
+ align:start position:0%
+there are the dimensions of the cells to
+match the physics a very natural thing
+
+ align:start position:0%
+match the physics a very natural thing
+ 
+
+ align:start position:0%
+match the physics a very natural thing
+to want to do is to pick same say I've
+
+ align:start position:0%
+to want to do is to pick same say I've
+ 
+
+ align:start position:0%
+to want to do is to pick same say I've
+got this square grid is to pick the
+
+ align:start position:0%
+got this square grid is to pick the
+ 
+
+ align:start position:0%
+got this square grid is to pick the
+number of grid points to discretize with
+
+ align:start position:0%
+number of grid points to discretize with
+ 
+
+ align:start position:0%
+number of grid points to discretize with
+right say I'm gonna use a hundred points
+
+ align:start position:0%
+right say I'm gonna use a hundred points
+ 
+
+ align:start position:0%
+right say I'm gonna use a hundred points
+in this dimension and a hundred points
+
+ align:start position:0%
+in this dimension and a hundred points
+ 
+
+ align:start position:0%
+in this dimension and a hundred points
+in that dimension actually tells me
+
+ align:start position:0%
+in that dimension actually tells me
+ 
+
+ align:start position:0%
+in that dimension actually tells me
+nothing that's an irrelevant number okay
+
+ align:start position:0%
+nothing that's an irrelevant number okay
+ 
+
+ align:start position:0%
+nothing that's an irrelevant number okay
+the physics has no idea how many grid
+
+ align:start position:0%
+the physics has no idea how many grid
+ 
+
+ align:start position:0%
+the physics has no idea how many grid
+nodes you put in there
+
+ align:start position:0%
+nodes you put in there
+ 
+
+ align:start position:0%
+nodes you put in there
+doesn't care okay there are length
+
+ align:start position:0%
+doesn't care okay there are length
+ 
+
+ align:start position:0%
+doesn't care okay there are length
+scales that are intrinsic to the problem
+
+ align:start position:0%
+scales that are intrinsic to the problem
+ 
+
+ align:start position:0%
+scales that are intrinsic to the problem
+you're trying to study and the
+
+ align:start position:0%
+you're trying to study and the
+ 
+
+ align:start position:0%
+you're trying to study and the
+discretization should resolve those
+
+ align:start position:0%
+discretization should resolve those
+ 
+
+ align:start position:0%
+discretization should resolve those
+physically relevant length scales okay
+
+ align:start position:0%
+physically relevant length scales okay
+ 
+
+ align:start position:0%
+physically relevant length scales okay
+so it might be the case that I only need
+
+ align:start position:0%
+so it might be the case that I only need
+ 
+
+ align:start position:0%
+so it might be the case that I only need
+a resolution of you know one part in ten
+
+ align:start position:0%
+a resolution of you know one part in ten
+ 
+
+ align:start position:0%
+a resolution of you know one part in ten
+along this dimension and one part in ten
+
+ align:start position:0%
+along this dimension and one part in ten
+ 
+
+ align:start position:0%
+along this dimension and one part in ten
+along this dimension because the physics
+
+ align:start position:0%
+along this dimension because the physics
+ 
+
+ align:start position:0%
+along this dimension because the physics
+are such that that's that's good to get
+
+ align:start position:0%
+are such that that's that's good to get
+ 
+
+ align:start position:0%
+are such that that's that's good to get
+a description of the solution to this
+
+ align:start position:0%
+a description of the solution to this
+ 
+
+ align:start position:0%
+a description of the solution to this
+problem it might be that I need one part
+
+ align:start position:0%
+problem it might be that I need one part
+ 
+
+ align:start position:0%
+problem it might be that I need one part
+in a million in this dimension and one
+
+ align:start position:0%
+in a million in this dimension and one
+ 
+
+ align:start position:0%
+in a million in this dimension and one
+part in ten in that dimension because
+
+ align:start position:0%
+part in ten in that dimension because
+ 
+
+ align:start position:0%
+part in ten in that dimension because
+the physics are that way okay so you
+
+ align:start position:0%
+the physics are that way okay so you
+ 
+
+ align:start position:0%
+the physics are that way okay so you
+really want to think about length scales
+
+ align:start position:0%
+really want to think about length scales
+ 
+
+ align:start position:0%
+really want to think about length scales
+not numbers of nodes is a very common
+
+ align:start position:0%
+not numbers of nodes is a very common
+ 
+
+ align:start position:0%
+not numbers of nodes is a very common
+mistake you say oh I a hundred and a
+
+ align:start position:0%
+mistake you say oh I a hundred and a
+ 
+
+ align:start position:0%
+mistake you say oh I a hundred and a
+hundred that makes sense or ten in ten
+
+ align:start position:0%
+hundred that makes sense or ten in ten
+ 
+
+ align:start position:0%
+hundred that makes sense or ten in ten
+or you know you pick these randomly but
+
+ align:start position:0%
+or you know you pick these randomly but
+ 
+
+ align:start position:0%
+or you know you pick these randomly but
+you won't think about physics instead
+
+ align:start position:0%
+you won't think about physics instead
+ 
+
+ align:start position:0%
+you won't think about physics instead
+here's a good example right this is my
+
+ align:start position:0%
+here's a good example right this is my
+ 
+
+ align:start position:0%
+here's a good example right this is my
+phone you'll solve a problem like this
+
+ align:start position:0%
+phone you'll solve a problem like this
+ 
+
+ align:start position:0%
+phone you'll solve a problem like this
+you already saw it in some sense in the
+
+ align:start position:0%
+you already saw it in some sense in the
+ 
+
+ align:start position:0%
+you already saw it in some sense in the
+finite finite element or COMSOL tutorial
+
+ align:start position:0%
+finite finite element or COMSOL tutorial
+ 
+
+ align:start position:0%
+finite finite element or COMSOL tutorial
+all right there's a little drug patch
+
+ align:start position:0%
+all right there's a little drug patch
+ 
+
+ align:start position:0%
+all right there's a little drug patch
+here near this red zone all right it's
+
+ align:start position:0%
+here near this red zone all right it's
+ 
+
+ align:start position:0%
+here near this red zone all right it's
+leaking drug into a shear flow and it's
+
+ align:start position:0%
+leaking drug into a shear flow and it's
+ 
+
+ align:start position:0%
+leaking drug into a shear flow and it's
+all being infected down okay here's
+
+ align:start position:0%
+all being infected down okay here's
+ 
+
+ align:start position:0%
+all being infected down okay here's
+here's here's here's my solution to the
+
+ align:start position:0%
+here's here's here's my solution to the
+ 
+
+ align:start position:0%
+here's here's here's my solution to the
+problem I think is pretty good one
+
+ align:start position:0%
+problem I think is pretty good one
+ 
+
+ align:start position:0%
+problem I think is pretty good one
+here's a solution from when I taught the
+
+ align:start position:0%
+here's a solution from when I taught the
+ 
+
+ align:start position:0%
+here's a solution from when I taught the
+course two years ago that the T is
+
+ align:start position:0%
+course two years ago that the T is
+ 
+
+ align:start position:0%
+course two years ago that the T is
+produced and I didn't I didn't talk with
+
+ align:start position:0%
+produced and I didn't I didn't talk with
+ 
+
+ align:start position:0%
+produced and I didn't I didn't talk with
+the TAS about this issue with length
+
+ align:start position:0%
+the TAS about this issue with length
+ 
+
+ align:start position:0%
+the TAS about this issue with length
+scales and it's it's sort of got the
+
+ align:start position:0%
+scales and it's it's sort of got the
+ 
+
+ align:start position:0%
+scales and it's it's sort of got the
+right structure you can see here's the
+
+ align:start position:0%
+right structure you can see here's the
+ 
+
+ align:start position:0%
+right structure you can see here's the
+patch and there's some advection and
+
+ align:start position:0%
+patch and there's some advection and
+ 
+
+ align:start position:0%
+patch and there's some advection and
+diffusion but it's it's not a very
+
+ align:start position:0%
+diffusion but it's it's not a very
+ 
+
+ align:start position:0%
+diffusion but it's it's not a very
+stable solution it turns out it's also
+
+ align:start position:0%
+stable solution it turns out it's also
+ 
+
+ align:start position:0%
+stable solution it turns out it's also
+not very accurate it doesn't reflect the
+
+ align:start position:0%
+not very accurate it doesn't reflect the
+ 
+
+ align:start position:0%
+not very accurate it doesn't reflect the
+essential physics and the point is
+
+ align:start position:0%
+essential physics and the point is
+ 
+
+ align:start position:0%
+essential physics and the point is
+actually the scales so here the patch
+
+ align:start position:0%
+actually the scales so here the patch
+ 
+
+ align:start position:0%
+actually the scales so here the patch
+was one centimeter in diameter okay and
+
+ align:start position:0%
+was one centimeter in diameter okay and
+ 
+
+ align:start position:0%
+was one centimeter in diameter okay and
+so here you got many centimeters along
+
+ align:start position:0%
+so here you got many centimeters along
+ 
+
+ align:start position:0%
+so here you got many centimeters along
+this direction where you get advection
+
+ align:start position:0%
+this direction where you get advection
+ 
+
+ align:start position:0%
+this direction where you get advection
+here you've got two centimeters in this
+
+ align:start position:0%
+here you've got two centimeters in this
+ 
+
+ align:start position:0%
+here you've got two centimeters in this
+direction but actually the solution it's
+
+ align:start position:0%
+direction but actually the solution it's
+ 
+
+ align:start position:0%
+direction but actually the solution it's
+really confined down to this small space
+
+ align:start position:0%
+really confined down to this small space
+ 
+
+ align:start position:0%
+really confined down to this small space
+right the physics all happens at
+
+ align:start position:0%
+right the physics all happens at
+ 
+
+ align:start position:0%
+right the physics all happens at
+fractions of a centimeter okay
+
+ align:start position:0%
+fractions of a centimeter okay
+ 
+
+ align:start position:0%
+fractions of a centimeter okay
+you took transport so you know that this
+
+ align:start position:0%
+you took transport so you know that this
+ 
+
+ align:start position:0%
+you took transport so you know that this
+is a problem in which there's a boundary
+
+ align:start position:0%
+is a problem in which there's a boundary
+ 
+
+ align:start position:0%
+is a problem in which there's a boundary
+layer and all the change in
+
+ align:start position:0%
+layer and all the change in
+ 
+
+ align:start position:0%
+layer and all the change in
+concentration is confined to that little
+
+ align:start position:0%
+concentration is confined to that little
+ 
+
+ align:start position:0%
+concentration is confined to that little
+boundary layer okay so really when you
+
+ align:start position:0%
+boundary layer okay so really when you
+ 
+
+ align:start position:0%
+boundary layer okay so really when you
+do your numerical solution you wanna do
+
+ align:start position:0%
+do your numerical solution you wanna do
+ 
+
+ align:start position:0%
+do your numerical solution you wanna do
+like like what's done up here now that
+
+ align:start position:0%
+like like what's done up here now that
+ 
+
+ align:start position:0%
+like like what's done up here now that
+lengths are made dimensionless on the
+
+ align:start position:0%
+lengths are made dimensionless on the
+ 
+
+ align:start position:0%
+lengths are made dimensionless on the
+width of the patch but they're you know
+
+ align:start position:0%
+width of the patch but they're you know
+ 
+
+ align:start position:0%
+width of the patch but they're you know
+you could think these is measured in
+
+ align:start position:0%
+you could think these is measured in
+ 
+
+ align:start position:0%
+you could think these is measured in
+centimeters but look at the dimension
+
+ align:start position:0%
+centimeters but look at the dimension
+ 
+
+ align:start position:0%
+centimeters but look at the dimension
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+right we need to resolve the solution
+
+ align:start position:0%
+right we need to resolve the solution
+ 
+
+ align:start position:0%
+right we need to resolve the solution
+down at the 0.1 centimeter and smaller
+
+ align:start position:0%
+down at the 0.1 centimeter and smaller
+ 
+
+ align:start position:0%
+down at the 0.1 centimeter and smaller
+scale I want to put all my little disk
+
+ align:start position:0%
+scale I want to put all my little disk
+ 
+
+ align:start position:0%
+scale I want to put all my little disk
+rotation or my nodes down here so they
+
+ align:start position:0%
+rotation or my nodes down here so they
+ 
+
+ align:start position:0%
+rotation or my nodes down here so they
+can see how the concentration field
+
+ align:start position:0%
+can see how the concentration field
+ 
+
+ align:start position:0%
+can see how the concentration field
+changes okay as a function of distance I
+
+ align:start position:0%
+changes okay as a function of distance I
+ 
+
+ align:start position:0%
+changes okay as a function of distance I
+have to know something about the physics
+
+ align:start position:0%
+have to know something about the physics
+ 
+
+ align:start position:0%
+have to know something about the physics
+to do that though okay can't just solve
+
+ align:start position:0%
+to do that though okay can't just solve
+ 
+
+ align:start position:0%
+to do that though okay can't just solve
+this blindly it may or may not be the
+
+ align:start position:0%
+this blindly it may or may not be the
+ 
+
+ align:start position:0%
+this blindly it may or may not be the
+case the calm saw recognizes the
+
+ align:start position:0%
+case the calm saw recognizes the
+ 
+
+ align:start position:0%
+case the calm saw recognizes the
+physical situation and Ramesh's your
+
+ align:start position:0%
+physical situation and Ramesh's your
+ 
+
+ align:start position:0%
+physical situation and Ramesh's your
+problem to put mesh points down where
+
+ align:start position:0%
+problem to put mesh points down where
+ 
+
+ align:start position:0%
+problem to put mesh points down where
+they matter okay it may do that it may
+
+ align:start position:0%
+they matter okay it may do that it may
+ 
+
+ align:start position:0%
+they matter okay it may do that it may
+not do that it just doesn't know people
+
+ align:start position:0%
+not do that it just doesn't know people
+ 
+
+ align:start position:0%
+not do that it just doesn't know people
+build heuristics to try to solve these
+
+ align:start position:0%
+build heuristics to try to solve these
+ 
+
+ align:start position:0%
+build heuristics to try to solve these
+rameshan problems but they may not
+
+ align:start position:0%
+rameshan problems but they may not
+ 
+
+ align:start position:0%
+rameshan problems but they may not
+always apply so it's good to understand
+
+ align:start position:0%
+always apply so it's good to understand
+ 
+
+ align:start position:0%
+always apply so it's good to understand
+the physics of the problem this rough
+
+ align:start position:0%
+the physics of the problem this rough
+ 
+
+ align:start position:0%
+the physics of the problem this rough
+patch problem this is a pretty common
+
+ align:start position:0%
+patch problem this is a pretty common
+ 
+
+ align:start position:0%
+patch problem this is a pretty common
+transport problem did the professor
+
+ align:start position:0%
+transport problem did the professor
+ 
+
+ align:start position:0%
+transport problem did the professor
+bazan give you guys a talk during your
+
+ align:start position:0%
+bazan give you guys a talk during your
+ 
+
+ align:start position:0%
+bazan give you guys a talk during your
+visit weekend was that this last year is
+
+ align:start position:0%
+visit weekend was that this last year is
+ 
+
+ align:start position:0%
+visit weekend was that this last year is
+that two years ago it was two years ago
+
+ align:start position:0%
+that two years ago it was two years ago
+ 
+
+ align:start position:0%
+that two years ago it was two years ago
+he does problems with bromine flow
+
+ align:start position:0%
+he does problems with bromine flow
+ 
+
+ align:start position:0%
+he does problems with bromine flow
+batteries right and they work exactly
+
+ align:start position:0%
+batteries right and they work exactly
+ 
+
+ align:start position:0%
+batteries right and they work exactly
+this way have flow of a you have flow of
+
+ align:start position:0%
+this way have flow of a you have flow of
+ 
+
+ align:start position:0%
+this way have flow of a you have flow of
+bromine in an electrochemical reaction
+
+ align:start position:0%
+bromine in an electrochemical reaction
+ 
+
+ align:start position:0%
+bromine in an electrochemical reaction
+takes place at the surface this entire
+
+ align:start position:0%
+takes place at the surface this entire
+ 
+
+ align:start position:0%
+takes place at the surface this entire
+thing is premise on the fact that you
+
+ align:start position:0%
+thing is premise on the fact that you
+ 
+
+ align:start position:0%
+thing is premise on the fact that you
+have a very thin boundary layer in which
+
+ align:start position:0%
+have a very thin boundary layer in which
+ 
+
+ align:start position:0%
+have a very thin boundary layer in which
+the electrochemical you know in which
+
+ align:start position:0%
+the electrochemical you know in which
+ 
+
+ align:start position:0%
+the electrochemical you know in which
+the reagents are confined and if that
+
+ align:start position:0%
+the reagents are confined and if that
+ 
+
+ align:start position:0%
+the reagents are confined and if that
+boundary layer gets too thick and
+
+ align:start position:0%
+boundary layer gets too thick and
+ 
+
+ align:start position:0%
+boundary layer gets too thick and
+reaches the other electrode it screws up
+
+ align:start position:0%
+reaches the other electrode it screws up
+ 
+
+ align:start position:0%
+reaches the other electrode it screws up
+the reaction and doesn't work as a
+
+ align:start position:0%
+the reaction and doesn't work as a
+ 
+
+ align:start position:0%
+the reaction and doesn't work as a
+battery anymore okay so being able to
+
+ align:start position:0%
+battery anymore okay so being able to
+ 
+
+ align:start position:0%
+battery anymore okay so being able to
+resolve right concentration gradients in
+
+ align:start position:0%
+resolve right concentration gradients in
+ 
+
+ align:start position:0%
+resolve right concentration gradients in
+this small domain so it's just important
+
+ align:start position:0%
+this small domain so it's just important
+ 
+
+ align:start position:0%
+this small domain so it's just important
+for this drug problems important in
+
+ align:start position:0%
+for this drug problems important in
+ 
+
+ align:start position:0%
+for this drug problems important in
+general common sort of transport
+
+ align:start position:0%
+general common sort of transport
+ 
+
+ align:start position:0%
+general common sort of transport
+transport a type problem and the
+
+ align:start position:0%
+transport a type problem and the
+ 
+
+ align:start position:0%
+transport a type problem and the
+numerical solution is really going to
+
+ align:start position:0%
+numerical solution is really going to
+ 
+
+ align:start position:0%
+numerical solution is really going to
+hinge on your ability to recognize the
+
+ align:start position:0%
+hinge on your ability to recognize the
+ 
+
+ align:start position:0%
+hinge on your ability to recognize the
+physics and resolve the solution over
+
+ align:start position:0%
+physics and resolve the solution over
+ 
+
+ align:start position:0%
+physics and resolve the solution over
+the length scales that are important in
+
+ align:start position:0%
+the length scales that are important in
+ 
+
+ align:start position:0%
+the length scales that are important in
+the problem okay so that's the number
+
+ align:start position:0%
+the problem okay so that's the number
+ 
+
+ align:start position:0%
+the problem okay so that's the number
+one most important thing for doing these
+
+ align:start position:0%
+one most important thing for doing these
+ 
+
+ align:start position:0%
+one most important thing for doing these
+PDS the rest of the notes okay well take
+
+ align:start position:0%
+PDS the rest of the notes okay well take
+ 
+
+ align:start position:0%
+PDS the rest of the notes okay well take
+take you through the construction of a
+
+ align:start position:0%
+take you through the construction of a
+ 
+
+ align:start position:0%
+take you through the construction of a
+numerical solution to the diffusion
+
+ align:start position:0%
+numerical solution to the diffusion
+ 
+
+ align:start position:0%
+numerical solution to the diffusion
+equation in 2d okay and some different
+
+ align:start position:0%
+equation in 2d okay and some different
+ 
+
+ align:start position:0%
+equation in 2d okay and some different
+scenarios that you might try to employ
+
+ align:start position:0%
+scenarios that you might try to employ
+ 
+
+ align:start position:0%
+scenarios that you might try to employ
+in MATLAB to solve them and how you can
+
+ align:start position:0%
+in MATLAB to solve them and how you can
+ 
+
+ align:start position:0%
+in MATLAB to solve them and how you can
+accelerate the solution using different
+
+ align:start position:0%
+accelerate the solution using different
+ 
+
+ align:start position:0%
+accelerate the solution using different
+MATLAB functions it's fun to try out and
+
+ align:start position:0%
+MATLAB functions it's fun to try out and
+ 
+
+ align:start position:0%
+MATLAB functions it's fun to try out and
+play with you'll see that I can I can
+
+ align:start position:0%
+play with you'll see that I can I can
+ 
+
+ align:start position:0%
+play with you'll see that I can I can
+make the solution to this problem go
+
+ align:start position:0%
+make the solution to this problem go
+ 
+
+ align:start position:0%
+make the solution to this problem go
+very fast for a domain that's quite
+
+ align:start position:0%
+very fast for a domain that's quite
+ 
+
+ align:start position:0%
+very fast for a domain that's quite
+highly discretized by recognizing
+
+ align:start position:0%
+highly discretized by recognizing
+ 
+
+ align:start position:0%
+highly discretized by recognizing
+certain forms of the equations choosing
+
+ align:start position:0%
+certain forms of the equations choosing
+ 
+
+ align:start position:0%
+certain forms of the equations choosing
+certain solvers to solve with okay good
+
+ align:start position:0%
+certain solvers to solve with okay good
+ 
+
+ align:start position:0%
+certain solvers to solve with okay good
+all right I'll meet you guys I'm back
+
+ align:start position:0%
+all right I'll meet you guys I'm back
+ 
+
+ align:start position:0%
+all right I'll meet you guys I'm back
+and we'll hand out these gift cards and
+
+ align:start position:0%
+and we'll hand out these gift cards and
+ 
+
+ align:start position:0%
+and we'll hand out these gift cards and
+good luck on your quiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/ufM3HLTZ47k.txt b/ufM3HLTZ47k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..abd5b3ac1c4d8a2e9be1861dbdacf15a31fbd270
--- /dev/null
+++ b/ufM3HLTZ47k.txt
@@ -0,0 +1,11979 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu. Okay, welcome back. Well,
+
+ align:start position:0%
+ocw.mit.edu. Okay, welcome back. Well,
+ 
+
+ align:start position:0%
+ocw.mit.edu. Okay, welcome back. Well,
+sorry, I wasn't here on It's more
+
+ align:start position:0%
+sorry, I wasn't here on It's more
+ 
+
+ align:start position:0%
+sorry, I wasn't here on It's more
+dramatic for me, I guess, than if I had
+
+ align:start position:0%
+dramatic for me, I guess, than if I had
+ 
+
+ align:start position:0%
+dramatic for me, I guess, than if I had
+been here on Tuesday. I hope John did a
+
+ align:start position:0%
+been here on Tuesday. I hope John did a
+ 
+
+ align:start position:0%
+been here on Tuesday. I hope John did a
+did a good job uh covering for me. I'm
+
+ align:start position:0%
+did a good job uh covering for me. I'm
+ 
+
+ align:start position:0%
+did a good job uh covering for me. I'm
+sure he I'm sure he did. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you learned about walking robots.
+
+ align:start position:0%
+um you learned about walking robots.
+ 
+
+ align:start position:0%
+um you learned about walking robots.
+You've learned about lots of robots. You
+
+ align:start position:0%
+You've learned about lots of robots. You
+ 
+
+ align:start position:0%
+You've learned about lots of robots. You
+learned with a handful of very powerful
+
+ align:start position:0%
+learned with a handful of very powerful
+ 
+
+ align:start position:0%
+learned with a handful of very powerful
+uh techniques, I think, for designing
+
+ align:start position:0%
+uh techniques, I think, for designing
+ 
+
+ align:start position:0%
+uh techniques, I think, for designing
+motions for these robots. Um some of my
+
+ align:start position:0%
+motions for these robots. Um some of my
+ 
+
+ align:start position:0%
+motions for these robots. Um some of my
+favorite these days are things like the
+
+ align:start position:0%
+favorite these days are things like the
+ 
+
+ align:start position:0%
+favorite these days are things like the
+durall type methods.
+
+ align:start position:0%
+durall type methods.
+ 
+
+ align:start position:0%
+durall type methods.
+So let's consider um the problem of
+
+ align:start position:0%
+So let's consider um the problem of
+ 
+
+ align:start position:0%
+So let's consider um the problem of
+taking some robot described by our
+
+ align:start position:0%
+taking some robot described by our
+ 
+
+ align:start position:0%
+taking some robot described by our
+standard some nonlinear dynamics
+
+ align:start position:0%
+standard some nonlinear dynamics
+ 
+
+ align:start position:0%
+standard some nonlinear dynamics
+form and taking that robot from an
+
+ align:start position:0%
+form and taking that robot from an
+ 
+
+ align:start position:0%
+form and taking that robot from an
+initial
+
+ align:start position:0%
+initial
+ 
+
+ align:start position:0%
+initial
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+x0 and getting it to some final
+
+ align:start position:0%
+x0 and getting it to some final
+ 
+
+ align:start position:0%
+x0 and getting it to some final
+condition. I don't even care about the
+
+ align:start position:0%
+condition. I don't even care about the
+ 
+
+ align:start position:0%
+condition. I don't even care about the
+time. Say just getting it to um some
+
+ align:start position:0%
+time. Say just getting it to um some
+ 
+
+ align:start position:0%
+time. Say just getting it to um some
+other state x
+
+ align:start position:0%
+other state x
+ 
+
+ align:start position:0%
+other state x
+goal. So what tools have we already got
+
+ align:start position:0%
+goal. So what tools have we already got
+ 
+
+ align:start position:0%
+goal. So what tools have we already got
+um that could help us drive this system
+
+ align:start position:0%
+um that could help us drive this system
+ 
+
+ align:start position:0%
+um that could help us drive this system
+from some initial condition to some goal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state? The answer is a lot of tools,
+
+ align:start position:0%
+state? The answer is a lot of tools,
+ 
+
+ align:start position:0%
+state? The answer is a lot of tools,
+right? Um, if the systems if the state
+
+ align:start position:0%
+right? Um, if the systems if the state
+ 
+
+ align:start position:0%
+right? Um, if the systems if the state
+space is small enough, you could imagine
+
+ align:start position:0%
+space is small enough, you could imagine
+ 
+
+ align:start position:0%
+space is small enough, you could imagine
+designing an optimal control cost
+
+ align:start position:0%
+designing an optimal control cost
+ 
+
+ align:start position:0%
+designing an optimal control cost
+function that we could do dynamic
+
+ align:start position:0%
+function that we could do dynamic
+ 
+
+ align:start position:0%
+function that we could do dynamic
+programming on that would get us to that
+
+ align:start position:0%
+programming on that would get us to that
+ 
+
+ align:start position:0%
+programming on that would get us to that
+goal if we only rewarded ourselves from
+
+ align:start position:0%
+goal if we only rewarded ourselves from
+ 
+
+ align:start position:0%
+goal if we only rewarded ourselves from
+being away from the goal. Um, we could
+
+ align:start position:0%
+being away from the goal. Um, we could
+ 
+
+ align:start position:0%
+being away from the goal. Um, we could
+do a shooting method, right? Um we can
+
+ align:start position:0%
+do a shooting method, right? Um we can
+ 
+
+ align:start position:0%
+do a shooting method, right? Um we can
+even in if we if we if we're using our
+
+ align:start position:0%
+even in if we if we if we're using our
+ 
+
+ align:start position:0%
+even in if we if we if we're using our
+SQP um our snapped type interface to the
+
+ align:start position:0%
+SQP um our snapped type interface to the
+ 
+
+ align:start position:0%
+SQP um our snapped type interface to the
+shooting methods then we could provide a
+
+ align:start position:0%
+shooting methods then we could provide a
+ 
+
+ align:start position:0%
+shooting methods then we could provide a
+final value constraint
+
+ align:start position:0%
+final value constraint
+ 
+
+ align:start position:0%
+final value constraint
+um which says I want the end point of my
+
+ align:start position:0%
+um which says I want the end point of my
+ 
+
+ align:start position:0%
+um which says I want the end point of my
+trajectory to be exactly at the goal and
+
+ align:start position:0%
+trajectory to be exactly at the goal and
+ 
+
+ align:start position:0%
+trajectory to be exactly at the goal and
+that would that would solve this problem
+
+ align:start position:0%
+that would that would solve this problem
+ 
+
+ align:start position:0%
+that would that would solve this problem
+in some cases. Okay. But both of those
+
+ align:start position:0%
+in some cases. Okay. But both of those
+ 
+
+ align:start position:0%
+in some cases. Okay. But both of those
+methods have problems right? The DP
+
+ align:start position:0%
+methods have problems right? The DP
+ 
+
+ align:start position:0%
+methods have problems right? The DP
+doesn't scale.
+
+ align:start position:0%
+doesn't scale.
+ 
+
+ align:start position:0%
+doesn't scale.
+the shooting methods scale
+
+ align:start position:0%
+the shooting methods scale
+ 
+
+ align:start position:0%
+the shooting methods scale
+nicely, but if you ask your shooting
+
+ align:start position:0%
+nicely, but if you ask your shooting
+ 
+
+ align:start position:0%
+nicely, but if you ask your shooting
+method to drive you from X0 to X goal,
+
+ align:start position:0%
+method to drive you from X0 to X goal,
+ 
+
+ align:start position:0%
+method to drive you from X0 to X goal,
+um there's some chance it's going to
+
+ align:start position:0%
+um there's some chance it's going to
+ 
+
+ align:start position:0%
+um there's some chance it's going to
+just say I can't do it, right? I can't
+
+ align:start position:0%
+just say I can't do it, right? I can't
+ 
+
+ align:start position:0%
+just say I can't do it, right? I can't
+satisfy that constraint because it's a
+
+ align:start position:0%
+satisfy that constraint because it's a
+ 
+
+ align:start position:0%
+satisfy that constraint because it's a
+based on a local gradient
+
+ align:start position:0%
+based on a local gradient
+ 
+
+ align:start position:0%
+based on a local gradient
+optimization. And if there's local
+
+ align:start position:0%
+optimization. And if there's local
+ 
+
+ align:start position:0%
+optimization. And if there's local
+minima,
+
+ align:start position:0%
+minima,
+ 
+
+ align:start position:0%
+minima,
+um, snap will just say, I can't satisfy
+
+ align:start position:0%
+um, snap will just say, I can't satisfy
+ 
+
+ align:start position:0%
+um, snap will just say, I can't satisfy
+the constraint, um, x at time final
+
+ align:start position:0%
+the constraint, um, x at time final
+ 
+
+ align:start position:0%
+the constraint, um, x at time final
+equals x goal. Happens a lot. If you're
+
+ align:start position:0%
+equals x goal. Happens a lot. If you're
+ 
+
+ align:start position:0%
+equals x goal. Happens a lot. If you're
+looking at hard enough, interesting
+
+ align:start position:0%
+looking at hard enough, interesting
+ 
+
+ align:start position:0%
+looking at hard enough, interesting
+enough problems, it'll happen to you.
+
+ align:start position:0%
+enough problems, it'll happen to you.
+ 
+
+ align:start position:0%
+enough problems, it'll happen to you.
+Okay. So, what do you do? Do you just
+
+ align:start position:0%
+Okay. So, what do you do? Do you just
+ 
+
+ align:start position:0%
+Okay. So, what do you do? Do you just
+say, you know, find a new research
+
+ align:start position:0%
+say, you know, find a new research
+ 
+
+ align:start position:0%
+say, you know, find a new research
+problem, tell my adviser, I got to find
+
+ align:start position:0%
+problem, tell my adviser, I got to find
+ 
+
+ align:start position:0%
+problem, tell my adviser, I got to find
+something else. Okay. There's more
+
+ align:start position:0%
+something else. Okay. There's more
+ 
+
+ align:start position:0%
+something else. Okay. There's more
+things you can try, right? Um
+
+ align:start position:0%
+things you can try, right? Um
+ 
+
+ align:start position:0%
+things you can try, right? Um
+the methods I want to talk about
+
+ align:start position:0%
+the methods I want to talk about
+ 
+
+ align:start position:0%
+the methods I want to talk about
+today are the feasible motion planning
+
+ align:start position:0%
+today are the feasible motion planning
+ 
+
+ align:start position:0%
+today are the feasible motion planning
+algorithms. Okay. So motion planning is
+
+ align:start position:0%
+algorithms. Okay. So motion planning is
+ 
+
+ align:start position:0%
+algorithms. Okay. So motion planning is
+a is a very broad term. It's used all
+
+ align:start position:0%
+a is a very broad term. It's used all
+ 
+
+ align:start position:0%
+a is a very broad term. It's used all
+the time in
+
+ align:start position:0%
+the time in
+ 
+
+ align:start position:0%
+the time in
+robotics. I'd say roughly everything
+
+ align:start position:0%
+robotics. I'd say roughly everything
+ 
+
+ align:start position:0%
+robotics. I'd say roughly everything
+we've done to date has been a motion
+
+ align:start position:0%
+we've done to date has been a motion
+ 
+
+ align:start position:0%
+we've done to date has been a motion
+planning algorithm. It's like saying
+
+ align:start position:0%
+planning algorithm. It's like saying
+ 
+
+ align:start position:0%
+planning algorithm. It's like saying
+it's a control algorithm. It's a very
+
+ align:start position:0%
+it's a control algorithm. It's a very
+ 
+
+ align:start position:0%
+it's a control algorithm. It's a very
+general term. Some people um debate when
+
+ align:start position:0%
+general term. Some people um debate when
+ 
+
+ align:start position:0%
+general term. Some people um debate when
+something you know whether whether an
+
+ align:start position:0%
+something you know whether whether an
+ 
+
+ align:start position:0%
+something you know whether whether an
+algorithm is a motion planning algorithm
+
+ align:start position:0%
+algorithm is a motion planning algorithm
+ 
+
+ align:start position:0%
+algorithm is a motion planning algorithm
+or an optimal control algorithm or
+
+ align:start position:0%
+or an optimal control algorithm or
+ 
+
+ align:start position:0%
+or an optimal control algorithm or
+whatever. I think that's sort of a waste
+
+ align:start position:0%
+whatever. I think that's sort of a waste
+ 
+
+ align:start position:0%
+whatever. I think that's sort of a waste
+of time. I would say they're all motion
+
+ align:start position:0%
+of time. I would say they're all motion
+ 
+
+ align:start position:0%
+of time. I would say they're all motion
+planning algorithms. Most of the things
+
+ align:start position:0%
+planning algorithms. Most of the things
+ 
+
+ align:start position:0%
+planning algorithms. Most of the things
+we've talked about so
+
+ align:start position:0%
+we've talked about so
+ 
+
+ align:start position:0%
+we've talked about so
+far I would call optimal motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planning, right? where we actually had a
+
+ align:start position:0%
+planning, right? where we actually had a
+ 
+
+ align:start position:0%
+planning, right? where we actually had a
+cost function flying around to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it. Often times motion plans go from a
+
+ align:start position:0%
+it. Often times motion plans go from a
+ 
+
+ align:start position:0%
+it. Often times motion plans go from a
+start to a goal. Oftent times they're
+
+ align:start position:0%
+start to a goal. Oftent times they're
+ 
+
+ align:start position:0%
+start to a goal. Oftent times they're
+open loop but that's not really
+
+ align:start position:0%
+open loop but that's not really
+ 
+
+ align:start position:0%
+open loop but that's not really
+defining. You can do feedback motion
+
+ align:start position:0%
+defining. You can do feedback motion
+ 
+
+ align:start position:0%
+defining. You can do feedback motion
+planning and motion planning is just a
+
+ align:start position:0%
+planning and motion planning is just a
+ 
+
+ align:start position:0%
+planning and motion planning is just a
+very general term saying I'm designing
+
+ align:start position:0%
+very general term saying I'm designing
+ 
+
+ align:start position:0%
+very general term saying I'm designing
+the the motions of my machine.
+
+ align:start position:0%
+the the motions of my machine.
+ 
+
+ align:start position:0%
+the the motions of my machine.
+The reason I want to use motion planning
+
+ align:start position:0%
+The reason I want to use motion planning
+ 
+
+ align:start position:0%
+The reason I want to use motion planning
+in the title for this lecture and next
+
+ align:start position:0%
+in the title for this lecture and next
+ 
+
+ align:start position:0%
+in the title for this lecture and next
+lecture um is because there's another
+
+ align:start position:0%
+lecture um is because there's another
+ 
+
+ align:start position:0%
+lecture um is because there's another
+set of motion there's an important class
+
+ align:start position:0%
+set of motion there's an important class
+ 
+
+ align:start position:0%
+set of motion there's an important class
+of motion planning algorithms that are
+
+ align:start position:0%
+of motion planning algorithms that are
+ 
+
+ align:start position:0%
+of motion planning algorithms that are
+not covered by the optimal control
+
+ align:start position:0%
+not covered by the optimal control
+ 
+
+ align:start position:0%
+not covered by the optimal control
+algorithms and that's these feasible
+
+ align:start position:0%
+algorithms and that's these feasible
+ 
+
+ align:start position:0%
+algorithms and that's these feasible
+motion planning you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+algorithms. So the optimal motion
+
+ align:start position:0%
+algorithms. So the optimal motion
+ 
+
+ align:start position:0%
+algorithms. So the optimal motion
+planning algorithms try to get me from
+
+ align:start position:0%
+planning algorithms try to get me from
+ 
+
+ align:start position:0%
+planning algorithms try to get me from
+X0 to X goal in some way that's good by
+
+ align:start position:0%
+X0 to X goal in some way that's good by
+ 
+
+ align:start position:0%
+X0 to X goal in some way that's good by
+some ascored by some cost
+
+ align:start position:0%
+some ascored by some cost
+ 
+
+ align:start position:0%
+some ascored by some cost
+function. Feasible motion planning
+
+ align:start position:0%
+function. Feasible motion planning
+ 
+
+ align:start position:0%
+function. Feasible motion planning
+algorithms aspire to do less right they
+
+ align:start position:0%
+algorithms aspire to do less right they
+ 
+
+ align:start position:0%
+algorithms aspire to do less right they
+I just say I'll get me any state any
+
+ align:start position:0%
+I just say I'll get me any state any
+ 
+
+ align:start position:0%
+I just say I'll get me any state any
+trajectory that gets me from the start
+
+ align:start position:0%
+trajectory that gets me from the start
+ 
+
+ align:start position:0%
+trajectory that gets me from the start
+to the goal. Okay because they sacrifice
+
+ align:start position:0%
+to the goal. Okay because they sacrifice
+ 
+
+ align:start position:0%
+to the goal. Okay because they sacrifice
+their claims on optimality oftentimes
+
+ align:start position:0%
+their claims on optimality oftentimes
+ 
+
+ align:start position:0%
+their claims on optimality oftentimes
+these algorithms will work for more
+
+ align:start position:0%
+these algorithms will work for more
+ 
+
+ align:start position:0%
+these algorithms will work for more
+complicated systems.
+
+ align:start position:0%
+complicated systems.
+ 
+
+ align:start position:0%
+complicated systems.
+Okay. So the the the message I want to
+
+ align:start position:0%
+Okay. So the the the message I want to
+ 
+
+ align:start position:0%
+Okay. So the the the message I want to
+sort of deliver today is that there are
+
+ align:start position:0%
+sort of deliver today is that there are
+ 
+
+ align:start position:0%
+sort of deliver today is that there are
+a lot of good feasible motion planning
+
+ align:start position:0%
+a lot of good feasible motion planning
+ 
+
+ align:start position:0%
+a lot of good feasible motion planning
+algorithms out there in the world. We'll
+
+ align:start position:0%
+algorithms out there in the world. We'll
+ 
+
+ align:start position:0%
+algorithms out there in the world. We'll
+we'll talk about a some of the most
+
+ align:start position:0%
+we'll talk about a some of the most
+ 
+
+ align:start position:0%
+we'll talk about a some of the most
+exciting ones I think. And actually even
+
+ align:start position:0%
+exciting ones I think. And actually even
+ 
+
+ align:start position:0%
+exciting ones I think. And actually even
+if you care about optimality, even if
+
+ align:start position:0%
+if you care about optimality, even if
+ 
+
+ align:start position:0%
+if you care about optimality, even if
+deep down in your core you say this is a
+
+ align:start position:0%
+deep down in your core you say this is a
+ 
+
+ align:start position:0%
+deep down in your core you say this is a
+cost function that I must
+
+ align:start position:0%
+cost function that I must
+ 
+
+ align:start position:0%
+cost function that I must
+optimize for my life to be
+
+ align:start position:0%
+optimize for my life to be
+ 
+
+ align:start position:0%
+optimize for my life to be
+complete, you still should care about
+
+ align:start position:0%
+complete, you still should care about
+ 
+
+ align:start position:0%
+complete, you still should care about
+feasible motion planning algorithms.
+
+ align:start position:0%
+feasible motion planning algorithms.
+ 
+
+ align:start position:0%
+feasible motion planning algorithms.
+because they can do something like
+
+ align:start position:0%
+because they can do something like
+ 
+
+ align:start position:0%
+because they can do something like
+seed a durall method, let's say, uh, and
+
+ align:start position:0%
+seed a durall method, let's say, uh, and
+ 
+
+ align:start position:0%
+seed a durall method, let's say, uh, and
+get it out of local minima. So, let's
+
+ align:start position:0%
+get it out of local minima. So, let's
+ 
+
+ align:start position:0%
+get it out of local minima. So, let's
+say I have an Acrobot that I'm trying to
+
+ align:start position:0%
+say I have an Acrobot that I'm trying to
+ 
+
+ align:start position:0%
+say I have an Acrobot that I'm trying to
+swing up and I've got a a table right
+
+ align:start position:0%
+swing up and I've got a a table right
+ 
+
+ align:start position:0%
+swing up and I've got a a table right
+here, so I can't swing that way. And
+
+ align:start position:0%
+here, so I can't swing that way. And
+ 
+
+ align:start position:0%
+here, so I can't swing that way. And
+whatever my my initial um my initial
+
+ align:start position:0%
+whatever my my initial um my initial
+ 
+
+ align:start position:0%
+whatever my my initial um my initial
+guess at the trajectory, the system
+
+ align:start position:0%
+guess at the trajectory, the system
+ 
+
+ align:start position:0%
+guess at the trajectory, the system
+keeps banging up against this. It can't
+
+ align:start position:0%
+keeps banging up against this. It can't
+ 
+
+ align:start position:0%
+keeps banging up against this. It can't
+figure out a way to to turn around and
+
+ align:start position:0%
+figure out a way to to turn around and
+ 
+
+ align:start position:0%
+figure out a way to to turn around and
+go back the opposite way to get to the
+
+ align:start position:0%
+go back the opposite way to get to the
+ 
+
+ align:start position:0%
+go back the opposite way to get to the
+top, right? Or maybe there's a, you
+
+ align:start position:0%
+top, right? Or maybe there's a, you
+ 
+
+ align:start position:0%
+top, right? Or maybe there's a, you
+know, a table that you have to go
+
+ align:start position:0%
+know, a table that you have to go
+ 
+
+ align:start position:0%
+know, a table that you have to go
+through it just in a certain way,
+
+ align:start position:0%
+through it just in a certain way,
+ 
+
+ align:start position:0%
+through it just in a certain way,
+right? I would say if your if
+
+ align:start position:0%
+right? I would say if your if
+ 
+
+ align:start position:0%
+right? I would say if your if
+your shooting method is having a trouble
+
+ align:start position:0%
+your shooting method is having a trouble
+ 
+
+ align:start position:0%
+your shooting method is having a trouble
+finding its way to the goal, maybe you
+
+ align:start position:0%
+finding its way to the goal, maybe you
+ 
+
+ align:start position:0%
+finding its way to the goal, maybe you
+should back off on optimality. Just find
+
+ align:start position:0%
+should back off on optimality. Just find
+ 
+
+ align:start position:0%
+should back off on optimality. Just find
+any old trajectory that gets to the goal
+
+ align:start position:0%
+any old trajectory that gets to the goal
+ 
+
+ align:start position:0%
+any old trajectory that gets to the goal
+and then take that result of that motion
+
+ align:start position:0%
+and then take that result of that motion
+ 
+
+ align:start position:0%
+and then take that result of that motion
+planning algorithm, hand it to Durall,
+
+ align:start position:0%
+planning algorithm, hand it to Durall,
+ 
+
+ align:start position:0%
+planning algorithm, hand it to Durall,
+and let it then do the rest of the
+
+ align:start position:0%
+and let it then do the rest of the
+ 
+
+ align:start position:0%
+and let it then do the rest of the
+optimization. Okay, we'll we'll say more
+
+ align:start position:0%
+optimization. Okay, we'll we'll say more
+ 
+
+ align:start position:0%
+optimization. Okay, we'll we'll say more
+about this. I just wanted to to give you
+
+ align:start position:0%
+about this. I just wanted to to give you
+ 
+
+ align:start position:0%
+about this. I just wanted to to give you
+some context about why we want to talk
+
+ align:start position:0%
+some context about why we want to talk
+ 
+
+ align:start position:0%
+some context about why we want to talk
+about this extra set of
+
+ align:start position:0%
+about this extra set of
+ 
+
+ align:start position:0%
+about this extra set of
+algorithms. In general, we're going to
+
+ align:start position:0%
+algorithms. In general, we're going to
+ 
+
+ align:start position:0%
+algorithms. In general, we're going to
+expect these um these to scale to
+
+ align:start position:0%
+expect these um these to scale to
+ 
+
+ align:start position:0%
+expect these um these to scale to
+slightly higher dimensional systems than
+
+ align:start position:0%
+slightly higher dimensional systems than
+ 
+
+ align:start position:0%
+slightly higher dimensional systems than
+the optimal control algorithms we've
+
+ align:start position:0%
+the optimal control algorithms we've
+ 
+
+ align:start position:0%
+the optimal control algorithms we've
+talked about so far and to be more
+
+ align:start position:0%
+talked about so far and to be more
+ 
+
+ align:start position:0%
+talked about so far and to be more
+global than uh than the shooting
+
+ align:start position:0%
+global than uh than the shooting
+ 
+
+ align:start position:0%
+global than uh than the shooting
+methods.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There's a great book on all of this
+
+ align:start position:0%
+There's a great book on all of this
+ 
+
+ align:start position:0%
+There's a great book on all of this
+stuff.
+
+ align:start position:0%
+stuff.
+ 
+
+ align:start position:0%
+stuff.
+Um called uh I guess it should be
+
+ align:start position:0%
+Um called uh I guess it should be
+ 
+
+ align:start position:0%
+Um called uh I guess it should be
+underlined, planning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithms. So I pro I just spelled
+
+ align:start position:0%
+algorithms. So I pro I just spelled
+ 
+
+ align:start position:0%
+algorithms. So I pro I just spelled
+planning wrong, right? So I'm I'm
+
+ align:start position:0%
+planning wrong, right? So I'm I'm
+ 
+
+ align:start position:0%
+planning wrong, right? So I'm I'm
+completely sleepd deprived. If I do
+
+ align:start position:0%
+completely sleepd deprived. If I do
+ 
+
+ align:start position:0%
+completely sleepd deprived. If I do
+stupid things like that, uh call them
+
+ align:start position:0%
+stupid things like that, uh call them
+ 
+
+ align:start position:0%
+stupid things like that, uh call them
+out. I'll fix them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something about kid number two, the the
+
+ align:start position:0%
+something about kid number two, the the
+ 
+
+ align:start position:0%
+something about kid number two, the the
+first kid stays awake while the other
+
+ align:start position:0%
+first kid stays awake while the other
+ 
+
+ align:start position:0%
+first kid stays awake while the other
+kid sleeps and vice versa. It just makes
+
+ align:start position:0%
+kid sleeps and vice versa. It just makes
+ 
+
+ align:start position:0%
+kid sleeps and vice versa. It just makes
+it that much more interesting.
+
+ align:start position:0%
+it that much more interesting.
+ 
+
+ align:start position:0%
+it that much more interesting.
+Yeah. And planning algorithms, the book
+
+ align:start position:0%
+Yeah. And planning algorithms, the book
+ 
+
+ align:start position:0%
+Yeah. And planning algorithms, the book
+by Steve Lavel is actually Steve's got
+
+ align:start position:0%
+by Steve Lavel is actually Steve's got
+ 
+
+ align:start position:0%
+by Steve Lavel is actually Steve's got
+it on his website, the full version. uh
+
+ align:start position:0%
+it on his website, the full version. uh
+ 
+
+ align:start position:0%
+it on his website, the full version. uh
+you can download for free. So it's nice
+
+ align:start position:0%
+you can download for free. So it's nice
+ 
+
+ align:start position:0%
+you can download for free. So it's nice
+accessible text that you can check out
+
+ align:start position:0%
+accessible text that you can check out
+ 
+
+ align:start position:0%
+accessible text that you can check out
+if if you like
+
+ align:start position:0%
+if if you like
+ 
+
+ align:start position:0%
+if if you like
+it. Okay. So before we get into our
+
+ align:start position:0%
+it. Okay. So before we get into our
+ 
+
+ align:start position:0%
+it. Okay. So before we get into our
+first feasible motion planning
+
+ align:start position:0%
+first feasible motion planning
+ 
+
+ align:start position:0%
+first feasible motion planning
+algorithm, let me give you just a little
+
+ align:start position:0%
+algorithm, let me give you just a little
+ 
+
+ align:start position:0%
+algorithm, let me give you just a little
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+culture. The motion planning algorithms
+
+ align:start position:0%
+culture. The motion planning algorithms
+ 
+
+ align:start position:0%
+culture. The motion planning algorithms
+I think um actually grew up not so much
+
+ align:start position:0%
+I think um actually grew up not so much
+ 
+
+ align:start position:0%
+I think um actually grew up not so much
+in the controls community but in the
+
+ align:start position:0%
+in the controls community but in the
+ 
+
+ align:start position:0%
+in the controls community but in the
+more the artificial intelligence
+
+ align:start position:0%
+more the artificial intelligence
+ 
+
+ align:start position:0%
+more the artificial intelligence
+community, right? Um and there's a
+
+ align:start position:0%
+community, right? Um and there's a
+ 
+
+ align:start position:0%
+community, right? Um and there's a
+reason for that. Um there are serious
+
+ align:start position:0%
+reason for that. Um there are serious
+ 
+
+ align:start position:0%
+reason for that. Um there are serious
+people out there that think the only
+
+ align:start position:0%
+people out there that think the only
+ 
+
+ align:start position:0%
+people out there that think the only
+thing there is to
+
+ align:start position:0%
+thing there is to
+ 
+
+ align:start position:0%
+thing there is to
+intelligence is the ability to do
+
+ align:start position:0%
+intelligence is the ability to do
+ 
+
+ align:start position:0%
+intelligence is the ability to do
+search. Okay. So I I I think that
+
+ align:start position:0%
+search. Okay. So I I I think that
+ 
+
+ align:start position:0%
+search. Okay. So I I I think that
+uh artificial intelligence via
+
+ align:start position:0%
+uh artificial intelligence via
+ 
+
+ align:start position:0%
+uh artificial intelligence via
+search to some extent sounds
+
+ align:start position:0%
+search to some extent sounds
+ 
+
+ align:start position:0%
+search to some extent sounds
+ridiculous but it's pretty hard to
+
+ align:start position:0%
+ridiculous but it's pretty hard to
+ 
+
+ align:start position:0%
+ridiculous but it's pretty hard to
+disprove and some people really think
+
+ align:start position:0%
+disprove and some people really think
+ 
+
+ align:start position:0%
+disprove and some people really think
+that that's that's uh that's the way it
+
+ align:start position:0%
+that that's that's uh that's the way it
+ 
+
+ align:start position:0%
+that that's that's uh that's the way it
+happens. So let me give you some some
+
+ align:start position:0%
+happens. So let me give you some some
+ 
+
+ align:start position:0%
+happens. So let me give you some some
+cultural examples of where that came
+
+ align:start position:0%
+cultural examples of where that came
+ 
+
+ align:start position:0%
+cultural examples of where that came
+from. Right? The the original some of
+
+ align:start position:0%
+from. Right? The the original some of
+ 
+
+ align:start position:0%
+from. Right? The the original some of
+the original um efforts in artificial
+
+ align:start position:0%
+the original um efforts in artificial
+ 
+
+ align:start position:0%
+the original um efforts in artificial
+intelligence. They thought um I can my
+
+ align:start position:0%
+intelligence. They thought um I can my
+ 
+
+ align:start position:0%
+intelligence. They thought um I can my
+computer program will be intelligent if
+
+ align:start position:0%
+computer program will be intelligent if
+ 
+
+ align:start position:0%
+computer program will be intelligent if
+it can play a game like checkers or
+
+ align:start position:0%
+it can play a game like checkers or
+ 
+
+ align:start position:0%
+it can play a game like checkers or
+chess, right? And as early as like the
+
+ align:start position:0%
+chess, right? And as early as like the
+ 
+
+ align:start position:0%
+chess, right? And as early as like the
+50s, Art Samuels building checker
+
+ align:start position:0%
+50s, Art Samuels building checker
+ 
+
+ align:start position:0%
+50s, Art Samuels building checker
+playing robots that are basically doing
+
+ align:start position:0%
+playing robots that are basically doing
+ 
+
+ align:start position:0%
+playing robots that are basically doing
+search in order to try to figure out how
+
+ align:start position:0%
+search in order to try to figure out how
+ 
+
+ align:start position:0%
+search in order to try to figure out how
+to to beat their opponent in in chess,
+
+ align:start position:0%
+to to beat their opponent in in chess,
+ 
+
+ align:start position:0%
+to to beat their opponent in in chess,
+right? So or in checkers, sorry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um like checkers there's Samuel in the
+
+ align:start position:0%
+Um like checkers there's Samuel in the
+ 
+
+ align:start position:0%
+Um like checkers there's Samuel in the
+50s.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um chess we can leap forward to uh IBM's
+
+ align:start position:0%
+um chess we can leap forward to uh IBM's
+ 
+
+ align:start position:0%
+um chess we can leap forward to uh IBM's
+deep blue let's say uh in the last
+
+ align:start position:0%
+deep blue let's say uh in the last
+ 
+
+ align:start position:0%
+deep blue let's say uh in the last
+decade right
+
+ align:start position:0%
+decade right
+ 
+
+ align:start position:0%
+decade right
+um these are computer programs that at
+
+ align:start position:0%
+um these are computer programs that at
+ 
+
+ align:start position:0%
+um these are computer programs that at
+times can play with the sophistication
+
+ align:start position:0%
+times can play with the sophistication
+ 
+
+ align:start position:0%
+times can play with the sophistication
+of a trained human right and they're
+
+ align:start position:0%
+of a trained human right and they're
+ 
+
+ align:start position:0%
+of a trained human right and they're
+based on simply having the rules of the
+
+ align:start position:0%
+based on simply having the rules of the
+ 
+
+ align:start position:0%
+based on simply having the rules of the
+game
+
+ align:start position:0%
+game
+ 
+
+ align:start position:0%
+game
+programmed some databases of of moves
+
+ align:start position:0%
+programmed some databases of of moves
+ 
+
+ align:start position:0%
+programmed some databases of of moves
+that they've stored up a lot of them in
+
+ align:start position:0%
+that they've stored up a lot of them in
+ 
+
+ align:start position:0%
+that they've stored up a lot of them in
+the deep blue
+
+ align:start position:0%
+the deep blue
+ 
+
+ align:start position:0%
+the deep blue
+and search, right? Finding um the way to
+
+ align:start position:0%
+and search, right? Finding um the way to
+ 
+
+ align:start position:0%
+and search, right? Finding um the way to
+move my robot from X0 to X goal, you can
+
+ align:start position:0%
+move my robot from X0 to X goal, you can
+ 
+
+ align:start position:0%
+move my robot from X0 to X goal, you can
+imagine being very very analogous to
+
+ align:start position:0%
+imagine being very very analogous to
+ 
+
+ align:start position:0%
+imagine being very very analogous to
+finding my uh take my taking my computer
+
+ align:start position:0%
+finding my uh take my taking my computer
+ 
+
+ align:start position:0%
+finding my uh take my taking my computer
+game and finding from an initial board
+
+ align:start position:0%
+game and finding from an initial board
+ 
+
+ align:start position:0%
+game and finding from an initial board
+configuration to a a winning board
+
+ align:start position:0%
+configuration to a a winning board
+ 
+
+ align:start position:0%
+configuration to a a winning board
+configuration. They're exactly the same
+
+ align:start position:0%
+configuration. They're exactly the same
+ 
+
+ align:start position:0%
+configuration. They're exactly the same
+problem. Okay. So because of things like
+
+ align:start position:0%
+problem. Okay. So because of things like
+ 
+
+ align:start position:0%
+problem. Okay. So because of things like
+computer games, the artificial
+
+ align:start position:0%
+computer games, the artificial
+ 
+
+ align:start position:0%
+computer games, the artificial
+intelligence community really started
+
+ align:start position:0%
+intelligence community really started
+ 
+
+ align:start position:0%
+intelligence community really started
+building up these these search
+
+ align:start position:0%
+building up these these search
+ 
+
+ align:start position:0%
+building up these these search
+algorithms and and they were very
+
+ align:start position:0%
+algorithms and and they were very
+ 
+
+ align:start position:0%
+algorithms and and they were very
+fundamental. The other
+
+ align:start position:0%
+fundamental. The other
+ 
+
+ align:start position:0%
+fundamental. The other
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+um the other big uh push I think from
+
+ align:start position:0%
+um the other big uh push I think from
+ 
+
+ align:start position:0%
+um the other big uh push I think from
+the AI community was in ideas like
+
+ align:start position:0%
+the AI community was in ideas like
+ 
+
+ align:start position:0%
+the AI community was in ideas like
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proving, right? So
+
+ align:start position:0%
+proving, right? So
+ 
+
+ align:start position:0%
+proving, right? So
+a, you know, an AI zealot of of 40 years
+
+ align:start position:0%
+a, you know, an AI zealot of of 40 years
+ 
+
+ align:start position:0%
+a, you know, an AI zealot of of 40 years
+ago might have told you that mathematics
+
+ align:start position:0%
+ago might have told you that mathematics
+ 
+
+ align:start position:0%
+ago might have told you that mathematics
+would be obsolete by now because all you
+
+ align:start position:0%
+would be obsolete by now because all you
+ 
+
+ align:start position:0%
+would be obsolete by now because all you
+have to do is program the basic rules of
+
+ align:start position:0%
+have to do is program the basic rules of
+ 
+
+ align:start position:0%
+have to do is program the basic rules of
+mathematics into a into a a set of rules
+
+ align:start position:0%
+mathematics into a into a a set of rules
+ 
+
+ align:start position:0%
+mathematics into a into a a set of rules
+that your computer program could uh
+
+ align:start position:0%
+that your computer program could uh
+ 
+
+ align:start position:0%
+that your computer program could uh
+could evaluate. and then proving where
+
+ align:start position:0%
+could evaluate. and then proving where
+ 
+
+ align:start position:0%
+could evaluate. and then proving where
+whether something was true or not is
+
+ align:start position:0%
+whether something was true or not is
+ 
+
+ align:start position:0%
+whether something was true or not is
+just a matter of finding the right chain
+
+ align:start position:0%
+just a matter of finding the right chain
+ 
+
+ align:start position:0%
+just a matter of finding the right chain
+of of small logical deductions to put
+
+ align:start position:0%
+of of small logical deductions to put
+ 
+
+ align:start position:0%
+of of small logical deductions to put
+together to find to be able to prove
+
+ align:start position:0%
+together to find to be able to prove
+ 
+
+ align:start position:0%
+together to find to be able to prove
+that P equals NP or something like that,
+
+ align:start position:0%
+that P equals NP or something like that,
+ 
+
+ align:start position:0%
+that P equals NP or something like that,
+right? Okay. Uh and actually, you know,
+
+ align:start position:0%
+right? Okay. Uh and actually, you know,
+ 
+
+ align:start position:0%
+right? Okay. Uh and actually, you know,
+I I joke, but that's actually a very
+
+ align:start position:0%
+I I joke, but that's actually a very
+ 
+
+ align:start position:0%
+I I joke, but that's actually a very
+powerful thing that works today, right?
+
+ align:start position:0%
+powerful thing that works today, right?
+ 
+
+ align:start position:0%
+powerful thing that works today, right?
+If you've used Mathematica or Maple and
+
+ align:start position:0%
+If you've used Mathematica or Maple and
+ 
+
+ align:start position:0%
+If you've used Mathematica or Maple and
+you've asked it to simplify, right?
+
+ align:start position:0%
+you've asked it to simplify, right?
+ 
+
+ align:start position:0%
+you've asked it to simplify, right?
+That's a result of of theorem proving
+
+ align:start position:0%
+That's a result of of theorem proving
+ 
+
+ align:start position:0%
+That's a result of of theorem proving
+work that people did in artificial
+
+ align:start position:0%
+work that people did in artificial
+ 
+
+ align:start position:0%
+work that people did in artificial
+intelligence a long time ago, right? And
+
+ align:start position:0%
+intelligence a long time ago, right? And
+ 
+
+ align:start position:0%
+intelligence a long time ago, right? And
+again, it's a matter of designing the
+
+ align:start position:0%
+again, it's a matter of designing the
+ 
+
+ align:start position:0%
+again, it's a matter of designing the
+rules of the game, which is a collection
+
+ align:start position:0%
+rules of the game, which is a collection
+ 
+
+ align:start position:0%
+rules of the game, which is a collection
+in that case of mathematical primitives
+
+ align:start position:0%
+in that case of mathematical primitives
+ 
+
+ align:start position:0%
+in that case of mathematical primitives
+and finding a a path from from your
+
+ align:start position:0%
+and finding a a path from from your
+ 
+
+ align:start position:0%
+and finding a a path from from your
+initial uh knowledge to some proof,
+
+ align:start position:0%
+initial uh knowledge to some proof,
+ 
+
+ align:start position:0%
+initial uh knowledge to some proof,
+let's say.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But even going beyond that, there's
+
+ align:start position:0%
+But even going beyond that, there's
+ 
+
+ align:start position:0%
+But even going beyond that, there's
+people out there that um my favorite my
+
+ align:start position:0%
+people out there that um my favorite my
+ 
+
+ align:start position:0%
+people out there that um my favorite my
+favorite instance of this is there's a
+
+ align:start position:0%
+favorite instance of this is there's a
+ 
+
+ align:start position:0%
+favorite instance of this is there's a
+guy um David Lynette who's um somewhere
+
+ align:start position:0%
+guy um David Lynette who's um somewhere
+ 
+
+ align:start position:0%
+guy um David Lynette who's um somewhere
+in Texas right now typing well he's got
+
+ align:start position:0%
+in Texas right now typing well he's got
+ 
+
+ align:start position:0%
+in Texas right now typing well he's got
+teams of people typing random factoids
+
+ align:start position:0%
+teams of people typing random factoids
+ 
+
+ align:start position:0%
+teams of people typing random factoids
+into computers um he's got this project
+
+ align:start position:0%
+into computers um he's got this project
+ 
+
+ align:start position:0%
+into computers um he's got this project
+called uh
+
+ align:start position:0%
+called uh
+ 
+
+ align:start position:0%
+called uh
+sick. How many people have heard of sik?
+
+ align:start position:0%
+sick. How many people have heard of sik?
+ 
+
+ align:start position:0%
+sick. How many people have heard of sik?
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+So, I think this guy believes that um if
+
+ align:start position:0%
+So, I think this guy believes that um if
+ 
+
+ align:start position:0%
+So, I think this guy believes that um if
+I can get enough people to type in
+
+ align:start position:0%
+I can get enough people to type in
+ 
+
+ align:start position:0%
+I can get enough people to type in
+things like dogs chase cats and you know
+
+ align:start position:0%
+things like dogs chase cats and you know
+ 
+
+ align:start position:0%
+things like dogs chase cats and you know
+balloons go up or something, I don't
+
+ align:start position:0%
+balloons go up or something, I don't
+ 
+
+ align:start position:0%
+balloons go up or something, I don't
+know, enough random factoids into this
+
+ align:start position:0%
+know, enough random factoids into this
+ 
+
+ align:start position:0%
+know, enough random factoids into this
+computer and he builds up an ontology of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knowledge, just some big collection of
+
+ align:start position:0%
+knowledge, just some big collection of
+ 
+
+ align:start position:0%
+knowledge, just some big collection of
+facts that and a good search algorithm
+
+ align:start position:0%
+facts that and a good search algorithm
+ 
+
+ align:start position:0%
+facts that and a good search algorithm
+to back it
+
+ align:start position:0%
+to back it
+ 
+
+ align:start position:0%
+to back it
+that his computer will will achieve
+
+ align:start position:0%
+that his computer will will achieve
+ 
+
+ align:start position:0%
+that his computer will will achieve
+intelligence. You'll be able to answer
+
+ align:start position:0%
+intelligence. You'll be able to answer
+ 
+
+ align:start position:0%
+intelligence. You'll be able to answer
+any query, be completely
+
+ align:start position:0%
+any query, be completely
+ 
+
+ align:start position:0%
+any query, be completely
+indistinguishable from a human. You
+
+ align:start position:0%
+indistinguishable from a human. You
+ 
+
+ align:start position:0%
+indistinguishable from a human. You
+could ask it any query and as long as
+
+ align:start position:0%
+could ask it any query and as long as
+ 
+
+ align:start position:0%
+could ask it any query and as long as
+it's got the right chain of factoids
+
+ align:start position:0%
+it's got the right chain of factoids
+ 
+
+ align:start position:0%
+it's got the right chain of factoids
+stored away and a good search algorithm
+
+ align:start position:0%
+stored away and a good search algorithm
+ 
+
+ align:start position:0%
+stored away and a good search algorithm
+behind it, then this thing is
+
+ align:start position:0%
+behind it, then this thing is
+ 
+
+ align:start position:0%
+behind it, then this thing is
+intelligent. Mhm. And it's been, you
+
+ align:start position:0%
+intelligent. Mhm. And it's been, you
+ 
+
+ align:start position:0%
+intelligent. Mhm. And it's been, you
+know, people have been typing things in
+
+ align:start position:0%
+know, people have been typing things in
+ 
+
+ align:start position:0%
+know, people have been typing things in
+for a really long time. And you can
+
+ align:start position:0%
+for a really long time. And you can
+ 
+
+ align:start position:0%
+for a really long time. And you can
+actually, you know, you can go and you
+
+ align:start position:0%
+actually, you know, you can go and you
+ 
+
+ align:start position:0%
+actually, you know, you can go and you
+can get the student version or whatever
+
+ align:start position:0%
+can get the student version or whatever
+ 
+
+ align:start position:0%
+can get the student version or whatever
+and and ask it questions and you can get
+
+ align:start position:0%
+and and ask it questions and you can get
+ 
+
+ align:start position:0%
+and and ask it questions and you can get
+the research version and and ask it
+
+ align:start position:0%
+the research version and and ask it
+ 
+
+ align:start position:0%
+the research version and and ask it
+questions and people use it. And
+
+ align:start position:0%
+questions and people use it. And
+ 
+
+ align:start position:0%
+questions and people use it. And
+um I mean Google I think works better
+
+ align:start position:0%
+um I mean Google I think works better
+ 
+
+ align:start position:0%
+um I mean Google I think works better
+because it's accessing word net which is
+
+ align:start position:0%
+because it's accessing word net which is
+ 
+
+ align:start position:0%
+because it's accessing word net which is
+a basically an ontology of of synonyms
+
+ align:start position:0%
+a basically an ontology of of synonyms
+ 
+
+ align:start position:0%
+a basically an ontology of of synonyms
+and things like this. These sound
+
+ align:start position:0%
+and things like this. These sound
+ 
+
+ align:start position:0%
+and things like this. These sound
+crazy. Um but they're the backbone of
+
+ align:start position:0%
+crazy. Um but they're the backbone of
+ 
+
+ align:start position:0%
+crazy. Um but they're the backbone of
+some of the things that you use every
+
+ align:start position:0%
+some of the things that you use every
+ 
+
+ align:start position:0%
+some of the things that you use every
+day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Okay. So for whatever reason, you
+
+ align:start position:0%
+right? Okay. So for whatever reason, you
+ 
+
+ align:start position:0%
+right? Okay. So for whatever reason, you
+know, for these kind of reasons, the
+
+ align:start position:0%
+know, for these kind of reasons, the
+ 
+
+ align:start position:0%
+know, for these kind of reasons, the
+search algorithms, the motion planning
+
+ align:start position:0%
+search algorithms, the motion planning
+ 
+
+ align:start position:0%
+search algorithms, the motion planning
+algorithms that that we're going to talk
+
+ align:start position:0%
+algorithms that that we're going to talk
+ 
+
+ align:start position:0%
+algorithms that that we're going to talk
+about, which are today used a lot in
+
+ align:start position:0%
+about, which are today used a lot in
+ 
+
+ align:start position:0%
+about, which are today used a lot in
+robotics, grew up under the computer
+
+ align:start position:0%
+robotics, grew up under the computer
+ 
+
+ align:start position:0%
+robotics, grew up under the computer
+science umbrella, under artificial
+
+ align:start position:0%
+science umbrella, under artificial
+ 
+
+ align:start position:0%
+science umbrella, under artificial
+intelligence. Mhm.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the term motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planning, you know, typically implies
+
+ align:start position:0%
+planning, you know, typically implies
+ 
+
+ align:start position:0%
+planning, you know, typically implies
+that you've got some dynamical system
+
+ align:start position:0%
+that you've got some dynamical system
+ 
+
+ align:start position:0%
+that you've got some dynamical system
+you're you're shoving around, let's
+
+ align:start position:0%
+you're you're shoving around, let's
+ 
+
+ align:start position:0%
+you're you're shoving around, let's
+say, but it's it's clearly
+
+ align:start position:0%
+say, but it's it's clearly
+ 
+
+ align:start position:0%
+say, but it's it's clearly
+just an instance of this search problem.
+
+ align:start position:0%
+just an instance of this search problem.
+ 
+
+ align:start position:0%
+just an instance of this search problem.
+When people talk about motion planning
+
+ align:start position:0%
+When people talk about motion planning
+ 
+
+ align:start position:0%
+When people talk about motion planning
+in robotics,
+
+ align:start position:0%
+in robotics,
+ 
+
+ align:start position:0%
+in robotics,
+um there are problems that that people
+
+ align:start position:0%
+um there are problems that that people
+ 
+
+ align:start position:0%
+um there are problems that that people
+care about a lot.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um a majority of the motion planning
+
+ align:start position:0%
+Um a majority of the motion planning
+ 
+
+ align:start position:0%
+Um a majority of the motion planning
+literature in robotics is cons concerned
+
+ align:start position:0%
+literature in robotics is cons concerned
+ 
+
+ align:start position:0%
+literature in robotics is cons concerned
+with kinematic motion planning.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um often with obstacles or something
+
+ align:start position:0%
+um often with obstacles or something
+ 
+
+ align:start position:0%
+um often with obstacles or something
+like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, if I have a a robotic arm with 10
+
+ align:start position:0%
+So, if I have a a robotic arm with 10
+ 
+
+ align:start position:0%
+So, if I have a a robotic arm with 10
+degrees of freedom and I want to reach
+
+ align:start position:0%
+degrees of freedom and I want to reach
+ 
+
+ align:start position:0%
+degrees of freedom and I want to reach
+through some complicated geometry to get
+
+ align:start position:0%
+through some complicated geometry to get
+ 
+
+ align:start position:0%
+through some complicated geometry to get
+uh to turn a a doorork knob or to to
+
+ align:start position:0%
+uh to turn a a doorork knob or to to
+ 
+
+ align:start position:0%
+uh to turn a a doorork knob or to to
+reach down and pick up some apart from
+
+ align:start position:0%
+reach down and pick up some apart from
+ 
+
+ align:start position:0%
+reach down and pick up some apart from
+assembly, then that's a complicated
+
+ align:start position:0%
+assembly, then that's a complicated
+ 
+
+ align:start position:0%
+assembly, then that's a complicated
+geometric problem.
+
+ align:start position:0%
+geometric problem.
+ 
+
+ align:start position:0%
+geometric problem.
+Um, typically you assume that the
+
+ align:start position:0%
+Um, typically you assume that the
+ 
+
+ align:start position:0%
+Um, typically you assume that the
+systems are fully actuated. You don't
+
+ align:start position:0%
+systems are fully actuated. You don't
+ 
+
+ align:start position:0%
+systems are fully actuated. You don't
+worry about actually handling the
+
+ align:start position:0%
+worry about actually handling the
+ 
+
+ align:start position:0%
+worry about actually handling the
+trajectory once you get there. that's
+
+ align:start position:0%
+trajectory once you get there. that's
+ 
+
+ align:start position:0%
+trajectory once you get there. that's
+are normally assumed away and they
+
+ align:start position:0%
+are normally assumed away and they
+ 
+
+ align:start position:0%
+are normally assumed away and they
+assume that all trajectories are
+
+ align:start position:0%
+assume that all trajectories are
+ 
+
+ align:start position:0%
+assume that all trajectories are
+feasible. They're just trying to find
+
+ align:start position:0%
+feasible. They're just trying to find
+ 
+
+ align:start position:0%
+feasible. They're just trying to find
+some um path through the obstacle field.
+
+ align:start position:0%
+some um path through the obstacle field.
+ 
+
+ align:start position:0%
+some um path through the obstacle field.
+Okay. So um one of the key problems that
+
+ align:start position:0%
+Okay. So um one of the key problems that
+ 
+
+ align:start position:0%
+Okay. So um one of the key problems that
+you can sort of think about in in that
+
+ align:start position:0%
+you can sort of think about in in that
+ 
+
+ align:start position:0%
+you can sort of think about in in that
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world is a piano movers problem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How many people know the piano mover's
+
+ align:start position:0%
+How many people know the piano mover's
+ 
+
+ align:start position:0%
+How many people know the piano mover's
+problem? Okay. How many people have ever
+
+ align:start position:0%
+problem? Okay. How many people have ever
+ 
+
+ align:start position:0%
+problem? Okay. How many people have ever
+moved a couch into a dorm room? Okay.
+
+ align:start position:0%
+moved a couch into a dorm room? Okay.
+ 
+
+ align:start position:0%
+moved a couch into a dorm room? Okay.
+You all know the the piano movers
+
+ align:start position:0%
+You all know the the piano movers
+ 
+
+ align:start position:0%
+You all know the the piano movers
+problem then,
+
+ align:start position:0%
+problem then,
+ 
+
+ align:start position:0%
+problem then,
+right? Basic task is you have some 3D
+
+ align:start position:0%
+right? Basic task is you have some 3D
+ 
+
+ align:start position:0%
+right? Basic task is you have some 3D
+shape. You have a bunch of obstacles.
+
+ align:start position:0%
+shape. You have a bunch of obstacles.
+ 
+
+ align:start position:0%
+shape. You have a bunch of obstacles.
+You have to find a position and, you
+
+ align:start position:0%
+You have to find a position and, you
+ 
+
+ align:start position:0%
+You have to find a position and, you
+know, position and orientation
+
+ align:start position:0%
+know, position and orientation
+ 
+
+ align:start position:0%
+know, position and orientation
+trajectory that will maneuver your big
+
+ align:start position:0%
+trajectory that will maneuver your big
+ 
+
+ align:start position:0%
+trajectory that will maneuver your big
+piano through a world of obstacles. It's
+
+ align:start position:0%
+piano through a world of obstacles. It's
+ 
+
+ align:start position:0%
+piano through a world of obstacles. It's
+just like going up the stairs with your
+
+ align:start position:0%
+just like going up the stairs with your
+ 
+
+ align:start position:0%
+just like going up the stairs with your
+with your uh couch,
+
+ align:start position:0%
+with your uh couch,
+ 
+
+ align:start position:0%
+with your uh couch,
+uh, you know, marking the walls and
+
+ align:start position:0%
+uh, you know, marking the walls and
+ 
+
+ align:start position:0%
+uh, you know, marking the walls and
+bending your couch as you go. Okay. And
+
+ align:start position:0%
+bending your couch as you go. Okay. And
+ 
+
+ align:start position:0%
+bending your couch as you go. Okay. And
+that's sort of the the um some of the
+
+ align:start position:0%
+that's sort of the the um some of the
+ 
+
+ align:start position:0%
+that's sort of the the um some of the
+driving problems in uh in the motion
+
+ align:start position:0%
+driving problems in uh in the motion
+ 
+
+ align:start position:0%
+driving problems in uh in the motion
+planning space. So it's things like that
+
+ align:start position:0%
+planning space. So it's things like that
+ 
+
+ align:start position:0%
+planning space. So it's things like that
+finding a collision free path for a
+
+ align:start position:0%
+finding a collision free path for a
+ 
+
+ align:start position:0%
+finding a collision free path for a
+complicated geometry uh through a an
+
+ align:start position:0%
+complicated geometry uh through a an
+ 
+
+ align:start position:0%
+complicated geometry uh through a an
+obstacle
+
+ align:start position:0%
+obstacle
+ 
+
+ align:start position:0%
+obstacle
+um based
+
+ align:start position:0%
+um based
+ 
+
+ align:start position:0%
+um based
+environment. Okay, just trying to give
+
+ align:start position:0%
+environment. Okay, just trying to give
+ 
+
+ align:start position:0%
+environment. Okay, just trying to give
+you a little culture here. There's and
+
+ align:start position:0%
+you a little culture here. There's and
+ 
+
+ align:start position:0%
+you a little culture here. There's and
+and in that world um one of the most
+
+ align:start position:0%
+and in that world um one of the most
+ 
+
+ align:start position:0%
+and in that world um one of the most
+important concepts I think is the uh is
+
+ align:start position:0%
+important concepts I think is the uh is
+ 
+
+ align:start position:0%
+important concepts I think is the uh is
+the configuration space concept.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which actually you know who came up with
+
+ align:start position:0%
+which actually you know who came up with
+ 
+
+ align:start position:0%
+which actually you know who came up with
+configuration
+
+ align:start position:0%
+configuration
+ 
+
+ align:start position:0%
+configuration
+spaces he's sitting right upstairs it's
+
+ align:start position:0%
+spaces he's sitting right upstairs it's
+ 
+
+ align:start position:0%
+spaces he's sitting right upstairs it's
+Tomas Lozano Perez is is I think
+
+ align:start position:0%
+Tomas Lozano Perez is is I think
+ 
+
+ align:start position:0%
+Tomas Lozano Perez is is I think
+credited with configuration space
+
+ align:start position:0%
+credited with configuration space
+ 
+
+ align:start position:0%
+credited with configuration space
+idea and the idea is that these problems
+
+ align:start position:0%
+idea and the idea is that these problems
+ 
+
+ align:start position:0%
+idea and the idea is that these problems
+can get a lot um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simpler let's say I have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a square robot going through some
+
+ align:start position:0%
+a square robot going through some
+ 
+
+ align:start position:0%
+a square robot going through some
+complicated obstacle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field.
+
+ align:start position:0%
+field.
+ 
+
+ align:start position:0%
+field.
+Um, and I want to find a path from some
+
+ align:start position:0%
+Um, and I want to find a path from some
+ 
+
+ align:start position:0%
+Um, and I want to find a path from some
+start to the goal.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, instead of reasoning about um the
+
+ align:start position:0%
+Well, instead of reasoning about um the
+ 
+
+ align:start position:0%
+Well, instead of reasoning about um the
+geometry of this relative to the
+
+ align:start position:0%
+geometry of this relative to the
+ 
+
+ align:start position:0%
+geometry of this relative to the
+geometry of this all the time, the
+
+ align:start position:0%
+geometry of this all the time, the
+ 
+
+ align:start position:0%
+geometry of this all the time, the
+configuration space tells you you should
+
+ align:start position:0%
+configuration space tells you you should
+ 
+
+ align:start position:0%
+configuration space tells you you should
+actually add the volume of this um of
+
+ align:start position:0%
+actually add the volume of this um of
+ 
+
+ align:start position:0%
+actually add the volume of this um of
+your robot to your obstacles, coming up
+
+ align:start position:0%
+your robot to your obstacles, coming up
+ 
+
+ align:start position:0%
+your robot to your obstacles, coming up
+with configuration space obstacles.
+
+ align:start position:0%
+with configuration space obstacles.
+ 
+
+ align:start position:0%
+with configuration space obstacles.
+Yeah, if you if you actually add the
+
+ align:start position:0%
+Yeah, if you if you actually add the
+ 
+
+ align:start position:0%
+Yeah, if you if you actually add the
+volume of your robot to the obstacles,
+
+ align:start position:0%
+volume of your robot to the obstacles,
+ 
+
+ align:start position:0%
+volume of your robot to the obstacles,
+I'm doing this very um hand wavy here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then you can turn the problem of
+
+ align:start position:0%
+but then you can turn the problem of
+ 
+
+ align:start position:0%
+but then you can turn the problem of
+finding a a big geometry through another
+
+ align:start position:0%
+finding a a big geometry through another
+ 
+
+ align:start position:0%
+finding a a big geometry through another
+geometric field to taking a point and
+
+ align:start position:0%
+geometric field to taking a point and
+ 
+
+ align:start position:0%
+geometric field to taking a point and
+driving it through the the geometric
+
+ align:start position:0%
+driving it through the the geometric
+ 
+
+ align:start position:0%
+driving it through the the geometric
+field. And that's a a critical critical
+
+ align:start position:0%
+field. And that's a a critical critical
+ 
+
+ align:start position:0%
+field. And that's a a critical critical
+idea in the world of kinematic motion
+
+ align:start position:0%
+idea in the world of kinematic motion
+ 
+
+ align:start position:0%
+idea in the world of kinematic motion
+planning.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We don't really care about kinematic
+
+ align:start position:0%
+We don't really care about kinematic
+ 
+
+ align:start position:0%
+We don't really care about kinematic
+motion planning uh in this class, right?
+
+ align:start position:0%
+motion planning uh in this class, right?
+ 
+
+ align:start position:0%
+motion planning uh in this class, right?
+We've got enough troubles without
+
+ align:start position:0%
+We've got enough troubles without
+ 
+
+ align:start position:0%
+We've got enough troubles without
+obstacles. We just care about having
+
+ align:start position:0%
+obstacles. We just care about having
+ 
+
+ align:start position:0%
+obstacles. We just care about having
+interesting dynamical system uh to move
+
+ align:start position:0%
+interesting dynamical system uh to move
+ 
+
+ align:start position:0%
+interesting dynamical system uh to move
+around. Okay?
+
+ align:start position:0%
+around. Okay?
+ 
+
+ align:start position:0%
+around. Okay?
+So the things we're talking about uh in
+
+ align:start position:0%
+So the things we're talking about uh in
+ 
+
+ align:start position:0%
+So the things we're talking about uh in
+this class fall under the
+
+ align:start position:0%
+this class fall under the
+ 
+
+ align:start position:0%
+this class fall under the
+heading
+
+ align:start position:0%
+heading
+ 
+
+ align:start position:0%
+heading
+ko
+
+ align:start position:0%
+ko
+ 
+
+ align:start position:0%
+ko
+dynamic motion planning.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And of course the uh the non-holinomic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh motion planning ideas are are very
+
+ align:start position:0%
+uh motion planning ideas are are very
+ 
+
+ align:start position:0%
+uh motion planning ideas are are very
+related
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too.
+
+ align:start position:0%
+too.
+ 
+
+ align:start position:0%
+too.
+Okay. We care about the dynamics. care
+
+ align:start position:0%
+Okay. We care about the dynamics. care
+ 
+
+ align:start position:0%
+Okay. We care about the dynamics. care
+about things that are forced to follow
+
+ align:start position:0%
+about things that are forced to follow
+ 
+
+ align:start position:0%
+about things that are forced to follow
+some trajectories like non-alomic
+
+ align:start position:0%
+some trajectories like non-alomic
+ 
+
+ align:start position:0%
+some trajectories like non-alomic
+systems are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too. Okay. So, if you're out there
+
+ align:start position:0%
+too. Okay. So, if you're out there
+ 
+
+ align:start position:0%
+too. Okay. So, if you're out there
+seeing papers and talks and everything
+
+ align:start position:0%
+seeing papers and talks and everything
+ 
+
+ align:start position:0%
+seeing papers and talks and everything
+about motion planning, I just want you
+
+ align:start position:0%
+about motion planning, I just want you
+ 
+
+ align:start position:0%
+about motion planning, I just want you
+to to sort of see that they're they're
+
+ align:start position:0%
+to to sort of see that they're they're
+ 
+
+ align:start position:0%
+to to sort of see that they're they're
+certainly related to the optimal control
+
+ align:start position:0%
+certainly related to the optimal control
+ 
+
+ align:start position:0%
+certainly related to the optimal control
+things we've talked about, but sometimes
+
+ align:start position:0%
+things we've talked about, but sometimes
+ 
+
+ align:start position:0%
+things we've talked about, but sometimes
+they let go of optimality.
+
+ align:start position:0%
+they let go of optimality.
+ 
+
+ align:start position:0%
+they let go of optimality.
+They're often about kinematics, but
+
+ align:start position:0%
+They're often about kinematics, but
+ 
+
+ align:start position:0%
+They're often about kinematics, but
+there's a good subset of them, which is
+
+ align:start position:0%
+there's a good subset of them, which is
+ 
+
+ align:start position:0%
+there's a good subset of them, which is
+thinking about exactly the problems we
+
+ align:start position:0%
+thinking about exactly the problems we
+ 
+
+ align:start position:0%
+thinking about exactly the problems we
+care about with these kenodnamic motion
+
+ align:start position:0%
+care about with these kenodnamic motion
+ 
+
+ align:start position:0%
+care about with these kenodnamic motion
+planning. Excellent. Okay, so now let's
+
+ align:start position:0%
+planning. Excellent. Okay, so now let's
+ 
+
+ align:start position:0%
+planning. Excellent. Okay, so now let's
+do some motion planning. The culture is
+
+ align:start position:0%
+do some motion planning. The culture is
+ 
+
+ align:start position:0%
+do some motion planning. The culture is
+there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um when we did dynamic programming, I
+
+ align:start position:0%
+Um when we did dynamic programming, I
+ 
+
+ align:start position:0%
+Um when we did dynamic programming, I
+already sort of forced upon you the idea
+
+ align:start position:0%
+already sort of forced upon you the idea
+ 
+
+ align:start position:0%
+already sort of forced upon you the idea
+that we could potentially at great cost
+
+ align:start position:0%
+that we could potentially at great cost
+ 
+
+ align:start position:0%
+that we could potentially at great cost
+uh discretize our system and state and
+
+ align:start position:0%
+uh discretize our system and state and
+ 
+
+ align:start position:0%
+uh discretize our system and state and
+actions potentially. So let's do the
+
+ align:start position:0%
+actions potentially. So let's do the
+ 
+
+ align:start position:0%
+actions potentially. So let's do the
+same thing when we start off with motion
+
+ align:start position:0%
+same thing when we start off with motion
+ 
+
+ align:start position:0%
+same thing when we start off with motion
+planning and start with discrete um
+
+ align:start position:0%
+planning and start with discrete um
+ 
+
+ align:start position:0%
+planning and start with discrete um
+planning algorithms.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's say we've got our our uh phase
+
+ align:start position:0%
+So let's say we've got our our uh phase
+ 
+
+ align:start position:0%
+So let's say we've got our our uh phase
+plot of our simple pendulum and we're
+
+ align:start position:0%
+plot of our simple pendulum and we're
+ 
+
+ align:start position:0%
+plot of our simple pendulum and we're
+going to just for for kicks right now
+
+ align:start position:0%
+going to just for for kicks right now
+ 
+
+ align:start position:0%
+going to just for for kicks right now
+let's just start off with the trivial
+
+ align:start position:0%
+let's just start off with the trivial
+ 
+
+ align:start position:0%
+let's just start off with the trivial
+discretization. Let's say we're going to
+
+ align:start position:0%
+discretization. Let's say we're going to
+ 
+
+ align:start position:0%
+discretization. Let's say we're going to
+bin up our space like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+call each one of those a
+
+ align:start position:0%
+call each one of those a
+ 
+
+ align:start position:0%
+call each one of those a
+state, right? And try to start talking
+
+ align:start position:0%
+state, right? And try to start talking
+ 
+
+ align:start position:0%
+state, right? And try to start talking
+about um a graphbased representation of
+
+ align:start position:0%
+about um a graphbased representation of
+ 
+
+ align:start position:0%
+about um a graphbased representation of
+the dynamics of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system that tries to find a path. Let's
+
+ align:start position:0%
+system that tries to find a path. Let's
+ 
+
+ align:start position:0%
+system that tries to find a path. Let's
+say from our initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state to some goal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state, right? This isn't the only way to
+
+ align:start position:0%
+state, right? This isn't the only way to
+ 
+
+ align:start position:0%
+state, right? This isn't the only way to
+do discretization, but it's a good way
+
+ align:start position:0%
+do discretization, but it's a good way
+ 
+
+ align:start position:0%
+do discretization, but it's a good way
+to start thinking about it.
+
+ align:start position:0%
+to start thinking about it.
+ 
+
+ align:start position:0%
+to start thinking about it.
+Okay, so that turns the problem into
+
+ align:start position:0%
+Okay, so that turns the problem into
+ 
+
+ align:start position:0%
+Okay, so that turns the problem into
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+uh graphical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model where the control actions
+
+ align:start position:0%
+model where the control actions
+ 
+
+ align:start position:0%
+model where the control actions
+determine our our state transitions and
+
+ align:start position:0%
+determine our our state transitions and
+ 
+
+ align:start position:0%
+determine our our state transitions and
+I like to actually call them S and A in
+
+ align:start position:0%
+I like to actually call them S and A in
+ 
+
+ align:start position:0%
+I like to actually call them S and A in
+the discrete world.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so people know a lot about doing
+
+ align:start position:0%
+Okay, so people know a lot about doing
+ 
+
+ align:start position:0%
+Okay, so people know a lot about doing
+search on a graph and I'm certainly not
+
+ align:start position:0%
+search on a graph and I'm certainly not
+ 
+
+ align:start position:0%
+search on a graph and I'm certainly not
+going to I don't want to bore you with
+
+ align:start position:0%
+going to I don't want to bore you with
+ 
+
+ align:start position:0%
+going to I don't want to bore you with
+it, but I want to at least know the
+
+ align:start position:0%
+it, but I want to at least know the
+ 
+
+ align:start position:0%
+it, but I want to at least know the
+algorithms that are out there and be
+
+ align:start position:0%
+algorithms that are out there and be
+ 
+
+ align:start position:0%
+algorithms that are out there and be
+able to call upon them if you uh uh if
+
+ align:start position:0%
+able to call upon them if you uh uh if
+ 
+
+ align:start position:0%
+able to call upon them if you uh uh if
+they become useful.
+
+ align:start position:0%
+they become useful.
+ 
+
+ align:start position:0%
+they become useful.
+Okay, so let's say we've we've butchered
+
+ align:start position:0%
+Okay, so let's say we've we've butchered
+ 
+
+ align:start position:0%
+Okay, so let's say we've we've butchered
+up our system like this and we wanted to
+
+ align:start position:0%
+up our system like this and we wanted to
+ 
+
+ align:start position:0%
+up our system like this and we wanted to
+do uh we want to find a path from some
+
+ align:start position:0%
+do uh we want to find a path from some
+ 
+
+ align:start position:0%
+do uh we want to find a path from some
+starting discrete state to some goal
+
+ align:start position:0%
+starting discrete state to some goal
+ 
+
+ align:start position:0%
+starting discrete state to some goal
+state with a with a discrete set of
+
+ align:start position:0%
+state with a with a discrete set of
+ 
+
+ align:start position:0%
+state with a with a discrete set of
+actions. How can we do that?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Off the shelf search.
+
+ align:start position:0%
+Off the shelf search.
+ 
+
+ align:start position:0%
+Off the shelf search.
+AAR is a perfect example. Yep. Dynamic
+
+ align:start position:0%
+AAR is a perfect example. Yep. Dynamic
+ 
+
+ align:start position:0%
+AAR is a perfect example. Yep. Dynamic
+programming is is on the table too,
+
+ align:start position:0%
+programming is is on the table too,
+ 
+
+ align:start position:0%
+programming is is on the table too,
+right? The dynamic programming. That's
+
+ align:start position:0%
+right? The dynamic programming. That's
+ 
+
+ align:start position:0%
+right? The dynamic programming. That's
+actually the way I the reason I drew
+
+ align:start position:0%
+actually the way I the reason I drew
+ 
+
+ align:start position:0%
+actually the way I the reason I drew
+that picture before is because we talked
+
+ align:start position:0%
+that picture before is because we talked
+ 
+
+ align:start position:0%
+that picture before is because we talked
+about that as a way to think about
+
+ align:start position:0%
+about that as a way to think about
+ 
+
+ align:start position:0%
+about that as a way to think about
+dynamic programming. Yeah.
+
+ align:start position:0%
+dynamic programming. Yeah.
+ 
+
+ align:start position:0%
+dynamic programming. Yeah.
+And dynamic programming is incredibly
+
+ align:start position:0%
+And dynamic programming is incredibly
+ 
+
+ align:start position:0%
+And dynamic programming is incredibly
+efficient if what you care about is
+
+ align:start position:0%
+efficient if what you care about is
+ 
+
+ align:start position:0%
+efficient if what you care about is
+knowing the optimal feedback policy,
+
+ align:start position:0%
+knowing the optimal feedback policy,
+ 
+
+ align:start position:0%
+knowing the optimal feedback policy,
+right? The the how to get to the goal
+
+ align:start position:0%
+right? The the how to get to the goal
+ 
+
+ align:start position:0%
+right? The the how to get to the goal
+from every possible initial
+
+ align:start position:0%
+from every possible initial
+ 
+
+ align:start position:0%
+from every possible initial
+state.
+
+ align:start position:0%
+state.
+ 
+
+ align:start position:0%
+state.
+Yeah. If what you care about I mean the
+
+ align:start position:0%
+Yeah. If what you care about I mean the
+ 
+
+ align:start position:0%
+Yeah. If what you care about I mean the
+problem with that is if you have to look
+
+ align:start position:0%
+problem with that is if you have to look
+ 
+
+ align:start position:0%
+problem with that is if you have to look
+at every single initial state then it's
+
+ align:start position:0%
+at every single initial state then it's
+ 
+
+ align:start position:0%
+at every single initial state then it's
+not going to scale to high dimensions
+
+ align:start position:0%
+not going to scale to high dimensions
+ 
+
+ align:start position:0%
+not going to scale to high dimensions
+because there's going to be a lot of
+
+ align:start position:0%
+because there's going to be a lot of
+ 
+
+ align:start position:0%
+because there's going to be a lot of
+states. If you have a slightly higher
+
+ align:start position:0%
+states. If you have a slightly higher
+ 
+
+ align:start position:0%
+states. If you have a slightly higher
+dimensional system and you want to find
+
+ align:start position:0%
+dimensional system and you want to find
+ 
+
+ align:start position:0%
+dimensional system and you want to find
+a start to the goal but just a single
+
+ align:start position:0%
+a start to the goal but just a single
+ 
+
+ align:start position:0%
+a start to the goal but just a single
+path, you don't care about every
+
+ align:start position:0%
+path, you don't care about every
+ 
+
+ align:start position:0%
+path, you don't care about every
+possible state, then you can do not
+
+ align:start position:0%
+possible state, then you can do not
+ 
+
+ align:start position:0%
+possible state, then you can do not
+better than dynamic programming, but you
+
+ align:start position:0%
+better than dynamic programming, but you
+ 
+
+ align:start position:0%
+better than dynamic programming, but you
+can be more selective with your um with
+
+ align:start position:0%
+can be more selective with your um with
+ 
+
+ align:start position:0%
+can be more selective with your um with
+your dynamic programming algorithm um by
+
+ align:start position:0%
+your dynamic programming algorithm um by
+ 
+
+ align:start position:0%
+your dynamic programming algorithm um by
+doing these Dystra type and AAR type
+
+ align:start position:0%
+doing these Dystra type and AAR type
+ 
+
+ align:start position:0%
+doing these Dystra type and AAR type
+algorithms. So, let me just sort of do
+
+ align:start position:0%
+algorithms. So, let me just sort of do
+ 
+
+ align:start position:0%
+algorithms. So, let me just sort of do
+that quickly so you know so you know
+
+ align:start position:0%
+that quickly so you know so you know
+ 
+
+ align:start position:0%
+that quickly so you know so you know
+that that's
+
+ align:start position:0%
+that that's
+ 
+
+ align:start position:0%
+that that's
+there. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So dynamic programming again is
+
+ align:start position:0%
+So dynamic programming again is
+ 
+
+ align:start position:0%
+So dynamic programming again is
+definitely um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it's very efficient. It tends it it
+
+ align:start position:0%
+uh it's very efficient. It tends it it
+ 
+
+ align:start position:0%
+uh it's very efficient. It tends it it
+goes to a global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optima.
+
+ align:start position:0%
+optima.
+ 
+
+ align:start position:0%
+optima.
+Um but typically DP is is used to
+
+ align:start position:0%
+Um but typically DP is is used to
+ 
+
+ align:start position:0%
+Um but typically DP is is used to
+describe the the version where you're
+
+ align:start position:0%
+describe the the version where you're
+ 
+
+ align:start position:0%
+describe the the version where you're
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+solve for every state.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simultaneously,
+
+ align:start position:0%
+simultaneously,
+ 
+
+ align:start position:0%
+simultaneously,
+right? You can do a bit better. Um, you
+
+ align:start position:0%
+right? You can do a bit better. Um, you
+ 
+
+ align:start position:0%
+right? You can do a bit better. Um, you
+can be more selective if you just care
+
+ align:start position:0%
+can be more selective if you just care
+ 
+
+ align:start position:0%
+can be more selective if you just care
+about um from a start to a goal x0 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xg. It's a It's actually a little bit
+
+ align:start position:0%
+xg. It's a It's actually a little bit
+ 
+
+ align:start position:0%
+xg. It's a It's actually a little bit
+surprising to say that I can actually
+
+ align:start position:0%
+surprising to say that I can actually
+ 
+
+ align:start position:0%
+surprising to say that I can actually
+find my path from from a start to a goal
+
+ align:start position:0%
+find my path from from a start to a goal
+ 
+
+ align:start position:0%
+find my path from from a start to a goal
+and know that I'm at a global
+
+ align:start position:0%
+and know that I'm at a global
+ 
+
+ align:start position:0%
+and know that I'm at a global
+optima without ever expanding every
+
+ align:start position:0%
+optima without ever expanding every
+ 
+
+ align:start position:0%
+optima without ever expanding every
+single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node, right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then sometimes we don't even
+
+ align:start position:0%
+Okay. And then sometimes we don't even
+ 
+
+ align:start position:0%
+Okay. And then sometimes we don't even
+care about optimality at all. Like I
+
+ align:start position:0%
+care about optimality at all. Like I
+ 
+
+ align:start position:0%
+care about optimality at all. Like I
+said for some of these algorithms are
+
+ align:start position:0%
+said for some of these algorithms are
+ 
+
+ align:start position:0%
+said for some of these algorithms are
+just trying to find any old path to the
+
+ align:start position:0%
+just trying to find any old path to the
+ 
+
+ align:start position:0%
+just trying to find any old path to the
+goal. And then you can certainly imagine
+
+ align:start position:0%
+goal. And then you can certainly imagine
+ 
+
+ align:start position:0%
+goal. And then you can certainly imagine
+uh finding your path to the goal without
+
+ align:start position:0%
+uh finding your path to the goal without
+ 
+
+ align:start position:0%
+uh finding your path to the goal without
+expanding every possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node. Okay. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um, they all have a very simple recipe.
+
+ align:start position:0%
+um, they all have a very simple recipe.
+ 
+
+ align:start position:0%
+um, they all have a very simple recipe.
+Basically, you keep a a prioritized Q.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How many people know what a prioritized
+
+ align:start position:0%
+How many people know what a prioritized
+ 
+
+ align:start position:0%
+How many people know what a prioritized
+Q is? I should say it's often called Q,
+
+ align:start position:0%
+Q is? I should say it's often called Q,
+ 
+
+ align:start position:0%
+Q is? I should say it's often called Q,
+but it means Q. Yeah, it's another sleep
+
+ align:start position:0%
+but it means Q. Yeah, it's another sleep
+ 
+
+ align:start position:0%
+but it means Q. Yeah, it's another sleep
+deprivation thing
+
+ align:start position:0%
+deprivation thing
+ 
+
+ align:start position:0%
+deprivation thing
+there. Okay. So, I prioritize Q as a
+
+ align:start position:0%
+there. Okay. So, I prioritize Q as a
+ 
+
+ align:start position:0%
+there. Okay. So, I prioritize Q as a
+data structure that we use in computer
+
+ align:start position:0%
+data structure that we use in computer
+ 
+
+ align:start position:0%
+data structure that we use in computer
+science to um um that I'll I'll describe
+
+ align:start position:0%
+science to um um that I'll I'll describe
+ 
+
+ align:start position:0%
+science to um um that I'll I'll describe
+quickly here. So
+
+ align:start position:0%
+quickly here. So
+ 
+
+ align:start position:0%
+quickly here. So
+um we basically have a list of nodes
+
+ align:start position:0%
+um we basically have a list of nodes
+ 
+
+ align:start position:0%
+um we basically have a list of nodes
+that we that we want to consider
+
+ align:start position:0%
+that we that we want to consider
+ 
+
+ align:start position:0%
+that we that we want to consider
+expanding next stored in some list.
+
+ align:start position:0%
+expanding next stored in some list.
+ 
+
+ align:start position:0%
+expanding next stored in some list.
+Okay. But there but they're stored in
+
+ align:start position:0%
+Okay. But there but they're stored in
+ 
+
+ align:start position:0%
+Okay. But there but they're stored in
+that list in an ordered fashion ordered
+
+ align:start position:0%
+that list in an ordered fashion ordered
+ 
+
+ align:start position:0%
+that list in an ordered fashion ordered
+by how likely it is that we want to uh
+
+ align:start position:0%
+by how likely it is that we want to uh
+ 
+
+ align:start position:0%
+by how likely it is that we want to uh
+uh to to check that node next.
+
+ align:start position:0%
+uh to to check that node next.
+ 
+
+ align:start position:0%
+uh to to check that node next.
+Depending on the ways that you add nodes
+
+ align:start position:0%
+Depending on the ways that you add nodes
+ 
+
+ align:start position:0%
+Depending on the ways that you add nodes
+into the prioritized queue, you can do
+
+ align:start position:0%
+into the prioritized queue, you can do
+ 
+
+ align:start position:0%
+into the prioritized queue, you can do
+um any number of the standard
+
+ align:start position:0%
+um any number of the standard
+ 
+
+ align:start position:0%
+um any number of the standard
+um algorithms. The breadth
+
+ align:start position:0%
+um algorithms. The breadth
+ 
+
+ align:start position:0%
+um algorithms. The breadth
+first search, the depth first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+search. Dystras. Let me make sure I
+
+ align:start position:0%
+search. Dystras. Let me make sure I
+ 
+
+ align:start position:0%
+search. Dystras. Let me make sure I
+spell it right. It's DJI, right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What is it? Dig. Okay, good.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Thanks. Um, and you could do a star,
+
+ align:start position:0%
+Thanks. Um, and you could do a star,
+ 
+
+ align:start position:0%
+Thanks. Um, and you could do a star,
+let's say. There's more. There's
+
+ align:start position:0%
+let's say. There's more. There's
+ 
+
+ align:start position:0%
+let's say. There's more. There's
+iterative deepening things like this.
+
+ align:start position:0%
+iterative deepening things like this.
+ 
+
+ align:start position:0%
+iterative deepening things like this.
+Okay, they all go basically like this,
+
+ align:start position:0%
+Okay, they all go basically like this,
+ 
+
+ align:start position:0%
+Okay, they all go basically like this,
+right? I take my um my I have a queue of
+
+ align:start position:0%
+right? I take my um my I have a queue of
+ 
+
+ align:start position:0%
+right? I take my um my I have a queue of
+things I'm about to explore. I start off
+
+ align:start position:0%
+things I'm about to explore. I start off
+ 
+
+ align:start position:0%
+things I'm about to explore. I start off
+with the starting config, the starting
+
+ align:start position:0%
+with the starting config, the starting
+ 
+
+ align:start position:0%
+with the starting config, the starting
+state. I put that in my que. Okay, next
+
+ align:start position:0%
+state. I put that in my que. Okay, next
+ 
+
+ align:start position:0%
+state. I put that in my que. Okay, next
+step of the algorithm, take something
+
+ align:start position:0%
+step of the algorithm, take something
+ 
+
+ align:start position:0%
+step of the algorithm, take something
+out of the queue, consider its children,
+
+ align:start position:0%
+out of the queue, consider its children,
+ 
+
+ align:start position:0%
+out of the queue, consider its children,
+right? And um and then take the first
+
+ align:start position:0%
+right? And um and then take the first
+ 
+
+ align:start position:0%
+right? And um and then take the first
+one out of my priority queue, repeat.
+
+ align:start position:0%
+one out of my priority queue, repeat.
+ 
+
+ align:start position:0%
+one out of my priority queue, repeat.
+Okay, if I consider the children in a
+
+ align:start position:0%
+Okay, if I consider the children in a
+ 
+
+ align:start position:0%
+Okay, if I consider the children in a
+first in first out kind of way, if I add
+
+ align:start position:0%
+first in first out kind of way, if I add
+ 
+
+ align:start position:0%
+first in first out kind of way, if I add
+nodes and just say as soon as I uh as
+
+ align:start position:0%
+nodes and just say as soon as I uh as
+ 
+
+ align:start position:0%
+nodes and just say as soon as I uh as
+soon as I pick up a node, I'm going to
+
+ align:start position:0%
+soon as I pick up a node, I'm going to
+ 
+
+ align:start position:0%
+soon as I pick up a node, I'm going to
+go ahead and stick um those nodes into
+
+ align:start position:0%
+go ahead and stick um those nodes into
+ 
+
+ align:start position:0%
+go ahead and stick um those nodes into
+my queue in a sort of an first in first
+
+ align:start position:0%
+my queue in a sort of an first in first
+ 
+
+ align:start position:0%
+my queue in a sort of an first in first
+out kind of way. Then what I'm going to
+
+ align:start position:0%
+out kind of way. Then what I'm going to
+ 
+
+ align:start position:0%
+out kind of way. Then what I'm going to
+do is I'm going to proceed to look for
+
+ align:start position:0%
+do is I'm going to proceed to look for
+ 
+
+ align:start position:0%
+do is I'm going to proceed to look for
+the goal by going here, then here, then
+
+ align:start position:0%
+the goal by going here, then here, then
+ 
+
+ align:start position:0%
+the goal by going here, then here, then
+here, then here, then here, and write
+
+ align:start position:0%
+here, then here, then here, and write
+ 
+
+ align:start position:0%
+here, then here, then here, and write
+down the tree. That's a breath first
+
+ align:start position:0%
+down the tree. That's a breath first
+ 
+
+ align:start position:0%
+down the tree. That's a breath first
+search. If I do a prioritize queue where
+
+ align:start position:0%
+search. If I do a prioritize queue where
+ 
+
+ align:start position:0%
+search. If I do a prioritize queue where
+I when I add the the children, I just do
+
+ align:start position:0%
+I when I add the the children, I just do
+ 
+
+ align:start position:0%
+I when I add the the children, I just do
+a a last in first out. Yeah. Then I'll
+
+ align:start position:0%
+a a last in first out. Yeah. Then I'll
+ 
+
+ align:start position:0%
+a a last in first out. Yeah. Then I'll
+I'll go here, then I'll go here, then
+
+ align:start position:0%
+I'll go here, then I'll go here, then
+ 
+
+ align:start position:0%
+I'll go here, then I'll go here, then
+I'll go here, and I'll go as deep down
+
+ align:start position:0%
+I'll go here, and I'll go as deep down
+ 
+
+ align:start position:0%
+I'll go here, and I'll go as deep down
+the tree as I could possibly do before I
+
+ align:start position:0%
+the tree as I could possibly do before I
+ 
+
+ align:start position:0%
+the tree as I could possibly do before I
+come back and and go down the the other
+
+ align:start position:0%
+come back and and go down the the other
+ 
+
+ align:start position:0%
+come back and and go down the the other
+nodes. If I keep along
+
+ align:start position:0%
+nodes. If I keep along
+ 
+
+ align:start position:0%
+nodes. If I keep along
+um a uh let's call it a cost to come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to differentiate it from the cost to go.
+
+ align:start position:0%
+to differentiate it from the cost to go.
+ 
+
+ align:start position:0%
+to differentiate it from the cost to go.
+Right? If I keep a record of how much
+
+ align:start position:0%
+Right? If I keep a record of how much
+ 
+
+ align:start position:0%
+Right? If I keep a record of how much
+cost I incurred um for my cost function
+
+ align:start position:0%
+cost I incurred um for my cost function
+ 
+
+ align:start position:0%
+cost I incurred um for my cost function
+getting to that node and I always select
+
+ align:start position:0%
+getting to that node and I always select
+ 
+
+ align:start position:0%
+getting to that node and I always select
+to expand the node that would be the
+
+ align:start position:0%
+to expand the node that would be the
+ 
+
+ align:start position:0%
+to expand the node that would be the
+cheapest. Okay, then that's called
+
+ align:start position:0%
+cheapest. Okay, then that's called
+ 
+
+ align:start position:0%
+cheapest. Okay, then that's called
+Dyster's
+
+ align:start position:0%
+Dyster's
+ 
+
+ align:start position:0%
+Dyster's
+algorithm. It's exactly equivalent to to
+
+ align:start position:0%
+algorithm. It's exactly equivalent to to
+ 
+
+ align:start position:0%
+algorithm. It's exactly equivalent to to
+dynamic programming, but it's in the
+
+ align:start position:0%
+dynamic programming, but it's in the
+ 
+
+ align:start position:0%
+dynamic programming, but it's in the
+forward
+
+ align:start position:0%
+forward
+ 
+
+ align:start position:0%
+forward
+sense. Okay, and then a star is a
+
+ align:start position:0%
+sense. Okay, and then a star is a
+ 
+
+ align:start position:0%
+sense. Okay, and then a star is a
+is a even nicer way to do that which
+
+ align:start position:0%
+is a even nicer way to do that which
+ 
+
+ align:start position:0%
+is a even nicer way to do that which
+combines a cost to come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um plus some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heristic. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+My goal is to make sure you guys know
+
+ align:start position:0%
+My goal is to make sure you guys know
+ 
+
+ align:start position:0%
+My goal is to make sure you guys know
+these are out there. There's lots of
+
+ align:start position:0%
+these are out there. There's lots of
+ 
+
+ align:start position:0%
+these are out there. There's lots of
+good easy places to read about um about
+
+ align:start position:0%
+good easy places to read about um about
+ 
+
+ align:start position:0%
+good easy places to read about um about
+these algorithms uh especially Steve
+
+ align:start position:0%
+these algorithms uh especially Steve
+ 
+
+ align:start position:0%
+these algorithms uh especially Steve
+Laval's book.
+
+ align:start position:0%
+Laval's book.
+ 
+
+ align:start position:0%
+Laval's book.
+Okay. The s- the only surprising thing
+
+ align:start position:0%
+Okay. The s- the only surprising thing
+ 
+
+ align:start position:0%
+Okay. The s- the only surprising thing
+really about these algorithms is first
+
+ align:start position:0%
+really about these algorithms is first
+ 
+
+ align:start position:0%
+really about these algorithms is first
+of all that you can often very
+
+ align:start position:0%
+of all that you can often very
+ 
+
+ align:start position:0%
+of all that you can often very
+efficiently find your way to the goal
+
+ align:start position:0%
+efficiently find your way to the goal
+ 
+
+ align:start position:0%
+efficiently find your way to the goal
+without expanding as many nodes as you
+
+ align:start position:0%
+without expanding as many nodes as you
+ 
+
+ align:start position:0%
+without expanding as many nodes as you
+might
+
+ align:start position:0%
+might
+ 
+
+ align:start position:0%
+might
+think. Okay, AAR in particular if you
+
+ align:start position:0%
+think. Okay, AAR in particular if you
+ 
+
+ align:start position:0%
+think. Okay, AAR in particular if you
+can find a good heristic a heristic in
+
+ align:start position:0%
+can find a good heristic a heristic in
+ 
+
+ align:start position:0%
+can find a good heristic a heristic in
+this case is an estimate of the cost to
+
+ align:start position:0%
+this case is an estimate of the cost to
+ 
+
+ align:start position:0%
+this case is an estimate of the cost to
+go a guess at your value um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function. If you can guess your value
+
+ align:start position:0%
+function. If you can guess your value
+ 
+
+ align:start position:0%
+function. If you can guess your value
+function in a way
+
+ align:start position:0%
+function in a way
+ 
+
+ align:start position:0%
+function in a way
+um where you always underestimated again
+
+ align:start position:0%
+um where you always underestimated again
+ 
+
+ align:start position:0%
+um where you always underestimated again
+I'm not going to bore you with all the
+
+ align:start position:0%
+I'm not going to bore you with all the
+ 
+
+ align:start position:0%
+I'm not going to bore you with all the
+details here then actually you can you
+
+ align:start position:0%
+details here then actually you can you
+ 
+
+ align:start position:0%
+details here then actually you can you
+can sometimes expand very few nodes and
+
+ align:start position:0%
+can sometimes expand very few nodes and
+ 
+
+ align:start position:0%
+can sometimes expand very few nodes and
+find your way right to the goal very
+
+ align:start position:0%
+find your way right to the goal very
+ 
+
+ align:start position:0%
+find your way right to the goal very
+efficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithms.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, people out here use AAR all the
+
+ align:start position:0%
+Okay, people out here use AAR all the
+ 
+
+ align:start position:0%
+Okay, people out here use AAR all the
+time, right? For uh for the Grand
+
+ align:start position:0%
+time, right? For uh for the Grand
+ 
+
+ align:start position:0%
+time, right? For uh for the Grand
+Challenge, I think half the teams had
+
+ align:start position:0%
+Challenge, I think half the teams had
+ 
+
+ align:start position:0%
+Challenge, I think half the teams had
+AAR planners running on their their
+
+ align:start position:0%
+AAR planners running on their their
+ 
+
+ align:start position:0%
+AAR planners running on their their
+vehicle, right? For Little Dog, uh in
+
+ align:start position:0%
+vehicle, right? For Little Dog, uh in
+ 
+
+ align:start position:0%
+vehicle, right? For Little Dog, uh in
+our, you know, we're picking footholds
+
+ align:start position:0%
+our, you know, we're picking footholds
+ 
+
+ align:start position:0%
+our, you know, we're picking footholds
+to get from the start to the goal. We
+
+ align:start position:0%
+to get from the start to the goal. We
+ 
+
+ align:start position:0%
+to get from the start to the goal. We
+have an AAR planner in there, discreet
+
+ align:start position:0%
+have an AAR planner in there, discreet
+ 
+
+ align:start position:0%
+have an AAR planner in there, discreet
+time planners. These things are are
+
+ align:start position:0%
+time planners. These things are are
+ 
+
+ align:start position:0%
+time planners. These things are are
+real. They're good. They're fast. Um, if
+
+ align:start position:0%
+real. They're good. They're fast. Um, if
+ 
+
+ align:start position:0%
+real. They're good. They're fast. Um, if
+you can find a good heristic, they can
+
+ align:start position:0%
+you can find a good heristic, they can
+ 
+
+ align:start position:0%
+you can find a good heristic, they can
+be very, very efficient. If you care
+
+ align:start position:0%
+be very, very efficient. If you care
+ 
+
+ align:start position:0%
+be very, very efficient. If you care
+about a continuous time, a continuous
+
+ align:start position:0%
+about a continuous time, a continuous
+ 
+
+ align:start position:0%
+about a continuous time, a continuous
+state, continuous action plan that gets
+
+ align:start position:0%
+state, continuous action plan that gets
+ 
+
+ align:start position:0%
+state, continuous action plan that gets
+me from the goal, then they're not as
+
+ align:start position:0%
+me from the goal, then they're not as
+ 
+
+ align:start position:0%
+me from the goal, then they're not as
+satisfying because they relied on this
+
+ align:start position:0%
+satisfying because they relied on this
+ 
+
+ align:start position:0%
+satisfying because they relied on this
+discretization. Okay, but again,
+
+ align:start position:0%
+discretization. Okay, but again,
+ 
+
+ align:start position:0%
+discretization. Okay, but again,
+um, so we know when we're discretizing
+
+ align:start position:0%
+um, so we know when we're discretizing
+ 
+
+ align:start position:0%
+um, so we know when we're discretizing
+this thing, we're going to have some
+
+ align:start position:0%
+this thing, we're going to have some
+ 
+
+ align:start position:0%
+this thing, we're going to have some
+problems, right? We're going to um I'm
+
+ align:start position:0%
+problems, right? We're going to um I'm
+ 
+
+ align:start position:0%
+problems, right? We're going to um I'm
+going to just assume that there's a
+
+ align:start position:0%
+going to just assume that there's a
+ 
+
+ align:start position:0%
+going to just assume that there's a
+control action that gets me sort of
+
+ align:start position:0%
+control action that gets me sort of
+ 
+
+ align:start position:0%
+control action that gets me sort of
+squarely in the center of this um this
+
+ align:start position:0%
+squarely in the center of this um this
+ 
+
+ align:start position:0%
+squarely in the center of this um this
+next discretized cell and then go like
+
+ align:start position:0%
+next discretized cell and then go like
+ 
+
+ align:start position:0%
+next discretized cell and then go like
+this. If I were to execute out my
+
+ align:start position:0%
+this. If I were to execute out my
+ 
+
+ align:start position:0%
+this. If I were to execute out my
+actions from my discrete planning
+
+ align:start position:0%
+actions from my discrete planning
+ 
+
+ align:start position:0%
+actions from my discrete planning
+algorithm on the continuous time system,
+
+ align:start position:0%
+algorithm on the continuous time system,
+ 
+
+ align:start position:0%
+algorithm on the continuous time system,
+I'm going to quickly deviate from my
+
+ align:start position:0%
+I'm going to quickly deviate from my
+ 
+
+ align:start position:0%
+I'm going to quickly deviate from my
+plan. But these things are an excellent
+
+ align:start position:0%
+plan. But these things are an excellent
+ 
+
+ align:start position:0%
+plan. But these things are an excellent
+way to start to seed something like a
+
+ align:start position:0%
+way to start to seed something like a
+ 
+
+ align:start position:0%
+way to start to seed something like a
+direct collocation method, right? Find
+
+ align:start position:0%
+direct collocation method, right? Find
+ 
+
+ align:start position:0%
+direct collocation method, right? Find
+yourself a feasible optimal plan and
+
+ align:start position:0%
+yourself a feasible optimal plan and
+ 
+
+ align:start position:0%
+yourself a feasible optimal plan and
+then stabilize it. Let's say with the
+
+ align:start position:0%
+then stabilize it. Let's say with the
+ 
+
+ align:start position:0%
+then stabilize it. Let's say with the
+LTV
+
+ align:start position:0%
+LTV
+ 
+
+ align:start position:0%
+LTV
+feedback.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Good. So that world of planning
+
+ align:start position:0%
+Good. So that world of planning
+ 
+
+ align:start position:0%
+Good. So that world of planning
+algorithms is out there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But about I don't know 10 years ago now
+
+ align:start position:0%
+But about I don't know 10 years ago now
+ 
+
+ align:start position:0%
+But about I don't know 10 years ago now
+something big happened in robotic motion
+
+ align:start position:0%
+something big happened in robotic motion
+ 
+
+ align:start position:0%
+something big happened in robotic motion
+planning world. Um people started using
+
+ align:start position:0%
+planning world. Um people started using
+ 
+
+ align:start position:0%
+planning world. Um people started using
+uh sample based motion planning
+
+ align:start position:0%
+uh sample based motion planning
+ 
+
+ align:start position:0%
+uh sample based motion planning
+algorithms
+
+ align:start position:0%
+algorithms
+ 
+
+ align:start position:0%
+algorithms
+and there was sort of a revolution in
+
+ align:start position:0%
+and there was sort of a revolution in
+ 
+
+ align:start position:0%
+and there was sort of a revolution in
+people using motion planning in
+
+ align:start position:0%
+people using motion planning in
+ 
+
+ align:start position:0%
+people using motion planning in
+robotics. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's also sometimes called randomized
+
+ align:start position:0%
+It's also sometimes called randomized
+ 
+
+ align:start position:0%
+It's also sometimes called randomized
+motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planning. And these we are going to dig
+
+ align:start position:0%
+planning. And these we are going to dig
+ 
+
+ align:start position:0%
+planning. And these we are going to dig
+a little deeper in because they're I
+
+ align:start position:0%
+a little deeper in because they're I
+ 
+
+ align:start position:0%
+a little deeper in because they're I
+think they're a we use them all the
+
+ align:start position:0%
+think they're a we use them all the
+ 
+
+ align:start position:0%
+think they're a we use them all the
+time. I think they're an important class
+
+ align:start position:0%
+time. I think they're an important class
+ 
+
+ align:start position:0%
+time. I think they're an important class
+of algorithms. Okay. Okay. So, two of
+
+ align:start position:0%
+of algorithms. Okay. Okay. So, two of
+ 
+
+ align:start position:0%
+of algorithms. Okay. Okay. So, two of
+the most notable um sample based motion
+
+ align:start position:0%
+the most notable um sample based motion
+ 
+
+ align:start position:0%
+the most notable um sample based motion
+planning um ideas are the rapidly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exploring randomized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees and the probabilistic road map.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Another poll. How many people know about
+
+ align:start position:0%
+Another poll. How many people know about
+ 
+
+ align:start position:0%
+Another poll. How many people know about
+RTS?
+
+ align:start position:0%
+RTS?
+ 
+
+ align:start position:0%
+RTS?
+Awesome. How many people about know
+
+ align:start position:0%
+Awesome. How many people about know
+ 
+
+ align:start position:0%
+Awesome. How many people about know
+about PRM? Awesome. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They're pretty related to each other.
+
+ align:start position:0%
+They're pretty related to each other.
+ 
+
+ align:start position:0%
+They're pretty related to each other.
+Let's talk about rapidly exploring
+
+ align:start position:0%
+Let's talk about rapidly exploring
+ 
+
+ align:start position:0%
+Let's talk about rapidly exploring
+randomized trees
+
+ align:start position:0%
+randomized trees
+ 
+
+ align:start position:0%
+randomized trees
+first.
+
+ align:start position:0%
+first.
+ 
+
+ align:start position:0%
+first.
+Okay, so both of these are an attempt to
+
+ align:start position:0%
+Okay, so both of these are an attempt to
+ 
+
+ align:start position:0%
+Okay, so both of these are an attempt to
+get away from these very coarse um
+
+ align:start position:0%
+get away from these very coarse um
+ 
+
+ align:start position:0%
+get away from these very coarse um
+discretizations like this and sort of
+
+ align:start position:0%
+discretizations like this and sort of
+ 
+
+ align:start position:0%
+discretizations like this and sort of
+embrace the fact that we're working in a
+
+ align:start position:0%
+embrace the fact that we're working in a
+ 
+
+ align:start position:0%
+embrace the fact that we're working in a
+continuous state
+
+ align:start position:0%
+continuous state
+ 
+
+ align:start position:0%
+continuous state
+space. Okay, instead of discretizing it
+
+ align:start position:0%
+space. Okay, instead of discretizing it
+ 
+
+ align:start position:0%
+space. Okay, instead of discretizing it
+at at some known sites, we're going to
+
+ align:start position:0%
+at at some known sites, we're going to
+ 
+
+ align:start position:0%
+at at some known sites, we're going to
+discretise sort of at randomly chosen
+
+ align:start position:0%
+discretise sort of at randomly chosen
+ 
+
+ align:start position:0%
+discretise sort of at randomly chosen
+samples. Okay? And as we add more and
+
+ align:start position:0%
+samples. Okay? And as we add more and
+ 
+
+ align:start position:0%
+samples. Okay? And as we add more and
+more samples, we're going to worry less
+
+ align:start position:0%
+more samples, we're going to worry less
+ 
+
+ align:start position:0%
+more samples, we're going to worry less
+and less about the discretization,
+
+ align:start position:0%
+and less about the discretization,
+ 
+
+ align:start position:0%
+and less about the discretization,
+right? And eventually we're going to
+
+ align:start position:0%
+right? And eventually we're going to
+ 
+
+ align:start position:0%
+right? And eventually we're going to
+have some nice to say about the
+
+ align:start position:0%
+have some nice to say about the
+ 
+
+ align:start position:0%
+have some nice to say about the
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+space. So the rapidly exploring
+
+ align:start position:0%
+space. So the rapidly exploring
+ 
+
+ align:start position:0%
+space. So the rapidly exploring
+randomized trees, the RRTs are a very
+
+ align:start position:0%
+randomized trees, the RRTs are a very
+ 
+
+ align:start position:0%
+randomized trees, the RRTs are a very
+simple algorithm to explain.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, let's think about it in terms of
+
+ align:start position:0%
+Okay, let's think about it in terms of
+ 
+
+ align:start position:0%
+Okay, let's think about it in terms of
+moving a piano through a a 2D piano
+
+ align:start position:0%
+moving a piano through a a 2D piano
+ 
+
+ align:start position:0%
+moving a piano through a a 2D piano
+through a a 2D world in configuration
+
+ align:start position:0%
+through a a 2D world in configuration
+ 
+
+ align:start position:0%
+through a a 2D world in configuration
+space. So, we got a point moving through
+
+ align:start position:0%
+space. So, we got a point moving through
+ 
+
+ align:start position:0%
+space. So, we got a point moving through
+a a world. It should really be 3D
+
+ align:start position:0%
+a a world. It should really be 3D
+ 
+
+ align:start position:0%
+a a world. It should really be 3D
+actually if there's an orientation to
+
+ align:start position:0%
+actually if there's an orientation to
+ 
+
+ align:start position:0%
+actually if there's an orientation to
+the piano, but let's let's just look at
+
+ align:start position:0%
+the piano, but let's let's just look at
+ 
+
+ align:start position:0%
+the piano, but let's let's just look at
+the 2D problem here. So,
+
+ align:start position:0%
+the 2D problem here. So,
+ 
+
+ align:start position:0%
+the 2D problem here. So,
+um so I've got a point
+
+ align:start position:0%
+um so I've got a point
+ 
+
+ align:start position:0%
+um so I've got a point
+um an initial state, an initial goal in
+
+ align:start position:0%
+um an initial state, an initial goal in
+ 
+
+ align:start position:0%
+um an initial state, an initial goal in
+a 2D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+world. Let's call it XY. And I've got
+
+ align:start position:0%
+world. Let's call it XY. And I've got
+ 
+
+ align:start position:0%
+world. Let's call it XY. And I've got
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+obstacles. I like to find a path from
+
+ align:start position:0%
+obstacles. I like to find a path from
+ 
+
+ align:start position:0%
+obstacles. I like to find a path from
+the start to the goal without explicitly
+
+ align:start position:0%
+the start to the goal without explicitly
+ 
+
+ align:start position:0%
+the start to the goal without explicitly
+discretizing the space. Okay. The RTS do
+
+ align:start position:0%
+discretizing the space. Okay. The RTS do
+ 
+
+ align:start position:0%
+discretizing the space. Okay. The RTS do
+it like this. Pick a point from random
+
+ align:start position:0%
+it like this. Pick a point from random
+ 
+
+ align:start position:0%
+it like this. Pick a point from random
+at the state in the space. Yeah.
+
+ align:start position:0%
+at the state in the space. Yeah.
+ 
+
+ align:start position:0%
+at the state in the space. Yeah.
+try to connect your current tree which
+
+ align:start position:0%
+try to connect your current tree which
+ 
+
+ align:start position:0%
+try to connect your current tree which
+in the initial state is just this x0 to
+
+ align:start position:0%
+in the initial state is just this x0 to
+ 
+
+ align:start position:0%
+in the initial state is just this x0 to
+that um that new point. Okay, if I if I
+
+ align:start position:0%
+that um that new point. Okay, if I if I
+ 
+
+ align:start position:0%
+that um that new point. Okay, if I if I
+uh let's make it exactly clear that I
+
+ align:start position:0%
+uh let's make it exactly clear that I
+ 
+
+ align:start position:0%
+uh let's make it exactly clear that I
+can't do that. Okay, so that's going to
+
+ align:start position:0%
+can't do that. Okay, so that's going to
+ 
+
+ align:start position:0%
+can't do that. Okay, so that's going to
+actually my attempt to directly connect
+
+ align:start position:0%
+actually my attempt to directly connect
+ 
+
+ align:start position:0%
+actually my attempt to directly connect
+this is going to fail because it goes
+
+ align:start position:0%
+this is going to fail because it goes
+ 
+
+ align:start position:0%
+this is going to fail because it goes
+through an obstacle. Okay, so I can't
+
+ align:start position:0%
+through an obstacle. Okay, so I can't
+ 
+
+ align:start position:0%
+through an obstacle. Okay, so I can't
+add that node sample again randomly.
+
+ align:start position:0%
+add that node sample again randomly.
+ 
+
+ align:start position:0%
+add that node sample again randomly.
+Okay, at some point I'll get a node like
+
+ align:start position:0%
+Okay, at some point I'll get a node like
+ 
+
+ align:start position:0%
+Okay, at some point I'll get a node like
+here and I'm going to connect my
+
+ align:start position:0%
+here and I'm going to connect my
+ 
+
+ align:start position:0%
+here and I'm going to connect my
+um I'm going to make a branch of my tree
+
+ align:start position:0%
+um I'm going to make a branch of my tree
+ 
+
+ align:start position:0%
+um I'm going to make a branch of my tree
+that connects those two points. Okay,
+
+ align:start position:0%
+that connects those two points. Okay,
+ 
+
+ align:start position:0%
+that connects those two points. Okay,
+pick a new random point something. Let's
+
+ align:start position:0%
+pick a new random point something. Let's
+ 
+
+ align:start position:0%
+pick a new random point something. Let's
+say you get something here. Now you have
+
+ align:start position:0%
+say you get something here. Now you have
+ 
+
+ align:start position:0%
+say you get something here. Now you have
+to choose between these two random
+
+ align:start position:0%
+to choose between these two random
+ 
+
+ align:start position:0%
+to choose between these two random
+points. Decide decide which is the
+
+ align:start position:0%
+points. Decide decide which is the
+ 
+
+ align:start position:0%
+points. Decide decide which is the
+closest. The closest isn't always an
+
+ align:start position:0%
+closest. The closest isn't always an
+ 
+
+ align:start position:0%
+closest. The closest isn't always an
+easy thing to decide if you have
+
+ align:start position:0%
+easy thing to decide if you have
+ 
+
+ align:start position:0%
+easy thing to decide if you have
+complicated dynamics. In this problem,
+
+ align:start position:0%
+complicated dynamics. In this problem,
+ 
+
+ align:start position:0%
+complicated dynamics. In this problem,
+it's pretty easy. We could just use
+
+ align:start position:0%
+it's pretty easy. We could just use
+ 
+
+ align:start position:0%
+it's pretty easy. We could just use
+something like a ukitian distance. And
+
+ align:start position:0%
+something like a ukitian distance. And
+ 
+
+ align:start position:0%
+something like a ukitian distance. And
+I'll connect it up like this. I get a r
+
+ align:start position:0%
+I'll connect it up like this. I get a r
+ 
+
+ align:start position:0%
+I'll connect it up like this. I get a r
+another random point, I'll connect it up
+
+ align:start position:0%
+another random point, I'll connect it up
+ 
+
+ align:start position:0%
+another random point, I'll connect it up
+like this. I get some random points that
+
+ align:start position:0%
+like this. I get some random points that
+ 
+
+ align:start position:0%
+like this. I get some random points that
+go whatever way. If they end up here, I
+
+ align:start position:0%
+go whatever way. If they end up here, I
+ 
+
+ align:start position:0%
+go whatever way. If they end up here, I
+just throw them out. If they end up
+
+ align:start position:0%
+just throw them out. If they end up
+ 
+
+ align:start position:0%
+just throw them out. If they end up
+something that I can't connect, I'll
+
+ align:start position:0%
+something that I can't connect, I'll
+ 
+
+ align:start position:0%
+something that I can't connect, I'll
+just throw it out. But at some point,
+
+ align:start position:0%
+just throw it out. But at some point,
+ 
+
+ align:start position:0%
+just throw it out. But at some point,
+I'll start filling the space with these
+
+ align:start position:0%
+I'll start filling the space with these
+ 
+
+ align:start position:0%
+I'll start filling the space with these
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+trees. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lo and behold, if I do it enough, it
+
+ align:start position:0%
+Lo and behold, if I do it enough, it
+ 
+
+ align:start position:0%
+Lo and behold, if I do it enough, it
+doesn't actually necessarily take that
+
+ align:start position:0%
+doesn't actually necessarily take that
+ 
+
+ align:start position:0%
+doesn't actually necessarily take that
+long until I get up here and and get
+
+ align:start position:0%
+long until I get up here and and get
+ 
+
+ align:start position:0%
+long until I get up here and and get
+close in the vicinity of that goal.
+
+ align:start position:0%
+close in the vicinity of that goal.
+ 
+
+ align:start position:0%
+close in the vicinity of that goal.
+Okay, very simple random algorithm,
+
+ align:start position:0%
+Okay, very simple random algorithm,
+ 
+
+ align:start position:0%
+Okay, very simple random algorithm,
+right? Do you understand how it's sort
+
+ align:start position:0%
+right? Do you understand how it's sort
+ 
+
+ align:start position:0%
+right? Do you understand how it's sort
+of avoiding the the curse of
+
+ align:start position:0%
+of avoiding the the curse of
+ 
+
+ align:start position:0%
+of avoiding the the curse of
+discretization, right? It's just picking
+
+ align:start position:0%
+discretization, right? It's just picking
+ 
+
+ align:start position:0%
+discretization, right? It's just picking
+points at random from this continuous
+
+ align:start position:0%
+points at random from this continuous
+ 
+
+ align:start position:0%
+points at random from this continuous
+space. So there's no um no constraints
+
+ align:start position:0%
+space. So there's no um no constraints
+ 
+
+ align:start position:0%
+space. So there's no um no constraints
+uh no explicit constraints that it lies
+
+ align:start position:0%
+uh no explicit constraints that it lies
+ 
+
+ align:start position:0%
+uh no explicit constraints that it lies
+in some the center of some bucket or
+
+ align:start position:0%
+in some the center of some bucket or
+ 
+
+ align:start position:0%
+in some the center of some bucket or
+something like that right nodes could be
+
+ align:start position:0%
+something like that right nodes could be
+ 
+
+ align:start position:0%
+something like that right nodes could be
+arbitrarily close to each other I can
+
+ align:start position:0%
+arbitrarily close to each other I can
+ 
+
+ align:start position:0%
+arbitrarily close to each other I can
+get arbitrarily fine sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discretization
+
+ align:start position:0%
+discretization
+ 
+
+ align:start position:0%
+discretization
+what's really cool what makes these
+
+ align:start position:0%
+what's really cool what makes these
+ 
+
+ align:start position:0%
+what's really cool what makes these
+things tick is that the idea is so
+
+ align:start position:0%
+things tick is that the idea is so
+ 
+
+ align:start position:0%
+things tick is that the idea is so
+simple the code is so easy to write and
+
+ align:start position:0%
+simple the code is so easy to write and
+ 
+
+ align:start position:0%
+simple the code is so easy to write and
+they really really work fast Okay, let
+
+ align:start position:0%
+they really really work fast Okay, let
+ 
+
+ align:start position:0%
+they really really work fast Okay, let
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+just show you that basic example.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, this this time I'm going to do it
+
+ align:start position:0%
+Okay, this this time I'm going to do it
+ 
+
+ align:start position:0%
+Okay, this this time I'm going to do it
+even without uh
+
+ align:start position:0%
+even without uh
+ 
+
+ align:start position:0%
+even without uh
+um without any obstacles but just to
+
+ align:start position:0%
+um without any obstacles but just to
+ 
+
+ align:start position:0%
+um without any obstacles but just to
+show you the basic growth of these kind
+
+ align:start position:0%
+show you the basic growth of these kind
+ 
+
+ align:start position:0%
+show you the basic growth of these kind
+of um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planters.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Awesome. Okay. So,
+
+ align:start position:0%
+Awesome. Okay. So,
+ 
+
+ align:start position:0%
+Awesome. Okay. So,
+um my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh initial condition is just that blue
+
+ align:start position:0%
+uh initial condition is just that blue
+ 
+
+ align:start position:0%
+uh initial condition is just that blue
+point and I'm going to start growing a
+
+ align:start position:0%
+point and I'm going to start growing a
+ 
+
+ align:start position:0%
+point and I'm going to start growing a
+tree in every random direction. There's
+
+ align:start position:0%
+tree in every random direction. There's
+ 
+
+ align:start position:0%
+tree in every random direction. There's
+not even a goal in this problem. This is
+
+ align:start position:0%
+not even a goal in this problem. This is
+ 
+
+ align:start position:0%
+not even a goal in this problem. This is
+just to show you the basic growth of the
+
+ align:start position:0%
+just to show you the basic growth of the
+ 
+
+ align:start position:0%
+just to show you the basic growth of the
+tree. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Every point I grow at
+
+ align:start position:0%
+Every point I grow at
+ 
+
+ align:start position:0%
+Every point I grow at
+random. Every time I pick a point from a
+
+ align:start position:0%
+random. Every time I pick a point from a
+ 
+
+ align:start position:0%
+random. Every time I pick a point from a
+uniform distribution covering the space,
+
+ align:start position:0%
+uniform distribution covering the space,
+ 
+
+ align:start position:0%
+uniform distribution covering the space,
+I'm going to find the closest point in
+
+ align:start position:0%
+I'm going to find the closest point in
+ 
+
+ align:start position:0%
+I'm going to find the closest point in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+algorithm and I'm going to grow a
+
+ align:start position:0%
+algorithm and I'm going to grow a
+ 
+
+ align:start position:0%
+algorithm and I'm going to grow a
+closest point on the tree and I'm going
+
+ align:start position:0%
+closest point on the tree and I'm going
+ 
+
+ align:start position:0%
+closest point on the tree and I'm going
+to try to grow my tree towards that um
+
+ align:start position:0%
+to try to grow my tree towards that um
+ 
+
+ align:start position:0%
+to try to grow my tree towards that um
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+node. Yeah, sort of understand what's
+
+ align:start position:0%
+node. Yeah, sort of understand what's
+ 
+
+ align:start position:0%
+node. Yeah, sort of understand what's
+happening there. It's pretty faint, I
+
+ align:start position:0%
+happening there. It's pretty faint, I
+ 
+
+ align:start position:0%
+happening there. It's pretty faint, I
+think,
+
+ align:start position:0%
+think,
+ 
+
+ align:start position:0%
+think,
+but all right. So, watch what happens if
+
+ align:start position:0%
+but all right. So, watch what happens if
+ 
+
+ align:start position:0%
+but all right. So, watch what happens if
+I just let that run.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, trivial algorithm. It has what a
+
+ align:start position:0%
+Okay, trivial algorithm. It has what a
+ 
+
+ align:start position:0%
+Okay, trivial algorithm. It has what a
+lot of people like to call a fractal
+
+ align:start position:0%
+lot of people like to call a fractal
+ 
+
+ align:start position:0%
+lot of people like to call a fractal
+expansion of the uh of the coverage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, this happens if of course if
+
+ align:start position:0%
+Okay, this happens if of course if
+ 
+
+ align:start position:0%
+Okay, this happens if of course if
+there's obstacles it'll take a little
+
+ align:start position:0%
+there's obstacles it'll take a little
+ 
+
+ align:start position:0%
+there's obstacles it'll take a little
+longer to get around there. But the
+
+ align:start position:0%
+longer to get around there. But the
+ 
+
+ align:start position:0%
+longer to get around there. But the
+algorithm probabilistically covers the
+
+ align:start position:0%
+algorithm probabilistically covers the
+ 
+
+ align:start position:0%
+algorithm probabilistically covers the
+state space as I add more and more
+
+ align:start position:0%
+state space as I add more and more
+ 
+
+ align:start position:0%
+state space as I add more and more
+points. Yeah. And it's actually some
+
+ align:start position:0%
+points. Yeah. And it's actually some
+ 
+
+ align:start position:0%
+points. Yeah. And it's actually some
+people call them uh dense trees because
+
+ align:start position:0%
+people call them uh dense trees because
+ 
+
+ align:start position:0%
+people call them uh dense trees because
+they do this. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um if you noticed something about them,
+
+ align:start position:0%
+Um if you noticed something about them,
+ 
+
+ align:start position:0%
+Um if you noticed something about them,
+they have sort of surprisingly nice
+
+ align:start position:0%
+they have sort of surprisingly nice
+ 
+
+ align:start position:0%
+they have sort of surprisingly nice
+qualities. Okay. Um it filled the space
+
+ align:start position:0%
+qualities. Okay. Um it filled the space
+ 
+
+ align:start position:0%
+qualities. Okay. Um it filled the space
+pretty uniformly pretty quickly, right?
+
+ align:start position:0%
+pretty uniformly pretty quickly, right?
+ 
+
+ align:start position:0%
+pretty uniformly pretty quickly, right?
+It didn't just go off in one corner and
+
+ align:start position:0%
+It didn't just go off in one corner and
+ 
+
+ align:start position:0%
+It didn't just go off in one corner and
+start adding nodes on one side, right?
+
+ align:start position:0%
+start adding nodes on one side, right?
+ 
+
+ align:start position:0%
+start adding nodes on one side, right?
+Um or something like that. It actually
+
+ align:start position:0%
+Um or something like that. It actually
+ 
+
+ align:start position:0%
+Um or something like that. It actually
+has a property that people call the the
+
+ align:start position:0%
+has a property that people call the the
+ 
+
+ align:start position:0%
+has a property that people call the the
+voronoi bias.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the voronoi region of a graph.
+
+ align:start position:0%
+the voronoi region of a graph.
+ 
+
+ align:start position:0%
+the voronoi region of a graph.
+Well, the voroi bias implies that the
+
+ align:start position:0%
+Well, the voroi bias implies that the
+ 
+
+ align:start position:0%
+Well, the voroi bias implies that the
+tree has a has a um has a bias for
+
+ align:start position:0%
+tree has a has a um has a bias for
+ 
+
+ align:start position:0%
+tree has a has a um has a bias for
+always growing into the biggest open
+
+ align:start position:0%
+always growing into the biggest open
+ 
+
+ align:start position:0%
+always growing into the biggest open
+regions of the of the graph.
+
+ align:start position:0%
+regions of the of the graph.
+ 
+
+ align:start position:0%
+regions of the of the graph.
+Yeah. And that just comes from uni
+
+ align:start position:0%
+Yeah. And that just comes from uni
+ 
+
+ align:start position:0%
+Yeah. And that just comes from uni
+sampling uniformly, right? If I have
+
+ align:start position:0%
+sampling uniformly, right? If I have
+ 
+
+ align:start position:0%
+sampling uniformly, right? If I have
+some um some tree that has a big wide
+
+ align:start position:0%
+some um some tree that has a big wide
+ 
+
+ align:start position:0%
+some um some tree that has a big wide
+open area for whatever
+
+ align:start position:0%
+open area for whatever
+ 
+
+ align:start position:0%
+open area for whatever
+region, then with very high probability,
+
+ align:start position:0%
+region, then with very high probability,
+ 
+
+ align:start position:0%
+region, then with very high probability,
+I'm going to I'm going to pick a point
+
+ align:start position:0%
+I'm going to I'm going to pick a point
+ 
+
+ align:start position:0%
+I'm going to I'm going to pick a point
+that's inside this the biggest region,
+
+ align:start position:0%
+that's inside this the biggest region,
+ 
+
+ align:start position:0%
+that's inside this the biggest region,
+right? And the biggest regions in the
+
+ align:start position:0%
+right? And the biggest regions in the
+ 
+
+ align:start position:0%
+right? And the biggest regions in the
+space are the ones that have the highest
+
+ align:start position:0%
+space are the ones that have the highest
+ 
+
+ align:start position:0%
+space are the ones that have the highest
+probability of being chosen.
+
+ align:start position:0%
+probability of being chosen.
+ 
+
+ align:start position:0%
+probability of being chosen.
+So probabilistically this thing fills
+
+ align:start position:0%
+So probabilistically this thing fills
+ 
+
+ align:start position:0%
+So probabilistically this thing fills
+the biggest spaces the biggest open
+
+ align:start position:0%
+the biggest spaces the biggest open
+ 
+
+ align:start position:0%
+the biggest spaces the biggest open
+spaces in the uh in the search tree.
+
+ align:start position:0%
+spaces in the uh in the search tree.
+ 
+
+ align:start position:0%
+spaces in the uh in the search tree.
+Okay. Just by the virtue of of um of
+
+ align:start position:0%
+Okay. Just by the virtue of of um of
+ 
+
+ align:start position:0%
+Okay. Just by the virtue of of um of
+sampling
+
+ align:start position:0%
+sampling
+ 
+
+ align:start position:0%
+sampling
+uniformly. Okay. So you get these very
+
+ align:start position:0%
+uniformly. Okay. So you get these very
+ 
+
+ align:start position:0%
+uniformly. Okay. So you get these very
+very dense um fast uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees. Okay. Okay. And you can imagine
+
+ align:start position:0%
+trees. Okay. Okay. And you can imagine
+ 
+
+ align:start position:0%
+trees. Okay. Okay. And you can imagine
+if there's obstacles or something like
+
+ align:start position:0%
+if there's obstacles or something like
+ 
+
+ align:start position:0%
+if there's obstacles or something like
+that inside there, it's going to work
+
+ align:start position:0%
+that inside there, it's going to work
+ 
+
+ align:start position:0%
+that inside there, it's going to work
+its way just around the obstacles. Yeah.
+
+ align:start position:0%
+its way just around the obstacles. Yeah.
+ 
+
+ align:start position:0%
+its way just around the obstacles. Yeah.
+Does it slow down as you get more and
+
+ align:start position:0%
+Does it slow down as you get more and
+ 
+
+ align:start position:0%
+Does it slow down as you get more and
+more nodes in there? Good. So, so what
+
+ align:start position:0%
+more nodes in there? Good. So, so what
+ 
+
+ align:start position:0%
+more nodes in there? Good. So, so what
+is the computation that goes into it?
+
+ align:start position:0%
+is the computation that goes into it?
+ 
+
+ align:start position:0%
+is the computation that goes into it?
+What's the expensive part of the
+
+ align:start position:0%
+What's the expensive part of the
+ 
+
+ align:start position:0%
+What's the expensive part of the
+computation, would you guess?
+
+ align:start position:0%
+computation, would you guess?
+ 
+
+ align:start position:0%
+computation, would you guess?
+Finding nearest neighbor. Good. Right.
+
+ align:start position:0%
+Finding nearest neighbor. Good. Right.
+ 
+
+ align:start position:0%
+Finding nearest neighbor. Good. Right.
+So, um so yeah, it slows down with the
+
+ align:start position:0%
+So, um so yeah, it slows down with the
+ 
+
+ align:start position:0%
+So, um so yeah, it slows down with the
+nearest neighbor, but not as much as you
+
+ align:start position:0%
+nearest neighbor, but not as much as you
+ 
+
+ align:start position:0%
+nearest neighbor, but not as much as you
+expect. There's actually there's two
+
+ align:start position:0%
+expect. There's actually there's two
+ 
+
+ align:start position:0%
+expect. There's actually there's two
+expensive parts. Only one of the only
+
+ align:start position:0%
+expensive parts. Only one of the only
+ 
+
+ align:start position:0%
+expensive parts. Only one of the only
+the nearest neighbor one shows up here.
+
+ align:start position:0%
+the nearest neighbor one shows up here.
+ 
+
+ align:start position:0%
+the nearest neighbor one shows up here.
+The other one potentially is the
+
+ align:start position:0%
+The other one potentially is the
+ 
+
+ align:start position:0%
+The other one potentially is the
+collision checker and in some
+
+ align:start position:0%
+collision checker and in some
+ 
+
+ align:start position:0%
+collision checker and in some
+complicated systems checking if you're
+
+ align:start position:0%
+complicated systems checking if you're
+ 
+
+ align:start position:0%
+complicated systems checking if you're
+inside a collision in inside a region
+
+ align:start position:0%
+inside a collision in inside a region
+ 
+
+ align:start position:0%
+inside a collision in inside a region
+especially if you're a big robotic arm
+
+ align:start position:0%
+especially if you're a big robotic arm
+ 
+
+ align:start position:0%
+especially if you're a big robotic arm
+or something like that can be actually
+
+ align:start position:0%
+or something like that can be actually
+ 
+
+ align:start position:0%
+or something like that can be actually
+the dominant expensive thing right so um
+
+ align:start position:0%
+the dominant expensive thing right so um
+ 
+
+ align:start position:0%
+the dominant expensive thing right so um
+so these things in mat lab everything's
+
+ align:start position:0%
+so these things in mat lab everything's
+ 
+
+ align:start position:0%
+so these things in mat lab everything's
+vectorized it actually doesn't grow that
+
+ align:start position:0%
+vectorized it actually doesn't grow that
+ 
+
+ align:start position:0%
+vectorized it actually doesn't grow that
+badly with the number of nodes but
+
+ align:start position:0%
+badly with the number of nodes but
+ 
+
+ align:start position:0%
+badly with the number of nodes but
+certainly the the nearest neighbor
+
+ align:start position:0%
+certainly the the nearest neighbor
+ 
+
+ align:start position:0%
+certainly the the nearest neighbor
+calculation gets more and more expensive
+
+ align:start position:0%
+calculation gets more and more expensive
+ 
+
+ align:start position:0%
+calculation gets more and more expensive
+by default it's just checking every
+
+ align:start position:0%
+by default it's just checking every
+ 
+
+ align:start position:0%
+by default it's just checking every
+possible the distance between every it
+
+ align:start position:0%
+possible the distance between every it
+ 
+
+ align:start position:0%
+possible the distance between every it
+the new the sample point and every
+
+ align:start position:0%
+the new the sample point and every
+ 
+
+ align:start position:0%
+the new the sample point and every
+possible node could use like a KD. Yeah.
+
+ align:start position:0%
+possible node could use like a KD. Yeah.
+ 
+
+ align:start position:0%
+possible node could use like a KD. Yeah.
+Good. Yeah. So there there are different
+
+ align:start position:0%
+Good. Yeah. So there there are different
+ 
+
+ align:start position:0%
+Good. Yeah. So there there are different
+um some sort of structures that you can
+
+ align:start position:0%
+um some sort of structures that you can
+ 
+
+ align:start position:0%
+um some sort of structures that you can
+use to to make that look up more more
+
+ align:start position:0%
+use to to make that look up more more
+ 
+
+ align:start position:0%
+use to to make that look up more more
+efficient.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. So RTS have gone kind of come in
+
+ align:start position:0%
+Right. So RTS have gone kind of come in
+ 
+
+ align:start position:0%
+Right. So RTS have gone kind of come in
+and and and done things to robotics that
+
+ align:start position:0%
+and and and done things to robotics that
+ 
+
+ align:start position:0%
+and and and done things to robotics that
+uh people hadn't done before. So this is
+
+ align:start position:0%
+uh people hadn't done before. So this is
+ 
+
+ align:start position:0%
+uh people hadn't done before. So this is
+a two-dimensional example.
+
+ align:start position:0%
+a two-dimensional example.
+ 
+
+ align:start position:0%
+a two-dimensional example.
+Um, people would have said before I can
+
+ align:start position:0%
+Um, people would have said before I can
+ 
+
+ align:start position:0%
+Um, people would have said before I can
+do sort of motion planning effectively
+
+ align:start position:0%
+do sort of motion planning effectively
+ 
+
+ align:start position:0%
+do sort of motion planning effectively
+in maybe five or 10 dimensions, a little
+
+ align:start position:0%
+in maybe five or 10 dimensions, a little
+ 
+
+ align:start position:0%
+in maybe five or 10 dimensions, a little
+bit more than I could do with just DP,
+
+ align:start position:0%
+bit more than I could do with just DP,
+ 
+
+ align:start position:0%
+bit more than I could do with just DP,
+but but you know, not a lot more because
+
+ align:start position:0%
+but but you know, not a lot more because
+ 
+
+ align:start position:0%
+but but you know, not a lot more because
+I'm still doing these sort of random
+
+ align:start position:0%
+I'm still doing these sort of random
+ 
+
+ align:start position:0%
+I'm still doing these sort of random
+factorizations. Um, the guys that came
+
+ align:start position:0%
+factorizations. Um, the guys that came
+ 
+
+ align:start position:0%
+factorizations. Um, the guys that came
+out and started doing these RRTs, Laval
+
+ align:start position:0%
+out and started doing these RRTs, Laval
+ 
+
+ align:start position:0%
+out and started doing these RRTs, Laval
+being one of them, Cuffner being another
+
+ align:start position:0%
+being one of them, Cuffner being another
+ 
+
+ align:start position:0%
+being one of them, Cuffner being another
+one, started showing examples of robots
+
+ align:start position:0%
+one, started showing examples of robots
+ 
+
+ align:start position:0%
+one, started showing examples of robots
+with 32 degrees of freedom doing pretty
+
+ align:start position:0%
+with 32 degrees of freedom doing pretty
+ 
+
+ align:start position:0%
+with 32 degrees of freedom doing pretty
+complicated plans.
+
+ align:start position:0%
+complicated plans.
+ 
+
+ align:start position:0%
+complicated plans.
+Um, see if I have that the Cuffner video
+
+ align:start position:0%
+Um, see if I have that the Cuffner video
+ 
+
+ align:start position:0%
+Um, see if I have that the Cuffner video
+there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, it's a animated GIF. So I should,
+
+ align:start position:0%
+Yeah, it's a animated GIF. So I should,
+ 
+
+ align:start position:0%
+Yeah, it's a animated GIF. So I should,
+you know, this is a this is H7 at the
+
+ align:start position:0%
+you know, this is a this is H7 at the
+ 
+
+ align:start position:0%
+you know, this is a this is H7 at the
+time. This was the um University of
+
+ align:start position:0%
+time. This was the um University of
+ 
+
+ align:start position:0%
+time. This was the um University of
+Tokyo humanoid entry before everybody
+
+ align:start position:0%
+Tokyo humanoid entry before everybody
+ 
+
+ align:start position:0%
+Tokyo humanoid entry before everybody
+started giving out ASMO. beforehand to
+
+ align:start position:0%
+started giving out ASMO. beforehand to
+ 
+
+ align:start position:0%
+started giving out ASMO. beforehand to
+start giving out asmos. This is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and it's doing things like taking
+
+ align:start position:0%
+um and it's doing things like taking
+ 
+
+ align:start position:0%
+um and it's doing things like taking
+that 32 degree of freedom robot, finding
+
+ align:start position:0%
+that 32 degree of freedom robot, finding
+ 
+
+ align:start position:0%
+that 32 degree of freedom robot, finding
+a plan to have it bend down and pick up
+
+ align:start position:0%
+a plan to have it bend down and pick up
+ 
+
+ align:start position:0%
+a plan to have it bend down and pick up
+a flashlight under the table, right? And
+
+ align:start position:0%
+a flashlight under the table, right? And
+ 
+
+ align:start position:0%
+a flashlight under the table, right? And
+that sort of that sort of shocked
+
+ align:start position:0%
+that sort of that sort of shocked
+ 
+
+ align:start position:0%
+that sort of that sort of shocked
+people. Okay. Now, people have gone off
+
+ align:start position:0%
+people. Okay. Now, people have gone off
+ 
+
+ align:start position:0%
+people. Okay. Now, people have gone off
+and used RTS to do things like protein
+
+ align:start position:0%
+and used RTS to do things like protein
+ 
+
+ align:start position:0%
+and used RTS to do things like protein
+folding. It's a pretty is a pretty hot
+
+ align:start position:0%
+folding. It's a pretty is a pretty hot
+ 
+
+ align:start position:0%
+folding. It's a pretty is a pretty hot
+topic in the motion planning community
+
+ align:start position:0%
+topic in the motion planning community
+ 
+
+ align:start position:0%
+topic in the motion planning community
+and these other very high complexity
+
+ align:start position:0%
+and these other very high complexity
+ 
+
+ align:start position:0%
+and these other very high complexity
+geometric algorithms, geometric planning
+
+ align:start position:0%
+geometric algorithms, geometric planning
+ 
+
+ align:start position:0%
+geometric algorithms, geometric planning
+problems that people just hadn't done
+
+ align:start position:0%
+problems that people just hadn't done
+ 
+
+ align:start position:0%
+problems that people just hadn't done
+before. Okay. But even this guy, even
+
+ align:start position:0%
+before. Okay. But even this guy, even
+ 
+
+ align:start position:0%
+before. Okay. But even this guy, even
+though it's a it's a robot, um his feet
+
+ align:start position:0%
+though it's a it's a robot, um his feet
+ 
+
+ align:start position:0%
+though it's a it's a robot, um his feet
+are flat on the ground. Yeah. And
+
+ align:start position:0%
+are flat on the ground. Yeah. And
+ 
+
+ align:start position:0%
+are flat on the ground. Yeah. And
+they're still just assuming that you can
+
+ align:start position:0%
+they're still just assuming that you can
+ 
+
+ align:start position:0%
+they're still just assuming that you can
+search in position space and then find
+
+ align:start position:0%
+search in position space and then find
+ 
+
+ align:start position:0%
+search in position space and then find
+some controller that'll stabilize it. So
+
+ align:start position:0%
+some controller that'll stabilize it. So
+ 
+
+ align:start position:0%
+some controller that'll stabilize it. So
+they're not doing the underactuated um
+
+ align:start position:0%
+they're not doing the underactuated um
+ 
+
+ align:start position:0%
+they're not doing the underactuated um
+planning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example. All right. So I wouldn't be
+
+ align:start position:0%
+example. All right. So I wouldn't be
+ 
+
+ align:start position:0%
+example. All right. So I wouldn't be
+talking about it if I didn't think it
+
+ align:start position:0%
+talking about it if I didn't think it
+ 
+
+ align:start position:0%
+talking about it if I didn't think it
+was relevant for underactuated planning.
+
+ align:start position:0%
+was relevant for underactuated planning.
+ 
+
+ align:start position:0%
+was relevant for underactuated planning.
+So let's show you the
+
+ align:start position:0%
+So let's show you the
+ 
+
+ align:start position:0%
+So let's show you the
+um the basic story
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here. What happens if we do it on a
+
+ align:start position:0%
+here. What happens if we do it on a
+ 
+
+ align:start position:0%
+here. What happens if we do it on a
+simple pendulum?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There we go. So you see I'm plotting
+
+ align:start position:0%
+There we go. So you see I'm plotting
+ 
+
+ align:start position:0%
+There we go. So you see I'm plotting
+only uh every 30 nodes or something like
+
+ align:start position:0%
+only uh every 30 nodes or something like
+ 
+
+ align:start position:0%
+only uh every 30 nodes or something like
+that. I pick a point at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+random. I start growing the tree.
+
+ align:start position:0%
+random. I start growing the tree.
+ 
+
+ align:start position:0%
+random. I start growing the tree.
+The way I grow the tree now is I don't
+
+ align:start position:0%
+The way I grow the tree now is I don't
+ 
+
+ align:start position:0%
+The way I grow the tree now is I don't
+go all the way towards the goal because
+
+ align:start position:0%
+go all the way towards the goal because
+ 
+
+ align:start position:0%
+go all the way towards the goal because
+I can't necessarily go all the way
+
+ align:start position:0%
+I can't necessarily go all the way
+ 
+
+ align:start position:0%
+I can't necessarily go all the way
+towards the goal. I just take a step in
+
+ align:start position:0%
+towards the goal. I just take a step in
+ 
+
+ align:start position:0%
+towards the goal. I just take a step in
+the direction of the
+
+ align:start position:0%
+the direction of the
+ 
+
+ align:start position:0%
+the direction of the
+goal. How do I take a step in the
+
+ align:start position:0%
+goal. How do I take a step in the
+ 
+
+ align:start position:0%
+goal. How do I take a step in the
+direction of the goal? I just try five
+
+ align:start position:0%
+direction of the goal? I just try five
+ 
+
+ align:start position:0%
+direction of the goal? I just try five
+random actions, let's say, and pick the
+
+ align:start position:0%
+random actions, let's say, and pick the
+ 
+
+ align:start position:0%
+random actions, let's say, and pick the
+one that got closest to the goal. So, if
+
+ align:start position:0%
+one that got closest to the goal. So, if
+ 
+
+ align:start position:0%
+one that got closest to the goal. So, if
+you look closely, every time it expands
+
+ align:start position:0%
+you look closely, every time it expands
+ 
+
+ align:start position:0%
+you look closely, every time it expands
+a node, you'll see a bunch of different
+
+ align:start position:0%
+a node, you'll see a bunch of different
+ 
+
+ align:start position:0%
+a node, you'll see a bunch of different
+arrows coming out and it picked out it
+
+ align:start position:0%
+arrows coming out and it picked out it
+ 
+
+ align:start position:0%
+arrows coming out and it picked out it
+picked the one that got closest to that
+
+ align:start position:0%
+picked the one that got closest to that
+ 
+
+ align:start position:0%
+picked the one that got closest to that
+s random sample point. Okay? And it's
+
+ align:start position:0%
+s random sample point. Okay? And it's
+ 
+
+ align:start position:0%
+s random sample point. Okay? And it's
+still just using the uklidian distance
+
+ align:start position:0%
+still just using the uklidian distance
+ 
+
+ align:start position:0%
+still just using the uklidian distance
+to try to um find its find the closest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neighbor. This one's not I think I I
+
+ align:start position:0%
+neighbor. This one's not I think I I
+ 
+
+ align:start position:0%
+neighbor. This one's not I think I I
+didn't wasn't careful about doing the
+
+ align:start position:0%
+didn't wasn't careful about doing the
+ 
+
+ align:start position:0%
+didn't wasn't careful about doing the
+terminal condition, but I want you to to
+
+ align:start position:0%
+terminal condition, but I want you to to
+ 
+
+ align:start position:0%
+terminal condition, but I want you to to
+see what the most important thing about
+
+ align:start position:0%
+see what the most important thing about
+ 
+
+ align:start position:0%
+see what the most important thing about
+this is. What do you see in that
+
+ align:start position:0%
+this is. What do you see in that
+ 
+
+ align:start position:0%
+this is. What do you see in that
+plot besides a mess as it gets adding
+
+ align:start position:0%
+plot besides a mess as it gets adding
+ 
+
+ align:start position:0%
+plot besides a mess as it gets adding
+more and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more? What I see is I see the
+
+ align:start position:0%
+more? What I see is I see the
+ 
+
+ align:start position:0%
+more? What I see is I see the
+fundamental structure of the pendulum.
+
+ align:start position:0%
+fundamental structure of the pendulum.
+ 
+
+ align:start position:0%
+fundamental structure of the pendulum.
+Yeah. I see these spiral trajectories,
+
+ align:start position:0%
+Yeah. I see these spiral trajectories,
+ 
+
+ align:start position:0%
+Yeah. I see these spiral trajectories,
+right? It's amazing to me
+
+ align:start position:0%
+right? It's amazing to me
+ 
+
+ align:start position:0%
+right? It's amazing to me
+that trivial random randomized
+
+ align:start position:0%
+that trivial random randomized
+ 
+
+ align:start position:0%
+that trivial random randomized
+algorithms like this can probe the basic
+
+ align:start position:0%
+algorithms like this can probe the basic
+ 
+
+ align:start position:0%
+algorithms like this can probe the basic
+dynamics of my underactuated system.
+
+ align:start position:0%
+dynamics of my underactuated system.
+ 
+
+ align:start position:0%
+dynamics of my underactuated system.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So if you
+
+ align:start position:0%
+Right? So if you
+ 
+
+ align:start position:0%
+Right? So if you
+see the algorithm is
+
+ align:start position:0%
+see the algorithm is
+ 
+
+ align:start position:0%
+see the algorithm is
+now very simple, right? So I pick a
+
+ align:start position:0%
+now very simple, right? So I pick a
+ 
+
+ align:start position:0%
+now very simple, right? So I pick a
+point at random. That's actually a good
+
+ align:start position:0%
+point at random. That's actually a good
+ 
+
+ align:start position:0%
+point at random. That's actually a good
+example I just happened upon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? Pick a point at random. The blue,
+
+ align:start position:0%
+Right? Pick a point at random. The blue,
+ 
+
+ align:start position:0%
+Right? Pick a point at random. The blue,
+the red is my random sample point. The
+
+ align:start position:0%
+the red is my random sample point. The
+ 
+
+ align:start position:0%
+the red is my random sample point. The
+blue is the closest point in the tree in
+
+ align:start position:0%
+blue is the closest point in the tree in
+ 
+
+ align:start position:0%
+blue is the closest point in the tree in
+the uklidian sense. it happens to be a
+
+ align:start position:0%
+the uklidian sense. it happens to be a
+ 
+
+ align:start position:0%
+the uklidian sense. it happens to be a
+horrible choice for the closest point uh
+
+ align:start position:0%
+horrible choice for the closest point uh
+ 
+
+ align:start position:0%
+horrible choice for the closest point uh
+on the tree in the dynamic sense because
+
+ align:start position:0%
+on the tree in the dynamic sense because
+ 
+
+ align:start position:0%
+on the tree in the dynamic sense because
+I know in state space my dynamics can
+
+ align:start position:0%
+I know in state space my dynamics can
+ 
+
+ align:start position:0%
+I know in state space my dynamics can
+only go that way, right? So really uh
+
+ align:start position:0%
+only go that way, right? So really uh
+ 
+
+ align:start position:0%
+only go that way, right? So really uh
+I'd like to have picked up a point back
+
+ align:start position:0%
+I'd like to have picked up a point back
+ 
+
+ align:start position:0%
+I'd like to have picked up a point back
+there that was farther in uklidian
+
+ align:start position:0%
+there that was farther in uklidian
+ 
+
+ align:start position:0%
+there that was farther in uklidian
+distance but closer sort of in dynamic
+
+ align:start position:0%
+distance but closer sort of in dynamic
+ 
+
+ align:start position:0%
+distance but closer sort of in dynamic
+distance and I'll actually talk more
+
+ align:start position:0%
+distance and I'll actually talk more
+ 
+
+ align:start position:0%
+distance and I'll actually talk more
+next lecture about how you could do
+
+ align:start position:0%
+next lecture about how you could do
+ 
+
+ align:start position:0%
+next lecture about how you could do
+that. Okay. But from that node, I try 10
+
+ align:start position:0%
+that. Okay. But from that node, I try 10
+ 
+
+ align:start position:0%
+that. Okay. But from that node, I try 10
+different actions, see where it would
+
+ align:start position:0%
+different actions, see where it would
+ 
+
+ align:start position:0%
+different actions, see where it would
+have taken me, and pick the one that
+
+ align:start position:0%
+have taken me, and pick the one that
+ 
+
+ align:start position:0%
+have taken me, and pick the one that
+ended up closest in uklidian distance,
+
+ align:start position:0%
+ended up closest in uklidian distance,
+ 
+
+ align:start position:0%
+ended up closest in uklidian distance,
+which happens to have been the one that
+
+ align:start position:0%
+which happens to have been the one that
+ 
+
+ align:start position:0%
+which happens to have been the one that
+happened
+
+ align:start position:0%
+happened
+ 
+
+ align:start position:0%
+happened
+horizontally. That's enough to let this
+
+ align:start position:0%
+horizontally. That's enough to let this
+ 
+
+ align:start position:0%
+horizontally. That's enough to let this
+thing just sort of spread itself out
+
+ align:start position:0%
+thing just sort of spread itself out
+ 
+
+ align:start position:0%
+thing just sort of spread itself out
+into the world like a like a disease or
+
+ align:start position:0%
+into the world like a like a disease or
+ 
+
+ align:start position:0%
+into the world like a like a disease or
+something, right? Going just covering
+
+ align:start position:0%
+something, right? Going just covering
+ 
+
+ align:start position:0%
+something, right? Going just covering
+the the space a and probing the dynamics
+
+ align:start position:0%
+the the space a and probing the dynamics
+ 
+
+ align:start position:0%
+the the space a and probing the dynamics
+of the system. And you wait until you
+
+ align:start position:0%
+of the system. And you wait until you
+ 
+
+ align:start position:0%
+of the system. And you wait until you
+get close to the
+
+ align:start position:0%
+get close to the
+ 
+
+ align:start position:0%
+get close to the
+goal. Mhm.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RTS are a very very powerful way now to
+
+ align:start position:0%
+RTS are a very very powerful way now to
+ 
+
+ align:start position:0%
+RTS are a very very powerful way now to
+to start um trying to find reasonable
+
+ align:start position:0%
+to start um trying to find reasonable
+ 
+
+ align:start position:0%
+to start um trying to find reasonable
+plans uh on a
+
+ align:start position:0%
+plans uh on a
+ 
+
+ align:start position:0%
+plans uh on a
+robot. That's the vanilla RT algorithm.
+
+ align:start position:0%
+robot. That's the vanilla RT algorithm.
+ 
+
+ align:start position:0%
+robot. That's the vanilla RT algorithm.
+There's a lot of ways you can quickly
+
+ align:start position:0%
+There's a lot of ways you can quickly
+ 
+
+ align:start position:0%
+There's a lot of ways you can quickly
+improve them. Okay? And actually any of
+
+ align:start position:0%
+improve them. Okay? And actually any of
+ 
+
+ align:start position:0%
+improve them. Okay? And actually any of
+the the graph-based search algorithms
+
+ align:start position:0%
+the the graph-based search algorithms
+ 
+
+ align:start position:0%
+the the graph-based search algorithms
+um do this.
+
+ align:start position:0%
+um do this.
+ 
+
+ align:start position:0%
+um do this.
+So if I wanted to to u do some simple
+
+ align:start position:0%
+So if I wanted to to u do some simple
+ 
+
+ align:start position:0%
+So if I wanted to to u do some simple
+things to try to speed up that
+
+ align:start position:0%
+things to try to speed up that
+ 
+
+ align:start position:0%
+things to try to speed up that
+algorithm, what might you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggest? The only real reason it felt
+
+ align:start position:0%
+suggest? The only real reason it felt
+ 
+
+ align:start position:0%
+suggest? The only real reason it felt
+there's a couple reasons why it felt
+
+ align:start position:0%
+there's a couple reasons why it felt
+ 
+
+ align:start position:0%
+there's a couple reasons why it felt
+inefficient. One of them is because it's
+
+ align:start position:0%
+inefficient. One of them is because it's
+ 
+
+ align:start position:0%
+inefficient. One of them is because it's
+it's not doing a very nice job of of
+
+ align:start position:0%
+it's not doing a very nice job of of
+ 
+
+ align:start position:0%
+it's not doing a very nice job of of
+chasing these sort of intermediate
+
+ align:start position:0%
+chasing these sort of intermediate
+ 
+
+ align:start position:0%
+chasing these sort of intermediate
+goals, right? It's like like that
+
+ align:start position:0%
+goals, right? It's like like that
+ 
+
+ align:start position:0%
+goals, right? It's like like that
+example showed. The other thing is it it
+
+ align:start position:0%
+example showed. The other thing is it it
+ 
+
+ align:start position:0%
+example showed. The other thing is it it
+seems like it's not really making any
+
+ align:start position:0%
+seems like it's not really making any
+ 
+
+ align:start position:0%
+seems like it's not really making any
+effort to go towards the goal.
+
+ align:start position:0%
+effort to go towards the goal.
+ 
+
+ align:start position:0%
+effort to go towards the goal.
+Okay, so there's a handful of huristics
+
+ align:start position:0%
+Okay, so there's a handful of huristics
+ 
+
+ align:start position:0%
+Okay, so there's a handful of huristics
+that people use to make these things
+
+ align:start position:0%
+that people use to make these things
+ 
+
+ align:start position:0%
+that people use to make these things
+tick. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, one of them is a goal bias.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. If um the way the go I mean
+
+ align:start position:0%
+Okay. If um the way the go I mean
+ 
+
+ align:start position:0%
+Okay. If um the way the go I mean
+there's lots of ways to implement it.
+
+ align:start position:0%
+there's lots of ways to implement it.
+ 
+
+ align:start position:0%
+there's lots of ways to implement it.
+The standard way to implement it is um
+
+ align:start position:0%
+The standard way to implement it is um
+ 
+
+ align:start position:0%
+The standard way to implement it is um
+with let's say
+
+ align:start position:0%
+with let's say
+ 
+
+ align:start position:0%
+with let's say
+um probability
+
+ align:start position:0%
+um probability
+ 
+
+ align:start position:0%
+um probability
+um uh 0.5 or something like that 0.05 5.
+
+ align:start position:0%
+um uh 0.5 or something like that 0.05 5.
+ 
+
+ align:start position:0%
+um uh 0.5 or something like that 0.05 5.
+Um, choose my random sample to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Otherwise, my random sample is just the
+
+ align:start position:0%
+Otherwise, my random sample is just the
+ 
+
+ align:start position:0%
+Otherwise, my random sample is just the
+uniform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution. Okay.
+
+ align:start position:0%
+distribution. Okay.
+ 
+
+ align:start position:0%
+distribution. Okay.
+That would certainly encourage the
+
+ align:start position:0%
+That would certainly encourage the
+ 
+
+ align:start position:0%
+That would certainly encourage the
+system to find its way to the goal a lot
+
+ align:start position:0%
+system to find its way to the goal a lot
+ 
+
+ align:start position:0%
+system to find its way to the goal a lot
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+efficiently. What's
+
+ align:start position:0%
+efficiently. What's
+ 
+
+ align:start position:0%
+efficiently. What's
+another what's another possible way to
+
+ align:start position:0%
+another what's another possible way to
+ 
+
+ align:start position:0%
+another what's another possible way to
+speed this up?
+
+ align:start position:0%
+speed this up?
+ 
+
+ align:start position:0%
+speed this up?
+Birectional. Yeah. In fact, all of the
+
+ align:start position:0%
+Birectional. Yeah. In fact, all of the
+ 
+
+ align:start position:0%
+Birectional. Yeah. In fact, all of the
+search techniques, the breadth first,
+
+ align:start position:0%
+search techniques, the breadth first,
+ 
+
+ align:start position:0%
+search techniques, the breadth first,
+depth first, AAR on discrete graph
+
+ align:start position:0%
+depth first, AAR on discrete graph
+ 
+
+ align:start position:0%
+depth first, AAR on discrete graph
+searches, a lot of time, one of the
+
+ align:start position:0%
+searches, a lot of time, one of the
+ 
+
+ align:start position:0%
+searches, a lot of time, one of the
+standard things people do is they'll do
+
+ align:start position:0%
+standard things people do is they'll do
+ 
+
+ align:start position:0%
+standard things people do is they'll do
+a backwards search, right?
+
+ align:start position:0%
+a backwards search, right?
+ 
+
+ align:start position:0%
+a backwards search, right?
+start while you're growing out from the
+
+ align:start position:0%
+start while you're growing out from the
+ 
+
+ align:start position:0%
+start while you're growing out from the
+start to the towards the goal, might as
+
+ align:start position:0%
+start to the towards the goal, might as
+ 
+
+ align:start position:0%
+start to the towards the goal, might as
+well start from the goal and go
+
+ align:start position:0%
+well start from the goal and go
+ 
+
+ align:start position:0%
+well start from the goal and go
+backwards. Um, it feels a lot less like
+
+ align:start position:0%
+backwards. Um, it feels a lot less like
+ 
+
+ align:start position:0%
+backwards. Um, it feels a lot less like
+this. The problem with this is it feels
+
+ align:start position:0%
+this. The problem with this is it feels
+ 
+
+ align:start position:0%
+this. The problem with this is it feels
+like you're trying to find a needle in a
+
+ align:start position:0%
+like you're trying to find a needle in a
+ 
+
+ align:start position:0%
+like you're trying to find a needle in a
+hay stack, right? If you can grow a tree
+
+ align:start position:0%
+hay stack, right? If you can grow a tree
+ 
+
+ align:start position:0%
+hay stack, right? If you can grow a tree
+in both directions, then at least you
+
+ align:start position:0%
+in both directions, then at least you
+ 
+
+ align:start position:0%
+in both directions, then at least you
+got a lot of needles to look for. Yeah.
+
+ align:start position:0%
+got a lot of needles to look for. Yeah.
+ 
+
+ align:start position:0%
+got a lot of needles to look for. Yeah.
+And you just wait till the the trees
+
+ align:start position:0%
+And you just wait till the the trees
+ 
+
+ align:start position:0%
+And you just wait till the the trees
+come um fairly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close and even backward search sometimes
+
+ align:start position:0%
+close and even backward search sometimes
+ 
+
+ align:start position:0%
+close and even backward search sometimes
+by itself can be faster. It depends on
+
+ align:start position:0%
+by itself can be faster. It depends on
+ 
+
+ align:start position:0%
+by itself can be faster. It depends on
+the system.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Is that because like you if your goal is
+
+ align:start position:0%
+Is that because like you if your goal is
+ 
+
+ align:start position:0%
+Is that because like you if your goal is
+an unstable point the backward search is
+
+ align:start position:0%
+an unstable point the backward search is
+ 
+
+ align:start position:0%
+an unstable point the backward search is
+more likely to find that like
+
+ align:start position:0%
+more likely to find that like
+ 
+
+ align:start position:0%
+more likely to find that like
+intuitively what why sometimes a
+
+ align:start position:0%
+intuitively what why sometimes a
+ 
+
+ align:start position:0%
+intuitively what why sometimes a
+backwards search would look work better
+
+ align:start position:0%
+backwards search would look work better
+ 
+
+ align:start position:0%
+backwards search would look work better
+in cases like under
+
+ align:start position:0%
+in cases like under
+ 
+
+ align:start position:0%
+in cases like under
+it's a really good question because it
+
+ align:start position:0%
+it's a really good question because it
+ 
+
+ align:start position:0%
+it's a really good question because it
+you might have trouble going to some
+
+ align:start position:0%
+you might have trouble going to some
+ 
+
+ align:start position:0%
+you might have trouble going to some
+type of fix points but the backward
+
+ align:start position:0%
+type of fix points but the backward
+ 
+
+ align:start position:0%
+type of fix points but the backward
+search already starts you off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there. I I will I won't I won't put my
+
+ align:start position:0%
+there. I I will I won't I won't put my
+ 
+
+ align:start position:0%
+there. I I will I won't I won't put my
+weight behind it, but that that sounds
+
+ align:start position:0%
+weight behind it, but that that sounds
+ 
+
+ align:start position:0%
+weight behind it, but that that sounds
+like a pretty good explanation. Yeah,
+
+ align:start position:0%
+like a pretty good explanation. Yeah,
+ 
+
+ align:start position:0%
+like a pretty good explanation. Yeah,
+in practice we always do birectional
+
+ align:start position:0%
+in practice we always do birectional
+ 
+
+ align:start position:0%
+in practice we always do birectional
+trees, right? You always want to do
+
+ align:start position:0%
+trees, right? You always want to do
+ 
+
+ align:start position:0%
+trees, right? You always want to do
+both, right? Yeah. You'd never just go
+
+ align:start position:0%
+both, right? Yeah. You'd never just go
+ 
+
+ align:start position:0%
+both, right? Yeah. You'd never just go
+back. Yeah. But certainly in the
+
+ align:start position:0%
+back. Yeah. But certainly in the
+ 
+
+ align:start position:0%
+back. Yeah. But certainly in the
+kinematic case, you could definitely
+
+ align:start position:0%
+kinematic case, you could definitely
+ 
+
+ align:start position:0%
+kinematic case, you could definitely
+exam imagine cases where the backwards
+
+ align:start position:0%
+exam imagine cases where the backwards
+ 
+
+ align:start position:0%
+exam imagine cases where the backwards
+would could be faster. Let's say it's
+
+ align:start position:0%
+would could be faster. Let's say it's
+ 
+
+ align:start position:0%
+would could be faster. Let's say it's
+it's hiding in some little uh island,
+
+ align:start position:0%
+it's hiding in some little uh island,
+ 
+
+ align:start position:0%
+it's hiding in some little uh island,
+right? And you just want to get out and
+
+ align:start position:0%
+right? And you just want to get out and
+ 
+
+ align:start position:0%
+right? And you just want to get out and
+that much easier than finding your way
+
+ align:start position:0%
+that much easier than finding your way
+ 
+
+ align:start position:0%
+that much easier than finding your way
+into the island, let's say. Um the the
+
+ align:start position:0%
+into the island, let's say. Um the the
+ 
+
+ align:start position:0%
+into the island, let's say. Um the the
+instability. So certainly we've we've
+
+ align:start position:0%
+instability. So certainly we've we've
+ 
+
+ align:start position:0%
+instability. So certainly we've we've
+noticed um uh sensitivities to growing
+
+ align:start position:0%
+noticed um uh sensitivities to growing
+ 
+
+ align:start position:0%
+noticed um uh sensitivities to growing
+RTS around stable on very unstable fixed
+
+ align:start position:0%
+RTS around stable on very unstable fixed
+ 
+
+ align:start position:0%
+RTS around stable on very unstable fixed
+points. Um and it might be it might be
+
+ align:start position:0%
+points. Um and it might be it might be
+ 
+
+ align:start position:0%
+points. Um and it might be it might be
+exactly what you said. It might be.
+
+ align:start position:0%
+exactly what you said. It might be.
+ 
+
+ align:start position:0%
+exactly what you said. It might be.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Um is the uklidian norm the best metric
+
+ align:start position:0%
+Um is the uklidian norm the best metric
+ 
+
+ align:start position:0%
+Um is the uklidian norm the best metric
+for this? Good. The uklidian norm is a
+
+ align:start position:0%
+for this? Good. The uklidian norm is a
+ 
+
+ align:start position:0%
+for this? Good. The uklidian norm is a
+horrible metric for this. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do you think would be a better
+
+ align:start position:0%
+What do you think would be a better
+ 
+
+ align:start position:0%
+What do you think would be a better
+metric?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Awesome. So, energy is a good
+
+ align:start position:0%
+Awesome. So, energy is a good
+ 
+
+ align:start position:0%
+Awesome. So, energy is a good
+candidate. In fact, I think depending on
+
+ align:start position:0%
+candidate. In fact, I think depending on
+ 
+
+ align:start position:0%
+candidate. In fact, I think depending on
+what we put on the problem set, we might
+
+ align:start position:0%
+what we put on the problem set, we might
+ 
+
+ align:start position:0%
+what we put on the problem set, we might
+ask you to to try an energy metric. um
+
+ align:start position:0%
+ask you to to try an energy metric. um
+ 
+
+ align:start position:0%
+ask you to to try an energy metric. um
+to do it. Um so almost everybody says
+
+ align:start position:0%
+to do it. Um so almost everybody says
+ 
+
+ align:start position:0%
+to do it. Um so almost everybody says
+this would work better with a better
+
+ align:start position:0%
+this would work better with a better
+ 
+
+ align:start position:0%
+this would work better with a better
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+metric and almost nobody can tell you a
+
+ align:start position:0%
+metric and almost nobody can tell you a
+ 
+
+ align:start position:0%
+metric and almost nobody can tell you a
+better distance metric for these kind of
+
+ align:start position:0%
+better distance metric for these kind of
+ 
+
+ align:start position:0%
+better distance metric for these kind of
+systems.
+
+ align:start position:0%
+systems.
+ 
+
+ align:start position:0%
+systems.
+Okay. So
+
+ align:start position:0%
+Okay. So
+ 
+
+ align:start position:0%
+Okay. So
+uh we actually have a couple ideas uh
+
+ align:start position:0%
+uh we actually have a couple ideas uh
+ 
+
+ align:start position:0%
+uh we actually have a couple ideas uh
+that we've been working on in in lab.
+
+ align:start position:0%
+that we've been working on in in lab.
+ 
+
+ align:start position:0%
+that we've been working on in in lab.
+Elena has been uh been working on some
+
+ align:start position:0%
+Elena has been uh been working on some
+ 
+
+ align:start position:0%
+Elena has been uh been working on some
+LQR based distance metrics for instance.
+
+ align:start position:0%
+LQR based distance metrics for instance.
+ 
+
+ align:start position:0%
+LQR based distance metrics for instance.
+Okay. So what you what did you just say?
+
+ align:start position:0%
+Okay. So what you what did you just say?
+ 
+
+ align:start position:0%
+Okay. So what you what did you just say?
+You said um time to arrival. How would
+
+ align:start position:0%
+You said um time to arrival. How would
+ 
+
+ align:start position:0%
+You said um time to arrival. How would
+you compute a time to arrival? Yes. Do
+
+ align:start position:0%
+you compute a time to arrival? Yes. Do
+ 
+
+ align:start position:0%
+you compute a time to arrival? Yes. Do
+you like a million time, right?
+
+ align:start position:0%
+you like a million time, right?
+ 
+
+ align:start position:0%
+you like a million time, right?
+Exactly.
+
+ align:start position:0%
+Exactly.
+ 
+
+ align:start position:0%
+Exactly.
+So, you just guessed the one that's
+
+ align:start position:0%
+So, you just guessed the one that's
+ 
+
+ align:start position:0%
+So, you just guessed the one that's
+that's one of my favorites right now,
+
+ align:start position:0%
+that's one of my favorites right now,
+ 
+
+ align:start position:0%
+that's one of my favorites right now,
+right? switches. So, um, one idea
+
+ align:start position:0%
+right? switches. So, um, one idea
+ 
+
+ align:start position:0%
+right? switches. So, um, one idea
+here, not fully proven yet, but it's
+
+ align:start position:0%
+here, not fully proven yet, but it's
+ 
+
+ align:start position:0%
+here, not fully proven yet, but it's
+still in the oven here, is that
+
+ align:start position:0%
+still in the oven here, is that
+ 
+
+ align:start position:0%
+still in the oven here, is that
+um, that every time I pick a random
+
+ align:start position:0%
+um, that every time I pick a random
+ 
+
+ align:start position:0%
+um, that every time I pick a random
+sample point, yeah, I'll linearize a
+
+ align:start position:0%
+sample point, yeah, I'll linearize a
+ 
+
+ align:start position:0%
+sample point, yeah, I'll linearize a
+system around that point, let's say
+
+ align:start position:0%
+system around that point, let's say
+ 
+
+ align:start position:0%
+system around that point, let's say
+that's a cartoon of a linearization,
+
+ align:start position:0%
+that's a cartoon of a linearization,
+ 
+
+ align:start position:0%
+that's a cartoon of a linearization,
+yeah, compute a uh, LQR stabilizer
+
+ align:start position:0%
+yeah, compute a uh, LQR stabilizer
+ 
+
+ align:start position:0%
+yeah, compute a uh, LQR stabilizer
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+this and then use the value function for
+
+ align:start position:0%
+this and then use the value function for
+ 
+
+ align:start position:0%
+this and then use the value function for
+a minimum time problem. Yeah. So, so
+
+ align:start position:0%
+a minimum time problem. Yeah. So, so
+ 
+
+ align:start position:0%
+a minimum time problem. Yeah. So, so
+comput a
+
+ align:start position:0%
+comput a
+ 
+
+ align:start position:0%
+comput a
+um min time LQR
+
+ align:start position:0%
+um min time LQR
+ 
+
+ align:start position:0%
+um min time LQR
+actually around this point and then use
+
+ align:start position:0%
+actually around this point and then use
+ 
+
+ align:start position:0%
+actually around this point and then use
+the value function as a distance
+
+ align:start position:0%
+the value function as a distance
+ 
+
+ align:start position:0%
+the value function as a distance
+metric. The
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Okay. So, I like that idea a lot.
+
+ align:start position:0%
+the Okay. So, I like that idea a lot.
+ 
+
+ align:start position:0%
+the Okay. So, I like that idea a lot.
+Yeah. There's a couple subtleties that
+
+ align:start position:0%
+Yeah. There's a couple subtleties that
+ 
+
+ align:start position:0%
+Yeah. There's a couple subtleties that
+go into it. So when you pick a random
+
+ align:start position:0%
+go into it. So when you pick a random
+ 
+
+ align:start position:0%
+go into it. So when you pick a random
+point in state space, if it's got a
+
+ align:start position:0%
+point in state space, if it's got a
+ 
+
+ align:start position:0%
+point in state space, if it's got a
+velocity or you know most points you
+
+ align:start position:0%
+velocity or you know most points you
+ 
+
+ align:start position:0%
+velocity or you know most points you
+pick randomly in state space are not
+
+ align:start position:0%
+pick randomly in state space are not
+ 
+
+ align:start position:0%
+pick randomly in state space are not
+stabilizable. So you can't do an
+
+ align:start position:0%
+stabilizable. So you can't do an
+ 
+
+ align:start position:0%
+stabilizable. So you can't do an
+infinite horizon minimum time LQR. You
+
+ align:start position:0%
+infinite horizon minimum time LQR. You
+ 
+
+ align:start position:0%
+infinite horizon minimum time LQR. You
+have to do a finite horizon and then
+
+ align:start position:0%
+have to do a finite horizon and then
+ 
+
+ align:start position:0%
+have to do a finite horizon and then
+potentially search over horizon times.
+
+ align:start position:0%
+potentially search over horizon times.
+ 
+
+ align:start position:0%
+potentially search over horizon times.
+But you can do that actually pretty
+
+ align:start position:0%
+But you can do that actually pretty
+ 
+
+ align:start position:0%
+But you can do that actually pretty
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+efficiently. The other issue about it is
+
+ align:start position:0%
+efficiently. The other issue about it is
+ 
+
+ align:start position:0%
+efficiently. The other issue about it is
+that it's actually not a proper distance
+
+ align:start position:0%
+that it's actually not a proper distance
+ 
+
+ align:start position:0%
+that it's actually not a proper distance
+metric.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, why is it not a proper distance
+
+ align:start position:0%
+Um, why is it not a proper distance
+ 
+
+ align:start position:0%
+Um, why is it not a proper distance
+metric? Anybody? It doesn't follow the
+
+ align:start position:0%
+metric? Anybody? It doesn't follow the
+ 
+
+ align:start position:0%
+metric? Anybody? It doesn't follow the
+So, I think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it probably doesn't follow the triangle
+
+ align:start position:0%
+it probably doesn't follow the triangle
+ 
+
+ align:start position:0%
+it probably doesn't follow the triangle
+inequality. It certainly does. It
+
+ align:start position:0%
+inequality. It certainly does. It
+ 
+
+ align:start position:0%
+inequality. It certainly does. It
+doesn't even have symmetry, right?
+
+ align:start position:0%
+doesn't even have symmetry, right?
+ 
+
+ align:start position:0%
+doesn't even have symmetry, right?
+If I were to linearize around this point
+
+ align:start position:0%
+If I were to linearize around this point
+ 
+
+ align:start position:0%
+If I were to linearize around this point
+and comput its distance, linearize
+
+ align:start position:0%
+and comput its distance, linearize
+ 
+
+ align:start position:0%
+and comput its distance, linearize
+around this point, there's absolutely no
+
+ align:start position:0%
+around this point, there's absolutely no
+ 
+
+ align:start position:0%
+around this point, there's absolutely no
+guarantees that it would be the same.
+
+ align:start position:0%
+guarantees that it would be the same.
+ 
+
+ align:start position:0%
+guarantees that it would be the same.
+Um, but I don't care about that
+
+ align:start position:0%
+Um, but I don't care about that
+ 
+
+ align:start position:0%
+Um, but I don't care about that
+actually. I just have to put it in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paper. Yeah. As long as it works,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Okay.
+
+ align:start position:0%
+right? Okay.
+ 
+
+ align:start position:0%
+right? Okay.
+Um, it's also more expensive a little
+
+ align:start position:0%
+Um, it's also more expensive a little
+ 
+
+ align:start position:0%
+Um, it's also more expensive a little
+bit, but it can make a dramatic
+
+ align:start position:0%
+bit, but it can make a dramatic
+ 
+
+ align:start position:0%
+bit, but it can make a dramatic
+improvement in in the way it uh um it it
+
+ align:start position:0%
+improvement in in the way it uh um it it
+ 
+
+ align:start position:0%
+improvement in in the way it uh um it it
+spreads. There's another idea. I was
+
+ align:start position:0%
+spreads. There's another idea. I was
+ 
+
+ align:start position:0%
+spreads. There's another idea. I was
+actually planning to not to talk about
+
+ align:start position:0%
+actually planning to not to talk about
+ 
+
+ align:start position:0%
+actually planning to not to talk about
+some of the the more subtle ideas um uh
+
+ align:start position:0%
+some of the the more subtle ideas um uh
+ 
+
+ align:start position:0%
+some of the the more subtle ideas um uh
+next time, but why since we're at it,
+
+ align:start position:0%
+next time, but why since we're at it,
+ 
+
+ align:start position:0%
+next time, but why since we're at it,
+the other way to do it is to change um
+
+ align:start position:0%
+the other way to do it is to change um
+ 
+
+ align:start position:0%
+the other way to do it is to change um
+the sampling distribution.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, Alec Skull in our group has got um a
+
+ align:start position:0%
+So, Alec Skull in our group has got um a
+ 
+
+ align:start position:0%
+So, Alec Skull in our group has got um a
+very clever way to uh to grow these
+
+ align:start position:0%
+very clever way to uh to grow these
+ 
+
+ align:start position:0%
+very clever way to uh to grow these
+trees.
+
+ align:start position:0%
+trees.
+ 
+
+ align:start position:0%
+trees.
+Um where it uses um a sampling metric
+
+ align:start position:0%
+Um where it uses um a sampling metric
+ 
+
+ align:start position:0%
+Um where it uses um a sampling metric
+that doesn't try to to go where it can't
+
+ align:start position:0%
+that doesn't try to to go where it can't
+ 
+
+ align:start position:0%
+that doesn't try to to go where it can't
+go. Let me just see if I can say that
+
+ align:start position:0%
+go. Let me just see if I can say that
+ 
+
+ align:start position:0%
+go. Let me just see if I can say that
+more carefully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since I told DARPA about it 3 days ago.
+
+ align:start position:0%
+since I told DARPA about it 3 days ago.
+ 
+
+ align:start position:0%
+since I told DARPA about it 3 days ago.
+So, might as well show you the picture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, um, this is Alex's, uh,
+
+ align:start position:0%
+Okay. So, um, this is Alex's, uh,
+ 
+
+ align:start position:0%
+Okay. So, um, this is Alex's, uh,
+algorithm for,
+
+ align:start position:0%
+algorithm for,
+ 
+
+ align:start position:0%
+algorithm for,
+uh, being more clever at expanding. Uh,
+
+ align:start position:0%
+uh, being more clever at expanding. Uh,
+ 
+
+ align:start position:0%
+uh, being more clever at expanding. Uh,
+he changes the bias to the point where
+
+ align:start position:0%
+he changes the bias to the point where
+ 
+
+ align:start position:0%
+he changes the bias to the point where
+this is the tree we just saw, right?
+
+ align:start position:0%
+this is the tree we just saw, right?
+ 
+
+ align:start position:0%
+this is the tree we just saw, right?
+Basically, right? Um, and his new tree
+
+ align:start position:0%
+Basically, right? Um, and his new tree
+ 
+
+ align:start position:0%
+Basically, right? Um, and his new tree
+looks like that. So, that looks pretty
+
+ align:start position:0%
+looks like that. So, that looks pretty
+ 
+
+ align:start position:0%
+looks like that. So, that looks pretty
+compelling. Yeah. How did he do it?
+
+ align:start position:0%
+compelling. Yeah. How did he do it?
+ 
+
+ align:start position:0%
+compelling. Yeah. How did he do it?
+Um, he does this thing. Um, he calls
+
+ align:start position:0%
+Um, he does this thing. Um, he calls
+ 
+
+ align:start position:0%
+Um, he does this thing. Um, he calls
+reachability guided RRTs. Okay. Every
+
+ align:start position:0%
+reachability guided RRTs. Okay. Every
+ 
+
+ align:start position:0%
+reachability guided RRTs. Okay. Every
+time he uh expands a node, he also
+
+ align:start position:0%
+time he uh expands a node, he also
+ 
+
+ align:start position:0%
+time he uh expands a node, he also
+expands what what would happen if I had
+
+ align:start position:0%
+expands what what would happen if I had
+ 
+
+ align:start position:0%
+expands what what would happen if I had
+applied maximum torque and minimum
+
+ align:start position:0%
+applied maximum torque and minimum
+ 
+
+ align:start position:0%
+applied maximum torque and minimum
+torque. Okay, so he expands a couple
+
+ align:start position:0%
+torque. Okay, so he expands a couple
+ 
+
+ align:start position:0%
+torque. Okay, so he expands a couple
+nodes that that represent a cone of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+feasibility. The algorithm turns out to
+
+ align:start position:0%
+feasibility. The algorithm turns out to
+ 
+
+ align:start position:0%
+feasibility. The algorithm turns out to
+be trivial. Okay, so so now I take my
+
+ align:start position:0%
+be trivial. Okay, so so now I take my
+ 
+
+ align:start position:0%
+be trivial. Okay, so so now I take my
+uklidian distance metric or whatever it
+
+ align:start position:0%
+uklidian distance metric or whatever it
+ 
+
+ align:start position:0%
+uklidian distance metric or whatever it
+is, um pick my random sample point. If
+
+ align:start position:0%
+is, um pick my random sample point. If
+ 
+
+ align:start position:0%
+is, um pick my random sample point. If
+the closest point is one of these
+
+ align:start position:0%
+the closest point is one of these
+ 
+
+ align:start position:0%
+the closest point is one of these
+boundary feasible things, then that
+
+ align:start position:0%
+boundary feasible things, then that
+ 
+
+ align:start position:0%
+boundary feasible things, then that
+means there's room to grow the
+
+ align:start position:0%
+means there's room to grow the
+ 
+
+ align:start position:0%
+means there's room to grow the
+tree. If the closest point, however, is
+
+ align:start position:0%
+tree. If the closest point, however, is
+ 
+
+ align:start position:0%
+tree. If the closest point, however, is
+one of the nodes on my actual graph,
+
+ align:start position:0%
+one of the nodes on my actual graph,
+ 
+
+ align:start position:0%
+one of the nodes on my actual graph,
+that means I'm already there's I'm not
+
+ align:start position:0%
+that means I'm already there's I'm not
+ 
+
+ align:start position:0%
+that means I'm already there's I'm not
+feasible. I said that quickly, but long
+
+ align:start position:0%
+feasible. I said that quickly, but long
+ 
+
+ align:start position:0%
+feasible. I said that quickly, but long
+story short, there's a trivial check
+
+ align:start position:0%
+story short, there's a trivial check
+ 
+
+ align:start position:0%
+story short, there's a trivial check
+here which changes your s effectively
+
+ align:start position:0%
+here which changes your s effectively
+ 
+
+ align:start position:0%
+here which changes your s effectively
+changes your sampling distribution just
+
+ align:start position:0%
+changes your sampling distribution just
+ 
+
+ align:start position:0%
+changes your sampling distribution just
+by saying sample a point. If the closest
+
+ align:start position:0%
+by saying sample a point. If the closest
+ 
+
+ align:start position:0%
+by saying sample a point. If the closest
+point on there is not one of my boundary
+
+ align:start position:0%
+point on there is not one of my boundary
+ 
+
+ align:start position:0%
+point on there is not one of my boundary
+regions, but one of my normal tree
+
+ align:start position:0%
+regions, but one of my normal tree
+ 
+
+ align:start position:0%
+regions, but one of my normal tree
+elements, then I know I can't grow
+
+ align:start position:0%
+elements, then I know I can't grow
+ 
+
+ align:start position:0%
+elements, then I know I can't grow
+there. Okay? And if I get that, I just
+
+ align:start position:0%
+there. Okay? And if I get that, I just
+ 
+
+ align:start position:0%
+there. Okay? And if I get that, I just
+throw that point away. Pick another
+
+ align:start position:0%
+throw that point away. Pick another
+ 
+
+ align:start position:0%
+throw that point away. Pick another
+point. What that does is it effectively
+
+ align:start position:0%
+point. What that does is it effectively
+ 
+
+ align:start position:0%
+point. What that does is it effectively
+changes the sampling distribution to be
+
+ align:start position:0%
+changes the sampling distribution to be
+ 
+
+ align:start position:0%
+changes the sampling distribution to be
+the green region. it just throws out all
+
+ align:start position:0%
+the green region. it just throws out all
+ 
+
+ align:start position:0%
+the green region. it just throws out all
+these unnecessary points that you can't
+
+ align:start position:0%
+these unnecessary points that you can't
+ 
+
+ align:start position:0%
+these unnecessary points that you can't
+get towards and changes your sampling
+
+ align:start position:0%
+get towards and changes your sampling
+ 
+
+ align:start position:0%
+get towards and changes your sampling
+distribution. So, it's only trying to
+
+ align:start position:0%
+distribution. So, it's only trying to
+ 
+
+ align:start position:0%
+distribution. So, it's only trying to
+grow in places that it can actually go
+
+ align:start position:0%
+grow in places that it can actually go
+ 
+
+ align:start position:0%
+grow in places that it can actually go
+to where the trees got a a chance of
+
+ align:start position:0%
+to where the trees got a a chance of
+ 
+
+ align:start position:0%
+to where the trees got a a chance of
+growing towards. Okay. So, I think the
+
+ align:start position:0%
+growing towards. Okay. So, I think the
+ 
+
+ align:start position:0%
+growing towards. Okay. So, I think the
+the the world is still sort of small
+
+ align:start position:0%
+the the world is still sort of small
+ 
+
+ align:start position:0%
+the the world is still sort of small
+enough that people are still finding
+
+ align:start position:0%
+enough that people are still finding
+ 
+
+ align:start position:0%
+enough that people are still finding
+pretty clever little tricks to the RTS
+
+ align:start position:0%
+pretty clever little tricks to the RTS
+ 
+
+ align:start position:0%
+pretty clever little tricks to the RTS
+that make them grow a lot better in
+
+ align:start position:0%
+that make them grow a lot better in
+ 
+
+ align:start position:0%
+that make them grow a lot better in
+constrained systems like
+
+ align:start position:0%
+constrained systems like
+ 
+
+ align:start position:0%
+constrained systems like
+this. Okay. Okay, so that's happens to
+
+ align:start position:0%
+this. Okay. Okay, so that's happens to
+ 
+
+ align:start position:0%
+this. Okay. Okay, so that's happens to
+be I think a very good one for um for
+
+ align:start position:0%
+be I think a very good one for um for
+ 
+
+ align:start position:0%
+be I think a very good one for um for
+our kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems. But it also points out what
+
+ align:start position:0%
+problems. But it also points out what
+ 
+
+ align:start position:0%
+problems. But it also points out what
+RTS are bad at,
+
+ align:start position:0%
+RTS are bad at,
+ 
+
+ align:start position:0%
+RTS are bad at,
+right? So
+
+ align:start position:0%
+right? So
+ 
+
+ align:start position:0%
+right? So
+um so what kind of problems would you
+
+ align:start position:0%
+um so what kind of problems would you
+ 
+
+ align:start position:0%
+um so what kind of problems would you
+expect an RT to work on and what would
+
+ align:start position:0%
+expect an RT to work on and what would
+ 
+
+ align:start position:0%
+expect an RT to work on and what would
+you not expect an RT to work on?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The classic case of something you
+
+ align:start position:0%
+The classic case of something you
+ 
+
+ align:start position:0%
+The classic case of something you
+shouldn't expect an RT to do very well
+
+ align:start position:0%
+shouldn't expect an RT to do very well
+ 
+
+ align:start position:0%
+shouldn't expect an RT to do very well
+on is something uh that looks like this.
+
+ align:start position:0%
+on is something uh that looks like this.
+ 
+
+ align:start position:0%
+on is something uh that looks like this.
+Let's say uh X start is over here, X
+
+ align:start position:0%
+Let's say uh X start is over here, X
+ 
+
+ align:start position:0%
+Let's say uh X start is over here, X
+goal is over
+
+ align:start position:0%
+goal is over
+ 
+
+ align:start position:0%
+goal is over
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and my obstacles look like
+
+ align:start position:0%
+here and my obstacles look like
+ 
+
+ align:start position:0%
+here and my obstacles look like
+this. Right?
+
+ align:start position:0%
+this. Right?
+ 
+
+ align:start position:0%
+this. Right?
+In general, I think
+
+ align:start position:0%
+In general, I think
+ 
+
+ align:start position:0%
+In general, I think
+uh it's fair to say RRTs don't
+
+ align:start position:0%
+uh it's fair to say RRTs don't
+ 
+
+ align:start position:0%
+uh it's fair to say RRTs don't
+like tunnels and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tubes, right? What's going to happen if
+
+ align:start position:0%
+tubes, right? What's going to happen if
+ 
+
+ align:start position:0%
+tubes, right? What's going to happen if
+I run my RRT on this sort of a system?
+
+ align:start position:0%
+I run my RRT on this sort of a system?
+ 
+
+ align:start position:0%
+I run my RRT on this sort of a system?
+All right, so I I pick, you know, I got
+
+ align:start position:0%
+All right, so I I pick, you know, I got
+ 
+
+ align:start position:0%
+All right, so I I pick, you know, I got
+my tree here. Pick a point here. Fine.
+
+ align:start position:0%
+my tree here. Pick a point here. Fine.
+ 
+
+ align:start position:0%
+my tree here. Pick a point here. Fine.
+Pick a point here. I'll quickly cover
+
+ align:start position:0%
+Pick a point here. I'll quickly cover
+ 
+
+ align:start position:0%
+Pick a point here. I'll quickly cover
+this area. Pick a point here. I throw it
+
+ align:start position:0%
+this area. Pick a point here. I throw it
+ 
+
+ align:start position:0%
+this area. Pick a point here. I throw it
+away. Pick a point through here. Throw
+
+ align:start position:0%
+away. Pick a point through here. Throw
+ 
+
+ align:start position:0%
+away. Pick a point through here. Throw
+it away. I pick a point here. Can't get
+
+ align:start position:0%
+it away. I pick a point here. Can't get
+ 
+
+ align:start position:0%
+it away. I pick a point here. Can't get
+to it. Doesn't do me any good. You know,
+
+ align:start position:0%
+to it. Doesn't do me any good. You know,
+ 
+
+ align:start position:0%
+to it. Doesn't do me any good. You know,
+after my after a very long time, maybe I
+
+ align:start position:0%
+after my after a very long time, maybe I
+ 
+
+ align:start position:0%
+after my after a very long time, maybe I
+luck out and I pick a point here, right?
+
+ align:start position:0%
+luck out and I pick a point here, right?
+ 
+
+ align:start position:0%
+luck out and I pick a point here, right?
+Okay. But then I have to wait and pick a
+
+ align:start position:0%
+Okay. But then I have to wait and pick a
+ 
+
+ align:start position:0%
+Okay. But then I have to wait and pick a
+point. Yeah, I pick a point here. I
+
+ align:start position:0%
+point. Yeah, I pick a point here. I
+ 
+
+ align:start position:0%
+point. Yeah, I pick a point here. I
+can't get to it. Just throw out, you
+
+ align:start position:0%
+can't get to it. Just throw out, you
+ 
+
+ align:start position:0%
+can't get to it. Just throw out, you
+know, I'm just completely hopeless. If
+
+ align:start position:0%
+know, I'm just completely hopeless. If
+ 
+
+ align:start position:0%
+know, I'm just completely hopeless. If
+it's in two dimensional space, then you
+
+ align:start position:0%
+it's in two dimensional space, then you
+ 
+
+ align:start position:0%
+it's in two dimensional space, then you
+can imagine sort of getting lucky enough
+
+ align:start position:0%
+can imagine sort of getting lucky enough
+ 
+
+ align:start position:0%
+can imagine sort of getting lucky enough
+or or designing a sampling distribution
+
+ align:start position:0%
+or or designing a sampling distribution
+ 
+
+ align:start position:0%
+or or designing a sampling distribution
+that does this. But let's say it's in
+
+ align:start position:0%
+that does this. But let's say it's in
+ 
+
+ align:start position:0%
+that does this. But let's say it's in
+some you know 14dimensional space that
+
+ align:start position:0%
+some you know 14dimensional space that
+ 
+
+ align:start position:0%
+some you know 14dimensional space that
+you have no idea where the tunnels the
+
+ align:start position:0%
+you have no idea where the tunnels the
+ 
+
+ align:start position:0%
+you have no idea where the tunnels the
+tubes are. Um there are some problems
+
+ align:start position:0%
+tubes are. Um there are some problems
+ 
+
+ align:start position:0%
+tubes are. Um there are some problems
+where RTS just choke. So in general when
+
+ align:start position:0%
+where RTS just choke. So in general when
+ 
+
+ align:start position:0%
+where RTS just choke. So in general when
+your space of solutions feasible
+
+ align:start position:0%
+your space of solutions feasible
+ 
+
+ align:start position:0%
+your space of solutions feasible
+solutions is small is
+
+ align:start position:0%
+solutions is small is
+ 
+
+ align:start position:0%
+solutions is small is
+that fair to say because like this is a
+
+ align:start position:0%
+that fair to say because like this is a
+ 
+
+ align:start position:0%
+that fair to say because like this is a
+small very small set of your total
+
+ align:start position:0%
+small very small set of your total
+ 
+
+ align:start position:0%
+small very small set of your total
+space.
+
+ align:start position:0%
+space.
+ 
+
+ align:start position:0%
+space.
+It's a little hard to say that, right?
+
+ align:start position:0%
+It's a little hard to say that, right?
+ 
+
+ align:start position:0%
+It's a little hard to say that, right?
+Because I I
+
+ align:start position:0%
+Because I I
+ 
+
+ align:start position:0%
+Because I I
+mean lots of trajectories work, right?
+
+ align:start position:0%
+mean lots of trajectories work, right?
+ 
+
+ align:start position:0%
+mean lots of trajectories work, right?
+They this one works, you know, right?
+
+ align:start position:0%
+They this one works, you know, right?
+ 
+
+ align:start position:0%
+They this one works, you know, right?
+This works, you know, but I think when
+
+ align:start position:0%
+This works, you know, but I think when
+ 
+
+ align:start position:0%
+This works, you know, but I think when
+there's narrow passages, that's when it
+
+ align:start position:0%
+there's narrow passages, that's when it
+ 
+
+ align:start position:0%
+there's narrow passages, that's when it
+really I think that's a a more clear way
+
+ align:start position:0%
+really I think that's a a more clear way
+ 
+
+ align:start position:0%
+really I think that's a a more clear way
+to say it when it chokes.
+
+ align:start position:0%
+to say it when it chokes.
+ 
+
+ align:start position:0%
+to say it when it chokes.
+And so when you say chokes, I mean it's,
+
+ align:start position:0%
+And so when you say chokes, I mean it's,
+ 
+
+ align:start position:0%
+And so when you say chokes, I mean it's,
+you know, as time goes to infinity,
+
+ align:start position:0%
+you know, as time goes to infinity,
+ 
+
+ align:start position:0%
+you know, as time goes to infinity,
+it'll finally find it. It is actually
+
+ align:start position:0%
+it'll finally find it. It is actually
+ 
+
+ align:start position:0%
+it'll finally find it. It is actually
+Santa. Yes. Okay. Good.
+
+ align:start position:0%
+Santa. Yes. Okay. Good.
+ 
+
+ align:start position:0%
+Santa. Yes. Okay. Good.
+So these algorithms um mostly what you
+
+ align:start position:0%
+So these algorithms um mostly what you
+ 
+
+ align:start position:0%
+So these algorithms um mostly what you
+look for in a planning algorithm is
+
+ align:start position:0%
+look for in a planning algorithm is
+ 
+
+ align:start position:0%
+look for in a planning algorithm is
+completeness. You want to know that as
+
+ align:start position:0%
+completeness. You want to know that as
+ 
+
+ align:start position:0%
+completeness. You want to know that as
+you as you expand all the nodes, you're
+
+ align:start position:0%
+you as you expand all the nodes, you're
+ 
+
+ align:start position:0%
+you as you expand all the nodes, you're
+eventually if there's a path to the
+
+ align:start position:0%
+eventually if there's a path to the
+ 
+
+ align:start position:0%
+eventually if there's a path to the
+goal, you'll find the path to the goal.
+
+ align:start position:0%
+goal, you'll find the path to the goal.
+ 
+
+ align:start position:0%
+goal, you'll find the path to the goal.
+And even if there's not a path, it'll
+
+ align:start position:0%
+And even if there's not a path, it'll
+ 
+
+ align:start position:0%
+And even if there's not a path, it'll
+tell you there's no path, right? RRTs
+
+ align:start position:0%
+tell you there's no path, right? RRTs
+ 
+
+ align:start position:0%
+tell you there's no path, right? RRTs
+have probabilistic completeness
+
+ align:start position:0%
+have probabilistic completeness
+ 
+
+ align:start position:0%
+have probabilistic completeness
+guarantees. They say if you expand
+
+ align:start position:0%
+guarantees. They say if you expand
+ 
+
+ align:start position:0%
+guarantees. They say if you expand
+enough nodes, then you'll with the
+
+ align:start position:0%
+enough nodes, then you'll with the
+ 
+
+ align:start position:0%
+enough nodes, then you'll with the
+probability one, if there is a path,
+
+ align:start position:0%
+probability one, if there is a path,
+ 
+
+ align:start position:0%
+probability one, if there is a path,
+you'll find it. Probabil probabilistic
+
+ align:start position:0%
+you'll find it. Probabil probabilistic
+ 
+
+ align:start position:0%
+you'll find it. Probabil probabilistic
+completeness doesn't do as much for
+
+ align:start position:0%
+completeness doesn't do as much for
+ 
+
+ align:start position:0%
+completeness doesn't do as much for
+disproving the existence of a path,
+
+ align:start position:0%
+disproving the existence of a path,
+ 
+
+ align:start position:0%
+disproving the existence of a path,
+right? it would take a very long time to
+
+ align:start position:0%
+right? it would take a very long time to
+ 
+
+ align:start position:0%
+right? it would take a very long time to
+disprove it.
+
+ align:start position:0%
+disprove it.
+ 
+
+ align:start position:0%
+disprove it.
+Um, but probabilistically these things
+
+ align:start position:0%
+Um, but probabilistically these things
+ 
+
+ align:start position:0%
+Um, but probabilistically these things
+will find a path to the goal if it
+
+ align:start position:0%
+will find a path to the goal if it
+ 
+
+ align:start position:0%
+will find a path to the goal if it
+exists. That's good. That's that's
+
+ align:start position:0%
+exists. That's good. That's that's
+ 
+
+ align:start position:0%
+exists. That's good. That's that's
+um maybe that'll make you sleep better
+
+ align:start position:0%
+um maybe that'll make you sleep better
+ 
+
+ align:start position:0%
+um maybe that'll make you sleep better
+at night. But if you wait if you have to
+
+ align:start position:0%
+at night. But if you wait if you have to
+ 
+
+ align:start position:0%
+at night. But if you wait if you have to
+wait, you know, for something to be
+
+ align:start position:0%
+wait, you know, for something to be
+ 
+
+ align:start position:0%
+wait, you know, for something to be
+probabistically complete, um it's not
+
+ align:start position:0%
+probabistically complete, um it's not
+ 
+
+ align:start position:0%
+probabistically complete, um it's not
+going to be useful. The reason these
+
+ align:start position:0%
+going to be useful. The reason these
+ 
+
+ align:start position:0%
+going to be useful. The reason these
+things are used like crazy is that in
+
+ align:start position:0%
+things are used like crazy is that in
+ 
+
+ align:start position:0%
+things are used like crazy is that in
+practice it they're very fast. They can
+
+ align:start position:0%
+practice it they're very fast. They can
+ 
+
+ align:start position:0%
+practice it they're very fast. They can
+be very very fast for finding good
+
+ align:start position:0%
+be very very fast for finding good
+ 
+
+ align:start position:0%
+be very very fast for finding good
+solutions.
+
+ align:start position:0%
+solutions.
+ 
+
+ align:start position:0%
+solutions.
+So really, I mean, the the uh the Grand
+
+ align:start position:0%
+So really, I mean, the the uh the Grand
+ 
+
+ align:start position:0%
+So really, I mean, the the uh the Grand
+Challenge vehicles using RTS all the
+
+ align:start position:0%
+Challenge vehicles using RTS all the
+ 
+
+ align:start position:0%
+Challenge vehicles using RTS all the
+time to consider possible future paths
+
+ align:start position:0%
+time to consider possible future paths
+ 
+
+ align:start position:0%
+time to consider possible future paths
+um along the street, trying to avoid
+
+ align:start position:0%
+um along the street, trying to avoid
+ 
+
+ align:start position:0%
+um along the street, trying to avoid
+obstacles. It's doing it fast enough um
+
+ align:start position:0%
+obstacles. It's doing it fast enough um
+ 
+
+ align:start position:0%
+obstacles. It's doing it fast enough um
+in sort of in a receding horizon way.
+
+ align:start position:0%
+in sort of in a receding horizon way.
+ 
+
+ align:start position:0%
+in sort of in a receding horizon way.
+It's always planning, you know, a minute
+
+ align:start position:0%
+It's always planning, you know, a minute
+ 
+
+ align:start position:0%
+It's always planning, you know, a minute
+ahead. I'm not sure exactly what the
+
+ align:start position:0%
+ahead. I'm not sure exactly what the
+ 
+
+ align:start position:0%
+ahead. I'm not sure exactly what the
+window is, you know, in driving time and
+
+ align:start position:0%
+window is, you know, in driving time and
+ 
+
+ align:start position:0%
+window is, you know, in driving time and
+it's doing it every DT roughly
+
+ align:start position:0%
+it's doing it every DT roughly
+ 
+
+ align:start position:0%
+it's doing it every DT roughly
+recomputing its plan, right? Right?
+
+ align:start position:0%
+recomputing its plan, right? Right?
+ 
+
+ align:start position:0%
+recomputing its plan, right? Right?
+These things can be really really fast
+
+ align:start position:0%
+These things can be really really fast
+ 
+
+ align:start position:0%
+These things can be really really fast
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice to some extent. Um the dynamic
+
+ align:start position:0%
+practice to some extent. Um the dynamic
+ 
+
+ align:start position:0%
+practice to some extent. Um the dynamic
+constraints which we're talking about on
+
+ align:start position:0%
+constraints which we're talking about on
+ 
+
+ align:start position:0%
+constraints which we're talking about on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+pendulum are exactly this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem,
+
+ align:start position:0%
+problem,
+ 
+
+ align:start position:0%
+problem,
+right? Because the because the pendulum
+
+ align:start position:0%
+right? Because the because the pendulum
+ 
+
+ align:start position:0%
+right? Because the because the pendulum
+like we said it's it's coming here. We
+
+ align:start position:0%
+like we said it's it's coming here. We
+ 
+
+ align:start position:0%
+like we said it's it's coming here. We
+know what the the phase portrait of the
+
+ align:start position:0%
+know what the the phase portrait of the
+ 
+
+ align:start position:0%
+know what the the phase portrait of the
+pendulum look like and we know that if
+
+ align:start position:0%
+pendulum look like and we know that if
+ 
+
+ align:start position:0%
+pendulum look like and we know that if
+we're torque limited there's only a
+
+ align:start position:0%
+we're torque limited there's only a
+ 
+
+ align:start position:0%
+we're torque limited there's only a
+handful of places we can go to some
+
+ align:start position:0%
+handful of places we can go to some
+ 
+
+ align:start position:0%
+handful of places we can go to some
+extent kodnamic
+
+ align:start position:0%
+extent kodnamic
+ 
+
+ align:start position:0%
+extent kodnamic
+constraints like this dynamics um can
+
+ align:start position:0%
+constraints like this dynamics um can
+ 
+
+ align:start position:0%
+constraints like this dynamics um can
+look exactly like
+
+ align:start position:0%
+look exactly like
+ 
+
+ align:start position:0%
+look exactly like
+this. So if you take your vanilla RT you
+
+ align:start position:0%
+this. So if you take your vanilla RT you
+ 
+
+ align:start position:0%
+this. So if you take your vanilla RT you
+saw how effectively it grew on the
+
+ align:start position:0%
+saw how effectively it grew on the
+ 
+
+ align:start position:0%
+saw how effectively it grew on the
+pendulum. It took a lot a lot of nodes
+
+ align:start position:0%
+pendulum. It took a lot a lot of nodes
+ 
+
+ align:start position:0%
+pendulum. It took a lot a lot of nodes
+to to find its way out. Um the hope is
+
+ align:start position:0%
+to to find its way out. Um the hope is
+ 
+
+ align:start position:0%
+to to find its way out. Um the hope is
+that we know enough about this sort of
+
+ align:start position:0%
+that we know enough about this sort of
+ 
+
+ align:start position:0%
+that we know enough about this sort of
+dynamical system from our some of our
+
+ align:start position:0%
+dynamical system from our some of our
+ 
+
+ align:start position:0%
+dynamical system from our some of our
+other tools like LQR to do a distance
+
+ align:start position:0%
+other tools like LQR to do a distance
+ 
+
+ align:start position:0%
+other tools like LQR to do a distance
+metric from tricks like this then we can
+
+ align:start position:0%
+metric from tricks like this then we can
+ 
+
+ align:start position:0%
+metric from tricks like this then we can
+that we're effectively guiding this
+
+ align:start position:0%
+that we're effectively guiding this
+ 
+
+ align:start position:0%
+that we're effectively guiding this
+thing down down the differential
+
+ align:start position:0%
+thing down down the differential
+ 
+
+ align:start position:0%
+thing down down the differential
+constraint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tubes. Has there been any work with
+
+ align:start position:0%
+tubes. Has there been any work with
+ 
+
+ align:start position:0%
+tubes. Has there been any work with
+relaxing the number? Like for example,
+
+ align:start position:0%
+relaxing the number? Like for example,
+ 
+
+ align:start position:0%
+relaxing the number? Like for example,
+if you have like 15 dimensional robot,
+
+ align:start position:0%
+if you have like 15 dimensional robot,
+ 
+
+ align:start position:0%
+if you have like 15 dimensional robot,
+you want to get to go position and you
+
+ align:start position:0%
+you want to get to go position and you
+ 
+
+ align:start position:0%
+you want to get to go position and you
+relax some of those dimensions and then
+
+ align:start position:0%
+relax some of those dimensions and then
+ 
+
+ align:start position:0%
+relax some of those dimensions and then
+use the rest of it, design a control in
+
+ align:start position:0%
+use the rest of it, design a control in
+ 
+
+ align:start position:0%
+use the rest of it, design a control in
+a very low dimensional state space and
+
+ align:start position:0%
+a very low dimensional state space and
+ 
+
+ align:start position:0%
+a very low dimensional state space and
+then use that as a heristic. Awesome.
+
+ align:start position:0%
+then use that as a heristic. Awesome.
+ 
+
+ align:start position:0%
+then use that as a heristic. Awesome.
+Um, yes. So uh so Alec also had tell you
+
+ align:start position:0%
+Um, yes. So uh so Alec also had tell you
+ 
+
+ align:start position:0%
+Um, yes. So uh so Alec also had tell you
+what my next
+
+ align:start position:0%
+what my next
+ 
+
+ align:start position:0%
+what my next
+slide right
+
+ align:start position:0%
+slide right
+ 
+
+ align:start position:0%
+slide right
+uh this is Alex's other thing about uh
+
+ align:start position:0%
+uh this is Alex's other thing about uh
+ 
+
+ align:start position:0%
+uh this is Alex's other thing about uh
+planning in a task space which is
+
+ align:start position:0%
+planning in a task space which is
+ 
+
+ align:start position:0%
+planning in a task space which is
+exactly what you said I think there's
+
+ align:start position:0%
+exactly what you said I think there's
+ 
+
+ align:start position:0%
+exactly what you said I think there's
+lots of ways to do it I think Alec found
+
+ align:start position:0%
+lots of ways to do it I think Alec found
+ 
+
+ align:start position:0%
+lots of ways to do it I think Alec found
+a really good way to do it um this is
+
+ align:start position:0%
+a really good way to do it um this is
+ 
+
+ align:start position:0%
+a really good way to do it um this is
+just an example of a um a fivelink
+
+ align:start position:0%
+just an example of a um a fivelink
+ 
+
+ align:start position:0%
+just an example of a um a fivelink
+robotic arm just in configuration space
+
+ align:start position:0%
+robotic arm just in configuration space
+ 
+
+ align:start position:0%
+robotic arm just in configuration space
+that had to find its its way from that
+
+ align:start position:0%
+that had to find its its way from that
+ 
+
+ align:start position:0%
+that had to find its its way from that
+endpoint effect to the the goal
+
+ align:start position:0%
+endpoint effect to the the goal
+ 
+
+ align:start position:0%
+endpoint effect to the the goal
+endpoint. So you see at the top that
+
+ align:start position:0%
+endpoint. So you see at the top that
+ 
+
+ align:start position:0%
+endpoint. So you see at the top that
+little green arm is the resulting
+
+ align:start position:0%
+little green arm is the resulting
+ 
+
+ align:start position:0%
+little green arm is the resulting
+configuration of the robot. The standard
+
+ align:start position:0%
+configuration of the robot. The standard
+ 
+
+ align:start position:0%
+configuration of the robot. The standard
+RT looked all over the place to try to
+
+ align:start position:0%
+RT looked all over the place to try to
+ 
+
+ align:start position:0%
+RT looked all over the place to try to
+find that solution. If you instead just
+
+ align:start position:0%
+find that solution. If you instead just
+ 
+
+ align:start position:0%
+find that solution. If you instead just
+you it's a little subtle how we had to
+
+ align:start position:0%
+you it's a little subtle how we had to
+ 
+
+ align:start position:0%
+you it's a little subtle how we had to
+do it. You had to basically change the
+
+ align:start position:0%
+do it. You had to basically change the
+ 
+
+ align:start position:0%
+do it. You had to basically change the
+Voronoi bias to live in the in the uh
+
+ align:start position:0%
+Voronoi bias to live in the in the uh
+ 
+
+ align:start position:0%
+Voronoi bias to live in the in the uh
+task space but still sample uniformly
+
+ align:start position:0%
+task space but still sample uniformly
+ 
+
+ align:start position:0%
+task space but still sample uniformly
+from the other space. So that's not
+
+ align:start position:0%
+from the other space. So that's not
+ 
+
+ align:start position:0%
+from the other space. So that's not
+enough to tell you how to do it but
+
+ align:start position:0%
+enough to tell you how to do it but
+ 
+
+ align:start position:0%
+enough to tell you how to do it but
+that's enough to tell you it's not
+
+ align:start position:0%
+that's enough to tell you it's not
+ 
+
+ align:start position:0%
+that's enough to tell you it's not
+completely trivial.
+
+ align:start position:0%
+completely trivial.
+ 
+
+ align:start position:0%
+completely trivial.
+Uh then then he found these really
+
+ align:start position:0%
+Uh then then he found these really
+ 
+
+ align:start position:0%
+Uh then then he found these really
+really elegant solutions um to to plan
+
+ align:start position:0%
+really elegant solutions um to to plan
+ 
+
+ align:start position:0%
+really elegant solutions um to to plan
+in task space. And the the results his
+
+ align:start position:0%
+in task space. And the the results his
+ 
+
+ align:start position:0%
+in task space. And the the results his
+his sort of killer plot is that this is
+
+ align:start position:0%
+his sort of killer plot is that this is
+ 
+
+ align:start position:0%
+his sort of killer plot is that this is
+the number of um number of links in the
+
+ align:start position:0%
+the number of um number of links in the
+ 
+
+ align:start position:0%
+the number of um number of links in the
+robotic arm, right? Versus the number of
+
+ align:start position:0%
+robotic arm, right? Versus the number of
+ 
+
+ align:start position:0%
+robotic arm, right? Versus the number of
+nodes it took to find the goal. And the
+
+ align:start position:0%
+nodes it took to find the goal. And the
+ 
+
+ align:start position:0%
+nodes it took to find the goal. And the
+standard
+
+ align:start position:0%
+standard
+ 
+
+ align:start position:0%
+standard
+RT went like that. And after, you know,
+
+ align:start position:0%
+RT went like that. And after, you know,
+ 
+
+ align:start position:0%
+RT went like that. And after, you know,
+10 links, it just was hopeless. And
+
+ align:start position:0%
+10 links, it just was hopeless. And
+ 
+
+ align:start position:0%
+10 links, it just was hopeless. And
+after uh with with n going to over a
+
+ align:start position:0%
+after uh with with n going to over a
+ 
+
+ align:start position:0%
+after uh with with n going to over a
+thousand dimensions he was just planning
+
+ align:start position:0%
+thousand dimensions he was just planning
+ 
+
+ align:start position:0%
+thousand dimensions he was just planning
+in constant time basically right so yeah
+
+ align:start position:0%
+in constant time basically right so yeah
+ 
+
+ align:start position:0%
+in constant time basically right so yeah
+there's there's structure in the
+
+ align:start position:0%
+there's there's structure in the
+ 
+
+ align:start position:0%
+there's there's structure in the
+problems right
+
+ align:start position:0%
+problems right
+ 
+
+ align:start position:0%
+problems right
+um we also have a using the partial
+
+ align:start position:0%
+um we also have a using the partial
+ 
+
+ align:start position:0%
+um we also have a using the partial
+feedback linearization task space have
+
+ align:start position:0%
+feedback linearization task space have
+ 
+
+ align:start position:0%
+feedback linearization task space have
+tried doing it in underactuated systems
+
+ align:start position:0%
+tried doing it in underactuated systems
+ 
+
+ align:start position:0%
+tried doing it in underactuated systems
+um uh and and that sort of works too.
+
+ align:start position:0%
+um uh and and that sort of works too.
+ 
+
+ align:start position:0%
+um uh and and that sort of works too.
+Yeah, but it's not the norm.
+
+ align:start position:0%
+Yeah, but it's not the norm.
+ 
+
+ align:start position:0%
+Yeah, but it's not the norm.
+Actually, it's not the accepted version
+
+ align:start position:0%
+Actually, it's not the accepted version
+ 
+
+ align:start position:0%
+Actually, it's not the accepted version
+of the algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yet. RTS are beautiful things, right?
+
+ align:start position:0%
+yet. RTS are beautiful things, right?
+ 
+
+ align:start position:0%
+yet. RTS are beautiful things, right?
+They just grow on out, find their way to
+
+ align:start position:0%
+They just grow on out, find their way to
+ 
+
+ align:start position:0%
+They just grow on out, find their way to
+the goal. What potential complaint is
+
+ align:start position:0%
+the goal. What potential complaint is
+ 
+
+ align:start position:0%
+the goal. What potential complaint is
+when you're when you're done with it,
+
+ align:start position:0%
+when you're when you're done with it,
+ 
+
+ align:start position:0%
+when you're when you're done with it,
+you've got this sort of choppy uh disc
+
+ align:start position:0%
+you've got this sort of choppy uh disc
+ 
+
+ align:start position:0%
+you've got this sort of choppy uh disc
+discretized path that gets you to the
+
+ align:start position:0%
+discretized path that gets you to the
+ 
+
+ align:start position:0%
+discretized path that gets you to the
+goal, but then just hand it to your
+
+ align:start position:0%
+goal, but then just hand it to your
+ 
+
+ align:start position:0%
+goal, but then just hand it to your
+trajectory optimizer as an initial
+
+ align:start position:0%
+trajectory optimizer as an initial
+ 
+
+ align:start position:0%
+trajectory optimizer as an initial
+condition and let it smooth it out.
+
+ align:start position:0%
+condition and let it smooth it out.
+ 
+
+ align:start position:0%
+condition and let it smooth it out.
+Right? still satisfying obstacle
+
+ align:start position:0%
+Right? still satisfying obstacle
+ 
+
+ align:start position:0%
+Right? still satisfying obstacle
+constraints, torque constraints. We know
+
+ align:start position:0%
+constraints, torque constraints. We know
+ 
+
+ align:start position:0%
+constraints, torque constraints. We know
+how to do that and smooth it out and
+
+ align:start position:0%
+how to do that and smooth it out and
+ 
+
+ align:start position:0%
+how to do that and smooth it out and
+you've got yourself a good trajectory
+
+ align:start position:0%
+you've got yourself a good trajectory
+ 
+
+ align:start position:0%
+you've got yourself a good trajectory
+that gets from the start to the goal.
+
+ align:start position:0%
+that gets from the start to the goal.
+ 
+
+ align:start position:0%
+that gets from the start to the goal.
+It's a beautiful thing. People didn't I
+
+ align:start position:0%
+It's a beautiful thing. People didn't I
+ 
+
+ align:start position:0%
+It's a beautiful thing. People didn't I
+mean I think I to the point where Tomas
+
+ align:start position:0%
+mean I think I to the point where Tomas
+ 
+
+ align:start position:0%
+mean I think I to the point where Tomas
+Lozano Perez, right, invented
+
+ align:start position:0%
+Lozano Perez, right, invented
+ 
+
+ align:start position:0%
+Lozano Perez, right, invented
+configuration space, did motion planning
+
+ align:start position:0%
+configuration space, did motion planning
+ 
+
+ align:start position:0%
+configuration space, did motion planning
+for however long. He actually stopped
+
+ align:start position:0%
+for however long. He actually stopped
+ 
+
+ align:start position:0%
+for however long. He actually stopped
+robotics, went off and did computational
+
+ align:start position:0%
+robotics, went off and did computational
+ 
+
+ align:start position:0%
+robotics, went off and did computational
+biology for a while. And he says he came
+
+ align:start position:0%
+biology for a while. And he says he came
+ 
+
+ align:start position:0%
+biology for a while. And he says he came
+back to robotics this a few years ago
+
+ align:start position:0%
+back to robotics this a few years ago
+ 
+
+ align:start position:0%
+back to robotics this a few years ago
+because these kind of algorithms made a
+
+ align:start position:0%
+because these kind of algorithms made a
+ 
+
+ align:start position:0%
+because these kind of algorithms made a
+difference to the point where it was
+
+ align:start position:0%
+difference to the point where it was
+ 
+
+ align:start position:0%
+difference to the point where it was
+worth doing motion planning or robotics
+
+ align:start position:0%
+worth doing motion planning or robotics
+ 
+
+ align:start position:0%
+worth doing motion planning or robotics
+again. Yeah. I don't know a a more
+
+ align:start position:0%
+again. Yeah. I don't know a a more
+ 
+
+ align:start position:0%
+again. Yeah. I don't know a a more
+dramatic thing to say than that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Okay. So next time I'm going to go
+
+ align:start position:0%
+Yeah. Okay. So next time I'm going to go
+ 
+
+ align:start position:0%
+Yeah. Okay. So next time I'm going to go
+a little bit um um more into the using
+
+ align:start position:0%
+a little bit um um more into the using
+ 
+
+ align:start position:0%
+a little bit um um more into the using
+these planning algorithms and and also
+
+ align:start position:0%
+these planning algorithms and and also
+ 
+
+ align:start position:0%
+these planning algorithms and and also
+feedback motion planning um applied to
+
+ align:start position:0%
+feedback motion planning um applied to
+ 
+
+ align:start position:0%
+feedback motion planning um applied to
+our model systems. But I I don't want to
+
+ align:start position:0%
+our model systems. But I I don't want to
+ 
+
+ align:start position:0%
+our model systems. But I I don't want to
+completely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satur I mean the idea that a randomized
+
+ align:start position:0%
+satur I mean the idea that a randomized
+ 
+
+ align:start position:0%
+satur I mean the idea that a randomized
+algorithm can do better than our our
+
+ align:start position:0%
+algorithm can do better than our our
+ 
+
+ align:start position:0%
+algorithm can do better than our our
+explicit algorithms. It's all these
+
+ align:start position:0%
+explicit algorithms. It's all these
+ 
+
+ align:start position:0%
+explicit algorithms. It's all these
+these funny things. There's classes on
+
+ align:start position:0%
+these funny things. There's classes on
+ 
+
+ align:start position:0%
+these funny things. There's classes on
+randomized algorithms here. Every once
+
+ align:start position:0%
+randomized algorithms here. Every once
+ 
+
+ align:start position:0%
+randomized algorithms here. Every once
+in a while these things just really work
+
+ align:start position:0%
+in a while these things just really work
+ 
+
+ align:start position:0%
+in a while these things just really work
+nicely. Randomization can help, right?
+
+ align:start position:0%
+nicely. Randomization can help, right?
+ 
+
+ align:start position:0%
+nicely. Randomization can help, right?
+And the reason roughly maybe is that
+
+ align:start position:0%
+And the reason roughly maybe is that
+ 
+
+ align:start position:0%
+And the reason roughly maybe is that
+it's it's actually pretty cheap to pick
+
+ align:start position:0%
+it's it's actually pretty cheap to pick
+ 
+
+ align:start position:0%
+it's it's actually pretty cheap to pick
+a sample point. It's pretty cheap to
+
+ align:start position:0%
+a sample point. It's pretty cheap to
+ 
+
+ align:start position:0%
+a sample point. It's pretty cheap to
+evaluate if it's in a in a collision. Um
+
+ align:start position:0%
+evaluate if it's in a in a collision. Um
+ 
+
+ align:start position:0%
+evaluate if it's in a in a collision. Um
+and and so so why not just pick a lot
+
+ align:start position:0%
+and and so so why not just pick a lot
+ 
+
+ align:start position:0%
+and and so so why not just pick a lot
+instead of trying to reason about the
+
+ align:start position:0%
+instead of trying to reason about the
+ 
+
+ align:start position:0%
+instead of trying to reason about the
+geometry of your obstacles, right?
+
+ align:start position:0%
+geometry of your obstacles, right?
+ 
+
+ align:start position:0%
+geometry of your obstacles, right?
+Building configuration spaces, that's
+
+ align:start position:0%
+Building configuration spaces, that's
+ 
+
+ align:start position:0%
+Building configuration spaces, that's
+hard compared to just saying, "Okay,
+
+ align:start position:0%
+hard compared to just saying, "Okay,
+ 
+
+ align:start position:0%
+hard compared to just saying, "Okay,
+what if my robot was here? Was that a
+
+ align:start position:0%
+what if my robot was here? Was that a
+ 
+
+ align:start position:0%
+what if my robot was here? Was that a
+collision?" "Yeah, that's in collision."
+
+ align:start position:0%
+collision?" "Yeah, that's in collision."
+ 
+
+ align:start position:0%
+collision?" "Yeah, that's in collision."
+Okay, throw it out. And just sometimes
+
+ align:start position:0%
+Okay, throw it out. And just sometimes
+ 
+
+ align:start position:0%
+Okay, throw it out. And just sometimes
+randomized algorithms are
+
+ align:start position:0%
+randomized algorithms are
+ 
+
+ align:start position:0%
+randomized algorithms are
+better. Okay, see you next week.
\ No newline at end of file
diff --git a/v-5w8ZDIa4w.txt b/v-5w8ZDIa4w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..225d53b3e78ee8ca44b0783cea7523c4a7734290
--- /dev/null
+++ b/v-5w8ZDIa4w.txt
@@ -0,0 +1,263 @@
+We're on the home stretch now.
+
+For all the instructions up until now, the
+next instruction has come from the location
+
+following the current instruction - hence
+the "PC+4" logic.
+
+Branches and JMPs change that by altering
+the value in the PC.
+
+The JMP instruction simply takes the value
+in the RA register and makes it the next PC
+
+value.
+
+The PCSEL MUX in the upper left-hand corner
+lets the control logic select the source of
+
+the next PC value.
+
+When PCSEL is 0, the incremented PC value
+is chosen.
+
+When PCSEL is 2, the value of the RA register
+is chosen.
+
+We'll see how the other inputs to the PCSEL
+MUX are used in just a moment.
+
+The JMP and branch instructions also cause
+the address of the following instruction,
+
+i.e., the PC+4 value, to be written to the
+RC register.
+
+When WDSEL is 0, the "0" input of the WDSEL
+MUX is used to select the PC+4 value as the
+
+write-back data.
+
+Here's how the data flow works.
+
+The output of the PC+4 adder is is routed
+to the register file and WERF is set to 1
+
+to enable that value to be written at the
+end of the cycle.
+
+Meanwhile, the value of RA register coming
+out of the register file is connected to the
+
+"2" input of the PCSEL MUX.
+
+So setting PCSEL to 2 will select the value
+in the RA register as the next value for the
+
+PC.
+
+The rest of the control signals are "don't
+cares", except, of course for the memory write
+
+enable (MWR), which can never be "don't care"
+lest we cause an accidental write to some
+
+memory location.
+
+The branch instruction requires an additional
+adder to compute the target address by adding
+
+the scaled offset from the instruction's literal
+field to the current PC+4 value.
+
+Remember that we scale the offset by a factor
+of 4 to convert it from the word offset stored
+
+in the literal to the byte offset required
+for the PC.
+
+The output of the offset adder becomes the
+"1" input to the PCSEL MUX, where, if the
+
+branch is taken, it will become the next value
+of the PC.
+
+Note that multiplying by 4 is easily accomplished
+by shifting the literal two bits to the left,
+
+which inserts two 0-bits at the low-order
+end of the value.
+
+And, like before, the sign-extension just
+requires replicating bit ID[15], in this case
+
+fourteen times.
+
+So implementing this complicated-looking expression
+requires care in wiring up the input to the
+
+offset adder, but no additional logic!
+
+We do need some logic to determine if we should
+branch or not.
+
+The 32-bit NOR gate connected to the first
+read port of the register file tests the value
+
+of the RA register.
+
+The NOR's output Z will be 1 if all the bits
+of the RA register value are 0, and 0 otherwise.
+
+The Z value can be used by the control logic
+to determine the correct value for PCSEL.
+
+If Z indicates the branch is taken, PCSEL
+will be 1 and the output of the offset adder
+
+becomes the next value of the PC.
+
+If the branch is not taken, PCSEL will be
+0 and execution will continue with the next
+
+instruction at PC+4.
+
+As in the JMP instruction, the PC+4 value
+is routed to the register file to be written
+
+into the RC register at end of the cycle.
+
+Meanwhile, the value of Z is computed from
+the value of the RA register while the branch
+
+offset adder computes the address of the branch
+target.
+
+The output of the offset adder is routed to
+the PCSEL MUX where the value of the 3-bit
+
+PCSEL control signal, computed by the control
+logic based on Z, determines whether the next
+
+PC value is the branch target or the PC+4
+value.
+
+The remaining control signals are unused and
+set to their default "don't care" values.
+
+We have one last instruction to introduce:
+the LDR or load-relative instruction.
+
+LDR behaves like a normal LD instruction except
+that the memory address is taken from the
+
+branch offset adder.
+
+Why would it be useful to load a value from
+a location near the LDR instruction?
+
+Normally such addresses would refer to the
+neighboring instructions, so why would we
+
+want to load the binary encoding of an instruction
+into a register to be used as data?
+
+The use case for LDR is accessing large constants
+that have to be stored in main memory because
+
+they are too large to fit into the 16-bit
+literal field of an instruction.
+
+In the example shown here, the compiled code
+needs to load the constant 123456.
+
+So it uses an LDR instruction that refers
+to a nearby location C1: that has been initialized
+
+with the required value.
+
+Since this read-only constant is part of the
+program, it makes sense to store it with the
+
+instructions for the program, usually just
+after the code for a procedure.
+
+Note that we have to be careful to place the
+storage location so that it won't be executed
+
+as an instruction!
+
+To route the output of the offset adder to
+the main memory address port, we'll add ASEL
+
+MUX so we can select either the RA register
+value (when ASEL=0) or the output of the offset
+
+adder (when ASEL=1) as the first ALU operand.
+
+For LDR, ASEL will be 1, and we'll then ask
+the ALU compute the Boolean operation "A",
+
+i.e., the boolean function whose output is
+just the value of the first operand.
+
+This value then appears on the ALU output,
+which is connected to the main memory address
+
+port and the remainder of the execution proceeds
+just like it did for LD.
+
+This seems a bit complicated!
+
+Mr. Blue has a good question:
+why not just put the ASEL MUX on the wire
+
+leading to the main memory address port and
+bypass the ALU altogether?
+
+The answer has to do with the amount of time
+needed to compute the memory address.
+
+If we moved the ASEL MUX here, the data flow
+for LD and ST addresses would then pass through
+
+two MUXes, the BSEL MUX and the ASEL MUX,
+slowing down the arrival of the address by
+
+a small amount.
+
+This may not seem like a big deal, but the
+additional time would have to be added the
+
+clock period, thus slowing down every instruction
+by a little bit.
+
+When executing billions of instructions, a
+little extra time on each instruction really
+
+impacts the overall performance of the processor.
+
+By placing the ASEL MUX where we did, its
+propagation delay overlaps that of the BSEL
+
+MUX, so the increased functionality it provides
+comes with no cost in performance.
+
+Here's the data flow for the LDR instruction.
+
+The output of the offset adder is routed through
+the ASEL MUX to the ALU.
+
+The ALU performs the Boolean computation "A"
+and the result becomes the address for main
+
+memory.
+
+The returning data is routed through the WDSEL
+MUX so it can be written into the RC register
+
+at the end of the cycle.
+
+The remaining control values are given their
+usual default values.
\ No newline at end of file
diff --git a/vJAG4EzSQZA.txt b/vJAG4EzSQZA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d13434245bd4c5d5976345eeb02c9257a6ce9c84
--- /dev/null
+++ b/vJAG4EzSQZA.txt
@@ -0,0 +1,931 @@
+align:start position:0%
+ 
+we will now talk about conditional
+
+ align:start position:0%
+we will now talk about conditional
+ 
+
+ align:start position:0%
+we will now talk about conditional
+expectations of one random variable
+
+ align:start position:0%
+expectations of one random variable
+ 
+
+ align:start position:0%
+expectations of one random variable
+given another as we will see there will
+
+ align:start position:0%
+given another as we will see there will
+ 
+
+ align:start position:0%
+given another as we will see there will
+be nothing new here except for all the
+
+ align:start position:0%
+be nothing new here except for all the
+ 
+
+ align:start position:0%
+be nothing new here except for all the
+results but given a new notation any PMF
+
+ align:start position:0%
+results but given a new notation any PMF
+ 
+
+ align:start position:0%
+results but given a new notation any PMF
+has an Associated expectation and so
+
+ align:start position:0%
+has an Associated expectation and so
+ 
+
+ align:start position:0%
+has an Associated expectation and so
+conditional pmfs also have associated
+
+ align:start position:0%
+conditional pmfs also have associated
+ 
+
+ align:start position:0%
+conditional pmfs also have associated
+expectations which we call conditional
+
+ align:start position:0%
+expectations which we call conditional
+ 
+
+ align:start position:0%
+expectations which we call conditional
+expectations we have already seen them
+
+ align:start position:0%
+expectations we have already seen them
+ 
+
+ align:start position:0%
+expectations we have already seen them
+for the case where we conditioned on an
+
+ align:start position:0%
+for the case where we conditioned on an
+ 
+
+ align:start position:0%
+for the case where we conditioned on an
+event a the case where we conditioned on
+
+ align:start position:0%
+event a the case where we conditioned on
+ 
+
+ align:start position:0%
+event a the case where we conditioned on
+random variables is exactly the same we
+
+ align:start position:0%
+random variables is exactly the same we
+ 
+
+ align:start position:0%
+random variables is exactly the same we
+let the event a be the event that Y
+
+ align:start position:0%
+let the event a be the event that Y
+ 
+
+ align:start position:0%
+let the event a be the event that Y
+takes on a specific value and then we
+
+ align:start position:0%
+takes on a specific value and then we
+ 
+
+ align:start position:0%
+takes on a specific value and then we
+calculate the expectation using the
+
+ align:start position:0%
+calculate the expectation using the
+ 
+
+ align:start position:0%
+calculate the expectation using the
+relevant conditional probabilities those
+
+ align:start position:0%
+relevant conditional probabilities those
+ 
+
+ align:start position:0%
+relevant conditional probabilities those
+that are given by the conditional pmf so
+
+ align:start position:0%
+that are given by the conditional pmf so
+ 
+
+ align:start position:0%
+that are given by the conditional pmf so
+the conditional expectation of x given
+
+ align:start position:0%
+the conditional expectation of x given
+ 
+
+ align:start position:0%
+the conditional expectation of x given
+that Y takes on a certain value is
+
+ align:start position:0%
+that Y takes on a certain value is
+ 
+
+ align:start position:0%
+that Y takes on a certain value is
+defined as the usual expectation except
+
+ align:start position:0%
+defined as the usual expectation except
+ 
+
+ align:start position:0%
+defined as the usual expectation except
+that we use the conditional
+
+ align:start position:0%
+that we use the conditional
+ 
+
+ align:start position:0%
+that we use the conditional
+probabilities that apply given that Y
+
+ align:start position:0%
+probabilities that apply given that Y
+ 
+
+ align:start position:0%
+probabilities that apply given that Y
+takes on a specific value little Y
+
+ align:start position:0%
+takes on a specific value little Y
+ 
+
+ align:start position:0%
+takes on a specific value little Y
+recall now the expected value rule for
+
+ align:start position:0%
+recall now the expected value rule for
+ 
+
+ align:start position:0%
+recall now the expected value rule for
+ordinary expectations and also the
+
+ align:start position:0%
+ordinary expectations and also the
+ 
+
+ align:start position:0%
+ordinary expectations and also the
+expected value rule for conditional
+
+ align:start position:0%
+expected value rule for conditional
+ 
+
+ align:start position:0%
+expected value rule for conditional
+expectations given an event something
+
+ align:start position:0%
+expectations given an event something
+ 
+
+ align:start position:0%
+expectations given an event something
+that we have already seen now in PMF
+
+ align:start position:0%
+that we have already seen now in PMF
+ 
+
+ align:start position:0%
+that we have already seen now in PMF
+notation the expected value rule takes a
+
+ align:start position:0%
+notation the expected value rule takes a
+ 
+
+ align:start position:0%
+notation the expected value rule takes a
+similar form the event a is replaced by
+
+ align:start position:0%
+similar form the event a is replaced by
+ 
+
+ align:start position:0%
+similar form the event a is replaced by
+the specific event that Y takes on a
+
+ align:start position:0%
+the specific event that Y takes on a
+ 
+
+ align:start position:0%
+the specific event that Y takes on a
+specific value and in that case the
+
+ align:start position:0%
+specific value and in that case the
+ 
+
+ align:start position:0%
+specific value and in that case the
+conditional pmf given the event a is
+
+ align:start position:0%
+conditional pmf given the event a is
+ 
+
+ align:start position:0%
+conditional pmf given the event a is
+just the conditional pmf given that
+
+ align:start position:0%
+just the conditional pmf given that
+ 
+
+ align:start position:0%
+just the conditional pmf given that
+random variable Y takes on a specific
+
+ align:start position:0%
+random variable Y takes on a specific
+ 
+
+ align:start position:0%
+random variable Y takes on a specific
+value little Y for the case where we
+
+ align:start position:0%
+value little Y for the case where we
+ 
+
+ align:start position:0%
+value little Y for the case where we
+conditioned on events we also developed
+
+ align:start position:0%
+conditioned on events we also developed
+ 
+
+ align:start position:0%
+conditioned on events we also developed
+a version of the total probability
+
+ align:start position:0%
+a version of the total probability
+ 
+
+ align:start position:0%
+a version of the total probability
+theorem and the total expectation
+
+ align:start position:0%
+theorem and the total expectation
+ 
+
+ align:start position:0%
+theorem and the total expectation
+theorem we can do the same when we
+
+ align:start position:0%
+theorem we can do the same when we
+ 
+
+ align:start position:0%
+theorem we can do the same when we
+conditioned on random variables so
+
+ align:start position:0%
+conditioned on random variables so
+ 
+
+ align:start position:0%
+conditioned on random variables so
+suppose that the sample space has been
+
+ align:start position:0%
+suppose that the sample space has been
+ 
+
+ align:start position:0%
+suppose that the sample space has been
+partitioned into
+
+ align:start position:0%
+partitioned into
+ 
+
+ align:start position:0%
+partitioned into
+and disjoint scenarios the total
+
+ align:start position:0%
+and disjoint scenarios the total
+ 
+
+ align:start position:0%
+and disjoint scenarios the total
+probability theorem tells us that the
+
+ align:start position:0%
+probability theorem tells us that the
+ 
+
+ align:start position:0%
+probability theorem tells us that the
+probability of the event the event that
+
+ align:start position:0%
+probability of the event the event that
+ 
+
+ align:start position:0%
+probability of the event the event that
+random variable X takes on value little
+
+ align:start position:0%
+random variable X takes on value little
+ 
+
+ align:start position:0%
+random variable X takes on value little
+X can be found by taking the
+
+ align:start position:0%
+X can be found by taking the
+ 
+
+ align:start position:0%
+X can be found by taking the
+probabilities of this event under each
+
+ align:start position:0%
+probabilities of this event under each
+ 
+
+ align:start position:0%
+probabilities of this event under each
+one of the possible scenarios and then
+
+ align:start position:0%
+one of the possible scenarios and then
+ 
+
+ align:start position:0%
+one of the possible scenarios and then
+weighing those probabilities according
+
+ align:start position:0%
+weighing those probabilities according
+ 
+
+ align:start position:0%
+weighing those probabilities according
+to the probabilities of the different
+
+ align:start position:0%
+to the probabilities of the different
+ 
+
+ align:start position:0%
+to the probabilities of the different
+scenarios now suppose that we are
+
+ align:start position:0%
+scenarios now suppose that we are
+ 
+
+ align:start position:0%
+scenarios now suppose that we are
+dealing with a random variable that
+
+ align:start position:0%
+dealing with a random variable that
+ 
+
+ align:start position:0%
+dealing with a random variable that
+takes values in a set consisting of n
+
+ align:start position:0%
+takes values in a set consisting of n
+ 
+
+ align:start position:0%
+takes values in a set consisting of n
+elements and let us consider scenarios
+
+ align:start position:0%
+elements and let us consider scenarios
+ 
+
+ align:start position:0%
+elements and let us consider scenarios
+AI the eigth scenario is the event that
+
+ align:start position:0%
+AI the eigth scenario is the event that
+ 
+
+ align:start position:0%
+AI the eigth scenario is the event that
+the random variable Y takes on the eyes
+
+ align:start position:0%
+the random variable Y takes on the eyes
+ 
+
+ align:start position:0%
+the random variable Y takes on the eyes
+possible value we can apply the total
+
+ align:start position:0%
+possible value we can apply the total
+ 
+
+ align:start position:0%
+possible value we can apply the total
+probability theorem to this situation we
+
+ align:start position:0%
+probability theorem to this situation we
+ 
+
+ align:start position:0%
+probability theorem to this situation we
+can find the probability that the random
+
+ align:start position:0%
+can find the probability that the random
+ 
+
+ align:start position:0%
+can find the probability that the random
+variable X takes on a certain value
+
+ align:start position:0%
+variable X takes on a certain value
+ 
+
+ align:start position:0%
+variable X takes on a certain value
+little X by considering the probability
+
+ align:start position:0%
+little X by considering the probability
+ 
+
+ align:start position:0%
+little X by considering the probability
+of this event happening under each
+
+ align:start position:0%
+of this event happening under each
+ 
+
+ align:start position:0%
+of this event happening under each
+possible scenario where a scenario is
+
+ align:start position:0%
+possible scenario where a scenario is
+ 
+
+ align:start position:0%
+possible scenario where a scenario is
+that Y took on a specific value and then
+
+ align:start position:0%
+that Y took on a specific value and then
+ 
+
+ align:start position:0%
+that Y took on a specific value and then
+weigh those probabilities according to
+
+ align:start position:0%
+weigh those probabilities according to
+ 
+
+ align:start position:0%
+weigh those probabilities according to
+the probabilities of the different
+
+ align:start position:0%
+the probabilities of the different
+ 
+
+ align:start position:0%
+the probabilities of the different
+scenarios the story with the total
+
+ align:start position:0%
+scenarios the story with the total
+ 
+
+ align:start position:0%
+scenarios the story with the total
+expectation theorem is similar we know
+
+ align:start position:0%
+expectation theorem is similar we know
+ 
+
+ align:start position:0%
+expectation theorem is similar we know
+that an expectation can be found by
+
+ align:start position:0%
+that an expectation can be found by
+ 
+
+ align:start position:0%
+that an expectation can be found by
+taking the conditional expectations
+
+ align:start position:0%
+taking the conditional expectations
+ 
+
+ align:start position:0%
+taking the conditional expectations
+under each one of the scenarios and
+
+ align:start position:0%
+under each one of the scenarios and
+ 
+
+ align:start position:0%
+under each one of the scenarios and
+weighing them according to the
+
+ align:start position:0%
+weighing them according to the
+ 
+
+ align:start position:0%
+weighing them according to the
+probabilities of the different scenarios
+
+ align:start position:0%
+probabilities of the different scenarios
+ 
+
+ align:start position:0%
+probabilities of the different scenarios
+again let the event that Y takes on a
+
+ align:start position:0%
+again let the event that Y takes on a
+ 
+
+ align:start position:0%
+again let the event that Y takes on a
+specific value be a different scenario
+
+ align:start position:0%
+specific value be a different scenario
+ 
+
+ align:start position:0%
+specific value be a different scenario
+and with this correspondence we obtain
+
+ align:start position:0%
+and with this correspondence we obtain
+ 
+
+ align:start position:0%
+and with this correspondence we obtain
+the following version of the total
+
+ align:start position:0%
+the following version of the total
+ 
+
+ align:start position:0%
+the following version of the total
+expectation theorem we have a sum of
+
+ align:start position:0%
+expectation theorem we have a sum of
+ 
+
+ align:start position:0%
+expectation theorem we have a sum of
+different terms and each term in the sum
+
+ align:start position:0%
+different terms and each term in the sum
+ 
+
+ align:start position:0%
+different terms and each term in the sum
+is the probability of a given scenario
+
+ align:start position:0%
+is the probability of a given scenario
+ 
+
+ align:start position:0%
+is the probability of a given scenario
+times the expected value of X under this
+
+ align:start position:0%
+times the expected value of X under this
+ 
+
+ align:start position:0%
+times the expected value of X under this
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+stickler scenario at this point I have
+
+ align:start position:0%
+stickler scenario at this point I have
+ 
+
+ align:start position:0%
+stickler scenario at this point I have
+to add the comment of a more
+
+ align:start position:0%
+to add the comment of a more
+ 
+
+ align:start position:0%
+to add the comment of a more
+mathematical flavor we have been talking
+
+ align:start position:0%
+mathematical flavor we have been talking
+ 
+
+ align:start position:0%
+mathematical flavor we have been talking
+about the partition of the sample space
+
+ align:start position:0%
+about the partition of the sample space
+ 
+
+ align:start position:0%
+about the partition of the sample space
+into finitely many scenarios but if Y
+
+ align:start position:0%
+into finitely many scenarios but if Y
+ 
+
+ align:start position:0%
+into finitely many scenarios but if Y
+takes on values ended in a discrete but
+
+ align:start position:0%
+takes on values ended in a discrete but
+ 
+
+ align:start position:0%
+takes on values ended in a discrete but
+infinite set for example if Y can take
+
+ align:start position:0%
+infinite set for example if Y can take
+ 
+
+ align:start position:0%
+infinite set for example if Y can take
+on any integer value the argument that
+
+ align:start position:0%
+on any integer value the argument that
+ 
+
+ align:start position:0%
+on any integer value the argument that
+we have given is not quite complete
+
+ align:start position:0%
+we have given is not quite complete
+ 
+
+ align:start position:0%
+we have given is not quite complete
+fortunately the total probability
+
+ align:start position:0%
+fortunately the total probability
+ 
+
+ align:start position:0%
+fortunately the total probability
+theorem and the total expectation
+
+ align:start position:0%
+theorem and the total expectation
+ 
+
+ align:start position:0%
+theorem and the total expectation
+theorem they both remain true even for
+
+ align:start position:0%
+theorem they both remain true even for
+ 
+
+ align:start position:0%
+theorem they both remain true even for
+the case where Y ranges over an infinite
+
+ align:start position:0%
+the case where Y ranges over an infinite
+ 
+
+ align:start position:0%
+the case where Y ranges over an infinite
+set as long as the random variable X has
+
+ align:start position:0%
+set as long as the random variable X has
+ 
+
+ align:start position:0%
+set as long as the random variable X has
+a well-defined expectation for the total
+
+ align:start position:0%
+a well-defined expectation for the total
+ 
+
+ align:start position:0%
+a well-defined expectation for the total
+probability theorem the proof for the
+
+ align:start position:0%
+probability theorem the proof for the
+ 
+
+ align:start position:0%
+probability theorem the proof for the
+general case can be carried out without
+
+ align:start position:0%
+general case can be carried out without
+ 
+
+ align:start position:0%
+general case can be carried out without
+a lot of difficulty just using the
+
+ align:start position:0%
+a lot of difficulty just using the
+ 
+
+ align:start position:0%
+a lot of difficulty just using the
+countable additivity axiom however for
+
+ align:start position:0%
+countable additivity axiom however for
+ 
+
+ align:start position:0%
+countable additivity axiom however for
+the total expectation theorem it takes
+
+ align:start position:0%
+the total expectation theorem it takes
+ 
+
+ align:start position:0%
+the total expectation theorem it takes
+some harder mathematical work and this
+
+ align:start position:0%
+some harder mathematical work and this
+ 
+
+ align:start position:0%
+some harder mathematical work and this
+is beyond our scope but we will just
+
+ align:start position:0%
+is beyond our scope but we will just
+ 
+
+ align:start position:0%
+is beyond our scope but we will just
+take this fact for granted that the
+
+ align:start position:0%
+take this fact for granted that the
+ 
+
+ align:start position:0%
+take this fact for granted that the
+total expectation theorem carries over
+
+ align:start position:0%
+total expectation theorem carries over
+ 
+
+ align:start position:0%
+total expectation theorem carries over
+to the case where we are adding over an
+
+ align:start position:0%
+to the case where we are adding over an
+ 
+
+ align:start position:0%
+to the case where we are adding over an
+infinite sequence of possible values of
+
+ align:start position:0%
+infinite sequence of possible values of
+ 
+
+ align:start position:0%
+infinite sequence of possible values of
+Y in the rest of the course we will
+
+ align:start position:0%
+Y in the rest of the course we will
+ 
+
+ align:start position:0%
+Y in the rest of the course we will
+often use the total expectation theorem
+
+ align:start position:0%
+often use the total expectation theorem
+ 
+
+ align:start position:0%
+often use the total expectation theorem
+including in cases where Y ranges over
+
+ align:start position:0%
+including in cases where Y ranges over
+ 
+
+ align:start position:0%
+including in cases where Y ranges over
+an infinite discrete set in fact we will
+
+ align:start position:0%
+an infinite discrete set in fact we will
+ 
+
+ align:start position:0%
+an infinite discrete set in fact we will
+see that this theorem is an extremely
+
+ align:start position:0%
+see that this theorem is an extremely
+ 
+
+ align:start position:0%
+see that this theorem is an extremely
+useful tool that can be used to divide
+
+ align:start position:0%
+useful tool that can be used to divide
+ 
+
+ align:start position:0%
+useful tool that can be used to divide
+and conquer complicated models
\ No newline at end of file
diff --git a/vYURcLuJEZs.txt b/vYURcLuJEZs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42e8b2b4c406d810e79b9ab0def694a7c9ec8448
--- /dev/null
+++ b/vYURcLuJEZs.txt
@@ -0,0 +1,6736 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Uh in this module we're going to
+
+ align:start position:0%
+Okay. Uh in this module we're going to
+ 
+
+ align:start position:0%
+Okay. Uh in this module we're going to
+talk about quality and uh uh let me just
+
+ align:start position:0%
+talk about quality and uh uh let me just
+ 
+
+ align:start position:0%
+talk about quality and uh uh let me just
+say that that you know the whole lean
+
+ align:start position:0%
+say that that you know the whole lean
+ 
+
+ align:start position:0%
+say that that you know the whole lean
+process doesn't work without quality and
+
+ align:start position:0%
+process doesn't work without quality and
+ 
+
+ align:start position:0%
+process doesn't work without quality and
+everybody thinks of quality you think of
+
+ align:start position:0%
+everybody thinks of quality you think of
+ 
+
+ align:start position:0%
+everybody thinks of quality you think of
+manufacturing. Okay. Uh let me suggest
+
+ align:start position:0%
+manufacturing. Okay. Uh let me suggest
+ 
+
+ align:start position:0%
+manufacturing. Okay. Uh let me suggest
+here that as we extended manufacturing
+
+ align:start position:0%
+here that as we extended manufacturing
+ 
+
+ align:start position:0%
+here that as we extended manufacturing
+to our suppliers, if the supplier ships
+
+ align:start position:0%
+to our suppliers, if the supplier ships
+ 
+
+ align:start position:0%
+to our suppliers, if the supplier ships
+incomplete, incorrect parts to us, u uh
+
+ align:start position:0%
+incomplete, incorrect parts to us, u uh
+ 
+
+ align:start position:0%
+incomplete, incorrect parts to us, u uh
+doesn't do us any good. I had F-15
+
+ align:start position:0%
+doesn't do us any good. I had F-15
+ 
+
+ align:start position:0%
+doesn't do us any good. I had F-15
+composite assemblies coming in from
+
+ align:start position:0%
+composite assemblies coming in from
+ 
+
+ align:start position:0%
+composite assemblies coming in from
+Israel and they were stacking up and
+
+ align:start position:0%
+Israel and they were stacking up and
+ 
+
+ align:start position:0%
+Israel and they were stacking up and
+when I when I got there, uh it was
+
+ align:start position:0%
+when I when I got there, uh it was
+ 
+
+ align:start position:0%
+when I when I got there, uh it was
+before my time. I didn't start that line
+
+ align:start position:0%
+before my time. I didn't start that line
+ 
+
+ align:start position:0%
+before my time. I didn't start that line
+and they were shipping and getting paid
+
+ align:start position:0%
+and they were shipping and getting paid
+ 
+
+ align:start position:0%
+and they were shipping and getting paid
+for these composite sections on the F-15
+
+ align:start position:0%
+for these composite sections on the F-15
+ 
+
+ align:start position:0%
+for these composite sections on the F-15
+and my guys were rejecting them because
+
+ align:start position:0%
+and my guys were rejecting them because
+ 
+
+ align:start position:0%
+and my guys were rejecting them because
+of voids or you know discrepancies and
+
+ align:start position:0%
+of voids or you know discrepancies and
+ 
+
+ align:start position:0%
+of voids or you know discrepancies and
+then we were trying to figure out how
+
+ align:start position:0%
+then we were trying to figure out how
+ 
+
+ align:start position:0%
+then we were trying to figure out how
+from an engineering standpoint to uh
+
+ align:start position:0%
+from an engineering standpoint to uh
+ 
+
+ align:start position:0%
+from an engineering standpoint to uh
+disposition those from a standpoint do
+
+ align:start position:0%
+disposition those from a standpoint do
+ 
+
+ align:start position:0%
+disposition those from a standpoint do
+we have to cut out the cut out the nom
+
+ align:start position:0%
+we have to cut out the cut out the nom
+ 
+
+ align:start position:0%
+we have to cut out the cut out the nom
+Nomx and put a patch on it and that kind
+
+ align:start position:0%
+Nomx and put a patch on it and that kind
+ 
+
+ align:start position:0%
+Nomx and put a patch on it and that kind
+of stuff. And I said wait a minute wait
+
+ align:start position:0%
+of stuff. And I said wait a minute wait
+ 
+
+ align:start position:0%
+of stuff. And I said wait a minute wait
+a minute this is wrong. You know, we
+
+ align:start position:0%
+a minute this is wrong. You know, we
+ 
+
+ align:start position:0%
+a minute this is wrong. You know, we
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+Israeli Aircraft Industries to make a
+
+ align:start position:0%
+Israeli Aircraft Industries to make a
+ 
+
+ align:start position:0%
+Israeli Aircraft Industries to make a
+perfect part to inspect it to get our
+
+ align:start position:0%
+perfect part to inspect it to get our
+ 
+
+ align:start position:0%
+perfect part to inspect it to get our
+acceptance on that part and ship a good
+
+ align:start position:0%
+acceptance on that part and ship a good
+ 
+
+ align:start position:0%
+acceptance on that part and ship a good
+part so I can put it right on top, you
+
+ align:start position:0%
+part so I can put it right on top, you
+ 
+
+ align:start position:0%
+part so I can put it right on top, you
+know, right in the in the assembly line.
+
+ align:start position:0%
+know, right in the in the assembly line.
+ 
+
+ align:start position:0%
+know, right in the in the assembly line.
+And so there's no way that you can
+
+ align:start position:0%
+And so there's no way that you can
+ 
+
+ align:start position:0%
+And so there's no way that you can
+achieve cycle time, can achieve manh
+
+ align:start position:0%
+achieve cycle time, can achieve manh
+ 
+
+ align:start position:0%
+achieve cycle time, can achieve manh
+hours and personnel hours. I'm gender
+
+ align:start position:0%
+hours and personnel hours. I'm gender
+ 
+
+ align:start position:0%
+hours and personnel hours. I'm gender
+center. See, I'm an old guy and when I
+
+ align:start position:0%
+center. See, I'm an old guy and when I
+ 
+
+ align:start position:0%
+center. See, I'm an old guy and when I
+started in this business, it was man
+
+ align:start position:0%
+started in this business, it was man
+ 
+
+ align:start position:0%
+started in this business, it was man
+hours. and now it's labor hours and uh
+
+ align:start position:0%
+hours. and now it's labor hours and uh
+ 
+
+ align:start position:0%
+hours. and now it's labor hours and uh
+so uh you can't achieve your unit cost
+
+ align:start position:0%
+so uh you can't achieve your unit cost
+ 
+
+ align:start position:0%
+so uh you can't achieve your unit cost
+uh or your schedule with bad quality and
+
+ align:start position:0%
+uh or your schedule with bad quality and
+ 
+
+ align:start position:0%
+uh or your schedule with bad quality and
+most people think of this kind of an
+
+ align:start position:0%
+most people think of this kind of an
+ 
+
+ align:start position:0%
+most people think of this kind of an
+example in terms of manufacturing and
+
+ align:start position:0%
+example in terms of manufacturing and
+ 
+
+ align:start position:0%
+example in terms of manufacturing and
+that kind of stuff now and I've just
+
+ align:start position:0%
+that kind of stuff now and I've just
+ 
+
+ align:start position:0%
+that kind of stuff now and I've just
+given you a manufacturing example in the
+
+ align:start position:0%
+given you a manufacturing example in the
+ 
+
+ align:start position:0%
+given you a manufacturing example in the
+factory and a supplier giving us bad
+
+ align:start position:0%
+factory and a supplier giving us bad
+ 
+
+ align:start position:0%
+factory and a supplier giving us bad
+parts but in engineering if we have
+
+ align:start position:0%
+parts but in engineering if we have
+ 
+
+ align:start position:0%
+parts but in engineering if we have
+incorrect drawings or we have mistakes
+
+ align:start position:0%
+incorrect drawings or we have mistakes
+ 
+
+ align:start position:0%
+incorrect drawings or we have mistakes
+on the drawing where the tolerances are
+
+ align:start position:0%
+on the drawing where the tolerances are
+ 
+
+ align:start position:0%
+on the drawing where the tolerances are
+wrong or we leave out a material call
+
+ align:start position:0%
+wrong or we leave out a material call
+ 
+
+ align:start position:0%
+wrong or we leave out a material call
+out or call out the wrong material spec
+
+ align:start position:0%
+out or call out the wrong material spec
+ 
+
+ align:start position:0%
+out or call out the wrong material spec
+or something like that. We send those
+
+ align:start position:0%
+or something like that. We send those
+ 
+
+ align:start position:0%
+or something like that. We send those
+drawings or the equivalent 3D solid
+
+ align:start position:0%
+drawings or the equivalent 3D solid
+ 
+
+ align:start position:0%
+drawings or the equivalent 3D solid
+um technical data out to the suppliers,
+
+ align:start position:0%
+um technical data out to the suppliers,
+ 
+
+ align:start position:0%
+um technical data out to the suppliers,
+they get it wrong, it comes in wrong or
+
+ align:start position:0%
+they get it wrong, it comes in wrong or
+ 
+
+ align:start position:0%
+they get it wrong, it comes in wrong or
+our factory builds it wrong. So of the
+
+ align:start position:0%
+our factory builds it wrong. So of the
+ 
+
+ align:start position:0%
+our factory builds it wrong. So of the
+of all the elements of achieving a lean
+
+ align:start position:0%
+of all the elements of achieving a lean
+ 
+
+ align:start position:0%
+of all the elements of achieving a lean
+enterprise quality is is you know
+
+ align:start position:0%
+enterprise quality is is you know
+ 
+
+ align:start position:0%
+enterprise quality is is you know
+critical and it's quality and accounting
+
+ align:start position:0%
+critical and it's quality and accounting
+ 
+
+ align:start position:0%
+critical and it's quality and accounting
+data quality and everything. Okay. So I
+
+ align:start position:0%
+data quality and everything. Okay. So I
+ 
+
+ align:start position:0%
+data quality and everything. Okay. So I
+mean I'll say this about 10 times and if
+
+ align:start position:0%
+mean I'll say this about 10 times and if
+ 
+
+ align:start position:0%
+mean I'll say this about 10 times and if
+you if you give me a a low mark for
+
+ align:start position:0%
+you if you give me a a low mark for
+ 
+
+ align:start position:0%
+you if you give me a a low mark for
+saying he's repetitive I'll take that
+
+ align:start position:0%
+saying he's repetitive I'll take that
+ 
+
+ align:start position:0%
+saying he's repetitive I'll take that
+because it's for emphasis. Okay. Very
+
+ align:start position:0%
+because it's for emphasis. Okay. Very
+ 
+
+ align:start position:0%
+because it's for emphasis. Okay. Very
+very important. So, we're going to
+
+ align:start position:0%
+very important. So, we're going to
+ 
+
+ align:start position:0%
+very important. So, we're going to
+talk about how quality is essential to
+
+ align:start position:0%
+talk about how quality is essential to
+ 
+
+ align:start position:0%
+talk about how quality is essential to
+achieving customer satisfaction. I don't
+
+ align:start position:0%
+achieving customer satisfaction. I don't
+ 
+
+ align:start position:0%
+achieving customer satisfaction. I don't
+want two cardboard boxes in the back of
+
+ align:start position:0%
+want two cardboard boxes in the back of
+ 
+
+ align:start position:0%
+want two cardboard boxes in the back of
+my brand new car that says take it to
+
+ align:start position:0%
+my brand new car that says take it to
+ 
+
+ align:start position:0%
+my brand new car that says take it to
+the dealer, you know, because we they
+
+ align:start position:0%
+the dealer, you know, because we they
+ 
+
+ align:start position:0%
+the dealer, you know, because we they
+delivered a car without 100% of the
+
+ align:start position:0%
+delivered a car without 100% of the
+ 
+
+ align:start position:0%
+delivered a car without 100% of the
+components in it. And that happens.
+
+ align:start position:0%
+components in it. And that happens.
+ 
+
+ align:start position:0%
+components in it. And that happens.
+We're going to talk about product
+
+ align:start position:0%
+We're going to talk about product
+ 
+
+ align:start position:0%
+We're going to talk about product
+quality and process quality. And the
+
+ align:start position:0%
+quality and process quality. And the
+ 
+
+ align:start position:0%
+quality and process quality. And the
+fact is it's very very difficult to get
+
+ align:start position:0%
+fact is it's very very difficult to get
+ 
+
+ align:start position:0%
+fact is it's very very difficult to get
+product quality without good processes.
+
+ align:start position:0%
+product quality without good processes.
+ 
+
+ align:start position:0%
+product quality without good processes.
+We're going to talk about the some tools
+
+ align:start position:0%
+We're going to talk about the some tools
+ 
+
+ align:start position:0%
+We're going to talk about the some tools
+and these are tools that you may not
+
+ align:start position:0%
+and these are tools that you may not
+ 
+
+ align:start position:0%
+and these are tools that you may not
+have been exposed to before and we're
+
+ align:start position:0%
+have been exposed to before and we're
+ 
+
+ align:start position:0%
+have been exposed to before and we're
+going to talk about you remember in the
+
+ align:start position:0%
+going to talk about you remember in the
+ 
+
+ align:start position:0%
+going to talk about you remember in the
+beginning Earl mentioned the fact that
+
+ align:start position:0%
+beginning Earl mentioned the fact that
+ 
+
+ align:start position:0%
+beginning Earl mentioned the fact that
+we've got lean and then we've got six
+
+ align:start position:0%
+we've got lean and then we've got six
+ 
+
+ align:start position:0%
+we've got lean and then we've got six
+sigma and industry basically now is
+
+ align:start position:0%
+sigma and industry basically now is
+ 
+
+ align:start position:0%
+sigma and industry basically now is
+talking about lean six sigma and u we're
+
+ align:start position:0%
+talking about lean six sigma and u we're
+ 
+
+ align:start position:0%
+talking about lean six sigma and u we're
+trying to achieve the customer
+
+ align:start position:0%
+trying to achieve the customer
+ 
+
+ align:start position:0%
+trying to achieve the customer
+satisfaction you there are there are
+
+ align:start position:0%
+satisfaction you there are there are
+ 
+
+ align:start position:0%
+satisfaction you there are there are
+people that are consultants now that are
+
+ align:start position:0%
+people that are consultants now that are
+ 
+
+ align:start position:0%
+people that are consultants now that are
+making
+
+ align:start position:0%
+making
+ 
+
+ align:start position:0%
+making
+their livelihood about saying, "Use our
+
+ align:start position:0%
+their livelihood about saying, "Use our
+ 
+
+ align:start position:0%
+their livelihood about saying, "Use our
+process and we're going to get an
+
+ align:start position:0%
+process and we're going to get an
+ 
+
+ align:start position:0%
+process and we're going to get an
+overjoyed customer." You know, that that
+
+ align:start position:0%
+overjoyed customer." You know, that that
+ 
+
+ align:start position:0%
+overjoyed customer." You know, that that
+kind of stuff, you know, deliriously
+
+ align:start position:0%
+kind of stuff, you know, deliriously
+ 
+
+ align:start position:0%
+kind of stuff, you know, deliriously
+happy customer. Well, that's what we
+
+ align:start position:0%
+happy customer. Well, that's what we
+ 
+
+ align:start position:0%
+happy customer. Well, that's what we
+want, too. I heard someone mention,
+
+ align:start position:0%
+want, too. I heard someone mention,
+ 
+
+ align:start position:0%
+want, too. I heard someone mention,
+maybe it's Mark or somebody before
+
+ align:start position:0%
+maybe it's Mark or somebody before
+ 
+
+ align:start position:0%
+maybe it's Mark or somebody before
+talking about the iceberg effect. This
+
+ align:start position:0%
+talking about the iceberg effect. This
+ 
+
+ align:start position:0%
+talking about the iceberg effect. This
+is a typical typical um drawing now
+
+ align:start position:0%
+is a typical typical um drawing now
+ 
+
+ align:start position:0%
+is a typical typical um drawing now
+because this is classically, you know,
+
+ align:start position:0%
+because this is classically, you know,
+ 
+
+ align:start position:0%
+because this is classically, you know,
+the Titanic didn't see this to the end.
+
+ align:start position:0%
+the Titanic didn't see this to the end.
+ 
+
+ align:start position:0%
+the Titanic didn't see this to the end.
+The problem what sunk the sunk the ship
+
+ align:start position:0%
+The problem what sunk the sunk the ship
+ 
+
+ align:start position:0%
+The problem what sunk the sunk the ship
+was this big hunk of the iceberg that
+
+ align:start position:0%
+was this big hunk of the iceberg that
+ 
+
+ align:start position:0%
+was this big hunk of the iceberg that
+was below the water and uh the stuff
+
+ align:start position:0%
+was below the water and uh the stuff
+ 
+
+ align:start position:0%
+was below the water and uh the stuff
+that we can measure uh very readily is
+
+ align:start position:0%
+that we can measure uh very readily is
+ 
+
+ align:start position:0%
+that we can measure uh very readily is
+scrap and rework service calls
+
+ align:start position:0%
+scrap and rework service calls
+ 
+
+ align:start position:0%
+scrap and rework service calls
+warranties scrap and rework I mean
+
+ align:start position:0%
+warranties scrap and rework I mean
+ 
+
+ align:start position:0%
+warranties scrap and rework I mean
+typically you can have 10% scrap and 15%
+
+ align:start position:0%
+typically you can have 10% scrap and 15%
+ 
+
+ align:start position:0%
+typically you can have 10% scrap and 15%
+rework in the old days that's 25% of the
+
+ align:start position:0%
+rework in the old days that's 25% of the
+ 
+
+ align:start position:0%
+rework in the old days that's 25% of the
+product cost the reason that Detroit
+
+ align:start position:0%
+product cost the reason that Detroit
+ 
+
+ align:start position:0%
+product cost the reason that Detroit
+can't compete with you know Honda and
+
+ align:start position:0%
+can't compete with you know Honda and
+ 
+
+ align:start position:0%
+can't compete with you know Honda and
+Nissan and and and uh uh Toyota is the
+
+ align:start position:0%
+Nissan and and and uh uh Toyota is the
+ 
+
+ align:start position:0%
+Nissan and and and uh uh Toyota is the
+fact is that we've got very high rates
+
+ align:start position:0%
+fact is that we've got very high rates
+ 
+
+ align:start position:0%
+fact is that we've got very high rates
+of this in the US.
+
+ align:start position:0%
+of this in the US.
+ 
+
+ align:start position:0%
+of this in the US.
+And so they can get a 25% cost advantage
+
+ align:start position:0%
+And so they can get a 25% cost advantage
+ 
+
+ align:start position:0%
+And so they can get a 25% cost advantage
+just by getting perfect quality. You
+
+ align:start position:0%
+just by getting perfect quality. You
+ 
+
+ align:start position:0%
+just by getting perfect quality. You
+remember yesterday I said Lexus's next
+
+ align:start position:0%
+remember yesterday I said Lexus's next
+ 
+
+ align:start position:0%
+remember yesterday I said Lexus's next
+time you see the the Lexus logo or on
+
+ align:start position:0%
+time you see the the Lexus logo or on
+ 
+
+ align:start position:0%
+time you see the the Lexus logo or on
+advertising uh on the on TV and all that
+
+ align:start position:0%
+advertising uh on the on TV and all that
+ 
+
+ align:start position:0%
+advertising uh on the on TV and all that
+Lexus the relentless pursuit of
+
+ align:start position:0%
+Lexus the relentless pursuit of
+ 
+
+ align:start position:0%
+Lexus the relentless pursuit of
+perfection. That means getting rid of
+
+ align:start position:0%
+perfection. That means getting rid of
+ 
+
+ align:start position:0%
+perfection. That means getting rid of
+this stuff. And that's a roughly a 20
+
+ align:start position:0%
+this stuff. And that's a roughly a 20
+ 
+
+ align:start position:0%
+this stuff. And that's a roughly a 20
+25% cost advantage. And it helps us
+
+ align:start position:0%
+25% cost advantage. And it helps us
+ 
+
+ align:start position:0%
+25% cost advantage. And it helps us
+deliver a competitive product to our
+
+ align:start position:0%
+deliver a competitive product to our
+ 
+
+ align:start position:0%
+deliver a competitive product to our
+customers. Service calls, you know, that
+
+ align:start position:0%
+customers. Service calls, you know, that
+ 
+
+ align:start position:0%
+customers. Service calls, you know, that
+that's the may you know the old before
+
+ align:start position:0%
+that's the may you know the old before
+ 
+
+ align:start position:0%
+that's the may you know the old before
+your time, but in early days of
+
+ align:start position:0%
+your time, but in early days of
+ 
+
+ align:start position:0%
+your time, but in early days of
+television, there used to be an ad of a
+
+ align:start position:0%
+television, there used to be an ad of a
+ 
+
+ align:start position:0%
+television, there used to be an ad of a
+guy who just died recently, the May Tag
+
+ align:start position:0%
+guy who just died recently, the May Tag
+ 
+
+ align:start position:0%
+guy who just died recently, the May Tag
+repairmen, and he used to sit there and
+
+ align:start position:0%
+repairmen, and he used to sit there and
+ 
+
+ align:start position:0%
+repairmen, and he used to sit there and
+he was sitting there drinking drinking
+
+ align:start position:0%
+he was sitting there drinking drinking
+ 
+
+ align:start position:0%
+he was sitting there drinking drinking
+coffee and uh having a cigarette. And
+
+ align:start position:0%
+coffee and uh having a cigarette. And
+ 
+
+ align:start position:0%
+coffee and uh having a cigarette. And
+Mate used to say their quality was so
+
+ align:start position:0%
+Mate used to say their quality was so
+ 
+
+ align:start position:0%
+Mate used to say their quality was so
+good that our repairmen had nothing to
+
+ align:start position:0%
+good that our repairmen had nothing to
+ 
+
+ align:start position:0%
+good that our repairmen had nothing to
+do. Nobody ever called them because our
+
+ align:start position:0%
+do. Nobody ever called them because our
+ 
+
+ align:start position:0%
+do. Nobody ever called them because our
+washing machines and our dishwashers may
+
+ align:start position:0%
+washing machines and our dishwashers may
+ 
+
+ align:start position:0%
+washing machines and our dishwashers may
+tag is the quality. I mean that's a used
+
+ align:start position:0%
+tag is the quality. I mean that's a used
+ 
+
+ align:start position:0%
+tag is the quality. I mean that's a used
+to be a standard joke. But it turns out
+
+ align:start position:0%
+to be a standard joke. But it turns out
+ 
+
+ align:start position:0%
+to be a standard joke. But it turns out
+that that's what that a service call uh
+
+ align:start position:0%
+that that's what that a service call uh
+ 
+
+ align:start position:0%
+that that's what that a service call uh
+while on a brand new product, you know,
+
+ align:start position:0%
+while on a brand new product, you know,
+ 
+
+ align:start position:0%
+while on a brand new product, you know,
+uh is is waste and it makes unhappy
+
+ align:start position:0%
+uh is is waste and it makes unhappy
+ 
+
+ align:start position:0%
+uh is is waste and it makes unhappy
+customers because they're calling you
+
+ align:start position:0%
+customers because they're calling you
+ 
+
+ align:start position:0%
+customers because they're calling you
+because they have a problem.
+
+ align:start position:0%
+because they have a problem.
+ 
+
+ align:start position:0%
+because they have a problem.
+Typically, if it's under warranty, guess
+
+ align:start position:0%
+Typically, if it's under warranty, guess
+ 
+
+ align:start position:0%
+Typically, if it's under warranty, guess
+who pays for it? You know, we have to
+
+ align:start position:0%
+who pays for it? You know, we have to
+ 
+
+ align:start position:0%
+who pays for it? You know, we have to
+pay. So, we have to send somebody out to
+
+ align:start position:0%
+pay. So, we have to send somebody out to
+ 
+
+ align:start position:0%
+pay. So, we have to send somebody out to
+Fort Rucker to fix an Apache. It's on
+
+ align:start position:0%
+Fort Rucker to fix an Apache. It's on
+ 
+
+ align:start position:0%
+Fort Rucker to fix an Apache. It's on
+us. You know, that kind of stuff. So,
+
+ align:start position:0%
+us. You know, that kind of stuff. So,
+ 
+
+ align:start position:0%
+us. You know, that kind of stuff. So,
+that's not great. And then concessions.
+
+ align:start position:0%
+that's not great. And then concessions.
+ 
+
+ align:start position:0%
+that's not great. And then concessions.
+I mean, this is Boeing is going to wind
+
+ align:start position:0%
+I mean, this is Boeing is going to wind
+ 
+
+ align:start position:0%
+I mean, this is Boeing is going to wind
+up paying concessions to the airlines
+
+ align:start position:0%
+up paying concessions to the airlines
+ 
+
+ align:start position:0%
+up paying concessions to the airlines
+for being delivering late. Airbus is
+
+ align:start position:0%
+for being delivering late. Airbus is
+ 
+
+ align:start position:0%
+for being delivering late. Airbus is
+paying millions, hundreds of millions
+
+ align:start position:0%
+paying millions, hundreds of millions
+ 
+
+ align:start position:0%
+paying millions, hundreds of millions
+because the Airbus A380 is late. So, we
+
+ align:start position:0%
+because the Airbus A380 is late. So, we
+ 
+
+ align:start position:0%
+because the Airbus A380 is late. So, we
+don't, you know, and that's all poor
+
+ align:start position:0%
+don't, you know, and that's all poor
+ 
+
+ align:start position:0%
+don't, you know, and that's all poor
+quality.
+
+ align:start position:0%
+quality.
+ 
+
+ align:start position:0%
+quality.
+And then you've got excess inventory. I
+
+ align:start position:0%
+And then you've got excess inventory. I
+ 
+
+ align:start position:0%
+And then you've got excess inventory. I
+mean, we had a great example of that
+
+ align:start position:0%
+mean, we had a great example of that
+ 
+
+ align:start position:0%
+mean, we had a great example of that
+yesterday. You remember at the end of
+
+ align:start position:0%
+yesterday. You remember at the end of
+ 
+
+ align:start position:0%
+yesterday. You remember at the end of
+the round if you had it, you know, it
+
+ align:start position:0%
+the round if you had it, you know, it
+ 
+
+ align:start position:0%
+the round if you had it, you know, it
+comes off your bottom line. Overtime,
+
+ align:start position:0%
+comes off your bottom line. Overtime,
+ 
+
+ align:start position:0%
+comes off your bottom line. Overtime,
+boy. Oh, boy. I bet you they're spending
+
+ align:start position:0%
+boy. Oh, boy. I bet you they're spending
+ 
+
+ align:start position:0%
+boy. Oh, boy. I bet you they're spending
+millions in Seattle making sure the 787
+
+ align:start position:0%
+millions in Seattle making sure the 787
+ 
+
+ align:start position:0%
+millions in Seattle making sure the 787
+is delivered as fast as they can and
+
+ align:start position:0%
+is delivered as fast as they can and
+ 
+
+ align:start position:0%
+is delivered as fast as they can and
+those guys are working seven day weeks.
+
+ align:start position:0%
+those guys are working seven day weeks.
+ 
+
+ align:start position:0%
+those guys are working seven day weeks.
+Seven day weeks.
+
+ align:start position:0%
+Seven day weeks.
+ 
+
+ align:start position:0%
+Seven day weeks.
+Absolutely. Nonvalue added steps. We
+
+ align:start position:0%
+Absolutely. Nonvalue added steps. We
+ 
+
+ align:start position:0%
+Absolutely. Nonvalue added steps. We
+talked about that cues and delays. I
+
+ align:start position:0%
+talked about that cues and delays. I
+ 
+
+ align:start position:0%
+talked about that cues and delays. I
+told you that classically everybody has
+
+ align:start position:0%
+told you that classically everybody has
+ 
+
+ align:start position:0%
+told you that classically everybody has
+tattooed on their arm. The biggest waste
+
+ align:start position:0%
+tattooed on their arm. The biggest waste
+ 
+
+ align:start position:0%
+tattooed on their arm. The biggest waste
+are move and queue. Moving stuff between
+
+ align:start position:0%
+are move and queue. Moving stuff between
+ 
+
+ align:start position:0%
+are move and queue. Moving stuff between
+machines and all that. You don't have to
+
+ align:start position:0%
+machines and all that. You don't have to
+ 
+
+ align:start position:0%
+machines and all that. You don't have to
+remember the the in in the athletic shoe
+
+ align:start position:0%
+remember the the in in the athletic shoe
+ 
+
+ align:start position:0%
+remember the the in in the athletic shoe
+department, the ladies were just moving
+
+ align:start position:0%
+department, the ladies were just moving
+ 
+
+ align:start position:0%
+department, the ladies were just moving
+that stuff between each other, you know,
+
+ align:start position:0%
+that stuff between each other, you know,
+ 
+
+ align:start position:0%
+that stuff between each other, you know,
+on on the production line there.
+
+ align:start position:0%
+on on the production line there.
+ 
+
+ align:start position:0%
+on on the production line there.
+One of the issues that came with the
+
+ align:start position:0%
+One of the issues that came with the
+ 
+
+ align:start position:0%
+One of the issues that came with the
+industrial revolution that I showed you
+
+ align:start position:0%
+industrial revolution that I showed you
+ 
+
+ align:start position:0%
+industrial revolution that I showed you
+on my very first chart um a couple of
+
+ align:start position:0%
+on my very first chart um a couple of
+ 
+
+ align:start position:0%
+on my very first chart um a couple of
+days ago was the fact is that that we
+
+ align:start position:0%
+days ago was the fact is that that we
+ 
+
+ align:start position:0%
+days ago was the fact is that that we
+went from the craft the master jeweler
+
+ align:start position:0%
+went from the craft the master jeweler
+ 
+
+ align:start position:0%
+went from the craft the master jeweler
+making the that he knew exactly how to
+
+ align:start position:0%
+making the that he knew exactly how to
+ 
+
+ align:start position:0%
+making the that he knew exactly how to
+build that watch to the mass production
+
+ align:start position:0%
+build that watch to the mass production
+ 
+
+ align:start position:0%
+build that watch to the mass production
+system Henry Ford and is the best
+
+ align:start position:0%
+system Henry Ford and is the best
+ 
+
+ align:start position:0%
+system Henry Ford and is the best
+example of it but other people did that
+
+ align:start position:0%
+example of it but other people did that
+ 
+
+ align:start position:0%
+example of it but other people did that
+where in fact we built something and
+
+ align:start position:0%
+where in fact we built something and
+ 
+
+ align:start position:0%
+where in fact we built something and
+then inspected it. The problem with that
+
+ align:start position:0%
+then inspected it. The problem with that
+ 
+
+ align:start position:0%
+then inspected it. The problem with that
+is the fact is that it's difficult.
+
+ align:start position:0%
+is the fact is that it's difficult.
+ 
+
+ align:start position:0%
+is the fact is that it's difficult.
+Inspection is subject to errors. How
+
+ align:start position:0%
+Inspection is subject to errors. How
+ 
+
+ align:start position:0%
+Inspection is subject to errors. How
+well trained is the inspection? How good
+
+ align:start position:0%
+well trained is the inspection? How good
+ 
+
+ align:start position:0%
+well trained is the inspection? How good
+is his inspection equipment? Um his
+
+ align:start position:0%
+is his inspection equipment? Um his
+ 
+
+ align:start position:0%
+is his inspection equipment? Um his
+measurement capability and then um you
+
+ align:start position:0%
+measurement capability and then um you
+ 
+
+ align:start position:0%
+measurement capability and then um you
+know is it you know is it a Monday
+
+ align:start position:0%
+know is it you know is it a Monday
+ 
+
+ align:start position:0%
+know is it you know is it a Monday
+morning and he had a tough weekend after
+
+ align:start position:0%
+morning and he had a tough weekend after
+ 
+
+ align:start position:0%
+morning and he had a tough weekend after
+a Super Bowl party? You know that kind
+
+ align:start position:0%
+a Super Bowl party? You know that kind
+ 
+
+ align:start position:0%
+a Super Bowl party? You know that kind
+of stuff. here. Uh, in your packet,
+
+ align:start position:0%
+of stuff. here. Uh, in your packet,
+ 
+
+ align:start position:0%
+of stuff. here. Uh, in your packet,
+there's a thing called F exercise.
+
+ align:start position:0%
+there's a thing called F exercise.
+ 
+
+ align:start position:0%
+there's a thing called F exercise.
+Everybody got Okay, great. Thanks. All
+
+ align:start position:0%
+Everybody got Okay, great. Thanks. All
+ 
+
+ align:start position:0%
+Everybody got Okay, great. Thanks. All
+right. What we're going to do, what
+
+ align:start position:0%
+right. What we're going to do, what
+ 
+
+ align:start position:0%
+right. What we're going to do, what
+we're going to do, let me just see if I
+
+ align:start position:0%
+we're going to do, let me just see if I
+ 
+
+ align:start position:0%
+we're going to do, let me just see if I
+can get
+
+ align:start position:0%
+can get
+ 
+
+ align:start position:0%
+can get
+We're going to time this exercise. We're
+
+ align:start position:0%
+We're going to time this exercise. We're
+ 
+
+ align:start position:0%
+We're going to time this exercise. We're
+big on stopwatches around here. Okay.
+
+ align:start position:0%
+big on stopwatches around here. Okay.
+ 
+
+ align:start position:0%
+big on stopwatches around here. Okay.
+And what I want you to do is to circle
+
+ align:start position:0%
+And what I want you to do is to circle
+ 
+
+ align:start position:0%
+And what I want you to do is to circle
+all the Fs. Look up here. The Fs or the
+
+ align:start position:0%
+all the Fs. Look up here. The Fs or the
+ 
+
+ align:start position:0%
+all the Fs. Look up here. The Fs or the
+capital Fs, okay? On the page. We're
+
+ align:start position:0%
+capital Fs, okay? On the page. We're
+ 
+
+ align:start position:0%
+capital Fs, okay? On the page. We're
+going to give you 30 seconds. And what
+
+ align:start position:0%
+going to give you 30 seconds. And what
+ 
+
+ align:start position:0%
+going to give you 30 seconds. And what
+we want you to do is to circle circle
+
+ align:start position:0%
+we want you to do is to circle circle
+ 
+
+ align:start position:0%
+we want you to do is to circle circle
+all those Fs and then count them, okay?
+
+ align:start position:0%
+all those Fs and then count them, okay?
+ 
+
+ align:start position:0%
+all those Fs and then count them, okay?
+And tell me how many how many that you
+
+ align:start position:0%
+And tell me how many how many that you
+ 
+
+ align:start position:0%
+And tell me how many how many that you
+found, okay? And uh when I say go, uh
+
+ align:start position:0%
+found, okay? And uh when I say go, uh
+ 
+
+ align:start position:0%
+found, okay? And uh when I say go, uh
+ready, set, go.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Stop. Stop. Okay. All right. Um 13 to
+
+ align:start position:0%
+Stop. Stop. Okay. All right. Um 13 to
+ 
+
+ align:start position:0%
+Stop. Stop. Okay. All right. Um 13 to
+17. Yes.
+
+ align:start position:0%
+17. Yes.
+ 
+
+ align:start position:0%
+17. Yes.
+Nobody was 13 or 17. Again, this is not
+
+ align:start position:0%
+Nobody was 13 or 17. Again, this is not
+ 
+
+ align:start position:0%
+Nobody was 13 or 17. Again, this is not
+a test. Low numbers are part of the data
+
+ align:start position:0%
+a test. Low numbers are part of the data
+ 
+
+ align:start position:0%
+a test. Low numbers are part of the data
+collection process. 18 to 22. 18 to 22.
+
+ align:start position:0%
+collection process. 18 to 22. 18 to 22.
+ 
+
+ align:start position:0%
+collection process. 18 to 22. 18 to 22.
+One, two, three, four, four. Um,
+
+ align:start position:0%
+One, two, three, four, four. Um,
+ 
+
+ align:start position:0%
+One, two, three, four, four. Um,
+right there. There we go. Um, oh, do a
+
+ align:start position:0%
+right there. There we go. Um, oh, do a
+ 
+
+ align:start position:0%
+right there. There we go. Um, oh, do a
+bar, please. A bar. Yeah,
+
+ align:start position:0%
+bar, please. A bar. Yeah,
+ 
+
+ align:start position:0%
+bar, please. A bar. Yeah,
+um, 23 to 27.
+
+ align:start position:0%
+um, 23 to 27.
+ 
+
+ align:start position:0%
+um, 23 to 27.
+Whoa, lots of those. 1, two, three,
+
+ align:start position:0%
+Whoa, lots of those. 1, two, three,
+ 
+
+ align:start position:0%
+Whoa, lots of those. 1, two, three,
+four, five, six, seven, eight, 9, 10,
+
+ align:start position:0%
+four, five, six, seven, eight, 9, 10,
+ 
+
+ align:start position:0%
+four, five, six, seven, eight, 9, 10,
+11, 12, 13, 14, 15. My count's 15.
+
+ align:start position:0%
+11, 12, 13, 14, 15. My count's 15.
+ 
+
+ align:start position:0%
+11, 12, 13, 14, 15. My count's 15.
+15. Okay, that's off the chart. It's up
+
+ align:start position:0%
+15. Okay, that's off the chart. It's up
+ 
+
+ align:start position:0%
+15. Okay, that's off the chart. It's up
+here somewhere. Okay, 15 folks in that
+
+ align:start position:0%
+here somewhere. Okay, 15 folks in that
+ 
+
+ align:start position:0%
+here somewhere. Okay, 15 folks in that
+box.
+
+ align:start position:0%
+box.
+ 
+
+ align:start position:0%
+box.
+All righty. Um, 28 to 32. 28 to 32. One,
+
+ align:start position:0%
+All righty. Um, 28 to 32. 28 to 32. One,
+ 
+
+ align:start position:0%
+All righty. Um, 28 to 32. 28 to 32. One,
+two, three. All right, looks like we
+
+ align:start position:0%
+two, three. All right, looks like we
+ 
+
+ align:start position:0%
+two, three. All right, looks like we
+found our uh looks like we found our
+
+ align:start position:0%
+found our uh looks like we found our
+ 
+
+ align:start position:0%
+found our uh looks like we found our
+peak here.
+
+ align:start position:0%
+peak here.
+ 
+
+ align:start position:0%
+peak here.
+See, that first one was four. So, this
+
+ align:start position:0%
+See, that first one was four. So, this
+ 
+
+ align:start position:0%
+See, that first one was four. So, this
+was three. Lower.
+
+ align:start position:0%
+was three. Lower.
+ 
+
+ align:start position:0%
+was three. Lower.
+Higher. Um, there we go.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And anybody get more than 33 or more? 33
+
+ align:start position:0%
+And anybody get more than 33 or more? 33
+ 
+
+ align:start position:0%
+And anybody get more than 33 or more? 33
+or more? Nobody got 33 or more. I just
+
+ align:start position:0%
+or more? Nobody got 33 or more. I just
+ 
+
+ align:start position:0%
+or more? Nobody got 33 or more. I just
+went to get a calculator. You guys made
+
+ align:start position:0%
+went to get a calculator. You guys made
+ 
+
+ align:start position:0%
+went to get a calculator. You guys made
+my job easy. Well, let me show you.
+
+ align:start position:0%
+my job easy. Well, let me show you.
+ 
+
+ align:start position:0%
+my job easy. Well, let me show you.
+There they are. Do you know how many Fs
+
+ align:start position:0%
+There they are. Do you know how many Fs
+ 
+
+ align:start position:0%
+There they are. Do you know how many Fs
+there are?
+
+ align:start position:0%
+there are?
+ 
+
+ align:start position:0%
+there are?
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+36 Now the issue is the issue is that I
+
+ align:start position:0%
+36 Now the issue is the issue is that I
+ 
+
+ align:start position:0%
+36 Now the issue is the issue is that I
+mean I was going to calculate what
+
+ align:start position:0%
+mean I was going to calculate what
+ 
+
+ align:start position:0%
+mean I was going to calculate what
+percent of the class got the answer
+
+ align:start position:0%
+percent of the class got the answer
+ 
+
+ align:start position:0%
+percent of the class got the answer
+right or what percent of the class got
+
+ align:start position:0%
+right or what percent of the class got
+ 
+
+ align:start position:0%
+right or what percent of the class got
+that we now have a 100% of the class
+
+ align:start position:0%
+that we now have a 100% of the class
+ 
+
+ align:start position:0%
+that we now have a 100% of the class
+that got it wrong and the point is that
+
+ align:start position:0%
+that got it wrong and the point is that
+ 
+
+ align:start position:0%
+that got it wrong and the point is that
+all of
+
+ align:start position:0%
+all of
+ 
+
+ align:start position:0%
+all of
+you know all of this this area is I mean
+
+ align:start position:0%
+you know all of this this area is I mean
+ 
+
+ align:start position:0%
+you know all of this this area is I mean
+the the ones that we've missed are what
+
+ align:start position:0%
+the the ones that we've missed are what
+ 
+
+ align:start position:0%
+the the ones that we've missed are what
+we call in the business escapement ments
+
+ align:start position:0%
+we call in the business escapement ments
+ 
+
+ align:start position:0%
+we call in the business escapement ments
+escapements and it's a quality
+
+ align:start position:0%
+escapements and it's a quality
+ 
+
+ align:start position:0%
+escapements and it's a quality
+escapement. What does that mean? The
+
+ align:start position:0%
+escapement. What does that mean? The
+ 
+
+ align:start position:0%
+escapement. What does that mean? The
+whatever process that we put in place uh
+
+ align:start position:0%
+whatever process that we put in place uh
+ 
+
+ align:start position:0%
+whatever process that we put in place uh
+didn't catch the defect. Didn't catch
+
+ align:start position:0%
+didn't catch the defect. Didn't catch
+ 
+
+ align:start position:0%
+didn't catch the defect. Didn't catch
+the defect. I was at Mesa last week. I
+
+ align:start position:0%
+the defect. I was at Mesa last week. I
+ 
+
+ align:start position:0%
+the defect. I was at Mesa last week. I
+told you on this Ruden exercise and
+
+ align:start position:0%
+told you on this Ruden exercise and
+ 
+
+ align:start position:0%
+told you on this Ruden exercise and
+we're looking for voids using ultrasonic
+
+ align:start position:0%
+we're looking for voids using ultrasonic
+ 
+
+ align:start position:0%
+we're looking for voids using ultrasonic
+thermography and X-rays to catch voids
+
+ align:start position:0%
+thermography and X-rays to catch voids
+ 
+
+ align:start position:0%
+thermography and X-rays to catch voids
+in the Apache Attack helicopter block 3
+
+ align:start position:0%
+in the Apache Attack helicopter block 3
+ 
+
+ align:start position:0%
+in the Apache Attack helicopter block 3
+improved aerodynamic rolblade. And the
+
+ align:start position:0%
+improved aerodynamic rolblade. And the
+ 
+
+ align:start position:0%
+improved aerodynamic rolblade. And the
+point is that we want a foolproof system
+
+ align:start position:0%
+point is that we want a foolproof system
+ 
+
+ align:start position:0%
+point is that we want a foolproof system
+to catch the errors. Why? Because in
+
+ align:start position:0%
+to catch the errors. Why? Because in
+ 
+
+ align:start position:0%
+to catch the errors. Why? Because in
+fact it won't, you know, it'll fatigue
+
+ align:start position:0%
+fact it won't, you know, it'll fatigue
+ 
+
+ align:start position:0%
+fact it won't, you know, it'll fatigue
+and you know we'll we'll kill a couple
+
+ align:start position:0%
+and you know we'll we'll kill a couple
+ 
+
+ align:start position:0%
+and you know we'll we'll kill a couple
+pilot a pilot and a co-pilot gunner
+
+ align:start position:0%
+pilot a pilot and a co-pilot gunner
+ 
+
+ align:start position:0%
+pilot a pilot and a co-pilot gunner
+can't do that. So we have to be good.
+
+ align:start position:0%
+can't do that. So we have to be good.
+ 
+
+ align:start position:0%
+can't do that. So we have to be good.
+Now the issue is that inspection
+
+ align:start position:0%
+Now the issue is that inspection
+ 
+
+ align:start position:0%
+Now the issue is that inspection
+inspection is costly and inspection is
+
+ align:start position:0%
+inspection is costly and inspection is
+ 
+
+ align:start position:0%
+inspection is costly and inspection is
+costly and in fact the the what has come
+
+ align:start position:0%
+costly and in fact the the what has come
+ 
+
+ align:start position:0%
+costly and in fact the the what has come
+out of the the the systems and all of
+
+ align:start position:0%
+out of the the the systems and all of
+ 
+
+ align:start position:0%
+out of the the the systems and all of
+our knowledge and experience now is that
+
+ align:start position:0%
+our knowledge and experience now is that
+ 
+
+ align:start position:0%
+our knowledge and experience now is that
+you cannot inspect listen to this now
+
+ align:start position:0%
+you cannot inspect listen to this now
+ 
+
+ align:start position:0%
+you cannot inspect listen to this now
+you cannot inspect quality into the
+
+ align:start position:0%
+you cannot inspect quality into the
+ 
+
+ align:start position:0%
+you cannot inspect quality into the
+product. You can't inspect it because
+
+ align:start position:0%
+product. You can't inspect it because
+ 
+
+ align:start position:0%
+product. You can't inspect it because
+even as we improve our inspection
+
+ align:start position:0%
+even as we improve our inspection
+ 
+
+ align:start position:0%
+even as we improve our inspection
+techniques you're going to miss
+
+ align:start position:0%
+techniques you're going to miss
+ 
+
+ align:start position:0%
+techniques you're going to miss
+something. And so all the things that
+
+ align:start position:0%
+something. And so all the things that
+ 
+
+ align:start position:0%
+something. And so all the things that
+we're trying to do in lean are to in
+
+ align:start position:0%
+we're trying to do in lean are to in
+ 
+
+ align:start position:0%
+we're trying to do in lean are to in
+fact foolproof Murphy proof the system
+
+ align:start position:0%
+fact foolproof Murphy proof the system
+ 
+
+ align:start position:0%
+fact foolproof Murphy proof the system
+so that the tools the design
+
+ align:start position:0%
+so that the tools the design
+ 
+
+ align:start position:0%
+so that the tools the design
+uh and the individual operators
+
+ align:start position:0%
+uh and the individual operators
+ 
+
+ align:start position:0%
+uh and the individual operators
+proficiency you remember I keep on
+
+ align:start position:0%
+proficiency you remember I keep on
+ 
+
+ align:start position:0%
+proficiency you remember I keep on
+saying that the the expert in the system
+
+ align:start position:0%
+saying that the the expert in the system
+ 
+
+ align:start position:0%
+saying that the the expert in the system
+is the person the guy or the gal that
+
+ align:start position:0%
+is the person the guy or the gal that
+ 
+
+ align:start position:0%
+is the person the guy or the gal that
+does the job every day. They know what's
+
+ align:start position:0%
+does the job every day. They know what's
+ 
+
+ align:start position:0%
+does the job every day. They know what's
+wrong and they can stop it and they have
+
+ align:start position:0%
+wrong and they can stop it and they have
+ 
+
+ align:start position:0%
+wrong and they can stop it and they have
+to stop it. If the if the workforce is
+
+ align:start position:0%
+to stop it. If the if the workforce is
+ 
+
+ align:start position:0%
+to stop it. If the if the workforce is
+not motivated and not trained, it's very
+
+ align:start position:0%
+not motivated and not trained, it's very
+ 
+
+ align:start position:0%
+not motivated and not trained, it's very
+very difficult. But we try upstream, you
+
+ align:start position:0%
+very difficult. But we try upstream, you
+ 
+
+ align:start position:0%
+very difficult. But we try upstream, you
+know, the smart engineers, the smart
+
+ align:start position:0%
+know, the smart engineers, the smart
+ 
+
+ align:start position:0%
+know, the smart engineers, the smart
+quality engineers that design the
+
+ align:start position:0%
+quality engineers that design the
+ 
+
+ align:start position:0%
+quality engineers that design the
+process system is to in fact make it so
+
+ align:start position:0%
+process system is to in fact make it so
+ 
+
+ align:start position:0%
+process system is to in fact make it so
+that we can't make a mistake. Earl
+
+ align:start position:0%
+that we can't make a mistake. Earl
+ 
+
+ align:start position:0%
+that we can't make a mistake. Earl
+showed you a chart the other day, the
+
+ align:start position:0%
+showed you a chart the other day, the
+ 
+
+ align:start position:0%
+showed you a chart the other day, the
+one that had the elephant on it. And
+
+ align:start position:0%
+one that had the elephant on it. And
+ 
+
+ align:start position:0%
+one that had the elephant on it. And
+then right after that, we we showed the
+
+ align:start position:0%
+then right after that, we we showed the
+ 
+
+ align:start position:0%
+then right after that, we we showed the
+ones where the the pieces cannot be
+
+ align:start position:0%
+ones where the the pieces cannot be
+ 
+
+ align:start position:0%
+ones where the the pieces cannot be
+installed incorrectly. And we use all
+
+ align:start position:0%
+installed incorrectly. And we use all
+ 
+
+ align:start position:0%
+installed incorrectly. And we use all
+sorts of techniques like, you know, an
+
+ align:start position:0%
+sorts of techniques like, you know, an
+ 
+
+ align:start position:0%
+sorts of techniques like, you know, an
+electrical, you know, a yellow wire with
+
+ align:start position:0%
+electrical, you know, a yellow wire with
+ 
+
+ align:start position:0%
+electrical, you know, a yellow wire with
+a yellow plug and we put it on like that
+
+ align:start position:0%
+a yellow plug and we put it on like that
+ 
+
+ align:start position:0%
+a yellow plug and we put it on like that
+or we we use a a great big fat lug and a
+
+ align:start position:0%
+or we we use a a great big fat lug and a
+ 
+
+ align:start position:0%
+or we we use a a great big fat lug and a
+big fat wire to fit on that lug and it
+
+ align:start position:0%
+big fat wire to fit on that lug and it
+ 
+
+ align:start position:0%
+big fat wire to fit on that lug and it
+the it won't fit on the other ones. We
+
+ align:start position:0%
+the it won't fit on the other ones. We
+ 
+
+ align:start position:0%
+the it won't fit on the other ones. We
+try to take all opportunities
+
+ align:start position:0%
+try to take all opportunities
+ 
+
+ align:start position:0%
+try to take all opportunities
+opportunities for errors out of the
+
+ align:start position:0%
+opportunities for errors out of the
+ 
+
+ align:start position:0%
+opportunities for errors out of the
+system.
+
+ align:start position:0%
+system.
+ 
+
+ align:start position:0%
+system.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+anyway, we'll talk more about that.
+
+ align:start position:0%
+anyway, we'll talk more about that.
+ 
+
+ align:start position:0%
+anyway, we'll talk more about that.
+Terrific.
+
+ align:start position:0%
+Terrific.
+ 
+
+ align:start position:0%
+Terrific.
+Okay. Now, here's an interesting thing.
+
+ align:start position:0%
+Okay. Now, here's an interesting thing.
+ 
+
+ align:start position:0%
+Okay. Now, here's an interesting thing.
+Inspection and quality typically are 10%
+
+ align:start position:0%
+Inspection and quality typically are 10%
+ 
+
+ align:start position:0%
+Inspection and quality typically are 10%
+of the cost. I mean, we try to get it
+
+ align:start position:0%
+of the cost. I mean, we try to get it
+ 
+
+ align:start position:0%
+of the cost. I mean, we try to get it
+down to 10% of the cost and try to do
+
+ align:start position:0%
+down to 10% of the cost and try to do
+ 
+
+ align:start position:0%
+down to 10% of the cost and try to do
+better than that. So, quality is an
+
+ align:start position:0%
+better than that. So, quality is an
+ 
+
+ align:start position:0%
+better than that. So, quality is an
+expensive part of it. You remember I
+
+ align:start position:0%
+expensive part of it. You remember I
+ 
+
+ align:start position:0%
+expensive part of it. You remember I
+said scrap and we were could be 25%.
+
+ align:start position:0%
+said scrap and we were could be 25%.
+ 
+
+ align:start position:0%
+said scrap and we were could be 25%.
+We're trying to get that down to zero.
+
+ align:start position:0%
+We're trying to get that down to zero.
+ 
+
+ align:start position:0%
+We're trying to get that down to zero.
+We're trying to get our quality perfect.
+
+ align:start position:0%
+We're trying to get our quality perfect.
+ 
+
+ align:start position:0%
+We're trying to get our quality perfect.
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+it turns out that inspector efficiency
+
+ align:start position:0%
+it turns out that inspector efficiency
+ 
+
+ align:start position:0%
+it turns out that inspector efficiency
+if you look this way you know I was
+
+ align:start position:0%
+if you look this way you know I was
+ 
+
+ align:start position:0%
+if you look this way you know I was
+going to calculate your efficiency and
+
+ align:start position:0%
+going to calculate your efficiency and
+ 
+
+ align:start position:0%
+going to calculate your efficiency and
+say well we well actually if you do it
+
+ align:start position:0%
+say well we well actually if you do it
+ 
+
+ align:start position:0%
+say well we well actually if you do it
+by by f it's about 70%. Yeah probably
+
+ align:start position:0%
+by by f it's about 70%. Yeah probably
+ 
+
+ align:start position:0%
+by by f it's about 70%. Yeah probably
+about 70%. Yeah which is this red.
+
+ align:start position:0%
+about 70%. Yeah which is this red.
+ 
+
+ align:start position:0%
+about 70%. Yeah which is this red.
+So it turns out that it turns out that
+
+ align:start position:0%
+So it turns out that it turns out that
+ 
+
+ align:start position:0%
+So it turns out that it turns out that
+the name of the you know some people say
+
+ align:start position:0%
+the name of the you know some people say
+ 
+
+ align:start position:0%
+the name of the you know some people say
+well the quality is bad add more
+
+ align:start position:0%
+well the quality is bad add more
+ 
+
+ align:start position:0%
+well the quality is bad add more
+inspectors add more inspectors you know
+
+ align:start position:0%
+inspectors add more inspectors you know
+ 
+
+ align:start position:0%
+inspectors add more inspectors you know
+wrong. Okay I mean yeah you can in fact
+
+ align:start position:0%
+wrong. Okay I mean yeah you can in fact
+ 
+
+ align:start position:0%
+wrong. Okay I mean yeah you can in fact
+add
+
+ align:start position:0%
+add
+ 
+
+ align:start position:0%
+add
+multiple inspections or multiple
+
+ align:start position:0%
+multiple inspections or multiple
+ 
+
+ align:start position:0%
+multiple inspections or multiple
+inspectors to the to the point if we can
+
+ align:start position:0%
+inspectors to the to the point if we can
+ 
+
+ align:start position:0%
+inspectors to the to the point if we can
+get six sigma with 11 of these people in
+
+ align:start position:0%
+get six sigma with 11 of these people in
+ 
+
+ align:start position:0%
+get six sigma with 11 of these people in
+a row. Yeah but that is not 10% quality.
+
+ align:start position:0%
+a row. Yeah but that is not 10% quality.
+ 
+
+ align:start position:0%
+a row. Yeah but that is not 10% quality.
+You see the problem is that you can't
+
+ align:start position:0%
+You see the problem is that you can't
+ 
+
+ align:start position:0%
+You see the problem is that you can't
+you can't be competitive with very high
+
+ align:start position:0%
+you can't be competitive with very high
+ 
+
+ align:start position:0%
+you can't be competitive with very high
+amount. These are the escapements and
+
+ align:start position:0%
+amount. These are the escapements and
+ 
+
+ align:start position:0%
+amount. These are the escapements and
+and this is a new term maybe for you
+
+ align:start position:0%
+and this is a new term maybe for you
+ 
+
+ align:start position:0%
+and this is a new term maybe for you
+defects per million uh that is a
+
+ align:start position:0%
+defects per million uh that is a
+ 
+
+ align:start position:0%
+defects per million uh that is a
+technique for you know that is is used
+
+ align:start position:0%
+technique for you know that is is used
+ 
+
+ align:start position:0%
+technique for you know that is is used
+as a as a a parameter but the point is
+
+ align:start position:0%
+as a as a a parameter but the point is
+ 
+
+ align:start position:0%
+as a as a a parameter but the point is
+as you try to strive for perfection
+
+ align:start position:0%
+as you try to strive for perfection
+ 
+
+ align:start position:0%
+as you try to strive for perfection
+you're adding more and more quality
+
+ align:start position:0%
+you're adding more and more quality
+ 
+
+ align:start position:0%
+you're adding more and more quality
+personnel and it's the wrong way to go.
+
+ align:start position:0%
+personnel and it's the wrong way to go.
+ 
+
+ align:start position:0%
+personnel and it's the wrong way to go.
+We don't want to do that. We want to be
+
+ align:start position:0%
+We don't want to do that. We want to be
+ 
+
+ align:start position:0%
+We don't want to do that. We want to be
+able to make our inspection processes.
+
+ align:start position:0%
+able to make our inspection processes.
+ 
+
+ align:start position:0%
+able to make our inspection processes.
+And so this issue I was talking about
+
+ align:start position:0%
+And so this issue I was talking about
+ 
+
+ align:start position:0%
+And so this issue I was talking about
+yesterday or just before we were using a
+
+ align:start position:0%
+yesterday or just before we were using a
+ 
+
+ align:start position:0%
+yesterday or just before we were using a
+artificial intelligence system
+
+ align:start position:0%
+artificial intelligence system
+ 
+
+ align:start position:0%
+artificial intelligence system
+artificial intelligence system which in
+
+ align:start position:0%
+artificial intelligence system which in
+ 
+
+ align:start position:0%
+artificial intelligence system which in
+a new technique called thermography
+
+ align:start position:0%
+a new technique called thermography
+ 
+
+ align:start position:0%
+a new technique called thermography
+which was in fact scanning scanning the
+
+ align:start position:0%
+which was in fact scanning scanning the
+ 
+
+ align:start position:0%
+which was in fact scanning scanning the
+rotolades for voids and defects by using
+
+ align:start position:0%
+rotolades for voids and defects by using
+ 
+
+ align:start position:0%
+rotolades for voids and defects by using
+a bright strobe light that in fact
+
+ align:start position:0%
+a bright strobe light that in fact
+ 
+
+ align:start position:0%
+a bright strobe light that in fact
+created a slight amount of heat on the
+
+ align:start position:0%
+created a slight amount of heat on the
+ 
+
+ align:start position:0%
+created a slight amount of heat on the
+surface of the part. So that if there
+
+ align:start position:0%
+surface of the part. So that if there
+ 
+
+ align:start position:0%
+surface of the part. So that if there
+was a void, there would be a a delta t
+
+ align:start position:0%
+was a void, there would be a a delta t
+ 
+
+ align:start position:0%
+was a void, there would be a a delta t
+where the void was compared to the the
+
+ align:start position:0%
+where the void was compared to the the
+ 
+
+ align:start position:0%
+where the void was compared to the the
+basic rotor blade and that it took a a
+
+ align:start position:0%
+basic rotor blade and that it took a a
+ 
+
+ align:start position:0%
+basic rotor blade and that it took a a
+thermog a a infrared picture of that and
+
+ align:start position:0%
+thermog a a infrared picture of that and
+ 
+
+ align:start position:0%
+thermog a a infrared picture of that and
+we could detect the voids and we were
+
+ align:start position:0%
+we could detect the voids and we were
+ 
+
+ align:start position:0%
+we could detect the voids and we were
+developing software to be able to read
+
+ align:start position:0%
+developing software to be able to read
+ 
+
+ align:start position:0%
+developing software to be able to read
+that and say that void does not meet our
+
+ align:start position:0%
+that and say that void does not meet our
+ 
+
+ align:start position:0%
+that and say that void does not meet our
+spec. it's greater than a quarter inch
+
+ align:start position:0%
+spec. it's greater than a quarter inch
+ 
+
+ align:start position:0%
+spec. it's greater than a quarter inch
+or something like that and whatever the
+
+ align:start position:0%
+or something like that and whatever the
+ 
+
+ align:start position:0%
+or something like that and whatever the
+we're going to talk about upper and
+
+ align:start position:0%
+we're going to talk about upper and
+ 
+
+ align:start position:0%
+we're going to talk about upper and
+lower control limits for those kinds of
+
+ align:start position:0%
+lower control limits for those kinds of
+ 
+
+ align:start position:0%
+lower control limits for those kinds of
+things but we would like to be able to
+
+ align:start position:0%
+things but we would like to be able to
+ 
+
+ align:start position:0%
+things but we would like to be able to
+automate it because we can't depend on
+
+ align:start position:0%
+automate it because we can't depend on
+ 
+
+ align:start position:0%
+automate it because we can't depend on
+people pure inspection to do that. So
+
+ align:start position:0%
+people pure inspection to do that. So
+ 
+
+ align:start position:0%
+people pure inspection to do that. So
+this is this is tough stuff. Tough stuff
+
+ align:start position:0%
+this is this is tough stuff. Tough stuff
+ 
+
+ align:start position:0%
+this is this is tough stuff. Tough stuff
+when we're making very complex products
+
+ align:start position:0%
+when we're making very complex products
+ 
+
+ align:start position:0%
+when we're making very complex products
+that you folks are going to be working
+
+ align:start position:0%
+that you folks are going to be working
+ 
+
+ align:start position:0%
+that you folks are going to be working
+on whether it's you know computers or
+
+ align:start position:0%
+on whether it's you know computers or
+ 
+
+ align:start position:0%
+on whether it's you know computers or
+automobiles or airplanes or rockets or
+
+ align:start position:0%
+automobiles or airplanes or rockets or
+ 
+
+ align:start position:0%
+automobiles or airplanes or rockets or
+spacecraft. Diamond this stuff is tough.
+
+ align:start position:0%
+spacecraft. Diamond this stuff is tough.
+ 
+
+ align:start position:0%
+spacecraft. Diamond this stuff is tough.
+We talk about NASA talks about man-
+
+ align:start position:0%
+We talk about NASA talks about man-
+ 
+
+ align:start position:0%
+We talk about NASA talks about man-
+rated that means you know somebody's
+
+ align:start position:0%
+rated that means you know somebody's
+ 
+
+ align:start position:0%
+rated that means you know somebody's
+life is at stake and um so we have to be
+
+ align:start position:0%
+life is at stake and um so we have to be
+ 
+
+ align:start position:0%
+life is at stake and um so we have to be
+good. Okay. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conformance to this to the spec and to
+
+ align:start position:0%
+conformance to this to the spec and to
+ 
+
+ align:start position:0%
+conformance to this to the spec and to
+our tolerance band for acceptable
+
+ align:start position:0%
+our tolerance band for acceptable
+ 
+
+ align:start position:0%
+our tolerance band for acceptable
+quality. Now, when I say acceptable
+
+ align:start position:0%
+quality. Now, when I say acceptable
+ 
+
+ align:start position:0%
+quality. Now, when I say acceptable
+quality, I'll tell you about a you know,
+
+ align:start position:0%
+quality, I'll tell you about a you know,
+ 
+
+ align:start position:0%
+quality, I'll tell you about a you know,
+we talk about machine parts plus or
+
+ align:start position:0%
+we talk about machine parts plus or
+ 
+
+ align:start position:0%
+we talk about machine parts plus or
+minus 15,000. That's a a normal kind of
+
+ align:start position:0%
+minus 15,000. That's a a normal kind of
+ 
+
+ align:start position:0%
+minus 15,000. That's a a normal kind of
+a a tolerance band. And uh and we're
+
+ align:start position:0%
+a a tolerance band. And uh and we're
+ 
+
+ align:start position:0%
+a a tolerance band. And uh and we're
+going to talk about process capability
+
+ align:start position:0%
+going to talk about process capability
+ 
+
+ align:start position:0%
+going to talk about process capability
+here pretty soon. And uh but sometimes
+
+ align:start position:0%
+here pretty soon. And uh but sometimes
+ 
+
+ align:start position:0%
+here pretty soon. And uh but sometimes
+the processes are are very very smaller
+
+ align:start position:0%
+the processes are are very very smaller
+ 
+
+ align:start position:0%
+the processes are are very very smaller
+than that. I used to make 60 M242 guns a
+
+ align:start position:0%
+than that. I used to make 60 M242 guns a
+ 
+
+ align:start position:0%
+than that. I used to make 60 M242 guns a
+month for the for the Bradley fighting
+
+ align:start position:0%
+month for the for the Bradley fighting
+ 
+
+ align:start position:0%
+month for the for the Bradley fighting
+vehicle for the uh M242 chain gun. The
+
+ align:start position:0%
+vehicle for the uh M242 chain gun. The
+ 
+
+ align:start position:0%
+vehicle for the uh M242 chain gun. The
+chain gun fired 600 rounds a minute, 10
+
+ align:start position:0%
+chain gun fired 600 rounds a minute, 10
+ 
+
+ align:start position:0%
+chain gun fired 600 rounds a minute, 10
+a second. Those moving parts were
+
+ align:start position:0%
+a second. Those moving parts were
+ 
+
+ align:start position:0%
+a second. Those moving parts were
+zooming and there the the the the spec
+
+ align:start position:0%
+zooming and there the the the the spec
+ 
+
+ align:start position:0%
+zooming and there the the the the spec
+on those parts, the tolerance on that
+
+ align:start position:0%
+on those parts, the tolerance on that
+ 
+
+ align:start position:0%
+on those parts, the tolerance on that
+was 210,000 of an inch. 210,000 of an
+
+ align:start position:0%
+was 210,000 of an inch. 210,000 of an
+ 
+
+ align:start position:0%
+was 210,000 of an inch. 210,000 of an
+inch. And my friends at Prattton
+
+ align:start position:0%
+inch. And my friends at Prattton
+ 
+
+ align:start position:0%
+inch. And my friends at Prattton
+Whitney, I mean, they can relate to
+
+ align:start position:0%
+Whitney, I mean, they can relate to
+ 
+
+ align:start position:0%
+Whitney, I mean, they can relate to
+20,000 RPM uh uh rotors and compressors
+
+ align:start position:0%
+20,000 RPM uh uh rotors and compressors
+ 
+
+ align:start position:0%
+20,000 RPM uh uh rotors and compressors
+and stuff like that. And the tolerances
+
+ align:start position:0%
+and stuff like that. And the tolerances
+ 
+
+ align:start position:0%
+and stuff like that. And the tolerances
+are very very small when you're talking
+
+ align:start position:0%
+are very very small when you're talking
+ 
+
+ align:start position:0%
+are very very small when you're talking
+about that much. And they and while
+
+ align:start position:0%
+about that much. And they and while
+ 
+
+ align:start position:0%
+about that much. And they and while
+we're on that subject, you just not you
+
+ align:start position:0%
+we're on that subject, you just not you
+ 
+
+ align:start position:0%
+we're on that subject, you just not you
+cannot just take any old machine and get
+
+ align:start position:0%
+cannot just take any old machine and get
+ 
+
+ align:start position:0%
+cannot just take any old machine and get
+that kind of capability. And so we're
+
+ align:start position:0%
+that kind of capability. And so we're
+ 
+
+ align:start position:0%
+that kind of capability. And so we're
+going to have to match the machine to
+
+ align:start position:0%
+going to have to match the machine to
+ 
+
+ align:start position:0%
+going to have to match the machine to
+the process requirements we have because
+
+ align:start position:0%
+the process requirements we have because
+ 
+
+ align:start position:0%
+the process requirements we have because
+you just can't put it at vendor A or
+
+ align:start position:0%
+you just can't put it at vendor A or
+ 
+
+ align:start position:0%
+you just can't put it at vendor A or
+vendor B because they may not have a
+
+ align:start position:0%
+vendor B because they may not have a
+ 
+
+ align:start position:0%
+vendor B because they may not have a
+machine that can do that or we may not
+
+ align:start position:0%
+machine that can do that or we may not
+ 
+
+ align:start position:0%
+machine that can do that or we may not
+have a machine. We have to go find
+
+ align:start position:0%
+have a machine. We have to go find
+ 
+
+ align:start position:0%
+have a machine. We have to go find
+somebody can do that stuff. So engineers
+
+ align:start position:0%
+somebody can do that stuff. So engineers
+ 
+
+ align:start position:0%
+somebody can do that stuff. So engineers
+have got to be sensitive this.
+
+ align:start position:0%
+have got to be sensitive this.
+ 
+
+ align:start position:0%
+have got to be sensitive this.
+So we're talking about upper and lower
+
+ align:start position:0%
+So we're talking about upper and lower
+ 
+
+ align:start position:0%
+So we're talking about upper and lower
+control limits or upper and lower
+
+ align:start position:0%
+control limits or upper and lower
+ 
+
+ align:start position:0%
+control limits or upper and lower
+specification limit. So when I said plus
+
+ align:start position:0%
+specification limit. So when I said plus
+ 
+
+ align:start position:0%
+specification limit. So when I said plus
+or minus upper spec limit, lower spec
+
+ align:start position:0%
+or minus upper spec limit, lower spec
+ 
+
+ align:start position:0%
+or minus upper spec limit, lower spec
+limit, plus or minus 15,000s, that would
+
+ align:start position:0%
+limit, plus or minus 15,000s, that would
+ 
+
+ align:start position:0%
+limit, plus or minus 15,000s, that would
+be what we're trying to control to. And
+
+ align:start position:0%
+be what we're trying to control to. And
+ 
+
+ align:start position:0%
+be what we're trying to control to. And
+we're going to talk about control
+
+ align:start position:0%
+we're going to talk about control
+ 
+
+ align:start position:0%
+we're going to talk about control
+charts. Process quality is a measure of
+
+ align:start position:0%
+charts. Process quality is a measure of
+ 
+
+ align:start position:0%
+charts. Process quality is a measure of
+the capability to be able to produce it.
+
+ align:start position:0%
+the capability to be able to produce it.
+ 
+
+ align:start position:0%
+the capability to be able to produce it.
+When we want very very precise holes, we
+
+ align:start position:0%
+When we want very very precise holes, we
+ 
+
+ align:start position:0%
+When we want very very precise holes, we
+use a a machine called a jig boring
+
+ align:start position:0%
+use a a machine called a jig boring
+ 
+
+ align:start position:0%
+use a a machine called a jig boring
+machine. And they're made in Switzerland
+
+ align:start position:0%
+machine. And they're made in Switzerland
+ 
+
+ align:start position:0%
+machine. And they're made in Switzerland
+quite often. And they make the best
+
+ align:start position:0%
+quite often. And they make the best
+ 
+
+ align:start position:0%
+quite often. And they make the best
+machines. And you can you can drill very
+
+ align:start position:0%
+machines. And you can you can drill very
+ 
+
+ align:start position:0%
+machines. And you can you can drill very
+very precise holes. You just can't take
+
+ align:start position:0%
+very precise holes. You just can't take
+ 
+
+ align:start position:0%
+very precise holes. You just can't take
+you know the Sears Robuck uh drill press
+
+ align:start position:0%
+you know the Sears Robuck uh drill press
+ 
+
+ align:start position:0%
+you know the Sears Robuck uh drill press
+and get that kind of uh dimensional
+
+ align:start position:0%
+and get that kind of uh dimensional
+ 
+
+ align:start position:0%
+and get that kind of uh dimensional
+quality. Okay. So, how can we assure
+
+ align:start position:0%
+quality. Okay. So, how can we assure
+ 
+
+ align:start position:0%
+quality. Okay. So, how can we assure
+process quality and we're going to talk
+
+ align:start position:0%
+process quality and we're going to talk
+ 
+
+ align:start position:0%
+process quality and we're going to talk
+about some of that. So, there's a series
+
+ align:start position:0%
+about some of that. So, there's a series
+ 
+
+ align:start position:0%
+about some of that. So, there's a series
+of tools there's a series of tools that
+
+ align:start position:0%
+of tools there's a series of tools that
+ 
+
+ align:start position:0%
+of tools there's a series of tools that
+we use in the quality business.
+
+ align:start position:0%
+we use in the quality business.
+ 
+
+ align:start position:0%
+we use in the quality business.
+Flowcharts you've seen that now what
+
+ align:start position:0%
+Flowcharts you've seen that now what
+ 
+
+ align:start position:0%
+Flowcharts you've seen that now what
+basically do is take a flowchart and say
+
+ align:start position:0%
+basically do is take a flowchart and say
+ 
+
+ align:start position:0%
+basically do is take a flowchart and say
+what are all the processes to build our
+
+ align:start position:0%
+what are all the processes to build our
+ 
+
+ align:start position:0%
+what are all the processes to build our
+part. And we used to kit around at the,
+
+ align:start position:0%
+part. And we used to kit around at the,
+ 
+
+ align:start position:0%
+part. And we used to kit around at the,
+you know, when we talk about a
+
+ align:start position:0%
+you know, when we talk about a
+ 
+
+ align:start position:0%
+you know, when we talk about a
+flowchart, mill, drill, tap, and scrap.
+
+ align:start position:0%
+flowchart, mill, drill, tap, and scrap.
+ 
+
+ align:start position:0%
+flowchart, mill, drill, tap, and scrap.
+Now, how's that? Mill it, drill it, tap
+
+ align:start position:0%
+Now, how's that? Mill it, drill it, tap
+ 
+
+ align:start position:0%
+Now, how's that? Mill it, drill it, tap
+it, and then, gee, we didn't make the,
+
+ align:start position:0%
+it, and then, gee, we didn't make the,
+ 
+
+ align:start position:0%
+it, and then, gee, we didn't make the,
+we didn't make the the spec, so we scrap
+
+ align:start position:0%
+we didn't make the the spec, so we scrap
+ 
+
+ align:start position:0%
+we didn't make the the spec, so we scrap
+it, you know, mill, drill, tap, and
+
+ align:start position:0%
+it, you know, mill, drill, tap, and
+ 
+
+ align:start position:0%
+it, you know, mill, drill, tap, and
+scrap. But a flowchart is exactly what
+
+ align:start position:0%
+scrap. But a flowchart is exactly what
+ 
+
+ align:start position:0%
+scrap. But a flowchart is exactly what
+we did the other day, uh, when we were
+
+ align:start position:0%
+we did the other day, uh, when we were
+ 
+
+ align:start position:0%
+we did the other day, uh, when we were
+talking about, you know, uh, building
+
+ align:start position:0%
+talking about, you know, uh, building
+ 
+
+ align:start position:0%
+talking about, you know, uh, building
+airplanes.
+
+ align:start position:0%
+airplanes.
+ 
+
+ align:start position:0%
+airplanes.
+But we do that because of the fact that
+
+ align:start position:0%
+But we do that because of the fact that
+ 
+
+ align:start position:0%
+But we do that because of the fact that
+the quality engineers and incidentally
+
+ align:start position:0%
+the quality engineers and incidentally
+ 
+
+ align:start position:0%
+the quality engineers and incidentally
+that's another whole brand of quality
+
+ align:start position:0%
+that's another whole brand of quality
+ 
+
+ align:start position:0%
+that's another whole brand of quality
+type of engineers that we have aerero
+
+ align:start position:0%
+type of engineers that we have aerero
+ 
+
+ align:start position:0%
+type of engineers that we have aerero
+engineers and chem engineers and civil
+
+ align:start position:0%
+engineers and chem engineers and civil
+ 
+
+ align:start position:0%
+engineers and chem engineers and civil
+engineers but there's a thing called
+
+ align:start position:0%
+engineers but there's a thing called
+ 
+
+ align:start position:0%
+engineers but there's a thing called
+quality engineers and these folks are
+
+ align:start position:0%
+quality engineers and these folks are
+ 
+
+ align:start position:0%
+quality engineers and these folks are
+real engineers that in fact help us work
+
+ align:start position:0%
+real engineers that in fact help us work
+ 
+
+ align:start position:0%
+real engineers that in fact help us work
+on these uh uh and so we lay out the
+
+ align:start position:0%
+on these uh uh and so we lay out the
+ 
+
+ align:start position:0%
+on these uh uh and so we lay out the
+sequence the manufacturing engineers lay
+
+ align:start position:0%
+sequence the manufacturing engineers lay
+ 
+
+ align:start position:0%
+sequence the manufacturing engineers lay
+out the sequence of all the the
+
+ align:start position:0%
+out the sequence of all the the
+ 
+
+ align:start position:0%
+out the sequence of all the the
+flowchart on how we're going to mill it
+
+ align:start position:0%
+flowchart on how we're going to mill it
+ 
+
+ align:start position:0%
+flowchart on how we're going to mill it
+drill it heat uh rough machine stress
+
+ align:start position:0%
+drill it heat uh rough machine stress
+ 
+
+ align:start position:0%
+drill it heat uh rough machine stress
+relieve finish machine you grind, those
+
+ align:start position:0%
+relieve finish machine you grind, those
+ 
+
+ align:start position:0%
+relieve finish machine you grind, those
+kinds of things. And then we have check
+
+ align:start position:0%
+kinds of things. And then we have check
+ 
+
+ align:start position:0%
+kinds of things. And then we have check
+sheets. And in each operation, if it's a
+
+ align:start position:0%
+sheets. And in each operation, if it's a
+ 
+
+ align:start position:0%
+sheets. And in each operation, if it's a
+heat treating operation, we have a check
+
+ align:start position:0%
+heat treating operation, we have a check
+ 
+
+ align:start position:0%
+heat treating operation, we have a check
+sheet that says, make sure that the oven
+
+ align:start position:0%
+sheet that says, make sure that the oven
+ 
+
+ align:start position:0%
+sheet that says, make sure that the oven
+is up to 350°. Make sure that the tool
+
+ align:start position:0%
+is up to 350°. Make sure that the tool
+ 
+
+ align:start position:0%
+is up to 350°. Make sure that the tool
+is in the proper place. So, we have a
+
+ align:start position:0%
+is in the proper place. So, we have a
+ 
+
+ align:start position:0%
+is in the proper place. So, we have a
+check sheet to make sure that the
+
+ align:start position:0%
+check sheet to make sure that the
+ 
+
+ align:start position:0%
+check sheet to make sure that the
+employees follow the process. This is a
+
+ align:start position:0%
+employees follow the process. This is a
+ 
+
+ align:start position:0%
+employees follow the process. This is a
+histogram, a histogram of the data. Lean
+
+ align:start position:0%
+histogram, a histogram of the data. Lean
+ 
+
+ align:start position:0%
+histogram, a histogram of the data. Lean
+is a data-driven exercise. And we always
+
+ align:start position:0%
+is a data-driven exercise. And we always
+ 
+
+ align:start position:0%
+is a data-driven exercise. And we always
+collect data. No more opinions, get me
+
+ align:start position:0%
+collect data. No more opinions, get me
+ 
+
+ align:start position:0%
+collect data. No more opinions, get me
+the data kind of thing. Okay, so that's
+
+ align:start position:0%
+the data kind of thing. Okay, so that's
+ 
+
+ align:start position:0%
+the data kind of thing. Okay, so that's
+a tool. A Pareto chart, it looks like a
+
+ align:start position:0%
+a tool. A Pareto chart, it looks like a
+ 
+
+ align:start position:0%
+a tool. A Pareto chart, it looks like a
+histogram except that a Pareto chart
+
+ align:start position:0%
+histogram except that a Pareto chart
+ 
+
+ align:start position:0%
+histogram except that a Pareto chart
+basically plots the biggest and then the
+
+ align:start position:0%
+basically plots the biggest and then the
+ 
+
+ align:start position:0%
+basically plots the biggest and then the
+next biggest and all the way down to the
+
+ align:start position:0%
+next biggest and all the way down to the
+ 
+
+ align:start position:0%
+next biggest and all the way down to the
+bottom because we want to be able in our
+
+ align:start position:0%
+bottom because we want to be able in our
+ 
+
+ align:start position:0%
+bottom because we want to be able in our
+business find the kinds of errors and
+
+ align:start position:0%
+business find the kinds of errors and
+ 
+
+ align:start position:0%
+business find the kinds of errors and
+work on the biggest ones first because
+
+ align:start position:0%
+work on the biggest ones first because
+ 
+
+ align:start position:0%
+work on the biggest ones first because
+we don't have unlimited resources. Okay,
+
+ align:start position:0%
+we don't have unlimited resources. Okay,
+ 
+
+ align:start position:0%
+we don't have unlimited resources. Okay,
+so we won't spend a lot of time on that.
+
+ align:start position:0%
+so we won't spend a lot of time on that.
+ 
+
+ align:start position:0%
+so we won't spend a lot of time on that.
+So here's a fun exercise. These are your
+
+ align:start position:0%
+So here's a fun exercise. These are your
+ 
+
+ align:start position:0%
+So here's a fun exercise. These are your
+dessert for lunch. Okay, open up the
+
+ align:start position:0%
+dessert for lunch. Okay, open up the
+ 
+
+ align:start position:0%
+dessert for lunch. Okay, open up the
+bag. Please don't eat them. You want to
+
+ align:start position:0%
+bag. Please don't eat them. You want to
+ 
+
+ align:start position:0%
+bag. Please don't eat them. You want to
+get the sheet out? Yeah. Get Get there's
+
+ align:start position:0%
+get the sheet out? Yeah. Get Get there's
+ 
+
+ align:start position:0%
+get the sheet out? Yeah. Get Get there's
+a a sheet that looks like this. It says
+
+ align:start position:0%
+a a sheet that looks like this. It says
+ 
+
+ align:start position:0%
+a a sheet that looks like this. It says
+blank a blank Pareto chart. Blank PTO
+
+ align:start position:0%
+blank a blank Pareto chart. Blank PTO
+ 
+
+ align:start position:0%
+blank a blank Pareto chart. Blank PTO
+chart. Now uh if everybody's everybody's
+
+ align:start position:0%
+chart. Now uh if everybody's everybody's
+ 
+
+ align:start position:0%
+chart. Now uh if everybody's everybody's
+got their Pareto chart blank. Um uh what
+
+ align:start position:0%
+got their Pareto chart blank. Um uh what
+ 
+
+ align:start position:0%
+got their Pareto chart blank. Um uh what
+I want you to do now don't I want you to
+
+ align:start position:0%
+I want you to do now don't I want you to
+ 
+
+ align:start position:0%
+I want you to do now don't I want you to
+open them and put them right in front of
+
+ align:start position:0%
+open them and put them right in front of
+ 
+
+ align:start position:0%
+open them and put them right in front of
+you and I want you to count them. Okay?
+
+ align:start position:0%
+you and I want you to count them. Okay?
+ 
+
+ align:start position:0%
+you and I want you to count them. Okay?
+Count them the total number of each of
+
+ align:start position:0%
+Count them the total number of each of
+ 
+
+ align:start position:0%
+Count them the total number of each of
+you count them. And up in the corner up
+
+ align:start position:0%
+you count them. And up in the corner up
+ 
+
+ align:start position:0%
+you count them. And up in the corner up
+in the corner of your chart, up in the
+
+ align:start position:0%
+in the corner of your chart, up in the
+ 
+
+ align:start position:0%
+in the corner of your chart, up in the
+top corner of the chart, just tell me
+
+ align:start position:0%
+top corner of the chart, just tell me
+ 
+
+ align:start position:0%
+top corner of the chart, just tell me
+how many you've counted.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You can eat the half. Don't don't count
+
+ align:start position:0%
+You can eat the half. Don't don't count
+ 
+
+ align:start position:0%
+You can eat the half. Don't don't count
+the broken ones. You can eat you can eat
+
+ align:start position:0%
+the broken ones. You can eat you can eat
+ 
+
+ align:start position:0%
+the broken ones. You can eat you can eat
+the broken one and don't break anymore.
+
+ align:start position:0%
+the broken one and don't break anymore.
+ 
+
+ align:start position:0%
+the broken one and don't break anymore.
+The next step, if you The first thing
+
+ align:start position:0%
+The next step, if you The first thing
+ 
+
+ align:start position:0%
+The next step, if you The first thing
+was to count the total. The second step
+
+ align:start position:0%
+was to count the total. The second step
+ 
+
+ align:start position:0%
+was to count the total. The second step
+I want you to do is to sort the colors.
+
+ align:start position:0%
+I want you to do is to sort the colors.
+ 
+
+ align:start position:0%
+I want you to do is to sort the colors.
+How many reds? How many oranges? How
+
+ align:start position:0%
+How many reds? How many oranges? How
+ 
+
+ align:start position:0%
+How many reds? How many oranges? How
+many browns? How many greens, etc.
+
+ align:start position:0%
+many browns? How many greens, etc.
+ 
+
+ align:start position:0%
+many browns? How many greens, etc.
+Well, no. It says right here. Yeah.
+
+ align:start position:0%
+Well, no. It says right here. Yeah.
+ 
+
+ align:start position:0%
+Well, no. It says right here. Yeah.
+How we doing on numbers? Absolute
+
+ align:start position:0%
+How we doing on numbers? Absolute
+ 
+
+ align:start position:0%
+How we doing on numbers? Absolute
+number. Does everybody get the numbers
+
+ align:start position:0%
+number. Does everybody get the numbers
+ 
+
+ align:start position:0%
+number. Does everybody get the numbers
+down? Okay. So, we're going to start
+
+ align:start position:0%
+down? Okay. So, we're going to start
+ 
+
+ align:start position:0%
+down? Okay. So, we're going to start
+right here. How many numbers did you How
+
+ align:start position:0%
+right here. How many numbers did you How
+ 
+
+ align:start position:0%
+right here. How many numbers did you How
+many5?
+
+ align:start position:0%
+many5?
+ 
+
+ align:start position:0%
+many5?
+Let's just Let's just do it on mass. How
+
+ align:start position:0%
+Let's just Let's just do it on mass. How
+ 
+
+ align:start position:0%
+Let's just Let's just do it on mass. How
+many you got? 55. 55. Who else got 55?
+
+ align:start position:0%
+many you got? 55. 55. Who else got 55?
+ 
+
+ align:start position:0%
+many you got? 55. 55. Who else got 55?
+One, two, three, four, five. 55s.
+
+ align:start position:0%
+One, two, three, four, five. 55s.
+ 
+
+ align:start position:0%
+One, two, three, four, five. 55s.
+56.
+
+ align:start position:0%
+56.
+ 
+
+ align:start position:0%
+56.
+Two, three 56s.
+
+ align:start position:0%
+Two, three 56s.
+ 
+
+ align:start position:0%
+Two, three 56s.
+54. 57.
+
+ align:start position:0%
+54. 57.
+ 
+
+ align:start position:0%
+54. 57.
+54.
+
+ align:start position:0%
+54.
+ 
+
+ align:start position:0%
+54.
+Two 57.
+
+ align:start position:0%
+Two 57.
+ 
+
+ align:start position:0%
+Two 57.
+Yeah. Okay. We'll go the other way. 257.
+
+ align:start position:0%
+Yeah. Okay. We'll go the other way. 257.
+ 
+
+ align:start position:0%
+Yeah. Okay. We'll go the other way. 257.
+We're just kind of letting this run out.
+
+ align:start position:0%
+We're just kind of letting this run out.
+ 
+
+ align:start position:0%
+We're just kind of letting this run out.
+58. The 158.
+
+ align:start position:0%
+58. The 158.
+ 
+
+ align:start position:0%
+58. The 158.
+Okay. Uh, looks like we're biased in the
+
+ align:start position:0%
+Okay. Uh, looks like we're biased in the
+ 
+
+ align:start position:0%
+Okay. Uh, looks like we're biased in the
+other direction. 54.
+
+ align:start position:0%
+other direction. 54.
+ 
+
+ align:start position:0%
+other direction. 54.
+Two. Three. This is a spread. 54. Wait,
+
+ align:start position:0%
+Two. Three. This is a spread. 54. Wait,
+ 
+
+ align:start position:0%
+Two. Three. This is a spread. 54. Wait,
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+two more. 54 is 53.
+
+ align:start position:0%
+two more. 54 is 53.
+ 
+
+ align:start position:0%
+two more. 54 is 53.
+15 253.
+
+ align:start position:0%
+15 253.
+ 
+
+ align:start position:0%
+15 253.
+Okay. And that's it. 60. Whoa. Never
+
+ align:start position:0%
+Okay. And that's it. 60. Whoa. Never
+ 
+
+ align:start position:0%
+Okay. And that's it. 60. Whoa. Never
+seen Never seen any other high lows. 30
+
+ align:start position:0%
+seen Never seen any other high lows. 30
+ 
+
+ align:start position:0%
+seen Never seen any other high lows. 30
+times doing it. Never seen. Yeah. This
+
+ align:start position:0%
+times doing it. Never seen. Yeah. This
+ 
+
+ align:start position:0%
+times doing it. Never seen. Yeah. This
+is This is interesting. This is the
+
+ align:start position:0%
+is This is interesting. This is the
+ 
+
+ align:start position:0%
+is This is interesting. This is the
+highest ever. I think Eminem's process
+
+ align:start position:0%
+highest ever. I think Eminem's process
+ 
+
+ align:start position:0%
+highest ever. I think Eminem's process
+controls.
+
+ align:start position:0%
+controls.
+ 
+
+ align:start position:0%
+controls.
+This is this is the biggest spread we've
+
+ align:start position:0%
+This is this is the biggest spread we've
+ 
+
+ align:start position:0%
+This is this is the biggest spread we've
+ever seen by quite a bit. So you learn
+
+ align:start position:0%
+ever seen by quite a bit. So you learn
+ 
+
+ align:start position:0%
+ever seen by quite a bit. So you learn
+things from
+
+ align:start position:0%
+things from
+ 
+
+ align:start position:0%
+things from
+Okay. So we're 53
+
+ align:start position:0%
+Okay. So we're 53
+ 
+
+ align:start position:0%
+Okay. So we're 53
+6 7 8 9
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is five.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One of the lessons here is that this
+
+ align:start position:0%
+One of the lessons here is that this
+ 
+
+ align:start position:0%
+One of the lessons here is that this
+doesn't have to be complicated, right?
+
+ align:start position:0%
+doesn't have to be complicated, right?
+ 
+
+ align:start position:0%
+doesn't have to be complicated, right?
+This is very simple data. But uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's 53 54.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now this is a this is a histogram
+
+ align:start position:0%
+Now this is a this is a histogram
+ 
+
+ align:start position:0%
+Now this is a this is a histogram
+histogram and it's a way of displaying
+
+ align:start position:0%
+histogram and it's a way of displaying
+ 
+
+ align:start position:0%
+histogram and it's a way of displaying
+data way of displaying data. Now we're
+
+ align:start position:0%
+data way of displaying data. Now we're
+ 
+
+ align:start position:0%
+data way of displaying data. Now we're
+going to relate that to the factory and
+
+ align:start position:0%
+going to relate that to the factory and
+ 
+
+ align:start position:0%
+going to relate that to the factory and
+to the engineering um and to our to our
+
+ align:start position:0%
+to the engineering um and to our to our
+ 
+
+ align:start position:0%
+to the engineering um and to our to our
+quality process. But we want you to be
+
+ align:start position:0%
+quality process. But we want you to be
+ 
+
+ align:start position:0%
+quality process. But we want you to be
+able to recognize that we we send you
+
+ align:start position:0%
+able to recognize that we we send you
+ 
+
+ align:start position:0%
+able to recognize that we we send you
+out to the to to solve problems and we
+
+ align:start position:0%
+out to the to to solve problems and we
+ 
+
+ align:start position:0%
+out to the to to solve problems and we
+want efficient ways of of plotting the
+
+ align:start position:0%
+want efficient ways of of plotting the
+ 
+
+ align:start position:0%
+want efficient ways of of plotting the
+data and um so this is a very very
+
+ align:start position:0%
+data and um so this is a very very
+ 
+
+ align:start position:0%
+data and um so this is a very very
+interesting and this shows a couple of
+
+ align:start position:0%
+interesting and this shows a couple of
+ 
+
+ align:start position:0%
+interesting and this shows a couple of
+things. One that there's a wide wide
+
+ align:start position:0%
+things. One that there's a wide wide
+ 
+
+ align:start position:0%
+things. One that there's a wide wide
+variability wide variability in in the
+
+ align:start position:0%
+variability wide variability in in the
+ 
+
+ align:start position:0%
+variability wide variability in in the
+the count. Now um how just here's a
+
+ align:start position:0%
+the count. Now um how just here's a
+ 
+
+ align:start position:0%
+the count. Now um how just here's a
+question. Is everybody done sorting
+
+ align:start position:0%
+question. Is everybody done sorting
+ 
+
+ align:start position:0%
+question. Is everybody done sorting
+their everybody done sorting? I think
+
+ align:start position:0%
+their everybody done sorting? I think
+ 
+
+ align:start position:0%
+their everybody done sorting? I think
+most of the folks are done count I mean
+
+ align:start position:0%
+most of the folks are done count I mean
+ 
+
+ align:start position:0%
+most of the folks are done count I mean
+count how many reds and okay but all
+
+ align:start position:0%
+count how many reds and okay but all
+ 
+
+ align:start position:0%
+count how many reds and okay but all
+right now it turns out
+
+ align:start position:0%
+right now it turns out
+ 
+
+ align:start position:0%
+right now it turns out
+looking at this data do you think that
+
+ align:start position:0%
+looking at this data do you think that
+ 
+
+ align:start position:0%
+looking at this data do you think that
+Eminem controls their process by the
+
+ align:start position:0%
+Eminem controls their process by the
+ 
+
+ align:start position:0%
+Eminem controls their process by the
+count?
+
+ align:start position:0%
+count?
+ 
+
+ align:start position:0%
+count?
+What do you think they control it by?
+
+ align:start position:0%
+What do you think they control it by?
+ 
+
+ align:start position:0%
+What do you think they control it by?
+Weight. Right. Good. Now, if you take a
+
+ align:start position:0%
+Weight. Right. Good. Now, if you take a
+ 
+
+ align:start position:0%
+Weight. Right. Good. Now, if you take a
+look on your bag, take a look on the bag
+
+ align:start position:0%
+look on your bag, take a look on the bag
+ 
+
+ align:start position:0%
+look on your bag, take a look on the bag
+on the front of it. Ah, you've already
+
+ align:start position:0%
+on the front of it. Ah, you've already
+ 
+
+ align:start position:0%
+on the front of it. Ah, you've already
+eaten it up, right? Okay. Okay. You see
+
+ align:start position:0%
+eaten it up, right? Okay. Okay. You see
+ 
+
+ align:start position:0%
+eaten it up, right? Okay. Okay. You see
+the net weight is 1.69 1.69 ounces. Now,
+
+ align:start position:0%
+the net weight is 1.69 1.69 ounces. Now,
+ 
+
+ align:start position:0%
+the net weight is 1.69 1.69 ounces. Now,
+to two decimal places or three
+
+ align:start position:0%
+to two decimal places or three
+ 
+
+ align:start position:0%
+to two decimal places or three
+significant places there, that's how
+
+ align:start position:0%
+significant places there, that's how
+ 
+
+ align:start position:0%
+significant places there, that's how
+they control the weight because the Food
+
+ align:start position:0%
+they control the weight because the Food
+ 
+
+ align:start position:0%
+they control the weight because the Food
+and Drug Administration and the weights
+
+ align:start position:0%
+and Drug Administration and the weights
+ 
+
+ align:start position:0%
+and Drug Administration and the weights
+and measures of the whatever state, you
+
+ align:start position:0%
+and measures of the whatever state, you
+ 
+
+ align:start position:0%
+and measures of the whatever state, you
+know, say that you cannot fraudulently
+
+ align:start position:0%
+know, say that you cannot fraudulently
+ 
+
+ align:start position:0%
+know, say that you cannot fraudulently
+uh, you know, uh, deceive the customer.
+
+ align:start position:0%
+uh, you know, uh, deceive the customer.
+ 
+
+ align:start position:0%
+uh, you know, uh, deceive the customer.
+So that's the the upper and lower
+
+ align:start position:0%
+So that's the the upper and lower
+ 
+
+ align:start position:0%
+So that's the the upper and lower
+control limits in their process
+
+ align:start position:0%
+control limits in their process
+ 
+
+ align:start position:0%
+control limits in their process
+typically is um you know is going to be
+
+ align:start position:0%
+typically is um you know is going to be
+ 
+
+ align:start position:0%
+typically is um you know is going to be
+on weight because they they can't they
+
+ align:start position:0%
+on weight because they they can't they
+ 
+
+ align:start position:0%
+on weight because they they can't they
+can't deceive the customer for whatever
+
+ align:start position:0%
+can't deceive the customer for whatever
+ 
+
+ align:start position:0%
+can't deceive the customer for whatever
+they charge for M&M's these days. In
+
+ align:start position:0%
+they charge for M&M's these days. In
+ 
+
+ align:start position:0%
+they charge for M&M's these days. In
+fact on this on this chart you can see
+
+ align:start position:0%
+fact on this on this chart you can see
+ 
+
+ align:start position:0%
+fact on this on this chart you can see
+something else interesting. Is this
+
+ align:start position:0%
+something else interesting. Is this
+ 
+
+ align:start position:0%
+something else interesting. Is this
+symmetrical?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No. And where's the where's the steep
+
+ align:start position:0%
+No. And where's the where's the steep
+ 
+
+ align:start position:0%
+No. And where's the where's the steep
+edge?
+
+ align:start position:0%
+edge?
+ 
+
+ align:start position:0%
+edge?
+you know, below it because because
+
+ align:start position:0%
+you know, below it because because
+ 
+
+ align:start position:0%
+you know, below it because because
+they'll get in trouble if they
+
+ align:start position:0%
+they'll get in trouble if they
+ 
+
+ align:start position:0%
+they'll get in trouble if they
+underweight people, right? And they're
+
+ align:start position:0%
+underweight people, right? And they're
+ 
+
+ align:start position:0%
+underweight people, right? And they're
+probably a real strict legal spec on on
+
+ align:start position:0%
+probably a real strict legal spec on on
+ 
+
+ align:start position:0%
+probably a real strict legal spec on on
+how often you can screw up here. Well,
+
+ align:start position:0%
+how often you can screw up here. Well,
+ 
+
+ align:start position:0%
+how often you can screw up here. Well,
+this that's just M&M's, right? They
+
+ align:start position:0%
+this that's just M&M's, right? They
+ 
+
+ align:start position:0%
+this that's just M&M's, right? They
+don't want to give you too many extra,
+
+ align:start position:0%
+don't want to give you too many extra,
+ 
+
+ align:start position:0%
+don't want to give you too many extra,
+but you get a couple that if you get 60
+
+ align:start position:0%
+but you get a couple that if you get 60
+ 
+
+ align:start position:0%
+but you get a couple that if you get 60
+every now and then, that's fine with
+
+ align:start position:0%
+every now and then, that's fine with
+ 
+
+ align:start position:0%
+every now and then, that's fine with
+them. Want to do some colors?
+
+ align:start position:0%
+them. Want to do some colors?
+ 
+
+ align:start position:0%
+them. Want to do some colors?
+So, uh, let's How many How many folks?
+
+ align:start position:0%
+So, uh, let's How many How many folks?
+ 
+
+ align:start position:0%
+So, uh, let's How many How many folks?
+Uh, let's talk about everybody. How How
+
+ align:start position:0%
+Uh, let's talk about everybody. How How
+ 
+
+ align:start position:0%
+Uh, let's talk about everybody. How How
+many red ones did you get? One. One.
+
+ align:start position:0%
+many red ones did you get? One. One.
+ 
+
+ align:start position:0%
+many red ones did you get? One. One.
+One.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Really? Yeah. See, that's a good How
+
+ align:start position:0%
+Really? Yeah. See, that's a good How
+ 
+
+ align:start position:0%
+Really? Yeah. See, that's a good How
+about blues? How many blues?
+
+ align:start position:0%
+about blues? How many blues?
+ 
+
+ align:start position:0%
+about blues? How many blues?
+What is the difference between blue and
+
+ align:start position:0%
+What is the difference between blue and
+ 
+
+ align:start position:0%
+What is the difference between blue and
+Oh,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you got
+
+ align:start position:0%
+you got
+ 
+
+ align:start position:0%
+you got
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+those.
+
+ align:start position:0%
+those.
+ 
+
+ align:start position:0%
+those.
+How many How many blues did you get?
+
+ align:start position:0%
+How many How many blues did you get?
+ 
+
+ align:start position:0%
+How many How many blues did you get?
+18 11 14
+
+ align:start position:0%
+18 11 14
+ 
+
+ align:start position:0%
+18 11 14
+Yeah, that's it. See, they don't control
+
+ align:start position:0%
+Yeah, that's it. See, they don't control
+ 
+
+ align:start position:0%
+Yeah, that's it. See, they don't control
+like they they mix them up very well,
+
+ align:start position:0%
+like they they mix them up very well,
+ 
+
+ align:start position:0%
+like they they mix them up very well,
+but I mean if anybody has little kids
+
+ align:start position:0%
+but I mean if anybody has little kids
+ 
+
+ align:start position:0%
+but I mean if anybody has little kids
+and the folks in the back have all been
+
+ align:start position:0%
+and the folks in the back have all been
+ 
+
+ align:start position:0%
+and the folks in the back have all been
+through that little kids fight over I
+
+ align:start position:0%
+through that little kids fight over I
+ 
+
+ align:start position:0%
+through that little kids fight over I
+want a red one. I want a yellow one. So
+
+ align:start position:0%
+want a red one. I want a yellow one. So
+ 
+
+ align:start position:0%
+want a red one. I want a yellow one. So
+they they try to mix them up, but we
+
+ align:start position:0%
+they they try to mix them up, but we
+ 
+
+ align:start position:0%
+they they try to mix them up, but we
+control the How about yellow? One,
+
+ align:start position:0%
+control the How about yellow? One,
+ 
+
+ align:start position:0%
+control the How about yellow? One,
+nine and one 10. Wow. Brown seven
+
+ align:start position:0%
+nine and one 10. Wow. Brown seven
+ 
+
+ align:start position:0%
+nine and one 10. Wow. Brown seven
+12.
+
+ align:start position:0%
+12.
+ 
+
+ align:start position:0%
+12.
+It's interesting because little kids
+
+ align:start position:0%
+It's interesting because little kids
+ 
+
+ align:start position:0%
+It's interesting because little kids
+typically don't like that color, you
+
+ align:start position:0%
+typically don't like that color, you
+ 
+
+ align:start position:0%
+typically don't like that color, you
+know. How about green? 15.
+
+ align:start position:0%
+know. How about green? 15.
+ 
+
+ align:start position:0%
+know. How about green? 15.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Wow. Look at that. See? Okay. So, you
+
+ align:start position:0%
+Wow. Look at that. See? Okay. So, you
+ 
+
+ align:start position:0%
+Wow. Look at that. See? Okay. So, you
+get the You get the picture. We're not
+
+ align:start position:0%
+get the You get the picture. We're not
+ 
+
+ align:start position:0%
+get the You get the picture. We're not
+They They try to randomly control them,
+
+ align:start position:0%
+They They try to randomly control them,
+ 
+
+ align:start position:0%
+They They try to randomly control them,
+but in fact, they don't do it. But the
+
+ align:start position:0%
+but in fact, they don't do it. But the
+ 
+
+ align:start position:0%
+but in fact, they don't do it. But the
+the point of the story is and many of
+
+ align:start position:0%
+the point of the story is and many of
+ 
+
+ align:start position:0%
+the point of the story is and many of
+you many of them some of the folks over
+
+ align:start position:0%
+you many of them some of the folks over
+ 
+
+ align:start position:0%
+you many of them some of the folks over
+here and like here actually have them
+
+ align:start position:0%
+here and like here actually have them
+ 
+
+ align:start position:0%
+here and like here actually have them
+stacked in Pareto water and they
+
+ align:start position:0%
+stacked in Pareto water and they
+ 
+
+ align:start position:0%
+stacked in Pareto water and they
+actually have the M&M's stacked just
+
+ align:start position:0%
+actually have the M&M's stacked just
+ 
+
+ align:start position:0%
+actually have the M&M's stacked just
+like this and that's a PTO chart. Now
+
+ align:start position:0%
+like this and that's a PTO chart. Now
+ 
+
+ align:start position:0%
+like this and that's a PTO chart. Now
+let me just grab a blank piece of paper.
+
+ align:start position:0%
+let me just grab a blank piece of paper.
+ 
+
+ align:start position:0%
+let me just grab a blank piece of paper.
+The point the point of the tour and Earl
+
+ align:start position:0%
+The point the point of the tour and Earl
+ 
+
+ align:start position:0%
+The point the point of the tour and Earl
+and Hugh have heard me say this. There's
+
+ align:start position:0%
+and Hugh have heard me say this. There's
+ 
+
+ align:start position:0%
+and Hugh have heard me say this. There's
+probably no more important tool, no more
+
+ align:start position:0%
+probably no more important tool, no more
+ 
+
+ align:start position:0%
+probably no more important tool, no more
+important tool in the whole business of
+
+ align:start position:0%
+important tool in the whole business of
+ 
+
+ align:start position:0%
+important tool in the whole business of
+quality uh than than the PTO chart. Why?
+
+ align:start position:0%
+quality uh than than the PTO chart. Why?
+ 
+
+ align:start position:0%
+quality uh than than the PTO chart. Why?
+Because the PTO chart's easy to do. I
+
+ align:start position:0%
+Because the PTO chart's easy to do. I
+ 
+
+ align:start position:0%
+Because the PTO chart's easy to do. I
+mean, you know, you can do it just with
+
+ align:start position:0%
+mean, you know, you can do it just with
+ 
+
+ align:start position:0%
+mean, you know, you can do it just with
+the M&M's you can see here. But the
+
+ align:start position:0%
+the M&M's you can see here. But the
+ 
+
+ align:start position:0%
+the M&M's you can see here. But the
+point is quality is a data-driven
+
+ align:start position:0%
+point is quality is a data-driven
+ 
+
+ align:start position:0%
+point is quality is a data-driven
+exercise. And we have a problem a
+
+ align:start position:0%
+exercise. And we have a problem a
+ 
+
+ align:start position:0%
+exercise. And we have a problem a
+problem out in the factory delivering
+
+ align:start position:0%
+problem out in the factory delivering
+ 
+
+ align:start position:0%
+problem out in the factory delivering
+Honeywell
+
+ align:start position:0%
+Honeywell
+ 
+
+ align:start position:0%
+Honeywell
+Honeywell um uh computers for the flight
+
+ align:start position:0%
+Honeywell um uh computers for the flight
+ 
+
+ align:start position:0%
+Honeywell um uh computers for the flight
+control system of a MD11 using that as
+
+ align:start position:0%
+control system of a MD11 using that as
+ 
+
+ align:start position:0%
+control system of a MD11 using that as
+example and the point is we go out there
+
+ align:start position:0%
+example and the point is we go out there
+ 
+
+ align:start position:0%
+example and the point is we go out there
+and we in fact analyze them you know we
+
+ align:start position:0%
+and we in fact analyze them you know we
+ 
+
+ align:start position:0%
+and we in fact analyze them you know we
+try to find out what's going on and we
+
+ align:start position:0%
+try to find out what's going on and we
+ 
+
+ align:start position:0%
+try to find out what's going on and we
+take a whole bunch of the computers and
+
+ align:start position:0%
+take a whole bunch of the computers and
+ 
+
+ align:start position:0%
+take a whole bunch of the computers and
+try to find out what the root cause of
+
+ align:start position:0%
+try to find out what the root cause of
+ 
+
+ align:start position:0%
+try to find out what the root cause of
+the problem is and so we wind up you
+
+ align:start position:0%
+the problem is and so we wind up you
+ 
+
+ align:start position:0%
+the problem is and so we wind up you
+know with a Pareto chart and we said
+
+ align:start position:0%
+know with a Pareto chart and we said
+ 
+
+ align:start position:0%
+know with a Pareto chart and we said
+part of them in fact is the the is the
+
+ align:start position:0%
+part of them in fact is the the is the
+ 
+
+ align:start position:0%
+part of them in fact is the the is the
+power supplies and you know this number
+
+ align:start position:0%
+power supplies and you know this number
+ 
+
+ align:start position:0%
+power supplies and you know this number
+of these guys had defective grounds
+
+ align:start position:0%
+of these guys had defective grounds
+ 
+
+ align:start position:0%
+of these guys had defective grounds
+and these number you know basically had
+
+ align:start position:0%
+and these number you know basically had
+ 
+
+ align:start position:0%
+and these number you know basically had
+a tolerance problem you know on the
+
+ align:start position:0%
+a tolerance problem you know on the
+ 
+
+ align:start position:0%
+a tolerance problem you know on the
+output you know that kind of thing. So
+
+ align:start position:0%
+output you know that kind of thing. So
+ 
+
+ align:start position:0%
+output you know that kind of thing. So
+what we do is that you know with that
+
+ align:start position:0%
+what we do is that you know with that
+ 
+
+ align:start position:0%
+what we do is that you know with that
+kind of data go back to the engineers
+
+ align:start position:0%
+kind of data go back to the engineers
+ 
+
+ align:start position:0%
+kind of data go back to the engineers
+and say holy cow you know what's going
+
+ align:start position:0%
+and say holy cow you know what's going
+ 
+
+ align:start position:0%
+and say holy cow you know what's going
+on the power supply and he said you know
+
+ align:start position:0%
+on the power supply and he said you know
+ 
+
+ align:start position:0%
+on the power supply and he said you know
+we just changed suppliers we just went
+
+ align:start position:0%
+we just changed suppliers we just went
+ 
+
+ align:start position:0%
+we just changed suppliers we just went
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+you know General Electric to
+
+ align:start position:0%
+you know General Electric to
+ 
+
+ align:start position:0%
+you know General Electric to
+Westinghouse on that in fact this is a
+
+ align:start position:0%
+Westinghouse on that in fact this is a
+ 
+
+ align:start position:0%
+Westinghouse on that in fact this is a
+real case on Westinghouse Westinghouse
+
+ align:start position:0%
+real case on Westinghouse Westinghouse
+ 
+
+ align:start position:0%
+real case on Westinghouse Westinghouse
+offloaded to an outfit in Puerto Rico
+
+ align:start position:0%
+offloaded to an outfit in Puerto Rico
+ 
+
+ align:start position:0%
+offloaded to an outfit in Puerto Rico
+and you know we were getting terrible
+
+ align:start position:0%
+and you know we were getting terrible
+ 
+
+ align:start position:0%
+and you know we were getting terrible
+terrible quality okay that's one kind of
+
+ align:start position:0%
+terrible quality okay that's one kind of
+ 
+
+ align:start position:0%
+terrible quality okay that's one kind of
+a thing let's talk about
+
+ align:start position:0%
+a thing let's talk about
+ 
+
+ align:start position:0%
+a thing let's talk about
+let's talk about late deliveries. Why
+
+ align:start position:0%
+let's talk about late deliveries. Why
+ 
+
+ align:start position:0%
+let's talk about late deliveries. Why
+are we getting late deliveries of an
+
+ align:start position:0%
+are we getting late deliveries of an
+ 
+
+ align:start position:0%
+are we getting late deliveries of an
+actuator? Okay,
+
+ align:start position:0%
+actuator? Okay,
+ 
+
+ align:start position:0%
+actuator? Okay,
+we failed test.
+
+ align:start position:0%
+we failed test.
+ 
+
+ align:start position:0%
+we failed test.
+We had a supply problem. Didn't get all
+
+ align:start position:0%
+We had a supply problem. Didn't get all
+ 
+
+ align:start position:0%
+We had a supply problem. Didn't get all
+the parts.
+
+ align:start position:0%
+the parts.
+ 
+
+ align:start position:0%
+the parts.
+We wound up with a situation where we
+
+ align:start position:0%
+We wound up with a situation where we
+ 
+
+ align:start position:0%
+We wound up with a situation where we
+had an engineering error in the Okay,
+
+ align:start position:0%
+had an engineering error in the Okay,
+ 
+
+ align:start position:0%
+had an engineering error in the Okay,
+that wasn't caught. Uh it was actually
+
+ align:start position:0%
+that wasn't caught. Uh it was actually
+ 
+
+ align:start position:0%
+that wasn't caught. Uh it was actually
+an engineering change. Okay. So you know
+
+ align:start position:0%
+an engineering change. Okay. So you know
+ 
+
+ align:start position:0%
+an engineering change. Okay. So you know
+we what's wrong with the test Earl
+
+ align:start position:0%
+we what's wrong with the test Earl
+ 
+
+ align:start position:0%
+we what's wrong with the test Earl
+yesterday? And and do you remember the
+
+ align:start position:0%
+yesterday? And and do you remember the
+ 
+
+ align:start position:0%
+yesterday? And and do you remember the
+drill about the five W's? The five W's,
+
+ align:start position:0%
+drill about the five W's? The five W's,
+ 
+
+ align:start position:0%
+drill about the five W's? The five W's,
+you know, why is the test wrong? Is it
+
+ align:start position:0%
+you know, why is the test wrong? Is it
+ 
+
+ align:start position:0%
+you know, why is the test wrong? Is it
+the So we drive it down to the next
+
+ align:start position:0%
+the So we drive it down to the next
+ 
+
+ align:start position:0%
+the So we drive it down to the next
+area, you know, and is it is it
+
+ align:start position:0%
+area, you know, and is it is it
+ 
+
+ align:start position:0%
+area, you know, and is it is it
+calibration?
+
+ align:start position:0%
+calibration?
+ 
+
+ align:start position:0%
+calibration?
+You know, is it a bad setup? So you just
+
+ align:start position:0%
+You know, is it a bad setup? So you just
+ 
+
+ align:start position:0%
+You know, is it a bad setup? So you just
+keep on drilling down. Now the other
+
+ align:start position:0%
+keep on drilling down. Now the other
+ 
+
+ align:start position:0%
+keep on drilling down. Now the other
+issue from a lean standpoint if you go
+
+ align:start position:0%
+issue from a lean standpoint if you go
+ 
+
+ align:start position:0%
+issue from a lean standpoint if you go
+out and work in a lean environment and
+
+ align:start position:0%
+out and work in a lean environment and
+ 
+
+ align:start position:0%
+out and work in a lean environment and
+Ida can tell you you know they don't
+
+ align:start position:0%
+Ida can tell you you know they don't
+ 
+
+ align:start position:0%
+Ida can tell you you know they don't
+give you unlimited lean budget you got a
+
+ align:start position:0%
+give you unlimited lean budget you got a
+ 
+
+ align:start position:0%
+give you unlimited lean budget you got a
+lean staff and the point is where are we
+
+ align:start position:0%
+lean staff and the point is where are we
+ 
+
+ align:start position:0%
+lean staff and the point is where are we
+going to spend our money to solve the
+
+ align:start position:0%
+going to spend our money to solve the
+ 
+
+ align:start position:0%
+going to spend our money to solve the
+biggest problems first and where are our
+
+ align:start position:0%
+biggest problems first and where are our
+ 
+
+ align:start position:0%
+biggest problems first and where are our
+biggest problems and if we can make you
+
+ align:start position:0%
+biggest problems and if we can make you
+ 
+
+ align:start position:0%
+biggest problems and if we can make you
+know with a red line here if we can make
+
+ align:start position:0%
+know with a red line here if we can make
+ 
+
+ align:start position:0%
+know with a red line here if we can make
+you know a 25%
+
+ align:start position:0%
+you know a 25%
+ 
+
+ align:start position:0%
+you know a 25%
+improvement in our biggest item it's
+
+ align:start position:0%
+improvement in our biggest item it's
+ 
+
+ align:start position:0%
+improvement in our biggest item it's
+better than you know eliminating a whole
+
+ align:start position:0%
+better than you know eliminating a whole
+ 
+
+ align:start position:0%
+better than you know eliminating a whole
+problem over And we only Which ones do
+
+ align:start position:0%
+problem over And we only Which ones do
+ 
+
+ align:start position:0%
+problem over And we only Which ones do
+we attack first? Which budget item?
+
+ align:start position:0%
+we attack first? Which budget item?
+ 
+
+ align:start position:0%
+we attack first? Which budget item?
+We're over We're over budget. We're over
+
+ align:start position:0%
+We're over We're over budget. We're over
+ 
+
+ align:start position:0%
+We're over We're over budget. We're over
+budget.
+
+ align:start position:0%
+budget.
+ 
+
+ align:start position:0%
+budget.
+Why? Well, where are we spending our
+
+ align:start position:0%
+Why? Well, where are we spending our
+ 
+
+ align:start position:0%
+Why? Well, where are we spending our
+money? Where are we spending our money?
+
+ align:start position:0%
+money? Where are we spending our money?
+ 
+
+ align:start position:0%
+money? Where are we spending our money?
+We're spending our money in uh
+
+ align:start position:0%
+We're spending our money in uh
+ 
+
+ align:start position:0%
+We're spending our money in uh
+utilities.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We're spending our money in, you know,
+
+ align:start position:0%
+We're spending our money in, you know,
+ 
+
+ align:start position:0%
+We're spending our money in, you know,
+capital. We're spending our money in,
+
+ align:start position:0%
+capital. We're spending our money in,
+ 
+
+ align:start position:0%
+capital. We're spending our money in,
+you know, overhead kind of stuff. Well,
+
+ align:start position:0%
+you know, overhead kind of stuff. Well,
+ 
+
+ align:start position:0%
+you know, overhead kind of stuff. Well,
+you know, we go through a big drill.
+
+ align:start position:0%
+you know, we go through a big drill.
+ 
+
+ align:start position:0%
+you know, we go through a big drill.
+What what part of this is what part of
+
+ align:start position:0%
+What what part of this is what part of
+ 
+
+ align:start position:0%
+What what part of this is what part of
+that utility budget is electricity?
+
+ align:start position:0%
+that utility budget is electricity?
+ 
+
+ align:start position:0%
+that utility budget is electricity?
+Turns out to be very very high. Very
+
+ align:start position:0%
+Turns out to be very very high. Very
+ 
+
+ align:start position:0%
+Turns out to be very very high. Very
+very high. And so you go and put in and
+
+ align:start position:0%
+very high. And so you go and put in and
+ 
+
+ align:start position:0%
+very high. And so you go and put in and
+I wound up putting in a whole big plant
+
+ align:start position:0%
+I wound up putting in a whole big plant
+ 
+
+ align:start position:0%
+I wound up putting in a whole big plant
+of um uh a uh thermal generating plant
+
+ align:start position:0%
+of um uh a uh thermal generating plant
+ 
+
+ align:start position:0%
+of um uh a uh thermal generating plant
+to to reduce our electricity cost. So
+
+ align:start position:0%
+to to reduce our electricity cost. So
+ 
+
+ align:start position:0%
+to to reduce our electricity cost. So
+another another great tool is called the
+
+ align:start position:0%
+another another great tool is called the
+ 
+
+ align:start position:0%
+another another great tool is called the
+the cause and effect diagram. This is
+
+ align:start position:0%
+the cause and effect diagram. This is
+ 
+
+ align:start position:0%
+the cause and effect diagram. This is
+the the Japanese name for this is the
+
+ align:start position:0%
+the the Japanese name for this is the
+ 
+
+ align:start position:0%
+the the Japanese name for this is the
+Ishikawa diagram because Dr. Ishikawa
+
+ align:start position:0%
+Ishikawa diagram because Dr. Ishikawa
+ 
+
+ align:start position:0%
+Ishikawa diagram because Dr. Ishikawa
+came up with this. And in the old days,
+
+ align:start position:0%
+came up with this. And in the old days,
+ 
+
+ align:start position:0%
+came up with this. And in the old days,
+in the old days, this was called the 5M.
+
+ align:start position:0%
+in the old days, this was called the 5M.
+ 
+
+ align:start position:0%
+in the old days, this was called the 5M.
+It was measurement, material, methods,
+
+ align:start position:0%
+It was measurement, material, methods,
+ 
+
+ align:start position:0%
+It was measurement, material, methods,
+machine, and manpower. Now we call it
+
+ align:start position:0%
+machine, and manpower. Now we call it
+ 
+
+ align:start position:0%
+machine, and manpower. Now we call it
+personnel. Okay? And we've added the
+
+ align:start position:0%
+personnel. Okay? And we've added the
+ 
+
+ align:start position:0%
+personnel. Okay? And we've added the
+environment to it. And you can you can
+
+ align:start position:0%
+environment to it. And you can you can
+ 
+
+ align:start position:0%
+environment to it. And you can you can
+say we're trying to understand we're
+
+ align:start position:0%
+say we're trying to understand we're
+ 
+
+ align:start position:0%
+say we're trying to understand we're
+trying to understand you know this
+
+ align:start position:0%
+trying to understand you know this
+ 
+
+ align:start position:0%
+trying to understand you know this
+Honeywell uh computer problem and we
+
+ align:start position:0%
+Honeywell uh computer problem and we
+ 
+
+ align:start position:0%
+Honeywell uh computer problem and we
+have this issue in terms of the testing
+
+ align:start position:0%
+have this issue in terms of the testing
+ 
+
+ align:start position:0%
+have this issue in terms of the testing
+you know that so now we say what's wrong
+
+ align:start position:0%
+you know that so now we say what's wrong
+ 
+
+ align:start position:0%
+you know that so now we say what's wrong
+so we look at measurement and and this
+
+ align:start position:0%
+so we look at measurement and and this
+ 
+
+ align:start position:0%
+so we look at measurement and and this
+is a brainstorming technique you get all
+
+ align:start position:0%
+is a brainstorming technique you get all
+ 
+
+ align:start position:0%
+is a brainstorming technique you get all
+the engineers the manufacturing guys the
+
+ align:start position:0%
+the engineers the manufacturing guys the
+ 
+
+ align:start position:0%
+the engineers the manufacturing guys the
+tooling guys there and you say you know
+
+ align:start position:0%
+tooling guys there and you say you know
+ 
+
+ align:start position:0%
+tooling guys there and you say you know
+is it a test calibration issue is
+
+ align:start position:0%
+is it a test calibration issue is
+ 
+
+ align:start position:0%
+is it a test calibration issue is
+the precision, we can't measure it close
+
+ align:start position:0%
+the precision, we can't measure it close
+ 
+
+ align:start position:0%
+the precision, we can't measure it close
+enough. Is it the fact that we're not
+
+ align:start position:0%
+enough. Is it the fact that we're not
+ 
+
+ align:start position:0%
+enough. Is it the fact that we're not
+getting repeatability?
+
+ align:start position:0%
+getting repeatability?
+ 
+
+ align:start position:0%
+getting repeatability?
+You know, in a material thing, we're
+
+ align:start position:0%
+You know, in a material thing, we're
+ 
+
+ align:start position:0%
+You know, in a material thing, we're
+getting bad tolerances on that piston
+
+ align:start position:0%
+getting bad tolerances on that piston
+ 
+
+ align:start position:0%
+getting bad tolerances on that piston
+that we're we're for the compressor, you
+
+ align:start position:0%
+that we're we're for the compressor, you
+ 
+
+ align:start position:0%
+that we're we're for the compressor, you
+know, a standard old fashioned
+
+ align:start position:0%
+know, a standard old fashioned
+ 
+
+ align:start position:0%
+know, a standard old fashioned
+compressor, you know, is it a M&P
+
+ align:start position:0%
+compressor, you know, is it a M&P
+ 
+
+ align:start position:0%
+compressor, you know, is it a M&P
+material process issue? Is it a geometry
+
+ align:start position:0%
+material process issue? Is it a geometry
+ 
+
+ align:start position:0%
+material process issue? Is it a geometry
+problem? Is there inclusions in the
+
+ align:start position:0%
+problem? Is there inclusions in the
+ 
+
+ align:start position:0%
+problem? Is there inclusions in the
+titanium forging which causes defects in
+
+ align:start position:0%
+titanium forging which causes defects in
+ 
+
+ align:start position:0%
+titanium forging which causes defects in
+it? And so forth. So you basically
+
+ align:start position:0%
+it? And so forth. So you basically
+ 
+
+ align:start position:0%
+it? And so forth. So you basically
+brainstorm the things that could be
+
+ align:start position:0%
+brainstorm the things that could be
+ 
+
+ align:start position:0%
+brainstorm the things that could be
+driving the issue and then you send a
+
+ align:start position:0%
+driving the issue and then you send a
+ 
+
+ align:start position:0%
+driving the issue and then you send a
+little team out to get get some
+
+ align:start position:0%
+little team out to get get some
+ 
+
+ align:start position:0%
+little team out to get get some
+measurements and then have a meeting
+
+ align:start position:0%
+measurements and then have a meeting
+ 
+
+ align:start position:0%
+measurements and then have a meeting
+next week and say what' you find about
+
+ align:start position:0%
+next week and say what' you find about
+ 
+
+ align:start position:0%
+next week and say what' you find about
+the calibration. The guy says okay so
+
+ align:start position:0%
+the calibration. The guy says okay so
+ 
+
+ align:start position:0%
+the calibration. The guy says okay so
+that may not be the issue. So th this is
+
+ align:start position:0%
+that may not be the issue. So th this is
+ 
+
+ align:start position:0%
+that may not be the issue. So th this is
+a great way of displaying the results of
+
+ align:start position:0%
+a great way of displaying the results of
+ 
+
+ align:start position:0%
+a great way of displaying the results of
+brainstorming and giving your
+
+ align:start position:0%
+brainstorming and giving your
+ 
+
+ align:start position:0%
+brainstorming and giving your
+uh the quality engineers and engineers
+
+ align:start position:0%
+uh the quality engineers and engineers
+ 
+
+ align:start position:0%
+uh the quality engineers and engineers
+uh a tremendous way of organizing your
+
+ align:start position:0%
+uh a tremendous way of organizing your
+ 
+
+ align:start position:0%
+uh a tremendous way of organizing your
+your uh search efforts to get rid of the
+
+ align:start position:0%
+your uh search efforts to get rid of the
+ 
+
+ align:start position:0%
+your uh search efforts to get rid of the
+the errors and get high quality. So
+
+ align:start position:0%
+the errors and get high quality. So
+ 
+
+ align:start position:0%
+the errors and get high quality. So
+we're talking about inputs. You know,
+
+ align:start position:0%
+we're talking about inputs. You know,
+ 
+
+ align:start position:0%
+we're talking about inputs. You know,
+Earl talked to you about a process the
+
+ align:start position:0%
+Earl talked to you about a process the
+ 
+
+ align:start position:0%
+Earl talked to you about a process the
+other day, and one of the things that we
+
+ align:start position:0%
+other day, and one of the things that we
+ 
+
+ align:start position:0%
+other day, and one of the things that we
+want to do is to be able to get a
+
+ align:start position:0%
+want to do is to be able to get a
+ 
+
+ align:start position:0%
+want to do is to be able to get a
+repeatable process. I mentioned machine
+
+ align:start position:0%
+repeatable process. I mentioned machine
+ 
+
+ align:start position:0%
+repeatable process. I mentioned machine
+part plus or minus 15,000 and we measure
+
+ align:start position:0%
+part plus or minus 15,000 and we measure
+ 
+
+ align:start position:0%
+part plus or minus 15,000 and we measure
+the parts that are coming out of the
+
+ align:start position:0%
+the parts that are coming out of the
+ 
+
+ align:start position:0%
+the parts that are coming out of the
+process and uh we want to ensure
+
+ align:start position:0%
+process and uh we want to ensure
+ 
+
+ align:start position:0%
+process and uh we want to ensure
+that a high percentage of our output
+
+ align:start position:0%
+that a high percentage of our output
+ 
+
+ align:start position:0%
+that a high percentage of our output
+would like to have 100% of the output in
+
+ align:start position:0%
+would like to have 100% of the output in
+ 
+
+ align:start position:0%
+would like to have 100% of the output in
+fact meet our tolerances. So what we're
+
+ align:start position:0%
+fact meet our tolerances. So what we're
+ 
+
+ align:start position:0%
+fact meet our tolerances. So what we're
+trying to do is basically
+
+ align:start position:0%
+trying to do is basically
+ 
+
+ align:start position:0%
+trying to do is basically
+if we have if we have
+
+ align:start position:0%
+if we have if we have
+ 
+
+ align:start position:0%
+if we have if we have
+nonquality we want to identify the
+
+ align:start position:0%
+nonquality we want to identify the
+ 
+
+ align:start position:0%
+nonquality we want to identify the
+opportunities we want to define them. We
+
+ align:start position:0%
+opportunities we want to define them. We
+ 
+
+ align:start position:0%
+opportunities we want to define them. We
+define them with histograms and so forth
+
+ align:start position:0%
+define them with histograms and so forth
+ 
+
+ align:start position:0%
+define them with histograms and so forth
+and then we pareto them and then we want
+
+ align:start position:0%
+and then we pareto them and then we want
+ 
+
+ align:start position:0%
+and then we pareto them and then we want
+to identify the root cause and we want
+
+ align:start position:0%
+to identify the root cause and we want
+ 
+
+ align:start position:0%
+to identify the root cause and we want
+to take corrective action and then we
+
+ align:start position:0%
+to take corrective action and then we
+ 
+
+ align:start position:0%
+to take corrective action and then we
+want to see if we can get if the
+
+ align:start position:0%
+want to see if we can get if the
+ 
+
+ align:start position:0%
+want to see if we can get if the
+corrective action brings our
+
+ align:start position:0%
+corrective action brings our
+ 
+
+ align:start position:0%
+corrective action brings our
+measured output the measured output
+
+ align:start position:0%
+measured output the measured output
+ 
+
+ align:start position:0%
+measured output the measured output
+within the upper and lower control
+
+ align:start position:0%
+within the upper and lower control
+ 
+
+ align:start position:0%
+within the upper and lower control
+limits of a control chart and we're
+
+ align:start position:0%
+limits of a control chart and we're
+ 
+
+ align:start position:0%
+limits of a control chart and we're
+going to move into that. So there's a
+
+ align:start position:0%
+going to move into that. So there's a
+ 
+
+ align:start position:0%
+going to move into that. So there's a
+couple of terms that are used common
+
+ align:start position:0%
+couple of terms that are used common
+ 
+
+ align:start position:0%
+couple of terms that are used common
+cause and special cause. Common cause is
+
+ align:start position:0%
+cause and special cause. Common cause is
+ 
+
+ align:start position:0%
+cause and special cause. Common cause is
+basically variability that you saw in
+
+ align:start position:0%
+basically variability that you saw in
+ 
+
+ align:start position:0%
+basically variability that you saw in
+rolling the dice and so forth. And that
+
+ align:start position:0%
+rolling the dice and so forth. And that
+ 
+
+ align:start position:0%
+rolling the dice and so forth. And that
+happens uh in in um uh in uh measurement
+
+ align:start position:0%
+happens uh in in um uh in uh measurement
+ 
+
+ align:start position:0%
+happens uh in in um uh in uh measurement
+of uh machine parts or in electricity
+
+ align:start position:0%
+of uh machine parts or in electricity
+ 
+
+ align:start position:0%
+of uh machine parts or in electricity
+and so forth. But special causes are the
+
+ align:start position:0%
+and so forth. But special causes are the
+ 
+
+ align:start position:0%
+and so forth. But special causes are the
+fact is that there's something wrong.
+
+ align:start position:0%
+fact is that there's something wrong.
+ 
+
+ align:start position:0%
+fact is that there's something wrong.
+We haven't trained the people right. We
+
+ align:start position:0%
+We haven't trained the people right. We
+ 
+
+ align:start position:0%
+We haven't trained the people right. We
+have a machine that's not operating. We
+
+ align:start position:0%
+have a machine that's not operating. We
+ 
+
+ align:start position:0%
+have a machine that's not operating. We
+have defects in the material. the method
+
+ align:start position:0%
+have defects in the material. the method
+ 
+
+ align:start position:0%
+have defects in the material. the method
+has been changed and the the folks
+
+ align:start position:0%
+has been changed and the the folks
+ 
+
+ align:start position:0%
+has been changed and the the folks
+didn't catch that and and the occurrence
+
+ align:start position:0%
+didn't catch that and and the occurrence
+ 
+
+ align:start position:0%
+didn't catch that and and the occurrence
+of a special or what we call it
+
+ align:start position:0%
+of a special or what we call it
+ 
+
+ align:start position:0%
+of a special or what we call it
+assignable cause
+
+ align:start position:0%
+assignable cause
+ 
+
+ align:start position:0%
+assignable cause
+typically drives an out of control
+
+ align:start position:0%
+typically drives an out of control
+ 
+
+ align:start position:0%
+typically drives an out of control
+condition and and so we have to go look
+
+ align:start position:0%
+condition and and so we have to go look
+ 
+
+ align:start position:0%
+condition and and so we have to go look
+for that and we use a control chart to
+
+ align:start position:0%
+for that and we use a control chart to
+ 
+
+ align:start position:0%
+for that and we use a control chart to
+do that. So control charting is the
+
+ align:start position:0%
+do that. So control charting is the
+ 
+
+ align:start position:0%
+do that. So control charting is the
+primary tool of statistical process
+
+ align:start position:0%
+primary tool of statistical process
+ 
+
+ align:start position:0%
+primary tool of statistical process
+control. And you I showed your chart the
+
+ align:start position:0%
+control. And you I showed your chart the
+ 
+
+ align:start position:0%
+control. And you I showed your chart the
+other day and you'll probably see it
+
+ align:start position:0%
+other day and you'll probably see it
+ 
+
+ align:start position:0%
+other day and you'll probably see it
+again here that the fact is that what we
+
+ align:start position:0%
+again here that the fact is that what we
+ 
+
+ align:start position:0%
+again here that the fact is that what we
+we want engineering to design in a
+
+ align:start position:0%
+we want engineering to design in a
+ 
+
+ align:start position:0%
+we want engineering to design in a
+robust method so that our suppliers and
+
+ align:start position:0%
+robust method so that our suppliers and
+ 
+
+ align:start position:0%
+robust method so that our suppliers and
+our in-house fabrication can put their
+
+ align:start position:0%
+our in-house fabrication can put their
+ 
+
+ align:start position:0%
+our in-house fabrication can put their
+parts into statistical process control
+
+ align:start position:0%
+parts into statistical process control
+ 
+
+ align:start position:0%
+parts into statistical process control
+so that we get repeatable high quality.
+
+ align:start position:0%
+so that we get repeatable high quality.
+ 
+
+ align:start position:0%
+so that we get repeatable high quality.
+Repeatable high quality. And so what we
+
+ align:start position:0%
+Repeatable high quality. And so what we
+ 
+
+ align:start position:0%
+Repeatable high quality. And so what we
+want to do is so we're going to talk
+
+ align:start position:0%
+want to do is so we're going to talk
+ 
+
+ align:start position:0%
+want to do is so we're going to talk
+about SPC charts, statistical process
+
+ align:start position:0%
+about SPC charts, statistical process
+ 
+
+ align:start position:0%
+about SPC charts, statistical process
+control charts, time sequence charts
+
+ align:start position:0%
+control charts, time sequence charts
+ 
+
+ align:start position:0%
+control charts, time sequence charts
+that are important.
\ No newline at end of file
diff --git a/w_JWcGLiifU.txt b/w_JWcGLiifU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bcb26e8db5087d59866876e04fedc5a41a1235f0
--- /dev/null
+++ b/w_JWcGLiifU.txt
@@ -0,0 +1,2004 @@
+ANNOUNCER: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+mitopencourseware@ocw.mit.edu.
+
+PROFESSOR: Hi.
+
+Welcome once again to our
+lectures in Calculus
+
+Revisited, where today we are
+going to talk about the
+
+calculus of composite
+functions.
+
+Now, recall that we have already
+mentioned in previous
+
+lectures the notion of
+a composite function.
+
+And what we're going to do today
+is to emphasize the idea
+
+as to how often we are called
+upon to find functional
+
+relationships, where the first
+variable is given in terms of
+
+a second variable, and the
+second variable, say, is given
+
+in terms of the third
+variable.
+
+And we wish to find, say,
+the first variable in
+
+terms of the third.
+
+Fact here is where the name "the
+chain rule" seems to come
+
+from, a chain reaction where the
+variables are related in a
+
+chain this way.
+
+Now, we can see this quite
+easily in terms of a diagram.
+
+Suppose, for example,
+that I have a graph
+
+of 'x' versus 'y'.
+
+And suppose also, I have a
+graph of 't' versus 'x'.
+
+Without any reference
+to calculus--
+
+and this is rather important--
+
+without any reference to
+calculus, notice that these
+
+two graphs together allow
+me to visualize
+
+'y' in terms of 't'.
+
+For example, given a particular
+value of 't'--
+
+let's call it 't sub 1'--
+
+given a value of 't', from that
+value of 't', I can find
+
+the corresponding
+value of 'x'.
+
+Let's call that 'x sub 1'.
+
+Now, knowing 'x sub 1', I can
+come to this diagram.
+
+Knowing what 'x sub 1' is,
+I can find 'y sub 1'.
+
+And so you see in this chain of
+two diagrams, a particular
+
+value of 't' allows me to find
+a particular value of 'y'.
+
+And in this particular way,
+I can visualize 'y' as a
+
+function of 't'.
+
+And you see at this stage of the
+game, there is absolutely
+
+no need to have to have any
+knowledge of calculus to
+
+understand what it is that
+we're discussing.
+
+The place that calculus comes
+in is in the following way.
+
+Let's suppose it happened in
+this first diagram that the
+
+graph of 'y' versus
+'x' was smooth.
+
+In other words, let's assume
+that 'y' is a differentiable
+
+function of 'x'.
+
+In particular, the way I've
+drawn this diagram here, we're
+
+saying suppose 'dy dx' evaluated
+at 'x' equals 'x1'
+
+happens to exist.
+
+And suppose also that this graph
+of 'x' versus 't', this
+
+also happens to be a smooth
+curve-- in other words, that
+
+'x' is a differentiable
+function of 't'.
+
+Again, in the language of
+calculus, what we're saying is
+
+the slope of this curve exists
+at this particular point, and
+
+it's given by the 'x dt'
+evaluated at 't' equals 't1'.
+
+Now, without going into a proof
+at this stage, all we're
+
+saying is this.
+
+We suspect that if 'y' is a
+differentiable function of
+
+'x', and 'x' is a differentiable
+function of
+
+'t', that therefore, 'y'
+should also be a
+
+differentiable function
+of 't'.
+
+Notice it's not a conjecture
+at all that if 'y' is a
+
+function of 'x' and 'x' is a
+function of 't', that 'y' is a
+
+function of 't'.
+
+That part is clear.
+
+The conjecture is that we
+suspect that if 'y' is a
+
+differentiable function
+of 'x', and 'x' is a
+
+differentiable function of
+'t', that 'y' will be a
+
+differentiable function
+of 't'.
+
+In still other words, our
+suspicion is perhaps that a
+
+differentiable function of a
+differentiable function is
+
+again a differentiable
+function.
+
+But even more to the point, not
+only do we suspect, for
+
+example, that the 'dy dt' exists
+here when 't' equals
+
+'t1', but in line with our
+lecture of last time, we might
+
+even begin to suspect, in
+terms of this fractional
+
+notation, that not only does
+the 'dy dt' exist at 't'
+
+equals 't1', but it can be found
+by multiplying 'dy dx'
+
+evaluated at 'x' equals 'x1' by
+the 'x dt' evaluated at 't'
+
+equals 't1'.
+
+Again, almost as if the 'dx'
+from the numerator here
+
+canceled with the 'dx' from the
+denominator here, the same
+
+as what we hope our
+differential
+
+notation would be.
+
+The question is granted that
+we would like a result like
+
+this to hold true, in a course
+such as calculus, where we're
+
+working with very tiny numbers
+and quotients of small
+
+numbers, places where we've seen
+that our intuition often
+
+leads us astray, it becomes
+fairly apparent that we had
+
+better have something stronger
+than just intuition in helping
+
+us derive certain results, no
+matter how natural these
+
+results might look.
+
+Now, the way we proceed here
+is as follows again, and
+
+notice again the building
+blocks of calculus.
+
+We go back to the fundamental
+result of last time.
+
+You see, after all, to find
+'dy dt', we want 'delta y'
+
+divided by 'delta t', and then
+we'll take the limit as 'delta
+
+t' approaches 0.
+
+The question is, first of all,
+do we have a nice expression
+
+for 'delta y'?
+
+And in terms of the lecture of
+last time, we saw that if 'y'
+
+was a differentiable function of
+'x', that 'x' equals 'x1',
+
+that 'delta y' was given by ''dy
+dx', evaluated 'x' equals
+
+'x1' times 'delta x'' plus
+'k times delta x'--
+
+and this is crucial now-- where
+the limit of 'k' as
+
+'delta x' approaches 0 was 0.
+
+Now you see, this recipe
+here is ironclad.
+
+I emphasized it from a geometric
+point of view last
+
+time, but you may recall that I
+proved it from an analytical
+
+point of view.
+
+In other words, whether you
+want to visualize this or
+
+derive it, it makes
+no difference.
+
+The key factors that this
+statement here is ironclad.
+
+It's something that we now
+know to be true in our
+
+so-called game of calculus.
+
+The point is, again, now how do
+we use this to check over
+
+our conjectured result?
+
+Again, the answer is almost
+straightforward.
+
+If you keep track of these
+things, you'll notice that
+
+calculus is a one-step-at-a-time
+procedure.
+
+Namely, we want 'dy dt'.
+
+That suggests we first want
+'delta y' divided by 'delta
+
+t', and then we'll take
+the limit as 'delta
+
+t' approaches 0.
+
+So first, we do this.
+
+Namely, starting with our
+known recipe, we divide
+
+through by 'delta t', and
+why can we do this?
+
+We can do this because, of
+course, 'delta t' is not 0.
+
+Now we take the limit of both
+sides of the equality as
+
+'delta t' approaches 0.
+
+We observe that on the left-hand
+side, the limit of
+
+'delta y' divided by 'delta t',
+as 'delta t' approaches 0,
+
+is precisely 'dy dt', and
+in this particular case,
+
+evaluated at 't' equals 't1'.
+
+In other words, notice that the
+left-hand side here, as we
+
+let 'delta t' approach 0,
+becomes the left-hand side of
+
+our conjecture.
+
+Now we recall again that the
+limit of the sum is the sum of
+
+the limits, and we now take
+the limit of each of these
+
+terms separately, each
+term as a product.
+
+The limit of a product is the
+product of the limits.
+
+'dy dx' evaluated at 'x' equals
+'x1' is a constant.
+
+In fact, that's just
+what, it's 'dy'.
+
+The limit of 'dy dx' evaluated
+'x' equals 'x1', as 'delta t'
+
+approaches 0, is just 'dy dx'
+evaluated 'x' equals 'x1'.
+
+On the other hand, by
+definition, the limit of
+
+'delta x' divided by 'delta t',
+as 'delta t' approaches 0,
+
+is just 'dx dt'.
+
+And keeping track of the
+subscripts here, later on
+
+we'll become sloppy and leave
+the subscripts out.
+
+There really is no great
+harm done in
+
+calculus of a single variable.
+
+We shall find, in calculus of
+several variables, that it is
+
+extremely important to keep
+track of the subscripts and
+
+where the variables are being
+evaluated and things of this
+
+particular type.
+
+But I just want to get you used
+to the fact that these
+
+are specific numbers that
+we're using over here.
+
+Now let's continue.
+
+We take the limit of this term
+as 'delta t' approaches 0.
+
+We observe that this becomes 'dx
+dt', and the limit of 'k'
+
+as 'delta t' approaches 0--
+
+well, as 'delta t' approaches
+0, the fact that 'x' is a
+
+differentiable function of
+'t' means that 'delta x'
+
+approaches 0.
+
+And since the limit of 'k' as
+'delta x' approaches 0 is 0,
+
+this term becomes 0.
+
+0 times anything is, any
+finite number, is 0.
+
+That means that this term here
+in the limit becomes 0, and
+
+we're left with the
+desired result.
+
+But notice that we did not
+arrive at this desired result
+
+by hand waving.
+
+We did not say this term 'delta
+x' is getting small, so
+
+it's becoming negligible.
+
+I can't emphasize this point
+enough that it is true that
+
+'delta x' is becoming small
+here, but so is 'delta t', and
+
+that indicates, essentially,
+you're 0 over 0 form.
+
+And the thing that saves us,
+the thing that makes this
+
+whole term drop out, is the key
+fact that 'k' itself goes
+
+to 0, as 'delta x' goes to 0.
+
+By the way, there are easier
+ways of intuitively trying to
+
+remember the chain rule.
+
+For example, one way that people
+often try to visualize
+
+the chain rule is this.
+
+They'll say, OK, we
+want 'dy dt'.
+
+So let's take 'delta y' divided
+by 'delta t', and then
+
+we'll take the limit as 'delta
+t' approaches 0.
+
+Now, you see in this notation
+here, 'delta y' and 'delta t'
+
+are actually numbers.
+
+As numbers, we can write these
+things in fractional notation,
+
+and we could write, what, that
+'delta y' divided by 'delta t'
+
+is ''delta y' divided by 'delta
+x'' times ''delta x'
+
+divided by 'delta t''.
+
+Then we could take the limit,
+as delta t approaches 0, and
+
+we would arrive at
+the same result.
+
+But again, without trying
+to make this thing too
+
+obnoxiously long here, the thing
+to keep in mind is that
+
+'x' is a function of 't'.
+
+And from a rigorous point of
+view, the danger with this
+
+shortcut technique--
+
+and it can be patched up but
+requires a great deal of
+
+mathematical analysis--
+
+the danger here is that as
+'delta t' approaches 0, it's
+
+quite possible that 'delta
+x' will be 0.
+
+In other words, it's possible
+that for a given change in
+
+'t', there is no
+change in 'x'.
+
+Now, if 'delta x' happens to
+equal 0, then we're in
+
+trouble over here.
+
+In other words, in many cases,
+this shortened version gives
+
+us an idea as to what's
+going on.
+
+But our so-called longer method
+has no pitfalls to it.
+
+But enough said for what
+this recipe is.
+
+This result is known as the
+chain rule, and this will be
+
+the topic of the rest
+of today's lecture.
+
+Now, let's take a look at
+some of these things
+
+in a bit more detail.
+
+For example, let's look
+at an illustration.
+
+Suppose we want to find 'dy dx',
+if 'y' is equal to ''x
+
+squared + 1' squared'.
+
+Let me first do this problem
+the wrong way.
+
+Let's put a question
+mark over here.
+
+People learn things like, what,
+bring the exponent down
+
+and replace it by one less.
+
+Now certainly, if I bring the
+exponent down here, and
+
+replace it by one less, this
+is the answer that I get.
+
+Of course the question is,
+is this the right answer?
+
+Well, you see, notice one very
+nice way about finding out
+
+whether an answer is wrong, is
+to first find out by another
+
+way which is the right answer.
+
+For example, if 'y' equals ''x
+squared + 1' squared', it
+
+happens that we know how
+to square this thing.
+
+We can find directly
+that another way of
+
+expressing 'y' is what?
+
+It's 'x' to the fourth plus '2x
+squared' plus 1, but we
+
+have previously learned how to
+differentiate a polynomial.
+
+Through the polynomial is what,
+this is going to be
+
+what? '4 x cubed' plus '4x'.
+
+And you see somehow or other,
+this does not seem to give--
+
+well, for one thing, we
+see that these are
+
+two different answers.
+
+For another thing, if this is
+the one that happens to be the
+
+right answer, this is the one
+that is the wrong answer.
+
+And since we know from previous
+material this is the
+
+right answer, there is something
+wrong with this
+
+regardless of how right
+it might look.
+
+In fact, how much are
+we off by over here?
+
+If we factor this thing
+out, what can we do?
+
+We can write this as '4x'
+times 'x squared + 1'.
+
+And what we really had
+over here was twice
+
+'x squared + 1'.
+
+It seems that the correction
+factor is '2x'.
+
+Now again, notice that the
+derivative of what's inside
+
+the parentheses over here just
+happens to be exactly '2x'.
+
+Now how does the chain rule
+come into play in a
+
+problem of this type?
+
+You see, the thing is, that what
+we should do over here is
+
+rewrite this.
+
+Namely, for example, let 'u'
+equal 'x squared + 1'.
+
+Then what this says is what? 'y'
+is equal to 'u squared',
+
+where 'u' is equal to
+'x squared + 1'.
+
+This is just another way of
+writing this, and in this
+
+particular form, the
+chain rule seems to
+
+be emphasized more.
+
+You see, 'y' is a function of
+'u', 'u' is a function of 'x'.
+
+Notice that from the first
+equation, it is relatively
+
+easy to find 'dy du'.
+
+In fact, it's just what, '2u'.
+
+We'll write that down later.
+
+From the second equation, it's
+easy to find 'du dx'.
+
+And by the chain rule, all we're
+saying is that 'dy du'
+
+times 'du dx' is 'dy dx'.
+
+See, what will that give
+us in this case?
+
+'dy du' is '2u'.
+
+'du dx' is '2x'.
+
+That gives us '4x' times 'u'.
+
+'u' is 'x squared + 1', and so
+this becomes '4x' times 'x
+
+squared + 1'.
+
+And if we now compare this
+with what was the correct
+
+answer, we see that
+in this case,
+
+everything worked out fine.
+
+I suppose what we should do here
+is to comment now on the
+
+danger of memorizing recipes
+without thoroughly
+
+understanding them.
+
+The idea, that said when you
+want to differentiate
+
+something raised to a power that
+you bring the power down
+
+and replace it by one less,
+hinged on the fact that the
+
+thing that was being raised
+to the power was the same
+
+variable with respect to which
+you were doing the
+
+differentiation.
+
+You see, for example, when we
+had 'y' equaled 'x squared',
+
+and then we wrote that 'dy dx'
+is '2x', the thing that was
+
+important over here was
+the fact that what?
+
+The thing that was being raised
+to the second power is
+
+precisely the variable with
+respect to which we were doing
+
+the differentiation.
+
+You see, in the problem 'y'
+equals 'x squared + 1'
+
+squared, the thing that was
+being raised to the second
+
+power was 'x squared + 1'.
+
+The variable with respect
+to which we were
+
+differentiating was 'x'.
+
+In other words, to write this
+thing more symbolically, if
+
+'y' is equal to something,
+square it, then the derivative
+
+that's equal to twice that
+something is the derivative of
+
+'y' with respect to
+that something.
+
+You see, the place the chain
+rule comes in is when the
+
+variable which appears here,
+is not the same as the
+
+variable which appears here, and
+we'll see this in greater
+
+detail as we go along.
+
+By the way, the chain rule comes
+up in another form known
+
+as parametric equations, and
+this form comes up very often.
+
+It's a twist of what we were
+talking about before.
+
+This is the situation in which
+frequently we want to compare
+
+two variables.
+
+Let's call them 'x' and
+'y', all right?
+
+And it happens that both
+variables, 'x' and 'y', can be
+
+expressed more simply in terms
+of a third variable, 't'.
+
+And frequently, what one does
+is try to talk about the
+
+relationship that exists between
+'y' and 'x' in terms
+
+of eliminating t between
+these two equations.
+
+By the way, in terms of
+differential language, there
+
+seems to be an easier way
+of handling this.
+
+Namely, you see, if we
+differentiate the first
+
+equation, we get what, that
+'dy dt' is 'f prime of t'.
+
+If we differentiate the second
+equation, we get that 'dx dt'
+
+is 'g prime of t'.
+
+Now if, as we said in our last
+lecture, we can pretend that
+
+this is really a fraction,
+that it's
+
+'dy' divided by 'dt'--
+
+in other words, if we think of
+'dy' as being 'delta y-tan',
+
+of 'dx' as being 'delta x-tan',
+and 'dt' as being
+
+'delta t', it would appear that
+we could say, what, that
+
+'dy dt' divided by 'dx dt'
+would just be what?
+
+'dy dx'.
+
+In other words, ''dy' divided
+by 'dt'' divided by ''dx'
+
+divided by 'dt'', which is what
+this would say if this
+
+was in differential form,
+would just be 'dy dx'.
+
+In other words, we get the
+feeling that to find the
+
+derivative here, all we have
+to do is differentiate 'y'
+
+with respect to 't', and divide
+that by the derivative
+
+of 'x' with respect to 't'.
+
+And by the way, you see, this
+becomes a particularly
+
+powerful tool in those
+computational cases where we
+
+do not know how to eliminate
+'t', and to solve specifically
+
+for 'y' in terms of 'x'.
+
+You see, in terms of this
+particular recipe over here,
+
+we are allowed to leave 'x'
+and 'y' in terms of 't'.
+
+Again, the same old bugaboo
+comes up to plague us.
+
+The fact that something seems
+natural is not enough to allow
+
+us to believe that it's
+actually correct.
+
+Is there a more rigorous way of
+obtaining the same result?
+
+Again, the answer is yes.
+
+And not only is the answer yes,
+but it goes back to the
+
+fundamental recipe that we
+were discussing in our
+
+previous lecture.
+
+Namely, we know that 'delta y'
+is ''f prime of t' times
+
+'delta t'' plus 'k1 delta t',
+and the 'delta x' is ''g prime
+
+of t' times 'delta t'' plus 'k2
+delta t', where both the
+
+limit of 'k1' and 'k2' as
+'delta t' approach 0.
+
+And this is a notation, I think,
+that takes a while to
+
+get used to.
+
+We're used to seeing letters
+like 'k' stand for constants,
+
+but it's important over here
+to understand that 'k1' and
+
+'k2' are functions of 'delta
+t', that the difference
+
+between 'delta y' and 'delta
+y-tan', 'delta x' and 'delta
+
+x-tan', that difference, which
+is 'k delta x' or 'k delta y',
+
+depending on which problem
+we're dealing with that's
+
+certainly 'k' in that case, does
+depend on how big 'delta
+
+t' happens to be.
+
+At any rate, the important thing
+is that as 'delta t'
+
+approaches 0, these
+go to 0 also.
+
+Now you see if we take this, and
+actually compute 'delta y'
+
+divided by 'delta x'--
+
+and we'll write this a little
+bit more suggestively, factor
+
+out 'delta t' from both
+numerator and denominator--
+
+it rigorously tells us what
+'delta y' divided
+
+by 'delta x' is.
+
+Now we take the limit, as
+'delta x' approaches 0.
+
+That, by definition, is what?
+
+That's by definition 'dy dx'.
+
+Well, you see, first of all,
+we cancel out the 'delta t'
+
+over here, see, 'delta t' is
+not 0, we're assuming.
+
+Since it's not 0 it can be
+canceled out, and once we've
+
+canceled out 'delta t', notice
+that as 'delta t' approaches
+
+0, so does 'delta x'.
+
+As 'delta x' approaches
+0, so does 'delta t'.
+
+That makes 'k1' and
+'k2' go to 0.
+
+And then since the limit of a
+quotient is the quotient of
+
+the limits, provided only the
+'g prime of t' is not 0, we
+
+see that in the eliminating
+process, we
+
+get the same answer.
+
+And by the way, see, once we
+get the same answer, as we
+
+would have got the short way,
+then we can use the
+
+convenience of the
+short recipe.
+
+However, the fact that the short
+recipe was nice is not
+
+enough of a guarantee
+that it was giving
+
+us the correct answer.
+
+As a case in point, it's rather
+interesting to point
+
+out that if you want the
+second derivative--
+
+in other words, let's recall
+what we have here.
+
+We have what? 'y' was given
+to 'b', say 'f of t'.
+
+'x' was given by 'g of t'.
+
+And you see from these two
+equations, what we
+
+could do is find what?
+
+We could find the second
+derivative of 'y with respect
+
+to t', and we could also find
+from this equation the second
+
+derivative of 'x' with
+respect to 't'.
+
+This we could certainly do.
+
+And mechanically, we could
+certainly say, let's cancel
+
+the common denominator.
+
+The interesting thing is that
+when you form that quotient,
+
+whatever that quotient is, it
+does not come out to be the
+
+second derivative of 'y'
+with respect to 'x'.
+
+And there is an interesting
+piece of folklore over here.
+
+I don't know if this ever
+bothered you or not, but it
+
+used to bother me.
+
+I never understood why, when
+you talk about the second
+
+derivative, that the exponent
+was written between the 'd'
+
+and the variable in one case,
+but written at the end in the
+
+other case.
+
+In other words, notice that the
+2 here appears between the
+
+'d' and the 'y', but
+in the denominator,
+
+the 'd' appears outside.
+
+And again, it was the foresight
+of the fathers of
+
+differential calculus who
+noticed rather interestingly
+
+that if mechanically you did
+agree to cancel the common
+
+denominator here, that what you
+would wind up with is not
+
+'d2y dx squared',
+but rather what?
+
+'d2y d2x'.
+
+In other words, if you
+mechanically carried this out,
+
+notice that the notation
+would be incorrect.
+
+The 2 comes out to be in the
+wrong place over here.
+
+You see, again, the interesting
+point is we don't
+
+have to rely on taking
+my word for it.
+
+Somebody might say to me, now
+look, all you've told me is
+
+that I get the wrong answer
+solving this problem this
+
+particular way.
+
+And you've given me a nice
+lecture about how the 2's come
+
+out the wrong way
+and everything.
+
+How do I know that this
+is the wrong answer?
+
+See, and again, everything
+comes back to
+
+fundamentals again.
+
+To find 'd2y dx squared',
+observe that by definition,
+
+that's just 'd dx' of 'dy dx'.
+
+That definition doesn't depend
+on what functions we're
+
+dealing with.
+
+The second derivative with
+respect to 'x' is the
+
+derivative with respect to 'x'
+of the first derivative.
+
+Now, once we have this, you see,
+knowing from our previous
+
+case, that what?
+
+'dy dx' was 'f prime of t'
+divided by 'g prime of t'.
+
+We can now do what?
+
+Take this derivative.
+
+By the way, again, notice
+how the chain
+
+rule comes up in practice.
+
+It's not always dictated
+to us.
+
+If you look at the expression
+inside the parentheses, what
+
+do we have?
+
+Inside the parentheses, we have
+a function of 't' only.
+
+This is a function of 't'.
+
+We want to differentiate
+it with respect to 'x'.
+
+The most natural variable to
+differentiate a function of
+
+'t' with respect to
+is 't' itself.
+
+In other words, what would've
+been nice is if this was the
+
+derivative of 'f prime of t'
+over 'g prime of t', with
+
+respect to 't'.
+
+See, this would be
+easier to handle.
+
+We would then use the quotient
+rule, et cetera.
+
+You see, we can differentiate
+a function of 't'
+
+with respect to 't'.
+
+The trouble is we have
+the derivative
+
+with respect to 'x'.
+
+And if we just change this to
+a 't', that's cheating.
+
+See, I mean, you pretend you
+copy it wrong, because it's an
+
+easier problem to
+solve that way.
+
+The beauty of the chain rule is
+that it allows us to do the
+
+problem the easier way, and
+to doctor up the resulting
+
+incorrect answer by
+the right answer.
+
+Namely, you see what we wanted
+to wind up with here is what,
+
+the derivative not with respect
+to 't', but with
+
+respect to 'x'.
+
+And so, by using the chain
+rule, you see we do what?
+
+We take the derivative with
+respect to 't', multiply that
+
+by 'dt dx'--
+
+again, mechanically, almost
+as if these canceled.
+
+But this is the way the chain
+rule works, and now, you see,
+
+I can work this out by
+the regular quotient
+
+rule, which says what?
+
+It's the denominator times the
+derivative of the numerator.
+
+See, and I am differentiating
+out respect to 't', the
+
+natural variable, minus the
+numerator times the derivative
+
+of the denominator over the
+square of the denominator.
+
+Now, that's a mess by itself,
+meaning, what,
+
+computationally, it's
+not that obvious.
+
+I mean, it's quite a bit of work
+to do here, and then that
+
+whole thing must be multiplied
+by 'dt dx'.
+
+And this, you see, is how one
+goes around finding the second
+
+derivative of 'y' with respect
+to 'x' in terms
+
+of parametric equations.
+
+And more than once, if you're
+not careful, you're going to
+
+find yourself making serious
+mistakes, by forgetting to put
+
+in this factor of 'dt dx'.
+
+By the way, an interesting
+point is that we have not
+
+computed 'dt dx'.
+
+We have computed 'dx dt'.
+
+Let's go back here.
+
+See, 'x' was 'g of t'.
+
+So from that, 'dx dt'
+is 'g prime of t'.
+
+And the question is if 'dx dt'
+is 'g prime of t', how does
+
+one find 'dt dx'?
+
+And again, I think your
+intuition is going to tell you
+
+to just take reciprocals.
+
+And again, the question is it's
+true that this suggests
+
+taking reciprocals, but how do
+we know that we can do this,
+
+and if we can do this, what
+does it really mean?
+
+You see, what this is leading
+into is what's going to be the
+
+subject of our lecture next
+time, called 'Inverse
+
+Functions'.
+
+And just to give you a preview
+of what that lecture is about,
+
+and how we work things like
+this, let's take a look at
+
+what we mean by inverse
+functions.
+
+Well, we won't even mention
+it in much detail.
+
+But let's take a look and see
+what's going on over here.
+
+Let's suppose that the first--
+
+and by the way, I've started to
+abandon using the 't' over
+
+here all the time.
+
+I think those of us in
+engineering work primarily
+
+keep thinking of 't' as being
+time, and you may get the
+
+mistaken notion that if the
+variable isn't time, the thing
+
+doesn't work this way.
+
+In most cases, physically, the
+variable that we're interested
+
+in will be time.
+
+But just for the idea of getting
+you used to the fact
+
+that it makes no difference what
+the name of the variable
+
+is, I've taken the liberty
+of writing this slightly
+
+differently.
+
+Namely, I now assume that y is
+a differentiable function of
+
+'u', and that 'u' is a
+
+differentiable function of 'x'.
+
+By the chain rule, I now know
+that 'y' is a differentiable
+
+function of 'x', and that 'dy
+dx' is 'dy du' times 'du dx'.
+
+The interesting thing here is,
+is that there is nothing in
+
+the statement of the chain rule
+that says that the first
+
+variable in the third that
+'x' and 'y' must
+
+be different variables.
+
+In fact, it might happen that
+'x' and 'y' are synonyms for
+
+one another.
+
+If 'x' and 'y' happen
+to be synonyms--
+
+suppose 'x' and 'y'
+are synonyms--
+
+look what happens over here.
+
+'dy dx' is then just 'dy
+dy', which is 1.
+
+See, let's write that down.
+
+That's 'dy dy'.
+
+This would be 'dy du', and
+if 'x' is equal to
+
+'y', this is 'du dy'.
+
+And if this is equal to 1, and
+this is 'dy du', and this is
+
+'du dy', what does this tell
+us about the relationship
+
+between 'dy du' and 'du dy'?
+
+It says their product is 1.
+
+And if the product is 1, that
+by definition means that the
+
+two factors are reciprocals.
+
+Now, what I want you to observe
+over here is what this
+
+whole thing means.
+
+Namely, if 'y' happens to equal
+'x', do you see what
+
+this thing says?
+
+It says that 'y' is a
+differentiable function of
+
+'u', and 'u' in turn is a
+
+differentiable function of 'y'.
+
+That's precisely what we
+meant when we talked
+
+about inverse functions.
+
+We don't know when an inverse
+function exists.
+
+All we're saying is, is that
+if 'f inverse' happens to
+
+exist over here, to find 'du
+dy', all we have to do is take
+
+the reciprocal of 'dy du'.
+
+Now again, this is
+going to be the
+
+subject of our next lecture.
+
+All I wanted to do was to make
+this aside for the time being.
+
+What I want to do to complete
+today's lecture is to get to
+
+something more tangible.
+
+See, now that we've talked about
+the chain rule, we've
+
+talked about inverse functions a
+little bit, and talked about
+
+these things from a highly
+theoretical point of view,
+
+let's go ahead and
+try to solve a
+
+particularly simple problem.
+
+By particularly simple,
+I mean this.
+
+I have chosen the numbers to
+come out in a very, very easy
+
+way, so we don't get lost
+in the maze of details.
+
+In other words, there was a
+danger that we will confuse
+
+the computational details
+with the theory.
+
+So to emphasize the theory,
+I've tried to pick a
+
+straightforward simple problem,
+but let's see how
+
+this thing works out.
+
+Let's suppose that we're given
+that 'y' is equal to 't to the
+
+fourth power', and 'x' is
+equal to 't squared'.
+
+What we would like to do-- and
+by the way, notice what this
+
+thing says, a given value of 't'
+determines both an 'x' and
+
+the 'y', so that makes 'x' and
+'y' functionally related.
+
+Notice that from the first
+equation, we can find that 'dy
+
+dt' is '4 t cubed'.
+
+From the second equation, we can
+find that 'dx dt' is '2t'.
+
+And if we now use the chain
+rule, 'dy dx' will be what?
+
+It'll be 'dy dt' divided
+by 'dx dt', and
+
+that's just '2 t squared'.
+
+By the way, as a check,
+notice this.
+
+If 'y' is equal to 't to the
+fourth', and 'x' is equal to
+
+'t squared', since 't to the
+fourth' is the square of 't
+
+squared', that says 'y' is
+equal to ''t squared'
+
+squared', 'y' is equal
+to 'x squared'.
+
+And if 'y' is equal to 'x
+squared', in this case, it's
+
+very easy to see that 'dy
+dx' is equal to '2x'.
+
+By the way, when we try to
+compare these two answers,
+
+they look different, but
+that's because they're
+
+expressed in terms of
+different variables.
+
+If we return to our original
+equations, and we see that 'x'
+
+is equal to 't squared'--
+
+'x' is a synonym for
+'t squared'--
+
+this is the check that we have
+received the right answer.
+
+By the way, before I conclude
+today's lecture, I would like
+
+to make a rather
+important aside
+
+about parametric equations.
+
+After one works the problem this
+way, and comes down to
+
+the check, and says, hey, after
+all of this mess over
+
+here, I could have replaced
+it by just 'y' equals 'x
+
+squared', why did I have
+to work with this
+
+in the first place?
+
+We are going to have many, many
+examples throughout the
+
+course that will illustrate
+this.
+
+But at least once in a lecture,
+I would like to go on
+
+record as pointing out that this
+pair of equations tells
+
+you much more than this
+equation here.
+
+This equation simply
+tells you this.
+
+If a particle were moving along
+a curve with respect to
+
+time according to these
+equations, this equation here
+
+simply tells you what path the
+particle would follow.
+
+Namely, the parabola 'y'
+equals 'x squared'.
+
+On the other hand, these
+two equations tell you
+
+much more than that.
+
+These not only tell you that the
+particle moved along the
+
+parabola 'y' equals 'x squared',
+but rather, it tells
+
+you at a particular time the
+point on the parabola that the
+
+particle was at.
+
+What I mean is this.
+
+As another example, suppose we
+had 'y' equals 't squared,'
+
+and 'x' equals 't'.
+
+If we eliminate 't' from these
+two equations, we also find
+
+that 'y' is equal
+to 'x squared'.
+
+Yet notice that this is not the
+same as our original set
+
+of equations.
+
+For example, here, when 't' is
+2, when 't' is 2 over here,
+
+what point are we on as far as
+the parabola is concerned?
+
+When 't' is 2, this is
+2, and this is 4.
+
+That would be the
+point 2 comma 4.
+
+On the other hand, with respect
+to this equation, when
+
+'t' is 2, 'x' is 4, and 'y' is
+16, you see both of these
+
+particles would follow the same
+curve, but they are at
+
+different points at
+different times.
+
+So don't belittle the
+parametric approach.
+
+Having the parameter 't' in
+there tells you more than just
+
+what the path of
+the motion is.
+
+It tells you at what time
+a particle was at what
+
+particular point.
+
+Well, enough about that.
+
+Let's go ahead and find the
+second derivative now.
+
+You see, we already know that
+'dy dx' is '2 t squared'.
+
+Now what we'd like to find
+is 'd2y dx squared'.
+
+Again, the same basic
+definition.
+
+'d2y dx squared'.
+
+The second derivative is the
+derivative of the first
+
+derivative.
+
+The first derivative we saw was
+'2 t squared', so this is
+
+the derivative of
+'2 t squared'.
+
+Again, and this is where most
+of the mistakes are made,
+
+people get sloppy.
+
+They forget the 'x'
+is in here.
+
+They say I know the derivative
+of this, it's '4t'.
+
+Well, the derivative of this is
+'4t' with respect to 't'.
+
+We want to differentiate
+with respect to 'x'.
+
+And the way the chain rule comes
+in, we say OK, since 't'
+
+is the natural variable with
+respect to which to
+
+differentiate, let's do it.
+
+We'll differentiate
+in respect to 't'.
+
+But since the final answer has
+to be with respect to 'x', our
+
+correction factor by the chain
+rule will be 'dt dx'.
+
+Well, the derivative of '2 t
+squared' with respect to 't'
+
+is clearly '4t'.
+
+The derivative of 't' with
+respect to 'x', assuming that
+
+we know something about inverse
+functions, that's the
+
+reciprocal of 'dx dt'.
+
+We just saw that 'dx
+dt' was '2t'.
+
+Therefore, 'dt dx' is 1 over
+'2t', and therefore, the
+
+correct answer appears
+to be 2.
+
+Again, this is why I picked
+the simple case.
+
+Given that 'y' equals 'x
+squared', we see at a glance
+
+that 'dy dx' is equal to '2x',
+and also at a glance,
+
+therefore, that 'd2y dx squared'
+is equal to 2.
+
+By the way, that's exactly
+what this is equal to.
+
+You see, had we forgot the chain
+rule, and had we left
+
+this factor out, this would
+have given us--
+
+in other words, to simply write
+down that the answer was
+
+'4t', which is the most common
+mistake that's made, would
+
+have given us the
+wrong answer.
+
+That's why I put such
+an easy problem.
+
+You see, if I had picked a
+tougher computational problem,
+
+the theory would have
+remained the same.
+
+But when I got two different
+answers, it would have been
+
+difficult to determine which
+was the correct answer, and
+
+which was the incorrect
+answer.
+
+But again, to summarize today's
+lecture, it was a
+
+continuation in a way of the
+lecture of last time, when we
+
+developed the primary recipe
+involving differentials.
+
+Now we applied that
+to find something
+
+called the chain rule.
+
+In the process of emphasizing
+the chain rule, we talked
+
+about the necessity of
+knowing something
+
+about inverse functions.
+
+Consequently, that dictates what
+our next lecture will be
+
+concerned with, namely
+inverse functions.
+
+And so until next
+time, goodbye.
+
+ANNOUNCER: Funding for the
+publication of this video was
+
+provided by the Gabriella and
+Paul Rosenbaum Foundation.
+
+Help OCW continue to provide
+free and open access to MIT
+
+courses by making a donation
+at ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/x0y7z-50ICc.txt b/x0y7z-50ICc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f072856c1081a27fade2c64d24a82f0017e7c01b
--- /dev/null
+++ b/x0y7z-50ICc.txt
@@ -0,0 +1,7755 @@
+align:start position:0%
+ 
+Well, last time
+
+ align:start position:0%
+Well, last time
+ 
+
+ align:start position:0%
+Well, last time
+we had seen that when you write this
+
+ align:start position:0%
+we had seen that when you write this
+ 
+
+ align:start position:0%
+we had seen that when you write this
+electron configuration
+
+ align:start position:0%
+electron configuration
+ 
+
+ align:start position:0%
+electron configuration
+that that electron configuration
+
+ align:start position:0%
+that that electron configuration
+ 
+
+ align:start position:0%
+that that electron configuration
+is a shorthand way of writing the wave
+
+ align:start position:0%
+is a shorthand way of writing the wave
+ 
+
+ align:start position:0%
+is a shorthand way of writing the wave
+functions for the electrons in a
+
+ align:start position:0%
+functions for the electrons in a
+ 
+
+ align:start position:0%
+functions for the electrons in a
+multi-electron atom within this one
+
+ align:start position:0%
+multi-electron atom within this one
+ 
+
+ align:start position:0%
+multi-electron atom within this one
+electron wave approximation.
+
+ align:start position:0%
+electron wave approximation.
+ 
+
+ align:start position:0%
+electron wave approximation.
+But we also noted
+
+ align:start position:0%
+But we also noted
+ 
+
+ align:start position:0%
+But we also noted
+that at most we gave or we assigned a
+
+ align:start position:0%
+that at most we gave or we assigned a
+ 
+
+ align:start position:0%
+that at most we gave or we assigned a
+hydrogen-like
+
+ align:start position:0%
+hydrogen-like
+ 
+
+ align:start position:0%
+hydrogen-like
+wave function to two electrons.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we noted that that was because of
+
+ align:start position:0%
+And we noted that that was because of
+ 
+
+ align:start position:0%
+And we noted that that was because of
+something you already knew about called
+
+ align:start position:0%
+something you already knew about called
+ 
+
+ align:start position:0%
+something you already knew about called
+spin.
+
+ align:start position:0%
+spin.
+ 
+
+ align:start position:0%
+spin.
+And spin last time
+
+ align:start position:0%
+And spin last time
+ 
+
+ align:start position:0%
+And spin last time
+we saw was a quantum mechanical
+
+ align:start position:0%
+we saw was a quantum mechanical
+ 
+
+ align:start position:0%
+we saw was a quantum mechanical
+phenomena. Spin is the intrinsic angular
+
+ align:start position:0%
+phenomena. Spin is the intrinsic angular
+ 
+
+ align:start position:0%
+phenomena. Spin is the intrinsic angular
+momentum built into the particle.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we saw that that spin is designated
+
+ align:start position:0%
+And we saw that that spin is designated
+ 
+
+ align:start position:0%
+And we saw that that spin is designated
+by a fourth quantum number. That fourth
+
+ align:start position:0%
+by a fourth quantum number. That fourth
+ 
+
+ align:start position:0%
+by a fourth quantum number. That fourth
+quantum number here is m subs and it had
+
+ align:start position:0%
+quantum number here is m subs and it had
+ 
+
+ align:start position:0%
+quantum number here is m subs and it had
+two allowed values.
+
+ align:start position:0%
+two allowed values.
+ 
+
+ align:start position:0%
+two allowed values.
+And those allowed values were 1/2 and
+
+ align:start position:0%
+And those allowed values were 1/2 and
+ 
+
+ align:start position:0%
+And those allowed values were 1/2 and
+minus one/2.
+
+ align:start position:0%
+minus one/2.
+ 
+
+ align:start position:0%
+minus one/2.
+And we said that those two allowed
+
+ align:start position:0%
+And we said that those two allowed
+ 
+
+ align:start position:0%
+And we said that those two allowed
+values for those two states represented
+
+ align:start position:0%
+values for those two states represented
+ 
+
+ align:start position:0%
+values for those two states represented
+a spin up and a spin down.
+
+ align:start position:0%
+a spin up and a spin down.
+ 
+
+ align:start position:0%
+a spin up and a spin down.
+Two different polarities in a sense of
+
+ align:start position:0%
+Two different polarities in a sense of
+ 
+
+ align:start position:0%
+Two different polarities in a sense of
+this quantum mechanical phenomenon
+
+ align:start position:0%
+this quantum mechanical phenomenon
+ 
+
+ align:start position:0%
+this quantum mechanical phenomenon
+called spin.
+
+ align:start position:0%
+called spin.
+ 
+
+ align:start position:0%
+called spin.
+All right. Now, how was uh spin actually
+
+ align:start position:0%
+All right. Now, how was uh spin actually
+ 
+
+ align:start position:0%
+All right. Now, how was uh spin actually
+uh experimentally observed? Well,
+
+ align:start position:0%
+uh experimentally observed? Well,
+ 
+
+ align:start position:0%
+uh experimentally observed? Well,
+really thanks to these two gentlemen.
+
+ align:start position:0%
+really thanks to these two gentlemen.
+ 
+
+ align:start position:0%
+really thanks to these two gentlemen.
+Here's Ulenbeck and Hoochmitt.
+
+ align:start position:0%
+Here's Ulenbeck and Hoochmitt.
+ 
+
+ align:start position:0%
+Here's Ulenbeck and Hoochmitt.
+These were very young scientists, I
+
+ align:start position:0%
+These were very young scientists, I
+ 
+
+ align:start position:0%
+These were very young scientists, I
+think posttocks at the time. And what
+
+ align:start position:0%
+think posttocks at the time. And what
+ 
+
+ align:start position:0%
+think posttocks at the time. And what
+they were doing,
+
+ align:start position:0%
+they were doing,
+ 
+
+ align:start position:0%
+they were doing,
+what they were doing was looking at the
+
+ align:start position:0%
+what they were doing was looking at the
+ 
+
+ align:start position:0%
+what they were doing was looking at the
+emission spectra from sodium atoms.
+
+ align:start position:0%
+emission spectra from sodium atoms.
+ 
+
+ align:start position:0%
+emission spectra from sodium atoms.
+And this is 1925. And so they knew
+
+ align:start position:0%
+And this is 1925. And so they knew
+ 
+
+ align:start position:0%
+And this is 1925. And so they knew
+enough already to know at what frequency
+
+ align:start position:0%
+enough already to know at what frequency
+ 
+
+ align:start position:0%
+enough already to know at what frequency
+they should expect to see some emission.
+
+ align:start position:0%
+they should expect to see some emission.
+ 
+
+ align:start position:0%
+they should expect to see some emission.
+And so they looked at the emission,
+
+ align:start position:0%
+And so they looked at the emission,
+ 
+
+ align:start position:0%
+And so they looked at the emission,
+dispersed it, looked at that frequency.
+
+ align:start position:0%
+dispersed it, looked at that frequency.
+ 
+
+ align:start position:0%
+dispersed it, looked at that frequency.
+And instead of seeing emission at that
+
+ align:start position:0%
+And instead of seeing emission at that
+ 
+
+ align:start position:0%
+And instead of seeing emission at that
+particular frequency where they
+
+ align:start position:0%
+particular frequency where they
+ 
+
+ align:start position:0%
+particular frequency where they
+expected,
+
+ align:start position:0%
+expected,
+ 
+
+ align:start position:0%
+expected,
+they saw so this is the expected what
+
+ align:start position:0%
+they saw so this is the expected what
+ 
+
+ align:start position:0%
+they saw so this is the expected what
+they really saw was some emission at a
+
+ align:start position:0%
+they really saw was some emission at a
+ 
+
+ align:start position:0%
+they really saw was some emission at a
+little bit lower frequency and some
+
+ align:start position:0%
+little bit lower frequency and some
+ 
+
+ align:start position:0%
+little bit lower frequency and some
+emission at a little bit higher
+
+ align:start position:0%
+emission at a little bit higher
+ 
+
+ align:start position:0%
+emission at a little bit higher
+frequency. Not much but a little bit
+
+ align:start position:0%
+frequency. Not much but a little bit
+ 
+
+ align:start position:0%
+frequency. Not much but a little bit
+lower and a little bit higher. Okay. And
+
+ align:start position:0%
+lower and a little bit higher. Okay. And
+ 
+
+ align:start position:0%
+lower and a little bit higher. Okay. And
+in spectroscopy, this kind of emission
+
+ align:start position:0%
+in spectroscopy, this kind of emission
+ 
+
+ align:start position:0%
+in spectroscopy, this kind of emission
+is actually called a dublet.
+
+ align:start position:0%
+is actually called a dublet.
+ 
+
+ align:start position:0%
+is actually called a dublet.
+Well, they were quite excited about it
+
+ align:start position:0%
+Well, they were quite excited about it
+ 
+
+ align:start position:0%
+Well, they were quite excited about it
+and thought much about the reason why
+
+ align:start position:0%
+and thought much about the reason why
+ 
+
+ align:start position:0%
+and thought much about the reason why
+there might be a dlet.
+
+ align:start position:0%
+there might be a dlet.
+ 
+
+ align:start position:0%
+there might be a dlet.
+And they reasoned that they could
+
+ align:start position:0%
+And they reasoned that they could
+ 
+
+ align:start position:0%
+And they reasoned that they could
+explain that dlet
+
+ align:start position:0%
+explain that dlet
+ 
+
+ align:start position:0%
+explain that dlet
+if the electron
+
+ align:start position:0%
+if the electron
+ 
+
+ align:start position:0%
+if the electron
+were existing in one of two states, one
+
+ align:start position:0%
+were existing in one of two states, one
+ 
+
+ align:start position:0%
+were existing in one of two states, one
+of two spin states. Hey, so this was
+
+ align:start position:0%
+of two spin states. Hey, so this was
+ 
+
+ align:start position:0%
+of two spin states. Hey, so this was
+revolutionary.
+
+ align:start position:0%
+revolutionary.
+ 
+
+ align:start position:0%
+revolutionary.
+And so they uh took their results
+
+ align:start position:0%
+And so they uh took their results
+ 
+
+ align:start position:0%
+And so they uh took their results
+excitedly to the resident established
+
+ align:start position:0%
+excitedly to the resident established
+ 
+
+ align:start position:0%
+excitedly to the resident established
+scientist that was uh closest who was
+
+ align:start position:0%
+scientist that was uh closest who was
+ 
+
+ align:start position:0%
+scientist that was uh closest who was
+Wolf Gang Powley.
+
+ align:start position:0%
+Wolf Gang Powley.
+ 
+
+ align:start position:0%
+Wolf Gang Powley.
+And Wolf Gang Powie was not a nice man.
+
+ align:start position:0%
+And Wolf Gang Powie was not a nice man.
+ 
+
+ align:start position:0%
+And Wolf Gang Powie was not a nice man.
+But they told Wolf Gang Powley about
+
+ align:start position:0%
+But they told Wolf Gang Powley about
+ 
+
+ align:start position:0%
+But they told Wolf Gang Powley about
+what they saw. And Wolf Gang said,
+
+ align:start position:0%
+what they saw. And Wolf Gang said,
+ 
+
+ align:start position:0%
+what they saw. And Wolf Gang said,
+"Rubbish. you publish that and you will
+
+ align:start position:0%
+"Rubbish. you publish that and you will
+ 
+
+ align:start position:0%
+"Rubbish. you publish that and you will
+destroy your scientific careers.
+
+ align:start position:0%
+destroy your scientific careers.
+ 
+
+ align:start position:0%
+destroy your scientific careers.
+And so they left dejectedly.
+
+ align:start position:0%
+And so they left dejectedly.
+ 
+
+ align:start position:0%
+And so they left dejectedly.
+No sooner had the door shut than Wolf
+
+ align:start position:0%
+No sooner had the door shut than Wolf
+ 
+
+ align:start position:0%
+No sooner had the door shut than Wolf
+Gang sat down and write wrote a paper on
+
+ align:start position:0%
+Gang sat down and write wrote a paper on
+ 
+
+ align:start position:0%
+Gang sat down and write wrote a paper on
+the presence of a fourth quantum number
+
+ align:start position:0%
+the presence of a fourth quantum number
+ 
+
+ align:start position:0%
+the presence of a fourth quantum number
+M subs. Okay, one of the travesties
+
+ align:start position:0%
+M subs. Okay, one of the travesties
+ 
+
+ align:start position:0%
+M subs. Okay, one of the travesties
+really in the history of science that's
+
+ align:start position:0%
+really in the history of science that's
+ 
+
+ align:start position:0%
+really in the history of science that's
+well known now.
+
+ align:start position:0%
+well known now.
+ 
+
+ align:start position:0%
+well known now.
+But um it really did take though dac
+
+ align:start position:0%
+But um it really did take though dac
+ 
+
+ align:start position:0%
+But um it really did take though dac
+another three years later to actually uh
+
+ align:start position:0%
+another three years later to actually uh
+ 
+
+ align:start position:0%
+another three years later to actually uh
+show where this m subs came from this
+
+ align:start position:0%
+show where this m subs came from this
+ 
+
+ align:start position:0%
+show where this m subs came from this
+fourth quantum number came from he had
+
+ align:start position:0%
+fourth quantum number came from he had
+ 
+
+ align:start position:0%
+fourth quantum number came from he had
+to use the relativistic Schroinger
+
+ align:start position:0%
+to use the relativistic Schroinger
+ 
+
+ align:start position:0%
+to use the relativistic Schroinger
+equation which we didn't look at he
+
+ align:start position:0%
+equation which we didn't look at he
+ 
+
+ align:start position:0%
+equation which we didn't look at he
+solved that and when he solve that out
+
+ align:start position:0%
+solved that and when he solve that out
+ 
+
+ align:start position:0%
+solved that and when he solve that out
+drops this fourth quantum number m subs
+
+ align:start position:0%
+drops this fourth quantum number m subs
+ 
+
+ align:start position:0%
+drops this fourth quantum number m subs
+okay but pie did make a contribution
+
+ align:start position:0%
+okay but pie did make a contribution
+ 
+
+ align:start position:0%
+okay but pie did make a contribution
+what he uh he worked on this problem and
+
+ align:start position:0%
+what he uh he worked on this problem and
+ 
+
+ align:start position:0%
+what he uh he worked on this problem and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+worked on the theoretical basis of it
+
+ align:start position:0%
+worked on the theoretical basis of it
+ 
+
+ align:start position:0%
+worked on the theoretical basis of it
+and in the end came out something called
+
+ align:start position:0%
+and in the end came out something called
+ 
+
+ align:start position:0%
+and in the end came out something called
+the powi exclusion principle
+
+ align:start position:0%
+the powi exclusion principle
+ 
+
+ align:start position:0%
+the powi exclusion principle
+and the pi exclusion principle here
+
+ align:start position:0%
+and the pi exclusion principle here
+ 
+
+ align:start position:0%
+and the pi exclusion principle here
+simply says that no two electrons in the
+
+ align:start position:0%
+simply says that no two electrons in the
+ 
+
+ align:start position:0%
+simply says that no two electrons in the
+same atom can have the same electron
+
+ align:start position:0%
+same atom can have the same electron
+ 
+
+ align:start position:0%
+same atom can have the same electron
+wave function.
+
+ align:start position:0%
+wave function.
+ 
+
+ align:start position:0%
+wave function.
+and the same spin.
+
+ align:start position:0%
+and the same spin.
+ 
+
+ align:start position:0%
+and the same spin.
+Or another way to state that is that no
+
+ align:start position:0%
+Or another way to state that is that no
+ 
+
+ align:start position:0%
+Or another way to state that is that no
+two electrons in the same atom can have
+
+ align:start position:0%
+two electrons in the same atom can have
+ 
+
+ align:start position:0%
+two electrons in the same atom can have
+the same set of four quantum numbers.
+
+ align:start position:0%
+the same set of four quantum numbers.
+ 
+
+ align:start position:0%
+the same set of four quantum numbers.
+So for example, in our electron
+
+ align:start position:0%
+So for example, in our electron
+ 
+
+ align:start position:0%
+So for example, in our electron
+configuration here for neon, we've got
+
+ align:start position:0%
+configuration here for neon, we've got
+ 
+
+ align:start position:0%
+configuration here for neon, we've got
+two electrons in this 1s state.
+
+ align:start position:0%
+two electrons in this 1s state.
+ 
+
+ align:start position:0%
+two electrons in this 1s state.
+Well, this electron here has the quantum
+
+ align:start position:0%
+Well, this electron here has the quantum
+ 
+
+ align:start position:0%
+Well, this electron here has the quantum
+number 1 0 0 and 1/2.
+
+ align:start position:0%
+number 1 0 0 and 1/2.
+ 
+
+ align:start position:0%
+number 1 0 0 and 1/2.
+This electron also in that 1s state has
+
+ align:start position:0%
+This electron also in that 1s state has
+ 
+
+ align:start position:0%
+This electron also in that 1s state has
+the quantum numbers 1 0 0 minus one/2.
+
+ align:start position:0%
+the quantum numbers 1 0 0 minus one/2.
+ 
+
+ align:start position:0%
+the quantum numbers 1 0 0 minus one/2.
+So the nl and m quantum numbers are the
+
+ align:start position:0%
+So the nl and m quantum numbers are the
+ 
+
+ align:start position:0%
+So the nl and m quantum numbers are the
+same for these two electrons. But what's
+
+ align:start position:0%
+same for these two electrons. But what's
+ 
+
+ align:start position:0%
+same for these two electrons. But what's
+different is the spin quantum number.
+
+ align:start position:0%
+different is the spin quantum number.
+ 
+
+ align:start position:0%
+different is the spin quantum number.
+one is 1/2 and the other is minus one/2
+
+ align:start position:0%
+one is 1/2 and the other is minus one/2
+ 
+
+ align:start position:0%
+one is 1/2 and the other is minus one/2
+according to the poly exclusion
+
+ align:start position:0%
+according to the poly exclusion
+ 
+
+ align:start position:0%
+according to the poly exclusion
+principle that says you can't have two
+
+ align:start position:0%
+principle that says you can't have two
+ 
+
+ align:start position:0%
+principle that says you can't have two
+electrons in the same atom with the same
+
+ align:start position:0%
+electrons in the same atom with the same
+ 
+
+ align:start position:0%
+electrons in the same atom with the same
+set of four quantum numbers and likewise
+
+ align:start position:0%
+set of four quantum numbers and likewise
+ 
+
+ align:start position:0%
+set of four quantum numbers and likewise
+for example this electron right here
+
+ align:start position:0%
+for example this electron right here
+ 
+
+ align:start position:0%
+for example this electron right here
+quantum numbers 2 1 minus one and plus
+
+ align:start position:0%
+quantum numbers 2 1 minus one and plus
+ 
+
+ align:start position:0%
+quantum numbers 2 1 minus one and plus
+one/2
+
+ align:start position:0%
+one/2
+ 
+
+ align:start position:0%
+one/2
+but this electron quantum numbers 2 1 -
+
+ align:start position:0%
+but this electron quantum numbers 2 1 -
+ 
+
+ align:start position:0%
+but this electron quantum numbers 2 1 -
+one minus one minus one/2 no two
+
+ align:start position:0%
+one minus one minus one/2 no two
+ 
+
+ align:start position:0%
+one minus one minus one/2 no two
+electrons have the same set of four
+
+ align:start position:0%
+electrons have the same set of four
+ 
+
+ align:start position:0%
+electrons have the same set of four
+quantum numbers. All right. So that's
+
+ align:start position:0%
+quantum numbers. All right. So that's
+ 
+
+ align:start position:0%
+quantum numbers. All right. So that's
+why when we were um actually writing
+
+ align:start position:0%
+why when we were um actually writing
+ 
+
+ align:start position:0%
+why when we were um actually writing
+these electron configurations which is
+
+ align:start position:0%
+these electron configurations which is
+ 
+
+ align:start position:0%
+these electron configurations which is
+the shorthand representation for the
+
+ align:start position:0%
+the shorthand representation for the
+ 
+
+ align:start position:0%
+the shorthand representation for the
+wave functions
+
+ align:start position:0%
+wave functions
+ 
+
+ align:start position:0%
+wave functions
+in the one electron approximation for
+
+ align:start position:0%
+in the one electron approximation for
+ 
+
+ align:start position:0%
+in the one electron approximation for
+these multi-electron atoms. That's why
+
+ align:start position:0%
+these multi-electron atoms. That's why
+ 
+
+ align:start position:0%
+these multi-electron atoms. That's why
+we didn't give the 10 electrons in neon
+
+ align:start position:0%
+we didn't give the 10 electrons in neon
+ 
+
+ align:start position:0%
+we didn't give the 10 electrons in neon
+for example. We didn't all give that a
+
+ align:start position:0%
+for example. We didn't all give that a
+ 
+
+ align:start position:0%
+for example. We didn't all give that a
+1s hydrogen-like wave function. Okay.
+
+ align:start position:0%
+1s hydrogen-like wave function. Okay.
+ 
+
+ align:start position:0%
+1s hydrogen-like wave function. Okay.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now what we want to do is we want to
+
+ align:start position:0%
+So now what we want to do is we want to
+ 
+
+ align:start position:0%
+So now what we want to do is we want to
+take a look at what the wave functions
+
+ align:start position:0%
+take a look at what the wave functions
+ 
+
+ align:start position:0%
+take a look at what the wave functions
+for the individual electrons in a
+
+ align:start position:0%
+for the individual electrons in a
+ 
+
+ align:start position:0%
+for the individual electrons in a
+multi-electron atom actually look like.
+
+ align:start position:0%
+multi-electron atom actually look like.
+ 
+
+ align:start position:0%
+multi-electron atom actually look like.
+And to do that we're going to look at
+
+ align:start position:0%
+And to do that we're going to look at
+ 
+
+ align:start position:0%
+And to do that we're going to look at
+the radial probability distribution
+
+ align:start position:0%
+the radial probability distribution
+ 
+
+ align:start position:0%
+the radial probability distribution
+function. All right? because that tells
+
+ align:start position:0%
+function. All right? because that tells
+ 
+
+ align:start position:0%
+function. All right? because that tells
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+a little bit about what the wave
+
+ align:start position:0%
+a little bit about what the wave
+ 
+
+ align:start position:0%
+a little bit about what the wave
+functions look like, right? Because the
+
+ align:start position:0%
+functions look like, right? Because the
+ 
+
+ align:start position:0%
+functions look like, right? Because the
+radial probability distribution function
+
+ align:start position:0%
+radial probability distribution function
+ 
+
+ align:start position:0%
+radial probability distribution function
+as a function of r is the probability of
+
+ align:start position:0%
+as a function of r is the probability of
+ 
+
+ align:start position:0%
+as a function of r is the probability of
+finding the electron a distance between
+
+ align:start position:0%
+finding the electron a distance between
+ 
+
+ align:start position:0%
+finding the electron a distance between
+r and r + dr. All right, that's what the
+
+ align:start position:0%
+r and r + dr. All right, that's what the
+ 
+
+ align:start position:0%
+r and r + dr. All right, that's what the
+radial probability distribution function
+
+ align:start position:0%
+radial probability distribution function
+ 
+
+ align:start position:0%
+radial probability distribution function
+tells us.
+
+ align:start position:0%
+tells us.
+ 
+
+ align:start position:0%
+tells us.
+And so what I did here is to plot the
+
+ align:start position:0%
+And so what I did here is to plot the
+ 
+
+ align:start position:0%
+And so what I did here is to plot the
+wave the radial probability distribution
+
+ align:start position:0%
+wave the radial probability distribution
+ 
+
+ align:start position:0%
+wave the radial probability distribution
+functions for each one of the electrons
+
+ align:start position:0%
+functions for each one of the electrons
+ 
+
+ align:start position:0%
+functions for each one of the electrons
+in um the argon atom. Each one of the
+
+ align:start position:0%
+in um the argon atom. Each one of the
+ 
+
+ align:start position:0%
+in um the argon atom. Each one of the
+electrons in the different states for
+
+ align:start position:0%
+electrons in the different states for
+ 
+
+ align:start position:0%
+electrons in the different states for
+the argon atom. And the first thing that
+
+ align:start position:0%
+the argon atom. And the first thing that
+ 
+
+ align:start position:0%
+the argon atom. And the first thing that
+I want you to notice is that these
+
+ align:start position:0%
+I want you to notice is that these
+ 
+
+ align:start position:0%
+I want you to notice is that these
+radial probability distribution
+
+ align:start position:0%
+radial probability distribution
+ 
+
+ align:start position:0%
+radial probability distribution
+functions for each one of these
+
+ align:start position:0%
+functions for each one of these
+ 
+
+ align:start position:0%
+functions for each one of these
+electrons look very similar in shape to
+
+ align:start position:0%
+electrons look very similar in shape to
+ 
+
+ align:start position:0%
+electrons look very similar in shape to
+the radial probability distribution
+
+ align:start position:0%
+the radial probability distribution
+ 
+
+ align:start position:0%
+the radial probability distribution
+functions for the electron in a hydrogen
+
+ align:start position:0%
+functions for the electron in a hydrogen
+ 
+
+ align:start position:0%
+functions for the electron in a hydrogen
+atom. Okay, in fact they have the same
+
+ align:start position:0%
+atom. Okay, in fact they have the same
+ 
+
+ align:start position:0%
+atom. Okay, in fact they have the same
+shape. If you look here at the uh let me
+
+ align:start position:0%
+shape. If you look here at the uh let me
+ 
+
+ align:start position:0%
+shape. If you look here at the uh let me
+see if you look here at the 1s wave
+
+ align:start position:0%
+see if you look here at the 1s wave
+ 
+
+ align:start position:0%
+see if you look here at the 1s wave
+function which is in green here. All
+
+ align:start position:0%
+function which is in green here. All
+ 
+
+ align:start position:0%
+function which is in green here. All
+right. You see it starts out at zero as
+
+ align:start position:0%
+right. You see it starts out at zero as
+ 
+
+ align:start position:0%
+right. You see it starts out at zero as
+all radial probabilities do, increases,
+
+ align:start position:0%
+all radial probabilities do, increases,
+ 
+
+ align:start position:0%
+all radial probabilities do, increases,
+goes to a maximum, and then drops off
+
+ align:start position:0%
+goes to a maximum, and then drops off
+ 
+
+ align:start position:0%
+goes to a maximum, and then drops off
+exponentially. Hey, that's exactly what
+
+ align:start position:0%
+exponentially. Hey, that's exactly what
+ 
+
+ align:start position:0%
+exponentially. Hey, that's exactly what
+the 1s wave function did in a hydrogen
+
+ align:start position:0%
+the 1s wave function did in a hydrogen
+ 
+
+ align:start position:0%
+the 1s wave function did in a hydrogen
+atom. If you look at the 2s wave
+
+ align:start position:0%
+atom. If you look at the 2s wave
+ 
+
+ align:start position:0%
+atom. If you look at the 2s wave
+function, it starts out at zero, goes to
+
+ align:start position:0%
+function, it starts out at zero, goes to
+ 
+
+ align:start position:0%
+function, it starts out at zero, goes to
+a maximum, and then there's a node.
+
+ align:start position:0%
+a maximum, and then there's a node.
+ 
+
+ align:start position:0%
+a maximum, and then there's a node.
+There's a node right here, and then
+
+ align:start position:0%
+There's a node right here, and then
+ 
+
+ align:start position:0%
+There's a node right here, and then
+there goes to another maximum,
+
+ align:start position:0%
+there goes to another maximum,
+ 
+
+ align:start position:0%
+there goes to another maximum,
+exponentially decays. Hey, that's
+
+ align:start position:0%
+exponentially decays. Hey, that's
+ 
+
+ align:start position:0%
+exponentially decays. Hey, that's
+exactly what the 2s wave function looked
+
+ align:start position:0%
+exactly what the 2s wave function looked
+ 
+
+ align:start position:0%
+exactly what the 2s wave function looked
+like in the hydrogen atom.
+
+ align:start position:0%
+like in the hydrogen atom.
+ 
+
+ align:start position:0%
+like in the hydrogen atom.
+So for the multi-electron atoms, these
+
+ align:start position:0%
+So for the multi-electron atoms, these
+ 
+
+ align:start position:0%
+So for the multi-electron atoms, these
+wave functions have the same basic shape
+
+ align:start position:0%
+wave functions have the same basic shape
+ 
+
+ align:start position:0%
+wave functions have the same basic shape
+and they have the same nodal structure.
+
+ align:start position:0%
+and they have the same nodal structure.
+ 
+
+ align:start position:0%
+and they have the same nodal structure.
+All right, they have the same number of
+
+ align:start position:0%
+All right, they have the same number of
+ 
+
+ align:start position:0%
+All right, they have the same number of
+radial nodes, same number of angular
+
+ align:start position:0%
+radial nodes, same number of angular
+ 
+
+ align:start position:0%
+radial nodes, same number of angular
+nodes.
+
+ align:start position:0%
+nodes.
+ 
+
+ align:start position:0%
+nodes.
+The big difference between these wave
+
+ align:start position:0%
+The big difference between these wave
+ 
+
+ align:start position:0%
+The big difference between these wave
+functions and the hydrogen atom is the
+
+ align:start position:0%
+functions and the hydrogen atom is the
+ 
+
+ align:start position:0%
+functions and the hydrogen atom is the
+distance they the distances from the
+
+ align:start position:0%
+distance they the distances from the
+ 
+
+ align:start position:0%
+distance they the distances from the
+nucleus. For example, if you look at the
+
+ align:start position:0%
+nucleus. For example, if you look at the
+ 
+
+ align:start position:0%
+nucleus. For example, if you look at the
+1s radial probability distribution
+
+ align:start position:0%
+1s radial probability distribution
+ 
+
+ align:start position:0%
+1s radial probability distribution
+for argon, you find that that most
+
+ align:start position:0%
+for argon, you find that that most
+ 
+
+ align:start position:0%
+for argon, you find that that most
+probable value of r is a tenth of an a
+
+ align:start position:0%
+probable value of r is a tenth of an a
+ 
+
+ align:start position:0%
+probable value of r is a tenth of an a
+knot, right? a tenth of a bore radius.
+
+ align:start position:0%
+knot, right? a tenth of a bore radius.
+ 
+
+ align:start position:0%
+knot, right? a tenth of a bore radius.
+What was it for a hydrogen atom in the
+
+ align:start position:0%
+What was it for a hydrogen atom in the
+ 
+
+ align:start position:0%
+What was it for a hydrogen atom in the
+ground state?
+
+ align:start position:0%
+ground state?
+ 
+
+ align:start position:0%
+ground state?
+A not. Right? So this 1s electron here
+
+ align:start position:0%
+A not. Right? So this 1s electron here
+ 
+
+ align:start position:0%
+A not. Right? So this 1s electron here
+is 10 times closer on the average into
+
+ align:start position:0%
+is 10 times closer on the average into
+ 
+
+ align:start position:0%
+is 10 times closer on the average into
+the nucleus
+
+ align:start position:0%
+the nucleus
+ 
+
+ align:start position:0%
+the nucleus
+than the electron in a hydrogen atom.
+
+ align:start position:0%
+than the electron in a hydrogen atom.
+ 
+
+ align:start position:0%
+than the electron in a hydrogen atom.
+And the same is the case for the 2s wave
+
+ align:start position:0%
+And the same is the case for the 2s wave
+ 
+
+ align:start position:0%
+And the same is the case for the 2s wave
+function. 2p 3s 3p. It's all a lot
+
+ align:start position:0%
+function. 2p 3s 3p. It's all a lot
+ 
+
+ align:start position:0%
+function. 2p 3s 3p. It's all a lot
+closer in if you compared those actual
+
+ align:start position:0%
+closer in if you compared those actual
+ 
+
+ align:start position:0%
+closer in if you compared those actual
+values. And the reason it is is because
+
+ align:start position:0%
+values. And the reason it is is because
+ 
+
+ align:start position:0%
+values. And the reason it is is because
+of the kum attraction between the
+
+ align:start position:0%
+of the kum attraction between the
+ 
+
+ align:start position:0%
+of the kum attraction between the
+electron and the nucleus. As you go to
+
+ align:start position:0%
+electron and the nucleus. As you go to
+ 
+
+ align:start position:0%
+electron and the nucleus. As you go to
+argon, right, which has now a + 18 * e
+
+ align:start position:0%
+argon, right, which has now a + 18 * e
+ 
+
+ align:start position:0%
+argon, right, which has now a + 18 * e
+charge on the nucleus. Hey, that's a
+
+ align:start position:0%
+charge on the nucleus. Hey, that's a
+ 
+
+ align:start position:0%
+charge on the nucleus. Hey, that's a
+greater attractive interaction. The
+
+ align:start position:0%
+greater attractive interaction. The
+ 
+
+ align:start position:0%
+greater attractive interaction. The
+culum interaction is the charge on the
+
+ align:start position:0%
+culum interaction is the charge on the
+ 
+
+ align:start position:0%
+culum interaction is the charge on the
+electron times the charge on the
+
+ align:start position:0%
+electron times the charge on the
+ 
+
+ align:start position:0%
+electron times the charge on the
+nucleus. It is that greater electron uh
+
+ align:start position:0%
+nucleus. It is that greater electron uh
+ 
+
+ align:start position:0%
+nucleus. It is that greater electron uh
+attraction that pulls the electrons in
+
+ align:start position:0%
+attraction that pulls the electrons in
+ 
+
+ align:start position:0%
+attraction that pulls the electrons in
+closer to the nucleus. That's why that
+
+ align:start position:0%
+closer to the nucleus. That's why that
+ 
+
+ align:start position:0%
+closer to the nucleus. That's why that
+1s electron that most probable value of
+
+ align:start position:0%
+1s electron that most probable value of
+ 
+
+ align:start position:0%
+1s electron that most probable value of
+r is at a tenth of a knot instead of one
+
+ align:start position:0%
+r is at a tenth of a knot instead of one
+ 
+
+ align:start position:0%
+r is at a tenth of a knot instead of one
+a kn. Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trying to make larger and larger
+
+ align:start position:0%
+trying to make larger and larger
+ 
+
+ align:start position:0%
+trying to make larger and larger
+collapse.
+
+ align:start position:0%
+collapse.
+ 
+
+ align:start position:0%
+collapse.
+Um well certain they they don't collapse
+
+ align:start position:0%
+Um well certain they they don't collapse
+ 
+
+ align:start position:0%
+Um well certain they they don't collapse
+in a sense. They don't collapse into the
+
+ align:start position:0%
+in a sense. They don't collapse into the
+ 
+
+ align:start position:0%
+in a sense. They don't collapse into the
+nucleus. Certainly the probability of
+
+ align:start position:0%
+nucleus. Certainly the probability of
+ 
+
+ align:start position:0%
+nucleus. Certainly the probability of
+finding the electron closer to the
+
+ align:start position:0%
+finding the electron closer to the
+ 
+
+ align:start position:0%
+finding the electron closer to the
+nucleus is greater. But it is true that
+
+ align:start position:0%
+nucleus is greater. But it is true that
+ 
+
+ align:start position:0%
+nucleus is greater. But it is true that
+as you get larger and larger atoms, you
+
+ align:start position:0%
+as you get larger and larger atoms, you
+ 
+
+ align:start position:0%
+as you get larger and larger atoms, you
+have more and more electrons. And so
+
+ align:start position:0%
+have more and more electrons. And so
+ 
+
+ align:start position:0%
+have more and more electrons. And so
+they do generally get bigger, right? and
+
+ align:start position:0%
+they do generally get bigger, right? and
+ 
+
+ align:start position:0%
+they do generally get bigger, right? and
+and we'll see that when we actually look
+
+ align:start position:0%
+and we'll see that when we actually look
+ 
+
+ align:start position:0%
+and we'll see that when we actually look
+at the size and look at the trends in
+
+ align:start position:0%
+at the size and look at the trends in
+ 
+
+ align:start position:0%
+at the size and look at the trends in
+the radius as we go across and down the
+
+ align:start position:0%
+the radius as we go across and down the
+ 
+
+ align:start position:0%
+the radius as we go across and down the
+periodic table. We'll look at that a
+
+ align:start position:0%
+periodic table. We'll look at that a
+ 
+
+ align:start position:0%
+periodic table. We'll look at that a
+little bit more in detail. Okay? And
+
+ align:start position:0%
+little bit more in detail. Okay? And
+ 
+
+ align:start position:0%
+little bit more in detail. Okay? And
+we'll see that in general if you add
+
+ align:start position:0%
+we'll see that in general if you add
+ 
+
+ align:start position:0%
+we'll see that in general if you add
+electrons they get bigger, right?
+
+ align:start position:0%
+electrons they get bigger, right?
+ 
+
+ align:start position:0%
+electrons they get bigger, right?
+Because you do in fact have more
+
+ align:start position:0%
+Because you do in fact have more
+ 
+
+ align:start position:0%
+Because you do in fact have more
+electrons and you put them in these
+
+ align:start position:0%
+electrons and you put them in these
+ 
+
+ align:start position:0%
+electrons and you put them in these
+outer shells. All right? But if you just
+
+ align:start position:0%
+outer shells. All right? But if you just
+ 
+
+ align:start position:0%
+outer shells. All right? But if you just
+do a one-on-one comparison of 1 S to 1 S
+
+ align:start position:0%
+do a one-on-one comparison of 1 S to 1 S
+ 
+
+ align:start position:0%
+do a one-on-one comparison of 1 S to 1 S
+in hydrogen, this is closer in. This is
+
+ align:start position:0%
+in hydrogen, this is closer in. This is
+ 
+
+ align:start position:0%
+in hydrogen, this is closer in. This is
+closer in. This is closer in. Right?
+
+ align:start position:0%
+closer in. This is closer in. Right?
+ 
+
+ align:start position:0%
+closer in. This is closer in. Right?
+Make sense?
+
+ align:start position:0%
+Make sense?
+ 
+
+ align:start position:0%
+Make sense?
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+But now also since I have this diagram
+
+ align:start position:0%
+But now also since I have this diagram
+ 
+
+ align:start position:0%
+But now also since I have this diagram
+up here on the board, I want to just uh
+
+ align:start position:0%
+up here on the board, I want to just uh
+ 
+
+ align:start position:0%
+up here on the board, I want to just uh
+convey an idea that you I think are
+
+ align:start position:0%
+convey an idea that you I think are
+ 
+
+ align:start position:0%
+convey an idea that you I think are
+already familiar with and that is this
+
+ align:start position:0%
+already familiar with and that is this
+ 
+
+ align:start position:0%
+already familiar with and that is this
+idea of shells.
+
+ align:start position:0%
+idea of shells.
+ 
+
+ align:start position:0%
+idea of shells.
+When you say a shell, you think of well
+
+ align:start position:0%
+When you say a shell, you think of well
+ 
+
+ align:start position:0%
+When you say a shell, you think of well
+the n=3 shell, the n equal2 shell, the n
+
+ align:start position:0%
+the n=3 shell, the n equal2 shell, the n
+ 
+
+ align:start position:0%
+the n=3 shell, the n equal2 shell, the n
+equal1 shell, right? But the word shell
+
+ align:start position:0%
+equal1 shell, right? But the word shell
+ 
+
+ align:start position:0%
+equal1 shell, right? But the word shell
+also conotes some spatial uh
+
+ align:start position:0%
+also conotes some spatial uh
+ 
+
+ align:start position:0%
+also conotes some spatial uh
+information, right? And you can see that
+
+ align:start position:0%
+information, right? And you can see that
+ 
+
+ align:start position:0%
+information, right? And you can see that
+spatial information here in this radial
+
+ align:start position:0%
+spatial information here in this radial
+ 
+
+ align:start position:0%
+spatial information here in this radial
+probability distribution function. What
+
+ align:start position:0%
+probability distribution function. What
+ 
+
+ align:start position:0%
+probability distribution function. What
+I want to point out is that the most
+
+ align:start position:0%
+I want to point out is that the most
+ 
+
+ align:start position:0%
+I want to point out is that the most
+probable value of r for the n=3 shell,
+
+ align:start position:0%
+probable value of r for the n=3 shell,
+ 
+
+ align:start position:0%
+probable value of r for the n=3 shell,
+well, those most probable values aren't
+
+ align:start position:0%
+well, those most probable values aren't
+ 
+
+ align:start position:0%
+well, those most probable values aren't
+identical for 3p and 3s, but they're
+
+ align:start position:0%
+identical for 3p and 3s, but they're
+ 
+
+ align:start position:0%
+identical for 3p and 3s, but they're
+very similar. They're similar compared
+
+ align:start position:0%
+very similar. They're similar compared
+ 
+
+ align:start position:0%
+very similar. They're similar compared
+to the most probable value for any
+
+ align:start position:0%
+to the most probable value for any
+ 
+
+ align:start position:0%
+to the most probable value for any
+electron in the n equal 2 shell. And
+
+ align:start position:0%
+electron in the n equal 2 shell. And
+ 
+
+ align:start position:0%
+electron in the n equal 2 shell. And
+those are similar than the most probable
+
+ align:start position:0%
+those are similar than the most probable
+ 
+
+ align:start position:0%
+those are similar than the most probable
+value for the electron in the 1s shell.
+
+ align:start position:0%
+value for the electron in the 1s shell.
+ 
+
+ align:start position:0%
+value for the electron in the 1s shell.
+So here you can see that spatial
+
+ align:start position:0%
+So here you can see that spatial
+ 
+
+ align:start position:0%
+So here you can see that spatial
+information. You can see that on the
+
+ align:start position:0%
+information. You can see that on the
+ 
+
+ align:start position:0%
+information. You can see that on the
+average the n=3 shell is further out
+
+ align:start position:0%
+average the n=3 shell is further out
+ 
+
+ align:start position:0%
+average the n=3 shell is further out
+from the nucleus than the n equal 2
+
+ align:start position:0%
+from the nucleus than the n equal 2
+ 
+
+ align:start position:0%
+from the nucleus than the n equal 2
+shell than the n=1 shell. All right. So
+
+ align:start position:0%
+shell than the n=1 shell. All right. So
+ 
+
+ align:start position:0%
+shell than the n=1 shell. All right. So
+I just wanted to illustrate the concept
+
+ align:start position:0%
+I just wanted to illustrate the concept
+ 
+
+ align:start position:0%
+I just wanted to illustrate the concept
+of shells because we have that radial
+
+ align:start position:0%
+of shells because we have that radial
+ 
+
+ align:start position:0%
+of shells because we have that radial
+probability distribution function up
+
+ align:start position:0%
+probability distribution function up
+ 
+
+ align:start position:0%
+probability distribution function up
+here and it shows you kind of nicely how
+
+ align:start position:0%
+here and it shows you kind of nicely how
+ 
+
+ align:start position:0%
+here and it shows you kind of nicely how
+those shells are indeed separated in
+
+ align:start position:0%
+those shells are indeed separated in
+ 
+
+ align:start position:0%
+those shells are indeed separated in
+space on the average. All right, and
+
+ align:start position:0%
+space on the average. All right, and
+ 
+
+ align:start position:0%
+space on the average. All right, and
+that's important as we're going to see
+
+ align:start position:0%
+that's important as we're going to see
+ 
+
+ align:start position:0%
+that's important as we're going to see
+in a moment. Okay.
+
+ align:start position:0%
+in a moment. Okay.
+ 
+
+ align:start position:0%
+in a moment. Okay.
+Okay. So, that's a quick description of
+
+ align:start position:0%
+Okay. So, that's a quick description of
+ 
+
+ align:start position:0%
+Okay. So, that's a quick description of
+what the wave functions look like for
+
+ align:start position:0%
+what the wave functions look like for
+ 
+
+ align:start position:0%
+what the wave functions look like for
+the electrons in a multi-electron atom.
+
+ align:start position:0%
+the electrons in a multi-electron atom.
+ 
+
+ align:start position:0%
+the electrons in a multi-electron atom.
+They have the similar structure as the
+
+ align:start position:0%
+They have the similar structure as the
+ 
+
+ align:start position:0%
+They have the similar structure as the
+hydrogen atom wave functions. They're
+
+ align:start position:0%
+hydrogen atom wave functions. They're
+ 
+
+ align:start position:0%
+hydrogen atom wave functions. They're
+just all closer in because of the charge
+
+ align:start position:0%
+just all closer in because of the charge
+ 
+
+ align:start position:0%
+just all closer in because of the charge
+on the nucleus.
+
+ align:start position:0%
+on the nucleus.
+ 
+
+ align:start position:0%
+on the nucleus.
+All right. But now what we've got to do
+
+ align:start position:0%
+All right. But now what we've got to do
+ 
+
+ align:start position:0%
+All right. But now what we've got to do
+is that we have to look at the energies
+
+ align:start position:0%
+is that we have to look at the energies
+ 
+
+ align:start position:0%
+is that we have to look at the energies
+of the different states for these
+
+ align:start position:0%
+of the different states for these
+ 
+
+ align:start position:0%
+of the different states for these
+electrons.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we looked at the wave functions and
+
+ align:start position:0%
+So we looked at the wave functions and
+ 
+
+ align:start position:0%
+So we looked at the wave functions and
+now we got to talk about the energies.
+
+ align:start position:0%
+now we got to talk about the energies.
+ 
+
+ align:start position:0%
+now we got to talk about the energies.
+So here is that energy level diagram for
+
+ align:start position:0%
+So here is that energy level diagram for
+ 
+
+ align:start position:0%
+So here is that energy level diagram for
+the hydrogen atom that we drew uh a few
+
+ align:start position:0%
+the hydrogen atom that we drew uh a few
+ 
+
+ align:start position:0%
+the hydrogen atom that we drew uh a few
+days ago.
+
+ align:start position:0%
+days ago.
+ 
+
+ align:start position:0%
+days ago.
+You see that the n equal1 state here
+
+ align:start position:0%
+You see that the n equal1 state here
+ 
+
+ align:start position:0%
+You see that the n equal1 state here
+which is the 1s state is lowest in
+
+ align:start position:0%
+which is the 1s state is lowest in
+ 
+
+ align:start position:0%
+which is the 1s state is lowest in
+energy. The n equal2 state here is
+
+ align:start position:0%
+energy. The n equal2 state here is
+ 
+
+ align:start position:0%
+energy. The n equal2 state here is
+higher in energy.
+
+ align:start position:0%
+higher in energy.
+ 
+
+ align:start position:0%
+higher in energy.
+n equ= 3 n equal 4. And you see that we
+
+ align:start position:0%
+n equ= 3 n equal 4. And you see that we
+ 
+
+ align:start position:0%
+n equ= 3 n equal 4. And you see that we
+have four degenerate states at n equal
+
+ align:start position:0%
+have four degenerate states at n equal
+ 
+
+ align:start position:0%
+have four degenerate states at n equal
+2. That is the 2s state is the same
+
+ align:start position:0%
+2. That is the 2s state is the same
+ 
+
+ align:start position:0%
+2. That is the 2s state is the same
+energy as all the two p states. And at n
+
+ align:start position:0%
+energy as all the two p states. And at n
+ 
+
+ align:start position:0%
+energy as all the two p states. And at n
+equal 3 we got nine degenerate states.
+
+ align:start position:0%
+equal 3 we got nine degenerate states.
+ 
+
+ align:start position:0%
+equal 3 we got nine degenerate states.
+And at n equal 4 we got 16 degenerate
+
+ align:start position:0%
+And at n equal 4 we got 16 degenerate
+ 
+
+ align:start position:0%
+And at n equal 4 we got 16 degenerate
+states. Okay,
+
+ align:start position:0%
+states. Okay,
+ 
+
+ align:start position:0%
+states. Okay,
+but in a multi-electron atom that means
+
+ align:start position:0%
+but in a multi-electron atom that means
+ 
+
+ align:start position:0%
+but in a multi-electron atom that means
+starting with helium in a multi-electron
+
+ align:start position:0%
+starting with helium in a multi-electron
+ 
+
+ align:start position:0%
+starting with helium in a multi-electron
+atom things change.
+
+ align:start position:0%
+atom things change.
+ 
+
+ align:start position:0%
+atom things change.
+And the first big change is that all of
+
+ align:start position:0%
+And the first big change is that all of
+ 
+
+ align:start position:0%
+And the first big change is that all of
+these energies here are lower compared
+
+ align:start position:0%
+these energies here are lower compared
+ 
+
+ align:start position:0%
+these energies here are lower compared
+to the hydrogen atom. The energy of the
+
+ align:start position:0%
+to the hydrogen atom. The energy of the
+ 
+
+ align:start position:0%
+to the hydrogen atom. The energy of the
+1s state is lower than it is in the
+
+ align:start position:0%
+1s state is lower than it is in the
+ 
+
+ align:start position:0%
+1s state is lower than it is in the
+hydrogen atom. The 2s state is lower.
+
+ align:start position:0%
+hydrogen atom. The 2s state is lower.
+ 
+
+ align:start position:0%
+hydrogen atom. The 2s state is lower.
+The twop state is lower. The 3s state is
+
+ align:start position:0%
+The twop state is lower. The 3s state is
+ 
+
+ align:start position:0%
+The twop state is lower. The 3s state is
+lower. All of them are lower. Why do you
+
+ align:start position:0%
+lower. All of them are lower. Why do you
+ 
+
+ align:start position:0%
+lower. All of them are lower. Why do you
+think that's the case?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Anybody?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pardon?
+
+ align:start position:0%
+Pardon?
+ 
+
+ align:start position:0%
+Pardon?
+It's closer to the nucleus. Yeah, it's
+
+ align:start position:0%
+It's closer to the nucleus. Yeah, it's
+ 
+
+ align:start position:0%
+It's closer to the nucleus. Yeah, it's
+closer to the nucleus because the coolum
+
+ align:start position:0%
+closer to the nucleus because the coolum
+ 
+
+ align:start position:0%
+closer to the nucleus because the coolum
+interaction is greater. Right. So that
+
+ align:start position:0%
+interaction is greater. Right. So that
+ 
+
+ align:start position:0%
+interaction is greater. Right. So that
+culum attraction is greater. That energy
+
+ align:start position:0%
+culum attraction is greater. That energy
+ 
+
+ align:start position:0%
+culum attraction is greater. That energy
+is greater. the binding energy is
+
+ align:start position:0%
+is greater. the binding energy is
+ 
+
+ align:start position:0%
+is greater. the binding energy is
+greater. It's more negative. All right?
+
+ align:start position:0%
+greater. It's more negative. All right?
+ 
+
+ align:start position:0%
+greater. It's more negative. All right?
+Same reason as the wave functions were
+
+ align:start position:0%
+Same reason as the wave functions were
+ 
+
+ align:start position:0%
+Same reason as the wave functions were
+in closer to the nucleus. Right? So
+
+ align:start position:0%
+in closer to the nucleus. Right? So
+ 
+
+ align:start position:0%
+in closer to the nucleus. Right? So
+these energies are lower because of the
+
+ align:start position:0%
+these energies are lower because of the
+ 
+
+ align:start position:0%
+these energies are lower because of the
+attraction that larger attraction
+
+ align:start position:0%
+attraction that larger attraction
+ 
+
+ align:start position:0%
+attraction that larger attraction
+because that nucleus is has a greater
+
+ align:start position:0%
+because that nucleus is has a greater
+ 
+
+ align:start position:0%
+because that nucleus is has a greater
+charge on it greater positive charge.
+
+ align:start position:0%
+charge on it greater positive charge.
+ 
+
+ align:start position:0%
+charge on it greater positive charge.
+All right. But the other thing that you
+
+ align:start position:0%
+All right. But the other thing that you
+ 
+
+ align:start position:0%
+All right. But the other thing that you
+see is that the 2s state has no longer
+
+ align:start position:0%
+see is that the 2s state has no longer
+ 
+
+ align:start position:0%
+see is that the 2s state has no longer
+the same energy as the 2p state. The 2s
+
+ align:start position:0%
+the same energy as the 2p state. The 2s
+ 
+
+ align:start position:0%
+the same energy as the 2p state. The 2s
+state is no longer degenerate with the
+
+ align:start position:0%
+state is no longer degenerate with the
+ 
+
+ align:start position:0%
+state is no longer degenerate with the
+2p state.
+
+ align:start position:0%
+2p state.
+ 
+
+ align:start position:0%
+2p state.
+And the 3s state is no longer degenerate
+
+ align:start position:0%
+And the 3s state is no longer degenerate
+ 
+
+ align:start position:0%
+And the 3s state is no longer degenerate
+with the 3p state. And the 3p state is
+
+ align:start position:0%
+with the 3p state. And the 3p state is
+ 
+
+ align:start position:0%
+with the 3p state. And the 3p state is
+no longer degenerate with the 3d state
+
+ align:start position:0%
+no longer degenerate with the 3d state
+ 
+
+ align:start position:0%
+no longer degenerate with the 3d state
+like it is in a hydrogen atom. So how
+
+ align:start position:0%
+like it is in a hydrogen atom. So how
+ 
+
+ align:start position:0%
+like it is in a hydrogen atom. So how
+are we going to uh understand that? All
+
+ align:start position:0%
+are we going to uh understand that? All
+ 
+
+ align:start position:0%
+are we going to uh understand that? All
+right. Why is this degeneracy broken or
+
+ align:start position:0%
+right. Why is this degeneracy broken or
+ 
+
+ align:start position:0%
+right. Why is this degeneracy broken or
+lifted as it's sometimes uh called?
+
+ align:start position:0%
+lifted as it's sometimes uh called?
+ 
+
+ align:start position:0%
+lifted as it's sometimes uh called?
+Well, to explain that, what I'm going to
+
+ align:start position:0%
+Well, to explain that, what I'm going to
+ 
+
+ align:start position:0%
+Well, to explain that, what I'm going to
+have to do here is to talk about a
+
+ align:start position:0%
+have to do here is to talk about a
+ 
+
+ align:start position:0%
+have to do here is to talk about a
+concept called shielding.
+
+ align:start position:0%
+concept called shielding.
+ 
+
+ align:start position:0%
+concept called shielding.
+And shielding then is what uh that
+
+ align:start position:0%
+And shielding then is what uh that
+ 
+
+ align:start position:0%
+And shielding then is what uh that
+affects or or or creates what we call an
+
+ align:start position:0%
+affects or or or creates what we call an
+ 
+
+ align:start position:0%
+affects or or or creates what we call an
+effective charge that we're going to
+
+ align:start position:0%
+effective charge that we're going to
+ 
+
+ align:start position:0%
+effective charge that we're going to
+talk about.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now to do so I want to point out this
+
+ align:start position:0%
+Now to do so I want to point out this
+ 
+
+ align:start position:0%
+Now to do so I want to point out this
+that all of these binding energies right
+
+ align:start position:0%
+that all of these binding energies right
+ 
+
+ align:start position:0%
+that all of these binding energies right
+here these binding energies E subm E
+
+ align:start position:0%
+here these binding energies E subm E
+ 
+
+ align:start position:0%
+here these binding energies E subm E
+subn but now it's E subn L it depends on
+
+ align:start position:0%
+subn but now it's E subn L it depends on
+ 
+
+ align:start position:0%
+subn but now it's E subn L it depends on
+the angular momentum quantum number
+
+ align:start position:0%
+the angular momentum quantum number
+ 
+
+ align:start position:0%
+the angular momentum quantum number
+right those binding energies are minus
+
+ align:start position:0%
+right those binding energies are minus
+ 
+
+ align:start position:0%
+right those binding energies are minus
+the ionization energy
+
+ align:start position:0%
+the ionization energy
+ 
+
+ align:start position:0%
+the ionization energy
+right of the electron in that NL state
+
+ align:start position:0%
+right of the electron in that NL state
+ 
+
+ align:start position:0%
+right of the electron in that NL state
+that's the physical significance of that
+
+ align:start position:0%
+that's the physical significance of that
+ 
+
+ align:start position:0%
+that's the physical significance of that
+but what we're going to do here is that
+
+ align:start position:0%
+but what we're going to do here is that
+ 
+
+ align:start position:0%
+but what we're going to do here is that
+we're going to
+
+ align:start position:0%
+we're going to
+ 
+
+ align:start position:0%
+we're going to
+uh set that energy that binding energy
+
+ align:start position:0%
+uh set that energy that binding energy
+ 
+
+ align:start position:0%
+uh set that energy that binding energy
+equal to this
+
+ align:start position:0%
+equal to this
+ 
+
+ align:start position:0%
+equal to this
+this effective z^2 r subh n squ all
+
+ align:start position:0%
+this effective z^2 r subh n squ all
+ 
+
+ align:start position:0%
+this effective z^2 r subh n squ all
+right and now I'm going to switch to the
+
+ align:start position:0%
+right and now I'm going to switch to the
+ 
+
+ align:start position:0%
+right and now I'm going to switch to the
+board and um we'll talk about that a
+
+ align:start position:0%
+board and um we'll talk about that a
+ 
+
+ align:start position:0%
+board and um we'll talk about that a
+little bit and explain this effective
+
+ align:start position:0%
+little bit and explain this effective
+ 
+
+ align:start position:0%
+little bit and explain this effective
+charge and the shielding so that we can
+
+ align:start position:0%
+charge and the shielding so that we can
+ 
+
+ align:start position:0%
+charge and the shielding so that we can
+understand by the uh so that we can
+
+ align:start position:0%
+understand by the uh so that we can
+ 
+
+ align:start position:0%
+understand by the uh so that we can
+understand why the um 2s state is lower
+
+ align:start position:0%
+understand why the um 2s state is lower
+ 
+
+ align:start position:0%
+understand why the um 2s state is lower
+in energy than the 2p state.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So I just said these states E
+
+ align:start position:0%
+Okay. So I just said these states E
+ 
+
+ align:start position:0%
+Okay. So I just said these states E
+subnl
+
+ align:start position:0%
+subnl
+ 
+
+ align:start position:0%
+subnl
+physically significant is that they are
+
+ align:start position:0%
+physically significant is that they are
+ 
+
+ align:start position:0%
+physically significant is that they are
+minus the ionization energy right
+
+ align:start position:0%
+minus the ionization energy right
+ 
+
+ align:start position:0%
+minus the ionization energy right
+and I'm going to approximate
+
+ align:start position:0%
+and I'm going to approximate
+ 
+
+ align:start position:0%
+and I'm going to approximate
+that binding energy as a hydrogen atom
+
+ align:start position:0%
+that binding energy as a hydrogen atom
+ 
+
+ align:start position:0%
+that binding energy as a hydrogen atom
+binding energy in the sense that I'm
+
+ align:start position:0%
+binding energy in the sense that I'm
+ 
+
+ align:start position:0%
+binding energy in the sense that I'm
+going to make that set that equal to
+
+ align:start position:0%
+going to make that set that equal to
+ 
+
+ align:start position:0%
+going to make that set that equal to
+that RBER constant R subH H over N2 and
+
+ align:start position:0%
+that RBER constant R subH H over N2 and
+ 
+
+ align:start position:0%
+that RBER constant R subH H over N2 and
+this is minus.
+
+ align:start position:0%
+this is minus.
+ 
+
+ align:start position:0%
+this is minus.
+But out here I'm going to put a Z. But
+
+ align:start position:0%
+But out here I'm going to put a Z. But
+ 
+
+ align:start position:0%
+But out here I'm going to put a Z. But
+this Z is not going to be the charge on
+
+ align:start position:0%
+this Z is not going to be the charge on
+ 
+
+ align:start position:0%
+this Z is not going to be the charge on
+the nucleus, but rather it's going to be
+
+ align:start position:0%
+the nucleus, but rather it's going to be
+ 
+
+ align:start position:0%
+the nucleus, but rather it's going to be
+something called the effective charge.
+
+ align:start position:0%
+something called the effective charge.
+ 
+
+ align:start position:0%
+something called the effective charge.
+So Z E FF and it's going to depend on
+
+ align:start position:0%
+So Z E FF and it's going to depend on
+ 
+
+ align:start position:0%
+So Z E FF and it's going to depend on
+both N and L quantum numbers.
+
+ align:start position:0%
+both N and L quantum numbers.
+ 
+
+ align:start position:0%
+both N and L quantum numbers.
+This I'm calling the effective charge.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And what I'm going to do
+
+ align:start position:0%
+Okay. And what I'm going to do
+ 
+
+ align:start position:0%
+Okay. And what I'm going to do
+eventually here
+
+ align:start position:0%
+eventually here
+ 
+
+ align:start position:0%
+eventually here
+is to use the experimentally measured
+
+ align:start position:0%
+is to use the experimentally measured
+ 
+
+ align:start position:0%
+is to use the experimentally measured
+ionization energies
+
+ align:start position:0%
+ionization energies
+ 
+
+ align:start position:0%
+ionization energies
+to back out an effective charge for each
+
+ align:start position:0%
+to back out an effective charge for each
+ 
+
+ align:start position:0%
+to back out an effective charge for each
+electron in each n subl state. That's
+
+ align:start position:0%
+electron in each n subl state. That's
+ 
+
+ align:start position:0%
+electron in each n subl state. That's
+what I'm going to do.
+
+ align:start position:0%
+what I'm going to do.
+ 
+
+ align:start position:0%
+what I'm going to do.
+All right. But now what is this
+
+ align:start position:0%
+All right. But now what is this
+ 
+
+ align:start position:0%
+All right. But now what is this
+effective charge?
+
+ align:start position:0%
+effective charge?
+ 
+
+ align:start position:0%
+effective charge?
+Well, suppose I take a helium atom and
+
+ align:start position:0%
+Well, suppose I take a helium atom and
+ 
+
+ align:start position:0%
+Well, suppose I take a helium atom and
+we have a nucleus here and the charge on
+
+ align:start position:0%
+we have a nucleus here and the charge on
+ 
+
+ align:start position:0%
+we have a nucleus here and the charge on
+that nucleus is plus two
+
+ align:start position:0%
+that nucleus is plus two
+ 
+
+ align:start position:0%
+that nucleus is plus two
+and of course helium has two electrons
+
+ align:start position:0%
+and of course helium has two electrons
+ 
+
+ align:start position:0%
+and of course helium has two electrons
+and so I have say an electron number one
+
+ align:start position:0%
+and so I have say an electron number one
+ 
+
+ align:start position:0%
+and so I have say an electron number one
+over here and I have electron number two
+
+ align:start position:0%
+over here and I have electron number two
+ 
+
+ align:start position:0%
+over here and I have electron number two
+over here. Okay.
+
+ align:start position:0%
+over here. Okay.
+ 
+
+ align:start position:0%
+over here. Okay.
+But the bottom line is that for this
+
+ align:start position:0%
+But the bottom line is that for this
+ 
+
+ align:start position:0%
+But the bottom line is that for this
+electron one right over here,
+
+ align:start position:0%
+electron one right over here,
+ 
+
+ align:start position:0%
+electron one right over here,
+this electron one does not experience
+
+ align:start position:0%
+this electron one does not experience
+ 
+
+ align:start position:0%
+this electron one does not experience
+the full nuclear charge.
+
+ align:start position:0%
+the full nuclear charge.
+ 
+
+ align:start position:0%
+the full nuclear charge.
+Why? Because on the average there's
+
+ align:start position:0%
+Why? Because on the average there's
+ 
+
+ align:start position:0%
+Why? Because on the average there's
+another electron in between it and the
+
+ align:start position:0%
+another electron in between it and the
+ 
+
+ align:start position:0%
+another electron in between it and the
+nucleus.
+
+ align:start position:0%
+nucleus.
+ 
+
+ align:start position:0%
+nucleus.
+And so the charge, the nuclear charge
+
+ align:start position:0%
+And so the charge, the nuclear charge
+ 
+
+ align:start position:0%
+And so the charge, the nuclear charge
+that's experienced by this electron is
+
+ align:start position:0%
+that's experienced by this electron is
+ 
+
+ align:start position:0%
+that's experienced by this electron is
+actually lower than the full nuclear
+
+ align:start position:0%
+actually lower than the full nuclear
+ 
+
+ align:start position:0%
+actually lower than the full nuclear
+charge because this electron here is
+
+ align:start position:0%
+charge because this electron here is
+ 
+
+ align:start position:0%
+charge because this electron here is
+negatively charged and it in effect
+
+ align:start position:0%
+negatively charged and it in effect
+ 
+
+ align:start position:0%
+negatively charged and it in effect
+cancels part of this positive charge on
+
+ align:start position:0%
+cancels part of this positive charge on
+ 
+
+ align:start position:0%
+cancels part of this positive charge on
+the nucleus.
+
+ align:start position:0%
+the nucleus.
+ 
+
+ align:start position:0%
+the nucleus.
+And so this electron doesn't experience
+
+ align:start position:0%
+And so this electron doesn't experience
+ 
+
+ align:start position:0%
+And so this electron doesn't experience
+the full nuclear charge. it experiences
+
+ align:start position:0%
+the full nuclear charge. it experiences
+ 
+
+ align:start position:0%
+the full nuclear charge. it experiences
+something smaller than the full nuclear
+
+ align:start position:0%
+something smaller than the full nuclear
+ 
+
+ align:start position:0%
+something smaller than the full nuclear
+charge.
+
+ align:start position:0%
+charge.
+ 
+
+ align:start position:0%
+charge.
+And that charge that something smaller
+
+ align:start position:0%
+And that charge that something smaller
+ 
+
+ align:start position:0%
+And that charge that something smaller
+than the full nuclear charge is what we
+
+ align:start position:0%
+than the full nuclear charge is what we
+ 
+
+ align:start position:0%
+than the full nuclear charge is what we
+call the effective charge. All right.
+
+ align:start position:0%
+call the effective charge. All right.
+ 
+
+ align:start position:0%
+call the effective charge. All right.
+So, how are we going to determine that
+
+ align:start position:0%
+So, how are we going to determine that
+ 
+
+ align:start position:0%
+So, how are we going to determine that
+effective charge? Well, we're going to
+
+ align:start position:0%
+effective charge? Well, we're going to
+ 
+
+ align:start position:0%
+effective charge? Well, we're going to
+use some experimental measurements to do
+
+ align:start position:0%
+use some experimental measurements to do
+ 
+
+ align:start position:0%
+use some experimental measurements to do
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+We're going to look up the ionization
+
+ align:start position:0%
+We're going to look up the ionization
+ 
+
+ align:start position:0%
+We're going to look up the ionization
+energies or measure the ionization
+
+ align:start position:0%
+energies or measure the ionization
+ 
+
+ align:start position:0%
+energies or measure the ionization
+energies and we'll see how we do that a
+
+ align:start position:0%
+energies and we'll see how we do that a
+ 
+
+ align:start position:0%
+energies and we'll see how we do that a
+little bit later, but you can guess how
+
+ align:start position:0%
+little bit later, but you can guess how
+ 
+
+ align:start position:0%
+little bit later, but you can guess how
+we do that. We're going to look them up
+
+ align:start position:0%
+we do that. We're going to look them up
+ 
+
+ align:start position:0%
+we do that. We're going to look them up
+and we're going to back out the
+
+ align:start position:0%
+and we're going to back out the
+ 
+
+ align:start position:0%
+and we're going to back out the
+effective charge. All right. So, let's
+
+ align:start position:0%
+effective charge. All right. So, let's
+ 
+
+ align:start position:0%
+effective charge. All right. So, let's
+do that for a um let's do that for
+
+ align:start position:0%
+do that for a um let's do that for
+ 
+
+ align:start position:0%
+do that for a um let's do that for
+helium.
+
+ align:start position:0%
+helium.
+ 
+
+ align:start position:0%
+helium.
+If you go and you look up the ionization
+
+ align:start position:0%
+If you go and you look up the ionization
+ 
+
+ align:start position:0%
+If you go and you look up the ionization
+energy for a helium atom, you find that
+
+ align:start position:0%
+energy for a helium atom, you find that
+ 
+
+ align:start position:0%
+energy for a helium atom, you find that
+it is 3.94*
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 -8 jewels.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what I can do is I can rearrange that
+
+ align:start position:0%
+So what I can do is I can rearrange that
+ 
+
+ align:start position:0%
+So what I can do is I can rearrange that
+equation for the effective charge Z E FF
+
+ align:start position:0%
+equation for the effective charge Z E FF
+ 
+
+ align:start position:0%
+equation for the effective charge Z E FF
+and it's N= 1 L= Z right
+
+ align:start position:0%
+and it's N= 1 L= Z right
+ 
+
+ align:start position:0%
+and it's N= 1 L= Z right
+and that will be N2
+
+ align:start position:0%
+and that will be N2
+ 
+
+ align:start position:0%
+and that will be N2
+times that ionization energy
+
+ align:start position:0%
+times that ionization energy
+ 
+
+ align:start position:0%
+times that ionization energy
+over r subh
+
+ align:start position:0%
+over r subh
+ 
+
+ align:start position:0%
+over r subh
+all to the 12.
+
+ align:start position:0%
+all to the 12.
+ 
+
+ align:start position:0%
+all to the 12.
+The ionization energy when we talk about
+
+ align:start position:0%
+The ionization energy when we talk about
+ 
+
+ align:start position:0%
+The ionization energy when we talk about
+ionization energy it's usually from the
+
+ align:start position:0%
+ionization energy it's usually from the
+ 
+
+ align:start position:0%
+ionization energy it's usually from the
+ground state. So n is going to be equal
+
+ align:start position:0%
+ground state. So n is going to be equal
+ 
+
+ align:start position:0%
+ground state. So n is going to be equal
+to 1 here. All right. The ionization
+
+ align:start position:0%
+to 1 here. All right. The ionization
+ 
+
+ align:start position:0%
+to 1 here. All right. The ionization
+energy I just said was 3.94 * 10 -18
+
+ align:start position:0%
+energy I just said was 3.94 * 10 -18
+ 
+
+ align:start position:0%
+energy I just said was 3.94 * 10 -18
+juw. Ridberg's constant in jewels is
+
+ align:start position:0%
+juw. Ridberg's constant in jewels is
+ 
+
+ align:start position:0%
+juw. Ridberg's constant in jewels is
+2.180*
+
+ align:start position:0%
+2.180*
+ 
+
+ align:start position:0%
+2.180*
+10 the minus8 jewels. Hey if I solve
+
+ align:start position:0%
+10 the minus8 jewels. Hey if I solve
+ 
+
+ align:start position:0%
+10 the minus8 jewels. Hey if I solve
+that I find the effective charge is 1.34
+
+ align:start position:0%
+that I find the effective charge is 1.34
+ 
+
+ align:start position:0%
+that I find the effective charge is 1.34
+plus okay so the charge on the helium
+
+ align:start position:0%
+plus okay so the charge on the helium
+ 
+
+ align:start position:0%
+plus okay so the charge on the helium
+nucleus is + two but the effective
+
+ align:start position:0%
+nucleus is + two but the effective
+ 
+
+ align:start position:0%
+nucleus is + two but the effective
+charge for those electrons in the helium
+
+ align:start position:0%
+charge for those electrons in the helium
+ 
+
+ align:start position:0%
+charge for those electrons in the helium
+is less than that it's 1.34.
+
+ align:start position:0%
+is less than that it's 1.34.
+ 
+
+ align:start position:0%
+is less than that it's 1.34.
+Why? because on the average there is
+
+ align:start position:0%
+Why? because on the average there is
+ 
+
+ align:start position:0%
+Why? because on the average there is
+another electron in between that
+
+ align:start position:0%
+another electron in between that
+ 
+
+ align:start position:0%
+another electron in between that
+electron and the nucleus and so the full
+
+ align:start position:0%
+electron and the nucleus and so the full
+ 
+
+ align:start position:0%
+electron and the nucleus and so the full
+nuclear charge isn't experienced. That's
+
+ align:start position:0%
+nuclear charge isn't experienced. That's
+ 
+
+ align:start position:0%
+nuclear charge isn't experienced. That's
+the effective charge.
+
+ align:start position:0%
+the effective charge.
+ 
+
+ align:start position:0%
+the effective charge.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now this effective charge and and the
+
+ align:start position:0%
+So now this effective charge and and the
+ 
+
+ align:start position:0%
+So now this effective charge and and the
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+concept here of shielding that's what's
+
+ align:start position:0%
+concept here of shielding that's what's
+ 
+
+ align:start position:0%
+concept here of shielding that's what's
+so important in why the energy of the 2s
+
+ align:start position:0%
+so important in why the energy of the 2s
+ 
+
+ align:start position:0%
+so important in why the energy of the 2s
+state is lower than the energy of the 2p
+
+ align:start position:0%
+state is lower than the energy of the 2p
+ 
+
+ align:start position:0%
+state is lower than the energy of the 2p
+state. All right. So the energy of 2s
+
+ align:start position:0%
+state. All right. So the energy of 2s
+ 
+
+ align:start position:0%
+state. All right. So the energy of 2s
+the 2s state an electron in the 2s state
+
+ align:start position:0%
+the 2s state an electron in the 2s state
+ 
+
+ align:start position:0%
+the 2s state an electron in the 2s state
+is more strongly bound than in the 2p
+
+ align:start position:0%
+is more strongly bound than in the 2p
+ 
+
+ align:start position:0%
+is more strongly bound than in the 2p
+state. Right? that energy is lower than
+
+ align:start position:0%
+state. Right? that energy is lower than
+ 
+
+ align:start position:0%
+state. Right? that energy is lower than
+the 2p state. Why is that the case?
+
+ align:start position:0%
+the 2p state. Why is that the case?
+ 
+
+ align:start position:0%
+the 2p state. Why is that the case?
+Well, let's think of the lithium atom.
+
+ align:start position:0%
+Well, let's think of the lithium atom.
+ 
+
+ align:start position:0%
+Well, let's think of the lithium atom.
+All right, you know that the electron
+
+ align:start position:0%
+All right, you know that the electron
+ 
+
+ align:start position:0%
+All right, you know that the electron
+configuration of lithium is 1 s2 2 s1.
+
+ align:start position:0%
+configuration of lithium is 1 s2 2 s1.
+ 
+
+ align:start position:0%
+configuration of lithium is 1 s2 2 s1.
+The electron configuration of lithium is
+
+ align:start position:0%
+The electron configuration of lithium is
+ 
+
+ align:start position:0%
+The electron configuration of lithium is
+not 1 s2 2 p1, right? Because that's a
+
+ align:start position:0%
+not 1 s2 2 p1, right? Because that's a
+ 
+
+ align:start position:0%
+not 1 s2 2 p1, right? Because that's a
+higher energy. But why?
+
+ align:start position:0%
+higher energy. But why?
+ 
+
+ align:start position:0%
+higher energy. But why?
+Well, to answer that, we've got to look
+
+ align:start position:0%
+Well, to answer that, we've got to look
+ 
+
+ align:start position:0%
+Well, to answer that, we've got to look
+at a radial probability distribution
+
+ align:start position:0%
+at a radial probability distribution
+ 
+
+ align:start position:0%
+at a radial probability distribution
+again.
+
+ align:start position:0%
+again.
+ 
+
+ align:start position:0%
+again.
+And I'm going to draw it for the 2s
+
+ align:start position:0%
+And I'm going to draw it for the 2s
+ 
+
+ align:start position:0%
+And I'm going to draw it for the 2s
+state.
+
+ align:start position:0%
+state.
+ 
+
+ align:start position:0%
+state.
+So, here it is for the 2s state, right?
+
+ align:start position:0%
+So, here it is for the 2s state, right?
+ 
+
+ align:start position:0%
+So, here it is for the 2s state, right?
+And I'm going to draw it for the 2p
+
+ align:start position:0%
+And I'm going to draw it for the 2p
+ 
+
+ align:start position:0%
+And I'm going to draw it for the 2p
+state. So, here it is for the 2p state.
+
+ align:start position:0%
+state. So, here it is for the 2p state.
+ 
+
+ align:start position:0%
+state. So, here it is for the 2p state.
+All right. So, this is 2 p.
+
+ align:start position:0%
+All right. So, this is 2 p.
+ 
+
+ align:start position:0%
+All right. So, this is 2 p.
+And this is 2s.
+
+ align:start position:0%
+And this is 2s.
+ 
+
+ align:start position:0%
+And this is 2s.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Now we have to do a thought experiment
+
+ align:start position:0%
+Now we have to do a thought experiment
+ 
+
+ align:start position:0%
+Now we have to do a thought experiment
+here. And that is this. If you look at
+
+ align:start position:0%
+here. And that is this. If you look at
+ 
+
+ align:start position:0%
+here. And that is this. If you look at
+the 2s radial probability distribution
+
+ align:start position:0%
+the 2s radial probability distribution
+ 
+
+ align:start position:0%
+the 2s radial probability distribution
+function,
+
+ align:start position:0%
+function,
+ 
+
+ align:start position:0%
+function,
+there is a part of this distribution
+
+ align:start position:0%
+there is a part of this distribution
+ 
+
+ align:start position:0%
+there is a part of this distribution
+function that is really close to the
+
+ align:start position:0%
+function that is really close to the
+ 
+
+ align:start position:0%
+function that is really close to the
+nucleus.
+
+ align:start position:0%
+nucleus.
+ 
+
+ align:start position:0%
+nucleus.
+And for the sake of this argument, let
+
+ align:start position:0%
+And for the sake of this argument, let
+ 
+
+ align:start position:0%
+And for the sake of this argument, let
+me say that for this part of the radial
+
+ align:start position:0%
+me say that for this part of the radial
+ 
+
+ align:start position:0%
+me say that for this part of the radial
+probability distribution function,
+
+ align:start position:0%
+probability distribution function,
+ 
+
+ align:start position:0%
+probability distribution function,
+the effective nuclear charge is plus
+
+ align:start position:0%
+the effective nuclear charge is plus
+ 
+
+ align:start position:0%
+the effective nuclear charge is plus
+three. All right. Now, that's of course
+
+ align:start position:0%
+three. All right. Now, that's of course
+ 
+
+ align:start position:0%
+three. All right. Now, that's of course
+not the case, but bear with me for a
+
+ align:start position:0%
+not the case, but bear with me for a
+ 
+
+ align:start position:0%
+not the case, but bear with me for a
+moment. Okay. We're saying for this part
+
+ align:start position:0%
+moment. Okay. We're saying for this part
+ 
+
+ align:start position:0%
+moment. Okay. We're saying for this part
+of the radial probability distribution
+
+ align:start position:0%
+of the radial probability distribution
+ 
+
+ align:start position:0%
+of the radial probability distribution
+function, the effective charge is plus
+
+ align:start position:0%
+function, the effective charge is plus
+ 
+
+ align:start position:0%
+function, the effective charge is plus
+three. Well, that is the nuclear charge,
+
+ align:start position:0%
+three. Well, that is the nuclear charge,
+ 
+
+ align:start position:0%
+three. Well, that is the nuclear charge,
+but we're saying it's close enough.
+
+ align:start position:0%
+but we're saying it's close enough.
+ 
+
+ align:start position:0%
+but we're saying it's close enough.
+We'll just call it plus three.
+
+ align:start position:0%
+We'll just call it plus three.
+ 
+
+ align:start position:0%
+We'll just call it plus three.
+However, for this part of the radial
+
+ align:start position:0%
+However, for this part of the radial
+ 
+
+ align:start position:0%
+However, for this part of the radial
+probability distribution function here
+
+ align:start position:0%
+probability distribution function here
+ 
+
+ align:start position:0%
+probability distribution function here
+for the 2s,
+
+ align:start position:0%
+for the 2s,
+ 
+
+ align:start position:0%
+for the 2s,
+we're going to say the effective charge
+
+ align:start position:0%
+we're going to say the effective charge
+ 
+
+ align:start position:0%
+we're going to say the effective charge
+Z FF, we're going to say that's plus one
+
+ align:start position:0%
+Z FF, we're going to say that's plus one
+ 
+
+ align:start position:0%
+Z FF, we're going to say that's plus one
+plus one E and plus three E here. All
+
+ align:start position:0%
+plus one E and plus three E here. All
+ 
+
+ align:start position:0%
+plus one E and plus three E here. All
+right. Why? Well, because in lithium
+
+ align:start position:0%
+right. Why? Well, because in lithium
+ 
+
+ align:start position:0%
+right. Why? Well, because in lithium
+there are these 1s electrons that are
+
+ align:start position:0%
+there are these 1s electrons that are
+ 
+
+ align:start position:0%
+there are these 1s electrons that are
+really close in here and we're going to
+
+ align:start position:0%
+really close in here and we're going to
+ 
+
+ align:start position:0%
+really close in here and we're going to
+say that those 2s electrons
+
+ align:start position:0%
+say that those 2s electrons
+ 
+
+ align:start position:0%
+say that those 2s electrons
+screen completely the nuclear charge. So
+
+ align:start position:0%
+screen completely the nuclear charge. So
+ 
+
+ align:start position:0%
+screen completely the nuclear charge. So
+if you've got so you've got a Z equ= +
+
+ align:start position:0%
+if you've got so you've got a Z equ= +
+ 
+
+ align:start position:0%
+if you've got so you've got a Z equ= +
+three and you've got two electrons here
+
+ align:start position:0%
+three and you've got two electrons here
+ 
+
+ align:start position:0%
+three and you've got two electrons here
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+got electron one and electron two and
+
+ align:start position:0%
+got electron one and electron two and
+ 
+
+ align:start position:0%
+got electron one and electron two and
+you got this electron number three out
+
+ align:start position:0%
+you got this electron number three out
+ 
+
+ align:start position:0%
+you got this electron number three out
+here right since this is a minus one and
+
+ align:start position:0%
+here right since this is a minus one and
+ 
+
+ align:start position:0%
+here right since this is a minus one and
+this is a minus one the effective charge
+
+ align:start position:0%
+this is a minus one the effective charge
+ 
+
+ align:start position:0%
+this is a minus one the effective charge
+here for this way out electron hey
+
+ align:start position:0%
+here for this way out electron hey
+ 
+
+ align:start position:0%
+here for this way out electron hey
+that's going to be plus one
+
+ align:start position:0%
+that's going to be plus one
+ 
+
+ align:start position:0%
+that's going to be plus one
+okay but now what about the 2p state if
+
+ align:start position:0%
+okay but now what about the 2p state if
+ 
+
+ align:start position:0%
+okay but now what about the 2p state if
+we had an electron in that 2p state.
+
+ align:start position:0%
+we had an electron in that 2p state.
+ 
+
+ align:start position:0%
+we had an electron in that 2p state.
+Well, what you can see is that because
+
+ align:start position:0%
+Well, what you can see is that because
+ 
+
+ align:start position:0%
+Well, what you can see is that because
+the most probable value of r of the 2p
+
+ align:start position:0%
+the most probable value of r of the 2p
+ 
+
+ align:start position:0%
+the most probable value of r of the 2p
+state isn't about the same place as it
+
+ align:start position:0%
+state isn't about the same place as it
+ 
+
+ align:start position:0%
+state isn't about the same place as it
+is for the 2s state. It's not exactly
+
+ align:start position:0%
+is for the 2s state. It's not exactly
+ 
+
+ align:start position:0%
+is for the 2s state. It's not exactly
+the same. It's actually a little closer
+
+ align:start position:0%
+the same. It's actually a little closer
+ 
+
+ align:start position:0%
+the same. It's actually a little closer
+in, but it's about the same place. We're
+
+ align:start position:0%
+in, but it's about the same place. We're
+ 
+
+ align:start position:0%
+in, but it's about the same place. We're
+going to say that for an electron in the
+
+ align:start position:0%
+going to say that for an electron in the
+ 
+
+ align:start position:0%
+going to say that for an electron in the
+2p state,
+
+ align:start position:0%
+2p state,
+ 
+
+ align:start position:0%
+2p state,
+the effective nuclear charge is going to
+
+ align:start position:0%
+the effective nuclear charge is going to
+ 
+
+ align:start position:0%
+the effective nuclear charge is going to
+be one.
+
+ align:start position:0%
+be one.
+ 
+
+ align:start position:0%
+be one.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. But now, in order to
+
+ align:start position:0%
+Okay. But now, in order to
+ 
+
+ align:start position:0%
+Okay. But now, in order to
+calculate or think about the total
+
+ align:start position:0%
+calculate or think about the total
+ 
+
+ align:start position:0%
+calculate or think about the total
+effective nuclear charge, what we're
+
+ align:start position:0%
+effective nuclear charge, what we're
+ 
+
+ align:start position:0%
+effective nuclear charge, what we're
+going to have to do is to average that
+
+ align:start position:0%
+going to have to do is to average that
+ 
+
+ align:start position:0%
+going to have to do is to average that
+effective charge over these probability
+
+ align:start position:0%
+effective charge over these probability
+ 
+
+ align:start position:0%
+effective charge over these probability
+distributions.
+
+ align:start position:0%
+distributions.
+ 
+
+ align:start position:0%
+distributions.
+So if the 2s probability distribution
+
+ align:start position:0%
+So if the 2s probability distribution
+ 
+
+ align:start position:0%
+So if the 2s probability distribution
+has a part of it where the effective
+
+ align:start position:0%
+has a part of it where the effective
+ 
+
+ align:start position:0%
+has a part of it where the effective
+charge is + three and part of it where
+
+ align:start position:0%
+charge is + three and part of it where
+ 
+
+ align:start position:0%
+charge is + three and part of it where
+it is + one, if I average over that,
+
+ align:start position:0%
+it is + one, if I average over that,
+ 
+
+ align:start position:0%
+it is + one, if I average over that,
+well the effective charge is going to
+
+ align:start position:0%
+well the effective charge is going to
+ 
+
+ align:start position:0%
+well the effective charge is going to
+be, I don't know, plus two or something.
+
+ align:start position:0%
+be, I don't know, plus two or something.
+ 
+
+ align:start position:0%
+be, I don't know, plus two or something.
+But for the 2pwave function where the
+
+ align:start position:0%
+But for the 2pwave function where the
+ 
+
+ align:start position:0%
+But for the 2pwave function where the
+effective charge is all plus one, it
+
+ align:start position:0%
+effective charge is all plus one, it
+ 
+
+ align:start position:0%
+effective charge is all plus one, it
+doesn't have this lobe that's really
+
+ align:start position:0%
+doesn't have this lobe that's really
+ 
+
+ align:start position:0%
+doesn't have this lobe that's really
+close to the nucleus where the effective
+
+ align:start position:0%
+close to the nucleus where the effective
+ 
+
+ align:start position:0%
+close to the nucleus where the effective
+charge is large.
+
+ align:start position:0%
+charge is large.
+ 
+
+ align:start position:0%
+charge is large.
+Well, that effective charge for the 2p
+
+ align:start position:0%
+Well, that effective charge for the 2p
+ 
+
+ align:start position:0%
+Well, that effective charge for the 2p
+is going to be smaller than it is for
+
+ align:start position:0%
+is going to be smaller than it is for
+ 
+
+ align:start position:0%
+is going to be smaller than it is for
+the 2s. All right. So, on the average
+
+ align:start position:0%
+the 2s. All right. So, on the average
+ 
+
+ align:start position:0%
+the 2s. All right. So, on the average
+here,
+
+ align:start position:0%
+here,
+ 
+
+ align:start position:0%
+here,
+the uh the the effective charge
+
+ align:start position:0%
+the uh the the effective charge
+ 
+
+ align:start position:0%
+the uh the the effective charge
+zf
+
+ align:start position:0%
+zf
+ 
+
+ align:start position:0%
+zf
+for the 2s
+
+ align:start position:0%
+for the 2s
+ 
+
+ align:start position:0%
+for the 2s
+is going to be greater than zf
+
+ align:start position:0%
+is going to be greater than zf
+ 
+
+ align:start position:0%
+is going to be greater than zf
+for the 2p electron.
+
+ align:start position:0%
+for the 2p electron.
+ 
+
+ align:start position:0%
+for the 2p electron.
+Since that effective charge is greater,
+
+ align:start position:0%
+Since that effective charge is greater,
+ 
+
+ align:start position:0%
+Since that effective charge is greater,
+well, we showed right up here, right,
+
+ align:start position:0%
+well, we showed right up here, right,
+ 
+
+ align:start position:0%
+well, we showed right up here, right,
+that the binding energy therefore is
+
+ align:start position:0%
+that the binding energy therefore is
+ 
+
+ align:start position:0%
+that the binding energy therefore is
+going to be more negative because that Z
+
+ align:start position:0%
+going to be more negative because that Z
+ 
+
+ align:start position:0%
+going to be more negative because that Z
+is larger. All right?
+
+ align:start position:0%
+is larger. All right?
+ 
+
+ align:start position:0%
+is larger. All right?
+And so that's why the 2s state is lower
+
+ align:start position:0%
+And so that's why the 2s state is lower
+ 
+
+ align:start position:0%
+And so that's why the 2s state is lower
+in energy than the 2p and so on and so
+
+ align:start position:0%
+in energy than the 2p and so on and so
+ 
+
+ align:start position:0%
+in energy than the 2p and so on and so
+forth. Two uh three 3p is lower than 3d
+
+ align:start position:0%
+forth. Two uh three 3p is lower than 3d
+ 
+
+ align:start position:0%
+forth. Two uh three 3p is lower than 3d
+etc etc. Okay, make sense?
+
+ align:start position:0%
+etc etc. Okay, make sense?
+ 
+
+ align:start position:0%
+etc etc. Okay, make sense?
+Okay, it's because of this phenomena of
+
+ align:start position:0%
+Okay, it's because of this phenomena of
+ 
+
+ align:start position:0%
+Okay, it's because of this phenomena of
+shielding and because the 2s wave
+
+ align:start position:0%
+shielding and because the 2s wave
+ 
+
+ align:start position:0%
+shielding and because the 2s wave
+function always has this probability of
+
+ align:start position:0%
+function always has this probability of
+ 
+
+ align:start position:0%
+function always has this probability of
+the electrons being really close to the
+
+ align:start position:0%
+the electrons being really close to the
+ 
+
+ align:start position:0%
+the electrons being really close to the
+nucleus where the effective nuclear
+
+ align:start position:0%
+nucleus where the effective nuclear
+ 
+
+ align:start position:0%
+nucleus where the effective nuclear
+charge is larger. If you average the
+
+ align:start position:0%
+charge is larger. If you average the
+ 
+
+ align:start position:0%
+charge is larger. If you average the
+nuclear charge over the probability
+
+ align:start position:0%
+nuclear charge over the probability
+ 
+
+ align:start position:0%
+nuclear charge over the probability
+distributions, well, the effective
+
+ align:start position:0%
+distributions, well, the effective
+ 
+
+ align:start position:0%
+distributions, well, the effective
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+for that 2s wave function is always
+
+ align:start position:0%
+for that 2s wave function is always
+ 
+
+ align:start position:0%
+for that 2s wave function is always
+going to be larger than the 2p wave
+
+ align:start position:0%
+going to be larger than the 2p wave
+ 
+
+ align:start position:0%
+going to be larger than the 2p wave
+function. So therefore, the 2s is lower
+
+ align:start position:0%
+function. So therefore, the 2s is lower
+ 
+
+ align:start position:0%
+function. So therefore, the 2s is lower
+in energy than the 3p.
+
+ align:start position:0%
+in energy than the 3p.
+ 
+
+ align:start position:0%
+in energy than the 3p.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay, that is an important point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we actually write the electron
+
+ align:start position:0%
+how do we actually write the electron
+ 
+
+ align:start position:0%
+how do we actually write the electron
+configurations for all of the atoms in
+
+ align:start position:0%
+configurations for all of the atoms in
+ 
+
+ align:start position:0%
+configurations for all of the atoms in
+the periodic table?
+
+ align:start position:0%
+the periodic table?
+ 
+
+ align:start position:0%
+the periodic table?
+Well, I think that you already know that
+
+ align:start position:0%
+Well, I think that you already know that
+ 
+
+ align:start position:0%
+Well, I think that you already know that
+we use something called the alpha
+
+ align:start position:0%
+we use something called the alpha
+ 
+
+ align:start position:0%
+we use something called the alpha
+principle.
+
+ align:start position:0%
+principle.
+ 
+
+ align:start position:0%
+principle.
+And the alpha principle is called is the
+
+ align:start position:0%
+And the alpha principle is called is the
+ 
+
+ align:start position:0%
+And the alpha principle is called is the
+building up principle.
+
+ align:start position:0%
+building up principle.
+ 
+
+ align:start position:0%
+building up principle.
+And what that says is that you make a
+
+ align:start position:0%
+And what that says is that you make a
+ 
+
+ align:start position:0%
+And what that says is that you make a
+list here of the states and you order
+
+ align:start position:0%
+list here of the states and you order
+ 
+
+ align:start position:0%
+list here of the states and you order
+the states
+
+ align:start position:0%
+the states
+ 
+
+ align:start position:0%
+the states
+according to their energy. the lowest
+
+ align:start position:0%
+according to their energy. the lowest
+ 
+
+ align:start position:0%
+according to their energy. the lowest
+energy at the bottom here and then keep
+
+ align:start position:0%
+energy at the bottom here and then keep
+ 
+
+ align:start position:0%
+energy at the bottom here and then keep
+on going and we'll talk about we'll talk
+
+ align:start position:0%
+on going and we'll talk about we'll talk
+ 
+
+ align:start position:0%
+on going and we'll talk about we'll talk
+about the uh energies of these states in
+
+ align:start position:0%
+about the uh energies of these states in
+ 
+
+ align:start position:0%
+about the uh energies of these states in
+a moment.
+
+ align:start position:0%
+a moment.
+ 
+
+ align:start position:0%
+a moment.
+But then in order to write the electron
+
+ align:start position:0%
+But then in order to write the electron
+ 
+
+ align:start position:0%
+But then in order to write the electron
+configuration you start putting in
+
+ align:start position:0%
+configuration you start putting in
+ 
+
+ align:start position:0%
+configuration you start putting in
+electrons into these states one electron
+
+ align:start position:0%
+electrons into these states one electron
+ 
+
+ align:start position:0%
+electrons into these states one electron
+at a time starting with the lowest
+
+ align:start position:0%
+at a time starting with the lowest
+ 
+
+ align:start position:0%
+at a time starting with the lowest
+energy state. So for hydrogen well that
+
+ align:start position:0%
+energy state. So for hydrogen well that
+ 
+
+ align:start position:0%
+energy state. So for hydrogen well that
+electron configuration is 1 s.
+
+ align:start position:0%
+electron configuration is 1 s.
+ 
+
+ align:start position:0%
+electron configuration is 1 s.
+for helium. Well, that electron
+
+ align:start position:0%
+for helium. Well, that electron
+ 
+
+ align:start position:0%
+for helium. Well, that electron
+configuration is going to be 1 s
+
+ align:start position:0%
+configuration is going to be 1 s
+ 
+
+ align:start position:0%
+configuration is going to be 1 s
+squared. But you already know that we
+
+ align:start position:0%
+squared. But you already know that we
+ 
+
+ align:start position:0%
+squared. But you already know that we
+have to put in that second electron
+
+ align:start position:0%
+have to put in that second electron
+ 
+
+ align:start position:0%
+have to put in that second electron
+obeying the poly exclusion principle.
+
+ align:start position:0%
+obeying the poly exclusion principle.
+ 
+
+ align:start position:0%
+obeying the poly exclusion principle.
+So, we're going to fill up these states
+
+ align:start position:0%
+So, we're going to fill up these states
+ 
+
+ align:start position:0%
+So, we're going to fill up these states
+one electron at a time, lowest energy
+
+ align:start position:0%
+one electron at a time, lowest energy
+ 
+
+ align:start position:0%
+one electron at a time, lowest energy
+first and then keep going to the next
+
+ align:start position:0%
+first and then keep going to the next
+ 
+
+ align:start position:0%
+first and then keep going to the next
+higher energy level. And we're going to
+
+ align:start position:0%
+higher energy level. And we're going to
+ 
+
+ align:start position:0%
+higher energy level. And we're going to
+do so heating the power exclusion
+
+ align:start position:0%
+do so heating the power exclusion
+ 
+
+ align:start position:0%
+do so heating the power exclusion
+principle as we go. All right. So that's
+
+ align:start position:0%
+principle as we go. All right. So that's
+ 
+
+ align:start position:0%
+principle as we go. All right. So that's
+helium. Here's lithium. All right. Now
+
+ align:start position:0%
+helium. Here's lithium. All right. Now
+ 
+
+ align:start position:0%
+helium. Here's lithium. All right. Now
+we got lithium. We're going to do
+
+ align:start position:0%
+we got lithium. We're going to do
+ 
+
+ align:start position:0%
+we got lithium. We're going to do
+burillium. Well, we have to heed the
+
+ align:start position:0%
+burillium. Well, we have to heed the
+ 
+
+ align:start position:0%
+burillium. Well, we have to heed the
+poly exclusion principle. Right. So that
+
+ align:start position:0%
+poly exclusion principle. Right. So that
+ 
+
+ align:start position:0%
+poly exclusion principle. Right. So that
+electron has to have the opposite spin
+
+ align:start position:0%
+electron has to have the opposite spin
+ 
+
+ align:start position:0%
+electron has to have the opposite spin
+of this electron.
+
+ align:start position:0%
+of this electron.
+ 
+
+ align:start position:0%
+of this electron.
+And now we come to the 2p state. Okay.
+
+ align:start position:0%
+And now we come to the 2p state. Okay.
+ 
+
+ align:start position:0%
+And now we come to the 2p state. Okay.
+We put an electron in the 2p state here.
+
+ align:start position:0%
+We put an electron in the 2p state here.
+ 
+
+ align:start position:0%
+We put an electron in the 2p state here.
+So, we're at nitrogen.
+
+ align:start position:0%
+So, we're at nitrogen.
+ 
+
+ align:start position:0%
+So, we're at nitrogen.
+And it doesn't matter whether you put it
+
+ align:start position:0%
+And it doesn't matter whether you put it
+ 
+
+ align:start position:0%
+And it doesn't matter whether you put it
+in 2px, 2py, or 2pz because they have
+
+ align:start position:0%
+in 2px, 2py, or 2pz because they have
+ 
+
+ align:start position:0%
+in 2px, 2py, or 2pz because they have
+all the same energy, right?
+
+ align:start position:0%
+all the same energy, right?
+ 
+
+ align:start position:0%
+all the same energy, right?
+All right. But now we got to add another
+
+ align:start position:0%
+All right. But now we got to add another
+ 
+
+ align:start position:0%
+All right. But now we got to add another
+electron. We got to get to carbon.
+
+ align:start position:0%
+electron. We got to get to carbon.
+ 
+
+ align:start position:0%
+electron. We got to get to carbon.
+And when we get to carbon here, we're
+
+ align:start position:0%
+And when we get to carbon here, we're
+ 
+
+ align:start position:0%
+And when we get to carbon here, we're
+going to have to follow something else
+
+ align:start position:0%
+going to have to follow something else
+ 
+
+ align:start position:0%
+going to have to follow something else
+called the Hunts rule. And Hunts rule
+
+ align:start position:0%
+called the Hunts rule. And Hunts rule
+ 
+
+ align:start position:0%
+called the Hunts rule. And Hunts rule
+says the following.
+
+ align:start position:0%
+says the following.
+ 
+
+ align:start position:0%
+says the following.
+It says that when electrons are added to
+
+ align:start position:0%
+It says that when electrons are added to
+ 
+
+ align:start position:0%
+It says that when electrons are added to
+the states of the same energy, which is
+
+ align:start position:0%
+the states of the same energy, which is
+ 
+
+ align:start position:0%
+the states of the same energy, which is
+what we've got right here, right?
+
+ align:start position:0%
+what we've got right here, right?
+ 
+
+ align:start position:0%
+what we've got right here, right?
+A single electron enters each state
+
+ align:start position:0%
+A single electron enters each state
+ 
+
+ align:start position:0%
+A single electron enters each state
+before a second one enters any state.
+
+ align:start position:0%
+before a second one enters any state.
+ 
+
+ align:start position:0%
+before a second one enters any state.
+and the electrons the spins remain
+
+ align:start position:0%
+and the electrons the spins remain
+ 
+
+ align:start position:0%
+and the electrons the spins remain
+parallel. So where do we put carbon's
+
+ align:start position:0%
+parallel. So where do we put carbon's
+ 
+
+ align:start position:0%
+parallel. So where do we put carbon's
+electron? Do we put it here?
+
+ align:start position:0%
+electron? Do we put it here?
+ 
+
+ align:start position:0%
+electron? Do we put it here?
+Okay. No, because we violate something
+
+ align:start position:0%
+Okay. No, because we violate something
+ 
+
+ align:start position:0%
+Okay. No, because we violate something
+called Hunts rule. All right. So it
+
+ align:start position:0%
+called Hunts rule. All right. So it
+ 
+
+ align:start position:0%
+called Hunts rule. All right. So it
+means that we have to put it in 2py or
+
+ align:start position:0%
+means that we have to put it in 2py or
+ 
+
+ align:start position:0%
+means that we have to put it in 2py or
+2pz.
+
+ align:start position:0%
+2pz.
+ 
+
+ align:start position:0%
+2pz.
+But do we put it in here? No. It's
+
+ align:start position:0%
+But do we put it in here? No. It's
+ 
+
+ align:start position:0%
+But do we put it in here? No. It's
+upside down. According to Hunt's rule,
+
+ align:start position:0%
+upside down. According to Hunt's rule,
+ 
+
+ align:start position:0%
+upside down. According to Hunt's rule,
+the spins have to remain parallel. Could
+
+ align:start position:0%
+the spins have to remain parallel. Could
+ 
+
+ align:start position:0%
+the spins have to remain parallel. Could
+you turn up the volume a little bit? The
+
+ align:start position:0%
+you turn up the volume a little bit? The
+ 
+
+ align:start position:0%
+you turn up the volume a little bit? The
+spins have to remain uh parallel, right?
+
+ align:start position:0%
+spins have to remain uh parallel, right?
+ 
+
+ align:start position:0%
+spins have to remain uh parallel, right?
+In order to have the lowest energy
+
+ align:start position:0%
+In order to have the lowest energy
+ 
+
+ align:start position:0%
+In order to have the lowest energy
+configuration.
+
+ align:start position:0%
+configuration.
+ 
+
+ align:start position:0%
+configuration.
+All right. And so we've got to put it in
+
+ align:start position:0%
+All right. And so we've got to put it in
+ 
+
+ align:start position:0%
+All right. And so we've got to put it in
+here, right? And with the spin being
+
+ align:start position:0%
+here, right? And with the spin being
+ 
+
+ align:start position:0%
+here, right? And with the spin being
+parallel to the original to the spin of
+
+ align:start position:0%
+parallel to the original to the spin of
+ 
+
+ align:start position:0%
+parallel to the original to the spin of
+the other electron.
+
+ align:start position:0%
+the other electron.
+ 
+
+ align:start position:0%
+the other electron.
+Okay. So now we get to uh oxygen
+
+ align:start position:0%
+Okay. So now we get to uh oxygen
+ 
+
+ align:start position:0%
+Okay. So now we get to uh oxygen
+and uh we put the electron again in one
+
+ align:start position:0%
+and uh we put the electron again in one
+ 
+
+ align:start position:0%
+and uh we put the electron again in one
+of the other two p states. The spin has
+
+ align:start position:0%
+of the other two p states. The spin has
+ 
+
+ align:start position:0%
+of the other two p states. The spin has
+to be parallel.
+
+ align:start position:0%
+to be parallel.
+ 
+
+ align:start position:0%
+to be parallel.
+Okay. And then we keep going. Now we can
+
+ align:start position:0%
+Okay. And then we keep going. Now we can
+ 
+
+ align:start position:0%
+Okay. And then we keep going. Now we can
+start to double up on the two p states.
+
+ align:start position:0%
+start to double up on the two p states.
+ 
+
+ align:start position:0%
+start to double up on the two p states.
+All right. That electron goes in the
+
+ align:start position:0%
+All right. That electron goes in the
+ 
+
+ align:start position:0%
+All right. That electron goes in the
+other spin. That one goes the other
+
+ align:start position:0%
+other spin. That one goes the other
+ 
+
+ align:start position:0%
+other spin. That one goes the other
+spin. That one goes in the other spin.
+
+ align:start position:0%
+spin. That one goes in the other spin.
+ 
+
+ align:start position:0%
+spin. That one goes in the other spin.
+So now we're finished with the two p
+
+ align:start position:0%
+So now we're finished with the two p
+ 
+
+ align:start position:0%
+So now we're finished with the two p
+states. And now we're going to put the
+
+ align:start position:0%
+states. And now we're going to put the
+ 
+
+ align:start position:0%
+states. And now we're going to put the
+electron in 3s state and the next one.
+
+ align:start position:0%
+electron in 3s state and the next one.
+ 
+
+ align:start position:0%
+electron in 3s state and the next one.
+Now we're ready for the 3p states again.
+
+ align:start position:0%
+Now we're ready for the 3p states again.
+ 
+
+ align:start position:0%
+Now we're ready for the 3p states again.
+So the first one goes into one of the
+
+ align:start position:0%
+So the first one goes into one of the
+ 
+
+ align:start position:0%
+So the first one goes into one of the
+three p states. The second one goes into
+
+ align:start position:0%
+three p states. The second one goes into
+ 
+
+ align:start position:0%
+three p states. The second one goes into
+one of the other three p states and the
+
+ align:start position:0%
+one of the other three p states and the
+ 
+
+ align:start position:0%
+one of the other three p states and the
+spins remain parallel.
+
+ align:start position:0%
+spins remain parallel.
+ 
+
+ align:start position:0%
+spins remain parallel.
+And we keep going.
+
+ align:start position:0%
+And we keep going.
+ 
+
+ align:start position:0%
+And we keep going.
+So that's the alphab principle. That's
+
+ align:start position:0%
+So that's the alphab principle. That's
+ 
+
+ align:start position:0%
+So that's the alphab principle. That's
+how you write the electron
+
+ align:start position:0%
+how you write the electron
+ 
+
+ align:start position:0%
+how you write the electron
+configurations here then for all of the
+
+ align:start position:0%
+configurations here then for all of the
+ 
+
+ align:start position:0%
+configurations here then for all of the
+atoms in the periodic table.
+
+ align:start position:0%
+atoms in the periodic table.
+ 
+
+ align:start position:0%
+atoms in the periodic table.
+All right, heating those two uh rules.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so uh let's take a look at this a
+
+ align:start position:0%
+Okay, so uh let's take a look at this a
+ 
+
+ align:start position:0%
+Okay, so uh let's take a look at this a
+little more in detail.
+
+ align:start position:0%
+little more in detail.
+ 
+
+ align:start position:0%
+little more in detail.
+We're going to start here just looking
+
+ align:start position:0%
+We're going to start here just looking
+ 
+
+ align:start position:0%
+We're going to start here just looking
+at the third period
+
+ align:start position:0%
+at the third period
+ 
+
+ align:start position:0%
+at the third period
+or the third row in the periodic table.
+
+ align:start position:0%
+or the third row in the periodic table.
+ 
+
+ align:start position:0%
+or the third row in the periodic table.
+So, we're starting here with sodium
+
+ align:start position:0%
+So, we're starting here with sodium
+ 
+
+ align:start position:0%
+So, we're starting here with sodium
+and going across.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And here is the um here is the electron
+
+ align:start position:0%
+And here is the um here is the electron
+ 
+
+ align:start position:0%
+And here is the um here is the electron
+configuration.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, here's the electron configuration
+
+ align:start position:0%
+Okay, here's the electron configuration
+ 
+
+ align:start position:0%
+Okay, here's the electron configuration
+of sodium.
+
+ align:start position:0%
+of sodium.
+ 
+
+ align:start position:0%
+of sodium.
+And you see I put two electrons in 2 px,
+
+ align:start position:0%
+And you see I put two electrons in 2 px,
+ 
+
+ align:start position:0%
+And you see I put two electrons in 2 px,
+two and 2p y, two and 2pz.
+
+ align:start position:0%
+two and 2p y, two and 2pz.
+ 
+
+ align:start position:0%
+two and 2p y, two and 2pz.
+Well, if I'm just writing it like this,
+
+ align:start position:0%
+Well, if I'm just writing it like this,
+ 
+
+ align:start position:0%
+Well, if I'm just writing it like this,
+I don't mind that you just write them as
+
+ align:start position:0%
+I don't mind that you just write them as
+ 
+
+ align:start position:0%
+I don't mind that you just write them as
+2p6,
+
+ align:start position:0%
+2p6,
+ 
+
+ align:start position:0%
+2p6,
+okay? Because you can't really tell the
+
+ align:start position:0%
+okay? Because you can't really tell the
+ 
+
+ align:start position:0%
+okay? Because you can't really tell the
+difference here anyway, right? So, you
+
+ align:start position:0%
+difference here anyway, right? So, you
+ 
+
+ align:start position:0%
+difference here anyway, right? So, you
+could just write it as 2p6.
+
+ align:start position:0%
+could just write it as 2p6.
+ 
+
+ align:start position:0%
+could just write it as 2p6.
+Now, just a few reminders of things that
+
+ align:start position:0%
+Now, just a few reminders of things that
+ 
+
+ align:start position:0%
+Now, just a few reminders of things that
+you probably already know and that is
+
+ align:start position:0%
+you probably already know and that is
+ 
+
+ align:start position:0%
+you probably already know and that is
+that these electrons 1 s 2s and the 2p6,
+
+ align:start position:0%
+that these electrons 1 s 2s and the 2p6,
+ 
+
+ align:start position:0%
+that these electrons 1 s 2s and the 2p6,
+they're are core electrons. They make up
+
+ align:start position:0%
+they're are core electrons. They make up
+ 
+
+ align:start position:0%
+they're are core electrons. They make up
+the inner gas configuration. So
+
+ align:start position:0%
+the inner gas configuration. So
+ 
+
+ align:start position:0%
+the inner gas configuration. So
+electrons that make up an inner gas
+
+ align:start position:0%
+electrons that make up an inner gas
+ 
+
+ align:start position:0%
+electrons that make up an inner gas
+configuration we call our core
+
+ align:start position:0%
+configuration we call our core
+ 
+
+ align:start position:0%
+configuration we call our core
+electrons.
+
+ align:start position:0%
+electrons.
+ 
+
+ align:start position:0%
+electrons.
+And this inner gas configuration is that
+
+ align:start position:0%
+And this inner gas configuration is that
+ 
+
+ align:start position:0%
+And this inner gas configuration is that
+of neon.
+
+ align:start position:0%
+of neon.
+ 
+
+ align:start position:0%
+of neon.
+And so actually if you were to write the
+
+ align:start position:0%
+And so actually if you were to write the
+ 
+
+ align:start position:0%
+And so actually if you were to write the
+sodium electron configuration, it's fine
+
+ align:start position:0%
+sodium electron configuration, it's fine
+ 
+
+ align:start position:0%
+sodium electron configuration, it's fine
+to just write it as neon
+
+ align:start position:0%
+to just write it as neon
+ 
+
+ align:start position:0%
+to just write it as neon
+and then with the 3s1 next to it. The
+
+ align:start position:0%
+and then with the 3s1 next to it. The
+ 
+
+ align:start position:0%
+and then with the 3s1 next to it. The
+3s1 of course is the veence electron.
+
+ align:start position:0%
+3s1 of course is the veence electron.
+ 
+
+ align:start position:0%
+3s1 of course is the veence electron.
+Veence electrons are those electrons
+
+ align:start position:0%
+Veence electrons are those electrons
+ 
+
+ align:start position:0%
+Veence electrons are those electrons
+that are beyond the uh closest electron
+
+ align:start position:0%
+that are beyond the uh closest electron
+ 
+
+ align:start position:0%
+that are beyond the uh closest electron
+gas configuration.
+
+ align:start position:0%
+gas configuration.
+ 
+
+ align:start position:0%
+gas configuration.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Okay. So if we went across here this uh
+
+ align:start position:0%
+Okay. So if we went across here this uh
+ 
+
+ align:start position:0%
+Okay. So if we went across here this uh
+third row we would just fill up then the
+
+ align:start position:0%
+third row we would just fill up then the
+ 
+
+ align:start position:0%
+third row we would just fill up then the
+three p states and then we get to the
+
+ align:start position:0%
+three p states and then we get to the
+ 
+
+ align:start position:0%
+three p states and then we get to the
+configuration the inner gas
+
+ align:start position:0%
+configuration the inner gas
+ 
+
+ align:start position:0%
+configuration the inner gas
+configuration here of argon.
+
+ align:start position:0%
+configuration here of argon.
+ 
+
+ align:start position:0%
+configuration here of argon.
+Okay, let's look at the uh fourth period
+
+ align:start position:0%
+Okay, let's look at the uh fourth period
+ 
+
+ align:start position:0%
+Okay, let's look at the uh fourth period
+here starting with potassium and going
+
+ align:start position:0%
+here starting with potassium and going
+ 
+
+ align:start position:0%
+here starting with potassium and going
+across.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, for potassium
+
+ align:start position:0%
+All right, for potassium
+ 
+
+ align:start position:0%
+All right, for potassium
+the electron configuration is that of
+
+ align:start position:0%
+the electron configuration is that of
+ 
+
+ align:start position:0%
+the electron configuration is that of
+argon
+
+ align:start position:0%
+argon
+ 
+
+ align:start position:0%
+argon
+plus one electron. And now what I want
+
+ align:start position:0%
+plus one electron. And now what I want
+ 
+
+ align:start position:0%
+plus one electron. And now what I want
+you to notice is that that extra
+
+ align:start position:0%
+you to notice is that that extra
+ 
+
+ align:start position:0%
+you to notice is that that extra
+electron went into this 4s state. it did
+
+ align:start position:0%
+electron went into this 4s state. it did
+ 
+
+ align:start position:0%
+electron went into this 4s state. it did
+not go into the 3d state. It turns out
+
+ align:start position:0%
+not go into the 3d state. It turns out
+ 
+
+ align:start position:0%
+not go into the 3d state. It turns out
+for potassium that the 4s state is
+
+ align:start position:0%
+for potassium that the 4s state is
+ 
+
+ align:start position:0%
+for potassium that the 4s state is
+actually lower in energy than the 3d
+
+ align:start position:0%
+actually lower in energy than the 3d
+ 
+
+ align:start position:0%
+actually lower in energy than the 3d
+state.
+
+ align:start position:0%
+state.
+ 
+
+ align:start position:0%
+state.
+Same thing here for calcium. The next
+
+ align:start position:0%
+Same thing here for calcium. The next
+ 
+
+ align:start position:0%
+Same thing here for calcium. The next
+electron, it goes into the 4s state. So
+
+ align:start position:0%
+electron, it goes into the 4s state. So
+ 
+
+ align:start position:0%
+electron, it goes into the 4s state. So
+the configuration is argon 4s2. It's not
+
+ align:start position:0%
+the configuration is argon 4s2. It's not
+ 
+
+ align:start position:0%
+the configuration is argon 4s2. It's not
+argon 3d2.
+
+ align:start position:0%
+argon 3d2.
+ 
+
+ align:start position:0%
+argon 3d2.
+4s is lower in energy than 3d. I'll show
+
+ align:start position:0%
+4s is lower in energy than 3d. I'll show
+ 
+
+ align:start position:0%
+4s is lower in energy than 3d. I'll show
+you a pneummonic pneummonic in a moment
+
+ align:start position:0%
+you a pneummonic pneummonic in a moment
+ 
+
+ align:start position:0%
+you a pneummonic pneummonic in a moment
+to try to remember that.
+
+ align:start position:0%
+to try to remember that.
+ 
+
+ align:start position:0%
+to try to remember that.
+Next, scandium another electron. Well,
+
+ align:start position:0%
+Next, scandium another electron. Well,
+ 
+
+ align:start position:0%
+Next, scandium another electron. Well,
+now the 3d states start filling up.
+
+ align:start position:0%
+now the 3d states start filling up.
+ 
+
+ align:start position:0%
+now the 3d states start filling up.
+Okay. 4s2 3d1.
+
+ align:start position:0%
+Okay. 4s2 3d1.
+ 
+
+ align:start position:0%
+Okay. 4s2 3d1.
+Titanium 4s2 3d2. Venadium 4s2 3d3.
+
+ align:start position:0%
+Titanium 4s2 3d2. Venadium 4s2 3d3.
+ 
+
+ align:start position:0%
+Titanium 4s2 3d2. Venadium 4s2 3d3.
+Chromium. We got a problem. All right.
+
+ align:start position:0%
+Chromium. We got a problem. All right.
+ 
+
+ align:start position:0%
+Chromium. We got a problem. All right.
+Chromium we got an exception here. You
+
+ align:start position:0%
+Chromium we got an exception here. You
+ 
+
+ align:start position:0%
+Chromium we got an exception here. You
+might expect it to be 4S23d4
+
+ align:start position:0%
+might expect it to be 4S23d4
+ 
+
+ align:start position:0%
+might expect it to be 4S23d4
+because we're just filling up the
+
+ align:start position:0%
+because we're just filling up the
+ 
+
+ align:start position:0%
+because we're just filling up the
+dstates. It turns out that's not the
+
+ align:start position:0%
+dstates. It turns out that's not the
+ 
+
+ align:start position:0%
+dstates. It turns out that's not the
+case.
+
+ align:start position:0%
+case.
+ 
+
+ align:start position:0%
+case.
+It turns out that the chromium
+
+ align:start position:0%
+It turns out that the chromium
+ 
+
+ align:start position:0%
+It turns out that the chromium
+configuration is 4S13d5.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How do you know this? You don't know
+
+ align:start position:0%
+How do you know this? You don't know
+ 
+
+ align:start position:0%
+How do you know this? You don't know
+this, right? There was no way to really
+
+ align:start position:0%
+this, right? There was no way to really
+ 
+
+ align:start position:0%
+this, right? There was no way to really
+predict this. This is an experimental
+
+ align:start position:0%
+predict this. This is an experimental
+ 
+
+ align:start position:0%
+predict this. This is an experimental
+observation.
+
+ align:start position:0%
+observation.
+ 
+
+ align:start position:0%
+observation.
+It turns out that having a half filled
+
+ align:start position:0%
+It turns out that having a half filled
+ 
+
+ align:start position:0%
+It turns out that having a half filled
+4s shell and a half filled 3d shell is
+
+ align:start position:0%
+4s shell and a half filled 3d shell is
+ 
+
+ align:start position:0%
+4s shell and a half filled 3d shell is
+more stable than having a filled 4s
+
+ align:start position:0%
+more stable than having a filled 4s
+ 
+
+ align:start position:0%
+more stable than having a filled 4s
+shell and four electrons in the 3d
+
+ align:start position:0%
+shell and four electrons in the 3d
+ 
+
+ align:start position:0%
+shell and four electrons in the 3d
+states. Okay, this is an exception. This
+
+ align:start position:0%
+states. Okay, this is an exception. This
+ 
+
+ align:start position:0%
+states. Okay, this is an exception. This
+is an exception you have to know.
+
+ align:start position:0%
+is an exception you have to know.
+ 
+
+ align:start position:0%
+is an exception you have to know.
+Okay. But now, yes,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I'm going to say that in a moment. It
+
+ align:start position:0%
+um I'm going to say that in a moment. It
+ 
+
+ align:start position:0%
+um I'm going to say that in a moment. It
+is an exception also for malibdum,
+
+ align:start position:0%
+is an exception also for malibdum,
+ 
+
+ align:start position:0%
+is an exception also for malibdum,
+right? And we'll talk about it. It is
+
+ align:start position:0%
+right? And we'll talk about it. It is
+ 
+
+ align:start position:0%
+right? And we'll talk about it. It is
+not the exception for tungsten or below.
+
+ align:start position:0%
+not the exception for tungsten or below.
+ 
+
+ align:start position:0%
+not the exception for tungsten or below.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So as we continue to go across
+
+ align:start position:0%
+Okay. So as we continue to go across
+ 
+
+ align:start position:0%
+Okay. So as we continue to go across
+manganese now we're going back to our
+
+ align:start position:0%
+manganese now we're going back to our
+ 
+
+ align:start position:0%
+manganese now we're going back to our
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+4s2 3d5
+
+ align:start position:0%
+4s2 3d5
+ 
+
+ align:start position:0%
+4s2 3d5
+iron 4s2 3d6 cobalt 4s2 3d7 nickel 4s2
+
+ align:start position:0%
+iron 4s2 3d6 cobalt 4s2 3d7 nickel 4s2
+ 
+
+ align:start position:0%
+iron 4s2 3d6 cobalt 4s2 3d7 nickel 4s2
+3d8 and here we got another exception
+
+ align:start position:0%
+3d8 and here we got another exception
+ 
+
+ align:start position:0%
+3d8 and here we got another exception
+copper
+
+ align:start position:0%
+copper
+ 
+
+ align:start position:0%
+copper
+copper if you followed our pattern you
+
+ align:start position:0%
+copper if you followed our pattern you
+ 
+
+ align:start position:0%
+copper if you followed our pattern you
+might expect to be 4s23d9
+
+ align:start position:0%
+might expect to be 4s23d9
+ 
+
+ align:start position:0%
+might expect to be 4s23d9
+it's not all All right,
+
+ align:start position:0%
+it's not all All right,
+ 
+
+ align:start position:0%
+it's not all All right,
+it is 4s1 3d10.
+
+ align:start position:0%
+it is 4s1 3d10.
+ 
+
+ align:start position:0%
+it is 4s1 3d10.
+Again, it turns out that the overall
+
+ align:start position:0%
+Again, it turns out that the overall
+ 
+
+ align:start position:0%
+Again, it turns out that the overall
+atom is more stable if that 4s state is
+
+ align:start position:0%
+atom is more stable if that 4s state is
+ 
+
+ align:start position:0%
+atom is more stable if that 4s state is
+half filled and the 3d state is totally
+
+ align:start position:0%
+half filled and the 3d state is totally
+ 
+
+ align:start position:0%
+half filled and the 3d state is totally
+filled.
+
+ align:start position:0%
+filled.
+ 
+
+ align:start position:0%
+filled.
+Did were would you be able to predict
+
+ align:start position:0%
+Did were would you be able to predict
+ 
+
+ align:start position:0%
+Did were would you be able to predict
+that? No, you're not going to be able to
+
+ align:start position:0%
+that? No, you're not going to be able to
+ 
+
+ align:start position:0%
+that? No, you're not going to be able to
+predict that. All right, this is an
+
+ align:start position:0%
+predict that. All right, this is an
+ 
+
+ align:start position:0%
+predict that. All right, this is an
+experimental observation
+
+ align:start position:0%
+experimental observation
+ 
+
+ align:start position:0%
+experimental observation
+and this is another exception that you
+
+ align:start position:0%
+and this is another exception that you
+ 
+
+ align:start position:0%
+and this is another exception that you
+do have to know.
+
+ align:start position:0%
+do have to know.
+ 
+
+ align:start position:0%
+do have to know.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+next zinc. Well, we're back to filling
+
+ align:start position:0%
+next zinc. Well, we're back to filling
+ 
+
+ align:start position:0%
+next zinc. Well, we're back to filling
+our pattern here or back to our pattern.
+
+ align:start position:0%
+our pattern here or back to our pattern.
+ 
+
+ align:start position:0%
+our pattern here or back to our pattern.
+This is 4s2 3d10.
+
+ align:start position:0%
+This is 4s2 3d10.
+ 
+
+ align:start position:0%
+This is 4s2 3d10.
+And then once the 3d10 states are filled
+
+ align:start position:0%
+And then once the 3d10 states are filled
+ 
+
+ align:start position:0%
+And then once the 3d10 states are filled
+or the 3d states are filled one that
+
+ align:start position:0%
+or the 3d states are filled one that
+ 
+
+ align:start position:0%
+or the 3d states are filled one that
+then we start filling the four p states
+
+ align:start position:0%
+then we start filling the four p states
+ 
+
+ align:start position:0%
+then we start filling the four p states
+as we go across here this fourth row and
+
+ align:start position:0%
+as we go across here this fourth row and
+ 
+
+ align:start position:0%
+as we go across here this fourth row and
+we get to the krypton inner gas
+
+ align:start position:0%
+we get to the krypton inner gas
+ 
+
+ align:start position:0%
+we get to the krypton inner gas
+configuration and these all follow a
+
+ align:start position:0%
+configuration and these all follow a
+ 
+
+ align:start position:0%
+configuration and these all follow a
+pattern just fill the four p states up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. All right. So chromium and copper
+
+ align:start position:0%
+Okay. All right. So chromium and copper
+ 
+
+ align:start position:0%
+Okay. All right. So chromium and copper
+are two exceptions you have to know.
+
+ align:start position:0%
+are two exceptions you have to know.
+ 
+
+ align:start position:0%
+are two exceptions you have to know.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+what happens as we go across the fifth
+
+ align:start position:0%
+what happens as we go across the fifth
+ 
+
+ align:start position:0%
+what happens as we go across the fifth
+period here right here. So we're
+
+ align:start position:0%
+period here right here. So we're
+ 
+
+ align:start position:0%
+period here right here. So we're
+starting with rubidium.
+
+ align:start position:0%
+starting with rubidium.
+ 
+
+ align:start position:0%
+starting with rubidium.
+Well again the electron goes into the 5s
+
+ align:start position:0%
+Well again the electron goes into the 5s
+ 
+
+ align:start position:0%
+Well again the electron goes into the 5s
+state and not the 4d state. 5s is lower
+
+ align:start position:0%
+state and not the 4d state. 5s is lower
+ 
+
+ align:start position:0%
+state and not the 4d state. 5s is lower
+than the 4d.
+
+ align:start position:0%
+than the 4d.
+ 
+
+ align:start position:0%
+than the 4d.
+And for strontium, the electron goes
+
+ align:start position:0%
+And for strontium, the electron goes
+ 
+
+ align:start position:0%
+And for strontium, the electron goes
+into the 5s state, not the 4d state. So
+
+ align:start position:0%
+into the 5s state, not the 4d state. So
+ 
+
+ align:start position:0%
+into the 5s state, not the 4d state. So
+you fill up those 4s states or the 5s
+
+ align:start position:0%
+you fill up those 4s states or the 5s
+ 
+
+ align:start position:0%
+you fill up those 4s states or the 5s
+states before you start filling up the
+
+ align:start position:0%
+states before you start filling up the
+ 
+
+ align:start position:0%
+states before you start filling up the
+three 4d states here. All right? And
+
+ align:start position:0%
+three 4d states here. All right? And
+ 
+
+ align:start position:0%
+three 4d states here. All right? And
+just like copper and chromium are
+
+ align:start position:0%
+just like copper and chromium are
+ 
+
+ align:start position:0%
+just like copper and chromium are
+exceptions in filling the 3D states,
+
+ align:start position:0%
+exceptions in filling the 3D states,
+ 
+
+ align:start position:0%
+exceptions in filling the 3D states,
+malibdinum and silver are exceptions in
+
+ align:start position:0%
+malibdinum and silver are exceptions in
+ 
+
+ align:start position:0%
+malibdinum and silver are exceptions in
+filling the 4D states. All right.
+
+ align:start position:0%
+filling the 4D states. All right.
+ 
+
+ align:start position:0%
+filling the 4D states. All right.
+So these four exceptions, chromium,
+
+ align:start position:0%
+So these four exceptions, chromium,
+ 
+
+ align:start position:0%
+So these four exceptions, chromium,
+copper, malibdinum, and silver are
+
+ align:start position:0%
+copper, malibdinum, and silver are
+ 
+
+ align:start position:0%
+copper, malibdinum, and silver are
+exceptions that you do have to know.
+
+ align:start position:0%
+exceptions that you do have to know.
+ 
+
+ align:start position:0%
+exceptions that you do have to know.
+along this fifth period here. There are
+
+ align:start position:0%
+along this fifth period here. There are
+ 
+
+ align:start position:0%
+along this fifth period here. There are
+other exceptions. I don't expect you to
+
+ align:start position:0%
+other exceptions. I don't expect you to
+ 
+
+ align:start position:0%
+other exceptions. I don't expect you to
+know that. All right. But there are four
+
+ align:start position:0%
+know that. All right. But there are four
+ 
+
+ align:start position:0%
+know that. All right. But there are four
+exceptions that you do need to know.
+
+ align:start position:0%
+exceptions that you do need to know.
+ 
+
+ align:start position:0%
+exceptions that you do need to know.
+Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+right. I actually don't care which way
+
+ align:start position:0%
+right. I actually don't care which way
+ 
+
+ align:start position:0%
+right. I actually don't care which way
+you write the electron configuration.
+
+ align:start position:0%
+you write the electron configuration.
+ 
+
+ align:start position:0%
+you write the electron configuration.
+Okay, I will care if I specifically ask
+
+ align:start position:0%
+Okay, I will care if I specifically ask
+ 
+
+ align:start position:0%
+Okay, I will care if I specifically ask
+you which state is lower in energy.
+
+ align:start position:0%
+you which state is lower in energy.
+ 
+
+ align:start position:0%
+you which state is lower in energy.
+Okay, but if you just write it, I
+
+ align:start position:0%
+Okay, but if you just write it, I
+ 
+
+ align:start position:0%
+Okay, but if you just write it, I
+actually don't care how you write it.
+
+ align:start position:0%
+actually don't care how you write it.
+ 
+
+ align:start position:0%
+actually don't care how you write it.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+All right. So now, how do you remember
+
+ align:start position:0%
+All right. So now, how do you remember
+ 
+
+ align:start position:0%
+All right. So now, how do you remember
+what the uh ordering is of these states?
+
+ align:start position:0%
+what the uh ordering is of these states?
+ 
+
+ align:start position:0%
+what the uh ordering is of these states?
+The energy ordering. Well, here's an uh
+
+ align:start position:0%
+The energy ordering. Well, here's an uh
+ 
+
+ align:start position:0%
+The energy ordering. Well, here's an uh
+pneummonic for you. Maybe you've seen
+
+ align:start position:0%
+pneummonic for you. Maybe you've seen
+ 
+
+ align:start position:0%
+pneummonic for you. Maybe you've seen
+this before.
+
+ align:start position:0%
+this before.
+ 
+
+ align:start position:0%
+this before.
+I'm going to start out writing 1 S like
+
+ align:start position:0%
+I'm going to start out writing 1 S like
+ 
+
+ align:start position:0%
+I'm going to start out writing 1 S like
+this. And then I'm going to write right
+
+ align:start position:0%
+this. And then I'm going to write right
+ 
+
+ align:start position:0%
+this. And then I'm going to write right
+underneath it 2 S. And then over one 2 P
+
+ align:start position:0%
+underneath it 2 S. And then over one 2 P
+ 
+
+ align:start position:0%
+underneath it 2 S. And then over one 2 P
+then 3 S 3 P 3d.
+
+ align:start position:0%
+then 3 S 3 P 3d.
+ 
+
+ align:start position:0%
+then 3 S 3 P 3d.
+Then 4S, 4 P, 4 D, 4 F. And then 5S, 5
+
+ align:start position:0%
+Then 4S, 4 P, 4 D, 4 F. And then 5S, 5
+ 
+
+ align:start position:0%
+Then 4S, 4 P, 4 D, 4 F. And then 5S, 5
+P, 5D, 5D, 5F, 6S, 6P, 6D, 7S, 7P. And
+
+ align:start position:0%
+P, 5D, 5D, 5F, 6S, 6P, 6D, 7S, 7P. And
+ 
+
+ align:start position:0%
+P, 5D, 5D, 5F, 6S, 6P, 6D, 7S, 7P. And
+that's all that's going to be important
+
+ align:start position:0%
+that's all that's going to be important
+ 
+
+ align:start position:0%
+that's all that's going to be important
+right now. Okay. And now, how do I use
+
+ align:start position:0%
+right now. Okay. And now, how do I use
+ 
+
+ align:start position:0%
+right now. Okay. And now, how do I use
+this pattern to generate the energy
+
+ align:start position:0%
+this pattern to generate the energy
+ 
+
+ align:start position:0%
+this pattern to generate the energy
+orderings? Well, of course, 1s is
+
+ align:start position:0%
+orderings? Well, of course, 1s is
+ 
+
+ align:start position:0%
+orderings? Well, of course, 1s is
+lowest,
+
+ align:start position:0%
+lowest,
+ 
+
+ align:start position:0%
+lowest,
+but now I'm going to draw diagonals
+
+ align:start position:0%
+but now I'm going to draw diagonals
+ 
+
+ align:start position:0%
+but now I'm going to draw diagonals
+through this. So for example 1 S is
+
+ align:start position:0%
+through this. So for example 1 S is
+ 
+
+ align:start position:0%
+through this. So for example 1 S is
+lowest and then the next higher energy
+
+ align:start position:0%
+lowest and then the next higher energy
+ 
+
+ align:start position:0%
+lowest and then the next higher energy
+state is 2 P
+
+ align:start position:0%
+state is 2 P
+ 
+
+ align:start position:0%
+state is 2 P
+and then the next higher energy I 2S
+
+ align:start position:0%
+and then the next higher energy I 2S
+ 
+
+ align:start position:0%
+and then the next higher energy I 2S
+then the next higher energy state is 2 P
+
+ align:start position:0%
+then the next higher energy state is 2 P
+ 
+
+ align:start position:0%
+then the next higher energy state is 2 P
+and the state after that that's higher
+
+ align:start position:0%
+and the state after that that's higher
+ 
+
+ align:start position:0%
+and the state after that that's higher
+in energy is 3S
+
+ align:start position:0%
+in energy is 3S
+ 
+
+ align:start position:0%
+in energy is 3S
+and then I draw another diagonal so that
+
+ align:start position:0%
+and then I draw another diagonal so that
+ 
+
+ align:start position:0%
+and then I draw another diagonal so that
+the next higher energy state is 4 P and
+
+ align:start position:0%
+the next higher energy state is 4 P and
+ 
+
+ align:start position:0%
+the next higher energy state is 4 P and
+uh 3 P and 4S
+
+ align:start position:0%
+uh 3 P and 4S
+ 
+
+ align:start position:0%
+uh 3 P and 4S
+and draw another diagonal 3D D 4 P5S
+
+ align:start position:0%
+and draw another diagonal 3D D 4 P5S
+ 
+
+ align:start position:0%
+and draw another diagonal 3D D 4 P5S
+draw another diagonal 4 D 5P 6S another
+
+ align:start position:0%
+draw another diagonal 4 D 5P 6S another
+ 
+
+ align:start position:0%
+draw another diagonal 4 D 5P 6S another
+diagonal 4 F 5D6P7S
+
+ align:start position:0%
+diagonal 4 F 5D6P7S
+ 
+
+ align:start position:0%
+diagonal 4 F 5D6P7S
+and another diagonal. All right. So
+
+ align:start position:0%
+and another diagonal. All right. So
+ 
+
+ align:start position:0%
+and another diagonal. All right. So
+that's how you remember the relative
+
+ align:start position:0%
+that's how you remember the relative
+ 
+
+ align:start position:0%
+that's how you remember the relative
+energy ordering of these states.
+
+ align:start position:0%
+energy ordering of these states.
+ 
+
+ align:start position:0%
+energy ordering of these states.
+So you should be able to write the
+
+ align:start position:0%
+So you should be able to write the
+ 
+
+ align:start position:0%
+So you should be able to write the
+electron configuration of all atoms in
+
+ align:start position:0%
+electron configuration of all atoms in
+ 
+
+ align:start position:0%
+electron configuration of all atoms in
+the periodic table including the four
+
+ align:start position:0%
+the periodic table including the four
+ 
+
+ align:start position:0%
+the periodic table including the four
+exceptions.
+
+ align:start position:0%
+exceptions.
+ 
+
+ align:start position:0%
+exceptions.
+There are other exceptions but I won't
+
+ align:start position:0%
+There are other exceptions but I won't
+ 
+
+ align:start position:0%
+There are other exceptions but I won't
+expect you to write those. Okay.
+
+ align:start position:0%
+expect you to write those. Okay.
+ 
+
+ align:start position:0%
+expect you to write those. Okay.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+I have to tell you about something that
+
+ align:start position:0%
+I have to tell you about something that
+ 
+
+ align:start position:0%
+I have to tell you about something that
+is a little confusing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is when we write down the
+
+ align:start position:0%
+and that is when we write down the
+ 
+
+ align:start position:0%
+and that is when we write down the
+electron configuration of ions.
+
+ align:start position:0%
+electron configuration of ions.
+ 
+
+ align:start position:0%
+electron configuration of ions.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+What I'm about to say has nothing to do
+
+ align:start position:0%
+What I'm about to say has nothing to do
+ 
+
+ align:start position:0%
+What I'm about to say has nothing to do
+or doesn't change in any way what I just
+
+ align:start position:0%
+or doesn't change in any way what I just
+ 
+
+ align:start position:0%
+or doesn't change in any way what I just
+told you about writing the electron
+
+ align:start position:0%
+told you about writing the electron
+ 
+
+ align:start position:0%
+told you about writing the electron
+configuration of neutrals.
+
+ align:start position:0%
+configuration of neutrals.
+ 
+
+ align:start position:0%
+configuration of neutrals.
+But it does have something to do in
+
+ align:start position:0%
+But it does have something to do in
+ 
+
+ align:start position:0%
+But it does have something to do in
+writing the configuration of positive
+
+ align:start position:0%
+writing the configuration of positive
+ 
+
+ align:start position:0%
+writing the configuration of positive
+ions.
+
+ align:start position:0%
+ions.
+ 
+
+ align:start position:0%
+ions.
+And here's the story.
+
+ align:start position:0%
+And here's the story.
+ 
+
+ align:start position:0%
+And here's the story.
+If I actually look at the energies of
+
+ align:start position:0%
+If I actually look at the energies of
+ 
+
+ align:start position:0%
+If I actually look at the energies of
+the individual 4s states and 3d states
+
+ align:start position:0%
+the individual 4s states and 3d states
+ 
+
+ align:start position:0%
+the individual 4s states and 3d states
+as we go across the uh fourth row,
+
+ align:start position:0%
+as we go across the uh fourth row,
+ 
+
+ align:start position:0%
+as we go across the uh fourth row,
+potassium, calcium, scandium, titanium.
+
+ align:start position:0%
+potassium, calcium, scandium, titanium.
+ 
+
+ align:start position:0%
+potassium, calcium, scandium, titanium.
+Well, the 4s states in potassium and
+
+ align:start position:0%
+Well, the 4s states in potassium and
+ 
+
+ align:start position:0%
+Well, the 4s states in potassium and
+calcium are actually lower in energy
+
+ align:start position:0%
+calcium are actually lower in energy
+ 
+
+ align:start position:0%
+calcium are actually lower in energy
+than the 3d states. And indeed when we
+
+ align:start position:0%
+than the 3d states. And indeed when we
+ 
+
+ align:start position:0%
+than the 3d states. And indeed when we
+wrote the electron configuration of the
+
+ align:start position:0%
+wrote the electron configuration of the
+ 
+
+ align:start position:0%
+wrote the electron configuration of the
+neutral, we put that electron that extra
+
+ align:start position:0%
+neutral, we put that electron that extra
+ 
+
+ align:start position:0%
+neutral, we put that electron that extra
+electron making the potassium in the 4s
+
+ align:start position:0%
+electron making the potassium in the 4s
+ 
+
+ align:start position:0%
+electron making the potassium in the 4s
+state and that extra electron in this in
+
+ align:start position:0%
+state and that extra electron in this in
+ 
+
+ align:start position:0%
+state and that extra electron in this in
+the calcium making the
+
+ align:start position:0%
+the calcium making the
+ 
+
+ align:start position:0%
+the calcium making the
+uh a 4s state. Okay. But it turns out
+
+ align:start position:0%
+uh a 4s state. Okay. But it turns out
+ 
+
+ align:start position:0%
+uh a 4s state. Okay. But it turns out
+that right at this element scandium
+
+ align:start position:0%
+that right at this element scandium
+ 
+
+ align:start position:0%
+that right at this element scandium
+Z equ= 21 the energy of that 3d state
+
+ align:start position:0%
+Z equ= 21 the energy of that 3d state
+ 
+
+ align:start position:0%
+Z equ= 21 the energy of that 3d state
+drops below the energy of the 4s state.
+
+ align:start position:0%
+drops below the energy of the 4s state.
+ 
+
+ align:start position:0%
+drops below the energy of the 4s state.
+Does that have a consequence for how you
+
+ align:start position:0%
+Does that have a consequence for how you
+ 
+
+ align:start position:0%
+Does that have a consequence for how you
+write the electron condition
+
+ align:start position:0%
+write the electron condition
+ 
+
+ align:start position:0%
+write the electron condition
+configuration of scandium or titanium
+
+ align:start position:0%
+configuration of scandium or titanium
+ 
+
+ align:start position:0%
+configuration of scandium or titanium
+for example? No.
+
+ align:start position:0%
+for example? No.
+ 
+
+ align:start position:0%
+for example? No.
+The electron configuration for titanium
+
+ align:start position:0%
+The electron configuration for titanium
+ 
+
+ align:start position:0%
+The electron configuration for titanium
+is still what I said argon 4s2 3d2.
+
+ align:start position:0%
+is still what I said argon 4s2 3d2.
+ 
+
+ align:start position:0%
+is still what I said argon 4s2 3d2.
+All right. The fact that this 3d state
+
+ align:start position:0%
+All right. The fact that this 3d state
+ 
+
+ align:start position:0%
+All right. The fact that this 3d state
+is now lower in energy does not affect
+
+ align:start position:0%
+is now lower in energy does not affect
+ 
+
+ align:start position:0%
+is now lower in energy does not affect
+writing the electron configuration of
+
+ align:start position:0%
+writing the electron configuration of
+ 
+
+ align:start position:0%
+writing the electron configuration of
+the neutral. Now you might ask okay if
+
+ align:start position:0%
+the neutral. Now you might ask okay if
+ 
+
+ align:start position:0%
+the neutral. Now you might ask okay if
+the 3d states here at titanium are lower
+
+ align:start position:0%
+the 3d states here at titanium are lower
+ 
+
+ align:start position:0%
+the 3d states here at titanium are lower
+in energy why don't the 4s hop over into
+
+ align:start position:0%
+in energy why don't the 4s hop over into
+ 
+
+ align:start position:0%
+in energy why don't the 4s hop over into
+the 3d? They don't because this
+
+ align:start position:0%
+the 3d? They don't because this
+ 
+
+ align:start position:0%
+the 3d? They don't because this
+configuration again minimizes the
+
+ align:start position:0%
+configuration again minimizes the
+ 
+
+ align:start position:0%
+configuration again minimizes the
+electron repulsion. If you put all four
+
+ align:start position:0%
+electron repulsion. If you put all four
+ 
+
+ align:start position:0%
+electron repulsion. If you put all four
+electrons in the 3d state, there would
+
+ align:start position:0%
+electrons in the 3d state, there would
+ 
+
+ align:start position:0%
+electrons in the 3d state, there would
+be a greater electron repulsion. And
+
+ align:start position:0%
+be a greater electron repulsion. And
+ 
+
+ align:start position:0%
+be a greater electron repulsion. And
+then the overall energy, the overall
+
+ align:start position:0%
+then the overall energy, the overall
+ 
+
+ align:start position:0%
+then the overall energy, the overall
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+would actually be higher. What I'm
+
+ align:start position:0%
+would actually be higher. What I'm
+ 
+
+ align:start position:0%
+would actually be higher. What I'm
+plotting here is just the energy of 3d
+
+ align:start position:0%
+plotting here is just the energy of 3d
+ 
+
+ align:start position:0%
+plotting here is just the energy of 3d
+and just the energy of 4s.
+
+ align:start position:0%
+and just the energy of 4s.
+ 
+
+ align:start position:0%
+and just the energy of 4s.
+But you what when you're looking at the
+
+ align:start position:0%
+But you what when you're looking at the
+ 
+
+ align:start position:0%
+But you what when you're looking at the
+electron configuration of an ion, you
+
+ align:start position:0%
+electron configuration of an ion, you
+ 
+
+ align:start position:0%
+electron configuration of an ion, you
+have to look at all the interactions and
+
+ align:start position:0%
+have to look at all the interactions and
+ 
+
+ align:start position:0%
+have to look at all the interactions and
+all of the energies. All right? So for
+
+ align:start position:0%
+all of the energies. All right? So for
+ 
+
+ align:start position:0%
+all of the energies. All right? So for
+the neutral, it's still what I said.
+
+ align:start position:0%
+the neutral, it's still what I said.
+ 
+
+ align:start position:0%
+the neutral, it's still what I said.
+However, now if I form an ion, if I take
+
+ align:start position:0%
+However, now if I form an ion, if I take
+ 
+
+ align:start position:0%
+However, now if I form an ion, if I take
+titanium and I make titanium 2+, hey,
+
+ align:start position:0%
+titanium and I make titanium 2+, hey,
+ 
+
+ align:start position:0%
+titanium and I make titanium 2+, hey,
+you know the electrons that come out,
+
+ align:start position:0%
+you know the electrons that come out,
+ 
+
+ align:start position:0%
+you know the electrons that come out,
+the electrons that come out are the
+
+ align:start position:0%
+the electrons that come out are the
+ 
+
+ align:start position:0%
+the electrons that come out are the
+electrons in the 4s state because
+
+ align:start position:0%
+electrons in the 4s state because
+ 
+
+ align:start position:0%
+electrons in the 4s state because
+they're the higher energy state. And so
+
+ align:start position:0%
+they're the higher energy state. And so
+ 
+
+ align:start position:0%
+they're the higher energy state. And so
+the electron configuration of titanium
+
+ align:start position:0%
+the electron configuration of titanium
+ 
+
+ align:start position:0%
+the electron configuration of titanium
+is the argon 3d^2.
+
+ align:start position:0%
+is the argon 3d^2.
+ 
+
+ align:start position:0%
+is the argon 3d^2.
+All right, that's important. And
+
+ align:start position:0%
+All right, that's important. And
+ 
+
+ align:start position:0%
+All right, that's important. And
+similarly for that fifth row
+
+ align:start position:0%
+similarly for that fifth row
+ 
+
+ align:start position:0%
+similarly for that fifth row
+right for rubidium strronium 5s is lower
+
+ align:start position:0%
+right for rubidium strronium 5s is lower
+ 
+
+ align:start position:0%
+right for rubidium strronium 5s is lower
+than 4d but right here at utbium 4d
+
+ align:start position:0%
+than 4d but right here at utbium 4d
+ 
+
+ align:start position:0%
+than 4d but right here at utbium 4d
+drops below 5s
+
+ align:start position:0%
+drops below 5s
+ 
+
+ align:start position:0%
+drops below 5s
+that does not affect the configuration
+
+ align:start position:0%
+that does not affect the configuration
+ 
+
+ align:start position:0%
+that does not affect the configuration
+that we wrote for the neutrals. So for
+
+ align:start position:0%
+that we wrote for the neutrals. So for
+ 
+
+ align:start position:0%
+that we wrote for the neutrals. So for
+example, here's silver.
+
+ align:start position:0%
+example, here's silver.
+ 
+
+ align:start position:0%
+example, here's silver.
+It's a 5S1 4d10. But if we make a silver
+
+ align:start position:0%
+It's a 5S1 4d10. But if we make a silver
+ 
+
+ align:start position:0%
+It's a 5S1 4d10. But if we make a silver
+ion, silver plus it's that 5s electron
+
+ align:start position:0%
+ion, silver plus it's that 5s electron
+ 
+
+ align:start position:0%
+ion, silver plus it's that 5s electron
+that leaves because it's the higher
+
+ align:start position:0%
+that leaves because it's the higher
+ 
+
+ align:start position:0%
+that leaves because it's the higher
+energy electron. And so the
+
+ align:start position:0%
+energy electron. And so the
+ 
+
+ align:start position:0%
+energy electron. And so the
+configuration is krypton 4d10.
+
+ align:start position:0%
+configuration is krypton 4d10.
+ 
+
+ align:start position:0%
+configuration is krypton 4d10.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. See you on Friday.
\ No newline at end of file
diff --git a/xeszYyi9ooM.txt b/xeszYyi9ooM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cffeb3bcaf3f6605b3499c7856bbd961abe3ec5d
--- /dev/null
+++ b/xeszYyi9ooM.txt
@@ -0,0 +1,93 @@
+Let us introduce
+the error measures
+
+we used in building
+the analytics models.
+
+We of course used R squared,
+but we also used other measures.
+
+Next measure, the
+so-called "penalty error,"
+
+is motivated by the fact
+that if you classify
+
+a very high-risk patient
+as a low-risk patient,
+
+this is more costly
+than the reverse,
+
+namely classifying
+a low-risk patient
+
+as a very high-risk patient.
+
+Motivated by this, we
+developed a penalty error.
+
+And the idea is to use
+asymmetric penalties.
+
+The graph here--
+so it's a matrix--
+
+where this is the outcome
+and this is the forecast.
+
+For example, whenever we
+classify a low-risk patient
+
+as high-risk, we
+pay a penalty of 2,
+
+which is a difference of 3 minus
+1, the difference in the error.
+
+But inversely, when you
+classify a bracket 3 patient
+
+as bracket 1 patient,
+this is double.
+
+The cost-- the penalty--
+is double the amount.
+
+So you observe that the off
+diagonal penalties are double
+
+the corresponding penalties
+in the lower diagonal.
+
+To judge the quality of the
+analytics models we developed,
+
+we compare it with a baseline.
+
+And the baseline is
+to simply predict
+
+that the cost in
+the next "period"
+
+will be the cost in
+the current period.
+
+We have observed that as far
+as identification of brackets
+
+is concerned, the
+accuracy was 75%.
+
+So namely, whenever we predict
+that the risk is bracket 3--
+
+indeed it is bracket 3--
+this happens 75% of the time,
+
+and the penalty error--
+the average penalty
+
+error of the
+baseline-- was 0.56.
\ No newline at end of file
diff --git a/xsO2Ip6eiaY.txt b/xsO2Ip6eiaY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..41903fc30d7f39b3ae7ba0970676cc608c23f885
--- /dev/null
+++ b/xsO2Ip6eiaY.txt
@@ -0,0 +1,4363 @@
+align:start position:0%
+ 
+about seaplanes and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two different designs you can have a
+
+ align:start position:0%
+two different designs you can have a
+ 
+
+ align:start position:0%
+two different designs you can have a
+boat whole seaplane or you can have a
+
+ align:start position:0%
+boat whole seaplane or you can have a
+ 
+
+ align:start position:0%
+boat whole seaplane or you can have a
+conventional airplane on floats so there
+
+ align:start position:0%
+conventional airplane on floats so there
+ 
+
+ align:start position:0%
+conventional airplane on floats so there
+at the bottom left is a part of the
+
+ align:start position:0%
+at the bottom left is a part of the
+ 
+
+ align:start position:0%
+at the bottom left is a part of the
+Grumman series they made a huge number
+
+ align:start position:0%
+Grumman series they made a huge number
+ 
+
+ align:start position:0%
+Grumman series they made a huge number
+of these around world war ii and many of
+
+ align:start position:0%
+of these around world war ii and many of
+ 
+
+ align:start position:0%
+of these around world war ii and many of
+them are still flying you can see always
+
+ align:start position:0%
+them are still flying you can see always
+ 
+
+ align:start position:0%
+them are still flying you can see always
+probably 15 or 20 of these at Oshkosh
+
+ align:start position:0%
+probably 15 or 20 of these at Oshkosh
+ 
+
+ align:start position:0%
+probably 15 or 20 of these at Oshkosh
+every year in different sizes the
+
+ align:start position:0%
+every year in different sizes the
+ 
+
+ align:start position:0%
+every year in different sizes the
+widgeon is the smallest the albatross is
+
+ align:start position:0%
+widgeon is the smallest the albatross is
+ 
+
+ align:start position:0%
+widgeon is the smallest the albatross is
+the biggest I forget if that's like a
+
+ align:start position:0%
+the biggest I forget if that's like a
+ 
+
+ align:start position:0%
+the biggest I forget if that's like a
+martin mars up there on the top left
+
+ align:start position:0%
+martin mars up there on the top left
+ 
+
+ align:start position:0%
+martin mars up there on the top left
+there were some huge truly huge sea
+
+ align:start position:0%
+there were some huge truly huge sea
+ 
+
+ align:start position:0%
+there were some huge truly huge sea
+planes boeing Sikorsky and martin I
+
+ align:start position:0%
+planes boeing Sikorsky and martin I
+ 
+
+ align:start position:0%
+planes boeing Sikorsky and martin I
+think all made huge sea planes during
+
+ align:start position:0%
+think all made huge sea planes during
+ 
+
+ align:start position:0%
+think all made huge sea planes during
+World War two and just before the bush
+
+ align:start position:0%
+World War two and just before the bush
+ 
+
+ align:start position:0%
+World War two and just before the bush
+pilots don't like the small boat hold
+
+ align:start position:0%
+pilots don't like the small boat hold
+ 
+
+ align:start position:0%
+pilots don't like the small boat hold
+sea planes like the lake amphibian and I
+
+ align:start position:0%
+sea planes like the lake amphibian and I
+ 
+
+ align:start position:0%
+sea planes like the lake amphibian and I
+guess the icon they probably wouldn't
+
+ align:start position:0%
+guess the icon they probably wouldn't
+ 
+
+ align:start position:0%
+guess the icon they probably wouldn't
+like if it ever did ship up there to
+
+ align:start position:0%
+like if it ever did ship up there to
+ 
+
+ align:start position:0%
+like if it ever did ship up there to
+Alaska I think one issue with the boat
+
+ align:start position:0%
+Alaska I think one issue with the boat
+ 
+
+ align:start position:0%
+Alaska I think one issue with the boat
+hull planes is they're very hard to dock
+
+ align:start position:0%
+hull planes is they're very hard to dock
+ 
+
+ align:start position:0%
+hull planes is they're very hard to dock
+you have to design some kind of special
+
+ align:start position:0%
+you have to design some kind of special
+ 
+
+ align:start position:0%
+you have to design some kind of special
+dock for them they really designed more
+
+ align:start position:0%
+dock for them they really designed more
+ 
+
+ align:start position:0%
+dock for them they really designed more
+for beaching whereas the float planes
+
+ align:start position:0%
+for beaching whereas the float planes
+ 
+
+ align:start position:0%
+for beaching whereas the float planes
+very naturally come up to a dock like a
+
+ align:start position:0%
+very naturally come up to a dock like a
+ 
+
+ align:start position:0%
+very naturally come up to a dock like a
+boat that's one issue so yeah you might
+
+ align:start position:0%
+boat that's one issue so yeah you might
+ 
+
+ align:start position:0%
+boat that's one issue so yeah you might
+think those float planes look so
+
+ align:start position:0%
+think those float planes look so
+ 
+
+ align:start position:0%
+think those float planes look so
+unstable but the bush pilots love them
+
+ align:start position:0%
+unstable but the bush pilots love them
+ 
+
+ align:start position:0%
+unstable but the bush pilots love them
+it's hard to get on and off the water
+
+ align:start position:0%
+it's hard to get on and off the water
+ 
+
+ align:start position:0%
+it's hard to get on and off the water
+which is why a practical sea plane
+
+ align:start position:0%
+which is why a practical sea plane
+ 
+
+ align:start position:0%
+which is why a practical sea plane
+really should have in most cases a
+
+ align:start position:0%
+really should have in most cases a
+ 
+
+ align:start position:0%
+really should have in most cases a
+turboprop engine to get enough power to
+
+ align:start position:0%
+turboprop engine to get enough power to
+ 
+
+ align:start position:0%
+turboprop engine to get enough power to
+really get off the water so we do have
+
+ align:start position:0%
+really get off the water so we do have
+ 
+
+ align:start position:0%
+really get off the water so we do have
+an Alaska locally it's called mean
+
+ align:start position:0%
+an Alaska locally it's called mean
+ 
+
+ align:start position:0%
+an Alaska locally it's called mean
+there's a fair amount of seaplane flying
+
+ align:start position:0%
+there's a fair amount of seaplane flying
+ 
+
+ align:start position:0%
+there's a fair amount of seaplane flying
+up there these are a couple US
+
+ align:start position:0%
+up there these are a couple US
+ 
+
+ align:start position:0%
+up there these are a couple US
+government planes if you want to know
+
+ align:start position:0%
+government planes if you want to know
+ 
+
+ align:start position:0%
+government planes if you want to know
+why your taxes are going in the
+
+ align:start position:0%
+why your taxes are going in the
+ 
+
+ align:start position:0%
+why your taxes are going in the
+direction that they're going look on the
+
+ align:start position:0%
+direction that they're going look on the
+ 
+
+ align:start position:0%
+direction that they're going look on the
+bottom right that was the government's I
+
+ align:start position:0%
+bottom right that was the government's I
+ 
+
+ align:start position:0%
+bottom right that was the government's I
+saw these two planes side-by-side on the
+
+ align:start position:0%
+saw these two planes side-by-side on the
+ 
+
+ align:start position:0%
+saw these two planes side-by-side on the
+ramp Portland Maine has a wonderful FBLA
+
+ align:start position:0%
+ramp Portland Maine has a wonderful FBLA
+ 
+
+ align:start position:0%
+ramp Portland Maine has a wonderful FBLA
+called Mack jets which is very
+
+ align:start position:0%
+called Mack jets which is very
+ 
+
+ align:start position:0%
+called Mack jets which is very
+hospitable they have crew cars
+
+ align:start position:0%
+hospitable they have crew cars
+ 
+
+ align:start position:0%
+hospitable they have crew cars
+reasonably priced hundred low-lead
+
+ align:start position:0%
+reasonably priced hundred low-lead
+ 
+
+ align:start position:0%
+reasonably priced hundred low-lead
+they're really just operating it as a
+
+ align:start position:0%
+they're really just operating it as a
+ 
+
+ align:start position:0%
+they're really just operating it as a
+gift to the piston crowd of course
+
+ align:start position:0%
+gift to the piston crowd of course
+ 
+
+ align:start position:0%
+gift to the piston crowd of course
+they're really there for the turbine as
+
+ align:start position:0%
+they're really there for the turbine as
+ 
+
+ align:start position:0%
+they're really there for the turbine as
+a business they're there for the jets
+
+ align:start position:0%
+a business they're there for the jets
+ 
+
+ align:start position:0%
+a business they're there for the jets
+but it's a great place that you can use
+
+ align:start position:0%
+but it's a great place that you can use
+ 
+
+ align:start position:0%
+but it's a great place that you can use
+and jump in the crew car going to town
+
+ align:start position:0%
+and jump in the crew car going to town
+ 
+
+ align:start position:0%
+and jump in the crew car going to town
+but anyway on the ramp I happen to see
+
+ align:start position:0%
+but anyway on the ramp I happen to see
+ 
+
+ align:start position:0%
+but anyway on the ramp I happen to see
+there's a little piston Cessna on floats
+
+ align:start position:0%
+there's a little piston Cessna on floats
+ 
+
+ align:start position:0%
+there's a little piston Cessna on floats
+that they bought
+
+ align:start position:0%
+that they bought
+ 
+
+ align:start position:0%
+that they bought
+fifteen or 20 years ago for Fish and
+
+ align:start position:0%
+fifteen or 20 years ago for Fish and
+ 
+
+ align:start position:0%
+fifteen or 20 years ago for Fish and
+Wildlife patrol or something I think
+
+ align:start position:0%
+Wildlife patrol or something I think
+ 
+
+ align:start position:0%
+Wildlife patrol or something I think
+this is a federal government airplane
+
+ align:start position:0%
+this is a federal government airplane
+ 
+
+ align:start position:0%
+this is a federal government airplane
+and now they have this monster thing
+
+ align:start position:0%
+and now they have this monster thing
+ 
+
+ align:start position:0%
+and now they have this monster thing
+that they were they're replacing it with
+
+ align:start position:0%
+that they were they're replacing it with
+ 
+
+ align:start position:0%
+that they were they're replacing it with
+it has a fire-breathing turboprop engine
+
+ align:start position:0%
+it has a fire-breathing turboprop engine
+ 
+
+ align:start position:0%
+it has a fire-breathing turboprop engine
+probably cost five times as much per
+
+ align:start position:0%
+probably cost five times as much per
+ 
+
+ align:start position:0%
+probably cost five times as much per
+hour to run okay every year in September
+
+ align:start position:0%
+hour to run okay every year in September
+ 
+
+ align:start position:0%
+hour to run okay every year in September
+there is the Moosehead Lake seaplane
+
+ align:start position:0%
+there is the Moosehead Lake seaplane
+ 
+
+ align:start position:0%
+there is the Moosehead Lake seaplane
+fly-in and you might ask can you fly in
+
+ align:start position:0%
+fly-in and you might ask can you fly in
+ 
+
+ align:start position:0%
+fly-in and you might ask can you fly in
+there and an East Coast
+
+ align:start position:0%
+there and an East Coast
+ 
+
+ align:start position:0%
+there and an East Coast
+Aero Club plane that you've rented the
+
+ align:start position:0%
+Aero Club plane that you've rented the
+ 
+
+ align:start position:0%
+Aero Club plane that you've rented the
+answer is yes although you probably
+
+ align:start position:0%
+answer is yes although you probably
+ 
+
+ align:start position:0%
+answer is yes although you probably
+can't fly back out if you choose the
+
+ align:start position:0%
+can't fly back out if you choose the
+ 
+
+ align:start position:0%
+can't fly back out if you choose the
+lake as your landing destination but
+
+ align:start position:0%
+lake as your landing destination but
+ 
+
+ align:start position:0%
+lake as your landing destination but
+there is a wheeled Airport there as well
+
+ align:start position:0%
+there is a wheeled Airport there as well
+ 
+
+ align:start position:0%
+there is a wheeled Airport there as well
+that's pretty reasonable I think it's
+
+ align:start position:0%
+that's pretty reasonable I think it's
+ 
+
+ align:start position:0%
+that's pretty reasonable I think it's
+about a 4,000 foot runway so if the
+
+ align:start position:0%
+about a 4,000 foot runway so if the
+ 
+
+ align:start position:0%
+about a 4,000 foot runway so if the
+weather is nice that's a great place to
+
+ align:start position:0%
+weather is nice that's a great place to
+ 
+
+ align:start position:0%
+weather is nice that's a great place to
+go up in Moosehead Lake it's a long
+
+ align:start position:0%
+go up in Moosehead Lake it's a long
+ 
+
+ align:start position:0%
+go up in Moosehead Lake it's a long
+drive it's about probably a five hour
+
+ align:start position:0%
+drive it's about probably a five hour
+ 
+
+ align:start position:0%
+drive it's about probably a five hour
+drive from here the hard thing about sea
+
+ align:start position:0%
+drive from here the hard thing about sea
+ 
+
+ align:start position:0%
+drive from here the hard thing about sea
+planes is if the float is all the way in
+
+ align:start position:0%
+planes is if the float is all the way in
+ 
+
+ align:start position:0%
+planes is if the float is all the way in
+the water it will never take off there's
+
+ align:start position:0%
+the water it will never take off there's
+ 
+
+ align:start position:0%
+the water it will never take off there's
+so much drag you have to get up on the
+
+ align:start position:0%
+so much drag you have to get up on the
+ 
+
+ align:start position:0%
+so much drag you have to get up on the
+step which if you're a boater
+
+ align:start position:0%
+step which if you're a boater
+ 
+
+ align:start position:0%
+step which if you're a boater
+corresponds to getting up on the plane I
+
+ align:start position:0%
+corresponds to getting up on the plane I
+ 
+
+ align:start position:0%
+corresponds to getting up on the plane I
+guess of a planing hull so basically you
+
+ align:start position:0%
+guess of a planing hull so basically you
+ 
+
+ align:start position:0%
+guess of a planing hull so basically you
+can't have the entire float in the water
+
+ align:start position:0%
+can't have the entire float in the water
+ 
+
+ align:start position:0%
+can't have the entire float in the water
+if you ever want to take off let's just
+
+ align:start position:0%
+if you ever want to take off let's just
+ 
+
+ align:start position:0%
+if you ever want to take off let's just
+show a short YouTube video here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have no sound oh well that's fine so
+
+ align:start position:0%
+we have no sound oh well that's fine so
+ 
+
+ align:start position:0%
+we have no sound oh well that's fine so
+you can see this caravan on floats I
+
+ align:start position:0%
+you can see this caravan on floats I
+ 
+
+ align:start position:0%
+you can see this caravan on floats I
+think it's a caravan it's beginning to
+
+ align:start position:0%
+think it's a caravan it's beginning to
+ 
+
+ align:start position:0%
+think it's a caravan it's beginning to
+get up on the step and finally it can
+
+ align:start position:0%
+get up on the step and finally it can
+ 
+
+ align:start position:0%
+get up on the step and finally it can
+break loose anyway that's how it's done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crosswind landing this is how it's done
+
+ align:start position:0%
+crosswind landing this is how it's done
+ 
+
+ align:start position:0%
+crosswind landing this is how it's done
+according to the FAA
+
+ align:start position:0%
+according to the FAA
+ 
+
+ align:start position:0%
+according to the FAA
+so the FAA is mission the FAA is mission
+
+ align:start position:0%
+so the FAA is mission the FAA is mission
+ 
+
+ align:start position:0%
+so the FAA is mission the FAA is mission
+is in addition to regulating aviation
+
+ align:start position:0%
+is in addition to regulating aviation
+ 
+
+ align:start position:0%
+is in addition to regulating aviation
+they're explicitly supposed to promote
+
+ align:start position:0%
+they're explicitly supposed to promote
+ 
+
+ align:start position:0%
+they're explicitly supposed to promote
+aviation
+
+ align:start position:0%
+aviation
+ 
+
+ align:start position:0%
+aviation
+it's a rare agency so part of their
+
+ align:start position:0%
+it's a rare agency so part of their
+ 
+
+ align:start position:0%
+it's a rare agency so part of their
+mission is to encourage people to fly
+
+ align:start position:0%
+mission is to encourage people to fly
+ 
+
+ align:start position:0%
+mission is to encourage people to fly
+and this is the best that they can do
+
+ align:start position:0%
+and this is the best that they can do
+ 
+
+ align:start position:0%
+and this is the best that they can do
+for sea planes so it does tell you like
+
+ align:start position:0%
+for sea planes so it does tell you like
+ 
+
+ align:start position:0%
+for sea planes so it does tell you like
+I was telling you the problem with sea
+
+ align:start position:0%
+I was telling you the problem with sea
+ 
+
+ align:start position:0%
+I was telling you the problem with sea
+planes is you know if you make a if you
+
+ align:start position:0%
+planes is you know if you make a if you
+ 
+
+ align:start position:0%
+planes is you know if you make a if you
+make an error on Hanscom on runway 2 9
+
+ align:start position:0%
+make an error on Hanscom on runway 2 9
+ 
+
+ align:start position:0%
+make an error on Hanscom on runway 2 9
+first of all it's 150 feet wide and the
+
+ align:start position:0%
+first of all it's 150 feet wide and the
+ 
+
+ align:start position:0%
+first of all it's 150 feet wide and the
+gear on your airplane might only be you
+
+ align:start position:0%
+gear on your airplane might only be you
+ 
+
+ align:start position:0%
+gear on your airplane might only be you
+know 10 feet wide so you can slide quite
+
+ align:start position:0%
+know 10 feet wide so you can slide quite
+ 
+
+ align:start position:0%
+know 10 feet wide so you can slide quite
+a bit left to right before you even
+
+ align:start position:0%
+a bit left to right before you even
+ 
+
+ align:start position:0%
+a bit left to right before you even
+leave the pavement if you do leave the
+
+ align:start position:0%
+leave the pavement if you do leave the
+ 
+
+ align:start position:0%
+leave the pavement if you do leave the
+pavement you're skipping along the grass
+
+ align:start position:0%
+pavement you're skipping along the grass
+ 
+
+ align:start position:0%
+pavement you're skipping along the grass
+and the owner is going to have some
+
+ align:start position:0%
+and the owner is going to have some
+ 
+
+ align:start position:0%
+and the owner is going to have some
+harsh words for you perhaps but
+
+ align:start position:0%
+harsh words for you perhaps but
+ 
+
+ align:start position:0%
+harsh words for you perhaps but
+otherwise nothing too dramatic is going
+
+ align:start position:0%
+otherwise nothing too dramatic is going
+ 
+
+ align:start position:0%
+otherwise nothing too dramatic is going
+to happen glass this is the FAA this is
+
+ align:start position:0%
+to happen glass this is the FAA this is
+ 
+
+ align:start position:0%
+to happen glass this is the FAA this is
+the FAA is glassy water landing
+
+ align:start position:0%
+the FAA is glassy water landing
+ 
+
+ align:start position:0%
+the FAA is glassy water landing
+demonstration so if there's no wind at
+
+ align:start position:0%
+demonstration so if there's no wind at
+ 
+
+ align:start position:0%
+demonstration so if there's no wind at
+all you might think that's great that's
+
+ align:start position:0%
+all you might think that's great that's
+ 
+
+ align:start position:0%
+all you might think that's great that's
+perfect for seaplane flying it's hard to
+
+ align:start position:0%
+perfect for seaplane flying it's hard to
+ 
+
+ align:start position:0%
+perfect for seaplane flying it's hard to
+judge where the water is a little bit of
+
+ align:start position:0%
+judge where the water is a little bit of
+ 
+
+ align:start position:0%
+judge where the water is a little bit of
+wind that causes some ripples on the
+
+ align:start position:0%
+wind that causes some ripples on the
+ 
+
+ align:start position:0%
+wind that causes some ripples on the
+water makes it much easier to judge your
+
+ align:start position:0%
+water makes it much easier to judge your
+ 
+
+ align:start position:0%
+water makes it much easier to judge your
+distance so here's your alternatives you
+
+ align:start position:0%
+distance so here's your alternatives you
+ 
+
+ align:start position:0%
+distance so here's your alternatives you
+can not flare it all and crash into the
+
+ align:start position:0%
+can not flare it all and crash into the
+ 
+
+ align:start position:0%
+can not flare it all and crash into the
+water that way or you can flare too high
+
+ align:start position:0%
+water that way or you can flare too high
+ 
+
+ align:start position:0%
+water that way or you can flare too high
+and then crash into the water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's that those are the only
+
+ align:start position:0%
+what's that those are the only
+ 
+
+ align:start position:0%
+what's that those are the only
+possibilities that's the question radar
+
+ align:start position:0%
+possibilities that's the question radar
+ 
+
+ align:start position:0%
+possibilities that's the question radar
+all radar altimeter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the question is do you wait until VR to
+
+ align:start position:0%
+the question is do you wait until VR to
+ 
+
+ align:start position:0%
+the question is do you wait until VR to
+take off or you just wait till the
+
+ align:start position:0%
+take off or you just wait till the
+ 
+
+ align:start position:0%
+take off or you just wait till the
+floats cleared the water and take off
+
+ align:start position:0%
+floats cleared the water and take off
+ 
+
+ align:start position:0%
+floats cleared the water and take off
+that's a good question
+
+ align:start position:0%
+that's a good question
+ 
+
+ align:start position:0%
+that's a good question
+it's so inefficient to be dragged into
+
+ align:start position:0%
+it's so inefficient to be dragged into
+ 
+
+ align:start position:0%
+it's so inefficient to be dragged into
+the water I think you lift out of the
+
+ align:start position:0%
+the water I think you lift out of the
+ 
+
+ align:start position:0%
+the water I think you lift out of the
+water just as soon as you can and then
+
+ align:start position:0%
+water just as soon as you can and then
+ 
+
+ align:start position:0%
+water just as soon as you can and then
+you'll probably you know float you'll
+
+ align:start position:0%
+you'll probably you know float you'll
+ 
+
+ align:start position:0%
+you'll probably you know float you'll
+fly along the ground effect for a little
+
+ align:start position:0%
+fly along the ground effect for a little
+ 
+
+ align:start position:0%
+fly along the ground effect for a little
+bit and then finally take off but yeah
+
+ align:start position:0%
+bit and then finally take off but yeah
+ 
+
+ align:start position:0%
+bit and then finally take off but yeah
+just like this just like on a soft field
+
+ align:start position:0%
+just like this just like on a soft field
+ 
+
+ align:start position:0%
+just like this just like on a soft field
+like you know slightly muddy grass or
+
+ align:start position:0%
+like you know slightly muddy grass or
+ 
+
+ align:start position:0%
+like you know slightly muddy grass or
+something the best thing you can do is
+
+ align:start position:0%
+something the best thing you can do is
+ 
+
+ align:start position:0%
+something the best thing you can do is
+to get away from the surface that's
+
+ align:start position:0%
+to get away from the surface that's
+ 
+
+ align:start position:0%
+to get away from the surface that's
+dragging dragging on you
+
+ align:start position:0%
+dragging dragging on you
+ 
+
+ align:start position:0%
+dragging dragging on you
+great question all right here's a
+
+ align:start position:0%
+great question all right here's a
+ 
+
+ align:start position:0%
+great question all right here's a
+docking and beaching so one challenge
+
+ align:start position:0%
+docking and beaching so one challenge
+ 
+
+ align:start position:0%
+docking and beaching so one challenge
+with the seaplane if you're all by
+
+ align:start position:0%
+with the seaplane if you're all by
+ 
+
+ align:start position:0%
+with the seaplane if you're all by
+yourself is you have to be tremendously
+
+ align:start position:0%
+yourself is you have to be tremendously
+ 
+
+ align:start position:0%
+yourself is you have to be tremendously
+agile and nimble to sort of get out of
+
+ align:start position:0%
+agile and nimble to sort of get out of
+ 
+
+ align:start position:0%
+agile and nimble to sort of get out of
+the plane kill the engine
+
+ align:start position:0%
+the plane kill the engine
+ 
+
+ align:start position:0%
+the plane kill the engine
+scramble around usually the front of the
+
+ align:start position:0%
+scramble around usually the front of the
+ 
+
+ align:start position:0%
+scramble around usually the front of the
+airplane and the propeller because
+
+ align:start position:0%
+airplane and the propeller because
+ 
+
+ align:start position:0%
+airplane and the propeller because
+you're sitting on the left and I don't
+
+ align:start position:0%
+you're sitting on the left and I don't
+ 
+
+ align:start position:0%
+you're sitting on the left and I don't
+know the passengers are gonna go off on
+
+ align:start position:0%
+know the passengers are gonna go off on
+ 
+
+ align:start position:0%
+know the passengers are gonna go off on
+the right and tie up the airplane to the
+
+ align:start position:0%
+the right and tie up the airplane to the
+ 
+
+ align:start position:0%
+the right and tie up the airplane to the
+dock it's very hard to do it's one of
+
+ align:start position:0%
+dock it's very hard to do it's one of
+ 
+
+ align:start position:0%
+dock it's very hard to do it's one of
+the hardest things I think about sea
+
+ align:start position:0%
+the hardest things I think about sea
+ 
+
+ align:start position:0%
+the hardest things I think about sea
+planes and also if the Magneto's aren't
+
+ align:start position:0%
+planes and also if the Magneto's aren't
+ 
+
+ align:start position:0%
+planes and also if the Magneto's aren't
+perfectly grounded airplane engines can
+
+ align:start position:0%
+perfectly grounded airplane engines can
+ 
+
+ align:start position:0%
+perfectly grounded airplane engines can
+start by themselves after saying you
+
+ align:start position:0%
+start by themselves after saying you
+ 
+
+ align:start position:0%
+start by themselves after saying you
+know we shouldn't tell you stuff that's
+
+ align:start position:0%
+know we shouldn't tell you stuff that's
+ 
+
+ align:start position:0%
+know we shouldn't tell you stuff that's
+scary you know if it's not perfectly
+
+ align:start position:0%
+scary you know if it's not perfectly
+ 
+
+ align:start position:0%
+scary you know if it's not perfectly
+grounded by that switch and you don't
+
+ align:start position:0%
+grounded by that switch and you don't
+ 
+
+ align:start position:0%
+grounded by that switch and you don't
+starve the engine of the fuel by killing
+
+ align:start position:0%
+starve the engine of the fuel by killing
+ 
+
+ align:start position:0%
+starve the engine of the fuel by killing
+it with the mixture it may be able to
+
+ align:start position:0%
+it with the mixture it may be able to
+ 
+
+ align:start position:0%
+it with the mixture it may be able to
+start all by itself at least run for you
+
+ align:start position:0%
+start all by itself at least run for you
+ 
+
+ align:start position:0%
+start all by itself at least run for you
+know half a rotation or full rotation
+
+ align:start position:0%
+know half a rotation or full rotation
+ 
+
+ align:start position:0%
+know half a rotation or full rotation
+and hurt somebody so you know you always
+
+ align:start position:0%
+and hurt somebody so you know you always
+ 
+
+ align:start position:0%
+and hurt somebody so you know you always
+want to be cautious around propellers
+
+ align:start position:0%
+want to be cautious around propellers
+ 
+
+ align:start position:0%
+want to be cautious around propellers
+and not spin them but of course if
+
+ align:start position:0%
+and not spin them but of course if
+ 
+
+ align:start position:0%
+and not spin them but of course if
+you're trying to get around the front -
+
+ align:start position:0%
+you're trying to get around the front -
+ 
+
+ align:start position:0%
+you're trying to get around the front -
+for your seaplane repellers the most
+
+ align:start position:0%
+for your seaplane repellers the most
+ 
+
+ align:start position:0%
+for your seaplane repellers the most
+obvious thing to grab on to anyway
+
+ align:start position:0%
+obvious thing to grab on to anyway
+ 
+
+ align:start position:0%
+obvious thing to grab on to anyway
+that's I don't think I would ever want
+
+ align:start position:0%
+that's I don't think I would ever want
+ 
+
+ align:start position:0%
+that's I don't think I would ever want
+to fly a seaplane unless there were dock
+
+ align:start position:0%
+to fly a seaplane unless there were dock
+ 
+
+ align:start position:0%
+to fly a seaplane unless there were dock
+handlers who were gonna deal with the
+
+ align:start position:0%
+handlers who were gonna deal with the
+ 
+
+ align:start position:0%
+handlers who were gonna deal with the
+that part of you know welcoming the
+
+ align:start position:0%
+that part of you know welcoming the
+ 
+
+ align:start position:0%
+that part of you know welcoming the
+airplane to the dock and tying it all
+
+ align:start position:0%
+airplane to the dock and tying it all
+ 
+
+ align:start position:0%
+airplane to the dock and tying it all
+out but of course the folks in Alaska
+
+ align:start position:0%
+out but of course the folks in Alaska
+ 
+
+ align:start position:0%
+out but of course the folks in Alaska
+they do this all the time
+
+ align:start position:0%
+they do this all the time
+ 
+
+ align:start position:0%
+they do this all the time
+so I have have respect when you see a
+
+ align:start position:0%
+so I have have respect when you see a
+ 
+
+ align:start position:0%
+so I have have respect when you see a
+seaplane so there are a lot of bad
+
+ align:start position:0%
+seaplane so there are a lot of bad
+ 
+
+ align:start position:0%
+seaplane so there are a lot of bad
+things that you can do believe it or not
+
+ align:start position:0%
+things that you can do believe it or not
+ 
+
+ align:start position:0%
+things that you can do believe it or not
+landing in the sea is something that's
+
+ align:start position:0%
+landing in the sea is something that's
+ 
+
+ align:start position:0%
+landing in the sea is something that's
+almost impractical it's almost
+
+ align:start position:0%
+almost impractical it's almost
+ 
+
+ align:start position:0%
+almost impractical it's almost
+impossible on a seaplane because there's
+
+ align:start position:0%
+impossible on a seaplane because there's
+ 
+
+ align:start position:0%
+impossible on a seaplane because there's
+too much in the way of waves they're
+
+ align:start position:0%
+too much in the way of waves they're
+ 
+
+ align:start position:0%
+too much in the way of waves they're
+really for harbors rivers lakes if you
+
+ align:start position:0%
+really for harbors rivers lakes if you
+ 
+
+ align:start position:0%
+really for harbors rivers lakes if you
+have more than a foot of so if the waves
+
+ align:start position:0%
+have more than a foot of so if the waves
+ 
+
+ align:start position:0%
+have more than a foot of so if the waves
+are more than about a foot it just hangs
+
+ align:start position:0%
+are more than about a foot it just hangs
+ 
+
+ align:start position:0%
+are more than about a foot it just hangs
+up the sea plane so much that it'll be
+
+ align:start position:0%
+up the sea plane so much that it'll be
+ 
+
+ align:start position:0%
+up the sea plane so much that it'll be
+damaged landing the amphibious playing
+
+ align:start position:0%
+damaged landing the amphibious playing
+ 
+
+ align:start position:0%
+damaged landing the amphibious playing
+with the wheels down is one of the most
+
+ align:start position:0%
+with the wheels down is one of the most
+ 
+
+ align:start position:0%
+with the wheels down is one of the most
+common mistakes you might think software
+
+ align:start position:0%
+common mistakes you might think software
+ 
+
+ align:start position:0%
+common mistakes you might think software
+would fix this and you know you have a
+
+ align:start position:0%
+would fix this and you know you have a
+ 
+
+ align:start position:0%
+would fix this and you know you have a
+database of where all the runways are in
+
+ align:start position:0%
+database of where all the runways are in
+ 
+
+ align:start position:0%
+database of where all the runways are in
+the US you have a database of you know
+
+ align:start position:0%
+the US you have a database of you know
+ 
+
+ align:start position:0%
+the US you have a database of you know
+where the lakes are and other bodies of
+
+ align:start position:0%
+where the lakes are and other bodies of
+ 
+
+ align:start position:0%
+where the lakes are and other bodies of
+water but you don't even really need
+
+ align:start position:0%
+water but you don't even really need
+ 
+
+ align:start position:0%
+water but you don't even really need
+that so you could have a lot and you
+
+ align:start position:0%
+that so you could have a lot and you
+ 
+
+ align:start position:0%
+that so you could have a lot and you
+have it you could have a camera out at
+
+ align:start position:0%
+have it you could have a camera out at
+ 
+
+ align:start position:0%
+have it you could have a camera out at
+the front that can tell the difference
+
+ align:start position:0%
+the front that can tell the difference
+ 
+
+ align:start position:0%
+the front that can tell the difference
+between water and not water so you would
+
+ align:start position:0%
+between water and not water so you would
+ 
+
+ align:start position:0%
+between water and not water so you would
+think that the airplane would provide
+
+ align:start position:0%
+think that the airplane would provide
+ 
+
+ align:start position:0%
+think that the airplane would provide
+significant assistance in configuring an
+
+ align:start position:0%
+significant assistance in configuring an
+ 
+
+ align:start position:0%
+significant assistance in configuring an
+amphibious plane without either wheels
+
+ align:start position:0%
+amphibious plane without either wheels
+ 
+
+ align:start position:0%
+amphibious plane without either wheels
+down for a hard surface or the floats or
+
+ align:start position:0%
+down for a hard surface or the floats or
+ 
+
+ align:start position:0%
+down for a hard surface or the floats or
+just the bare floats for water and
+
+ align:start position:0%
+just the bare floats for water and
+ 
+
+ align:start position:0%
+just the bare floats for water and
+there's there's very little of that
+
+ align:start position:0%
+there's there's very little of that
+ 
+
+ align:start position:0%
+there's there's very little of that
+unfortunately there's certainly nothing
+
+ align:start position:0%
+unfortunately there's certainly nothing
+ 
+
+ align:start position:0%
+unfortunately there's certainly nothing
+like the intelligence that I'm
+
+ align:start position:0%
+like the intelligence that I'm
+ 
+
+ align:start position:0%
+like the intelligence that I'm
+describing you know you might be able to
+
+ align:start position:0%
+describing you know you might be able to
+ 
+
+ align:start position:0%
+describing you know you might be able to
+like press a button and have that plane
+
+ align:start position:0%
+like press a button and have that plane
+ 
+
+ align:start position:0%
+like press a button and have that plane
+tell you or the synthesized voice is an
+
+ align:start position:0%
+tell you or the synthesized voice is an
+ 
+
+ align:start position:0%
+tell you or the synthesized voice is an
+aftermarket thing you know the wheels
+
+ align:start position:0%
+aftermarket thing you know the wheels
+ 
+
+ align:start position:0%
+aftermarket thing you know the wheels
+are down for runway landing or something
+
+ align:start position:0%
+are down for runway landing or something
+ 
+
+ align:start position:0%
+are down for runway landing or something
+so one common thing that people forget
+
+ align:start position:0%
+so one common thing that people forget
+ 
+
+ align:start position:0%
+so one common thing that people forget
+and not that common but this is an
+
+ align:start position:0%
+and not that common but this is an
+ 
+
+ align:start position:0%
+and not that common but this is an
+illustration of why you might want a to
+
+ align:start position:0%
+illustration of why you might want a to
+ 
+
+ align:start position:0%
+illustration of why you might want a to
+pilot crew but there's a video that's
+
+ align:start position:0%
+pilot crew but there's a video that's
+ 
+
+ align:start position:0%
+pilot crew but there's a video that's
+linked here from the slide about a
+
+ align:start position:0%
+linked here from the slide about a
+ 
+
+ align:start position:0%
+linked here from the slide about a
+father it sounds like a good pilot in a
+
+ align:start position:0%
+father it sounds like a good pilot in a
+ 
+
+ align:start position:0%
+father it sounds like a good pilot in a
+careful pilot he is with the son and he
+
+ align:start position:0%
+careful pilot he is with the son and he
+ 
+
+ align:start position:0%
+careful pilot he is with the son and he
+left the wheels down landed in the water
+
+ align:start position:0%
+left the wheels down landed in the water
+ 
+
+ align:start position:0%
+left the wheels down landed in the water
+flipped over and the son was killed
+
+ align:start position:0%
+flipped over and the son was killed
+ 
+
+ align:start position:0%
+flipped over and the son was killed
+really tragic so watch that if you want
+
+ align:start position:0%
+really tragic so watch that if you want
+ 
+
+ align:start position:0%
+really tragic so watch that if you want
+to cry but anyway I think it's a good
+
+ align:start position:0%
+to cry but anyway I think it's a good
+ 
+
+ align:start position:0%
+to cry but anyway I think it's a good
+illustration of you know seaplane out
+
+ align:start position:0%
+illustration of you know seaplane out
+ 
+
+ align:start position:0%
+illustration of you know seaplane out
+amphibious sea print operation is a
+
+ align:start position:0%
+amphibious sea print operation is a
+ 
+
+ align:start position:0%
+amphibious sea print operation is a
+great example of where two pilot crew
+
+ align:start position:0%
+great example of where two pilot crew
+ 
+
+ align:start position:0%
+great example of where two pilot crew
+with the checklist would be very
+
+ align:start position:0%
+with the checklist would be very
+ 
+
+ align:start position:0%
+with the checklist would be very
+unlikely to have that kind of accident
+
+ align:start position:0%
+unlikely to have that kind of accident
+ 
+
+ align:start position:0%
+unlikely to have that kind of accident
+so it also illustrates you know how it's
+
+ align:start position:0%
+so it also illustrates you know how it's
+ 
+
+ align:start position:0%
+so it also illustrates you know how it's
+too bad that these manned airplanes
+
+ align:start position:0%
+too bad that these manned airplanes
+ 
+
+ align:start position:0%
+too bad that these manned airplanes
+don't have 1/100 of the intelligence of
+
+ align:start position:0%
+don't have 1/100 of the intelligence of
+ 
+
+ align:start position:0%
+don't have 1/100 of the intelligence of
+a DJI drone they're rare exceptions like
+
+ align:start position:0%
+a DJI drone they're rare exceptions like
+ 
+
+ align:start position:0%
+a DJI drone they're rare exceptions like
+I said at Burning Man
+
+ align:start position:0%
+I said at Burning Man
+ 
+
+ align:start position:0%
+I said at Burning Man
+you know the terrain warning system had
+
+ align:start position:0%
+you know the terrain warning system had
+ 
+
+ align:start position:0%
+you know the terrain warning system had
+to be silenced because it was freaking
+
+ align:start position:0%
+to be silenced because it was freaking
+ 
+
+ align:start position:0%
+to be silenced because it was freaking
+out that we were not going to make it
+
+ align:start position:0%
+out that we were not going to make it
+ 
+
+ align:start position:0%
+out that we were not going to make it
+even though there was a 5,000 foot
+
+ align:start position:0%
+even though there was a 5,000 foot
+ 
+
+ align:start position:0%
+even though there was a 5,000 foot
+temporary runway that had been rolled
+
+ align:start position:0%
+temporary runway that had been rolled
+ 
+
+ align:start position:0%
+temporary runway that had been rolled
+out there by the burners the uber
+
+ align:start position:0%
+out there by the burners the uber
+ 
+
+ align:start position:0%
+out there by the burners the uber
+burners okay salt waters you know people
+
+ align:start position:0%
+burners okay salt waters you know people
+ 
+
+ align:start position:0%
+burners okay salt waters you know people
+do this commercially but you know the
+
+ align:start position:0%
+do this commercially but you know the
+ 
+
+ align:start position:0%
+do this commercially but you know the
+airplane has to be hosed off every day
+
+ align:start position:0%
+airplane has to be hosed off every day
+ 
+
+ align:start position:0%
+airplane has to be hosed off every day
+because the salt water is corrosive even
+
+ align:start position:0%
+because the salt water is corrosive even
+ 
+
+ align:start position:0%
+because the salt water is corrosive even
+to aluminum question swimmers and
+
+ align:start position:0%
+to aluminum question swimmers and
+ 
+
+ align:start position:0%
+to aluminum question swimmers and
+boaters in lakes and harbors yeah that's
+
+ align:start position:0%
+boaters in lakes and harbors yeah that's
+ 
+
+ align:start position:0%
+boaters in lakes and harbors yeah that's
+one of the challenges of sea planes you
+
+ align:start position:0%
+one of the challenges of sea planes you
+ 
+
+ align:start position:0%
+one of the challenges of sea planes you
+know if you're cleared land in an
+
+ align:start position:0%
+know if you're cleared land in an
+ 
+
+ align:start position:0%
+know if you're cleared land in an
+airport the air traffic controller has
+
+ align:start position:0%
+airport the air traffic controller has
+ 
+
+ align:start position:0%
+airport the air traffic controller has
+looked out of the runway you know made
+
+ align:start position:0%
+looked out of the runway you know made
+ 
+
+ align:start position:0%
+looked out of the runway you know made
+sure that there's no other aircraft
+
+ align:start position:0%
+sure that there's no other aircraft
+ 
+
+ align:start position:0%
+sure that there's no other aircraft
+pretty sure that there's no deer on the
+
+ align:start position:0%
+pretty sure that there's no deer on the
+ 
+
+ align:start position:0%
+pretty sure that there's no deer on the
+runway the you know the sea plane you
+
+ align:start position:0%
+runway the you know the sea plane you
+ 
+
+ align:start position:0%
+runway the you know the sea plane you
+have to kind of orbit around it's a
+
+ align:start position:0%
+have to kind of orbit around it's a
+ 
+
+ align:start position:0%
+have to kind of orbit around it's a
+little bit like landing a helicopter off
+
+ align:start position:0%
+little bit like landing a helicopter off
+ 
+
+ align:start position:0%
+little bit like landing a helicopter off
+Airport to really make sure that there's
+
+ align:start position:0%
+Airport to really make sure that there's
+ 
+
+ align:start position:0%
+Airport to really make sure that there's
+nobody in a canoe I will tell you that
+
+ align:start position:0%
+nobody in a canoe I will tell you that
+ 
+
+ align:start position:0%
+nobody in a canoe I will tell you that
+for my seaplane training up in me and I
+
+ align:start position:0%
+for my seaplane training up in me and I
+ 
+
+ align:start position:0%
+for my seaplane training up in me and I
+have a seaplane rating that I got up in
+
+ align:start position:0%
+have a seaplane rating that I got up in
+ 
+
+ align:start position:0%
+have a seaplane rating that I got up in
+Maine and there's a great school up
+
+ align:start position:0%
+Maine and there's a great school up
+ 
+
+ align:start position:0%
+Maine and there's a great school up
+there called Twitchell's
+
+ align:start position:0%
+there called Twitchell's
+ 
+
+ align:start position:0%
+there called Twitchell's
+but anyway yeah if you see like kayakers
+
+ align:start position:0%
+but anyway yeah if you see like kayakers
+ 
+
+ align:start position:0%
+but anyway yeah if you see like kayakers
+they can pal pretty fast when they see
+
+ align:start position:0%
+they can pal pretty fast when they see
+ 
+
+ align:start position:0%
+they can pal pretty fast when they see
+is he playing in the vicinity but yeah
+
+ align:start position:0%
+is he playing in the vicinity but yeah
+ 
+
+ align:start position:0%
+is he playing in the vicinity but yeah
+there could be a log in the water so
+
+ align:start position:0%
+there could be a log in the water so
+ 
+
+ align:start position:0%
+there could be a log in the water so
+there's just their hazards that you
+
+ align:start position:0%
+there's just their hazards that you
+ 
+
+ align:start position:0%
+there's just their hazards that you
+can't you can't control and get rid of
+
+ align:start position:0%
+can't you can't control and get rid of
+ 
+
+ align:start position:0%
+can't you can't control and get rid of
+so the accident rate does tend to be
+
+ align:start position:0%
+so the accident rate does tend to be
+ 
+
+ align:start position:0%
+so the accident rate does tend to be
+higher in the military I think there's a
+
+ align:start position:0%
+higher in the military I think there's a
+ 
+
+ align:start position:0%
+higher in the military I think there's a
+slide later where we talk about that
+
+ align:start position:0%
+slide later where we talk about that
+ 
+
+ align:start position:0%
+slide later where we talk about that
+they've gotten away from sea planes and
+
+ align:start position:0%
+they've gotten away from sea planes and
+ 
+
+ align:start position:0%
+they've gotten away from sea planes and
+into helicopters for that reason you
+
+ align:start position:0%
+into helicopters for that reason you
+ 
+
+ align:start position:0%
+into helicopters for that reason you
+know the helicopter you can be down to
+
+ align:start position:0%
+know the helicopter you can be down to
+ 
+
+ align:start position:0%
+know the helicopter you can be down to
+within two feet of the ground and say
+
+ align:start position:0%
+within two feet of the ground and say
+ 
+
+ align:start position:0%
+within two feet of the ground and say
+you know I don't like what I see I'm
+
+ align:start position:0%
+you know I don't like what I see I'm
+ 
+
+ align:start position:0%
+you know I don't like what I see I'm
+gonna go somewhere else the propeller
+
+ align:start position:0%
+gonna go somewhere else the propeller
+ 
+
+ align:start position:0%
+gonna go somewhere else the propeller
+tends to get beaten up you'll see some
+
+ align:start position:0%
+tends to get beaten up you'll see some
+ 
+
+ align:start position:0%
+tends to get beaten up you'll see some
+seaplane designs or the propellers you
+
+ align:start position:0%
+seaplane designs or the propellers you
+ 
+
+ align:start position:0%
+seaplane designs or the propellers you
+know up high and in the back and that's
+
+ align:start position:0%
+know up high and in the back and that's
+ 
+
+ align:start position:0%
+know up high and in the back and that's
+to keep the water you know propellers
+
+ align:start position:0%
+to keep the water you know propellers
+ 
+
+ align:start position:0%
+to keep the water you know propellers
+going you're supersonic speeds at the
+
+ align:start position:0%
+going you're supersonic speeds at the
+ 
+
+ align:start position:0%
+going you're supersonic speeds at the
+tips
+
+ align:start position:0%
+tips
+ 
+
+ align:start position:0%
+tips
+so if it gets water on it it'll it'll be
+
+ align:start position:0%
+so if it gets water on it it'll it'll be
+ 
+
+ align:start position:0%
+so if it gets water on it it'll it'll be
+eroded same deal with flying your
+
+ align:start position:0%
+eroded same deal with flying your
+ 
+
+ align:start position:0%
+eroded same deal with flying your
+airplane and heavy rain you can get
+
+ align:start position:0%
+airplane and heavy rain you can get
+ 
+
+ align:start position:0%
+airplane and heavy rain you can get
+erosion on the leading edges of the wing
+
+ align:start position:0%
+erosion on the leading edges of the wing
+ 
+
+ align:start position:0%
+erosion on the leading edges of the wing
+and on the prop alright so yeah the
+
+ align:start position:0%
+and on the prop alright so yeah the
+ 
+
+ align:start position:0%
+and on the prop alright so yeah the
+seaplane pilot skills include a lot more
+
+ align:start position:0%
+seaplane pilot skills include a lot more
+ 
+
+ align:start position:0%
+seaplane pilot skills include a lot more
+judgment there's some extent there'll be
+
+ align:start position:0%
+judgment there's some extent there'll be
+ 
+
+ align:start position:0%
+judgment there's some extent there'll be
+the dimensions of these lakes and you
+
+ align:start position:0%
+the dimensions of these lakes and you
+ 
+
+ align:start position:0%
+the dimensions of these lakes and you
+know even in Alaska there's even a
+
+ align:start position:0%
+know even in Alaska there's even a
+ 
+
+ align:start position:0%
+know even in Alaska there's even a
+lighted water runway but generally
+
+ align:start position:0%
+lighted water runway but generally
+ 
+
+ align:start position:0%
+lighted water runway but generally
+speaking you don't have a lot of
+
+ align:start position:0%
+speaking you don't have a lot of
+ 
+
+ align:start position:0%
+speaking you don't have a lot of
+information to go by so you've got to
+
+ align:start position:0%
+information to go by so you've got to
+ 
+
+ align:start position:0%
+information to go by so you've got to
+evaluate all the stuff by yourself one
+
+ align:start position:0%
+evaluate all the stuff by yourself one
+ 
+
+ align:start position:0%
+evaluate all the stuff by yourself one
+thing you can do I'll use this coffee
+
+ align:start position:0%
+thing you can do I'll use this coffee
+ 
+
+ align:start position:0%
+thing you can do I'll use this coffee
+cup is an example you can usually see
+
+ align:start position:0%
+cup is an example you can usually see
+ 
+
+ align:start position:0%
+cup is an example you can usually see
+where the winds coming from if there's
+
+ align:start position:0%
+where the winds coming from if there's
+ 
+
+ align:start position:0%
+where the winds coming from if there's
+trees all around the lake the lake will
+
+ align:start position:0%
+trees all around the lake the lake will
+ 
+
+ align:start position:0%
+trees all around the lake the lake will
+be calm right next let's assume this
+
+ align:start position:0%
+be calm right next let's assume this
+ 
+
+ align:start position:0%
+be calm right next let's assume this
+coffee cup is a tree the lake will be
+
+ align:start position:0%
+coffee cup is a tree the lake will be
+ 
+
+ align:start position:0%
+coffee cup is a tree the lake will be
+calm and glassy right next to the tree
+
+ align:start position:0%
+calm and glassy right next to the tree
+ 
+
+ align:start position:0%
+calm and glassy right next to the tree
+and that tells you the wind is coming
+
+ align:start position:0%
+and that tells you the wind is coming
+ 
+
+ align:start position:0%
+and that tells you the wind is coming
+from this direction because that part of
+
+ align:start position:0%
+from this direction because that part of
+ 
+
+ align:start position:0%
+from this direction because that part of
+the lake is being sheltered from the
+
+ align:start position:0%
+the lake is being sheltered from the
+ 
+
+ align:start position:0%
+the lake is being sheltered from the
+wind
+
+ align:start position:0%
+wind
+ 
+
+ align:start position:0%
+wind
+so you can't actually read the wind off
+
+ align:start position:0%
+so you can't actually read the wind off
+ 
+
+ align:start position:0%
+so you can't actually read the wind off
+the lake by looking at which parts are
+
+ align:start position:0%
+the lake by looking at which parts are
+ 
+
+ align:start position:0%
+the lake by looking at which parts are
+rippled and which parts are glassy but
+
+ align:start position:0%
+rippled and which parts are glassy but
+ 
+
+ align:start position:0%
+rippled and which parts are glassy but
+you still have to decide you know right
+
+ align:start position:0%
+you still have to decide you know right
+ 
+
+ align:start position:0%
+you still have to decide you know right
+are there floating logs in the water are
+
+ align:start position:0%
+are there floating logs in the water are
+ 
+
+ align:start position:0%
+are there floating logs in the water are
+there swimmers are there boats here are
+
+ align:start position:0%
+there swimmers are there boats here are
+ 
+
+ align:start position:0%
+there swimmers are there boats here are
+some unusual skills that you have to
+
+ align:start position:0%
+some unusual skills that you have to
+ 
+
+ align:start position:0%
+some unusual skills that you have to
+have well you might have to have after
+
+ align:start position:0%
+have well you might have to have after
+ 
+
+ align:start position:0%
+have well you might have to have after
+maintenance or to get their plane
+
+ align:start position:0%
+maintenance or to get their plane
+ 
+
+ align:start position:0%
+maintenance or to get their plane
+maintained
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that was straight floats in
+
+ align:start position:0%
+all right so that was straight floats in
+ 
+
+ align:start position:0%
+all right so that was straight floats in
+the grass so at the end of the season
+
+ align:start position:0%
+the grass so at the end of the season
+ 
+
+ align:start position:0%
+the grass so at the end of the season
+you want to get the airplane maintained
+
+ align:start position:0%
+you want to get the airplane maintained
+ 
+
+ align:start position:0%
+you want to get the airplane maintained
+there's not a lot of airplane mechanics
+
+ align:start position:0%
+there's not a lot of airplane mechanics
+ 
+
+ align:start position:0%
+there's not a lot of airplane mechanics
+hanging around the typical lake so you
+
+ align:start position:0%
+hanging around the typical lake so you
+ 
+
+ align:start position:0%
+hanging around the typical lake so you
+just land it on the floats in the grass
+
+ align:start position:0%
+just land it on the floats in the grass
+ 
+
+ align:start position:0%
+just land it on the floats in the grass
+at an airport and what about when you
+
+ align:start position:0%
+at an airport and what about when you
+ 
+
+ align:start position:0%
+at an airport and what about when you
+want to get it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you had to get the sound watch that at
+
+ align:start position:0%
+you had to get the sound watch that at
+ 
+
+ align:start position:0%
+you had to get the sound watch that at
+home
+
+ align:start position:0%
+home
+ 
+
+ align:start position:0%
+home
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as I said earlier the problem with
+
+ align:start position:0%
+so as I said earlier the problem with
+ 
+
+ align:start position:0%
+so as I said earlier the problem with
+you know seaplanes is that you know it's
+
+ align:start position:0%
+you know seaplanes is that you know it's
+ 
+
+ align:start position:0%
+you know seaplanes is that you know it's
+just a lot less forgiving than hard
+
+ align:start position:0%
+just a lot less forgiving than hard
+ 
+
+ align:start position:0%
+just a lot less forgiving than hard
+surface runway which is the most
+
+ align:start position:0%
+surface runway which is the most
+ 
+
+ align:start position:0%
+surface runway which is the most
+forgiving environment you can enhance
+
+ align:start position:0%
+forgiving environment you can enhance
+ 
+
+ align:start position:0%
+forgiving environment you can enhance
+that safety with the two pilot crew
+
+ align:start position:0%
+that safety with the two pilot crew
+ 
+
+ align:start position:0%
+that safety with the two pilot crew
+especially an experienced seaplane pilot
+
+ align:start position:0%
+especially an experienced seaplane pilot
+ 
+
+ align:start position:0%
+especially an experienced seaplane pilot
+or there's stuff that'll be on the test
+
+ align:start position:0%
+or there's stuff that'll be on the test
+ 
+
+ align:start position:0%
+or there's stuff that'll be on the test
+you can learn about accident reporting
+
+ align:start position:0%
+you can learn about accident reporting
+ 
+
+ align:start position:0%
+you can learn about accident reporting
+so this is a different part of the
+
+ align:start position:0%
+so this is a different part of the
+ 
+
+ align:start position:0%
+so this is a different part of the
+federal regulations this is the part
+
+ align:start position:0%
+federal regulations this is the part
+ 
+
+ align:start position:0%
+federal regulations this is the part
+that relates the that regulates what the
+
+ align:start position:0%
+that relates the that regulates what the
+ 
+
+ align:start position:0%
+that relates the that regulates what the
+NTS PD NTSB does National Transportation
+
+ align:start position:0%
+NTS PD NTSB does National Transportation
+ 
+
+ align:start position:0%
+NTS PD NTSB does National Transportation
+Safety Board so first they define what
+
+ align:start position:0%
+Safety Board so first they define what
+ 
+
+ align:start position:0%
+Safety Board so first they define what
+an accident is so there has to be you
+
+ align:start position:0%
+an accident is so there has to be you
+ 
+
+ align:start position:0%
+an accident is so there has to be you
+know a serious injury and they define if
+
+ align:start position:0%
+know a serious injury and they define if
+ 
+
+ align:start position:0%
+know a serious injury and they define if
+you go in there they kind of define what
+
+ align:start position:0%
+you go in there they kind of define what
+ 
+
+ align:start position:0%
+you go in there they kind of define what
+a serious injury is and I think
+
+ align:start position:0%
+a serious injury is and I think
+ 
+
+ align:start position:0%
+a serious injury is and I think
+substantial damage to the aircraft if
+
+ align:start position:0%
+substantial damage to the aircraft if
+ 
+
+ align:start position:0%
+substantial damage to the aircraft if
+it's just the landing gear that's a bit
+
+ align:start position:0%
+it's just the landing gear that's a bit
+ 
+
+ align:start position:0%
+it's just the landing gear that's a bit
+trashed I don't think that qualifies if
+
+ align:start position:0%
+trashed I don't think that qualifies if
+ 
+
+ align:start position:0%
+trashed I don't think that qualifies if
+somebody dies within 30 days of the
+
+ align:start position:0%
+somebody dies within 30 days of the
+ 
+
+ align:start position:0%
+somebody dies within 30 days of the
+accident it becomes fatal here's your
+
+ align:start position:0%
+accident it becomes fatal here's your
+ 
+
+ align:start position:0%
+accident it becomes fatal here's your
+here's your definition of serious injury
+
+ align:start position:0%
+here's your definition of serious injury
+ 
+
+ align:start position:0%
+here's your definition of serious injury
+not too much fun you have to immediately
+
+ align:start position:0%
+not too much fun you have to immediately
+ 
+
+ align:start position:0%
+not too much fun you have to immediately
+notify the NTSB if the flight controls
+
+ align:start position:0%
+notify the NTSB if the flight controls
+ 
+
+ align:start position:0%
+notify the NTSB if the flight controls
+malfunction they don't really care if
+
+ align:start position:0%
+malfunction they don't really care if
+ 
+
+ align:start position:0%
+malfunction they don't really care if
+the lycoming our continental piston
+
+ align:start position:0%
+the lycoming our continental piston
+ 
+
+ align:start position:0%
+the lycoming our continental piston
+engine fails in some way but if the
+
+ align:start position:0%
+engine fails in some way but if the
+ 
+
+ align:start position:0%
+engine fails in some way but if the
+flight controls fail and you can't Bank
+
+ align:start position:0%
+flight controls fail and you can't Bank
+ 
+
+ align:start position:0%
+flight controls fail and you can't Bank
+your session or Piper or cirrus that's
+
+ align:start position:0%
+your session or Piper or cirrus that's
+ 
+
+ align:start position:0%
+your session or Piper or cirrus that's
+something they want to hear about if
+
+ align:start position:0%
+something they want to hear about if
+ 
+
+ align:start position:0%
+something they want to hear about if
+more than half of your glass cockpit
+
+ align:start position:0%
+more than half of your glass cockpit
+ 
+
+ align:start position:0%
+more than half of your glass cockpit
+goes dark they want to hear about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think 830 . 15 is kind of in in the
+
+ align:start position:0%
+I think 830 . 15 is kind of in in the
+ 
+
+ align:start position:0%
+I think 830 . 15 is kind of in in the
+test something it's those time periods
+
+ align:start position:0%
+test something it's those time periods
+ 
+
+ align:start position:0%
+test something it's those time periods
+like report report within 10 days of the
+
+ align:start position:0%
+like report report within 10 days of the
+ 
+
+ align:start position:0%
+like report report within 10 days of the
+accident oh yeah and your required info
+
+ align:start position:0%
+accident oh yeah and your required info
+ 
+
+ align:start position:0%
+accident oh yeah and your required info
+when notifying okay
+
+ align:start position:0%
+when notifying okay
+ 
+
+ align:start position:0%
+when notifying okay
+so the bottom line on seaplanes is that
+
+ align:start position:0%
+so the bottom line on seaplanes is that
+ 
+
+ align:start position:0%
+so the bottom line on seaplanes is that
+it does combine you know the hazards of
+
+ align:start position:0%
+it does combine you know the hazards of
+ 
+
+ align:start position:0%
+it does combine you know the hazards of
+a boat and a plane and therefore you
+
+ align:start position:0%
+a boat and a plane and therefore you
+ 
+
+ align:start position:0%
+a boat and a plane and therefore you
+need the skills of both a sailor and a
+
+ align:start position:0%
+need the skills of both a sailor and a
+ 
+
+ align:start position:0%
+need the skills of both a sailor and a
+pilot
+
+ align:start position:0%
+pilot
+ 
+
+ align:start position:0%
+pilot
+to manage those hazards on the other
+
+ align:start position:0%
+to manage those hazards on the other
+ 
+
+ align:start position:0%
+to manage those hazards on the other
+hand I think it's a lot of fun you know
+
+ align:start position:0%
+hand I think it's a lot of fun you know
+ 
+
+ align:start position:0%
+hand I think it's a lot of fun you know
+when the icon first came out at $100,000
+
+ align:start position:0%
+when the icon first came out at $100,000
+ 
+
+ align:start position:0%
+when the icon first came out at $100,000
+and change I thought well this would be
+
+ align:start position:0%
+and change I thought well this would be
+ 
+
+ align:start position:0%
+and change I thought well this would be
+great well you just get one of these
+
+ align:start position:0%
+great well you just get one of these
+ 
+
+ align:start position:0%
+great well you just get one of these
+we'll split it four ways we'll keep it
+
+ align:start position:0%
+we'll split it four ways we'll keep it
+ 
+
+ align:start position:0%
+we'll split it four ways we'll keep it
+at Hanscom and then you know we'll go up
+
+ align:start position:0%
+at Hanscom and then you know we'll go up
+ 
+
+ align:start position:0%
+at Hanscom and then you know we'll go up
+for a 15-minute flight to New Hampshire
+
+ align:start position:0%
+for a 15-minute flight to New Hampshire
+ 
+
+ align:start position:0%
+for a 15-minute flight to New Hampshire
+slash and - come back and it'll be
+
+ align:start position:0%
+slash and - come back and it'll be
+ 
+
+ align:start position:0%
+slash and - come back and it'll be
+really cool now that it's a four hundred
+
+ align:start position:0%
+really cool now that it's a four hundred
+ 
+
+ align:start position:0%
+really cool now that it's a four hundred
+thousand dollar airplane you know it's
+
+ align:start position:0%
+thousand dollar airplane you know it's
+ 
+
+ align:start position:0%
+thousand dollar airplane you know it's
+not enough it's the question is let's go
+
+ align:start position:0%
+not enough it's the question is let's go
+ 
+
+ align:start position:0%
+not enough it's the question is let's go
+back to that slide
+
+ align:start position:0%
+back to that slide
+ 
+
+ align:start position:0%
+back to that slide
+yeah file report within seven days if an
+
+ align:start position:0%
+yeah file report within seven days if an
+ 
+
+ align:start position:0%
+yeah file report within seven days if an
+aircraft is overdue so that means you
+
+ align:start position:0%
+aircraft is overdue so that means you
+ 
+
+ align:start position:0%
+aircraft is overdue so that means you
+expected an airplane to come back from
+
+ align:start position:0%
+expected an airplane to come back from
+ 
+
+ align:start position:0%
+expected an airplane to come back from
+the fishing camp in Alaska and it hasn't
+
+ align:start position:0%
+the fishing camp in Alaska and it hasn't
+ 
+
+ align:start position:0%
+the fishing camp in Alaska and it hasn't
+returned so you don't know if it's
+
+ align:start position:0%
+returned so you don't know if it's
+ 
+
+ align:start position:0%
+returned so you don't know if it's
+crashed or not that was like me remember
+
+ align:start position:0%
+crashed or not that was like me remember
+ 
+
+ align:start position:0%
+crashed or not that was like me remember
+I told you that story about landing at
+
+ align:start position:0%
+I told you that story about landing at
+ 
+
+ align:start position:0%
+I told you that story about landing at
+PDK in Atlanta and I didn't forgot to
+
+ align:start position:0%
+PDK in Atlanta and I didn't forgot to
+ 
+
+ align:start position:0%
+PDK in Atlanta and I didn't forgot to
+close my flight plan and so my my
+
+ align:start position:0%
+close my flight plan and so my my
+ 
+
+ align:start position:0%
+close my flight plan and so my my
+diamond star was considered overdue and
+
+ align:start position:0%
+diamond star was considered overdue and
+ 
+
+ align:start position:0%
+diamond star was considered overdue and
+I kept rejecting calls from an
+
+ align:start position:0%
+I kept rejecting calls from an
+ 
+
+ align:start position:0%
+I kept rejecting calls from an
+unfamiliar phone number my proudest
+
+ align:start position:0%
+unfamiliar phone number my proudest
+ 
+
+ align:start position:0%
+unfamiliar phone number my proudest
+moment all right so insurance is kind of
+
+ align:start position:0%
+moment all right so insurance is kind of
+ 
+
+ align:start position:0%
+moment all right so insurance is kind of
+expensive as any other de specially for
+
+ align:start position:0%
+expensive as any other de specially for
+ 
+
+ align:start position:0%
+expensive as any other de specially for
+the amphibs Strait an airplane on
+
+ align:start position:0%
+the amphibs Strait an airplane on
+ 
+
+ align:start position:0%
+the amphibs Strait an airplane on
+straight flows isn't that much more
+
+ align:start position:0%
+straight flows isn't that much more
+ 
+
+ align:start position:0%
+straight flows isn't that much more
+expensive to insure than a regular
+
+ align:start position:0%
+expensive to insure than a regular
+ 
+
+ align:start position:0%
+expensive to insure than a regular
+airplane actually that's a great way to
+
+ align:start position:0%
+airplane actually that's a great way to
+ 
+
+ align:start position:0%
+airplane actually that's a great way to
+evaluate risk if an insurance company is
+
+ align:start position:0%
+evaluate risk if an insurance company is
+ 
+
+ align:start position:0%
+evaluate risk if an insurance company is
+willing to write a policy first that's
+
+ align:start position:0%
+willing to write a policy first that's
+ 
+
+ align:start position:0%
+willing to write a policy first that's
+not on floats it can't be all that can't
+
+ align:start position:0%
+not on floats it can't be all that can't
+ 
+
+ align:start position:0%
+not on floats it can't be all that can't
+be all that dangerous but like I said
+
+ align:start position:0%
+be all that dangerous but like I said
+ 
+
+ align:start position:0%
+be all that dangerous but like I said
+the military has decided what's do most
+
+ align:start position:0%
+the military has decided what's do most
+ 
+
+ align:start position:0%
+the military has decided what's do most
+of the things we used to do with sea
+
+ align:start position:0%
+of the things we used to do with sea
+ 
+
+ align:start position:0%
+of the things we used to do with sea
+planes with helicopters question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so aren't sure we've met personal
+
+ align:start position:0%
+so aren't sure we've met personal
+ 
+
+ align:start position:0%
+so aren't sure we've met personal
+insurance so I don't belong but we
+
+ align:start position:0%
+insurance so I don't belong but we
+ 
+
+ align:start position:0%
+insurance so I don't belong but we
+ourselves are
+
+ align:start position:0%
+ourselves are
+ 
+
+ align:start position:0%
+ 
+I think question is just your like
+
+ align:start position:0%
+I think question is just your like
+ 
+
+ align:start position:0%
+I think question is just your like
+regular medical insurance cover an
+
+ align:start position:0%
+regular medical insurance cover an
+ 
+
+ align:start position:0%
+regular medical insurance cover an
+injury from plying sure yeah there's no
+
+ align:start position:0%
+injury from plying sure yeah there's no
+ 
+
+ align:start position:0%
+injury from plying sure yeah there's no
+exclusion for that I think sometimes if
+
+ align:start position:0%
+exclusion for that I think sometimes if
+ 
+
+ align:start position:0%
+exclusion for that I think sometimes if
+you get like an umbrella liability
+
+ align:start position:0%
+you get like an umbrella liability
+ 
+
+ align:start position:0%
+you get like an umbrella liability
+policy they say well that's great but
+
+ align:start position:0%
+policy they say well that's great but
+ 
+
+ align:start position:0%
+policy they say well that's great but
+we're not gonna like to add five million
+
+ align:start position:0%
+we're not gonna like to add five million
+ 
+
+ align:start position:0%
+we're not gonna like to add five million
+dollars if you injure somebody with your
+
+ align:start position:0%
+dollars if you injure somebody with your
+ 
+
+ align:start position:0%
+dollars if you injure somebody with your
+Cessna so they can have exclusions AOPA
+
+ align:start position:0%
+Cessna so they can have exclusions AOPA
+ 
+
+ align:start position:0%
+Cessna so they can have exclusions AOPA
+has a big insurance business actually
+
+ align:start position:0%
+has a big insurance business actually
+ 
+
+ align:start position:0%
+has a big insurance business actually
+selling life insurance at pretty
+
+ align:start position:0%
+selling life insurance at pretty
+ 
+
+ align:start position:0%
+selling life insurance at pretty
+reasonable rates to pilots so there
+
+ align:start position:0%
+reasonable rates to pilots so there
+ 
+
+ align:start position:0%
+reasonable rates to pilots so there
+again that tells you you know when your
+
+ align:start position:0%
+again that tells you you know when your
+ 
+
+ align:start position:0%
+again that tells you you know when your
+friend says you know you're stupid why
+
+ align:start position:0%
+friend says you know you're stupid why
+ 
+
+ align:start position:0%
+friend says you know you're stupid why
+would you fly a Piper or a Cessna you
+
+ align:start position:0%
+would you fly a Piper or a Cessna you
+ 
+
+ align:start position:0%
+would you fly a Piper or a Cessna you
+know that thing's old it doesn't look
+
+ align:start position:0%
+know that thing's old it doesn't look
+ 
+
+ align:start position:0%
+know that thing's old it doesn't look
+safe you can say well like insurance
+
+ align:start position:0%
+safe you can say well like insurance
+ 
+
+ align:start position:0%
+safe you can say well like insurance
+companies aren't stupid and they have a
+
+ align:start position:0%
+companies aren't stupid and they have a
+ 
+
+ align:start position:0%
+companies aren't stupid and they have a
+huge business marketing life insurance
+
+ align:start position:0%
+huge business marketing life insurance
+ 
+
+ align:start position:0%
+huge business marketing life insurance
+to the members of AOPA who are all
+
+ align:start position:0%
+to the members of AOPA who are all
+ 
+
+ align:start position:0%
+to the members of AOPA who are all
+flying little airplanes like this and
+
+ align:start position:0%
+flying little airplanes like this and
+ 
+
+ align:start position:0%
+flying little airplanes like this and
+you know it's only a 10 percent higher
+
+ align:start position:0%
+you know it's only a 10 percent higher
+ 
+
+ align:start position:0%
+you know it's only a 10 percent higher
+rate than you know what you can get in
+
+ align:start position:0%
+rate than you know what you can get in
+ 
+
+ align:start position:0%
+rate than you know what you can get in
+the market elsewhere of course pilots
+
+ align:start position:0%
+the market elsewhere of course pilots
+ 
+
+ align:start position:0%
+the market elsewhere of course pilots
+are healthier than the that's that's
+
+ align:start position:0%
+are healthier than the that's that's
+ 
+
+ align:start position:0%
+are healthier than the that's that's
+that's one issue right since pilots by
+
+ align:start position:0%
+that's one issue right since pilots by
+ 
+
+ align:start position:0%
+that's one issue right since pilots by
+definition have passed a medical exam
+
+ align:start position:0%
+definition have passed a medical exam
+ 
+
+ align:start position:0%
+definition have passed a medical exam
+they tend to be a little bit healthier
+
+ align:start position:0%
+they tend to be a little bit healthier
+ 
+
+ align:start position:0%
+they tend to be a little bit healthier
+than average same reason like the
+
+ align:start position:0%
+than average same reason like the
+ 
+
+ align:start position:0%
+than average same reason like the
+military the death rate of people who
+
+ align:start position:0%
+military the death rate of people who
+ 
+
+ align:start position:0%
+military the death rate of people who
+serve in the military is quite a bit
+
+ align:start position:0%
+serve in the military is quite a bit
+ 
+
+ align:start position:0%
+serve in the military is quite a bit
+lower than the death rate of the same
+
+ align:start position:0%
+lower than the death rate of the same
+ 
+
+ align:start position:0%
+lower than the death rate of the same
+age people who are in the civilian
+
+ align:start position:0%
+age people who are in the civilian
+ 
+
+ align:start position:0%
+age people who are in the civilian
+workforce
+
+ align:start position:0%
+workforce
+ 
+
+ align:start position:0%
+workforce
+partly because not that many of them are
+
+ align:start position:0%
+partly because not that many of them are
+ 
+
+ align:start position:0%
+partly because not that many of them are
+actually you know in combat and partly
+
+ align:start position:0%
+actually you know in combat and partly
+ 
+
+ align:start position:0%
+actually you know in combat and partly
+because the military rejects people who
+
+ align:start position:0%
+because the military rejects people who
+ 
+
+ align:start position:0%
+because the military rejects people who
+are unhealthy so you're not going to die
+
+ align:start position:0%
+are unhealthy so you're not going to die
+ 
+
+ align:start position:0%
+are unhealthy so you're not going to die
+of cancer at age 23 if you're in the
+
+ align:start position:0%
+of cancer at age 23 if you're in the
+ 
+
+ align:start position:0%
+of cancer at age 23 if you're in the
+military because they would have not let
+
+ align:start position:0%
+military because they would have not let
+ 
+
+ align:start position:0%
+military because they would have not let
+you enlist probably if they saw that you
+
+ align:start position:0%
+you enlist probably if they saw that you
+ 
+
+ align:start position:0%
+you enlist probably if they saw that you
+were suffering from the beginning stages
+
+ align:start position:0%
+were suffering from the beginning stages
+ 
+
+ align:start position:0%
+were suffering from the beginning stages
+of cancer all right light sport flying
+
+ align:start position:0%
+of cancer all right light sport flying
+ 
+
+ align:start position:0%
+of cancer all right light sport flying
+boats array is fun this is a real one
+
+ align:start position:0%
+boats array is fun this is a real one
+ 
+
+ align:start position:0%
+boats array is fun this is a real one
+there's 700 of these out there and they
+
+ align:start position:0%
+there's 700 of these out there and they
+ 
+
+ align:start position:0%
+there's 700 of these out there and they
+sell it as a kit and they also sell it
+
+ align:start position:0%
+sell it as a kit and they also sell it
+ 
+
+ align:start position:0%
+sell it as a kit and they also sell it
+as a built airplane so here it is look
+
+ align:start position:0%
+as a built airplane so here it is look
+ 
+
+ align:start position:0%
+as a built airplane so here it is look
+how much fun some somebody put one of
+
+ align:start position:0%
+how much fun some somebody put one of
+ 
+
+ align:start position:0%
+how much fun some somebody put one of
+these on a yacht and flew it in all
+
+ align:start position:0%
+these on a yacht and flew it in all
+ 
+
+ align:start position:0%
+these on a yacht and flew it in all
+different parts of the world you know
+
+ align:start position:0%
+different parts of the world you know
+ 
+
+ align:start position:0%
+different parts of the world you know
+they would take off I guess they would
+
+ align:start position:0%
+they would take off I guess they would
+ 
+
+ align:start position:0%
+they would take off I guess they would
+winch it down into the water take off
+
+ align:start position:0%
+winch it down into the water take off
+ 
+
+ align:start position:0%
+winch it down into the water take off
+fly around and then winch it back up and
+
+ align:start position:0%
+fly around and then winch it back up and
+ 
+
+ align:start position:0%
+fly around and then winch it back up and
+I think they were in some fairly open
+
+ align:start position:0%
+I think they were in some fairly open
+ 
+
+ align:start position:0%
+I think they were in some fairly open
+oceans at the time none of the things
+
+ align:start position:0%
+oceans at the time none of the things
+ 
+
+ align:start position:0%
+oceans at the time none of the things
+survived so that's pretty cool they
+
+ align:start position:0%
+survived so that's pretty cool they
+ 
+
+ align:start position:0%
+survived so that's pretty cool they
+stuff a Garmin g3x glass cockpit in
+
+ align:start position:0%
+stuff a Garmin g3x glass cockpit in
+ 
+
+ align:start position:0%
+stuff a Garmin g3x glass cockpit in
+there that's the same that the things
+
+ align:start position:0%
+there that's the same that the things
+ 
+
+ align:start position:0%
+there that's the same that the things
+that Gabe gamebird has the light sport
+
+ align:start position:0%
+that Gabe gamebird has the light sport
+ 
+
+ align:start position:0%
+that Gabe gamebird has the light sport
+folks have a lot of flexibility it has a
+
+ align:start position:0%
+folks have a lot of flexibility it has a
+ 
+
+ align:start position:0%
+folks have a lot of flexibility it has a
+Rotax engine which is conventional the
+
+ align:start position:0%
+Rotax engine which is conventional the
+ 
+
+ align:start position:0%
+Rotax engine which is conventional the
+icon a5 is the airplane see look look at
+
+ align:start position:0%
+icon a5 is the airplane see look look at
+ 
+
+ align:start position:0%
+icon a5 is the airplane see look look at
+Oshkosh there there booth is always
+
+ align:start position:0%
+Oshkosh there there booth is always
+ 
+
+ align:start position:0%
+Oshkosh there there booth is always
+packed people love it people want it and
+
+ align:start position:0%
+packed people love it people want it and
+ 
+
+ align:start position:0%
+packed people love it people want it and
+it's one of the few airplanes that's
+
+ align:start position:0%
+it's one of the few airplanes that's
+ 
+
+ align:start position:0%
+it's one of the few airplanes that's
+marketed to people that don't have any
+
+ align:start position:0%
+marketed to people that don't have any
+ 
+
+ align:start position:0%
+marketed to people that don't have any
+flying experience
+
+ align:start position:0%
+flying experience
+ 
+
+ align:start position:0%
+flying experience
+I wrote a review of it in 2010 saying
+
+ align:start position:0%
+I wrote a review of it in 2010 saying
+ 
+
+ align:start position:0%
+I wrote a review of it in 2010 saying
+that it would be available until 2014 I
+
+ align:start position:0%
+that it would be available until 2014 I
+ 
+
+ align:start position:0%
+that it would be available until 2014 I
+think it had been originally promised
+
+ align:start position:0%
+think it had been originally promised
+ 
+
+ align:start position:0%
+think it had been originally promised
+for you know 2012 so it's just kind of
+
+ align:start position:0%
+for you know 2012 so it's just kind of
+ 
+
+ align:start position:0%
+for you know 2012 so it's just kind of
+coming out but these composite plants
+
+ align:start position:0%
+coming out but these composite plants
+ 
+
+ align:start position:0%
+coming out but these composite plants
+are hard to manufacture I talked to the
+
+ align:start position:0%
+are hard to manufacture I talked to the
+ 
+
+ align:start position:0%
+are hard to manufacture I talked to the
+gamebird guys they said they spend 500
+
+ align:start position:0%
+gamebird guys they said they spend 500
+ 
+
+ align:start position:0%
+gamebird guys they said they spend 500
+hours 500 person hours prepping the
+
+ align:start position:0%
+hours 500 person hours prepping the
+ 
+
+ align:start position:0%
+hours 500 person hours prepping the
+airplane to be painted just like sanding
+
+ align:start position:0%
+airplane to be painted just like sanding
+ 
+
+ align:start position:0%
+airplane to be painted just like sanding
+and smoothing everything to be painted
+
+ align:start position:0%
+and smoothing everything to be painted
+ 
+
+ align:start position:0%
+and smoothing everything to be painted
+so I think it's just very hard to make
+
+ align:start position:0%
+so I think it's just very hard to make
+ 
+
+ align:start position:0%
+so I think it's just very hard to make
+these things at an economical price I
+
+ align:start position:0%
+these things at an economical price I
+ 
+
+ align:start position:0%
+these things at an economical price I
+still don't have sound I don't think do
+
+ align:start position:0%
+still don't have sound I don't think do
+ 
+
+ align:start position:0%
+still don't have sound I don't think do
+we here's my review of the plane I made
+
+ align:start position:0%
+we here's my review of the plane I made
+ 
+
+ align:start position:0%
+we here's my review of the plane I made
+this little video that was fun well I
+
+ align:start position:0%
+this little video that was fun well I
+ 
+
+ align:start position:0%
+this little video that was fun well I
+thought it was fun I'm sure Ikon doesn't
+
+ align:start position:0%
+thought it was fun I'm sure Ikon doesn't
+ 
+
+ align:start position:0%
+thought it was fun I'm sure Ikon doesn't
+think it's fun alright questions about
+
+ align:start position:0%
+think it's fun alright questions about
+ 
+
+ align:start position:0%
+think it's fun alright questions about
+sea planes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who wants one who want who would buy an
+
+ align:start position:0%
+who wants one who want who would buy an
+ 
+
+ align:start position:0%
+who wants one who want who would buy an
+icon if it were reasonably priced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the question is you know what would
+
+ align:start position:0%
+yeah the question is you know what would
+ 
+
+ align:start position:0%
+yeah the question is you know what would
+buy in my opinion B of landing in the
+
+ align:start position:0%
+buy in my opinion B of landing in the
+ 
+
+ align:start position:0%
+buy in my opinion B of landing in the
+Great Lakes I think people do use do a
+
+ align:start position:0%
+Great Lakes I think people do use do a
+ 
+
+ align:start position:0%
+Great Lakes I think people do use do a
+lot of flying of sea planes up in the
+
+ align:start position:0%
+lot of flying of sea planes up in the
+ 
+
+ align:start position:0%
+lot of flying of sea planes up in the
+Great Lakes but there again you know the
+
+ align:start position:0%
+Great Lakes but there again you know the
+ 
+
+ align:start position:0%
+Great Lakes but there again you know the
+Great Lakes there are harbors there are
+
+ align:start position:0%
+Great Lakes there are harbors there are
+ 
+
+ align:start position:0%
+Great Lakes there are harbors there are
+column or areas I think they're not
+
+ align:start position:0%
+column or areas I think they're not
+ 
+
+ align:start position:0%
+column or areas I think they're not
+really landing in the middle of the
+
+ align:start position:0%
+really landing in the middle of the
+ 
+
+ align:start position:0%
+really landing in the middle of the
+Great Lake and then they don't say like
+
+ align:start position:0%
+Great Lake and then they don't say like
+ 
+
+ align:start position:0%
+Great Lake and then they don't say like
+I just want to go to the middle of Lake
+
+ align:start position:0%
+I just want to go to the middle of Lake
+ 
+
+ align:start position:0%
+I just want to go to the middle of Lake
+Superior and fish off the float for a
+
+ align:start position:0%
+Superior and fish off the float for a
+ 
+
+ align:start position:0%
+Superior and fish off the float for a
+while
+
+ align:start position:0%
+while
+ 
+
+ align:start position:0%
+while
+they're going to some destination and by
+
+ align:start position:0%
+they're going to some destination and by
+ 
+
+ align:start position:0%
+they're going to some destination and by
+definition you know the destination will
+
+ align:start position:0%
+definition you know the destination will
+ 
+
+ align:start position:0%
+definition you know the destination will
+have a calmer area for for boats to hang
+
+ align:start position:0%
+have a calmer area for for boats to hang
+ 
+
+ align:start position:0%
+have a calmer area for for boats to hang
+out and it's I think there's actually a
+
+ align:start position:0%
+out and it's I think there's actually a
+ 
+
+ align:start position:0%
+out and it's I think there's actually a
+commercial seaplane service that's
+
+ align:start position:0%
+commercial seaplane service that's
+ 
+
+ align:start position:0%
+commercial seaplane service that's
+starting up between Manhattan and Boston
+
+ align:start position:0%
+starting up between Manhattan and Boston
+ 
+
+ align:start position:0%
+starting up between Manhattan and Boston
+so you'll you'll go to the there's a
+
+ align:start position:0%
+so you'll you'll go to the there's a
+ 
+
+ align:start position:0%
+so you'll you'll go to the there's a
+seaplane I should have mentioned this
+
+ align:start position:0%
+seaplane I should have mentioned this
+ 
+
+ align:start position:0%
+seaplane I should have mentioned this
+for helicopters they're held at pads all
+
+ align:start position:0%
+for helicopters they're held at pads all
+ 
+
+ align:start position:0%
+for helicopters they're held at pads all
+around Manhattan so you can actually go
+
+ align:start position:0%
+around Manhattan so you can actually go
+ 
+
+ align:start position:0%
+around Manhattan so you can actually go
+to the downtown Wall Street heliport
+
+ align:start position:0%
+to the downtown Wall Street heliport
+ 
+
+ align:start position:0%
+to the downtown Wall Street heliport
+land it used to be really cheap it was
+
+ align:start position:0%
+land it used to be really cheap it was
+ 
+
+ align:start position:0%
+land it used to be really cheap it was
+$75 an hour for parking I think or maybe
+
+ align:start position:0%
+$75 an hour for parking I think or maybe
+ 
+
+ align:start position:0%
+$75 an hour for parking I think or maybe
+25 it was I don't know it was it was not
+
+ align:start position:0%
+25 it was I don't know it was it was not
+ 
+
+ align:start position:0%
+25 it was I don't know it was it was not
+that much more than parking in a car go
+
+ align:start position:0%
+that much more than parking in a car go
+ 
+
+ align:start position:0%
+that much more than parking in a car go
+and have lunch now they've leased those
+
+ align:start position:0%
+and have lunch now they've leased those
+ 
+
+ align:start position:0%
+and have lunch now they've leased those
+helmet pads to some government crony
+
+ align:start position:0%
+helmet pads to some government crony
+ 
+
+ align:start position:0%
+helmet pads to some government crony
+monopoly that owns all three of them and
+
+ align:start position:0%
+monopoly that owns all three of them and
+ 
+
+ align:start position:0%
+monopoly that owns all three of them and
+they crank the rates up by a factor of
+
+ align:start position:0%
+they crank the rates up by a factor of
+ 
+
+ align:start position:0%
+they crank the rates up by a factor of
+four on you know immediately but anyway
+
+ align:start position:0%
+four on you know immediately but anyway
+ 
+
+ align:start position:0%
+four on you know immediately but anyway
+they I don't know if it's the same
+
+ align:start position:0%
+they I don't know if it's the same
+ 
+
+ align:start position:0%
+they I don't know if it's the same
+company but they have a seaplane a
+
+ align:start position:0%
+company but they have a seaplane a
+ 
+
+ align:start position:0%
+company but they have a seaplane a
+public seaplane port they're on the East
+
+ align:start position:0%
+public seaplane port they're on the East
+ 
+
+ align:start position:0%
+public seaplane port they're on the East
+River and this I think it's a cape air
+
+ align:start position:0%
+River and this I think it's a cape air
+ 
+
+ align:start position:0%
+River and this I think it's a cape air
+affiliate maybe that's going to start
+
+ align:start position:0%
+affiliate maybe that's going to start
+ 
+
+ align:start position:0%
+affiliate maybe that's going to start
+operating downtown to downtown and
+
+ align:start position:0%
+operating downtown to downtown and
+ 
+
+ align:start position:0%
+operating downtown to downtown and
+assessment caravan on floats
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/yauQ7o1ZAAw.txt b/yauQ7o1ZAAw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..39a89003cd8a86a466f65528d2f1dccf41aa8220
--- /dev/null
+++ b/yauQ7o1ZAAw.txt
@@ -0,0 +1,264 @@
+Let's start by redrawing and simplifying the
+Beta data path so that it will be easier to
+
+reason about when we add pipelining.
+
+The first simplification is to focus on sequential
+execution and so leave out the branch addressing
+
+and PC mux logic.
+
+Our simplified Beta always executes the next
+instruction from PC+4.
+
+We'll add back the branch and jump logic when
+we discuss control hazards.
+
+The second simplification is to have the register
+file appear twice in the diagram so that we
+
+can tease apart the read and write operations
+that occur at different stages of instruction
+
+execution.
+
+The top Register File shows the combinational
+read ports, used to when reading the register
+
+operands in the RF stage.
+
+The bottom Register File shows the clocked
+write port, used to write the result into
+
+the destination register at the end of the
+WB stage.
+
+Physically, there's only one set of 32 registers,
+we've just drawn the read and write circuity
+
+as separate components in the diagram.
+
+If we add pipeline registers to the simplified
+diagram, we see that execution proceeds through
+
+the five stages from top to bottom.
+
+If we consider execution of instruction sequences
+with no data hazards, information is flowing
+
+down the pipeline and the pipeline will correctly
+overlap the execution of all the instructions
+
+in the pipeline.
+
+The diagram shows the components needed to
+implement each of the five stages.
+
+The IF stage contains the program counter
+and the main memory interface for fetching
+
+instructions.
+
+The RF stage has the register file and operand
+multiplexers.
+
+The ALU stage uses the operands and computes
+the result.
+
+The MEM stage handles the memory access for
+load and store operations.
+
+And the WB stage writes the result into the
+destination register.
+
+In each clock cycle, each stage does its part
+in the execution of a particular instruction.
+
+In a given clock cycle, there are five instructions
+in the pipeline.
+
+Note that data accesses to main memory span
+almost two clock cycles.
+
+Data accesses are initiated at the beginning
+of the MEM stage and returning data is only
+
+needed just before the end of the WB stage.
+
+The memory is itself pipelined and can simultaneously
+finish the access from an earlier instruction
+
+while starting an access for the next instruction.
+
+This simplified diagram isn't showing how
+the control logic is split across the pipeline
+
+stages.
+
+How does that work?
+
+Note that we've included instruction registers
+as part of each pipeline stage, so that each
+
+stage can compute the control signals it needs
+from its instruction register.
+
+The encoded instruction is simply passed from
+one stage to the next as the instruction flows
+
+through the pipeline..
+
+Each stage computes its control signals from
+the opcode field of its instruction register.
+
+The RF stage needs the RA, RB, and literal
+fields from its instruction register.
+
+And the WB stage needs the RC field from its
+instruction register.
+
+The required logic is very similar to the
+unpipelined implementation, it's just been
+
+split up and moved to the appropriate pipeline
+stage.
+
+We'll see that we will have to add some additional
+control logic to deal correctly with pipeline
+
+hazards.
+
+Our simplified diagram isn't so simple anymore!
+
+To see how the pipeline works, let's follow
+along as it executes this sequence of six
+
+instructions.
+
+Note that the instructions are reading and
+writing from different registers, so there
+
+are no potential data hazards.
+
+And there are no branches and jumps, so there
+are no potential control hazards.
+
+Since there are no potential hazards, the
+instruction executions can be overlapped and
+
+their overlapped execution in the pipeline
+will work correctly.
+
+Okay, here we go!
+
+During cycle 1, the IF stage sends the value
+from the program counter to main memory to
+
+fetch the first instruction (the green LD
+instruction), which will be stored in the
+
+RF-stage instruction register at the end of
+the cycle.
+
+Meanwhile, it's also computing PC+4, which
+will be the next value of the program counter.
+
+We've colored the next value blue to indicate
+that it's the address of the blue instruction
+
+in the sequence.
+
+We'll add the appropriately colored label
+on the right of each pipeline stage to indicate
+
+which instruction the stage is processing.
+
+At the start of cycle 2, we see that values
+in the PC and instruction registers for the
+
+RF stage now correspond to the green instruction.
+
+During the cycle the register file will be
+reading the register operands, in this case
+
+R1, which is needed for the green instruction.
+
+Since the green instruction is a LD, ASEL
+is 0 and BSEL is 1, selecting the appropriate
+
+values to be written into the A and B operand
+registers at the end of the cycle.
+
+Concurrently, the IF stage is fetching the
+blue instruction from main memory and computing
+
+an updated PC value for the next cycle.
+
+In cycle 3, the green instruction is now in
+the ALU stage, where the ALU is adding the
+
+values in its operand registers (in this case
+the value of R1 and the constant 4) and the
+
+result will be stored in Y_MEM register at
+the end of the cycle.
+
+In cycle 4, we're overlapping execution of
+four instructions.
+
+The MEM stage initiates a memory read for
+the green LD instruction.
+
+Note that the read data will first become
+available in the WB stage - it's not available
+
+to CPU in the current clock cycle.
+
+In cycle 5, the results of the main memory
+read initiated in cycle 4 are available for
+
+writing to the register file in the WB stage.
+
+So execution of the green LD instruction will
+be complete when the memory data is written
+
+to R2 at the end of cycle 5.
+
+Meanwhile, the MEM stage is initiating a memory
+read for the blue LD instruction.
+
+The pipeline continues to complete successive
+instructions in successive clock cycles.
+
+The latency for a particular instruction is
+5 clock cycles.
+
+The throughput of the pipelined CPU is 1 instruction/cycle.
+
+This is the same as the unpipelined implementation,
+except that the clock period is shorter because
+
+each pipeline stage has fewer components.
+
+Note that the effects of the green LD, i.e.,
+filling R2 with a new value, don't happen
+
+until the rising edge of the clock at the
+end of cycle 5.
+
+In other words, the results of the green LD
+aren't available to other instructions until
+
+cycle 6.
+
+If there were instructions in the pipeline
+that read R2 before cycle 6, they would have
+
+gotten an old value!
+
+This is an example of a data hazard.
+
+Not a problem for us, since our instruction
+sequence didn't trigger this data hazard.
+
+Tackling data hazards is our next task.
\ No newline at end of file
diff --git a/yoq0ENMiR4w.txt b/yoq0ENMiR4w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f8d4b7ce939d843a00057d623bfb5b56dfb72d43
--- /dev/null
+++ b/yoq0ENMiR4w.txt
@@ -0,0 +1,8763 @@
+align:start position:0%
+ 
+let me um continue with the eslm PC
+
+ align:start position:0%
+let me um continue with the eslm PC
+ 
+
+ align:start position:0%
+let me um continue with the eslm PC
+model in fact I want to I Rush a little
+
+ align:start position:0%
+model in fact I want to I Rush a little
+ 
+
+ align:start position:0%
+model in fact I want to I Rush a little
+because I was over excited with the svb
+
+ align:start position:0%
+because I was over excited with the svb
+ 
+
+ align:start position:0%
+because I was over excited with the svb
+bank event H and and I want to make sure
+
+ align:start position:0%
+bank event H and and I want to make sure
+ 
+
+ align:start position:0%
+bank event H and and I want to make sure
+that you
+
+ align:start position:0%
+that you
+ 
+
+ align:start position:0%
+that you
+certainly understand this this mle it's
+
+ align:start position:0%
+certainly understand this this mle it's
+ 
+
+ align:start position:0%
+certainly understand this this mle it's
+going to be very
+
+ align:start position:0%
+going to be very
+ 
+
+ align:start position:0%
+going to be very
+important and I think it's one of the
+
+ align:start position:0%
+important and I think it's one of the
+ 
+
+ align:start position:0%
+important and I think it's one of the
+most important moles in in this course
+
+ align:start position:0%
+most important moles in in this course
+ 
+
+ align:start position:0%
+most important moles in in this course
+as I said
+
+ align:start position:0%
+as I said
+ 
+
+ align:start position:0%
+as I said
+before also I want to use a little bit
+
+ align:start position:0%
+before also I want to use a little bit
+ 
+
+ align:start position:0%
+before also I want to use a little bit
+more the this Mo itself to explain what
+
+ align:start position:0%
+more the this Mo itself to explain what
+ 
+
+ align:start position:0%
+more the this Mo itself to explain what
+is going on right now today we got hit
+
+ align:start position:0%
+is going on right now today we got hit
+ 
+
+ align:start position:0%
+is going on right now today we got hit
+by a second shock from the financial
+
+ align:start position:0%
+by a second shock from the financial
+ 
+
+ align:start position:0%
+by a second shock from the financial
+system and uh so so it's getting it's
+
+ align:start position:0%
+system and uh so so it's getting it's
+ 
+
+ align:start position:0%
+system and uh so so it's getting it's
+getting exciting these days so let me
+
+ align:start position:0%
+getting exciting these days so let me
+ 
+
+ align:start position:0%
+getting exciting these days so let me
+skip all this and remind you that that's
+
+ align:start position:0%
+skip all this and remind you that that's
+ 
+
+ align:start position:0%
+skip all this and remind you that that's
+what we we that's that's the ISL MPC
+
+ align:start position:0%
+what we we that's that's the ISL MPC
+ 
+
+ align:start position:0%
+what we we that's that's the ISL MPC
+model which I said is nothing else and
+
+ align:start position:0%
+model which I said is nothing else and
+ 
+
+ align:start position:0%
+model which I said is nothing else and
+just integrating the islm analysis with
+
+ align:start position:0%
+just integrating the islm analysis with
+ 
+
+ align:start position:0%
+just integrating the islm analysis with
+the Philips curve this is the part and I
+
+ align:start position:0%
+the Philips curve this is the part and I
+ 
+
+ align:start position:0%
+the Philips curve this is the part and I
+said and at this point I will follow the
+
+ align:start position:0%
+said and at this point I will follow the
+ 
+
+ align:start position:0%
+said and at this point I will follow the
+book and and assume that the central
+
+ align:start position:0%
+book and and assume that the central
+ 
+
+ align:start position:0%
+book and and assume that the central
+bank can control the real interest rate
+
+ align:start position:0%
+bank can control the real interest rate
+ 
+
+ align:start position:0%
+bank can control the real interest rate
+rather than the nominal interest rate
+
+ align:start position:0%
+rather than the nominal interest rate
+ 
+
+ align:start position:0%
+rather than the nominal interest rate
+which is what really controls in
+
+ align:start position:0%
+which is what really controls in
+ 
+
+ align:start position:0%
+which is what really controls in
+practice H but I'm going to make that
+
+ align:start position:0%
+practice H but I'm going to make that
+ 
+
+ align:start position:0%
+practice H but I'm going to make that
+assumption so the pictures have less
+
+ align:start position:0%
+assumption so the pictures have less
+ 
+
+ align:start position:0%
+assumption so the pictures have less
+curves moving around when when things
+
+ align:start position:0%
+curves moving around when when things
+ 
+
+ align:start position:0%
+curves moving around when when things
+are mov moving H as when we do Dynamics
+
+ align:start position:0%
+are mov moving H as when we do Dynamics
+ 
+
+ align:start position:0%
+are mov moving H as when we do Dynamics
+okay but that's just a eslm nothing
+
+ align:start position:0%
+okay but that's just a eslm nothing
+ 
+
+ align:start position:0%
+okay but that's just a eslm nothing
+different um then we look at the Philips
+
+ align:start position:0%
+different um then we look at the Philips
+ 
+
+ align:start position:0%
+different um then we look at the Philips
+curve and I said well we can we can uh I
+
+ align:start position:0%
+curve and I said well we can we can uh I
+ 
+
+ align:start position:0%
+curve and I said well we can we can uh I
+this is not very useful because you know
+
+ align:start position:0%
+this is not very useful because you know
+ 
+
+ align:start position:0%
+this is not very useful because you know
+in the as part I have output here and in
+
+ align:start position:0%
+in the as part I have output here and in
+ 
+
+ align:start position:0%
+in the as part I have output here and in
+the Philips curves I have inflation but
+
+ align:start position:0%
+the Philips curves I have inflation but
+ 
+
+ align:start position:0%
+the Philips curves I have inflation but
+then I have an employment and I don't
+
+ align:start position:0%
+then I have an employment and I don't
+ 
+
+ align:start position:0%
+then I have an employment and I don't
+want to be carrying around sort of three
+
+ align:start position:0%
+want to be carrying around sort of three
+ 
+
+ align:start position:0%
+want to be carrying around sort of three
+variables endogenous variables
+
+ align:start position:0%
+variables endogenous variables
+ 
+
+ align:start position:0%
+variables endogenous variables
+ER and and and so it's you know it's
+
+ align:start position:0%
+ER and and and so it's you know it's
+ 
+
+ align:start position:0%
+ER and and and so it's you know it's
+difficult to diagrams in in three
+
+ align:start position:0%
+difficult to diagrams in in three
+ 
+
+ align:start position:0%
+difficult to diagrams in in three
+dimension is everything less clear so
+
+ align:start position:0%
+dimension is everything less clear so
+ 
+
+ align:start position:0%
+dimension is everything less clear so
+I'm going to replace H this unemployment
+
+ align:start position:0%
+I'm going to replace H this unemployment
+ 
+
+ align:start position:0%
+I'm going to replace H this unemployment
+here for for output and it's very easy
+
+ align:start position:0%
+here for for output and it's very easy
+ 
+
+ align:start position:0%
+here for for output and it's very easy
+to do that with the production function
+
+ align:start position:0%
+to do that with the production function
+ 
+
+ align:start position:0%
+to do that with the production function
+we have because output is just equal to
+
+ align:start position:0%
+we have because output is just equal to
+ 
+
+ align:start position:0%
+we have because output is just equal to
+employment and employment is just equal
+
+ align:start position:0%
+employment and employment is just equal
+ 
+
+ align:start position:0%
+employment and employment is just equal
+to the labor force time one minus the
+
+ align:start position:0%
+to the labor force time one minus the
+ 
+
+ align:start position:0%
+to the labor force time one minus the
+rate of unemployment and we could Define
+
+ align:start position:0%
+rate of unemployment and we could Define
+ 
+
+ align:start position:0%
+rate of unemployment and we could Define
+a concept of potential output as simply
+
+ align:start position:0%
+a concept of potential output as simply
+ 
+
+ align:start position:0%
+a concept of potential output as simply
+that output that happens when employment
+
+ align:start position:0%
+that output that happens when employment
+ 
+
+ align:start position:0%
+that output that happens when employment
+is equal to the Natural level of
+
+ align:start position:0%
+is equal to the Natural level of
+ 
+
+ align:start position:0%
+is equal to the Natural level of
+employment which is equal to the labor
+
+ align:start position:0%
+employment which is equal to the labor
+ 
+
+ align:start position:0%
+employment which is equal to the labor
+force Time 1 minus the natural rate of
+
+ align:start position:0%
+force Time 1 minus the natural rate of
+ 
+
+ align:start position:0%
+force Time 1 minus the natural rate of
+unemployment and taking the difference
+
+ align:start position:0%
+unemployment and taking the difference
+ 
+
+ align:start position:0%
+unemployment and taking the difference
+subtracting the second line from the
+
+ align:start position:0%
+subtracting the second line from the
+ 
+
+ align:start position:0%
+subtracting the second line from the
+first one you get a concept that is used
+
+ align:start position:0%
+first one you get a concept that is used
+ 
+
+ align:start position:0%
+first one you get a concept that is used
+very frequently in microeconomics which
+
+ align:start position:0%
+very frequently in microeconomics which
+ 
+
+ align:start position:0%
+very frequently in microeconomics which
+is called is a concept of the output gap
+
+ align:start position:0%
+is called is a concept of the output gap
+ 
+
+ align:start position:0%
+is called is a concept of the output gap
+an output Gap refers to the difference
+
+ align:start position:0%
+an output Gap refers to the difference
+ 
+
+ align:start position:0%
+an output Gap refers to the difference
+between actual output and potential
+
+ align:start position:0%
+between actual output and potential
+ 
+
+ align:start position:0%
+between actual output and potential
+output in which potential output is
+
+ align:start position:0%
+output in which potential output is
+ 
+
+ align:start position:0%
+output in which potential output is
+nothing else of the level of output that
+
+ align:start position:0%
+nothing else of the level of output that
+ 
+
+ align:start position:0%
+nothing else of the level of output that
+you get when employment when an
+
+ align:start position:0%
+you get when employment when an
+ 
+
+ align:start position:0%
+you get when employment when an
+employment is at the natural rate of an
+
+ align:start position:0%
+employment is at the natural rate of an
+ 
+
+ align:start position:0%
+employment is at the natural rate of an
+employment
+
+ align:start position:0%
+employment
+ 
+
+ align:start position:0%
+employment
+so we get this output Gap is related to
+
+ align:start position:0%
+so we get this output Gap is related to
+ 
+
+ align:start position:0%
+so we get this output Gap is related to
+the employment gap and now we can
+
+ align:start position:0%
+the employment gap and now we can
+ 
+
+ align:start position:0%
+the employment gap and now we can
+replace the employment gap from here
+
+ align:start position:0%
+replace the employment gap from here
+ 
+
+ align:start position:0%
+replace the employment gap from here
+with the output Gap and we end up with a
+
+ align:start position:0%
+with the output Gap and we end up with a
+ 
+
+ align:start position:0%
+with the output Gap and we end up with a
+Philip Cur in the space of inflation and
+
+ align:start position:0%
+Philip Cur in the space of inflation and
+ 
+
+ align:start position:0%
+Philip Cur in the space of inflation and
+output gap which is something we can
+
+ align:start position:0%
+output gap which is something we can
+ 
+
+ align:start position:0%
+output gap which is something we can
+integrate very easily withm model that
+
+ align:start position:0%
+integrate very easily withm model that
+ 
+
+ align:start position:0%
+integrate very easily withm model that
+has output in it okay so that's H so the
+
+ align:start position:0%
+has output in it okay so that's H so the
+ 
+
+ align:start position:0%
+has output in it okay so that's H so the
+snpc model is
+
+ align:start position:0%
+snpc model is
+ 
+
+ align:start position:0%
+snpc model is
+really combining this equation with that
+
+ align:start position:0%
+really combining this equation with that
+ 
+
+ align:start position:0%
+really combining this equation with that
+equation and some model about expected
+
+ align:start position:0%
+equation and some model about expected
+ 
+
+ align:start position:0%
+equation and some model about expected
+inflation that's what the MPC model is
+
+ align:start position:0%
+inflation that's what the MPC model is
+ 
+
+ align:start position:0%
+inflation that's what the MPC model is
+so I gave you one example here one model
+
+ align:start position:0%
+so I gave you one example here one model
+ 
+
+ align:start position:0%
+so I gave you one example here one model
+of inflation this is a case of that
+
+ align:start position:0%
+of inflation this is a case of that
+ 
+
+ align:start position:0%
+of inflation this is a case of that
+central banks do not like the an Anor
+
+ align:start position:0%
+central banks do not like the an Anor
+ 
+
+ align:start position:0%
+central banks do not like the an Anor
+unanchor inflation expectation that's my
+
+ align:start position:0%
+unanchor inflation expectation that's my
+ 
+
+ align:start position:0%
+unanchor inflation expectation that's my
+model of expectation then my Philips
+
+ align:start position:0%
+model of expectation then my Philips
+ 
+
+ align:start position:0%
+model of expectation then my Philips
+curve I plug this into my Philips curve
+
+ align:start position:0%
+curve I plug this into my Philips curve
+ 
+
+ align:start position:0%
+curve I plug this into my Philips curve
+and I get this relationship between the
+
+ align:start position:0%
+and I get this relationship between the
+ 
+
+ align:start position:0%
+and I get this relationship between the
+change in inflation and the output Gap
+
+ align:start position:0%
+change in inflation and the output Gap
+ 
+
+ align:start position:0%
+change in inflation and the output Gap
+and it's an increasing relationship and
+
+ align:start position:0%
+and it's an increasing relationship and
+ 
+
+ align:start position:0%
+and it's an increasing relationship and
+that's what I'm plotting here for any
+
+ align:start position:0%
+that's what I'm plotting here for any
+ 
+
+ align:start position:0%
+that's what I'm plotting here for any
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+level for any given level of YN then as
+
+ align:start position:0%
+level for any given level of YN then as
+ 
+
+ align:start position:0%
+level for any given level of YN then as
+a increase output the Philips curve the
+
+ align:start position:0%
+a increase output the Philips curve the
+ 
+
+ align:start position:0%
+a increase output the Philips curve the
+change in inflation the left hand side
+
+ align:start position:0%
+change in inflation the left hand side
+ 
+
+ align:start position:0%
+change in inflation the left hand side
+the difference between inflation expect
+
+ align:start position:0%
+the difference between inflation expect
+ 
+
+ align:start position:0%
+the difference between inflation expect
+to inflation Rises that's the reason
+
+ align:start position:0%
+to inflation Rises that's the reason
+ 
+
+ align:start position:0%
+to inflation Rises that's the reason
+this upward is sloping and the reason
+
+ align:start position:0%
+this upward is sloping and the reason
+ 
+
+ align:start position:0%
+this upward is sloping and the reason
+this Rises has to do with all the things
+
+ align:start position:0%
+this Rises has to do with all the things
+ 
+
+ align:start position:0%
+this Rises has to do with all the things
+that happen in the labor market no if an
+
+ align:start position:0%
+that happen in the labor market no if an
+ 
+
+ align:start position:0%
+that happen in the labor market no if an
+employment if output Rises meaning an
+
+ align:start position:0%
+employment if output Rises meaning an
+ 
+
+ align:start position:0%
+employment if output Rises meaning an
+employment is falling you need more
+
+ align:start position:0%
+employment is falling you need more
+ 
+
+ align:start position:0%
+employment is falling you need more
+employment to produce more output if
+
+ align:start position:0%
+employment to produce more output if
+ 
+
+ align:start position:0%
+employment to produce more output if
+that's the case it's more wage pressure
+
+ align:start position:0%
+that's the case it's more wage pressure
+ 
+
+ align:start position:0%
+that's the case it's more wage pressure
+that leads to a price pressure because
+
+ align:start position:0%
+that leads to a price pressure because
+ 
+
+ align:start position:0%
+that leads to a price pressure because
+there is a the market in between wages
+
+ align:start position:0%
+there is a the market in between wages
+ 
+
+ align:start position:0%
+there is a the market in between wages
+and prices and that's the way you get
+
+ align:start position:0%
+and prices and that's the way you get
+ 
+
+ align:start position:0%
+and prices and that's the way you get
+into inflation okay so I gave you one
+
+ align:start position:0%
+into inflation okay so I gave you one
+ 
+
+ align:start position:0%
+into inflation okay so I gave you one
+example says okay
+
+ align:start position:0%
+example says okay
+ 
+
+ align:start position:0%
+example says okay
+suppose that we have some equilibrium
+
+ align:start position:0%
+suppose that we have some equilibrium
+ 
+
+ align:start position:0%
+suppose that we have some equilibrium
+level of output this which is the result
+
+ align:start position:0%
+level of output this which is the result
+ 
+
+ align:start position:0%
+level of output this which is the result
+of this monetary policy this rate set by
+
+ align:start position:0%
+of this monetary policy this rate set by
+ 
+
+ align:start position:0%
+of this monetary policy this rate set by
+by by the central bank and and that's
+
+ align:start position:0%
+by by the central bank and and that's
+ 
+
+ align:start position:0%
+by by the central bank and and that's
+the is which is a function of you know
+
+ align:start position:0%
+the is which is a function of you know
+ 
+
+ align:start position:0%
+the is which is a function of you know
+the fiscal policy of the country how
+
+ align:start position:0%
+the fiscal policy of the country how
+ 
+
+ align:start position:0%
+the fiscal policy of the country how
+confident are consumers and all these
+
+ align:start position:0%
+confident are consumers and all these
+ 
+
+ align:start position:0%
+confident are consumers and all these
+kind of things so in quiz one we really
+
+ align:start position:0%
+kind of things so in quiz one we really
+ 
+
+ align:start position:0%
+kind of things so in quiz one we really
+worry only about this top diagram okay
+
+ align:start position:0%
+worry only about this top diagram okay
+ 
+
+ align:start position:0%
+worry only about this top diagram okay
+and all the shocks we had were shocks
+
+ align:start position:0%
+and all the shocks we had were shocks
+ 
+
+ align:start position:0%
+and all the shocks we had were shocks
+that happen in this top diagram and we
+
+ align:start position:0%
+that happen in this top diagram and we
+ 
+
+ align:start position:0%
+that happen in this top diagram and we
+and we look at what happened to Output
+
+ align:start position:0%
+and we look at what happened to Output
+ 
+
+ align:start position:0%
+and we look at what happened to Output
+to equilibrium output as a
+
+ align:start position:0%
+to equilibrium output as a
+ 
+
+ align:start position:0%
+to equilibrium output as a
+result now this hasn't changed it hasn't
+
+ align:start position:0%
+result now this hasn't changed it hasn't
+ 
+
+ align:start position:0%
+result now this hasn't changed it hasn't
+change that block is the same as it used
+
+ align:start position:0%
+change that block is the same as it used
+ 
+
+ align:start position:0%
+change that block is the same as it used
+to be the only difference that we have
+
+ align:start position:0%
+to be the only difference that we have
+ 
+
+ align:start position:0%
+to be the only difference that we have
+here is that this level of output H
+
+ align:start position:0%
+here is that this level of output H
+ 
+
+ align:start position:0%
+here is that this level of output H
+which is the equilibrium level of output
+
+ align:start position:0%
+which is the equilibrium level of output
+ 
+
+ align:start position:0%
+which is the equilibrium level of output
+at any point in time needs not be equal
+
+ align:start position:0%
+at any point in time needs not be equal
+ 
+
+ align:start position:0%
+at any point in time needs not be equal
+to potential output and if it is not
+
+ align:start position:0%
+to potential output and if it is not
+ 
+
+ align:start position:0%
+to potential output and if it is not
+equal to potential output that will lead
+
+ align:start position:0%
+equal to potential output that will lead
+ 
+
+ align:start position:0%
+equal to potential output that will lead
+to something with inflation either
+
+ align:start position:0%
+to something with inflation either
+ 
+
+ align:start position:0%
+to something with inflation either
+inflation disinflation or something of
+
+ align:start position:0%
+inflation disinflation or something of
+ 
+
+ align:start position:0%
+inflation disinflation or something of
+that kind in this particular case the
+
+ align:start position:0%
+that kind in this particular case the
+ 
+
+ align:start position:0%
+that kind in this particular case the
+equilibrium level of output which is
+
+ align:start position:0%
+equilibrium level of output which is
+ 
+
+ align:start position:0%
+equilibrium level of output which is
+still determined as we used to determine
+
+ align:start position:0%
+still determined as we used to determine
+ 
+
+ align:start position:0%
+still determined as we used to determine
+it happens to be higher than the natural
+
+ align:start position:0%
+it happens to be higher than the natural
+ 
+
+ align:start position:0%
+it happens to be higher than the natural
+rate of
+
+ align:start position:0%
+rate of
+ 
+
+ align:start position:0%
+rate of
+output and if if output is higher than
+
+ align:start position:0%
+output and if if output is higher than
+ 
+
+ align:start position:0%
+output and if if output is higher than
+the rate of output that means this is
+
+ align:start position:0%
+the rate of output that means this is
+ 
+
+ align:start position:0%
+the rate of output that means this is
+positive which means inflation is rising
+
+ align:start position:0%
+positive which means inflation is rising
+ 
+
+ align:start position:0%
+positive which means inflation is rising
+and that's exactly what we see here it
+
+ align:start position:0%
+and that's exactly what we see here it
+ 
+
+ align:start position:0%
+and that's exactly what we see here it
+means inflation is above expected
+
+ align:start position:0%
+means inflation is above expected
+ 
+
+ align:start position:0%
+means inflation is above expected
+inflation when expected inflation is
+
+ align:start position:0%
+inflation when expected inflation is
+ 
+
+ align:start position:0%
+inflation when expected inflation is
+equal to lag inflation
+
+ align:start position:0%
+equal to lag inflation
+ 
+
+ align:start position:0%
+equal to lag inflation
+then that means inflation is rising okay
+
+ align:start position:0%
+then that means inflation is rising okay
+ 
+
+ align:start position:0%
+then that means inflation is rising okay
+and that's what we have
+
+ align:start position:0%
+and that's what we have
+ 
+
+ align:start position:0%
+and that's what we have
+here so any question about that so this
+
+ align:start position:0%
+here so any question about that so this
+ 
+
+ align:start position:0%
+here so any question about that so this
+is we just what we did is kept analysis
+
+ align:start position:0%
+is we just what we did is kept analysis
+ 
+
+ align:start position:0%
+is we just what we did is kept analysis
+we used to have and now we added this
+
+ align:start position:0%
+we used to have and now we added this
+ 
+
+ align:start position:0%
+we used to have and now we added this
+diagram here at the bottom because it
+
+ align:start position:0%
+diagram here at the bottom because it
+ 
+
+ align:start position:0%
+diagram here at the bottom because it
+turns out that yes any equilibrium here
+
+ align:start position:0%
+turns out that yes any equilibrium here
+ 
+
+ align:start position:0%
+turns out that yes any equilibrium here
+if I move the inter around I'm going to
+
+ align:start position:0%
+if I move the inter around I'm going to
+ 
+
+ align:start position:0%
+if I move the inter around I'm going to
+change the equilibrium level of output
+
+ align:start position:0%
+change the equilibrium level of output
+ 
+
+ align:start position:0%
+change the equilibrium level of output
+those all those are equilibrium levels
+
+ align:start position:0%
+those all those are equilibrium levels
+ 
+
+ align:start position:0%
+those all those are equilibrium levels
+output but that doesn't mean that that
+
+ align:start position:0%
+output but that doesn't mean that that
+ 
+
+ align:start position:0%
+output but that doesn't mean that that
+they're consistent with the natural ER H
+
+ align:start position:0%
+they're consistent with the natural ER H
+ 
+
+ align:start position:0%
+they're consistent with the natural ER H
+with potential output and if it's not
+
+ align:start position:0%
+with potential output and if it's not
+ 
+
+ align:start position:0%
+with potential output and if it's not
+equal to potential output it's a valid
+
+ align:start position:0%
+equal to potential output it's a valid
+ 
+
+ align:start position:0%
+equal to potential output it's a valid
+equilibrium at any point in time but
+
+ align:start position:0%
+equilibrium at any point in time but
+ 
+
+ align:start position:0%
+equilibrium at any point in time but
+it's going to lead to issues on the
+
+ align:start position:0%
+it's going to lead to issues on the
+ 
+
+ align:start position:0%
+it's going to lead to issues on the
+inflation front that's all that the the
+
+ align:start position:0%
+inflation front that's all that the the
+ 
+
+ align:start position:0%
+inflation front that's all that the the
+second diagram here tells you that we
+
+ align:start position:0%
+second diagram here tells you that we
+ 
+
+ align:start position:0%
+second diagram here tells you that we
+get issues on the inflation front with
+
+ align:start position:0%
+get issues on the inflation front with
+ 
+
+ align:start position:0%
+get issues on the inflation front with
+any equilibrium level of output that is
+
+ align:start position:0%
+any equilibrium level of output that is
+ 
+
+ align:start position:0%
+any equilibrium level of output that is
+different from the natural rate of
+
+ align:start position:0%
+different from the natural rate of
+ 
+
+ align:start position:0%
+different from the natural rate of
+output that's what this diagram
+
+ align:start position:0%
+output that's what this diagram
+ 
+
+ align:start position:0%
+output that's what this diagram
+does so then I said well and that's what
+
+ align:start position:0%
+does so then I said well and that's what
+ 
+
+ align:start position:0%
+does so then I said well and that's what
+happen in the short run that's what it
+
+ align:start position:0%
+happen in the short run that's what it
+ 
+
+ align:start position:0%
+happen in the short run that's what it
+does so we keep doing what we used to do
+
+ align:start position:0%
+does so we keep doing what we used to do
+ 
+
+ align:start position:0%
+does so we keep doing what we used to do
+in the first seven lectures or so and uh
+
+ align:start position:0%
+in the first seven lectures or so and uh
+ 
+
+ align:start position:0%
+in the first seven lectures or so and uh
+this diagram just tells us what are the
+
+ align:start position:0%
+this diagram just tells us what are the
+ 
+
+ align:start position:0%
+this diagram just tells us what are the
+implications for inflation that's in the
+
+ align:start position:0%
+implications for inflation that's in the
+ 
+
+ align:start position:0%
+implications for inflation that's in the
+short run the medium run we said is when
+
+ align:start position:0%
+short run the medium run we said is when
+ 
+
+ align:start position:0%
+short run the medium run we said is when
+we is that process in which output
+
+ align:start position:0%
+we is that process in which output
+ 
+
+ align:start position:0%
+we is that process in which output
+converges back to the Natural rate to
+
+ align:start position:0%
+converges back to the Natural rate to
+ 
+
+ align:start position:0%
+converges back to the Natural rate to
+potential output how does that happen
+
+ align:start position:0%
+potential output how does that happen
+ 
+
+ align:start position:0%
+potential output how does that happen
+well it involves the central bank but
+
+ align:start position:0%
+well it involves the central bank but
+ 
+
+ align:start position:0%
+well it involves the central bank but
+it's not that the central bank is doing
+
+ align:start position:0%
+it's not that the central bank is doing
+ 
+
+ align:start position:0%
+it's not that the central bank is doing
+crazyy things effect Central Bank is
+
+ align:start position:0%
+crazyy things effect Central Bank is
+ 
+
+ align:start position:0%
+crazyy things effect Central Bank is
+reacting to what the economy is telling
+
+ align:start position:0%
+reacting to what the economy is telling
+ 
+
+ align:start position:0%
+reacting to what the economy is telling
+it needs to do here is a central bank
+
+ align:start position:0%
+it needs to do here is a central bank
+ 
+
+ align:start position:0%
+it needs to do here is a central bank
+that supposed had
+
+ align:start position:0%
+that supposed had
+ 
+
+ align:start position:0%
+that supposed had
+was before doing whatever change in the
+
+ align:start position:0%
+was before doing whatever change in the
+ 
+
+ align:start position:0%
+was before doing whatever change in the
+interest rate or in the deliver this
+
+ align:start position:0%
+interest rate or in the deliver this
+ 
+
+ align:start position:0%
+interest rate or in the deliver this
+equilibrium output here had an inflation
+
+ align:start position:0%
+equilibrium output here had an inflation
+ 
+
+ align:start position:0%
+equilibrium output here had an inflation
+of around 2% that was consistent with
+
+ align:start position:0%
+of around 2% that was consistent with
+ 
+
+ align:start position:0%
+of around 2% that was consistent with
+the target it had now suddenly it finds
+
+ align:start position:0%
+the target it had now suddenly it finds
+ 
+
+ align:start position:0%
+the target it had now suddenly it finds
+itself in a situation like this and
+
+ align:start position:0%
+itself in a situation like this and
+ 
+
+ align:start position:0%
+itself in a situation like this and
+inflation starts climbing okay you get
+
+ align:start position:0%
+inflation starts climbing okay you get
+ 
+
+ align:start position:0%
+inflation starts climbing okay you get
+3% one year 4% the next one 6 nine in a
+
+ align:start position:0%
+3% one year 4% the next one 6 nine in a
+ 
+
+ align:start position:0%
+3% one year 4% the next one 6 nine in a
+situation like that well it's very
+
+ align:start position:0%
+situation like that well it's very
+ 
+
+ align:start position:0%
+situation like that well it's very
+natural for that Central Bank if it's a
+
+ align:start position:0%
+natural for that Central Bank if it's a
+ 
+
+ align:start position:0%
+natural for that Central Bank if it's a
+responsible Central Bank to react to
+
+ align:start position:0%
+responsible Central Bank to react to
+ 
+
+ align:start position:0%
+responsible Central Bank to react to
+that and the only reaction a central
+
+ align:start position:0%
+that and the only reaction a central
+ 
+
+ align:start position:0%
+that and the only reaction a central
+bank can have
+
+ align:start position:0%
+bank can have
+ 
+
+ align:start position:0%
+bank can have
+the main the main reaction can have is
+
+ align:start position:0%
+the main the main reaction can have is
+ 
+
+ align:start position:0%
+the main the main reaction can have is
+to raise interest rates okay and that's
+
+ align:start position:0%
+to raise interest rates okay and that's
+ 
+
+ align:start position:0%
+to raise interest rates okay and that's
+exactly what it starts happening if the
+
+ align:start position:0%
+exactly what it starts happening if the
+ 
+
+ align:start position:0%
+exactly what it starts happening if the
+Central Bank finds itself with inflation
+
+ align:start position:0%
+Central Bank finds itself with inflation
+ 
+
+ align:start position:0%
+Central Bank finds itself with inflation
+in this Cas is that is accelerating it
+
+ align:start position:0%
+in this Cas is that is accelerating it
+ 
+
+ align:start position:0%
+in this Cas is that is accelerating it
+will start increasing interest rate and
+
+ align:start position:0%
+will start increasing interest rate and
+ 
+
+ align:start position:0%
+will start increasing interest rate and
+this process of acceleration of
+
+ align:start position:0%
+this process of acceleration of
+ 
+
+ align:start position:0%
+this process of acceleration of
+inflation in this case would only stop
+
+ align:start position:0%
+inflation in this case would only stop
+ 
+
+ align:start position:0%
+inflation in this case would only stop
+when output is equal to the Natural to
+
+ align:start position:0%
+when output is equal to the Natural to
+ 
+
+ align:start position:0%
+when output is equal to the Natural to
+potential output okay and output is
+
+ align:start position:0%
+potential output okay and output is
+ 
+
+ align:start position:0%
+potential output okay and output is
+equal we can Define implicitly what that
+
+ align:start position:0%
+equal we can Define implicitly what that
+ 
+
+ align:start position:0%
+equal we can Define implicitly what that
+interest rate is and we can call it the
+
+ align:start position:0%
+interest rate is and we can call it the
+ 
+
+ align:start position:0%
+interest rate is and we can call it the
+natural rate of interest rate sometimes
+
+ align:start position:0%
+natural rate of interest rate sometimes
+ 
+
+ align:start position:0%
+natural rate of interest rate sometimes
+we call it we sell
+
+ align:start position:0%
+we call it we sell
+ 
+
+ align:start position:0%
+we call it we sell
+interest rate of interest rate neutral
+
+ align:start position:0%
+interest rate of interest rate neutral
+ 
+
+ align:start position:0%
+interest rate of interest rate neutral
+interest rate R star lots of names for
+
+ align:start position:0%
+interest rate R star lots of names for
+ 
+
+ align:start position:0%
+interest rate R star lots of names for
+this interest rate but this interest is
+
+ align:start position:0%
+this interest rate but this interest is
+ 
+
+ align:start position:0%
+this interest rate but this interest is
+simply the one that gives us an
+
+ align:start position:0%
+simply the one that gives us an
+ 
+
+ align:start position:0%
+simply the one that gives us an
+equilibrium output in our asln diagram
+
+ align:start position:0%
+equilibrium output in our asln diagram
+ 
+
+ align:start position:0%
+equilibrium output in our asln diagram
+that is equal to potential output that's
+
+ align:start position:0%
+that is equal to potential output that's
+ 
+
+ align:start position:0%
+that is equal to potential output that's
+that's all that this RN means and here
+
+ align:start position:0%
+that's all that this RN means and here
+ 
+
+ align:start position:0%
+that's all that this RN means and here
+I'm solving it you know it's is the rate
+
+ align:start position:0%
+I'm solving it you know it's is the rate
+ 
+
+ align:start position:0%
+I'm solving it you know it's is the rate
+that implicitly gives us an equilibrium
+
+ align:start position:0%
+that implicitly gives us an equilibrium
+ 
+
+ align:start position:0%
+that implicitly gives us an equilibrium
+output here H that is equal to the
+
+ align:start position:0%
+output here H that is equal to the
+ 
+
+ align:start position:0%
+output here H that is equal to the
+Natural rate of output okay that defines
+
+ align:start position:0%
+Natural rate of output okay that defines
+ 
+
+ align:start position:0%
+Natural rate of output okay that defines
+it implicitly
+
+ align:start position:0%
+it implicitly
+ 
+
+ align:start position:0%
+it implicitly
+okay there we are is all that
+
+ align:start position:0%
+okay there we are is all that
+ 
+
+ align:start position:0%
+okay there we are is all that
+clear yes okay I think you're going to
+
+ align:start position:0%
+clear yes okay I think you're going to
+ 
+
+ align:start position:0%
+clear yes okay I think you're going to
+have a a big chunk of your current pie
+
+ align:start position:0%
+have a a big chunk of your current pie
+ 
+
+ align:start position:0%
+have a a big chunk of your current pie
+set is about this model and so on and
+
+ align:start position:0%
+set is about this model and so on and
+ 
+
+ align:start position:0%
+set is about this model and so on and
+and that's a good thing and you'll see
+
+ align:start position:0%
+and that's a good thing and you'll see
+ 
+
+ align:start position:0%
+and that's a good thing and you'll see
+it also in the next one this again I
+
+ align:start position:0%
+it also in the next one this again I
+ 
+
+ align:start position:0%
+it also in the next one this again I
+think this is important then I talk
+
+ align:start position:0%
+think this is important then I talk
+ 
+
+ align:start position:0%
+think this is important then I talk
+about the difference between anchor and
+
+ align:start position:0%
+about the difference between anchor and
+ 
+
+ align:start position:0%
+about the difference between anchor and
+an anchor expectations I said look here
+
+ align:start position:0%
+an anchor expectations I said look here
+ 
+
+ align:start position:0%
+an anchor expectations I said look here
+we have a situation that suppose we
+
+ align:start position:0%
+we have a situation that suppose we
+ 
+
+ align:start position:0%
+we have a situation that suppose we
+started at 2% and then we found ourself
+
+ align:start position:0%
+started at 2% and then we found ourself
+ 
+
+ align:start position:0%
+started at 2% and then we found ourself
+in a situation like that that means
+
+ align:start position:0%
+in a situation like that that means
+ 
+
+ align:start position:0%
+in a situation like that that means
+inflation start building up we got to 9%
+
+ align:start position:0%
+inflation start building up we got to 9%
+ 
+
+ align:start position:0%
+inflation start building up we got to 9%
+or so so now the FED gets scared and it
+
+ align:start position:0%
+or so so now the FED gets scared and it
+ 
+
+ align:start position:0%
+or so so now the FED gets scared and it
+starts raising interest rates so that's
+
+ align:start position:0%
+starts raising interest rates so that's
+ 
+
+ align:start position:0%
+starts raising interest rates so that's
+what we're moving up lower in output and
+
+ align:start position:0%
+what we're moving up lower in output and
+ 
+
+ align:start position:0%
+what we're moving up lower in output and
+as it lowers output reduces the output
+
+ align:start position:0%
+as it lowers output reduces the output
+ 
+
+ align:start position:0%
+as it lowers output reduces the output
+Gap and therefore reduces the change in
+
+ align:start position:0%
+Gap and therefore reduces the change in
+ 
+
+ align:start position:0%
+Gap and therefore reduces the change in
+inflation here but inflation keeps
+
+ align:start position:0%
+inflation here but inflation keeps
+ 
+
+ align:start position:0%
+inflation here but inflation keeps
+rising in this particular model because
+
+ align:start position:0%
+rising in this particular model because
+ 
+
+ align:start position:0%
+rising in this particular model because
+expected inflation is an anchor and I
+
+ align:start position:0%
+expected inflation is an anchor and I
+ 
+
+ align:start position:0%
+expected inflation is an anchor and I
+said well suppose that eventually the
+
+ align:start position:0%
+said well suppose that eventually the
+ 
+
+ align:start position:0%
+said well suppose that eventually the
+FED gets to that interest rate here so
+
+ align:start position:0%
+FED gets to that interest rate here so
+ 
+
+ align:start position:0%
+FED gets to that interest rate here so
+we get to situation like that and I
+
+ align:start position:0%
+we get to situation like that and I
+ 
+
+ align:start position:0%
+we get to situation like that and I
+asked the question has the FED solved
+
+ align:start position:0%
+asked the question has the FED solved
+ 
+
+ align:start position:0%
+asked the question has the FED solved
+the problem now okay finally we got to
+
+ align:start position:0%
+the problem now okay finally we got to
+ 
+
+ align:start position:0%
+the problem now okay finally we got to
+situation where the the interest rate is
+
+ align:start position:0%
+situation where the the interest rate is
+ 
+
+ align:start position:0%
+situation where the the interest rate is
+equal to an natural rate of interest
+
+ align:start position:0%
+equal to an natural rate of interest
+ 
+
+ align:start position:0%
+equal to an natural rate of interest
+rate that tells me that output is equal
+
+ align:start position:0%
+rate that tells me that output is equal
+ 
+
+ align:start position:0%
+rate that tells me that output is equal
+to potential output that tells me here
+
+ align:start position:0%
+to potential output that tells me here
+ 
+
+ align:start position:0%
+to potential output that tells me here
+that inflation is not changing problem
+
+ align:start position:0%
+that inflation is not changing problem
+ 
+
+ align:start position:0%
+that inflation is not changing problem
+is that we already had inflation of 9%
+
+ align:start position:0%
+is that we already had inflation of 9%
+ 
+
+ align:start position:0%
+is that we already had inflation of 9%
+at some point so so here inflation stops
+
+ align:start position:0%
+at some point so so here inflation stops
+ 
+
+ align:start position:0%
+at some point so so here inflation stops
+rising in this particular model with
+
+ align:start position:0%
+rising in this particular model with
+ 
+
+ align:start position:0%
+rising in this particular model with
+expected inflation an anchor expected
+
+ align:start position:0%
+expected inflation an anchor expected
+ 
+
+ align:start position:0%
+expected inflation an anchor expected
+inflation but stopping is not enough
+
+ align:start position:0%
+inflation but stopping is not enough
+ 
+
+ align:start position:0%
+inflation but stopping is not enough
+because that's gives leaves us level of
+
+ align:start position:0%
+because that's gives leaves us level of
+ 
+
+ align:start position:0%
+because that's gives leaves us level of
+inflation of
+
+ align:start position:0%
+inflation of
+ 
+
+ align:start position:0%
+inflation of
+9% that means that the FED in order to
+
+ align:start position:0%
+9% that means that the FED in order to
+ 
+
+ align:start position:0%
+9% that means that the FED in order to
+bring back inflation to 2% it needs to
+
+ align:start position:0%
+bring back inflation to 2% it needs to
+ 
+
+ align:start position:0%
+bring back inflation to 2% it needs to
+go into this region so inflation starts
+
+ align:start position:0%
+go into this region so inflation starts
+ 
+
+ align:start position:0%
+go into this region so inflation starts
+coming down from 9% 7% 6% 5% and so on
+
+ align:start position:0%
+coming down from 9% 7% 6% 5% and so on
+ 
+
+ align:start position:0%
+coming down from 9% 7% 6% 5% and so on
+okay so if you have an anchor
+
+ align:start position:0%
+okay so if you have an anchor
+ 
+
+ align:start position:0%
+okay so if you have an anchor
+expectation and and inflation overshoots
+
+ align:start position:0%
+expectation and and inflation overshoots
+ 
+
+ align:start position:0%
+expectation and and inflation overshoots
+you're going to have to cause a
+
+ align:start position:0%
+you're going to have to cause a
+ 
+
+ align:start position:0%
+you're going to have to cause a
+recession and probably a severe
+
+ align:start position:0%
+recession and probably a severe
+ 
+
+ align:start position:0%
+recession and probably a severe
+recession there's no way around that and
+
+ align:start position:0%
+recession there's no way around that and
+ 
+
+ align:start position:0%
+recession there's no way around that and
+that's what the FED has been struggling
+
+ align:start position:0%
+that's what the FED has been struggling
+ 
+
+ align:start position:0%
+that's what the FED has been struggling
+to do is is struggling not to because
+
+ align:start position:0%
+to do is is struggling not to because
+ 
+
+ align:start position:0%
+to do is is struggling not to because
+the Fed we are in a situation not only
+
+ align:start position:0%
+the Fed we are in a situation not only
+ 
+
+ align:start position:0%
+the Fed we are in a situation not only
+in the US but in the US in particular
+
+ align:start position:0%
+in the US but in the US in particular
+ 
+
+ align:start position:0%
+in the US but in the US in particular
+where inflation is way above the target
+
+ align:start position:0%
+where inflation is way above the target
+ 
+
+ align:start position:0%
+where inflation is way above the target
+level H but expected inflation has been
+
+ align:start position:0%
+level H but expected inflation has been
+ 
+
+ align:start position:0%
+level H but expected inflation has been
+more or less stable and so this when
+
+ align:start position:0%
+more or less stable and so this when
+ 
+
+ align:start position:0%
+more or less stable and so this when
+people talk about being able to restore
+
+ align:start position:0%
+people talk about being able to restore
+ 
+
+ align:start position:0%
+people talk about being able to restore
+sort of reasonable levels of inflation
+
+ align:start position:0%
+sort of reasonable levels of inflation
+ 
+
+ align:start position:0%
+sort of reasonable levels of inflation
+in a soft landed manner with a soft
+
+ align:start position:0%
+in a soft landed manner with a soft
+ 
+
+ align:start position:0%
+in a soft landed manner with a soft
+Landing that means that you don't need
+
+ align:start position:0%
+Landing that means that you don't need
+ 
+
+ align:start position:0%
+Landing that means that you don't need
+to cost a b recession to bring inflation
+
+ align:start position:0%
+to cost a b recession to bring inflation
+ 
+
+ align:start position:0%
+to cost a b recession to bring inflation
+back to 2% you just can bring it
+
+ align:start position:0%
+back to 2% you just can bring it
+ 
+
+ align:start position:0%
+back to 2% you just can bring it
+smoothly here with this model of
+
+ align:start position:0%
+smoothly here with this model of
+ 
+
+ align:start position:0%
+smoothly here with this model of
+expected inflation doesn't work but if
+
+ align:start position:0%
+expected inflation doesn't work but if
+ 
+
+ align:start position:0%
+expected inflation doesn't work but if
+expect if the Bank Central Bank has
+
+ align:start position:0%
+expect if the Bank Central Bank has
+ 
+
+ align:start position:0%
+expect if the Bank Central Bank has
+credibility H and inflation remain Anor
+
+ align:start position:0%
+credibility H and inflation remain Anor
+ 
+
+ align:start position:0%
+credibility H and inflation remain Anor
+people continue to believe that the FED
+
+ align:start position:0%
+people continue to believe that the FED
+ 
+
+ align:start position:0%
+people continue to believe that the FED
+will go back to 2% then you don't need
+
+ align:start position:0%
+will go back to 2% then you don't need
+ 
+
+ align:start position:0%
+will go back to 2% then you don't need
+to cause a big recession otherwise you
+
+ align:start position:0%
+to cause a big recession otherwise you
+ 
+
+ align:start position:0%
+to cause a big recession otherwise you
+need to invest in bringing expectations
+
+ align:start position:0%
+need to invest in bringing expectations
+ 
+
+ align:start position:0%
+need to invest in bringing expectations
+down and that the only way you can
+
+ align:start position:0%
+down and that the only way you can
+ 
+
+ align:start position:0%
+down and that the only way you can
+invest in doing that is causing a
+
+ align:start position:0%
+invest in doing that is causing a
+ 
+
+ align:start position:0%
+invest in doing that is causing a
+recession okay but that's the reason I
+
+ align:start position:0%
+recession okay but that's the reason I
+ 
+
+ align:start position:0%
+recession okay but that's the reason I
+said central banks worry so much about
+
+ align:start position:0%
+said central banks worry so much about
+ 
+
+ align:start position:0%
+said central banks worry so much about
+keeping inflation credibility because
+
+ align:start position:0%
+keeping inflation credibility because
+ 
+
+ align:start position:0%
+keeping inflation credibility because
+otherwise they need to
+
+ align:start position:0%
+otherwise they need to
+ 
+
+ align:start position:0%
+otherwise they need to
+overshoot in order to restore um long
+
+ align:start position:0%
+overshoot in order to restore um long
+ 
+
+ align:start position:0%
+overshoot in order to restore um long
+run balance
+
+ align:start position:0%
+run balance
+ 
+
+ align:start position:0%
+run balance
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+now you may Wonder well this I mean this
+
+ align:start position:0%
+now you may Wonder well this I mean this
+ 
+
+ align:start position:0%
+now you may Wonder well this I mean this
+looks pretty simple to do no just if you
+
+ align:start position:0%
+looks pretty simple to do no just if you
+ 
+
+ align:start position:0%
+looks pretty simple to do no just if you
+have a problem like this just go quickly
+
+ align:start position:0%
+have a problem like this just go quickly
+ 
+
+ align:start position:0%
+have a problem like this just go quickly
+to that point there no and then the
+
+ align:start position:0%
+to that point there no and then the
+ 
+
+ align:start position:0%
+to that point there no and then the
+problem is over you don't let inflation
+
+ align:start position:0%
+problem is over you don't let inflation
+ 
+
+ align:start position:0%
+problem is over you don't let inflation
+build to 9% or something like that you
+
+ align:start position:0%
+build to 9% or something like that you
+ 
+
+ align:start position:0%
+build to 9% or something like that you
+react immediately the problem is there's
+
+ align:start position:0%
+react immediately the problem is there's
+ 
+
+ align:start position:0%
+react immediately the problem is there's
+a f sentence that was going by Milton
+
+ align:start position:0%
+a f sentence that was going by Milton
+ 
+
+ align:start position:0%
+a f sentence that was going by Milton
+fredman is that monetary policy acts on
+
+ align:start position:0%
+fredman is that monetary policy acts on
+ 
+
+ align:start position:0%
+fredman is that monetary policy acts on
+the economy with long and variable lags
+
+ align:start position:0%
+the economy with long and variable lags
+ 
+
+ align:start position:0%
+the economy with long and variable lags
+so first of all it's very difficult at
+
+ align:start position:0%
+so first of all it's very difficult at
+ 
+
+ align:start position:0%
+so first of all it's very difficult at
+any point in time to know where is
+
+ align:start position:0%
+any point in time to know where is
+ 
+
+ align:start position:0%
+any point in time to know where is
+potential output or what is the natural
+
+ align:start position:0%
+potential output or what is the natural
+ 
+
+ align:start position:0%
+potential output or what is the natural
+rate of unemployment I mean you sort of
+
+ align:start position:0%
+rate of unemployment I mean you sort of
+ 
+
+ align:start position:0%
+rate of unemployment I mean you sort of
+sense it but the truth is that the only
+
+ align:start position:0%
+sense it but the truth is that the only
+ 
+
+ align:start position:0%
+sense it but the truth is that the only
+way you really know is is by looking at
+
+ align:start position:0%
+way you really know is is by looking at
+ 
+
+ align:start position:0%
+way you really know is is by looking at
+inflation so it's inflation that really
+
+ align:start position:0%
+inflation so it's inflation that really
+ 
+
+ align:start position:0%
+inflation so it's inflation that really
+tells you that you're one side of the
+
+ align:start position:0%
+tells you that you're one side of the
+ 
+
+ align:start position:0%
+tells you that you're one side of the
+other it's very difficult to you you
+
+ align:start position:0%
+other it's very difficult to you you
+ 
+
+ align:start position:0%
+other it's very difficult to you you
+have some historical average and so on
+
+ align:start position:0%
+have some historical average and so on
+ 
+
+ align:start position:0%
+have some historical average and so on
+but these things do move move around so
+
+ align:start position:0%
+but these things do move move around so
+ 
+
+ align:start position:0%
+but these things do move move around so
+it's difficult at any point in time to
+
+ align:start position:0%
+it's difficult at any point in time to
+ 
+
+ align:start position:0%
+it's difficult at any point in time to
+know whether you you are at our end or
+
+ align:start position:0%
+know whether you you are at our end or
+ 
+
+ align:start position:0%
+know whether you you are at our end or
+not the second thing is that here
+
+ align:start position:0%
+not the second thing is that here
+ 
+
+ align:start position:0%
+not the second thing is that here
+everything happens immediately if I move
+
+ align:start position:0%
+everything happens immediately if I move
+ 
+
+ align:start position:0%
+everything happens immediately if I move
+immediately then output immediately
+
+ align:start position:0%
+immediately then output immediately
+ 
+
+ align:start position:0%
+immediately then output immediately
+jumps here that's not the way monetary
+
+ align:start position:0%
+jumps here that's not the way monetary
+ 
+
+ align:start position:0%
+jumps here that's not the way monetary
+policy operates in practice it takes
+
+ align:start position:0%
+policy operates in practice it takes
+ 
+
+ align:start position:0%
+policy operates in practice it takes
+time for monetary policy to to to affect
+
+ align:start position:0%
+time for monetary policy to to to affect
+ 
+
+ align:start position:0%
+time for monetary policy to to to affect
+the economy and so this the situation
+
+ align:start position:0%
+the economy and so this the situation
+ 
+
+ align:start position:0%
+the economy and so this the situation
+that happened I I would say until last
+
+ align:start position:0%
+that happened I I would say until last
+ 
+
+ align:start position:0%
+that happened I I would say until last
+week was the FED knew that the inflation
+
+ align:start position:0%
+week was the FED knew that the inflation
+ 
+
+ align:start position:0%
+week was the FED knew that the inflation
+was still to too high but it but it also
+
+ align:start position:0%
+was still to too high but it but it also
+ 
+
+ align:start position:0%
+was still to too high but it but it also
+knew that it had done a lot he had hiked
+
+ align:start position:0%
+knew that it had done a lot he had hiked
+ 
+
+ align:start position:0%
+knew that it had done a lot he had hiked
+rates very aggressively by a lot and
+
+ align:start position:0%
+rates very aggressively by a lot and
+ 
+
+ align:start position:0%
+rates very aggressively by a lot and
+since there are lags between the the
+
+ align:start position:0%
+since there are lags between the the
+ 
+
+ align:start position:0%
+since there are lags between the the
+increasing interest rate and and the
+
+ align:start position:0%
+increasing interest rate and and the
+ 
+
+ align:start position:0%
+increasing interest rate and and the
+declining output the fed's concern was
+
+ align:start position:0%
+declining output the fed's concern was
+ 
+
+ align:start position:0%
+declining output the fed's concern was
+well it's clear that I still have
+
+ align:start position:0%
+well it's clear that I still have
+ 
+
+ align:start position:0%
+well it's clear that I still have
+inflation but it may well be the case
+
+ align:start position:0%
+inflation but it may well be the case
+ 
+
+ align:start position:0%
+inflation but it may well be the case
+that when this thing finally hits the
+
+ align:start position:0%
+that when this thing finally hits the
+ 
+
+ align:start position:0%
+that when this thing finally hits the
+economy it hits us too much and we end
+
+ align:start position:0%
+economy it hits us too much and we end
+ 
+
+ align:start position:0%
+economy it hits us too much and we end
+up in a recession and an unwanted
+
+ align:start position:0%
+up in a recession and an unwanted
+ 
+
+ align:start position:0%
+up in a recession and an unwanted
+recession that was a concern okay H now
+
+ align:start position:0%
+recession that was a concern okay H now
+ 
+
+ align:start position:0%
+recession that was a concern okay H now
+with what is happening right now there's
+
+ align:start position:0%
+with what is happening right now there's
+ 
+
+ align:start position:0%
+with what is happening right now there's
+a little bit of a concern that we got to
+
+ align:start position:0%
+a little bit of a concern that we got to
+ 
+
+ align:start position:0%
+a little bit of a concern that we got to
+that point because things were very slow
+
+ align:start position:0%
+that point because things were very slow
+ 
+
+ align:start position:0%
+that point because things were very slow
+for a variety of reasons but now
+
+ align:start position:0%
+for a variety of reasons but now
+ 
+
+ align:start position:0%
+for a variety of reasons but now
+something broke and the question is now
+
+ align:start position:0%
+something broke and the question is now
+ 
+
+ align:start position:0%
+something broke and the question is now
+that something has broken well will we
+
+ align:start position:0%
+that something has broken well will we
+ 
+
+ align:start position:0%
+that something has broken well will we
+sort of decelerate the economy very very
+
+ align:start position:0%
+sort of decelerate the economy very very
+ 
+
+ align:start position:0%
+sort of decelerate the economy very very
+fast and that's a concern that's what is
+
+ align:start position:0%
+fast and that's a concern that's what is
+ 
+
+ align:start position:0%
+fast and that's a concern that's what is
+happening right now okay but that's what
+
+ align:start position:0%
+happening right now okay but that's what
+ 
+
+ align:start position:0%
+happening right now okay but that's what
+makes monetary policy much more
+
+ align:start position:0%
+makes monetary policy much more
+ 
+
+ align:start position:0%
+makes monetary policy much more
+difficult than this little diagram is
+
+ align:start position:0%
+difficult than this little diagram is
+ 
+
+ align:start position:0%
+difficult than this little diagram is
+that you you have all this lags these
+
+ align:start position:0%
+that you you have all this lags these
+ 
+
+ align:start position:0%
+that you you have all this lags these
+uncertainties and all these
+
+ align:start position:0%
+uncertainties and all these
+ 
+
+ align:start position:0%
+uncertainties and all these
+nonlinearities and Sly things happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me tell you when things can go
+
+ align:start position:0%
+okay let me tell you when things can go
+ 
+
+ align:start position:0%
+okay let me tell you when things can go
+really really wrong it's not the issue
+
+ align:start position:0%
+really really wrong it's not the issue
+ 
+
+ align:start position:0%
+really really wrong it's not the issue
+now but but we're very close to that
+
+ align:start position:0%
+now but but we're very close to that
+ 
+
+ align:start position:0%
+now but but we're very close to that
+during the global recession Japan has
+
+ align:start position:0%
+during the global recession Japan has
+ 
+
+ align:start position:0%
+during the global recession Japan has
+experienced several episodes like this
+
+ align:start position:0%
+experienced several episodes like this
+ 
+
+ align:start position:0%
+experienced several episodes like this
+which is the following suppose you have
+
+ align:start position:0%
+which is the following suppose you have
+ 
+
+ align:start position:0%
+which is the following suppose you have
+a situation where ER your inflation is
+
+ align:start position:0%
+a situation where ER your inflation is
+ 
+
+ align:start position:0%
+a situation where ER your inflation is
+low typically these things happen in
+
+ align:start position:0%
+low typically these things happen in
+ 
+
+ align:start position:0%
+low typically these things happen in
+situations where your inflation is low
+
+ align:start position:0%
+situations where your inflation is low
+ 
+
+ align:start position:0%
+situations where your inflation is low
+and for whatever reason your natural
+
+ align:start position:0%
+and for whatever reason your natural
+ 
+
+ align:start position:0%
+and for whatever reason your natural
+rate of unemployment is is
+
+ align:start position:0%
+rate of unemployment is is
+ 
+
+ align:start position:0%
+rate of unemployment is is
+negative so you have inflation close to
+
+ align:start position:0%
+negative so you have inflation close to
+ 
+
+ align:start position:0%
+negative so you have inflation close to
+zero say and then the natural rate
+
+ align:start position:0%
+zero say and then the natural rate
+ 
+
+ align:start position:0%
+zero say and then the natural rate
+of interest rate is
+
+ align:start position:0%
+of interest rate is
+ 
+
+ align:start position:0%
+of interest rate is
+negative what's the problem suppose you
+
+ align:start position:0%
+negative what's the problem suppose you
+ 
+
+ align:start position:0%
+negative what's the problem suppose you
+have a zero lower
+
+ align:start position:0%
+have a zero lower
+ 
+
+ align:start position:0%
+have a zero lower
+bound well if you have a zero lower
+
+ align:start position:0%
+bound well if you have a zero lower
+ 
+
+ align:start position:0%
+bound well if you have a zero lower
+bound means that you're not going to hit
+
+ align:start position:0%
+bound means that you're not going to hit
+ 
+
+ align:start position:0%
+bound means that you're not going to hit
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+rate the best you can do if inflation is
+
+ align:start position:0%
+rate the best you can do if inflation is
+ 
+
+ align:start position:0%
+rate the best you can do if inflation is
+around zero then you set the nominal
+
+ align:start position:0%
+around zero then you set the nominal
+ 
+
+ align:start position:0%
+around zero then you set the nominal
+interest rate to zero and then the real
+
+ align:start position:0%
+interest rate to zero and then the real
+ 
+
+ align:start position:0%
+interest rate to zero and then the real
+interest rate is around
+
+ align:start position:0%
+interest rate is around
+ 
+
+ align:start position:0%
+interest rate is around
+zero well the problem is that at zero
+
+ align:start position:0%
+zero well the problem is that at zero
+ 
+
+ align:start position:0%
+zero well the problem is that at zero
+you generate negative
+
+ align:start position:0%
+you generate negative
+ 
+
+ align:start position:0%
+you generate negative
+inflation but if you generate negative
+
+ align:start position:0%
+inflation but if you generate negative
+ 
+
+ align:start position:0%
+inflation but if you generate negative
+inflation and the nominal interest rate
+
+ align:start position:0%
+inflation and the nominal interest rate
+ 
+
+ align:start position:0%
+inflation and the nominal interest rate
+is fixed at zero then now you get a
+
+ align:start position:0%
+is fixed at zero then now you get a
+ 
+
+ align:start position:0%
+is fixed at zero then now you get a
+positive real interest rate because the
+
+ align:start position:0%
+positive real interest rate because the
+ 
+
+ align:start position:0%
+positive real interest rate because the
+real interest rate is equal to the
+
+ align:start position:0%
+real interest rate is equal to the
+ 
+
+ align:start position:0%
+real interest rate is equal to the
+nominal interest rate which is zero
+
+ align:start position:0%
+nominal interest rate which is zero
+ 
+
+ align:start position:0%
+nominal interest rate which is zero
+minus inflation expected inflation but
+
+ align:start position:0%
+minus inflation expected inflation but
+ 
+
+ align:start position:0%
+minus inflation expected inflation but
+if expected inflation or inflation is
+
+ align:start position:0%
+if expected inflation or inflation is
+ 
+
+ align:start position:0%
+if expected inflation or inflation is
+negative minus minus is positive so that
+
+ align:start position:0%
+negative minus minus is positive so that
+ 
+
+ align:start position:0%
+negative minus minus is positive so that
+means your real interest rate is
+
+ align:start position:0%
+means your real interest rate is
+ 
+
+ align:start position:0%
+means your real interest rate is
+actually positive so your really you you
+
+ align:start position:0%
+actually positive so your really you you
+ 
+
+ align:start position:0%
+actually positive so your really you you
+wanted something negative but you end up
+
+ align:start position:0%
+wanted something negative but you end up
+ 
+
+ align:start position:0%
+wanted something negative but you end up
+with something
+
+ align:start position:0%
+with something
+ 
+
+ align:start position:0%
+with something
+positive that means now you have a big
+
+ align:start position:0%
+positive that means now you have a big
+ 
+
+ align:start position:0%
+positive that means now you have a big
+gap
+
+ align:start position:0%
+gap
+ 
+
+ align:start position:0%
+gap
+here so
+
+ align:start position:0%
+here so
+ 
+
+ align:start position:0%
+here so
+inflation you get into a deflation now
+
+ align:start position:0%
+inflation you get into a deflation now
+ 
+
+ align:start position:0%
+inflation you get into a deflation now
+now inflation is very very low it gets
+
+ align:start position:0%
+now inflation is very very low it gets
+ 
+
+ align:start position:0%
+now inflation is very very low it gets
+very negative well your real as
+
+ align:start position:0%
+very negative well your real as
+ 
+
+ align:start position:0%
+very negative well your real as
+inflation gets more and more negative
+
+ align:start position:0%
+inflation gets more and more negative
+ 
+
+ align:start position:0%
+inflation gets more and more negative
+your real interest keeps climbing so you
+
+ align:start position:0%
+your real interest keeps climbing so you
+ 
+
+ align:start position:0%
+your real interest keeps climbing so you
+keep moving further and further away
+
+ align:start position:0%
+keep moving further and further away
+ 
+
+ align:start position:0%
+keep moving further and further away
+from the natural rate of interest rate
+
+ align:start position:0%
+from the natural rate of interest rate
+ 
+
+ align:start position:0%
+from the natural rate of interest rate
+that's something that is very scary for
+
+ align:start position:0%
+that's something that is very scary for
+ 
+
+ align:start position:0%
+that's something that is very scary for
+an economy is a def deflationary trap
+
+ align:start position:0%
+an economy is a def deflationary trap
+ 
+
+ align:start position:0%
+an economy is a def deflationary trap
+and that's the way you get
+
+ align:start position:0%
+and that's the way you get
+ 
+
+ align:start position:0%
+and that's the way you get
+into deep recessions in fact that's what
+
+ align:start position:0%
+into deep recessions in fact that's what
+ 
+
+ align:start position:0%
+into deep recessions in fact that's what
+happened during the Great Recession in
+
+ align:start position:0%
+happened during the Great Recession in
+ 
+
+ align:start position:0%
+happened during the Great Recession in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+US the
+
+ align:start position:0%
+US the
+ 
+
+ align:start position:0%
+US the
+no during the Great Depression in the US
+
+ align:start position:0%
+no during the Great Depression in the US
+ 
+
+ align:start position:0%
+no during the Great Depression in the US
+okay during the Great Recession we were
+
+ align:start position:0%
+okay during the Great Recession we were
+ 
+
+ align:start position:0%
+okay during the Great Recession we were
+close to it but we didn't get quite
+
+ align:start position:0%
+close to it but we didn't get quite
+ 
+
+ align:start position:0%
+close to it but we didn't get quite
+there in in because lots of things were
+
+ align:start position:0%
+there in in because lots of things were
+ 
+
+ align:start position:0%
+there in in because lots of things were
+done to prevent a repeat of the Great
+
+ align:start position:0%
+done to prevent a repeat of the Great
+ 
+
+ align:start position:0%
+done to prevent a repeat of the Great
+Depression the one of the biggest
+
+ align:start position:0%
+Depression the one of the biggest
+ 
+
+ align:start position:0%
+Depression the one of the biggest
+problems with the Great Depression ER
+
+ align:start position:0%
+problems with the Great Depression ER
+ 
+
+ align:start position:0%
+problems with the Great Depression ER
+was that ER monetary policy was not
+
+ align:start position:0%
+was that ER monetary policy was not
+ 
+
+ align:start position:0%
+was that ER monetary policy was not
+against the zero lower bound but it was
+
+ align:start position:0%
+against the zero lower bound but it was
+ 
+
+ align:start position:0%
+against the zero lower bound but it was
+very slow to
+
+ align:start position:0%
+very slow to
+ 
+
+ align:start position:0%
+very slow to
+react okay they were in a situation like
+
+ align:start position:0%
+react okay they were in a situation like
+ 
+
+ align:start position:0%
+react okay they were in a situation like
+in this diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and and but they kept the interest
+
+ align:start position:0%
+here and and but they kept the interest
+ 
+
+ align:start position:0%
+here and and but they kept the interest
+rate high and they moveed very slowly
+
+ align:start position:0%
+rate high and they moveed very slowly
+ 
+
+ align:start position:0%
+rate high and they moveed very slowly
+and when they tried to catch up well
+
+ align:start position:0%
+and when they tried to catch up well
+ 
+
+ align:start position:0%
+and when they tried to catch up well
+they were into deflation environment so
+
+ align:start position:0%
+they were into deflation environment so
+ 
+
+ align:start position:0%
+they were into deflation environment so
+the real interet was moving away from
+
+ align:start position:0%
+the real interet was moving away from
+ 
+
+ align:start position:0%
+the real interet was moving away from
+them despite the fact that they were
+
+ align:start position:0%
+them despite the fact that they were
+ 
+
+ align:start position:0%
+them despite the fact that they were
+moving the nominal interest rate down
+
+ align:start position:0%
+moving the nominal interest rate down
+ 
+
+ align:start position:0%
+moving the nominal interest rate down
+and that you can see here so there the
+
+ align:start position:0%
+and that you can see here so there the
+ 
+
+ align:start position:0%
+and that you can see here so there the
+Great depression starts around 1929 it
+
+ align:start position:0%
+Great depression starts around 1929 it
+ 
+
+ align:start position:0%
+Great depression starts around 1929 it
+starts really in
+
+ align:start position:0%
+starts really in
+ 
+
+ align:start position:0%
+starts really in
+1929 H an employment initially was low
+
+ align:start position:0%
+1929 H an employment initially was low
+ 
+
+ align:start position:0%
+1929 H an employment initially was low
+then nominal interest rate was around 5%
+
+ align:start position:0%
+then nominal interest rate was around 5%
+ 
+
+ align:start position:0%
+then nominal interest rate was around 5%
+and inflation rate growth declined very
+
+ align:start position:0%
+and inflation rate growth declined very
+ 
+
+ align:start position:0%
+and inflation rate growth declined very
+rapidly in inflation rate was around
+
+ align:start position:0%
+rapidly in inflation rate was around
+ 
+
+ align:start position:0%
+rapidly in inflation rate was around
+zero so you had a one year the real
+
+ align:start position:0%
+zero so you had a one year the real
+ 
+
+ align:start position:0%
+zero so you had a one year the real
+interest rate was around 5% as well okay
+
+ align:start position:0%
+interest rate was around 5% as well okay
+ 
+
+ align:start position:0%
+interest rate was around 5% as well okay
+well things got worse and employment
+
+ align:start position:0%
+well things got worse and employment
+ 
+
+ align:start position:0%
+well things got worse and employment
+began to climb very rapidly and so the
+
+ align:start position:0%
+began to climb very rapidly and so the
+ 
+
+ align:start position:0%
+began to climb very rapidly and so the
+FED began to lower interest rates
+
+ align:start position:0%
+FED began to lower interest rates
+ 
+
+ align:start position:0%
+FED began to lower interest rates
+nominal interest rate you know it went
+
+ align:start position:0%
+nominal interest rate you know it went
+ 
+
+ align:start position:0%
+nominal interest rate you know it went
+from 5% to 4% those were unusually low
+
+ align:start position:0%
+from 5% to 4% those were unusually low
+ 
+
+ align:start position:0%
+from 5% to 4% those were unusually low
+interest rate for the time but the
+
+ align:start position:0%
+interest rate for the time but the
+ 
+
+ align:start position:0%
+interest rate for the time but the
+problem is that the inflation by then
+
+ align:start position:0%
+problem is that the inflation by then
+ 
+
+ align:start position:0%
+problem is that the inflation by then
+was minus 2 and a half% so the real
+
+ align:start position:0%
+was minus 2 and a half% so the real
+ 
+
+ align:start position:0%
+was minus 2 and a half% so the real
+interest rate they were lowering the
+
+ align:start position:0%
+interest rate they were lowering the
+ 
+
+ align:start position:0%
+interest rate they were lowering the
+nominal interest rate but the real
+
+ align:start position:0%
+nominal interest rate but the real
+ 
+
+ align:start position:0%
+nominal interest rate but the real
+interest rate was rising and
+
+ align:start position:0%
+interest rate was rising and
+ 
+
+ align:start position:0%
+interest rate was rising and
+unemployment accordingly was Rising as
+
+ align:start position:0%
+unemployment accordingly was Rising as
+ 
+
+ align:start position:0%
+unemployment accordingly was Rising as
+well it kept going no look see then they
+
+ align:start position:0%
+well it kept going no look see then they
+ 
+
+ align:start position:0%
+well it kept going no look see then they
+began to cut the interest rate more
+
+ align:start position:0%
+began to cut the interest rate more
+ 
+
+ align:start position:0%
+began to cut the interest rate more
+aggressively okay but but we got into
+
+ align:start position:0%
+aggressively okay but but we got into
+ 
+
+ align:start position:0%
+aggressively okay but but we got into
+real deflation minus 10% or so so the
+
+ align:start position:0%
+real deflation minus 10% or so so the
+ 
+
+ align:start position:0%
+real deflation minus 10% or so so the
+real interest rate kept
+
+ align:start position:0%
+real interest rate kept
+ 
+
+ align:start position:0%
+real interest rate kept
+climbing at that point was a very poor
+
+ align:start position:0%
+climbing at that point was a very poor
+ 
+
+ align:start position:0%
+climbing at that point was a very poor
+Le time interest rate hike was a
+
+ align:start position:0%
+Le time interest rate hike was a
+ 
+
+ align:start position:0%
+Le time interest rate hike was a
+disaster for unemployment and because it
+
+ align:start position:0%
+disaster for unemployment and because it
+ 
+
+ align:start position:0%
+disaster for unemployment and because it
+really hied the interest rate real
+
+ align:start position:0%
+really hied the interest rate real
+ 
+
+ align:start position:0%
+really hied the interest rate real
+interest rate even more and eventually
+
+ align:start position:0%
+interest rate even more and eventually
+ 
+
+ align:start position:0%
+interest rate even more and eventually
+got got out of it with a bunch of
+
+ align:start position:0%
+got got out of it with a bunch of
+ 
+
+ align:start position:0%
+got got out of it with a bunch of
+policies that were non monetary policies
+
+ align:start position:0%
+policies that were non monetary policies
+ 
+
+ align:start position:0%
+policies that were non monetary policies
+but but
+
+ align:start position:0%
+but but
+ 
+
+ align:start position:0%
+but but
+um but that's that's what happened so so
+
+ align:start position:0%
+um but that's that's what happened so so
+ 
+
+ align:start position:0%
+um but that's that's what happened so so
+the Great Depression was very much a
+
+ align:start position:0%
+the Great Depression was very much a
+ 
+
+ align:start position:0%
+the Great Depression was very much a
+story of this
+
+ align:start position:0%
+story of this
+ 
+
+ align:start position:0%
+story of this
+kind in which essentially we get we fall
+
+ align:start position:0%
+kind in which essentially we get we fall
+ 
+
+ align:start position:0%
+kind in which essentially we get we fall
+fell into depression so that interest
+
+ align:start position:0%
+fell into depression so that interest
+ 
+
+ align:start position:0%
+fell into depression so that interest
+rate when began to climb and got the
+
+ align:start position:0%
+rate when began to climb and got the
+ 
+
+ align:start position:0%
+rate when began to climb and got the
+economy deeper and deeper into recession
+
+ align:start position:0%
+economy deeper and deeper into recession
+ 
+
+ align:start position:0%
+economy deeper and deeper into recession
+and employment Higher and Higher and so
+
+ align:start position:0%
+and employment Higher and Higher and so
+ 
+
+ align:start position:0%
+and employment Higher and Higher and so
+on and at some point monetary policy
+
+ align:start position:0%
+on and at some point monetary policy
+ 
+
+ align:start position:0%
+on and at some point monetary policy
+just didn't work so that's the reason
+
+ align:start position:0%
+just didn't work so that's the reason
+ 
+
+ align:start position:0%
+just didn't work so that's the reason
+you have essentially do massive fiscal
+
+ align:start position:0%
+you have essentially do massive fiscal
+ 
+
+ align:start position:0%
+you have essentially do massive fiscal
+policy to get out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it let's let me talk about some of the
+
+ align:start position:0%
+it let's let me talk about some of the
+ 
+
+ align:start position:0%
+it let's let me talk about some of the
+shocks we have discussed in the context
+
+ align:start position:0%
+shocks we have discussed in the context
+ 
+
+ align:start position:0%
+shocks we have discussed in the context
+of this more complete model now ER and
+
+ align:start position:0%
+of this more complete model now ER and
+ 
+
+ align:start position:0%
+of this more complete model now ER and
+and actually okay let me go let me talk
+
+ align:start position:0%
+and actually okay let me go let me talk
+ 
+
+ align:start position:0%
+and actually okay let me go let me talk
+about sort of two canonical type shocks
+
+ align:start position:0%
+about sort of two canonical type shocks
+ 
+
+ align:start position:0%
+about sort of two canonical type shocks
+you can have two broad type of shocks or
+
+ align:start position:0%
+you can have two broad type of shocks or
+ 
+
+ align:start position:0%
+you can have two broad type of shocks or
+or policies in in this
+
+ align:start position:0%
+or policies in in this
+ 
+
+ align:start position:0%
+or policies in in this
+Ms that you want to
+
+ align:start position:0%
+Ms that you want to
+ 
+
+ align:start position:0%
+Ms that you want to
+analyze some of them are aggregate
+
+ align:start position:0%
+analyze some of them are aggregate
+ 
+
+ align:start position:0%
+analyze some of them are aggregate
+demand either policies or shocks
+
+ align:start position:0%
+demand either policies or shocks
+ 
+
+ align:start position:0%
+demand either policies or shocks
+whatever those are things that you know
+
+ align:start position:0%
+whatever those are things that you know
+ 
+
+ align:start position:0%
+whatever those are things that you know
+aggregate demand policies move the is
+
+ align:start position:0%
+aggregate demand policies move the is
+ 
+
+ align:start position:0%
+aggregate demand policies move the is
+curve okay the is and the LM but moves
+
+ align:start position:0%
+curve okay the is and the LM but moves
+ 
+
+ align:start position:0%
+curve okay the is and the LM but moves
+operates in the in the in the in the
+
+ align:start position:0%
+operates in the in the in the in the
+ 
+
+ align:start position:0%
+operates in the in the in the in the
+Goods Market so this is one case of a
+
+ align:start position:0%
+Goods Market so this is one case of a
+ 
+
+ align:start position:0%
+Goods Market so this is one case of a
+contractionary f policy no a fiscal
+
+ align:start position:0%
+contractionary f policy no a fiscal
+ 
+
+ align:start position:0%
+contractionary f policy no a fiscal
+consolidation so what happens here
+
+ align:start position:0%
+consolidation so what happens here
+ 
+
+ align:start position:0%
+consolidation so what happens here
+suppose you start an equilibrium level
+
+ align:start position:0%
+suppose you start an equilibrium level
+ 
+
+ align:start position:0%
+suppose you start an equilibrium level
+of output H equal to Natural rate of
+
+ align:start position:0%
+of output H equal to Natural rate of
+ 
+
+ align:start position:0%
+of output H equal to Natural rate of
+output but now for whatever reason we're
+
+ align:start position:0%
+output but now for whatever reason we're
+ 
+
+ align:start position:0%
+output but now for whatever reason we're
+running deficits that are very large you
+
+ align:start position:0%
+running deficits that are very large you
+ 
+
+ align:start position:0%
+running deficits that are very large you
+want to reduce the size of the deficit
+
+ align:start position:0%
+want to reduce the size of the deficit
+ 
+
+ align:start position:0%
+want to reduce the size of the deficit
+well you move the is to the left no you
+
+ align:start position:0%
+well you move the is to the left no you
+ 
+
+ align:start position:0%
+well you move the is to the left no you
+cut government expenditure you increase
+
+ align:start position:0%
+cut government expenditure you increase
+ 
+
+ align:start position:0%
+cut government expenditure you increase
+taxes that will bring output below the
+
+ align:start position:0%
+taxes that will bring output below the
+ 
+
+ align:start position:0%
+taxes that will bring output below the
+natural rate of output you go to the
+
+ align:start position:0%
+natural rate of output you go to the
+ 
+
+ align:start position:0%
+natural rate of output you go to the
+Philips curve here that means inflation
+
+ align:start position:0%
+Philips curve here that means inflation
+ 
+
+ align:start position:0%
+Philips curve here that means inflation
+now you you get into deflationary forces
+
+ align:start position:0%
+now you you get into deflationary forces
+ 
+
+ align:start position:0%
+now you you get into deflationary forces
+or inflation starts declining the result
+
+ align:start position:0%
+or inflation starts declining the result
+ 
+
+ align:start position:0%
+or inflation starts declining the result
+of that so in the short run you get
+
+ align:start position:0%
+of that so in the short run you get
+ 
+
+ align:start position:0%
+of that so in the short run you get
+exactly what we had in lecture five six
+
+ align:start position:0%
+exactly what we had in lecture five six
+ 
+
+ align:start position:0%
+exactly what we had in lecture five six
+or whatever know you get a contraction
+
+ align:start position:0%
+or whatever know you get a contraction
+ 
+
+ align:start position:0%
+or whatever know you get a contraction
+in real output but on top of that you
+
+ align:start position:0%
+in real output but on top of that you
+ 
+
+ align:start position:0%
+in real output but on top of that you
+start getting inflation coming down or
+
+ align:start position:0%
+start getting inflation coming down or
+ 
+
+ align:start position:0%
+start getting inflation coming down or
+even going negative and as a result of
+
+ align:start position:0%
+even going negative and as a result of
+ 
+
+ align:start position:0%
+even going negative and as a result of
+that the central bank will react and it
+
+ align:start position:0%
+that the central bank will react and it
+ 
+
+ align:start position:0%
+that the central bank will react and it
+will react and that reaction will stop
+
+ align:start position:0%
+will react and that reaction will stop
+ 
+
+ align:start position:0%
+will react and that reaction will stop
+when in the long run well when output
+
+ align:start position:0%
+when in the long run well when output
+ 
+
+ align:start position:0%
+when in the long run well when output
+goes back to the initial level of output
+
+ align:start position:0%
+goes back to the initial level of output
+ 
+
+ align:start position:0%
+goes back to the initial level of output
+it's natural rate of output okay so the
+
+ align:start position:0%
+it's natural rate of output okay so the
+ 
+
+ align:start position:0%
+it's natural rate of output okay so the
+point of this picture that is new
+
+ align:start position:0%
+point of this picture that is new
+ 
+
+ align:start position:0%
+point of this picture that is new
+relative to things you already knew
+
+ align:start position:0%
+relative to things you already knew
+ 
+
+ align:start position:0%
+relative to things you already knew
+is that in the short run you get very
+
+ align:start position:0%
+is that in the short run you get very
+ 
+
+ align:start position:0%
+is that in the short run you get very
+much the type of responses we had
+
+ align:start position:0%
+much the type of responses we had
+ 
+
+ align:start position:0%
+much the type of responses we had
+earlier on in the medium run that is
+
+ align:start position:0%
+earlier on in the medium run that is
+ 
+
+ align:start position:0%
+earlier on in the medium run that is
+when now in the medium run you don't get
+
+ align:start position:0%
+when now in the medium run you don't get
+ 
+
+ align:start position:0%
+when now in the medium run you don't get
+that a fiscal consolation does not
+
+ align:start position:0%
+that a fiscal consolation does not
+ 
+
+ align:start position:0%
+that a fiscal consolation does not
+reduce output in the medium Run Okay a
+
+ align:start position:0%
+reduce output in the medium Run Okay a
+ 
+
+ align:start position:0%
+reduce output in the medium Run Okay a
+fiscal consolation what does is reduces
+
+ align:start position:0%
+fiscal consolation what does is reduces
+ 
+
+ align:start position:0%
+fiscal consolation what does is reduces
+the real interest rate in the in the in
+
+ align:start position:0%
+the real interest rate in the in the in
+ 
+
+ align:start position:0%
+the real interest rate in the in the in
+the long in the medium run okay so you
+
+ align:start position:0%
+the long in the medium run okay so you
+ 
+
+ align:start position:0%
+the long in the medium run okay so you
+see here output eventually goes back to
+
+ align:start position:0%
+see here output eventually goes back to
+ 
+
+ align:start position:0%
+see here output eventually goes back to
+that level with a much lower real
+
+ align:start position:0%
+that level with a much lower real
+ 
+
+ align:start position:0%
+that level with a much lower real
+interest rate and and
+
+ align:start position:0%
+interest rate and and
+ 
+
+ align:start position:0%
+interest rate and and
+U the the point is sometimes this this
+
+ align:start position:0%
+U the the point is sometimes this this
+ 
+
+ align:start position:0%
+U the the point is sometimes this this
+path this path that takes you output
+
+ align:start position:0%
+path this path that takes you output
+ 
+
+ align:start position:0%
+path this path that takes you output
+down initially and then comes back can
+
+ align:start position:0%
+down initially and then comes back can
+ 
+
+ align:start position:0%
+down initially and then comes back can
+be very painful it can take a long time
+
+ align:start position:0%
+be very painful it can take a long time
+ 
+
+ align:start position:0%
+be very painful it can take a long time
+generate a recession and so on and
+
+ align:start position:0%
+generate a recession and so on and
+ 
+
+ align:start position:0%
+generate a recession and so on and
+sometimes it can happen in easier
+
+ align:start position:0%
+sometimes it can happen in easier
+ 
+
+ align:start position:0%
+sometimes it can happen in easier
+conditions and be faster and so on many
+
+ align:start position:0%
+conditions and be faster and so on many
+ 
+
+ align:start position:0%
+conditions and be faster and so on many
+of the policies agreements that people
+
+ align:start position:0%
+of the policies agreements that people
+ 
+
+ align:start position:0%
+of the policies agreements that people
+have people that understand what they're
+
+ align:start position:0%
+have people that understand what they're
+ 
+
+ align:start position:0%
+have people that understand what they're
+talking about had to do with the speed
+
+ align:start position:0%
+talking about had to do with the speed
+ 
+
+ align:start position:0%
+talking about had to do with the speed
+at which these things happen so
+
+ align:start position:0%
+at which these things happen so
+ 
+
+ align:start position:0%
+at which these things happen so
+sometimes you know people can agree that
+
+ align:start position:0%
+sometimes you know people can agree that
+ 
+
+ align:start position:0%
+sometimes you know people can agree that
+you need a fiscal consolidation but
+
+ align:start position:0%
+you need a fiscal consolidation but
+ 
+
+ align:start position:0%
+you need a fiscal consolidation but
+someone think no this stuff is going to
+
+ align:start position:0%
+someone think no this stuff is going to
+ 
+
+ align:start position:0%
+someone think no this stuff is going to
+be very slow and so I don't want to
+
+ align:start position:0%
+be very slow and so I don't want to
+ 
+
+ align:start position:0%
+be very slow and so I don't want to
+incur in a very deep recession for very
+
+ align:start position:0%
+incur in a very deep recession for very
+ 
+
+ align:start position:0%
+incur in a very deep recession for very
+long just to adjust a little bit the
+
+ align:start position:0%
+long just to adjust a little bit the
+ 
+
+ align:start position:0%
+long just to adjust a little bit the
+fiscal deficit and others may think the
+
+ align:start position:0%
+fiscal deficit and others may think the
+ 
+
+ align:start position:0%
+fiscal deficit and others may think the
+opposite okay it's it's mostly about the
+
+ align:start position:0%
+opposite okay it's it's mostly about the
+ 
+
+ align:start position:0%
+opposite okay it's it's mostly about the
+speed but shorter response to a fiscal
+
+ align:start position:0%
+speed but shorter response to a fiscal
+ 
+
+ align:start position:0%
+speed but shorter response to a fiscal
+consolidation or to any aggregate demand
+
+ align:start position:0%
+consolidation or to any aggregate demand
+ 
+
+ align:start position:0%
+consolidation or to any aggregate demand
+contraction is different than the medium
+
+ align:start position:0%
+contraction is different than the medium
+ 
+
+ align:start position:0%
+contraction is different than the medium
+ter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+response and again the signals for the
+
+ align:start position:0%
+response and again the signals for the
+ 
+
+ align:start position:0%
+response and again the signals for the
+central bank that it needs to move
+
+ align:start position:0%
+central bank that it needs to move
+ 
+
+ align:start position:0%
+central bank that it needs to move
+interest rate they all come from this
+
+ align:start position:0%
+interest rate they all come from this
+ 
+
+ align:start position:0%
+interest rate they all come from this
+block here inflation falling that tells
+
+ align:start position:0%
+block here inflation falling that tells
+ 
+
+ align:start position:0%
+block here inflation falling that tells
+the Central Bank oops we may have a
+
+ align:start position:0%
+the Central Bank oops we may have a
+ 
+
+ align:start position:0%
+the Central Bank oops we may have a
+problem and so on another kind of shock
+
+ align:start position:0%
+problem and so on another kind of shock
+ 
+
+ align:start position:0%
+problem and so on another kind of shock
+that is is is is is more complicated and
+
+ align:start position:0%
+that is is is is is more complicated and
+ 
+
+ align:start position:0%
+that is is is is is more complicated and
+that has played a role actually very
+
+ align:start position:0%
+that has played a role actually very
+ 
+
+ align:start position:0%
+that has played a role actually very
+much in the recovery from covid is some
+
+ align:start position:0%
+much in the recovery from covid is some
+ 
+
+ align:start position:0%
+much in the recovery from covid is some
+sort of supply side shock for example an
+
+ align:start position:0%
+sort of supply side shock for example an
+ 
+
+ align:start position:0%
+sort of supply side shock for example an
+oil shock okay price of energy goes up
+
+ align:start position:0%
+oil shock okay price of energy goes up
+ 
+
+ align:start position:0%
+oil shock okay price of energy goes up
+or something like that well that one how
+
+ align:start position:0%
+or something like that well that one how
+ 
+
+ align:start position:0%
+or something like that well that one how
+do you analyze that the a supply size
+
+ align:start position:0%
+do you analyze that the a supply size
+ 
+
+ align:start position:0%
+do you analyze that the a supply size
+shock is not something that comes from
+
+ align:start position:0%
+shock is not something that comes from
+ 
+
+ align:start position:0%
+shock is not something that comes from
+the that we go to the slm part of the
+
+ align:start position:0%
+the that we go to the slm part of the
+ 
+
+ align:start position:0%
+the that we go to the slm part of the
+mall a supply size shock remember we
+
+ align:start position:0%
+mall a supply size shock remember we
+ 
+
+ align:start position:0%
+mall a supply size shock remember we
+analyze it when we did analyze the
+
+ align:start position:0%
+analyze it when we did analyze the
+ 
+
+ align:start position:0%
+analyze it when we did analyze the
+natural rate of natural rate of
+
+ align:start position:0%
+natural rate of natural rate of
+ 
+
+ align:start position:0%
+natural rate of natural rate of
+unemployment it's something that affects
+
+ align:start position:0%
+unemployment it's something that affects
+ 
+
+ align:start position:0%
+unemployment it's something that affects
+the supply side of the economy we can
+
+ align:start position:0%
+the supply side of the economy we can
+ 
+
+ align:start position:0%
+the supply side of the economy we can
+model that as an increase in the markup
+
+ align:start position:0%
+model that as an increase in the markup
+ 
+
+ align:start position:0%
+model that as an increase in the markup
+and we know that an increase in the
+
+ align:start position:0%
+and we know that an increase in the
+ 
+
+ align:start position:0%
+and we know that an increase in the
+markup will increase the natural rate of
+
+ align:start position:0%
+markup will increase the natural rate of
+ 
+
+ align:start position:0%
+markup will increase the natural rate of
+unemployment that means that that that
+
+ align:start position:0%
+unemployment that means that that that
+ 
+
+ align:start position:0%
+unemployment that means that that that
+this shock will do what to potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output so an energy shock especially if
+
+ align:start position:0%
+output so an energy shock especially if
+ 
+
+ align:start position:0%
+output so an energy shock especially if
+it's a persist one will operate like a
+
+ align:start position:0%
+it's a persist one will operate like a
+ 
+
+ align:start position:0%
+it's a persist one will operate like a
+markup shock and that we know will
+
+ align:start position:0%
+markup shock and that we know will
+ 
+
+ align:start position:0%
+markup shock and that we know will
+increase the natural rate of
+
+ align:start position:0%
+increase the natural rate of
+ 
+
+ align:start position:0%
+increase the natural rate of
+unemployment so what happens to the to
+
+ align:start position:0%
+unemployment so what happens to the to
+ 
+
+ align:start position:0%
+unemployment so what happens to the to
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+output goes down of course it's it's
+
+ align:start position:0%
+output goes down of course it's it's
+ 
+
+ align:start position:0%
+output goes down of course it's it's
+know output is equal to employment to
+
+ align:start position:0%
+know output is equal to employment to
+ 
+
+ align:start position:0%
+know output is equal to employment to
+labor force times 1 minus the natural
+
+ align:start position:0%
+labor force times 1 minus the natural
+ 
+
+ align:start position:0%
+labor force times 1 minus the natural
+rate of unemployment if the natural rate
+
+ align:start position:0%
+rate of unemployment if the natural rate
+ 
+
+ align:start position:0%
+rate of unemployment if the natural rate
+of unemployment goes up then the
+
+ align:start position:0%
+of unemployment goes up then the
+ 
+
+ align:start position:0%
+of unemployment goes up then the
+potential output goes down so that is
+
+ align:start position:0%
+potential output goes down so that is
+ 
+
+ align:start position:0%
+potential output goes down so that is
+not a shift in the top diagram it's a
+
+ align:start position:0%
+not a shift in the top diagram it's a
+ 
+
+ align:start position:0%
+not a shift in the top diagram it's a
+shift in the lower diagram it says we
+
+ align:start position:0%
+shift in the lower diagram it says we
+ 
+
+ align:start position:0%
+shift in the lower diagram it says we
+used to have this Philips curve and now
+
+ align:start position:0%
+used to have this Philips curve and now
+ 
+
+ align:start position:0%
+used to have this Philips curve and now
+the Philips curve has shifted to the
+
+ align:start position:0%
+the Philips curve has shifted to the
+ 
+
+ align:start position:0%
+the Philips curve has shifted to the
+left because we have a new natural rate
+
+ align:start position:0%
+left because we have a new natural rate
+ 
+
+ align:start position:0%
+left because we have a new natural rate
+of an output and remember the natural
+
+ align:start position:0%
+of an output and remember the natural
+ 
+
+ align:start position:0%
+of an output and remember the natural
+rate of output is that point when a ER
+
+ align:start position:0%
+rate of output is that point when a ER
+ 
+
+ align:start position:0%
+rate of output is that point when a ER
+output equal to the Natural rate of
+
+ align:start position:0%
+output equal to the Natural rate of
+ 
+
+ align:start position:0%
+output equal to the Natural rate of
+output doesn't produce inflationary
+
+ align:start position:0%
+output doesn't produce inflationary
+ 
+
+ align:start position:0%
+output doesn't produce inflationary
+forces okay so what happened with this
+
+ align:start position:0%
+forces okay so what happened with this
+ 
+
+ align:start position:0%
+forces okay so what happened with this
+shock here so suppose the economy was in
+
+ align:start position:0%
+shock here so suppose the economy was in
+ 
+
+ align:start position:0%
+shock here so suppose the economy was in
+this equilibrium here and now it gets
+
+ align:start position:0%
+this equilibrium here and now it gets
+ 
+
+ align:start position:0%
+this equilibrium here and now it gets
+hit by an oil shock
+
+ align:start position:0%
+hit by an oil shock
+ 
+
+ align:start position:0%
+hit by an oil shock
+in the short run if no one reacts
+
+ align:start position:0%
+in the short run if no one reacts
+ 
+
+ align:start position:0%
+in the short run if no one reacts
+nothing happens to Output doesn't move
+
+ align:start position:0%
+nothing happens to Output doesn't move
+ 
+
+ align:start position:0%
+nothing happens to Output doesn't move
+much but what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens you see if I don't move
+
+ align:start position:0%
+happens you see if I don't move
+ 
+
+ align:start position:0%
+happens you see if I don't move
+something in this part of the diagram
+
+ align:start position:0%
+something in this part of the diagram
+ 
+
+ align:start position:0%
+something in this part of the diagram
+and not move equilibrium output in the
+
+ align:start position:0%
+and not move equilibrium output in the
+ 
+
+ align:start position:0%
+and not move equilibrium output in the
+short run equilibrium output is
+
+ align:start position:0%
+short run equilibrium output is
+ 
+
+ align:start position:0%
+short run equilibrium output is
+determined exactly in the same way we
+
+ align:start position:0%
+determined exactly in the same way we
+ 
+
+ align:start position:0%
+determined exactly in the same way we
+have determined up to now so if we get a
+
+ align:start position:0%
+have determined up to now so if we get a
+ 
+
+ align:start position:0%
+have determined up to now so if we get a
+markup shock nothing happens to Output
+
+ align:start position:0%
+markup shock nothing happens to Output
+ 
+
+ align:start position:0%
+markup shock nothing happens to Output
+if no no one no if no moves nothing
+
+ align:start position:0%
+if no no one no if no moves nothing
+ 
+
+ align:start position:0%
+if no no one no if no moves nothing
+happens to help in the short but what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens that we may not like yeah
+
+ align:start position:0%
+happens that we may not like yeah
+ 
+
+ align:start position:0%
+happens that we may not like yeah
+exactly what happen is the the Philips
+
+ align:start position:0%
+exactly what happen is the the Philips
+ 
+
+ align:start position:0%
+exactly what happen is the the Philips
+curve went up before that level of
+
+ align:start position:0%
+curve went up before that level of
+ 
+
+ align:start position:0%
+curve went up before that level of
+output was consistent with no changes in
+
+ align:start position:0%
+output was consistent with no changes in
+ 
+
+ align:start position:0%
+output was consistent with no changes in
+inflation now it's not we get an
+
+ align:start position:0%
+inflation now it's not we get an
+ 
+
+ align:start position:0%
+inflation now it's not we get an
+increase in inflation so the first place
+
+ align:start position:0%
+increase in inflation so the first place
+ 
+
+ align:start position:0%
+increase in inflation so the first place
+where you'll see a the effect of the of
+
+ align:start position:0%
+where you'll see a the effect of the of
+ 
+
+ align:start position:0%
+where you'll see a the effect of the of
+of of the oil shock here is inflation
+
+ align:start position:0%
+of of the oil shock here is inflation
+ 
+
+ align:start position:0%
+of of the oil shock here is inflation
+will pick up remember the price of
+
+ align:start position:0%
+will pick up remember the price of
+ 
+
+ align:start position:0%
+will pick up remember the price of
+gasoline going up and all those things
+
+ align:start position:0%
+gasoline going up and all those things
+ 
+
+ align:start position:0%
+gasoline going up and all those things
+well that's where you see it first
+
+ align:start position:0%
+well that's where you see it first
+ 
+
+ align:start position:0%
+well that's where you see it first
+before activity Falls you see it there
+
+ align:start position:0%
+before activity Falls you see it there
+ 
+
+ align:start position:0%
+before activity Falls you see it there
+that's what mess up the Philips curve
+
+ align:start position:0%
+that's what mess up the Philips curve
+ 
+
+ align:start position:0%
+that's what mess up the Philips curve
+also in the 70s and 80s we going to see
+
+ align:start position:0%
+also in the 70s and 80s we going to see
+ 
+
+ align:start position:0%
+also in the 70s and 80s we going to see
+lots of shocks of this kind initially
+
+ align:start position:0%
+lots of shocks of this kind initially
+ 
+
+ align:start position:0%
+lots of shocks of this kind initially
+unemployment didn't move M much but
+
+ align:start position:0%
+unemployment didn't move M much but
+ 
+
+ align:start position:0%
+unemployment didn't move M much but
+inflation keeps
+
+ align:start position:0%
+inflation keeps
+ 
+
+ align:start position:0%
+inflation keeps
+climbing so that's what happens well
+
+ align:start position:0%
+climbing so that's what happens well
+ 
+
+ align:start position:0%
+climbing so that's what happens well
+obviously when that happens if it's
+
+ align:start position:0%
+obviously when that happens if it's
+ 
+
+ align:start position:0%
+obviously when that happens if it's
+persistent typically central banks if
+
+ align:start position:0%
+persistent typically central banks if
+ 
+
+ align:start position:0%
+persistent typically central banks if
+they think it's very short live they're
+
+ align:start position:0%
+they think it's very short live they're
+ 
+
+ align:start position:0%
+they think it's very short live they're
+not going to react to this stuff but if
+
+ align:start position:0%
+not going to react to this stuff but if
+ 
+
+ align:start position:0%
+not going to react to this stuff but if
+if it is persistent and they think it's
+
+ align:start position:0%
+if it is persistent and they think it's
+ 
+
+ align:start position:0%
+if it is persistent and they think it's
+persistent then the reaction is what
+
+ align:start position:0%
+persistent then the reaction is what
+ 
+
+ align:start position:0%
+persistent then the reaction is what
+well they need to this only means that
+
+ align:start position:0%
+well they need to this only means that
+ 
+
+ align:start position:0%
+well they need to this only means that
+the natural rate of
+
+ align:start position:0%
+the natural rate of
+ 
+
+ align:start position:0%
+the natural rate of
+an the the natural rate of interest has
+
+ align:start position:0%
+an the the natural rate of interest has
+ 
+
+ align:start position:0%
+an the the natural rate of interest has
+gone up no because I need to for that
+
+ align:start position:0%
+gone up no because I need to for that
+ 
+
+ align:start position:0%
+gone up no because I need to for that
+same is I need to bring down equilibrium
+
+ align:start position:0%
+same is I need to bring down equilibrium
+ 
+
+ align:start position:0%
+same is I need to bring down equilibrium
+output that means I need a higher
+
+ align:start position:0%
+output that means I need a higher
+ 
+
+ align:start position:0%
+output that means I need a higher
+natural rate of interest rate or a
+
+ align:start position:0%
+natural rate of interest rate or a
+ 
+
+ align:start position:0%
+natural rate of interest rate or a
+higher rst star so what the FED needs to
+
+ align:start position:0%
+higher rst star so what the FED needs to
+ 
+
+ align:start position:0%
+higher rst star so what the FED needs to
+do the Central Bank needs to do is just
+
+ align:start position:0%
+do the Central Bank needs to do is just
+ 
+
+ align:start position:0%
+do the Central Bank needs to do is just
+start increasing interest rate that's an
+
+ align:start position:0%
+start increasing interest rate that's an
+ 
+
+ align:start position:0%
+start increasing interest rate that's an
+natural
+
+ align:start position:0%
+natural
+ 
+
+ align:start position:0%
+natural
+response a lot of what happened during
+
+ align:start position:0%
+response a lot of what happened during
+ 
+
+ align:start position:0%
+response a lot of what happened during
+the covid why inflation pick up so much
+
+ align:start position:0%
+the covid why inflation pick up so much
+ 
+
+ align:start position:0%
+the covid why inflation pick up so much
+much in in Co is because we had a shock
+
+ align:start position:0%
+much in in Co is because we had a shock
+ 
+
+ align:start position:0%
+much in in Co is because we had a shock
+of this kind it was not energy the
+
+ align:start position:0%
+of this kind it was not energy the
+ 
+
+ align:start position:0%
+of this kind it was not energy the
+energy shock came later but it was
+
+ align:start position:0%
+energy shock came later but it was
+ 
+
+ align:start position:0%
+energy shock came later but it was
+supply side transport transport cost and
+
+ align:start position:0%
+supply side transport transport cost and
+ 
+
+ align:start position:0%
+supply side transport transport cost and
+stuff like that the network the
+
+ align:start position:0%
+stuff like that the network the
+ 
+
+ align:start position:0%
+stuff like that the network the
+production Network and things like that
+
+ align:start position:0%
+production Network and things like that
+ 
+
+ align:start position:0%
+production Network and things like that
+that broke down but they thought it was
+
+ align:start position:0%
+that broke down but they thought it was
+ 
+
+ align:start position:0%
+that broke down but they thought it was
+going to be very temporary so
+
+ align:start position:0%
+going to be very temporary so
+ 
+
+ align:start position:0%
+going to be very temporary so
+understanding this model they thought
+
+ align:start position:0%
+understanding this model they thought
+ 
+
+ align:start position:0%
+understanding this model they thought
+okay look this this Curve will come back
+
+ align:start position:0%
+okay look this this Curve will come back
+ 
+
+ align:start position:0%
+okay look this this Curve will come back
+come back that but by itself so better
+
+ align:start position:0%
+come back that but by itself so better
+ 
+
+ align:start position:0%
+come back that but by itself so better
+not react right now why cause a
+
+ align:start position:0%
+not react right now why cause a
+ 
+
+ align:start position:0%
+not react right now why cause a
+recession if really this Curve will come
+
+ align:start position:0%
+recession if really this Curve will come
+ 
+
+ align:start position:0%
+recession if really this Curve will come
+down back down by itself well the
+
+ align:start position:0%
+down back down by itself well the
+ 
+
+ align:start position:0%
+down back down by itself well the
+problem is that it didn't come back by
+
+ align:start position:0%
+problem is that it didn't come back by
+ 
+
+ align:start position:0%
+problem is that it didn't come back by
+itself that fast some things came up
+
+ align:start position:0%
+itself that fast some things came up
+ 
+
+ align:start position:0%
+itself that fast some things came up
+fairly fast some others did not in
+
+ align:start position:0%
+fairly fast some others did not in
+ 
+
+ align:start position:0%
+fairly fast some others did not in
+particular labor for participation did
+
+ align:start position:0%
+particular labor for participation did
+ 
+
+ align:start position:0%
+particular labor for participation did
+not come sufficiently fast back and so
+
+ align:start position:0%
+not come sufficiently fast back and so
+ 
+
+ align:start position:0%
+not come sufficiently fast back and so
+that's the reason we stay too long in a
+
+ align:start position:0%
+that's the reason we stay too long in a
+ 
+
+ align:start position:0%
+that's the reason we stay too long in a
+situation like this and that's one of
+
+ align:start position:0%
+situation like this and that's one of
+ 
+
+ align:start position:0%
+situation like this and that's one of
+the main reasons inflation sort of creep
+
+ align:start position:0%
+the main reasons inflation sort of creep
+ 
+
+ align:start position:0%
+the main reasons inflation sort of creep
+up in in the US and also in other places
+
+ align:start position:0%
+up in in the US and also in other places
+ 
+
+ align:start position:0%
+up in in the US and also in other places
+in the world in Europe the big reason
+
+ align:start position:0%
+in the world in Europe the big reason
+ 
+
+ align:start position:0%
+in the world in Europe the big reason
+for for why inflation picked up there is
+
+ align:start position:0%
+for for why inflation picked up there is
+ 
+
+ align:start position:0%
+for for why inflation picked up there is
+because this curve move a lot up why is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that exactly you know they had a massive
+
+ align:start position:0%
+that exactly you know they had a massive
+ 
+
+ align:start position:0%
+that exactly you know they had a massive
+energy shock and so that moved that
+
+ align:start position:0%
+energy shock and so that moved that
+ 
+
+ align:start position:0%
+energy shock and so that moved that
+curve up a
+
+ align:start position:0%
+curve up a
+ 
+
+ align:start position:0%
+curve up a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+good let's I want to now return to what
+
+ align:start position:0%
+good let's I want to now return to what
+ 
+
+ align:start position:0%
+good let's I want to now return to what
+is going on right
+
+ align:start position:0%
+is going on right
+ 
+
+ align:start position:0%
+is going on right
+now ER oh actually first I'm going to
+
+ align:start position:0%
+now ER oh actually first I'm going to
+ 
+
+ align:start position:0%
+now ER oh actually first I'm going to
+yeah right now meaning the last few days
+
+ align:start position:0%
+yeah right now meaning the last few days
+ 
+
+ align:start position:0%
+yeah right now meaning the last few days
+so it turns out that this diagram that
+
+ align:start position:0%
+so it turns out that this diagram that
+ 
+
+ align:start position:0%
+so it turns out that this diagram that
+that I use for the fiscal consolidation
+
+ align:start position:0%
+that I use for the fiscal consolidation
+ 
+
+ align:start position:0%
+that I use for the fiscal consolidation
+shock can also be used to understand a
+
+ align:start position:0%
+shock can also be used to understand a
+ 
+
+ align:start position:0%
+shock can also be used to understand a
+little bit what happens with
+
+ align:start position:0%
+little bit what happens with
+ 
+
+ align:start position:0%
+little bit what happens with
+the um Silicon Valley Bank event okay
+
+ align:start position:0%
+the um Silicon Valley Bank event okay
+ 
+
+ align:start position:0%
+the um Silicon Valley Bank event okay
+remember we model that as a credit shock
+
+ align:start position:0%
+remember we model that as a credit shock
+ 
+
+ align:start position:0%
+remember we model that as a credit shock
+we say like like that X we had it's like
+
+ align:start position:0%
+we say like like that X we had it's like
+ 
+
+ align:start position:0%
+we say like like that X we had it's like
+X going up well X going up that's
+
+ align:start position:0%
+X going up well X going up that's
+ 
+
+ align:start position:0%
+X going up well X going up that's
+exactly that it moves the yes to the
+
+ align:start position:0%
+exactly that it moves the yes to the
+ 
+
+ align:start position:0%
+exactly that it moves the yes to the
+left so a shock to
+
+ align:start position:0%
+left so a shock to
+ 
+
+ align:start position:0%
+left so a shock to
+X to to the a panic of the kind that we
+
+ align:start position:0%
+X to to the a panic of the kind that we
+ 
+
+ align:start position:0%
+X to to the a panic of the kind that we
+saw is like that it moves the to the
+
+ align:start position:0%
+saw is like that it moves the to the
+ 
+
+ align:start position:0%
+saw is like that it moves the to the
+left why is
+
+ align:start position:0%
+left why is
+ 
+
+ align:start position:0%
+left why is
+that so for any given level of the safe
+
+ align:start position:0%
+that so for any given level of the safe
+ 
+
+ align:start position:0%
+that so for any given level of the safe
+real interest rate a panic a shock to
+
+ align:start position:0%
+real interest rate a panic a shock to
+ 
+
+ align:start position:0%
+real interest rate a panic a shock to
+credit and so on moves the a to the left
+
+ align:start position:0%
+credit and so on moves the a to the left
+ 
+
+ align:start position:0%
+credit and so on moves the a to the left
+why is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that exactly so so the real the safe
+
+ align:start position:0%
+that exactly so so the real the safe
+ 
+
+ align:start position:0%
+that exactly so so the real the safe
+interest rate doesn't go up but but but
+
+ align:start position:0%
+interest rate doesn't go up but but but
+ 
+
+ align:start position:0%
+interest rate doesn't go up but but but
+what goes up is is is the cost of
+
+ align:start position:0%
+what goes up is is is the cost of
+ 
+
+ align:start position:0%
+what goes up is is is the cost of
+borrowing because you know firms need to
+
+ align:start position:0%
+borrowing because you know firms need to
+ 
+
+ align:start position:0%
+borrowing because you know firms need to
+pay this this extra risk premium and and
+
+ align:start position:0%
+pay this this extra risk premium and and
+ 
+
+ align:start position:0%
+pay this this extra risk premium and and
+then for any given safe interest rate
+
+ align:start position:0%
+then for any given safe interest rate
+ 
+
+ align:start position:0%
+then for any given safe interest rate
+real interest rate firms have to pay
+
+ align:start position:0%
+real interest rate firms have to pay
+ 
+
+ align:start position:0%
+real interest rate firms have to pay
+more which means there is less
+
+ align:start position:0%
+more which means there is less
+ 
+
+ align:start position:0%
+more which means there is less
+investment for any given level of the
+
+ align:start position:0%
+investment for any given level of the
+ 
+
+ align:start position:0%
+investment for any given level of the
+real interest rate and so the is moves
+
+ align:start position:0%
+real interest rate and so the is moves
+ 
+
+ align:start position:0%
+real interest rate and so the is moves
+to the left and if that happens then you
+
+ align:start position:0%
+to the left and if that happens then you
+ 
+
+ align:start position:0%
+to the left and if that happens then you
+start getting deflationary
+
+ align:start position:0%
+start getting deflationary
+ 
+
+ align:start position:0%
+start getting deflationary
+forces okay so again all this happens
+
+ align:start position:0%
+forces okay so again all this happens
+ 
+
+ align:start position:0%
+forces okay so again all this happens
+very quickly here in reality I told you
+
+ align:start position:0%
+very quickly here in reality I told you
+ 
+
+ align:start position:0%
+very quickly here in reality I told you
+there are lots of lags and so on but
+
+ align:start position:0%
+there are lots of lags and so on but
+ 
+
+ align:start position:0%
+there are lots of lags and so on but
+markets begin to anticipate what will
+
+ align:start position:0%
+markets begin to anticipate what will
+ 
+
+ align:start position:0%
+markets begin to anticipate what will
+happen and
+
+ align:start position:0%
+happen and
+ 
+
+ align:start position:0%
+happen and
+so so markets begin to anticipate so so
+
+ align:start position:0%
+so so markets begin to anticipate so so
+ 
+
+ align:start position:0%
+so so markets begin to anticipate so so
+in the in the immediate output doesn't
+
+ align:start position:0%
+in the in the immediate output doesn't
+ 
+
+ align:start position:0%
+in the in the immediate output doesn't
+collapse immediately anything and
+
+ align:start position:0%
+collapse immediately anything and
+ 
+
+ align:start position:0%
+collapse immediately anything and
+inflation doesn't be doesn't collapse
+
+ align:start position:0%
+inflation doesn't be doesn't collapse
+ 
+
+ align:start position:0%
+inflation doesn't be doesn't collapse
+immediately but markets realize that
+
+ align:start position:0%
+immediately but markets realize that
+ 
+
+ align:start position:0%
+immediately but markets realize that
+there are Long Bar there lcks but but
+
+ align:start position:0%
+there are Long Bar there lcks but but
+ 
+
+ align:start position:0%
+there are Long Bar there lcks but but
+there is a shock already so so it's
+
+ align:start position:0%
+there is a shock already so so it's
+ 
+
+ align:start position:0%
+there is a shock already so so it's
+likely that these things will
+
+ align:start position:0%
+likely that these things will
+ 
+
+ align:start position:0%
+likely that these things will
+happen and and and and it's likely that
+
+ align:start position:0%
+happen and and and and it's likely that
+ 
+
+ align:start position:0%
+happen and and and and it's likely that
+this will happen and it's also likely
+
+ align:start position:0%
+this will happen and it's also likely
+ 
+
+ align:start position:0%
+this will happen and it's also likely
+that the FED will react to
+
+ align:start position:0%
+that the FED will react to
+ 
+
+ align:start position:0%
+that the FED will react to
+that what should be the reaction of the
+
+ align:start position:0%
+that what should be the reaction of the
+ 
+
+ align:start position:0%
+that what should be the reaction of the
+FED if this stuff gets to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+persistent how do you get out of a shock
+
+ align:start position:0%
+persistent how do you get out of a shock
+ 
+
+ align:start position:0%
+persistent how do you get out of a shock
+like that if you really want to go back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there you cut interest rates okay in the
+
+ align:start position:0%
+there you cut interest rates okay in the
+ 
+
+ align:start position:0%
+there you cut interest rates okay in the
+case of the US they were hiking
+
+ align:start position:0%
+case of the US they were hiking
+ 
+
+ align:start position:0%
+case of the US they were hiking
+interestate because we're deing with
+
+ align:start position:0%
+interestate because we're deing with
+ 
+
+ align:start position:0%
+interestate because we're deing with
+dealing with high inflation this tells
+
+ align:start position:0%
+dealing with high inflation this tells
+ 
+
+ align:start position:0%
+dealing with high inflation this tells
+you well you should slow down the pace
+
+ align:start position:0%
+you well you should slow down the pace
+ 
+
+ align:start position:0%
+you well you should slow down the pace
+of hiking again they don't do it
+
+ align:start position:0%
+of hiking again they don't do it
+ 
+
+ align:start position:0%
+of hiking again they don't do it
+immediately they meet next week but the
+
+ align:start position:0%
+immediately they meet next week but the
+ 
+
+ align:start position:0%
+immediately they meet next week but the
+markets don't need to wait for the FED
+
+ align:start position:0%
+markets don't need to wait for the FED
+ 
+
+ align:start position:0%
+markets don't need to wait for the FED
+they anticipate what the FED is likely
+
+ align:start position:0%
+they anticipate what the FED is likely
+ 
+
+ align:start position:0%
+they anticipate what the FED is likely
+to do okay and they start betting on
+
+ align:start position:0%
+to do okay and they start betting on
+ 
+
+ align:start position:0%
+to do okay and they start betting on
+that so let me show you next a bunch of
+
+ align:start position:0%
+that so let me show you next a bunch of
+ 
+
+ align:start position:0%
+that so let me show you next a bunch of
+charts that show you that someone in the
+
+ align:start position:0%
+charts that show you that someone in the
+ 
+
+ align:start position:0%
+charts that show you that someone in the
+market understand these mechanics okay a
+
+ align:start position:0%
+market understand these mechanics okay a
+ 
+
+ align:start position:0%
+market understand these mechanics okay a
+lot of people because the prices are
+
+ align:start position:0%
+lot of people because the prices are
+ 
+
+ align:start position:0%
+lot of people because the prices are
+moving exactly that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so
+
+ align:start position:0%
+way so
+ 
+
+ align:start position:0%
+way so
+this is the ER oh this is something this
+
+ align:start position:0%
+this is the ER oh this is something this
+ 
+
+ align:start position:0%
+this is the ER oh this is something this
+is the one year ahead inflation
+
+ align:start position:0%
+is the one year ahead inflation
+ 
+
+ align:start position:0%
+is the one year ahead inflation
+expectation as traded in the market it's
+
+ align:start position:0%
+expectation as traded in the market it's
+ 
+
+ align:start position:0%
+expectation as traded in the market it's
+called inflation break even the one-ear
+
+ align:start position:0%
+called inflation break even the one-ear
+ 
+
+ align:start position:0%
+called inflation break even the one-ear
+inflation break even so if you these
+
+ align:start position:0%
+inflation break even so if you these
+ 
+
+ align:start position:0%
+inflation break even so if you these
+things are traded in the market and you
+
+ align:start position:0%
+things are traded in the market and you
+ 
+
+ align:start position:0%
+things are traded in the market and you
+can trade expected inflation at all the
+
+ align:start position:0%
+can trade expected inflation at all the
+ 
+
+ align:start position:0%
+can trade expected inflation at all the
+maturities you want so this is what the
+
+ align:start position:0%
+maturities you want so this is what the
+ 
+
+ align:start position:0%
+maturities you want so this is what the
+market was expecting before this shock
+
+ align:start position:0%
+market was expecting before this shock
+ 
+
+ align:start position:0%
+market was expecting before this shock
+you know infl we getting hotter and
+
+ align:start position:0%
+you know infl we getting hotter and
+ 
+
+ align:start position:0%
+you know infl we getting hotter and
+hotter numbers so the economy was
+
+ align:start position:0%
+hotter numbers so the economy was
+ 
+
+ align:start position:0%
+hotter numbers so the economy was
+inflation expected inflation as price in
+
+ align:start position:0%
+inflation expected inflation as price in
+ 
+
+ align:start position:0%
+inflation expected inflation as price in
+the market Market was climbing okay one
+
+ align:start position:0%
+the market Market was climbing okay one
+ 
+
+ align:start position:0%
+the market Market was climbing okay one
+year out and then the shock came and
+
+ align:start position:0%
+year out and then the shock came and
+ 
+
+ align:start position:0%
+year out and then the shock came and
+look what happened to expect the
+
+ align:start position:0%
+look what happened to expect the
+ 
+
+ align:start position:0%
+look what happened to expect the
+inflation boom it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collapse okay why is that well people
+
+ align:start position:0%
+collapse okay why is that well people
+ 
+
+ align:start position:0%
+collapse okay why is that well people
+thought this shock that leads to that
+
+ align:start position:0%
+thought this shock that leads to that
+ 
+
+ align:start position:0%
+thought this shock that leads to that
+okay that's what they thought this
+
+ align:start position:0%
+okay that's what they thought this
+ 
+
+ align:start position:0%
+okay that's what they thought this
+bounce was markets got a little excited
+
+ align:start position:0%
+bounce was markets got a little excited
+ 
+
+ align:start position:0%
+bounce was markets got a little excited
+yesterday it was a little risk on
+
+ align:start position:0%
+yesterday it was a little risk on
+ 
+
+ align:start position:0%
+yesterday it was a little risk on
+environment today they lost all that
+
+ align:start position:0%
+environment today they lost all that
+ 
+
+ align:start position:0%
+environment today they lost all that
+but but for a shock I'm going to tell
+
+ align:start position:0%
+but but for a shock I'm going to tell
+ 
+
+ align:start position:0%
+but but for a shock I'm going to tell
+you about in a few minutes
+
+ align:start position:0%
+you about in a few minutes
+ 
+
+ align:start position:0%
+you about in a few minutes
+but anyways but the point I wanted to
+
+ align:start position:0%
+but anyways but the point I wanted to
+ 
+
+ align:start position:0%
+but anyways but the point I wanted to
+highlight is again expected inflation
+
+ align:start position:0%
+highlight is again expected inflation
+ 
+
+ align:start position:0%
+highlight is again expected inflation
+was getting a little out of control and
+
+ align:start position:0%
+was getting a little out of control and
+ 
+
+ align:start position:0%
+was getting a little out of control and
+then this x shock came the the Panic
+
+ align:start position:0%
+then this x shock came the the Panic
+ 
+
+ align:start position:0%
+then this x shock came the the Panic
+shock and then immediately expected
+
+ align:start position:0%
+shock and then immediately expected
+ 
+
+ align:start position:0%
+shock and then immediately expected
+inflation decline because people
+
+ align:start position:0%
+inflation decline because people
+ 
+
+ align:start position:0%
+inflation decline because people
+anticipated something like this okay the
+
+ align:start position:0%
+anticipated something like this okay the
+ 
+
+ align:start position:0%
+anticipated something like this okay the
+market anticipated something like that
+
+ align:start position:0%
+market anticipated something like that
+ 
+
+ align:start position:0%
+market anticipated something like that
+what is
+
+ align:start position:0%
+what is
+ 
+
+ align:start position:0%
+what is
+that this is the the
+
+ align:start position:0%
+that this is the the
+ 
+
+ align:start position:0%
+that this is the the
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um the markets expected next hike so
+
+ align:start position:0%
+um the markets expected next hike so
+ 
+
+ align:start position:0%
+um the markets expected next hike so
+March 22nd the the FED will decide on
+
+ align:start position:0%
+March 22nd the the FED will decide on
+ 
+
+ align:start position:0%
+March 22nd the the FED will decide on
+the increase in interest rate remember
+
+ align:start position:0%
+the increase in interest rate remember
+ 
+
+ align:start position:0%
+the increase in interest rate remember
+the FED had decided as I said in the
+
+ align:start position:0%
+the FED had decided as I said in the
+ 
+
+ align:start position:0%
+the FED had decided as I said in the
+previous lecture to go for a path of 50
+
+ align:start position:0%
+previous lecture to go for a path of 50
+ 
+
+ align:start position:0%
+previous lecture to go for a path of 50
+basis points initially very high but
+
+ align:start position:0%
+basis points initially very high but
+ 
+
+ align:start position:0%
+basis points initially very high but
+since a couple of meetings ago they
+
+ align:start position:0%
+since a couple of meetings ago they
+ 
+
+ align:start position:0%
+since a couple of meetings ago they
+decided to slow down to 25 basis points
+
+ align:start position:0%
+decided to slow down to 25 basis points
+ 
+
+ align:start position:0%
+decided to slow down to 25 basis points
+precisely because they want to wait and
+
+ align:start position:0%
+precisely because they want to wait and
+ 
+
+ align:start position:0%
+precisely because they want to wait and
+see a bit what what a mess do we have I
+
+ align:start position:0%
+see a bit what what a mess do we have I
+ 
+
+ align:start position:0%
+see a bit what what a mess do we have I
+mean there's long variable lacks they
+
+ align:start position:0%
+mean there's long variable lacks they
+ 
+
+ align:start position:0%
+mean there's long variable lacks they
+have increased rates a lot and and so on
+
+ align:start position:0%
+have increased rates a lot and and so on
+ 
+
+ align:start position:0%
+have increased rates a lot and and so on
+but so they had gone back to a pace of
+
+ align:start position:0%
+but so they had gone back to a pace of
+ 
+
+ align:start position:0%
+but so they had gone back to a pace of
+25 so if you see in you know somewhere
+
+ align:start position:0%
+25 so if you see in you know somewhere
+ 
+
+ align:start position:0%
+25 so if you see in you know somewhere
+here in in February 22nd if you ask the
+
+ align:start position:0%
+here in in February 22nd if you ask the
+ 
+
+ align:start position:0%
+here in in February 22nd if you ask the
+market what what do you think will be
+
+ align:start position:0%
+market what what do you think will be
+ 
+
+ align:start position:0%
+market what what do you think will be
+the next
+
+ align:start position:0%
+the next
+ 
+
+ align:start position:0%
+the next
+hike there will be lots of answers
+
+ align:start position:0%
+hike there will be lots of answers
+ 
+
+ align:start position:0%
+hike there will be lots of answers
+trades and so on but the the when I say
+
+ align:start position:0%
+trades and so on but the the when I say
+ 
+
+ align:start position:0%
+trades and so on but the the when I say
+answers I mean what is price what is
+
+ align:start position:0%
+answers I mean what is price what is
+ 
+
+ align:start position:0%
+answers I mean what is price what is
+traded this financial instrument the the
+
+ align:start position:0%
+traded this financial instrument the the
+ 
+
+ align:start position:0%
+traded this financial instrument the the
+average answer was 30 basis points 30
+
+ align:start position:0%
+average answer was 30 basis points 30
+ 
+
+ align:start position:0%
+average answer was 30 basis points 30
+basis point is that most of the people
+
+ align:start position:0%
+basis point is that most of the people
+ 
+
+ align:start position:0%
+basis point is that most of the people
+thought that they were going to increase
+
+ align:start position:0%
+thought that they were going to increase
+ 
+
+ align:start position:0%
+thought that they were going to increase
+the the interest rate by 25 basis points
+
+ align:start position:0%
+the the interest rate by 25 basis points
+ 
+
+ align:start position:0%
+the the interest rate by 25 basis points
+and there were a few guys out there that
+
+ align:start position:0%
+and there were a few guys out there that
+ 
+
+ align:start position:0%
+and there were a few guys out there that
+thought the FED doesn't increase the
+
+ align:start position:0%
+thought the FED doesn't increase the
+ 
+
+ align:start position:0%
+thought the FED doesn't increase the
+interest rate by 33 basis points that's
+
+ align:start position:0%
+interest rate by 33 basis points that's
+ 
+
+ align:start position:0%
+interest rate by 33 basis points that's
+25 50 75 okay so this 30 is meant that
+
+ align:start position:0%
+25 50 75 okay so this 30 is meant that
+ 
+
+ align:start position:0%
+25 50 75 okay so this 30 is meant that
+almost everyone thought it was going to
+
+ align:start position:0%
+almost everyone thought it was going to
+ 
+
+ align:start position:0%
+almost everyone thought it was going to
+be 25 but there were a few people that
+
+ align:start position:0%
+be 25 but there were a few people that
+ 
+
+ align:start position:0%
+be 25 but there were a few people that
+were concerned that could be higher than
+
+ align:start position:0%
+were concerned that could be higher than
+ 
+
+ align:start position:0%
+were concerned that could be higher than
+that what happened here we start getting
+
+ align:start position:0%
+that what happened here we start getting
+ 
+
+ align:start position:0%
+that what happened here we start getting
+very hot numbers on inflation and so all
+
+ align:start position:0%
+very hot numbers on inflation and so all
+ 
+
+ align:start position:0%
+very hot numbers on inflation and so all
+of a sudden the equilibrium changed
+
+ align:start position:0%
+of a sudden the equilibrium changed
+ 
+
+ align:start position:0%
+of a sudden the equilibrium changed
+dramatically and we went to 45 which
+
+ align:start position:0%
+dramatically and we went to 45 which
+ 
+
+ align:start position:0%
+dramatically and we went to 45 which
+means most people then thought in the
+
+ align:start position:0%
+means most people then thought in the
+ 
+
+ align:start position:0%
+means most people then thought in the
+market that the next hike in in in on on
+
+ align:start position:0%
+market that the next hike in in in on on
+ 
+
+ align:start position:0%
+market that the next hike in in in on on
+March 22nd was going to be 50 basis
+
+ align:start position:0%
+March 22nd was going to be 50 basis
+ 
+
+ align:start position:0%
+March 22nd was going to be 50 basis
+points and a few people St stay at 25
+
+ align:start position:0%
+points and a few people St stay at 25
+ 
+
+ align:start position:0%
+points and a few people St stay at 25
+that's the reason H this is not 0. five
+
+ align:start position:0%
+that's the reason H this is not 0. five
+ 
+
+ align:start position:0%
+that's the reason H this is not 0. five
+but it was almost price in that point
+
+ align:start position:0%
+but it was almost price in that point
+ 
+
+ align:start position:0%
+but it was almost price in that point
+when people say price in they're talking
+
+ align:start position:0%
+when people say price in they're talking
+ 
+
+ align:start position:0%
+when people say price in they're talking
+about this what is the hike that price
+
+ align:start position:0%
+about this what is the hike that price
+ 
+
+ align:start position:0%
+about this what is the hike that price
+in is this statistic look that's what
+
+ align:start position:0%
+in is this statistic look that's what
+ 
+
+ align:start position:0%
+in is this statistic look that's what
+happened with
+
+ align:start position:0%
+happened with
+ 
+
+ align:start position:0%
+happened with
+the Silicon Valley Bank event okay a
+
+ align:start position:0%
+the Silicon Valley Bank event okay a
+ 
+
+ align:start position:0%
+the Silicon Valley Bank event okay a
+collapse in this thing now now is is
+
+ align:start position:0%
+collapse in this thing now now is is
+ 
+
+ align:start position:0%
+collapse in this thing now now is is
+trading at around 13 basis points that
+
+ align:start position:0%
+trading at around 13 basis points that
+ 
+
+ align:start position:0%
+trading at around 13 basis points that
+means most of the people think that the
+
+ align:start position:0%
+means most of the people think that the
+ 
+
+ align:start position:0%
+means most of the people think that the
+Traders here think that there will be no
+
+ align:start position:0%
+Traders here think that there will be no
+ 
+
+ align:start position:0%
+Traders here think that there will be no
+hike at all okay so a few days ago they
+
+ align:start position:0%
+hike at all okay so a few days ago they
+ 
+
+ align:start position:0%
+hike at all okay so a few days ago they
+all thought there was going to be 50
+
+ align:start position:0%
+all thought there was going to be 50
+ 
+
+ align:start position:0%
+all thought there was going to be 50
+basis point which is a big hike H and
+
+ align:start position:0%
+basis point which is a big hike H and
+ 
+
+ align:start position:0%
+basis point which is a big hike H and
+now most people think there will be no
+
+ align:start position:0%
+now most people think there will be no
+ 
+
+ align:start position:0%
+now most people think there will be no
+hike whatsoever but a few think that
+
+ align:start position:0%
+hike whatsoever but a few think that
+ 
+
+ align:start position:0%
+hike whatsoever but a few think that
+it's going to be 25 me actually it's
+
+ align:start position:0%
+it's going to be 25 me actually it's
+ 
+
+ align:start position:0%
+it's going to be 25 me actually it's
+almost 50/50 no I think today is a
+
+ align:start position:0%
+almost 50/50 no I think today is a
+ 
+
+ align:start position:0%
+almost 50/50 no I think today is a
+little lower than that but it's almost
+
+ align:start position:0%
+little lower than that but it's almost
+ 
+
+ align:start position:0%
+little lower than that but it's almost
+50/50 that is 25 or zero that's that's
+
+ align:start position:0%
+50/50 that is 25 or zero that's that's
+ 
+
+ align:start position:0%
+50/50 that is 25 or zero that's that's
+what what it is but had you ask anyone
+
+ align:start position:0%
+what what it is but had you ask anyone
+ 
+
+ align:start position:0%
+what what it is but had you ask anyone
+around here and certainly around here is
+
+ align:start position:0%
+around here and certainly around here is
+ 
+
+ align:start position:0%
+around here and certainly around here is
+there any chance of zero and there would
+
+ align:start position:0%
+there any chance of zero and there would
+ 
+
+ align:start position:0%
+there any chance of zero and there would
+be no one literally is that contract was
+
+ align:start position:0%
+be no one literally is that contract was
+ 
+
+ align:start position:0%
+be no one literally is that contract was
+not traded okay well you see things
+
+ align:start position:0%
+not traded okay well you see things
+ 
+
+ align:start position:0%
+not traded okay well you see things
+happen accidents happen so now that's
+
+ align:start position:0%
+happen accidents happen so now that's
+ 
+
+ align:start position:0%
+happen accidents happen so now that's
+where where we are
+
+ align:start position:0%
+where where we are
+ 
+
+ align:start position:0%
+where where we are
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if this all last a week and and
+
+ align:start position:0%
+now if this all last a week and and
+ 
+
+ align:start position:0%
+now if this all last a week and and
+everything gets resolved it doesn't have
+
+ align:start position:0%
+everything gets resolved it doesn't have
+ 
+
+ align:start position:0%
+everything gets resolved it doesn't have
+a lot of macro iic consequences okay
+
+ align:start position:0%
+a lot of macro iic consequences okay
+ 
+
+ align:start position:0%
+a lot of macro iic consequences okay
+it's just a little Panic you know some
+
+ align:start position:0%
+it's just a little Panic you know some
+ 
+
+ align:start position:0%
+it's just a little Panic you know some
+people make money some people lose money
+
+ align:start position:0%
+people make money some people lose money
+ 
+
+ align:start position:0%
+people make money some people lose money
+and so on but but but but this can be a
+
+ align:start position:0%
+and so on but but but but this can be a
+ 
+
+ align:start position:0%
+and so on but but but but this can be a
+very problematic shock actually because
+
+ align:start position:0%
+very problematic shock actually because
+ 
+
+ align:start position:0%
+very problematic shock actually because
+what you see here is that this is a size
+
+ align:start position:0%
+what you see here is that this is a size
+ 
+
+ align:start position:0%
+what you see here is that this is a size
+this is Silicon Valley
+
+ align:start position:0%
+this is Silicon Valley
+ 
+
+ align:start position:0%
+this is Silicon Valley
+Bank these are all the rest the banks
+
+ align:start position:0%
+Bank these are all the rest the banks
+ 
+
+ align:start position:0%
+Bank these are all the rest the banks
+smaller than
+
+ align:start position:0%
+smaller than
+ 
+
+ align:start position:0%
+smaller than
+that H it turns out that all these bank
+
+ align:start position:0%
+that H it turns out that all these bank
+ 
+
+ align:start position:0%
+that H it turns out that all these bank
+at this moment are reshuffling their
+
+ align:start position:0%
+at this moment are reshuffling their
+ 
+
+ align:start position:0%
+at this moment are reshuffling their
+portfolios they're becoming very
+
+ align:start position:0%
+portfolios they're becoming very
+ 
+
+ align:start position:0%
+portfolios they're becoming very
+conservative because they don't want to
+
+ align:start position:0%
+conservative because they don't want to
+ 
+
+ align:start position:0%
+conservative because they don't want to
+be exposed to similar risk they realized
+
+ align:start position:0%
+be exposed to similar risk they realized
+ 
+
+ align:start position:0%
+be exposed to similar risk they realized
+the environment became very unfriendly
+
+ align:start position:0%
+the environment became very unfriendly
+ 
+
+ align:start position:0%
+the environment became very unfriendly
+to you know that can be runs on banks in
+
+ align:start position:0%
+to you know that can be runs on banks in
+ 
+
+ align:start position:0%
+to you know that can be runs on banks in
+any moment despite the fact that it's a
+
+ align:start position:0%
+any moment despite the fact that it's a
+ 
+
+ align:start position:0%
+any moment despite the fact that it's a
+big policy package out there but people
+
+ align:start position:0%
+big policy package out there but people
+ 
+
+ align:start position:0%
+big policy package out there but people
+are still withdrawing lots of deposits
+
+ align:start position:0%
+are still withdrawing lots of deposits
+ 
+
+ align:start position:0%
+are still withdrawing lots of deposits
+from a small Banks small and Regional
+
+ align:start position:0%
+from a small Banks small and Regional
+ 
+
+ align:start position:0%
+from a small Banks small and Regional
+Banks and they all deposi it in JP
+
+ align:start position:0%
+Banks and they all deposi it in JP
+ 
+
+ align:start position:0%
+Banks and they all deposi it in JP
+Morgan you know the big Banks so there's
+
+ align:start position:0%
+Morgan you know the big Banks so there's
+ 
+
+ align:start position:0%
+Morgan you know the big Banks so there's
+lots of deposits that despite the the
+
+ align:start position:0%
+lots of deposits that despite the the
+ 
+
+ align:start position:0%
+lots of deposits that despite the the
+the the insurance the the the the the
+
+ align:start position:0%
+the the insurance the the the the the
+ 
+
+ align:start position:0%
+the the insurance the the the the the
+blanket insurance that is implicit at
+
+ align:start position:0%
+blanket insurance that is implicit at
+ 
+
+ align:start position:0%
+blanket insurance that is implicit at
+least at the moment lots of deposits
+
+ align:start position:0%
+least at the moment lots of deposits
+ 
+
+ align:start position:0%
+least at the moment lots of deposits
+from these sectors are moving to these
+
+ align:start position:0%
+from these sectors are moving to these
+ 
+
+ align:start position:0%
+from these sectors are moving to these
+major Banks here okay that's called it's
+
+ align:start position:0%
+major Banks here okay that's called it's
+ 
+
+ align:start position:0%
+major Banks here okay that's called it's
+called a flight to
+
+ align:start position:0%
+called a flight to
+ 
+
+ align:start position:0%
+called a flight to
+Quality now the problem of that for the
+
+ align:start position:0%
+Quality now the problem of that for the
+ 
+
+ align:start position:0%
+Quality now the problem of that for the
+economy as a whole is that small Banks
+
+ align:start position:0%
+economy as a whole is that small Banks
+ 
+
+ align:start position:0%
+economy as a whole is that small Banks
+and Regional Banks play a huge role in
+
+ align:start position:0%
+and Regional Banks play a huge role in
+ 
+
+ align:start position:0%
+and Regional Banks play a huge role in
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+lending okay I
+
+ align:start position:0%
+lending okay I
+ 
+
+ align:start position:0%
+lending okay I
+think a little more than 50% for example
+
+ align:start position:0%
+think a little more than 50% for example
+ 
+
+ align:start position:0%
+think a little more than 50% for example
+of the commercial and Industrial loans
+
+ align:start position:0%
+of the commercial and Industrial loans
+ 
+
+ align:start position:0%
+of the commercial and Industrial loans
+are made by small Banks ER 80% of the
+
+ align:start position:0%
+are made by small Banks ER 80% of the
+ 
+
+ align:start position:0%
+are made by small Banks ER 80% of the
+mortgages are given by a small Banks so
+
+ align:start position:0%
+mortgages are given by a small Banks so
+ 
+
+ align:start position:0%
+mortgages are given by a small Banks so
+it so it has a big
+
+ align:start position:0%
+it so it has a big
+ 
+
+ align:start position:0%
+it so it has a big
+potential consequence what I'm trying to
+
+ align:start position:0%
+potential consequence what I'm trying to
+ 
+
+ align:start position:0%
+potential consequence what I'm trying to
+say is that X may stay high for quite a
+
+ align:start position:0%
+say is that X may stay high for quite a
+ 
+
+ align:start position:0%
+say is that X may stay high for quite a
+bit of time okay and that's a
+
+ align:start position:0%
+bit of time okay and that's a
+ 
+
+ align:start position:0%
+bit of time okay and that's a
+reason this is start there is
+
+ align:start position:0%
+reason this is start there is
+ 
+
+ align:start position:0%
+reason this is start there is
+anticipation that this will have
+
+ align:start position:0%
+anticipation that this will have
+ 
+
+ align:start position:0%
+anticipation that this will have
+macroeconomic consequences and as a
+
+ align:start position:0%
+macroeconomic consequences and as a
+ 
+
+ align:start position:0%
+macroeconomic consequences and as a
+result of that that the FED will react
+
+ align:start position:0%
+result of that that the FED will react
+ 
+
+ align:start position:0%
+result of that that the FED will react
+that inflation will change and all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so that's where we were at on
+
+ align:start position:0%
+that okay so that's where we were at on
+ 
+
+ align:start position:0%
+that okay so that's where we were at on
+Monday remember when we had the lecture
+
+ align:start position:0%
+Monday remember when we had the lecture
+ 
+
+ align:start position:0%
+Monday remember when we had the lecture
+I was telling you more or less that
+
+ align:start position:0%
+I was telling you more or less that
+ 
+
+ align:start position:0%
+I was telling you more or less that
+story ER what is this
+
+ align:start position:0%
+story ER what is this
+ 
+
+ align:start position:0%
+story ER what is this
+you can read it there but it may not
+
+ align:start position:0%
+you can read it there but it may not
+ 
+
+ align:start position:0%
+you can read it there but it may not
+mean M to much to you but I'm what I'm
+
+ align:start position:0%
+mean M to much to you but I'm what I'm
+ 
+
+ align:start position:0%
+mean M to much to you but I'm what I'm
+highlighting is this this is pretty big
+
+ align:start position:0%
+highlighting is this this is pretty big
+ 
+
+ align:start position:0%
+highlighting is this this is pretty big
+huh 35% decline this is an equity it's a
+
+ align:start position:0%
+huh 35% decline this is an equity it's a
+ 
+
+ align:start position:0%
+huh 35% decline this is an equity it's a
+share so this is
+
+ align:start position:0%
+share so this is
+ 
+
+ align:start position:0%
+share so this is
+the the value of the
+
+ align:start position:0%
+the the value of the
+ 
+
+ align:start position:0%
+the the value of the
+equity of a pretty major Bank credit
+
+ align:start position:0%
+equity of a pretty major Bank credit
+ 
+
+ align:start position:0%
+equity of a pretty major Bank credit
+Swiss okay so credit Swiss have been in
+
+ align:start position:0%
+Swiss okay so credit Swiss have been in
+ 
+
+ align:start position:0%
+Swiss okay so credit Swiss have been in
+trouble for a while but today got into
+
+ align:start position:0%
+trouble for a while but today got into
+ 
+
+ align:start position:0%
+trouble for a while but today got into
+really big trouble okay and and and you
+
+ align:start position:0%
+really big trouble okay and and and you
+ 
+
+ align:start position:0%
+really big trouble okay and and and you
+saw sort of a massive collap collapse in
+
+ align:start position:0%
+saw sort of a massive collap collapse in
+ 
+
+ align:start position:0%
+saw sort of a massive collap collapse in
+the equity shares in fact they stopped
+
+ align:start position:0%
+the equity shares in fact they stopped
+ 
+
+ align:start position:0%
+the equity shares in fact they stopped
+trading for a while and so
+
+ align:start position:0%
+trading for a while and so
+ 
+
+ align:start position:0%
+trading for a while and so
+on this thing here is H you know I
+
+ align:start position:0%
+on this thing here is H you know I
+ 
+
+ align:start position:0%
+on this thing here is H you know I
+updated your slides many times today
+
+ align:start position:0%
+updated your slides many times today
+ 
+
+ align:start position:0%
+updated your slides many times today
+because I began to look at this event
+
+ align:start position:0%
+because I began to look at this event
+ 
+
+ align:start position:0%
+because I began to look at this event
+around here and then this thing kept
+
+ align:start position:0%
+around here and then this thing kept
+ 
+
+ align:start position:0%
+around here and then this thing kept
+going then they stop kept going and so
+
+ align:start position:0%
+going then they stop kept going and so
+ 
+
+ align:start position:0%
+going then they stop kept going and so
+and I I'm not sure where it's at now I
+
+ align:start position:0%
+and I I'm not sure where it's at now I
+ 
+
+ align:start position:0%
+and I I'm not sure where it's at now I
+stopped at what time did I stop 9 in the
+
+ align:start position:0%
+stopped at what time did I stop 9 in the
+ 
+
+ align:start position:0%
+stopped at what time did I stop 9 in the
+morning I was awake at 4:44 today so
+
+ align:start position:0%
+morning I was awake at 4:44 today so
+ 
+
+ align:start position:0%
+morning I was awake at 4:44 today so
+they tell you this was this was a pretty
+
+ align:start position:0%
+they tell you this was this was a pretty
+ 
+
+ align:start position:0%
+they tell you this was this was a pretty
+intense um but this what this is is the
+
+ align:start position:0%
+intense um but this what this is is the
+ 
+
+ align:start position:0%
+intense um but this what this is is the
+credit default swaps on a credit swis
+
+ align:start position:0%
+credit default swaps on a credit swis
+ 
+
+ align:start position:0%
+credit default swaps on a credit swis
+credit swap is whenever it's a bond
+
+ align:start position:0%
+credit swap is whenever it's a bond
+ 
+
+ align:start position:0%
+credit swap is whenever it's a bond
+issued by a bank you can buy an
+
+ align:start position:0%
+issued by a bank you can buy an
+ 
+
+ align:start position:0%
+issued by a bank you can buy an
+insurance on that Bond okay so it's so
+
+ align:start position:0%
+insurance on that Bond okay so it's so
+ 
+
+ align:start position:0%
+insurance on that Bond okay so it's so
+so if the bond defaults on you you then
+
+ align:start position:0%
+so if the bond defaults on you you then
+ 
+
+ align:start position:0%
+so if the bond defaults on you you then
+use the insurance and you get
+
+ align:start position:0%
+use the insurance and you get
+ 
+
+ align:start position:0%
+use the insurance and you get
+paid so these things for banks normally
+
+ align:start position:0%
+paid so these things for banks normally
+ 
+
+ align:start position:0%
+paid so these things for banks normally
+are very small numbers but for credit SS
+
+ align:start position:0%
+are very small numbers but for credit SS
+ 
+
+ align:start position:0%
+are very small numbers but for credit SS
+bigger than for other big Banks because
+
+ align:start position:0%
+bigger than for other big Banks because
+ 
+
+ align:start position:0%
+bigger than for other big Banks because
+I've been in in trouble for a while all
+
+ align:start position:0%
+I've been in in trouble for a while all
+ 
+
+ align:start position:0%
+I've been in in trouble for a while all
+sort of trouble but look at that Spike
+
+ align:start position:0%
+sort of trouble but look at that Spike
+ 
+
+ align:start position:0%
+sort of trouble but look at that Spike
+there I mean that's pretty big for these
+
+ align:start position:0%
+there I mean that's pretty big for these
+ 
+
+ align:start position:0%
+there I mean that's pretty big for these
+kind of things you know it's not Lon yet
+
+ align:start position:0%
+kind of things you know it's not Lon yet
+ 
+
+ align:start position:0%
+kind of things you know it's not Lon yet
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+big so anyway that caused a little Panic
+
+ align:start position:0%
+big so anyway that caused a little Panic
+ 
+
+ align:start position:0%
+big so anyway that caused a little Panic
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+ER this is the the stock prices of the
+
+ align:start position:0%
+ER this is the the stock prices of the
+ 
+
+ align:start position:0%
+ER this is the the stock prices of the
+main European Banks this is all today
+
+ align:start position:0%
+main European Banks this is all today
+ 
+
+ align:start position:0%
+main European Banks this is all today
+yeah so look at this it was a little
+
+ align:start position:0%
+yeah so look at this it was a little
+ 
+
+ align:start position:0%
+yeah so look at this it was a little
+rally yesterday and so on I mean this is
+
+ align:start position:0%
+rally yesterday and so on I mean this is
+ 
+
+ align:start position:0%
+rally yesterday and so on I mean this is
+this is the decline as a result of the
+
+ align:start position:0%
+this is the decline as a result of the
+ 
+
+ align:start position:0%
+this is the decline as a result of the
+US problem the Silicon Valley Banks then
+
+ align:start position:0%
+US problem the Silicon Valley Banks then
+ 
+
+ align:start position:0%
+US problem the Silicon Valley Banks then
+a rally yesterday and then credit Swiss
+
+ align:start position:0%
+a rally yesterday and then credit Swiss
+ 
+
+ align:start position:0%
+a rally yesterday and then credit Swiss
+happen and you has a big decline in h in
+
+ align:start position:0%
+happen and you has a big decline in h in
+ 
+
+ align:start position:0%
+happen and you has a big decline in h in
+in all the major banks in in Europe the
+
+ align:start position:0%
+in all the major banks in in Europe the
+ 
+
+ align:start position:0%
+in all the major banks in in Europe the
+US banks are also declining but but that
+
+ align:start position:0%
+US banks are also declining but but that
+ 
+
+ align:start position:0%
+US banks are also declining but but that
+was bigger for the major
+
+ align:start position:0%
+was bigger for the major
+ 
+
+ align:start position:0%
+was bigger for the major
+Banks the vix remember I told you last
+
+ align:start position:0%
+Banks the vix remember I told you last
+ 
+
+ align:start position:0%
+Banks the vix remember I told you last
+last week last Monday about this
+
+ align:start position:0%
+last week last Monday about this
+ 
+
+ align:start position:0%
+last week last Monday about this
+indicator of fear in the market which is
+
+ align:start position:0%
+indicator of fear in the market which is
+ 
+
+ align:start position:0%
+indicator of fear in the market which is
+really the price put options I'm
+
+ align:start position:0%
+really the price put options I'm
+ 
+
+ align:start position:0%
+really the price put options I'm
+simplifying things I mean protection for
+
+ align:start position:0%
+simplifying things I mean protection for
+ 
+
+ align:start position:0%
+simplifying things I mean protection for
+for big declines on the equity Market H
+
+ align:start position:0%
+for big declines on the equity Market H
+ 
+
+ align:start position:0%
+for big declines on the equity Market H
+again it began to spike very very
+
+ align:start position:0%
+again it began to spike very very
+ 
+
+ align:start position:0%
+again it began to spike very very
+sharply as a result of this is what
+
+ align:start position:0%
+sharply as a result of this is what
+ 
+
+ align:start position:0%
+sharply as a result of this is what
+happened with the US event then
+
+ align:start position:0%
+happened with the US event then
+ 
+
+ align:start position:0%
+happened with the US event then
+yesterday we got a rally Rison type
+
+ align:start position:0%
+yesterday we got a rally Rison type
+ 
+
+ align:start position:0%
+yesterday we got a rally Rison type
+thing and then today we got a new
+
+ align:start position:0%
+thing and then today we got a new
+ 
+
+ align:start position:0%
+thing and then today we got a new
+event look at this I like this
+
+ align:start position:0%
+event look at this I like this
+ 
+
+ align:start position:0%
+event look at this I like this
+picture what this is let me let me tell
+
+ align:start position:0%
+picture what this is let me let me tell
+ 
+
+ align:start position:0%
+picture what this is let me let me tell
+you what the the the the the blue line
+
+ align:start position:0%
+you what the the the the the blue line
+ 
+
+ align:start position:0%
+you what the the the the the blue line
+is the blue line is is the
+
+ align:start position:0%
+is the blue line is is the
+ 
+
+ align:start position:0%
+is the blue line is is the
+market ER
+
+ align:start position:0%
+market ER
+ 
+
+ align:start position:0%
+market ER
+expected federal funds rate at different
+
+ align:start position:0%
+expected federal funds rate at different
+ 
+
+ align:start position:0%
+expected federal funds rate at different
+days in the future okay so you know
+
+ align:start position:0%
+days in the future okay so you know
+ 
+
+ align:start position:0%
+days in the future okay so you know
+today the federal funds rate is is is
+
+ align:start position:0%
+today the federal funds rate is is is
+ 
+
+ align:start position:0%
+today the federal funds rate is is is
+around four and a half and this is what
+
+ align:start position:0%
+around four and a half and this is what
+ 
+
+ align:start position:0%
+around four and a half and this is what
+what the market expects okay so they
+
+ align:start position:0%
+what the market expects okay so they
+ 
+
+ align:start position:0%
+what the market expects okay so they
+expected so they expected the FED to
+
+ align:start position:0%
+expected so they expected the FED to
+ 
+
+ align:start position:0%
+expected so they expected the FED to
+continue to hike interest rate and to
+
+ align:start position:0%
+continue to hike interest rate and to
+ 
+
+ align:start position:0%
+continue to hike interest rate and to
+reach a peak
+
+ align:start position:0%
+reach a peak
+ 
+
+ align:start position:0%
+reach a peak
+ER around in June 14th in that meeting
+
+ align:start position:0%
+ER around in June 14th in that meeting
+ 
+
+ align:start position:0%
+ER around in June 14th in that meeting
+of the order of five five 5.3% or so
+
+ align:start position:0%
+of the order of five five 5.3% or so
+ 
+
+ align:start position:0%
+of the order of five five 5.3% or so
+that's that's what the average there
+
+ align:start position:0%
+that's that's what the average there
+ 
+
+ align:start position:0%
+that's that's what the average there
+lots of dispersion there people betting
+
+ align:start position:0%
+lots of dispersion there people betting
+ 
+
+ align:start position:0%
+lots of dispersion there people betting
+on 6% but that's the average that's what
+
+ align:start position:0%
+on 6% but that's the average that's what
+ 
+
+ align:start position:0%
+on 6% but that's the average that's what
+people expected the yellow thinks it's
+
+ align:start position:0%
+people expected the yellow thinks it's
+ 
+
+ align:start position:0%
+people expected the yellow thinks it's
+the number of hikes that you're likely
+
+ align:start position:0%
+the number of hikes that you're likely
+ 
+
+ align:start position:0%
+the number of hikes that you're likely
+to see so you know you're likely to see
+
+ align:start position:0%
+to see so you know you're likely to see
+ 
+
+ align:start position:0%
+to see so you know you're likely to see
+one hike in the next meeting another one
+
+ align:start position:0%
+one hike in the next meeting another one
+ 
+
+ align:start position:0%
+one hike in the next meeting another one
+in the next meeting and another one in
+
+ align:start position:0%
+in the next meeting and another one in
+ 
+
+ align:start position:0%
+in the next meeting and another one in
+the next meeting and then stop and begin
+
+ align:start position:0%
+the next meeting and then stop and begin
+ 
+
+ align:start position:0%
+the next meeting and then stop and begin
+sort of cutting rates that's expect that
+
+ align:start position:0%
+sort of cutting rates that's expect that
+ 
+
+ align:start position:0%
+sort of cutting rates that's expect that
+was expected path on Friday 10th was
+
+ align:start position:0%
+was expected path on Friday 10th was
+ 
+
+ align:start position:0%
+was expected path on Friday 10th was
+Friday more or less around there maybe
+
+ align:start position:0%
+Friday more or less around there maybe
+ 
+
+ align:start position:0%
+Friday more or less around there maybe
+Thursday I don't remember but anyway
+
+ align:start position:0%
+Thursday I don't remember but anyway
+ 
+
+ align:start position:0%
+Thursday I don't remember but anyway
+that was expected path you see so still
+
+ align:start position:0%
+that was expected path you see so still
+ 
+
+ align:start position:0%
+that was expected path you see so still
+hike rates reach a peak of five 5.3% and
+
+ align:start position:0%
+hike rates reach a peak of five 5.3% and
+ 
+
+ align:start position:0%
+hike rates reach a peak of five 5.3% and
+still sort of pretty high interest rates
+
+ align:start position:0%
+still sort of pretty high interest rates
+ 
+
+ align:start position:0%
+still sort of pretty high interest rates
+by the end of the year okay that was
+
+ align:start position:0%
+by the end of the year okay that was
+ 
+
+ align:start position:0%
+by the end of the year okay that was
+expected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path that's the way it looks
+
+ align:start position:0%
+path that's the way it looks
+ 
+
+ align:start position:0%
+path that's the way it looks
+now very different no now
+
+ align:start position:0%
+now very different no now
+ 
+
+ align:start position:0%
+now very different no now
+people are expecting very small changes
+
+ align:start position:0%
+people are expecting very small changes
+ 
+
+ align:start position:0%
+people are expecting very small changes
+now I show you it's like 13 basis points
+
+ align:start position:0%
+now I show you it's like 13 basis points
+ 
+
+ align:start position:0%
+now I show you it's like 13 basis points
+what people expect okay the still people
+
+ align:start position:0%
+what people expect okay the still people
+ 
+
+ align:start position:0%
+what people expect okay the still people
+expect sort of a hike but but small one
+
+ align:start position:0%
+expect sort of a hike but but small one
+ 
+
+ align:start position:0%
+expect sort of a hike but but small one
+now they expect a peak to be sort of in
+
+ align:start position:0%
+now they expect a peak to be sort of in
+ 
+
+ align:start position:0%
+now they expect a peak to be sort of in
+May and then the FED to start cutting
+
+ align:start position:0%
+May and then the FED to start cutting
+ 
+
+ align:start position:0%
+May and then the FED to start cutting
+very aggressively to at the end of the
+
+ align:start position:0%
+very aggressively to at the end of the
+ 
+
+ align:start position:0%
+very aggressively to at the end of the
+year end up with much lower rates than
+
+ align:start position:0%
+year end up with much lower rates than
+ 
+
+ align:start position:0%
+year end up with much lower rates than
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+okay so this is exactly what I was
+
+ align:start position:0%
+okay so this is exactly what I was
+ 
+
+ align:start position:0%
+okay so this is exactly what I was
+telling you before the market is
+
+ align:start position:0%
+telling you before the market is
+ 
+
+ align:start position:0%
+telling you before the market is
+anticipating that that we had a huge
+
+ align:start position:0%
+anticipating that that we had a huge
+ 
+
+ align:start position:0%
+anticipating that that we had a huge
+contraction in the is because X went up
+
+ align:start position:0%
+contraction in the is because X went up
+ 
+
+ align:start position:0%
+contraction in the is because X went up
+a lot ER the immediate consequences
+
+ align:start position:0%
+a lot ER the immediate consequences
+ 
+
+ align:start position:0%
+a lot ER the immediate consequences
+that's going to be lower inflation yes
+
+ align:start position:0%
+that's going to be lower inflation yes
+ 
+
+ align:start position:0%
+that's going to be lower inflation yes
+we have a problem because I mean if if
+
+ align:start position:0%
+we have a problem because I mean if if
+ 
+
+ align:start position:0%
+we have a problem because I mean if if
+the US did not have a 5 and a half% of
+
+ align:start position:0%
+the US did not have a 5 and a half% of
+ 
+
+ align:start position:0%
+the US did not have a 5 and a half% of
+inflation
+
+ align:start position:0%
+inflation
+ 
+
+ align:start position:0%
+inflation
+today I can assure you that the FED
+
+ align:start position:0%
+today I can assure you that the FED
+ 
+
+ align:start position:0%
+today I can assure you that the FED
+would have come out and said we cut the
+
+ align:start position:0%
+would have come out and said we cut the
+ 
+
+ align:start position:0%
+would have come out and said we cut the
+rates right now the only reason they're
+
+ align:start position:0%
+rates right now the only reason they're
+ 
+
+ align:start position:0%
+rates right now the only reason they're
+not cutting right now is because we have
+
+ align:start position:0%
+not cutting right now is because we have
+ 
+
+ align:start position:0%
+not cutting right now is because we have
+a two problems we have the the financial
+
+ align:start position:0%
+a two problems we have the the financial
+ 
+
+ align:start position:0%
+a two problems we have the the financial
+Panic on one side and we have the High
+
+ align:start position:0%
+Panic on one side and we have the High
+ 
+
+ align:start position:0%
+Panic on one side and we have the High
+inflation on the other side so so they
+
+ align:start position:0%
+inflation on the other side so so they
+ 
+
+ align:start position:0%
+inflation on the other side so so they
+have to balance these two
+
+ align:start position:0%
+have to balance these two
+ 
+
+ align:start position:0%
+have to balance these two
+forces but but the expectation of the
+
+ align:start position:0%
+forces but but the expectation of the
+ 
+
+ align:start position:0%
+forces but but the expectation of the
+market is that the balance of two forces
+
+ align:start position:0%
+market is that the balance of two forces
+ 
+
+ align:start position:0%
+market is that the balance of two forces
+going to be dominated by the contraction
+
+ align:start position:0%
+going to be dominated by the contraction
+ 
+
+ align:start position:0%
+going to be dominated by the contraction
+and aggregate demand much sooner than
+
+ align:start position:0%
+and aggregate demand much sooner than
+ 
+
+ align:start position:0%
+and aggregate demand much sooner than
+people were expecting okay so that's
+
+ align:start position:0%
+people were expecting okay so that's
+ 
+
+ align:start position:0%
+people were expecting okay so that's
+what the market is pricing at the moment
+
+ align:start position:0%
+what the market is pricing at the moment
+ 
+
+ align:start position:0%
+what the market is pricing at the moment
+and what I'm saying is I was trying to
+
+ align:start position:0%
+and what I'm saying is I was trying to
+ 
+
+ align:start position:0%
+and what I'm saying is I was trying to
+highlight is that this is very
+
+ align:start position:0%
+highlight is that this is very
+ 
+
+ align:start position:0%
+highlight is that this is very
+consistent with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h with that okay it's just the market
+
+ align:start position:0%
+h with that okay it's just the market
+ 
+
+ align:start position:0%
+h with that okay it's just the market
+looking ahead of what it's likely to
+
+ align:start position:0%
+looking ahead of what it's likely to
+ 
+
+ align:start position:0%
+looking ahead of what it's likely to
+Happ happen it started from a situation
+
+ align:start position:0%
+Happ happen it started from a situation
+ 
+
+ align:start position:0%
+Happ happen it started from a situation
+which is a little bit more complicated
+
+ align:start position:0%
+which is a little bit more complicated
+ 
+
+ align:start position:0%
+which is a little bit more complicated
+again because we already had high
+
+ align:start position:0%
+again because we already had high
+ 
+
+ align:start position:0%
+again because we already had high
+inflation well I do not know really I
+
+ align:start position:0%
+inflation well I do not know really I
+ 
+
+ align:start position:0%
+inflation well I do not know really I
+mean it is on one end more complicated
+
+ align:start position:0%
+mean it is on one end more complicated
+ 
+
+ align:start position:0%
+mean it is on one end more complicated
+because we have a problem of high
+
+ align:start position:0%
+because we have a problem of high
+ 
+
+ align:start position:0%
+because we have a problem of high
+inflation on the other hand having high
+
+ align:start position:0%
+inflation on the other hand having high
+ 
+
+ align:start position:0%
+inflation on the other hand having high
+inflation allows you to cut the real
+
+ align:start position:0%
+inflation allows you to cut the real
+ 
+
+ align:start position:0%
+inflation allows you to cut the real
+interest rate much more aggressively
+
+ align:start position:0%
+interest rate much more aggressively
+ 
+
+ align:start position:0%
+interest rate much more aggressively
+because if you bring the nominal
+
+ align:start position:0%
+because if you bring the nominal
+ 
+
+ align:start position:0%
+because if you bring the nominal
+interest rate to zero and you have
+
+ align:start position:0%
+interest rate to zero and you have
+ 
+
+ align:start position:0%
+interest rate to zero and you have
+inflation of 5% that allows you to cut
+
+ align:start position:0%
+inflation of 5% that allows you to cut
+ 
+
+ align:start position:0%
+inflation of 5% that allows you to cut
+the real interest rate to minus 5% well
+
+ align:start position:0%
+the real interest rate to minus 5% well
+ 
+
+ align:start position:0%
+the real interest rate to minus 5% well
+if you start with a situation where your
+
+ align:start position:0%
+if you start with a situation where your
+ 
+
+ align:start position:0%
+if you start with a situation where your
+inflation is zero you don't have any
+
+ align:start position:0%
+inflation is zero you don't have any
+ 
+
+ align:start position:0%
+inflation is zero you don't have any
+space to cut the real interest rate so
+
+ align:start position:0%
+space to cut the real interest rate so
+ 
+
+ align:start position:0%
+space to cut the real interest rate so
+the FED can be very aggressive here and
+
+ align:start position:0%
+the FED can be very aggressive here and
+ 
+
+ align:start position:0%
+the FED can be very aggressive here and
+the only reason is not being very very
+
+ align:start position:0%
+the only reason is not being very very
+ 
+
+ align:start position:0%
+the only reason is not being very very
+aggressive they were very aggressive in
+
+ align:start position:0%
+aggressive they were very aggressive in
+ 
+
+ align:start position:0%
+aggressive they were very aggressive in
+terms of supporting deposits and all
+
+ align:start position:0%
+terms of supporting deposits and all
+ 
+
+ align:start position:0%
+terms of supporting deposits and all
+that but the the the the the they can be
+
+ align:start position:0%
+that but the the the the the they can be
+ 
+
+ align:start position:0%
+that but the the the the the they can be
+very aggressive in terms of interest
+
+ align:start position:0%
+very aggressive in terms of interest
+ 
+
+ align:start position:0%
+very aggressive in terms of interest
+rate cut if the need arises hopefully
+
+ align:start position:0%
+rate cut if the need arises hopefully
+ 
+
+ align:start position:0%
+rate cut if the need arises hopefully
+won't but but they have a space because
+
+ align:start position:0%
+won't but but they have a space because
+ 
+
+ align:start position:0%
+won't but but they have a space because
+we're starting from a much higher level
+
+ align:start position:0%
+we're starting from a much higher level
+ 
+
+ align:start position:0%
+we're starting from a much higher level
+of inflation that
+
+ align:start position:0%
+of inflation that
+ 
+
+ align:start position:0%
+of inflation that
+helps it it hurts in the sense that it
+
+ align:start position:0%
+helps it it hurts in the sense that it
+ 
+
+ align:start position:0%
+helps it it hurts in the sense that it
+will delay the reaction but it helps in
+
+ align:start position:0%
+will delay the reaction but it helps in
+ 
+
+ align:start position:0%
+will delay the reaction but it helps in
+the sense that they have much more space
+
+ align:start position:0%
+the sense that they have much more space
+ 
+
+ align:start position:0%
+the sense that they have much more space
+for for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+policy what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this oh this is just interest one year
+
+ align:start position:0%
+this oh this is just interest one year
+ 
+
+ align:start position:0%
+this oh this is just interest one year
+interest rates okay that that reflects
+
+ align:start position:0%
+interest rates okay that that reflects
+ 
+
+ align:start position:0%
+interest rates okay that that reflects
+the the the previous picture as well
+
+ align:start position:0%
+the the the previous picture as well
+ 
+
+ align:start position:0%
+the the the previous picture as well
+people you know one year out rates were
+
+ align:start position:0%
+people you know one year out rates were
+ 
+
+ align:start position:0%
+people you know one year out rates were
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+5% uh a few days ago and now are in the
+
+ align:start position:0%
+5% uh a few days ago and now are in the
+ 
+
+ align:start position:0%
+5% uh a few days ago and now are in the
+low
+
+ align:start position:0%
+low
+ 
+
+ align:start position:0%
+low
+force and this picture I kept updating
+
+ align:start position:0%
+force and this picture I kept updating
+ 
+
+ align:start position:0%
+force and this picture I kept updating
+as you can see it was really dropping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fast that's a big change me look the one
+
+ align:start position:0%
+fast that's a big change me look the one
+ 
+
+ align:start position:0%
+fast that's a big change me look the one
+year rate 60 basis points that's a big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change so that's where we're
+
+ align:start position:0%
+change so that's where we're
+ 
+
+ align:start position:0%
+change so that's where we're
+at I'm from the next lecture I want to
+
+ align:start position:0%
+at I'm from the next lecture I want to
+ 
+
+ align:start position:0%
+at I'm from the next lecture I want to
+start with growth but any questions
+
+ align:start position:0%
+start with growth but any questions
+ 
+
+ align:start position:0%
+start with growth but any questions
+about this or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay I don't want to start growth now
+
+ align:start position:0%
+no okay I don't want to start growth now
+ 
+
+ align:start position:0%
+no okay I don't want to start growth now
+in four minutes but uh so the set of
+
+ align:start position:0%
+in four minutes but uh so the set of
+ 
+
+ align:start position:0%
+in four minutes but uh so the set of
+topics we're going to discuss from the
+
+ align:start position:0%
+topics we're going to discuss from the
+ 
+
+ align:start position:0%
+topics we're going to discuss from the
+next lecture are very
+
+ align:start position:0%
+next lecture are very
+ 
+
+ align:start position:0%
+next lecture are very
+different ER subject to not having any
+
+ align:start position:0%
+different ER subject to not having any
+ 
+
+ align:start position:0%
+different ER subject to not having any
+major events if there is a major major
+
+ align:start position:0%
+major events if there is a major major
+ 
+
+ align:start position:0%
+major events if there is a major major
+event I'm going to reffle things so we
+
+ align:start position:0%
+event I'm going to reffle things so we
+ 
+
+ align:start position:0%
+event I'm going to reffle things so we
+can talk about financial panics and
+
+ align:start position:0%
+can talk about financial panics and
+ 
+
+ align:start position:0%
+can talk about financial panics and
+things of that kind let's hope that it
+
+ align:start position:0%
+things of that kind let's hope that it
+ 
+
+ align:start position:0%
+things of that kind let's hope that it
+can stick to the program and do
+
+ align:start position:0%
+can stick to the program and do
+ 
+
+ align:start position:0%
+can stick to the program and do
+growth in the in the next week okay good
+
+ align:start position:0%
+growth in the in the next week okay good
+ 
+
+ align:start position:0%
+growth in the in the next week okay good
+or would we do
\ No newline at end of file